NBSIR 88-3814
Progress Toward A General Analytical
Method for Predicting  Indoor Air
Pollution in Buildings
Indoor Air Quality Modeling
Phase III Report
James Axley
U.S. DEPARTMENT OF COMMERCE
National Bureau of Standards
National Engineering Laboratory
Center for Building Technology
Building Environment Division
Gaithersburg, MD 20899
July 1988
                                     75 Years Stimulating America's Progress
                                         1913-1988
U.S. Environmental Protection Agency
U.S. Department of Energy
U.S. Consumer Products Safety Commission

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NBSIR 88-3814
PROGRESS TOWARD A GENERAL ANALYTICAL
METHOD FOR PREDICTING INDOOR AIR
POLLUTION IN BUILDINGS

INDOOR AIR QUALITY MODELING
PHASE III REPORT
James Axley
U.S. DEPARTMENT OF COMMERCE
National Bureau of Standards
National Engineering Laboratory
Center for Building Technology
Building Environment Division
Gaithersburg, MD 20899
July 1988
Prepared for:
U.S. Environmental Protection Agency
U.S. Department of Energy
U.S. Consumer Products Safety Commission
U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary
NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

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Indoor Air Quality Model                                        ABSTRACT
Phase III  Report
                                 ABSTRACT

   This interim report presents the results of Phase III of the NBS General Indoor Air
Pollution Concentration Model Project.  It describes;

   a) a general element-assembly formulation of multi-zone contaminant dispersal
      analysis theory that provides a general framework for the development of detailed
      (element) models of  mass transport phenomena that may affect contaminant
      dispersal in  buildings,

   b) an approach to modeling the dispersal  of interactive contaminants involving
      contaminant mass transport phenomena governed by basic principals of kinetics
      and introduces a linear first order kinetics element to achieve this end,

   c) an  approach  to  modeling the details of  contaminant  dispersal driven by
      convection-diffusion processes  in one-dimensional flow situations (e.g., HVAC
      ductwork) and  introduces a convection-diffusion flow element to achieve this
      end,

   and

   d) the  features and use  of CONTAM87, a program that provides a computational
      implementation of the theory and methods discussed.

   The theory and methods presented are based upon a generalization of the building
idealization  employed earlier [Axley,  1987].  Here, building air flow systems are
idealized as assemblages of mass transport elements, rather than simply flow elements
as used previously, connected to discrete system nodes corresponding to well-mixed
air zones within the building and its HVAC system.   Equations governing contaminant
dispersal in the whole building air flow system due  to air flow and reaction or sorption
mass transport phenomena are formulated  by assembling element equations, that
characterize a specific instance of mass transport in the building air flow system, in such
a manner that the  fundamental requirement of conservation of mass is satisfied in each
zone.
KEY WORDS: building simulation, indoor air quality, contaminant dispersal analysis,
element assembly, discrete modeling techniques

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Indoor Air Quality Model                         ACKNOWLEDGEMENTS
Phase III Report
                        ACKNOWLEDGEMENT


   This work was supported by the following Interagency Agreements:

   IAG: DE AI01 -86-CD 21013 Amendment Number 4 with the Department of Energy,

   IAG: DW 1391103-01-2 with the Environmental Protection Agency, and

   IAG: 74-25 Task Number 87-4 with the Consumer Products Safety Commission.
                                  iii

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Indoor Air Quality Model                                   CONTENTS
Phase III  Report
                             CONTENTS

   ABSTRACT                	ii
   ACKNOWLEDGEMENTS	 iii
   CONTENTS                	iv
   PREFACE	vi
   NOTATION	viii
   PART I - THEORY           	1-1

   1.  Introduction              	1-1
      1.1 Indoor Air  Quality Analysis	1-1
      1.2 The Well-Mixed  Microscopic Model	1-4

   2.  Contaminant  Dispersal Analysis   	2-1
      2.1 Element  Equations    	2-1
      2.2 System Equations    	2-5
      2.3 Solution  of System Equations	2-9

   3.  Interactive Contaminant Dispersal Analysis	3-1
      3.1 Multiple, Noninteractive,  Contaminant Dispersal	3-1
      3.2 Basic Concepts of Reaction  Kinetics	3-4
      3.3 Kinetics  Element Equations   	   3-10

   4.  One Dimensional Convection-Diffusion Flow   	4-1
      4.1 Convection-Diffusion  Equation	4-1
      4.2 Convection-Diffusion Element Equations	4-6
      4.3 Use of the Convection-Diffusion Flow Element  	4-8
      4.4 Analytical Properties of the  Convection-Diffusion    ...   4-14
         Element Equations
      4.5 Comparison to Tanks-in-Series  Idealizations	   4-15
   PART II -  CONTAM87  USERS  MANUAL	5-1

   5. General Instructions     	5-1

   6. Command Conventions   	6-1

   7. Introductory Example	7-1


                                 iv

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Indoor Air Quality  Model                                  CONTENTS
Phase III Report
   8. Command  Reference     	8-1
     8.1  Intrinsic  Commands  	8-1
        8.1.1 HELP	8-1
        8.1.2 ECHO          	8-1
        8.1.3 LIST           	8-1
        8.1.4 PRINT  A=	8-1
        8.1.5 DIAGRAM A=	8-2
        8.1.6 SUBMIT  F=  	8-2
        8.1.7 PAUSE         	8-2
        8.1.8 RETURN        	8-2
        8.1.9 QUIT           	8-2
     8.2  CONTAM87  Commands	8-3
        8.2.1 FLOWSYS	8-3
        8.2.2 FLOWELEM    	8-5
        8.2.3 KINELEM	8-7
        8.2.4 FORM-[W]                                         8-9
        8.2.5 STEADY	   8-10
        8.2.6 TIMECONS     	   8-10
        8.2.7 Dynamic  Analysis	   8-11
           8.2.7.1  FLOWDAT	   8-11
           8.2.7.2 EXCITDAT	   8-13
           8.2.7.3 DYNAMIC	   8-13
           8.2.7.4 Dynamic Analysis Example	   8-15
        8.2.8 RESET         	   8-15

   9. Example Applications    	9-1
     9.1  IBR Test House Study  	9-1
     9.2  Carnegie-Mellon Townhouse Study	9-5
     9.3  NBS Office Building Study	   9-10
   10. Summary and Directions of Future Work	   10-1

   REFERENCES             	Ref-1

   APPENDIX  - CONTAM87 FORTRAN  77 Source Code   . .  .  Append-1

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Indoor  Air  Quality  Model                                           PREFACE
Phase III Report
                                  PREFACE

   The work reported here  is  a product  of  the General Indoor  Air  Pollution
Concentration Model Project initiated in 1985 at the National Bureau of Standards and
supported by the U. S. Environmental Protection Agency, the U.S. Department of
Energy, and the Consumer Products Safety Commission. The fundamental objective of
this project  is to develop a comprehensive  validated  computer  model to simulate
dynamic pollutant movement and concentration variation  in  buildings. The scope of the
project is ambitious;  a full-scale, multi-zone building contaminant dispersal model that
simulates  flow processes  (e.g., infiltration, dilution, &  exfiltration) and contaminant
generation, reaction, and removal processes is being developed.

   During the planning stage of this project it was decided to organize efforts into three
distinct phases:

   Phase  I:   formulation of a general framework for the  development of general indoor
             air quality analysis models (see [McNall et.al., 1986] for report of Phase I
             work),

   Phase  II:  development of  a residential-scale  model,  based  on  the simplifying
             assumption that  air is well-mixed within each building  zone, providing
             simple simulation of HVAC system interaction, and

   Phase  III:  extension of modeling capabilities to  allow more complete simulation of
             HVAC system interaction and consideration of rooms that are not well-
             mixed.

   This report presents analytical methods that, together  with those  methods developed
during Phase II of the project, satisfies  the scope and objectives set for Phase III of the
"General Indoor  Air Pollution Concentration Model" Project and, as such, completes
Phase III efforts.  The report is organized in two parts. In the first part of the report the
underlying theory is presented;

   Section 1: outlines the general aspects of indoor air quality analysis - making the
             distinction between contaminant dispersal analysis, inverse contaminant
             dispersal analysis, and air flow analysis -  that the project has attempted
             to  address, and defines the approach taken to modeling,

   Section 2:  presents a general formulation of multi-zone contaminant  dispersal
             theory, using an element assembly approach,

   Section 3: applies the theory from Section 2 to develop an interactive, multiple-
             contaminant dispersal analysis method based upon the  formulation of a
                                      VI

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Indoor Air Quality Model                                         PREFACE
Phase III  Report
             kinetics element designed to model mass transport phenomena governed
             by the principals of kinetics,

   Section 4: applies the theory from Section 2 to model the details of one-dimensional
             contaminant dispersal driven by combined convection-diffusion mass
             transport processes,

   The  second part of the report presents  the practical implementation of the
contaminant dispersal analysis theory in the program CONTAM87;

   Sections 5 -8: provide a users manual for the program CONTAM87, and

   Section 9: gives examples of application of CONTAM87 to representative problems
             of contaminant dispersal  analysis.

   The  last section, Section 10, provides a summary of the work reported here and
outlines  possible directions of future study.

   The complete source code for CONTAM87 is listed in the appendix.
                                     VII

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Indoor  Air Quality Mode!                                           PREFACE
Phase III Report
                                  NOTATION

Scalars

   Scalar variables will be designated by lower and upper case, plain, english and
greek characters. An equals sign enclosed in square brackets, [=], is used to designate
typical units of a variable. The more commonly used scalars are listed below:

   C     concentration in terms of mass fraction (mass-species/mass-air)
          [=] Ib-species/lb-air or kg-species/kg-air
   G     species generation rate (mass/unit time)
          [=] Ib-species/hr or kg-species/s
   M     mass of the volume of air within a given zone (mass-air)
          [=] Ib-air or kg-air
   P     pressure  (force/unit area)
          [=] Ib/ft2 or Pascals (Pa)
   t      time
   T     temperature
          [=] F or C
   v     velocity (e.g., of a fluid particle)
          [=] ft/hr or m/s
   w     mass transport rate (e.g., due to flow, chemical reaction, etc.)
          [=] Ib/hr or kg/s
   x.y.z  spacial coordinates

   K     reaction rate coefficient
          [=] s-1
   p     density (mass/unit volume)
          [=] Ib/ft3 or kg/m3
Indices

   The indicial notation used in this report is modeled  after the conventions that are
commonly used in structural analysis and Finite Element analysis literature. A variety of
indices may be  associated  with  any single  variable including  pre-subscripts,  pre-
superscripts, post-subscripts, and  post-superscripts.  Although the meaning of any
index should be clear from the context of the discussion, the conventions diagrammed
below will be followed to help maintain clarity.
                                       viii

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Indoor Air Quality Model                                           PREFACE
Phase III Report
                      species index -> a    a  <- element index
                                         X   <- variable
                 descriptive index  -  con    j  <- node index


(In some contexts the post-subscript is used to indicate an element of an array as well.)

    In addition to these indices which serve to specifically identify a variable, it will be
necessary to use additional indices to indicate the value (or approximation to the value)
of a variable at a discrete point in time  or for a discrete step in an iterative scheme.  In
both cases,  additional superscripts  and subscripts may have to be  introduced.  To
distinguish  these time-step or  iterative-step  indices  they shall  be  enclosed  in
parenthesis as indicated below.

                             g(k)    _  the "kth" iterate

                          X.
                      con   '(n + 1)<-  the "n+1th" time step


    Generally, the following conventions will be used for superscripts and subscripts:

    a,b,c,...      specific element indices
    e            general element index
    
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Indoor  Air  Quality Model                                  PART I - THEORY
Phase III Report                                                1.  Introduction
 PART I - THEORY

   The first section of this part of the report gives definition to the meaning of indoor air
quality analysis and describes the modeling approach taken to develop practical indoor
analysis  tools.  It will be seen that indoor air quality  analysis involves  (forward)
contaminant dispersal analysis, inverse contaminant  dispersal  analysis, air flow
analysis, and thermal analysis.  The following  three sections extend the contaminant
dispersal analysis theory developed during Phase II of the present project [Axley, 1987]
by first presenting a  more general formulation of multi-zone contaminant dispersal
analysis theory and then applying  this  more general theory to a) dispersal problems
involving interactions  between contaminant species and/or the building fabric and b)
dispersal  problems where the  details  of  convection-diffusion flow processes are
important (e.g., HVAC ductwork).  Current research  efforts focused on the inverse
contaminant dispersal  analysis problem have led to promising new multi-zone tracer gas
techniques, the Pulse Tracer Techniques and have provided a better understanding of
existing tracer gas techniques.  Formulations of building  air flow and thermal  analysis
theories that are compatible with the formulations of the forward and inverse contaminant
dispersal analysis theories have been presented earlier [Axley 1987; Axley 1985] and
will become the focus of future work.
1.  Introduction

    During  the past decade, indoor air pollution emerged as an. international  health
issue and, as a result, a new field of simulation, indoor air quality analysis, is emerging
to provide  the means to predict concentration variation of indoor air contaminants  in
existing and proposed buildings and, thereby, to assess the nature and severity  of
potential indoor air quality problems. It may be expected that this new field will come  to
play a key  role in the development of strategies to mitigate indoor air quality problems
and, eventually, become central to the design of high quality indoor air environments.
1.1  Indoor  Air Quality  Analysis

   The central concern  of indoor air  quality  analysis is  the  prediction  of airborne
contaminant  dispersal in buildings.   Airborne contaminants disperse  throughout
buildings in a complex manner that depends on the nature of air  movement in-to, out-of,
and  within the building  system; the influence of the heating, ventilating, and  air
conditioning (HVAC) systems; the possibility of removal,, by filtration, or contribution, by
generation, of contaminants;  and the possibility of chemical reaction,  radio-chemical
decay, settling, or sorption of contaminants.  In indoor air quality analysis we seek to
comprehensively model all of these phenomena.

   More precisely, in  indoor air quality  analysis we consider building air flow systems
to be three dimensional fields within which we seek to completely describe the state of
infinitesimal air parcels.  The  state of such an air parcel is defined by its temperature,
                                      1-1

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Indoor Air Quality  Model
Phase III Report
PART I  - THEORY
    1. Introduction
pressure, velocity, and contaminant concentration(s) - the state variables of indoor air
quality analysis.
                                     Air Parcel State Variables
                                      Temperature:   T(x,y,Z,t)

                                         Pressure:   P(x,y,z,t)

                                      Flow Velocity:  v( X ,y,Z ,t)

                                     Concentration: aC(x,y,Z ,t), PC(x,y,Z ,t  v
                                ttj1". :                                      >'
                                   ' .-" '           for species a  , (5,...
                    Figure 1-1  Indoor Air Quality State Variables

    The central problem of indoor air quality analysis is, then, the determination of the
spacial (x.y.z) and  temporal (t) variation of contaminant species concentrations or
contaminant dispersal analysis.

    For a single noninteractive^ species, a,  contaminant dispersal is driven by the air
velocity field and its variation with time  and thus the contaminant dispersal  analysis
problem, for this case, may be represented as:

                    Noninteractive Contaminant Dispersal Analysis


                            C(x,y,z,t) = C( v(x,y,z,t),...)

where the ellipses	are used to indicate  initial and boundary conditions required to
complete the definition of the analytical  problem.  To solve the contaminant dispersal
problem, then, the flow field must be either specified or determined.

    Two approaches to flow determination exist.  In the first approach a nonlinear flow
analysis problem and, in general, a coupled thermal analysis problem is formulated and
solved, given the environmental excitation (e.g., wind,  solar, and thermal  excitation)
acting on the building system. Alternatively,  for existing buildings it may be possible to
"measure" building air  flows using tracer gas techniques.  These techniques are based
on the formulation and solution of the inverse contaminant dispersal analysis problem.
Functionally, these related problems take the following  forms:
1  Noninteractive  Contaminant:  a contaminant whose dispersal is not affected by kinetics of
reaction, sorption, settling, or other similar or related mass transport phenomena.
                                       1-2

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Indoor Air Quality  Model                                   PART I - THEORY
Phase  III Report                                                 1.  Introduction
     Coupled Flow/Thermal Analysis        Inverse Contaminant Dispersal A nalysis

 v(x,y,z,t)  = v( P(x,y,z,t),...)  '
 P(x,y,z,t)  = P(T(x,y,z,t),...)
 T(x,y,z,t)  = T( v(x,y,z,t),...)
Flow Analysis          V(X,y,Z,t) = V( aC(X,y,Z,t), ...)

Buoyancy Effects       (the basis of tracer gas techniqu es)

Thermal Analysis
   When contaminant reaction,  settling,  sorption, etc.  kinetics is important, the
contaminant dispersal analysis problem becomes a coupled (and, generally, nonlinear)
analysis problem as (the rate of change of) each  species' concentration will depend
upon both species' concentrations and the air flow velocity field:

                     Interactive Contaminant Dispersal Analysis

                 C(x,y,z,t) = C( v(x,y,z,t), C(x,y,z,t), PC(x,y,z,t), ... )
For such cases we say the contaminant is an interactive contaminant and describe the
analytical problem as a problem of interactive contaminant dispersal analysis.

   A complete indoor air quality analysis package should provide the analyst with tools
to consider this relatively complex set of analytical problems related  to the central task
of contaminant dispersal analysis. As indicated in Figure 1-2 one may anticipate three
basic indoor air quality analysis scenarios;

   1 )  in some instances the analyst may choose  to simply specify the flow field (e.g., in
       design situations  or in those  cases where the HVAC  system  substantially
       determines air flow in the building system)  and directly consider the contaminant
       dispersal analysis problem for specific indoor air pollutant sources or sinks,

   2)  for existing buildings, tracer  gas techniques, based upon inverse contaminant
       dispersal analysis methods, may be used to determine airflows that may then be
       used to complete the required contaminant dispersal analysis for any number of
       specific indoor air pollutant sources or sinks, or

   3)  in some instances  the analyst may choose to complete an airflow analysis of the
       building system, given building and wind characteristics,  to determine the
       airflows needed to  complete the contaminant dispersal analysis task.

Many specific pollutant source or sink models will involve  chemical  or mass transport
governed  by the  kinetics  of the mass transport phenomena; thus analytical tools are
needed to properly  account for this.   Finally, when  airflow analysis is elected the
analyst will either have to specify the temperature field or determine it by solving the
coupled flow-thermal analysis problem to  properly account for buoyancy effects; a
complete indoor air quality analysis  package should provide this capability.
                                       1-3

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Indoor Air Quality Model
Phase III  Report
                     PART  I - THEORY
                         1.  Introduction
                                     or
              Flow
              Field
            Specified
                                                          Kinetics
                    Inverse
                 Contaminant
                Dispersal Anal.
                               Contaminant
                                 Disperal
                                 Analysis
             or
                       or
                                Flow Analysis
                                 Pressure B.C.s
                                   Specified
                                 Buoyancy Effects

          Temperature
              Field
            Specified
or
Thermal
Analysis
      Figure 1-2 The Central and Related Problems of Indoor Air Quality Analysis
1.2  The Well-Mixed Macroscopic Model

   To develop this needed indoor air quality analysis capability we follow the tradition
established by others in the field of indoor air quality analysis [Sinden, 1979, Sandberg,
1984, Walton, 1985] and model building air  flow systems using a well-mixed  zone
simplification  of the macroscopic  equations  of motion (i.e., mass, momentum, and
energy balances for flow systems) that, in essence,  transforms the indicated field
problems discussed above into spatially discrete, but temporally continuous, ordinary
differential equations. The present approach breaks from this tradition, however, in that
an element assembly approach is taken to formulate the respective analytical problems.
That is to say:

      building air flow systems (fields) will be idealized as assemblages of discrete
      flow elements, that are used to  model specific flow transport processes between
      well-mixed zones, and  kinetics elements, that are  used to  model specific
      transport  processes that  occur within the well-mixed  zones that may  be
      described using the principals of kinetics.

   Such  idealizations of building air flow systems may be represented  graphically in a
                                     1-4

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Indoor Air Quality Model
Phase III Report
         PART I  - THEORY
             1. Introduction
direct and intuitive way as illustrated in Figure 1-3 for a hypothetical building system.
                                            0 Zone Node
                                            2  Node Number
             Actual Building
                         -I
Air-Flow System Idealization
Flow Element
Element Flow-
          Fiure 1-3 Idealization of A Hothetical Building Air Flow Sstem
   With a knowledge of the air flow paths in the building system the analyst selects from
the library  of  available  air flow elements to assemble  graphically,  and, hence
mathematically, the building air-flow idealization.  Kinetics elements may then be added
to this assemblage to account for the  nonflow transport processes that may occur within
a given zone. Thus, for example, the idealization presented above would, conceivably,
be appropriate for the analysis of carbon monoxide dispersal.  The indicated flow
elements would model HVAC, infiltration,  and exfiltration flow paths and  the single
kinetics element (labeled  Rx ) would model the kinetics of carbon monoxide  generation
within the furnace system.  Note that in this case a well-mixed zone is associated with
the furnace, a junction of the  HVAC ducts, the exterior environment and each of the
rooms of the building system.

   Presently, the library of flow elements contains those indicated in Figure 1-4. The
kinetics element and the convection-diffusion element are presented in the next section
of this report; the other elements were presented earlier [Axley 1987].
       Library of Contaminant Dispersal Elements
<> 1 I-l

Element
 !]""=> Flow w/Filter
" Element

i!. . . .- Convect. -Diftus.
Flow Element
(p^ Kinetics
^-^ Element
Library of Flow Elements
           Flow Resistance
           Element
                                                              Fan/Pump
                                                              Element
          Figure 1-4 Current Library of Indoor Air Quality Analysis Elements
                                      1-5

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Indoor Air Quality Model                                    PART  I -  THEORY
Phase III Report                                                 1.  Introduction


   With  each well-mixed zone we associate a set of discrete state variables with a
distinct, but arbitrary point in the zone, the zone node.  These discrete variables are
meant to approximate the corresponding field variables in the zone at that point.  For a
system idealized as n well-mixed zones, then, the key discrete  state variables would
include:


{P} s {PL Pa... Pn}             . the vector of system pressure variables         (1.1)

("0 = fl"i. T2. - Tn}              : the vector of system temperature variables       (1.2)

and the vector of system concentration variables defined as:

 for the dispersal of a single species,  a:

/r*\ =  / <-f*   &f*     Qf* \
l  /    \   i *    t> ""*     n/                                                  i

 for the dispersal of two species,  a and (i:
                                         ^
r^i    r G/^   B/^   O/^   B/"*      Ot^    IV"* i
*'^t'^tl"*"ll''lirMJ                                   I

 etc.

where the subscripts are zone/node indices.  These variables will be referred to as the
system (state) variables.

   With  each element "e" in the  system assembly  we associate one or  more element
nodes. With each node we associate  variables that  define the state of the element - the
element (state) variables, which will normally be subsets of the system variables2,
and note their association with the system variables. Thus, for  example,  a contaminant
dispersal element  having three  nodes, i, j, and  k, would have the element state
variables;

 for the dispersal of a single species,  a:

           ft    a    A T
     - / cy*.  *V".   ot/^ \


 for the dispersal of two species,  a and (3:

       .cue pe  cue p_e  cue p_e T
     = ( Uj,  Oj,  Oj,  Uj,  Ok,  U|
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Indoor  Air  Quality  Model                                  PART I - THEORY
Phase III Report                                               1.  Introduction
general.

   With these element variables in  hand,  element  equations are  formulated that
describe the specific mass and/or energy transport phenomena that the element is
meant to represent and, by demanding conservation of mass or energy transport at each
of the system  nodes, these element  equations are then assembled to form system
equations governing the behavior of the building air flow system as a whole.

   From a practical point of view,  the  element assembly approach  is intuitively
satisfying and allows consideration of systems of arbitrary complexity.  From a research
and development point  of view this approach separates the general problem of indoor
air quality analysis into two primary subproblems; element development and
development of solution method. Research efforts can, thus, focus on the modeling of
specific transport phenomena to develop improved or new elements  or,  alternatively,
focus on  developing  improved  methods of solving  the resulting  equations while
accounting for the complex coupling that exists between the thermal, dispersal, and flow
analysis problems.

   The approach has been formulated to be  completely analogous and compatible with
approaches based  upon  Generalized Finite Element Method [Zienkiewicz,  1983]
solutions of the microscopic equation of motion for fluids and makes use of the numerical
methods and computational strategies that have  been  developed to support the Finite
Element and associated methods.   It is expected that this compatibility will, eventually,
allow the analyst to employ mixed idealizations of building air flow systems wherein a
portion of the building air flow system is modeled in detail using microscopic elements
(e.g., elements based upon Finite Element  approximations of the governing microscopic
continuum equations) while the rest of the air flow system is modeled using discrete
elements.  In this way the analyst may study the  details of dispersal in one area of the
system, accounting for whole-system interaction,  without the overhead of  modeling the
entire system  microscopically.  The  one-dimensional  convection-diffusion element
presented in the next section represents the first step in this direction.
                                     1-7

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Indoor  Air  Quality  Model                                  PART I - THEORY
Phase III Report                          2.  Contaminant  Dispersal Analysis
 2.  Contaminant  Dispersal  Analysis

   Multi-zone building  contaminant dispersal  analysis theory has placed  a singular
emphasis on contaminant dispersal driven by flow mass transport processes [ Sinden,
1979, Sandberg 1984, Walton 1985] even though it has long been recognized that the
dispersal of many important indoor air contaminants are affected by other mass transport
processes as well, most notably,  processes associated with reaction, sorption, and
settling  phenomena.   The flow-element-assembly formulation  of multi-zone building
contaminant dispersal analysis theory developed during Phase II of the current project
provides a conceptual framework to extend existing dispersal analysis theory to account
for these  other mass  transport processes.   Extending  the flow-element-assembly
approach, this section presents a general formulation of a multi-zone contaminant
dispersal analysis theory that provides a basis for the development of more complete
models of contaminant dispersal in  buildings.

   The  general formulation of multi-zone contaminant dispersal theory is straightforward.
We first establish a restricted, but  very general, form for equations that will be used to
describe  mass  transport  at the  element  level1.   Then,  by establishing  the
correspondence between the element concentration variables,  {Ce}, and the system
concentration variables, {C},  and demanding species mass conservation at each of the
system  nodes we  show that these  element equations may be  assembled to form
equations governing the system as a whole.  Consideration of boundary conditions, the
qualitative character of these equations, and the solution  of  these  equations was
presented  earlier [Axley 1987] and, therefore, will not be emphasized here.
2.1  Element Equations

   As indicated above, it will be useful to distinguish those elements that model the
transport of mass from zone to zone by flow processes from those elements that model
the transport mass within a zone from species to species  (e.g., by chemical or radio-
chemical reaction) or, possibly, from species to the environment of the zone, itself (e.g.,
by chemical or radio-chemical decay to a  "noncontaminant" product,  absorption,
adsorption, or settling processes).  In either case,  we shall attempt to describe the
behavior of an element by equations of the form:
                                                                          (2.1)

   where;
       {w )      is a vector of species mass transport rates into the element

         ({C  }) is a transformation of {C8} that has the form of a linear transformation
                that is specific to a given class of elements

1  That is to say, to model specific instances of mass transport phenomena in a building's air flow
system.
                                     2-1

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                                          PART I  - THEORY
                          2.  Contaminant Dispersal Analysis
       to!
is a vector of element derived species generation rates.
Element Mass Transport Rates  The  vector of species mass transport rates, {
for the dispersal of a single species a, may be represented diagrammatically as shown
below for a hypothetical three-node flow element and a single-node kinetics element,
where the arrows indicate positive mass transport rates.  In the case of the flow element,
mass is  transported physically
                        node k
          flow element Q    ; \
                                 zone k
                                      kinetics element e
                                   	J_
                                    zonei   rt|)
                                                     a e
                                         CT
                                                              a e
                                                               Wj
                                                        node i ""
                 Figure 2-1 Element Mass Transport Rate Variables

by the air flow moving from the zone into the element and, thus, the arrows used indicate
the sense or direction of the averaged or bulk fluid velocity - a common convention.
For the kinetics element mass transport is somewhat more subtle; mass may not literally
be transported out of the zone, rather mass of species a is, typically, converted from a
form that is considered to be a contaminant to another form (e.g., another compound or
phase) that is not of any special interest.  Thus,  for the  kinetics element the arrow
indicating mass transport is directed into  the "element" from the zone node to indicate
only that mass of species a is being removed from the zone by the element.  It should be
noted that:

      for each  of  the  element concentration  variables, cf, there  exists  a

      corresponding element mass transport rate variables, wf.

This will also be true for the dispersal of more than one species.

    For contaminant dispersal involving multiple  species, then, a single physical flow
element might be thought to transport each individual species from zone-to-zone while a
kinetics element might be thought to transport mass, by conversion, from each of the
species to any or all of the other species  and/or from any of the species to  a form that
has no special interest,  within the single zone associated with  the  kinetics element.
Extending this notion of an element, a combined flow and kinetics element, that not only
transports mass of one species from one zone to another, but transports, by conversion,
that species to another species or form during the flow passage, is  also not  only
                                     2-2

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conceivable but reasonable for many reactive contaminants such as NC>2 and the radon
chain of decay products.  (Inasmuch as it is difficult to represent these possible multi-
species mass transport/conversion phenomena diagrammatically we shall not attempt to
do so, here.)


Element Transformation  Operator  The element transformation operator L () is
restricted to the form of a linear transformation:
                                      dt                                   (2.2)

      where;
          [x8], [ye], [ze]  are transformation coefficient matrices
          [xe]           is the element transport matrix
          [y8]           is the element mass matrix

but we admit transformation coefficient-matrices that may, in fact, vary with time and/or
depend, nonlinearly, on
[x6] = [x.         ? jn general                                           (2.3a)

[yI=-[ye(t,{C^)]   , in general                                           (2.3b)

[z6] = [ ze( t, {C6}) ]   > in general                                           (2.3c)

etc.

thus a practically endless variety of element equations may be formulated that have this
form and, as such, the restriction to this form should not lead to any serious limitation.

Simple Flow Elements  By  assuming  flow through a two-node flow element  is
practically instantaneous and well-mixed, the mass transport  of a single species, say a,
from element  node i to j, due to an air mass flow rate we(t) from i  to j, may be described
by the following element equations [Axley 1987]:
                              ; we(t)  > 0

                                                                         (2.4a)

or, in this case we have:
(2.4b)
[x6] -rt = we(t) \ J]  ;  [y6] =[0]  ;  [z6) =[0]  ;  {ge} = {0}
                                     2-3

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                                                         PART I  - THEORY
                                        2. Contaminant Dispersal Analysis
  = {
              a e,T
               W,
                                                                          (2.4C)
where we identify the element transport matrix for this case as the element mass flow
rate matrix, [f6]. It should be noted that the transformation matrix [xe] is seen to vary with
time to account for the time variation of flow through the element.  (Figure 2-2, below,
should help to clarify the meaning of the element variables in this case.)
                                    element "e"
     Figure 2-2 Simple Two-Node Contaminant Dispersal Flow Element Variables
Simple Flow Element with Filter The simple flow element equations, above, may
be modified to account for the  action of a filter that removes a fraction, rj, of the
contaminant as  it passes  through the element [Axley 1987], to  yield the following
element equations;
  a  e
a e
 Wj
        - we(t)
0
0
                                                                          (2.53)
or, in this case we have:
[x6! = [f6] = we(t)
                 1
               (n-D
                                                                          (2.5b)
where, again, we identify the element transport matrix as the element mass flow rate
matrix, [f6]. In this case the time variation of the first transformation matrix, [xe], could be
due to both the time variation of flow through the element and the time variation of the
filter efficiency,  rj = t|(t). Furthermore, it should be recognized  that the filter efficiency
will, in general, vary with each contaminant so that this first transformation matrix may be
expected to be  species dependent.  Following the notational convention established  to
distinguish species  types (i.e., the use of a leading  superscript) we shall indicate this
species dependency as [axe], [Pxe] ,... for species a, p,... where:
                                      2-4

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Phase III Report                          2.  Contaminant  Dispersal Analysis
                    (Vi)    o
0

                                           (2.5C)
2.2  System Equations

   Equations governing the dispersal of contaminants in the system as a whole may be
assembled from element equations of the form of equation (2.1) by first transforming the
element equations so that they are expressed in terms of system variables.  To this end
we recognize that there exists a  one-to-one correspondence between an element's
concentration variables, {C6}, and the system's concentration variables, {C}, that may
be described by a simple Boolean transformation as:
                                                                          (2.6)

      where;
            B-
          IB1   is an m x n Boolean Transformation matrix (i.e., consisting of only
                ones and zeros) for an m-node element within an n-node system
                idealization

The Boolean transformation is simply a means to express the equality of each of the
element concentrations variables  with its associated system concentration variable
within the framework of concise vector notation; it defines the relation between the
(larger) vector of system concentration variables  and the (smaller) vector of a specific
elements concentration variables, a subset of the system variables.

   This same Boolean transformation matrix may be used to transform the vector
element mass transport rates, {w6}, into a "system-sized" vector of mass transport rates
for element "e", {W6},  as:

          T
{W6} = [B6]  {w8}                                                           (2.7)

This vector {We} will have the same number of elements as the system concentration
vector {C} ,  providing a correspondence between each system concentration variable
and a "system-sized" mass transport rate for the element "e".  It represents the net
species mass transport rate from each of the system nodes into a specific element "e"
and, therefore, the  sum of these mass transport vectors for all elements in the  system
assemblage  will equal a  vector describing the total mass transport from the  system
nodes into all elements combined.
                                     2-5

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                                                            PART I - THEORY
                                           2.  Contaminant Dispersal Analysis
-ah
               /    total species
          e,    I    mass transport
       {W } 55 /    fromeachnode
               1 into connected elements
               I      ateachnode
                                                                             (2.8)
    Demanding the conservation of species mass at each of the system nodes, the sum
of the quantity above plus the rate of change of species mass within each zone must be
equal to any species mass generated within the zone:
       where;
                                                                            (2.9)


                the (diagonal) zone air volume mass matrix defined as (for n zones):

                 for a single species (i.e., with {C} defined by equation (1.3a)):
                            M! 0  ... 0
                             0 M2 ... 0
                             0 0  ... Mn
                   for two species2 (i.e., with {C} defined by equation (1.3b)):
                                                                           (2.10a)
"M!
0
0
0
0
0
0
M!
0
0
0
0
0
0
M2
0
0
0
0 ...
0 ...
0 ...
M2...
0 ...
0 ...
0
0
0
0
Mn
0
0
0
0
0
0
Mn_
                                                                           (2.1 Ob)
                  etc.

                 Mj  = the mass of the air in the volume of zone i

          [G]    is the zone species generation rate vector, defined as

                  for a single species, a:
                                     ,...  "Gn}T
2 One could conceivably associate a different "active" zone air volume with each species and have, in
this case, a diagonal mass matrix of the form: diag ( aM-| , ^M-| , atJ\2 , ^2 ,   aMn , ^Mn ,).
                                       2-6

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                 for two species, a and (J:

                    /r.    . a_   p    a-   p_     a-.   p_  T
                    {G} s  { G! ,   G!, G2.  Q2,...  Gn>  Gn/             (2.

                 etc.

                 ot
                 Gj   = the mass generation rate of species a in zone i

General  Expression  for Multi-Zone   Dispersal  Analysis  Substituting  the
transformation relations, equations (2.6) and (2.7),  along with the general form of the
element  equations,  equation  (2.1), into  the species mass conservation relation,
equation (2.9), we  obtain  the final result   a general  expression  for multi-zone
contaminant dispersal analysis:
                                                                       (2.12a)

   where;
      e =a< b> ;                   the system (mass) transport matrix   (2.1 2b)



           8 = a> b> -              the system mass matrix             (2. 1 2c)


[Z]=
      e


etc.


{G} = {G}

                                the system generation vector        (2.1 2e)
                 8 =a- b> -
It should be noted that in this general formulation the system mass matrix and system
generation vector have element contributions that add to the more familar zonal values.
The kinetics element, that will be presented  in Section 2.2, will be seen to provide
element  contributions to the system  generation vector.   The convection-diffusion
element, that  will  be presented in Section  2.3, will  be seen to provide element
contributions to both the system mass matrix and the system generation vector.
                                     2-7

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The  Assembly Operator  The summation and Boolean  transformation  of element
matrices, contained in the expressions above, is an operation that recurs frequently in
the Finite Element and related discrete modeling literature and, therefore, has come to
be defined as a standard operation - the  assembly operation - designated  by the
symbol A, the so-called assembly operator where;


   A  {v6}  -    I   pflvl
e=a.b,...       e=a.b....                     for element vector assembly     (2.1 3a)

and


   A
e=a.b,...       e=a.b....                     for element matrix assembly     (2.1 3b)

The  assembly  operator is therefore simply  a generalization of the conventional
summation operator, S, and equal to  the summation  operator when the Boolean
transformation matrices equal the identity matrix.

   The assembly operation is important, theoretically, in that it provides the necessary
formal definition  of  the assembly process required for  subsequent mathematical
analysis.  It does not, however, define an efficient numerical procedure for assembling
the element arrays needed to form the system equations for practical contaminant
dispersal analysis  the indicated  Boolean transformations involve multiplications by
either zero or one and, therefore, need not  be actually implemented.  Practically, then,
the assembly operation is carried out using  relatively simple algorithms that accumulate
element array terms within system  array memory locations according  to the physical
connectivity of each element.  The  "LM Algorithm" presented by Bathe [ Bathe 1982]
provides an example of one possible algorithm.

Relation to the Phase II Formulation   Previously [Axley  1987],  we  considered
contaminant dispersal due only  to flow  mass transport via simple  elements, with  and
without filtration, and at that time the element transport matrices, [xe] , defined above by
equations (2.4b) and (2.5b) were identified as element mass flow rate matrices and
given the symbol [f8]. These element mass flow matrices were then assembled to form
the system transport matrix identified, then, as the system flow matrix and given the
symbol  [F].  We shall see that,  in the general case, the system transport  matrix [W],
defined above, will be equal to the sum of the system flow matrix and what will be called
the system kinetics matrix, [K], assembled from element kinetics transport matrices, [k8],
as:

    = [F]  + [K]                                                         (2.i4a)
[F]=     A
     flow elements                                                          (2.14b)
                                     2-8

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Phase III Report                         2.  Contaminant Dispersal Analysis
[K]  =     A
      kinetics elem ents                                                       /2
2.3  Solution of System Equations

   The contaminant dispersal elements developed to date are all described in terms of
first order linear transformations (i.e., involve only [xe] and [ye] transformation matrices)
having, in some cases, time varying element transport matrices  (i.e., having [xe] =
[xe(t)], consequently system equations assembled from these element equations will be
limited to  the first order form:

                 = (G}
where the system transport matrix will, in general, vary with time: [W] =  [W(t)].

   System equations of this form are identical, in form, to those system equations that
result from  idealizations restricted to assemblages of simple flow elements. Therefore,
the procedures used to account for boundary conditions and possibilities of massless
nodes,  the solution options  that  may be considered (i.e., steady state analysis,
eigenanalysis,  and dynamic analysis), and the numerical methods  that may be
employed to affect these solutions are identical to those discussed earlier [Axley 1987]
and will not be considered here. The qualitative character of equations (2.15) depends
critically upon the qualitative character of the element equations from which they are
assembled, therefore, the  qualitative analysis presented earlier  [Axley 1987] will have
to be reconsidered with the introduction of each new element.
                                     2-9

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Phase III Report              3. Interactive  Contaminant  Dispersal Analysis
 3. Interactive  Contaminant Dispersal Analysis

   Often, indoor air quality analysis will involve consideration of several contaminants
and their dispersal in a building. Some of these contaminants may:

   a)  be absorbed or adsorbed by building materials or other contaminant particles,

   b)  settle from suspension or precipitate from (gaseous) solution, or

   c)  decay  radiochemically,   decompose  chemically,  or react  with  other
       contaminants to produce product contaminants (or other substances that are of
       no particular interest).

That is to say, contaminant dispersal processes may be complicated by the kinetics of:

   a) sorption processes,

   b) settling or precipitation processes, or

   c) chemical or radio-chemical reaction processes

that must be accounted for.

   In this section  we shall  introduce a general  approach to extend noninteractive
contaminant dispersal theory to account for mass transport phenomena governed by the
kinetics of these processes, based upon the principals of reaction kinetics, to develop
an interactive contaminant dispersal theory.  We shall set the stage by first considering
possible forms of system equations for multiple, noninteractive contaminant dispersal
analysis then,  after a review of some basic concepts  of reaction kinetics, go  on to
develop the so-called kinetics element equations that will become the basis of the
interactive contaminant dispersal theory.


3.1  Multiple,  Noninteractive,  Contaminant   Dispersal

   The dispersal of each contaminant of a given set of noninteractive contaminants will
be governed by the single-species contaminant dispersal equation, thus the dispersal of
the noninteractive contaminant set may be represented by a set of equations of the form:
                        {aG}
                        {PG}
                                                                          (3.1)
                                     3-1

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Indoor  Air  Quality  Model
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                                                           PART  I - THEORY
                              3. Interactive  Contaminant  Dispersal Analysis
   where;
       a, (5,... are species indices

       I  n       is defined by equations (2.5c) and (2.13b)
       [M]        is by equations (2.10)

(Note that, in general, the flow matrices for each species may not be identical because
individual flow elements may act to filter contaminant species differently.)

   Contaminant dispersal analysis for  the  set could, then, be  computed by simply
completing  a separate analysis  for each species of interest.  If,  however, the system
characteristics  change with time (e.g., airflow within the building is nonsteady and thus
the flow matrix, [F], changes with time) and the flow matrices for each species are
identical then it would be computationally more efficient to simultaneously compute the
response of each species while  stepping  through time as suggested by  rewriting
equation (3.1) in the form:
[*F]KaC},{PC},...]
       for;
                         d{aC}  d{C}
                           dt  '  dt   ""

                            -...[>]
                                                                          (3.2)
   As an alternative approach, that will  help set the stage for  multiple interactive
contaminants, we may write the uncoupled set of equations given by equation (3.1) as
an expanded system of equations of the form:
                   ={G}
                                                                         (3.3a)
where system  variables are organized by  species for  each node of the system
idealization as:

mi   r
{} = (

                                 V    n    \
                             ,-..  Gn,  Gn,...}
(3.3b)

(3.3c)
The system flow transport matrix, [F], in this case, may be assembled by species and,
then, by element as:
[F]  =    A
       e = a,b,...
                 A    [V]
               o=a, p,...
                                                                         (3.3d)
       where;
          a  is a general species index ( a, (3,... are specific species indices)
                                     3-2

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                                                          PART I - THEORY
                             3. Interactive  Contaminant  Dispersal Analysis
          e  is a general element index (a, b,... are specific element indices)

   The inner assembly sum, by species, may be thought to generate element equations
for a noninteractive, multi-species flow element.  This multi-species flow element could,
then,  be  assembled in the usual  manner to form the system equations.  For three
contaminant species, a, p, y, the noninteractive,  multi-species, flow element transport
matrix  (with filtration of each species) would have the form:
   A
o=a,P,
                the noninteractive, multi-species, flow element transport matrix



(


1
0
0
VD
o (
0
0
1
0
0
V
0
                                      0

                                      0

                                      1

                                      0

                                      0
0

0

0

0

0

0
                                                   0

                                                   0

                                                   0

                                                   0

                                                   0

                                                   0
0

0

0

0

0

0
                                                                         (3.43)
for element flow from node i to node j and element concentration variables organized as:
               e    8     8
                                 YeT
   This noninteractive. multi-species, element flow matrix is seen to be very sparse.
Consequently, assemblies of such elements would result in extremely sparse system
equations.  It would, therefore, be computationally impractical to employ this approach
for noninteractive, multi-species, contaminant dispersal analysis  one should use the
strategies indicated by equations (3.1) or (3.2) instead.  It will be seen, however, that
kinetic interactions among contaminant species will act to couple the  species variables
at the system nodes (zones) with the result that system matrices will tend not only to be
much less sparse, but reasonably well-banded.  The  use  of noninteractive,  multi-
species,  flow  elements will, therefore,  become attractive when combined with the
kinetics  elements presented  subsequently for interactive  contaminant  dispersal
analysis.

   The program CONTAM87, documented in the second part of this report, organizes
system and element variables following equations (3.3b), (3.3c), and  (3.4b) and makes
use of the double assembly process for simple flow elements defined by equations
(3.3d) and (3.4a).
                                     3-3

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Phase III Report              3. Interactive Contaminant  Dispersal  Analysis
3.2  Basic Concepts of  Reaction  Kinetics

   Reaction kinetics involves the study of the rate of change of chemical components
m a single or related series of chemical reactions.  Some basic concepts of (isothermal,
constant volume) gas reaction kinetics will be  reviewed here; greater detail may be
found in one of several texts on the subject [Moore 1981, Nicholas 1976, Walas 1959].
Much of this material  may also be applied to sorption, settling or precipitation, radio-
chemical, and  other chemical  phenomena that  may be important for some interactive
contaminants in indoor air quality analysis.

   A general form of a chemical reaction involving reactants, a, (J	that react to form
products, p, a	may  be represented as;
            catalyst
a + p + ...>  p +a +...


       catalyst
where   _>   indicates the possible affect of catalysts on the reaction.
                                                                          (3.5)
    Given the rate of change of a selected component's concentration, say a, is defined
as;
       dC
 aR =  :^-r^- ; rate of reaction (\nterms of reactanta)
        dt
                                                                          (3.6)
       where:
          aC     is the concentration of species a measured in terms of mass of a per
                 unit mass of air (i.e., strictly speaking the mass fraction of a)

and the stoichiometry of the reaction, expressed in terms of relative masses. am, Pm, ....
of reactants and products as;
                   catalyst
 a       B                 p       a
  ma +   mp  + ...  >    mp +   ma + ..
                                                                          (3.7)
the rate of change of the other components' concentrations may be related to that of the
selected component's as;
        P.
        m
                         m
                          m
m
                                         R
                                                                           (3.8)
                                     3-4

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Indoor  Air  Quality Model                                 PART I  - THEORY
Phase III Report              3.  Interactive Contaminant Dispersal  Analysis
thus, the rate of a given chemical reaction may be described in terms of the rate of
change of concentration of any one of the reactants or products.

   In general, the rate  of a given chemical  reaction may depend upon a variety of
factors including reactant and catalyst concentrations, temperature, T, pressure, P, and
the detailed mechanisms of the chemical reaction, therefore, rate expressions take the
general functional form of;


            C, PC,... PC, "C,...T,P,...)                                     (3.9)
Constant Rate Expressions  In some instances the rate of reaction may remain more
or less constant:
    =    o                                                              (3.10a)

or depend solely on temperature and pressure:


  R =   R0(T, P)                                                          (3.1 Ob)

Examples include the catalytic decomposition of some gases, such as ammonia, the
radioactive decay of  isotopes with very long half lives, such as Ra226, the controlled
burning of fossil  fuels,  and other relatively slow reactions  driven by  reactant and
product concentrations that remain, more or less, constant over the time of interest.
Power Law Rate Expressions  In many cases the explicit form of a rate expression
will prove to be rather complex. In some cases, however, (empirical or semi-empirical)
rate expressions may be employed that take the form of so-called power expressions:


 R =  aK(T,P)(aC)a(PC)b..(PC)rC)S...                                    (3.11)

      where:
          K           = the rate constant [=] 1/time
          a, b, ...r, s,...      = constant exponents

Reactions governed by such power expression are classified by their overall order- the
sum of the constant exponents  - or by their order with respect to each kinetically active
component - the constant exponent of that component.  For the reaction described by
equation (3.11), then, the overall order will be (a + b + ... + r + s + ...) and the order with
respect to component a will be simply (a).
                                     3-5

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                                                             PART I - THEORY
                               3. Interactive Contaminant  Dispersal Analysis
First Order  Rate Expressions   Rate expressions  for certain general classes of
reactions, including single-reactant, consecutive, opposing, and  concurrent first order
reactions, often take the form of linear combinations of contaminant concentrations:
{R}=-[K]{C}

or
                                                                          (3.12a)
                act   aB        ao
                  K - K  ...  - K
                    PP
                      K
                oa   <
               -  K -
                             ao
                                                                          (3.12b)
where we have included the constant  component, {R0}, for completeness  and
recognize that,  again, the rate coefficient matrix, [K], and the constant component
vector, {R0}, will, in general, vary with temperature and pressure.  It should be noted
that equation (3.12b) has been written so that all rate coefficients, V^K ; \|/, co = oc.p,... o ,
will be positive for realistic reactions.

   In fact, it is possible, in principal, to linearize any given rate expression about some
(current) state of concentration, say (aC0 ,  PC0 , ...), by employing a Taylor's expansion
about that state, to obtain an approximate rate expression expressed as the sum of a
series of first order rate expressions, as:
 aR(aC,PC,...)
                  3aR(cb0,lfc0l...)I
                        apc
                                                                           (3.13)
that, together with equation (3.8), may be used to form a linearized system of first order
rate expressions of the form of equations (3.12).  One could, conceivably, employ this
linearization strategy, within an appropriate nonlinear solution method, to account for
arbitrarily complex  kinetics.  The  first .order kinetics element, that will be presented
subsequently, provides a first step in this direction.

    Linear systems of first order reaction expressions are defined by the characteristics
of their reaction rate coefficient matrices, [K].  To gain a better understanding of the types
and characteristics of such  reactions  several specific  classes of reactions are
described below.
                                      3-6

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                             PART  I - THEORY
3. Interactive  Contaminant  Dispersal  Analysis
Single-Reactant  First   Order   Reactions   For  reactions involving single
contaminant reactants that decompose or decay to  form  products (that are of little
particular interest):

a  - products
P  -> products
      products
the rate coefficient matrix takes the following form:
                                           (3.14)
[K]  =

act
K
0
0
0 ...
PPK ...
0 ...
0
0
oa
K
                                                                          (3.15)
Consecutive First Order Reactions  The radioactive decay chain of Radon gas is
an especially important example of a consecutive first order reaction series.  The
reaction rate expression for a simple two-step consecutive reaction will be discussed
first then the general case will be considered.

   For a two-step consecutive reaction series involving a single reactant at each step:
a  - p
P  - products

with reactions governed by rate expressions of the following form:
                                           (3.16)
        PaKaC-  PPKPC
the matrix of rate coefficients becomes:
[K]  =
        act
          K  0
                                                                          (3.17)
                                                                          (3.18)
   Here, the generalization to a multi-step reaction involving single reactants at each
step  is straightforward.  For a general multi-step consecutive reaction series:
                                     3-7

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Indoor Air Quality Model                                 PART I - THEORY
Phase III Report              3.  Interactive Contaminant Dispersal  Analysis
a  - p
p  -* ...
p  - a
a  -> products

governed by rate expressions of the form:
(3.19)
 "R =  -aaKaC
        KK C -  PPK PC
       PKPC-
the matrix of rate coefficients becomes:
[K]  =
aa 
K 0
0 0
0 0
... 0
... 0
pp
... K
0
0
0
oo
K
                                                                        (3.20)
                                                                        (3.21)
Opposing First Order Reactions  For simple reversible reactions involving a single
reactant and single product:
a  <- p
governed by rate expressions of the form:


 R =  -aaKaC+  aPKPC
(3.22)
                                                                        (3.23)
the matrix of rate coefficients becomes:
                                     3-8

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Indoor  Air Quality  Model
Phase III Report
                                                          PART I  - THEORY
                              3. Interactive  Contaminant Dispersal  Analysis
[K]  =
        act   aB
          K -  K

             PP
                                                                        (3.24)
   For the more general  case of a series of reversible reactions involving single
reactants and products:
a  <->P<-y<-8<-  ...
governed by rate expressions of the form:
                                                                        (3.25)
 R =  -
                 apKPC
       paKac-  PPKPC+  Vc
       *KPC  -  VC  +  Y5K5C
the matrix of rate coefficients takes the tridiagonal form:
                                                                        (3.26)
[K]  =

""K -aPK 0
-P\ PPK -\
0 A Tc
0 0 -5YK

0 ...
0 ...

68K ...
_
                                                                        (3.27)
Concurrent Linear Reactions  Due to their linearity, rate coefficient matrices for
concurrent linear reactions may simply be added to obtain an effective rate coefficient
matrix for all reactions combined. For example, consider a set of concurrent reactions
involving a single contaminant  reactant, a, that decays  or decomposes to produce
products (3, y, a :
a  - p   ; reaction "a"
a  - Y   ; reaction "b"
a  - 8   ; reaction "c"

governed by rate expressions of the form:
                                                                        (3.28)
                                     3-9

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Indoor Air Quality Model                                 PART I  - THEORY
Phase III  Report             3.  Interactive  Contaminant  Dispersal Analysis
 o_     . aa    aa     aa  . a_
  H = -(a K+  b K +  c K)  C
 'R  =

 8R  =
The matrix of rate coefficients is:
[K]  =
aa aa aa 1
a K + b K + c K)
Pa
"I*
"b ^
5a
C
0
0
0
0
0
0
0
0
0
0
0
0
                                                                       (3.29)
                                                                      (3.30a)
which is seen to be the sum of the individual reaction rate coefficient matrices:
aUK 0 0 0
-JK 0 0 0
0000

0 000





 at
bK 0 0 0
0 000
-bK 000

0 000





cK 0 0 0
0 000
0 000
Sa
-c K 000
                                                                      (3.30b)
3.3  Kinetics Element Equations

   The development of a general kinetics element is straightforward.  Limiting  our
considerations to mass transport phenomena occurring within  a specific zone "i",
containing a set of contaminant species, a, (3, y,.... we first identify the relevant element
variables as:
-  /
=  I
         ae
                   Ye
                                ; the element state variables
                                                                     (3.31)
and
a    raepeve    .T
 }  = t W| ,  w, ,  -W| ,...)
                                ; the element mass flow rate vector         (3.32)

Then, assuming that the mass transport phenomena to be modeled is governed by the
                                    3-10

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Indoor Air Quality Model                                  PART  I - THEORY
Phase III Report              3.  Interactive  Contaminant  Dispersal  Analysis
kinetics discussed above, a general kinetics element equation follows directly from the
definition of rate of  reaction, equation (3.6) and the general form of rate expressions,
equation (3.9), as:


{w } = -  [Mn {Rj ({Cl, T, P)}      . tne generai kinetics element equation      (3.33a)

       where;

                 "" diO 0 ...
                   0  0 Mj...
                                                                         (3.33b)
                                                                         (3.33C)

(The superscript e has been added to identify the specific kinetics element and  the
subscript i  has been added to identify the specific node/zone being considered.  The
negative sign is needed as species mass transport "into" the element (i.e., removed from
the zone) is defined to be positive.)

    Using the notation  introduced earlier (equations (2..1) and (2.2)) it is seen that the
general kinetics element is one defined by the following element arrays:
    = 0  ; [y8] = 0 ;  [z6] = 0 ;  ...  ;      =             ..                 (333d)

an element that is defined in terms of only element derived species generation rates.

    If the rate expressions are constant  rate expressions,  then the element derived
generation  rate terms will simply add to any direct species  generation rates specified
within a zone, after equation (2.12e) as:
             kinetics dements
                                                                          (3.34)
where {Gj} and {Gj} are the subsets of the system vectors {G} and {G} corresponding to
node/zone i.  In these cases there will be no practical difference between the physical
generation of species mass (e.g., by physical release of a contaminant) and the kinetics
generation of species mass (e.g., by chemical or physical-chemical processes) and,
                                     3-11

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Indoor Air Quality Model                                  PART I - THEORY
Phase III Report              3.  Interactive  Contaminant Dispersal  Analysis
therefore, the analyst may model either using  simple  noninteractive contaminant
dispersal analysis techniques.

   The form of equations (3.33) is deceptively simple.  The rate expressions defining
these element derived species generation rates depend on species concentration, in
general, so that the general kinetics element introduces a nonlinear species generation
contribution (i.e.,  a species generation rate that depends nonlinearly on the solution
vector {C}), which is distinctly different from the  (constant or time dependent)  nodal
direct generation contribution.   The solution of  the contaminant dispersal problem
involving general kinetics elements will, therefore, require the application of a nonlinear
solution strategy in the solution process.  While this adds complexity to the analysis
process it should  not be  difficult to develop an appropriate nonlinear solution strategy
(e.g., using one or more  of the strategies considered earlier to solve the nonlinear air
flow  analysis problem [Axley 1987]) for certain classes of kinetics.

   Few  interactive indoor contaminants have been studied in sufficient detail to
completely define their  kinetics, therefore, the  development  of nonlinear solution
techniques for arbitrary nonlinear kinetics would be premature at this time.  Instead we
have limited  our  attention  to kinetics described  by linear systems of first order rate
expressions (that  lead directly to linear systems of  equations for interactive contaminant
dispersal analysis) to  develop a practically useful interactive contaminant dispersal
analysis method.  It seems  likely, however, that more complex kinetics may be modeled
in the future by employing the combination of the linear method described below and the
Taylor's  expansion presented  earlier (equation (3.13)) to linearize rate expressions,
within an appropriate iterative solution scheme.
First Order  Kinetics  Element Equations   For reaction kinetics described  by
systems of first order equations, equations (3.12):
                                 ,                                         (335)


the kinetics element equations (3.33) become:


{w8}  =
                             oi                                           (336a)

or:


[x6] =  [M*HK] ;  [y6] ,= 0 ; [z6] = 0  ; ... ;  {g6} =  [M^R*.}                 (336b)


and, again, one must keep in mind that the rate coefficient matrix and  constant rate
component will, in general, be temperature and  pressure dependent:
                                     3-12

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Indoor Air Quality Model                                  PART  I -  THEORY
Phase III Report              3.  Interactive  Contaminant  Dispersal  Analysis
  e      e
[KJ]  = [K^Lr/j                                                           (3.36c)


{R0j} =  {R0i(T,P)}                                                       (336d)


   It will be convenient to introduce a new variable for the linear first order element
kinetics transport matrix, as:

             Q
[kj  = [Mjj[Kj]                   : the element kinetics transport matrix        (3.37)

and a corresponding variable for the system kinetics transport matrix, that is assembled
from the element kinetics transport matrices in the usual manner, as:


M        A     [k6!
      kinetics elements                tne system kinetics transport matrix         (3.38)

so that the system transport matrix, [W], (equation (2.12b)) may be thought to equal the
sum of the familiar system flow matrix, [F], and the system kinetics transport matrix as
noted in equations (2.13) and repeated here:
     = [F]  + [K]  =    A    [fl +     A
                   flow elements     kinetics elements                             /3 3g\
   The program CONTAM87, presented in the second part of this report implements the
interactive  contaminant dispersal theory, presented  above,  providing the linear first
order kinetics element in its library  of elements  and ordering system concentration
variables as discussed above (equation (3.3b)) to enable the proper assembly of flow
elements (i.e., by equation (3.3d)) for multi-contaminant dispersal analysis. Examples of
the application of these techniques are presented in Section 9.
                                     3-13

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Indoor Air Quality Model                                 PART I  - THEORY
Phase III  Report            4. One Dimensional Convection-Diffusion  Flow
 4.  One Dimensional Convection-Diffusion Flow

   The flow element presented earlier [Axley 1987] provides the simplest modeling of
species mass flow from one zone to another.  This simple element is based on the implicit
assumption that the volume and  the length of the flow passage is negligible and,
therefore does not account for any dynamic dispersal phenomena occurring within  the
flow passage.

   For problems where  zonal dynamics is of primary interest and  it is suspected that
flow passage dynamics need not be considered (i.e., for systems with zonal volumetric
masses much greater than flow passage volumetric masses and for which flow through
these passages is practically instantaneous) the simple flow element should suffice.  For
those problems where some interest is focused on the detail of flow passage dynamics,
or where it is  believed  that dynamic phenomena in the flow passages can not be
ignored, an alternative flow element is required.  In this section a convection-diffusion
flow element will be developed that will answer this need.
4.1 Convection-Diffusion Equation

   Consider the flow through a flow passage (e.g., a section of duct work) that connects
zone i to zone j;
                                                             a  e
                                                              Wi
    node i

X
J / 'V
fel In
AX ^(X,

t)+AC(

x,t);

node j
                   Figure 4-1  One Dimensional Flow Passage

   Isolating  a segment AX of the flow passage and demanding the conservation of
species mass flowing through this segment we may write;
we(aC-(aC+AaC))
                                                        31              (4.1)

or, in the limit as Ax -0;
                                    4-1

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Indoor Air Quality Model                                  PART I - THEORY
Phase III Report             4.  One Dimensional  Convection-Diffusion  Flow
       edU   d  W     a      . d  U
   -w	+   g = pA
         dX     dX              3t                                        /42)

       where;
          we    is the total fluid (air) mass flow rate through the flow passage
          aC    is the a species mass concentration
          aw'   is the a species mass flow rate relative to total fluid mass flow rate
          p     is the density of the fluid (air)
          A     is the cross-sectional area of the flow passage
          ag    is the a species mass generation rate per unit length of passage
          x, t    are distance and time,  respectively

   The first term above accounts for species mass  flow due to convection and  the
second term  accounts for species  mass flow due to species diffusion  that is
superimposed on the bulk flow.

   The generation term, g, may be replaced  by an  appropriate generation (kinetics)
rate expression.  For example, if the generation involves the single species a one could
replace the generation term with a linear generation rate expression of the form;
 a     a       , aa a_
  g =  g0 +  pA   KG
(4.3)
       a                                   owx
where   g0 is a constant rate component and   K is a generation rate constant.  This
form of generation rate expression would be appropriate, for example, for formaldehyde
emission from the flow passage walls [Mathews et. al. 1984, Grot et. al. 1985].

   The  diffusion of species mass relative to the (bulk) total mass fluid flow, aw', will, in
general, depend upon the details of the fluid velocity profile,  and  its turbulence
characteristics (e.g.,  the eddy  diffusivity),  and  molecular  diffusion  along  and
perpendicular to the  flow passage  length.  In many  practical situations, however, this
diffusion component  may be modeled using an expression based upon Pick's law of
diffusion which may be written as;


 O .       A r-vd C
  w'  = - pA  D	
                d*                 : By Analogy to Pick's Law                   (4.4)


where  aD is the axial dispersion coefficient of a in the flow fluid (air).

   Substituting equation (4.4), equation (4.2) may be  rewritten as;
                                      4-2

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Indoor  Air  Quality Model                                  PART I - THEORY
Phase III Report             4.  One  Dimensional  Convection-Diffusion Flow
  ,o_9C    a      .  3  C      e 3 C
pAT) -  +  g = pA - +  w  -
                                                                          (4.5a)
an equation that is commonly called the one dimensional convection-diffusion equation
that also appears in thermal convection-diffusion problems.  The convection-diffusion
equation is often expresses in dimensionless form as;


 1  3  b     a    9aC     3aC
      _  +   y = - +  
Pe
    3*                     "*                                             (4.5b)

      where;
                  \     uL
          Pe.
                pA  D     D      tne dimensionless Peclet Number           (4.5c)

          L  is the (characteristic) length of the flow passage
          X  is the dimensionless length  =  x/L
          i  is the dimensionless time =  t/t

           y is the dimensionless generation rate =  gLAve
          t  is the nominal transit time =  L/ u
          U  is the bulk fluid velocity = we/pA

The Peclet number alone, then, characterizes the convection-diffusion process in a flow
passage not involving a kinetic rate' expression. It provides a measure of the importance
of convection mass transport relative to diffusion mass transport.

   The convection-diffusion equation presented above,  equation (4.5), is referred to as
the axial  dispersion model or axial-dispersed plug-flow  model in the chemical
engineering literature where it has played an important role  in the simulation  of flow
systems found in the chemical process industries since 1908 when Langmuir introduced
it.  As one might suspect, the  utility of this equation  depends critically upon  the
determination  of the dispersion  coefficient to be used for a given set  of flow
circumstances.  A complete discussion this problem is well beyond  the scope of  this
report and the reader is, therefore, directed  to the excellent general discussion of  this
approach  by Nauman and Buffham [1983] and the more practically useful, reference
work by Wen  and Fan  [1975].  Suffice  it  to say that for turbulent, isothermal flow
conditions in relatively long flow passages, the dispersal coefficient is reasonably well
correlated  to the characteristic Reynolds number,  Re, of the flow and is practically
independent of species molecular diffusivity as indicated by the Taylor expression
(reported by Wen and Fan [1975 p. 47]):
                                     4-3

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Indoor  Air  Quality  Model
Phase III Report
                                          PART  I - THEORY
            4. One Dimensional Convection-Diffusion  Flow
              3 D- 2uR
                         3.0x10
                     1.35
          Re
                                     Re
                                        0.125
                               Re> 2000
                                                                          (4.6)
       where;
          R     is the flow passage radius
          Re  s 2puR4i
          |i     is the flow fluid's viscosity

Under turbulent flow conditions, the fluid velocity profile is relatively flat and diffusion is
dominated by mass transport by flow eddies rather than by molecular diffusion, thus the
dispersion  coefficient  becomes primarily dependent  upon  the  turbulence
characteristics, as measured by the Reynolds number, and is, therefore, often identified
as the eddy diffusivity.

   Under laminar flow conditions,  on the other hand, the velocity profile tends to be
parabolic, turbulence subsides and  as a result both radial and axial molecular diffusion
come to  play an important role and the diffusion becomes two dimensional in nature.
Nevertheless, if the fluid can be assumed to be homogenous, so that the radial and axial
molecular diffusivities may be assumed to be identical, then a solution  of the complete
two dimensional convection diffusion problem reveals that the asymptotic behavior is
equivalent to that described by the one dimensional convection diffusion equation using
the Taylor-Aris dispersal coefficient [Nauman  & Buffham 1983 pp.112-113]:
 D
             48
   ; Re<2000  ;^<0.16 
                n        a
                          
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Indoor  Air  Quality Model
Phase III Report
                                                            PART I  - THEORY
                              4.  One Dimensional  Convection-Diffusion  Flow
In practice, building air ducts are normally designed for bulk air flow velocities greater
than or equal to 2 m/s [ASHRAE 1985].  For this minimum operational flow rate, then, the
Reynolds number for the flow in this duct would be (pajr = 1.2 kg/m3 & p.air  1.8 x 10'5
kg/m-s at 20C):
               Re =
                           = 2(1.2kg/s)(2.0m/s)(Q.5m) =
                                         -5.
                                 (1.8x10  kg/m-s)
and, by the Taylor correlation, equation (4.6), the dispersal coefficient would be:
                  _  2.1      _  0.125]
                  Re       Re
           2(2.0 m/s )(0.5 m)
                             3.0x10
                                                1.35
                                                      0.125
                                           (1.33x1 05)   f
= 6.2x10"^^
Typical diffusivities of gas pairs are on the order of  1 to 2 x 10"5 m2/s. Thus, even under
these relatively low flow conditions the dispersal coefficient (eddy diffusivity, in  this
case) is  seen to  be over four orders of magnitude greater than  molecular diffusion.
Continuing, the Peclet number, for this case would be:

                        Pe = Hk =  (2-0m/sX10m)  =  32.3
                               D           -12
                                    6.2x10  m/s

   An examination of the turbulent correlation expression reveals that the dispersal
coefficient for turbulent conditions is dependent upon the average flow velocity and the
flow passage radius.  This dependency is plotted below for a range of flow velocities
and radii:
                                      4-5

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Indoor Air Quality Model
Phase III  Report
            4.  One Dimensional
                            PART I  - THEORY
                     Convection-Diffusion Flow
(m2/s)
      0.00
         0.00        0.50         1.00        1.50        2.00         2.50
                                      R  (m)

      Figure 4-3 Dispersal Coefficient for Turbulent Flow in Ducts (20C. 1 atrn^
4.2  Convection-Diffusion Element  Equations

   Finite element solutions of connective-diffusion equations of the form of equation
(4.5) have received  considerable attention in recent  years.   Following the one-
dimensional example discussed by Huebner and Thornton [1982] element equations for
a two-node flow element may be developed from equation (4.5) using linear shape
functions (i.e., assuming species  concentrations vary in a piece-wise linear manner
along the flow passage) and applying either  the (conventional) Galerkin method or the
(upwind) Petrov-Galerkin method in the formulation of these element equations.  The
resulting element equations are:
                                                                       (4.8a)
      where;
                . a  e  a  e,T
              = { W, ,  Wj }
W
                    1 1

                    -1-1
W [1 -1
2-11
                                                                       (4.8b)
                the convection component of the element flow transport matrix
                                    4-6

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Indoor  Air  Quality  Model
Phase III Report
                                                            PART I  - THEORY
                             4.  One  Dimensional  Convection-Diffusion  Flow
               the so-called upwind parameter, 0 < <|> < 1
                   L                                                     (4.8C)

                the diffusion component of the element flow transport matrix

          Le    the length of the element (i.e., a portion of the length of the flow path)
                      211   ApAJ/
                      12       4
                the element volume mass matrix
                                                                         (4.8d)
                                                                         (4.8e)
                the internal generation rate vector
for total fluid mass flow rate. we, through the flow passage from node i  to node j as
indicated in Figure 4-1.

The Upwind Parameter If  is set equal to 0, the  element equations become identical
to those that would be obtained using the (conventional) Galerkin approach of element
formulation.  Unfortunately, these conventional element equations lead to solution
approximations that exhibit spurious spacial variations when  convective transport is
large relative to transport by diffusion.  The upwind parameter, , has been introduced,
using the Petrov-Galerkin approach, to control this form of numerical instability, but at
the cost of  introducing artificial  diffusion (vis a vis the  second term on the right of
equation (4.8b)) that introduces inaccuracies.

Generation  Kinetics  If the generation term of  equation  (4.5) is replaced  by  the
generation (kinetics) rate expression of equation (4.3) the element equations will have
the slightly modified form of:
                                                                         (4.9a)
      where;
                    . eaa
                 pAL   K
                                 (DpAL9aaK
-1-1
1  1
                                                                         (4.9b)
                                     4-7

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Indoor  Air Quality Model                                 PART I - THEORY
Phase III Report             4.  One Dimensional Convection-Diffusion  Flow
                the kinetics component of the element flow transport matrix
                                                                        (4.9c)

                the constant component species generation rate vector

Lumped Element Mass Matrix  The convection diffusion element equations defined
by either equations (4.8) or (4.9) may be assembled, in the usual manner, along with the
simple flow element equations (equations (2.4) or (2.5)) and kinetics element equations
(equations  (3.36)) to form the system equations.  The convection-diffusion element
introduces, however, nondiagonal contributions to the system mass  matrix,  [M], that
adds  some complexity  to  the  assembly  and  solution algorithms used in the
computational  implementation of the contaminant dispersal theory.  To avoid this
complexity  one may replace the so-called consistent element volume mass matrix,
equation (4.6d), with a diagonal lumped mass approximation to it, given by:
[m6]
pALe
                       the element lumped mass matrix                      (4.10)
This approximation may be expected, however, to introduce some additional error.  The
program CONTAM87 provides convection-diffusion elements having this lumped mass
approximation.
4.3  Use of The  Convection-Diffusion Flow  Element

   In this application, we are using the Finite Element method to approximate the spatial
variation of contaminant concentration along a flow passage in a piece-wise linear
manner where each linear segment of the approximation will correspond to an individual
convection-diffusion flow element.  Clearly, if the form of the  actual concentration
variation along the flow path  is linear we could model  the flow passage with a single
element. In general, however, we will not have a priori knowledge about the form of the
concentration variation and, therefore, should employ a series of flow elements to obtain
a piece-wise approximation to the actual concentration variation.

   Without some experience, the analyst may not know how many convection-diffusion
elements to use in a given situation.  In such a situation, however, a first analysis may
be completed with a trial subdivision of the flow path then the analysis may be repeated
with  a  finer subdivision.   The finer subdivision may be expected to provide a better
approximation to the solution (providing numerically stability has been achieved)  and,
therefore, may  be used to access the accuracy of the solution. This  process of
subdivision  could,  then, be  repeated  until the solution  converges  to within an
acceptable accuracy.
                                     4-8

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Indoor  Air  Quality  Model                                 PART I  - THEORY
Phase III Report             4.  One Dimensional  Convection-Diffusion  Flow
Steady State Analysis  When  considering  steady-state  flow without internal
generation, Huebner and Thornton show that instability may be avoided if an upwind
parameter is selected satisfying the conditions;
  >1 -4  ;  Pee>2
         Pe
  = 0  ;  Pe<2
           6                                                             (4.11)
      where;
                  e. e    ,e
                w L    uL
                PAb    b                                             (4.-12)

             is the element Peclet number


(Note:  Pe  = (Pe/n)   for a flow passage idealized by an assembly of n equal-length
convection-diffusion elements.)

   To fix these ideas, consider the problem presented by Huebner and Thornton [1982];
the dispersal of a contaminant along a straight flow passage, under steady  flow
conditions, without generation, and with inlet contaminant concentration maintained at
C0 and outlet concentration maintained at zero, as diagrammed in Figure 4-4.

       C(0)   1                                             C(L) _ Q
                                                             Co "
f
t
t



we-
->
i
i
L i L
T
1

i

Steadv
Node Number
2^ 3
1\t 2
 3
State
4
* 4
i
Convection-Diffusion Problem
5
+ 5
6
f 6
7 8 9 10 11
^7 8 f9 lOf
           Element Number
                   Ten Convection-Diffusion Element Idealization
  Figure 4-4 A Steady State Convection-Diffusion Problem and Corresponding Finite
                              Element Idealization

   For this problem the convection-diffusion equation simplifies to:
                                     4-9

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Indoor Air Quality  Model                                  PART I - THEORY
Phase III Report             4. One Dimensional  Convection-Diffusion Flow
 1  d2C
Pe
            _ 0
      2  "  dx
   dx
which may be solved for the boundary conditions:

C(x=0) =C0
C(x=L) = 0

to obtain an exact solution:
                                                                       (4.133)
                                                                        (4.13b)
C(x/L)  _  e L     - e L  .
                  Pe
             1  - 6L
                        ;  0 = 0.0
and $ = 1.0.  The exact with the approximate solutions are compared below in Figure 4-
5.
 C(x)/Co 0.8



1.0 B


00 .


J
*
*
*
4T




 Pe=0.2, Exact  Pe=0.2, 0=0.0  Pe=0.2, 0=1.0
"-> Pe=20, Exact A pe=20. 0=0.0 A pe=20, 0=1.0


t
%
^


^
^
*
-*^!




J
^
*
m
*
m


%

%


' D








A
m
*
*
m
m
f
m
a
m
g
. f i
9
g




k

%
*
%
*



*
%

i
%
\
y^^:\
3



g
t

m

*

*


*

*
Bl-_
^*"^i







5^^^
^^i





1 >


3^^^






\

\

            0.0    0.1    0.2     0.3    0.4    0.5    0.6    0.7   0.8    0.9    1.0
                                           X/L

  Figure 4-5 Comparison of Exact and Finite Element Solutions for a-Steady Convection-
                                Diffusion Problem

   The results clearly demonstrate the numerical instability that may result when
                                    4-10

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Indoor  Air  Quality Model                                  PART I  - THEORY
Phase III Report             4.  One  Dimensional Convection-Diffusion  Flow
upwinding is not used for high element Peclet numbers.  For convection-dominated flow,
which should be expected  to be typical in  building  HVAC ductwork under operating
conditions, the  analyst may, then, choose to either use a fine subdivision of a given
duct or employ upwinding  to maintain numerical stability, keeping in mind  that the
upwinding will introduce artificial diffusion that may add error.  (A close examination of
the results above reveals that full upwinding  underestimated the concentration variation
slightly.)
Dynamic Analysis The convection-diffusion flow element may also be employed for
dynamic analysis, but the analyst must take special care to assure an accurate solution
has been obtained. In dynamic analysis, accuracy is affected not only by element size
(i.e., the subdivision of the flow path), and the degree of upwinding chosen, but also by
the integration time step selected to complete the dynamic solution.  Furthermore, the
use of the  lumped mass approximation, while avoiding the complexity demanded  by
nondiagonal mass contributions, tends to introduce spurious anomolies in the computed
solution in some cases [Huebner & Thornton 1982].

   Partly because of the challenge of these difficulties and partly because of the
importance of the convection-diffusion equation in the area of fluid  mechanics,  finite
element solutions of the convection-diffusion equation have become the focus of
considerable research in recent years.  Strategies  have been put forward to improve the
accuracy of the finite element  approximation presented above that are, regrettably,
beyond the scope of this presentation and the reader is, therefore, advised to review the
current and emerging literature.  The papers by Hughes and  Brooks [1982], Tezduyar
and Ganjoo [1986], and Yu and Heinrich [1986] are particularly useful in this regard.

   In spite of the numerical pitfalls that  await the use  of the  convection-diffusion flow
element presented above we shall proceed and employ these elements (with the lumped
mass approximation) to compute the transport of a  contaminant pulse through a length of
ductwork.   The conditions of this problem are diagrammed in Figure 4-6: fluid  flows
through a duct of length L and radius R at a mass flow rate we; a contaminant is injected
into the inlet stream at a rate G(t) for a short  time interval introducing a pulse of
contaminant of mass I into the inlet  stream;  the pulse is convected and dispersed as it
moves along the duct.   We seek to determine the concentration time history of the
contaminant as it emerges from the outlet of the duct.

   The exact solution to this problem is available for an impulse (i.e., a pulse defined by
the dirac delta function), for  "closed" inlet and outlet conditions, but  it is expressed  as
an infinite sum that is practically difficult to  use [Wen & Fan  1975 pp. 133-137].  For
Pe=0 the duct becomes a well-mixed system, the initial concentration throughout the
duct becomes, simply, (l/pAL), and the outlet concentration decays exponentially:

 C(L.t)  = e-t/f
(l/pAL)                              ;Pe=0                              (4.15)
                                     4-11

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Indoor Air Quality Model
Phase III Report
                                          PART I - THEORY
             4.  One  Dimensional Convection-Diffusion  Flow
For relatively large Peclet numbers the outlet concentration is well approximated by the
the following expression reported by Nauman and Buffham [1983 pp. 101-103]:
 C(L.t)
(1/pAL)
               Pe
                    e\
      -Pe(1 -t/F)
         4t/f
                 _ 3
                                    ;Pe > 16
                                                        (4.16)
and for very large Peclet numbers the outlet concentration approaches a Gaussian
distribution [Wen & Fan 1975 p. 133]:
 C(L.t)  _,/PT
(l/pAL)  "
       -2
-Pe(1 -t/t)
    4
                   ;Pe  16
                                                                        (4.17)
   Approximate solutions to this  problem were computed  using  a  10-element
subdivision,  as shown in Figure 4-6, and a twenty-element subdivision. The "closed"
boundary condition was modeled using the simple flow element as this element models
(instantaneous) plug flow conditions as required.  The  impulse was approximated by a
pulse of finite but small duration. In all studies the upwind parameter, , was chosen to
satisfy the lower bound (i.e., equality) of the stability requirement of equation (4.11). The
results are compared  below, Figure 4-7, to the solutions discussed above, equations
(4.15) to (4.17).

  G(t)J,


_l
~l
t
,/GWdt-l 11""
,t 
1 W
Rjl 	 >
->*
/\^


1 \
V. Plug-Flow
                       Impulse Transport Problem
                                                              "Closed Boundary"



1 
"Exterior
Zone"

Node Number
2 3'
-*
^^2
\.
4
+ 3

567
4*5*

8
6 f 7

Element Number
9 10 1
+ 8  9 4

Simple Flow
1 12
> 10 <>7>
/
Element
               Ten Convection-Diffusion Element Idealization


  Figure 4-6 The Transport of a Pulse in a Duct and the Corresponding Finite Element
                                  Idealization
                                    4-12

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Indoor Air Quality Model
Phase III Report
                              PART  I -  THEORY
4. One Dimensional  Convection-Diffusion Flow
    It is seen that in this case the approximate, finite element solution for the low Peclet
number,  Pe=1,  approaches the  exact  well-mixed solution, as expected.   The
approximate solution for the higher  Peclet  numbers has some difficulty in capturing the
amplitude of the exit pulse, although, the timing and the form of the pulse appear to be
well-approximated.  Some part of  this  error may  be attributed to approximating the
impulse of the analytic solutions by  a pulse of finite duration in the  computed solutions.
In these  studies the pulse duration was set at 0.001  units of dimensionless time,
increasing the pulse duration by a factor  of 4 resulted in an additional underestimation of
the pulse amplitude at Pe=20 of approximately 5%.

    Some part of the error may be attributed  to the coarseness of the finite element
subdivision.   A comparison  of the   results of  the 10-element and 20-element
approximations for  Pe=10 indicate that a convergent solution was obtained (i.e., further
subdivision would not alter the solution), yet when these results are compared to the
exact results reported by Wen and Fan [Wen & Fan 1975 Fig. 5-8 p. 136] the amplitude
appears to be underestimated by approximately 10%. This same comparison for Pe=20
indicates that a convergent solution was almost but not quite achieved.  An additional
subdivision  would presumably reveal convergence,  and the  error  in amplitude
estimation was approximately 20%. It  is interesting to note that the element Peclet
numbers  for these two (nearly) convergent solutions - the 10-element solution at Pe=10
and the 20-element solution at Pe=20 -  are both equal to 1.0, a condition that demands
no upwinding (i.e.,  for which $ may  be set  to 0) to maintain numerical stability.  Results
were also computed for cases violating the stability requirement of  equation (4.11) and,
as  expected,  spurious variations  in concentration responses - "wiggles"  - were
observed.
                                                              " Exact: Pe=0

                                                               Nauman: Pe=20

                                                              	 Gauss: Pe=20

                                                               20 Elem: Pe=20

                                                              a loElem:Pe=20

                                                              -A- 20 Elem: Pe=10

                                                              A 10Elem:Pe=10

                                                               20 Elem: Pe=1
           0   0.2  0.4   0.6   0.8   1    1.2  1.4  1.6  1.8    2
                             Dimensionless Time  t/(LAl)

 Figure 4-7 Comparison of Analytic Solutions with Finite Element Solutions for the Pulse
                               Transport Problem

   It may be useful to relate these nondimensional studies to more conventional units.
                                     4-13

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Indoor  Air  Quality  Model
Phase III Report
                                              PART I  - THEORY
                 4.  One  Dimensional Convection-Diffusion  Flow
The study for Pe=20 corresponds to studying the transport of a pulse through a circular
duct of 1 m radius having a length of 10 m with a bulk flow velocity of 2 m/s (the practical
minimum operational flow rate in HVAC ducts).  For these conditions, by Figure 4-3, the
dispersal coefficient may be expected to be about 1.0 m2/s.  The  results reported in
Figure 4-7 were  computed using a pulse duration of 0.005 sec (i.e.,  0.001  times the
nominal transit time, F = L/u = 10 m 12 m/s = 5 s).  The dynamic solution was computed
using  a time step of 0.001 second, in part to capture the short-time pulse accurately and
partly  to achieve  a practically convergent solution.

   In  practical situations the inaccuracies  revealed in these studies are likely to be
considered very small and,  thus, the convection-diffusion flow element should provide a
practically useful  analytical tool. Nevertheless, to minimize error the analyst is well
advised to seek  a convergent solution through both mesh refinement (i.e., repeated
subdivision of the flow path), starting, perhaps, with a subdivision that  results in an
element Peclet number of  1.0, and time step refinement, starting with a  time step
sufficiently small  to  capture the dynamic variation of  any excitation  with reasonable
accuracy,  being careful to  select an upwind factor so  that the stability requirement of
equation (4.11) is always satisfied.  When employing convection-diffusion elements in
an idealization of a building airflow system it is very likely that extremely small time steps
will be required to obtain a convergent solution.
4.4  Analytical  Properties  of  the  Convection-Diffusion  Element
Equations

   The numerical properties of the convection-diffusion flow element have been seen to
be dependent on the element Peclet number.  To investigate this dependency in greater
detail we may rewrite combined convection and diffusion components of the element
flow  transport matrices, equations (4.8b) and (4.8c),  in terms of the  element Peclet
number, as:
                             -l
                                                 DA  1 -1
       w
       ~2
1  1
-1-1
                                                                         (4.18)
The stability requirement of equation (4.11), which may be rewritten as,:
             ;  Pe>2

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Indoor Air Quality Model
Phase III Report
                                     PART I  - THEORY
       4. One Dimensional Convection-Diffusion  Flow
assures that the flow transport matrix will be an  M-matrix, which is to say it is a real
square matrix with positive diagonal elements and nonpositive off-diagonal elements

such that 11  u + ['] ] is strictly diagonally dominant for all scalars  > 0.

    It was shown earlier [Axley 1987] that element flow transport matrices satisfying this
condition (coupled with mass matrices that are positive diagonal matrices) lead to
system transport matrices that are not only nonsingular, but may be decomposed to
[L][U] form by a variant of Gauss elimination without the need for pivoting in an efficient
and numerically stable manner and will have stable homogeneous forms.
4.5  Comparison to Tanks-in-Series  Idealizations

   In the chemical engineering literature the so-called tanks-in-series idealization is
frequently employed to model the behavior of one dimensional convection-diffusion
transport processes or other processes whose inlet-outlet transformation characteristics
appear to match those described  by one dimensional convection-diffusion processes.
Below, in Figure 4-8, we compare a 5-element/6-node finite element idealization to a
corresponding 6-node tanks-in-series idealization where the the fluid mass of volume of
the flow path has been subdivided into four "unit" tanks containing one fifth of the total
fluid  mass each and two "half-unit"  tanks containing one tenth of the total fluid mass
each.
Node
                                 Conv-Diff Flow Element
     w
Simple Flow Element
"            l\v\A
                    Convection-Diffusion Element Idealization
                                                 w  f
                          Tanks-ln-Series Idealization
                                      wef
 Figure 4-8 Comparison of Tanks-in-Series Idealization with Finite Element Idealization

In the tanks-in-series idealization a portion of the flow, f, assumed to recirculate between
adjacent tanks is used to model the nature of turbulent and molecular diffusion.

   The subassemblage of this tanks-in-series  idealization consisting of half of two
adjacent "unit" tanks and the connecting simple flow elements, which we shall refer to
as a tanks-in-series element, may be compared directly to the convection-diffusion flow
element, as indicated in Figure 4-9, below:
                                     4-15

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Indoor Air Quality Model                                  PART I  - THEORY
Phase III  Report             4.  One Dimensional  Convection-Diffusion  Flow
               PAL
            Conv-Diff Flow ElemQnt
                               "Tanks-ln-Series" Element
 Figure 4-9 The Equivalence of the Convection-Diffusion Flow Element and a Tanks-in-
                                Series Element

Element equations for the tanks-in-series flow element may be assembled directly from
the simple flow element equations, equation (2.4a), producing:
        =  w
  1 0
  -1 0
+ fw
                                                      dcr
                                          pAL'hOl7  dt
                                                                        (4.20)
Comparing these equations with the convection-diffusion element equations, equations
(4.8), we see that they become equivalent when:
      e. e
    W L
Pee
                                                    (4.21)
and full upwinding, $ = 1.0, is used.
   It is interesting to note that the extreme of pure plug flow in the convection-diffusion
case corresponds to conditions having a dispersal coefficient equal to zero.  A fine
subdivision of the flow path into a large number of finite elements would be required to
provide a good approximation of the plug flow behavior.  In comparison, by equation
(4.21), plug flow would correspond to a tanks-in-series element with f = 0.0 - that is to
say an element without the recirculating backflow.  Nauman and Buffham [1983 pp. 58-
59] show that as the  number of tanks-in-series without backflow becomes large, the
behavior  of the assemblage of tanks approaches plug flow. The other extreme of well-
mixed conditions  may  be modeled with  an infinite dispersal coefficient in  the
convection-diffusion case. This corresponds to infinte recirculation in  the tank-in-series
element and we obtain the behavior of a simple well-mixed zone with either a  single
convection-diffusion element or a single tanks-in-series element.

The Imperfectly  Mixed "Zone  Element"  The  comparison  of  the convection-
diffusion  element and the tanks-in-series idealization, supports the conclusion drawn
above that, in general,  modeling high Peclet  number  flows will  demand a fine
subdivision of elements and modeling low Peclet number flows will not.  It also points out
                                    4-16

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Indoor  Air  Quality  Model                                  PART I  - THEORY
Phase III Report             4. One Dimensional  Convection-Diffusion  Flow
the fact that the convection-diffusion element may be used to model a zone that is not
perfectly  mixed.  In fact, although we developed the convection-diffusion element to
model  flow transport situations,  it should  now become apparent that this element
provides one means to model imperfectly mixed zones.  If the exit flow response of a flow
zone to a supply flow pulse takes the form of the solutions presented above, equations
(4.15)  to (4.17), then one may employ an assemblage of convection-diffusion flow
elements to model the global characteristics of that zone, even though the internal
mechanisms governing the imperfect mixing are not apparent.

    It may be shown that the variance of the nondimensional response, a2, is  related
directly to the Peclet number of the flow, for a "closed" system, as:
           Pe                                                           (4.22)

For  large  Peclet flows the form  of  the  (nondimensional) exit  response is  well
approximated by the form of a Gaussian distribution (e.g., see the results of Figure 4-7)
which has a variance of:

  2    2
aG = =
      Pe     ; for the Gaussian approximation equation (4.17)                 (4.23)

Either of these two expression provides a  means to determine an effective Peclet
number for a zone, from a rather straightforward statistical reduction of actual pulse
response measurements, that may, then, be used for modeling purposes.
   Chapter 2 presented the general formulation of a multi-zone contaminant dispersal
analysis theory,  based on element assembly techniques, and briefly presented the
element equations developed earlier: the simple flow element with and without filtration.
Chapter 3 outlined  a means to organize the multi-zone contaminant dispersal analysis
equations for the consideration of multiple  contaminants and introduced  a kinetics
element to account for chemical and physical interactions between contaminants and
the materials of the  building construction  and furnishings.  The present  chapter
introduced a fourth contaminant dispersal element, the one-dimensional convection
diffusion element that may be employed to either study the details of dispersal in one-
dimensional flow regimes (e.g.,  as found in  HVAC ducts)  or to simulate the general
behavior of certain imperfectly mixed zones.

   The program  CONTAM87 implements this theory.  Chapters 5 through 8 provide a
users manual to this program and Chapter 9 provides some examples of its use.
                                    4-17

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Indoor Air Quality Model
Phase III  Report
PART  II - CONTAM87 USERS  MANUAL
                 5.  General  Instructions
PART  II  -  CONTAM87 USERS  MANUAL
5.   General  Instructions

   The program CONTAM87 is a command processor; it responds to commands in the
order that they are presented and  processes data associated with each command.
Commands may be presented to the program interactively, using keyboard and monitor,
or through the use of command/data input files; that is to say, it offers two modes of
operation - interactive and batch modes.

   For most practical problems of contaminant dispersal analysis the  batch mode of
operation will be preferred.  For these problems, analysis involves three basic steps;
Step 1:
Idealization of the Building System and Excitation

                 Actual Building
      Zone Node      Flow Element-
      2 - Node Number   Element Flow-

          Air-Flow System Idealization
   Idealization of the building flow system involves a) discretization of the system as an
assemblage of appropriate flow elements connected at system nodes, b) identification
of boundary conditions, and c) numbering of system nodes optimally (i.e., to minimize
the bandwidth or, equivalently, node number difference of the system equations).

   The excitation (i.e., specified contaminant concentrations and generation rates) may
be modeled to be steady or defined in terms of arbitrary time histories. For the latter case
initial conditions of nodal contaminant concentration will have to also be specified.
                                    5-1

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 Indoor Air Quality Model
 Phase III  Report
PART  II - CONTAM87  USERS MANUAL
                 5. General  Instructions
Step 2:
Preparation of Command/Data Input File
                                             Edit
                 
    In the batch mode, the program reads ASCII text files of commands and associated
 data, collected together in distinct data groups, that define the building flow idealization
 and excitation. The command/data input file may be prepared with any available ASCII
 text editing program  and given a file name, ,  specified by the user. The
  must, however, consist of 8 or less alphanumeric characters  and can not
 include an extension (i.e., characters separated from the filename by a period,".").
 Step 3:
 Execution of CONTAM87
                    Plot Output File
                               .PLT
                                             Disk Storage Data File?
          Command/data
              Input File
                     
0010ft
01100
00011



0010^
01100
00011
       filename >.FEL  filename >.WDT
                                COIMTAM
                                  4-
        0010^1
        01100
        00011
0010'
01100
00011
       .RXN  filename >.EDT
                   Results Output File f^T^i
                               .OUT

    CONTAM87 is then executed. Initially CONTAM87 will be in the interactive mode.
 To enter the batch mode the command "SUBMIT F=" may be used to submit
 the command/data input file to the  program. The program will then  proceed to form
 element  and  system arrays and  compute the solution  to the  posed problem.
 CONTAM87 reads the  ASCII command/data input file  and creates an ASCII (i.e.,
 printable) output file .OUT. The results of an analysis, .OUT, may
 be conveniently reviewed using an ASCII editor and, from the editor,  portions or all of
 the results may be printed out.  Key response results are also written to the ASCII file
 .PLT in a format that may easily be transferred to spreadsheet and plotting
 programs (data values within each line are separated by the tab character and lines of
 data are separated by a carriage return) for plotting or subsequent processing.
                                      5-2

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Indoor Air Quality Model           PART  II -  CONTAM87  USERS  MANUAL
Phase III  Report                                     5. General  Instructions
   Depending upon the commands processed, CONTAM87 will also create a variety of
binary files for disk storage needed for subsequent processing. A summary of files read
and created includes;

   Files Read
       an ASCII input file specified by the user that contains commands and
                associated data

   Files Created
   .OUT  a printable ASCII output file that contains analysis results

   .PLT   an ASCII output file that contains key analysis results in a form
                    that may be transferred to spreadsheet and/or plotting programs

   .FEL   a binary file used for disk storage of flow element data

   .KIN   a binary file used for disk storage of kinetics element data

   .WDT  a binary file used for disk storage of element flow time
                    history data

   .EDT  a binary file used for disk storage of excitation time history
                    data

   In the interactive mode  is set to the default value of "CONTAM87" and
commands are read from the keyboard.  A help command, "HELP" or "H", will produce a
screen listing of intrinsic commands.
                                    5-3

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Indoor Air Quality Model           PART  II - CONTAM87  USERS MANUAL
Phase III Report                                 6.  Command Conventions
6.  Command Conventions

   Commands and their associated data (if any) may be single-line or multiple-line
command/data groups.

Single-Line Commands  Single line command/data groups begin with the command
keyword and may have any number of associated data items identified by data identifies
of the typical form;

   COMMAND  A=n1,n2,n3 B=n4  C=n5,n6  D=c1c2c3

where n1,n2,n3,... is numeric data and c1c2c3 is character data. In this example the
keyword COMMAND is the command keyword and the data identifiers are A=, B=,
C=, and D=.

Multiple-Line Commands  Multiple-line command/data groups are delimited by the
command keyword and the keyword END and may have any number of data subgroups
terminated by the less-than character "<" within. They have the typical form of;

   COMMAND  A=n1,n2
   n1  I=n2,n3,n4  B=n5  C=c1c2c3c4
   n1  I=n2,n3,n4  B=n5  C=c1c2c3c4
   n1  I=n2,n3,n4  B=n5  C=c1c2c3c4
   <
   n1,n2,n3  D=n4,n5,n6  E=n7  F=c1c2c3
   n1,n2,n3  D=n4,n5,n6  E=n7  F=c1c2c3
   n1,n2,n3  D=n4,n5,n6  E=n7  F=c1c2c3
   <
   Clc2c3c4c5c6
   END

Classes of  Commands  Two  general groups of  commands  are available, the
Intrinsic Commands and the CONTAM87 Commands. The intrinsic commands are
used to control the operation of the command processor CONTAM87 and to examine
arrays generated by the CONTAM87 commands. The CONTAM87 commands provide
contaminant dispersal analysis operations.

Command/data Lines  Normally the line length (i.e., the  number of character and
spaces on a line) is limited to 80.  A backslash "\" at the end of information on any line
will, however, allow the next line to be interpreted  as a continuation of the first line
providing an effective line length of 160.

   A less-than character "<" indicates the end of information on any line.  Information
entered to the right of the less-than character is ignored by the  program and  may,
therefore, be used to annotate a command/data input file.
                                   6-1

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Indoor  Air Quality Model           PART II -  CONTAM87 USERS MANUAL
Phase III Report                                   6.  Command Conventions


   An asterisk "*" at the beginning of any line will cause the line to be echoed as a
comment on the console and to the results output file.  Lines marked in this way may,
then, be used to annotate the results output file. Comment lines may also help indicate
the progress of computation when using the batch mode of operation.

Data Identifiers  Data identifiers and their associated data may be placed in any order
within each line of the command/data group (with the exception that the first line of a
command/data group must begin with the command keyword). In some instances data
may not be associated with a data identifier, such data must be placed first in a line.

Data  Decimal points are not required for real numeric data. Scientific notation of the
form nnE+nn or nn.nnE+nn (e.g., 5.79E-13) may be used. Simple arithmetic  expressions
employing the conventional  operators +, -,  *, and /  may be used.   The order of
evaluation is sequential from left to right -  unlike  FORTRAN or other  programing
languages where other "precedence"  rules are used.

   If fewer data values are supplied than required, the missing data will assumed to be
zero, blank, or set to default values as appropriate.
                                     6-2

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  Indoor Air Quality  Model
  Phase III  Report
PART  II -  CONTAM87 USERS MANUAL
                7. Introductory  Example
  7.  Introductory Example

     For purposes of contaminant dispersal analysis the specific command/data groups
  that need to be included in a command/data input file will depend upon the details of the
  flow system idealization, the nature of the excitation, and  the type of analysis to be
  computed.  A specific introductory example, should however, provide some useful
  insight into  the more general aspects  of  contaminant dispersal  analysis using
  CONTAM87

     Consider the two-story residence with basement shown, in section, below. In this
  residence interior air is circulated by a forced-air furnace and exterior air infiltrates the
  house through leaks around the two first-floor windows.  The flow system may be
  idealized using flow elements to model the ductwork, room-to-room, and infiltration flow
  paths as shown below.
  N02
Generation
  0.11
  g/hr
                         0.1 m3
                                                                           20 m3/hr
                                                      70 m3/hr
                                                Zone Node
                                              2  Node Number
                              70 m3/hr
                              Flow Element 
                              Element Flow _
              Actual Building
                                                      Air-Flow System Idealization
                     Figure 7-1 Hypothetical Residential Example
     For this building  idealization we shall  consider  the hypothetical problem of
  determining the steady state distribution of N02 generated by a kerosene heater placed
  in room "2", distributed by the furnace flow system operated at constant conditions, and
  diluted by infiltration at a constant rate. The N02 generation rate is assumed to be 0.11
  g/hr, exterior N02 concentration is  assumed to be negligible, and the  assumed air
  volumetric flow rates are indicated on the drawings above.  Inasmuch  as N02 is a
  reactive gas it will also  be assumed that  N02 is constantly transformed into other
  products that, here, are of no particular interest, as;

         N02  -> products
                                       7-1

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Indoor Air Quality Model           PART II -  CONTAM87 USERS MANUAL
Phase III Report                                    7. Introductory  Example
This reaction is often assumed to be governed by rate expressions of the form:
thus the matrix of rate coefficients for this case is a 1 x 1 matrix:
      [] = I


where    2K, the reaction rate constant for this reaction, will be assumed to have a value
of 0.40 hr- 1.  (These values of N02 generation and reaction rate are based on values
reported by Traynor [Traynor et. al. 1983] and Nitschke [Nitschke et. al. 1985].  The
generation rate is representative of that  produced by portable kerosene heaters.  The
reaction rate constant is thought to be representative of that to be expected indoors, but
the  kinetics of N02 chemical or physical-chemical behavior indoors is not yet well
understood.)

   The CONTAM87 command/data file to complete 'this steady state analysis is listed
below.  Command/data groups needed to complete  a time constant analysis and
dynamic  analysis for this building  idealization are presented  as  examples in the
reference section of this manual.
                                     7-2

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Indoor  Air  Quality Model
Phase III Report
 PART II - CONTAM87 USERS  MANUAL
                  7.  Introductory Example
Command/data File for Residential Example

   Note: CONTAM87 keywords and identifiers are displayed in boldface below.
Description
                       Column
Comments:
Comments
Comments
Comments
Comments
Comments
System Definition:
   No.Nodes &.Species, Species IDs
   Boundary Conditions

   Nodal Volumetric Mass
Flow Element Data:
   Element Number &  Connectivity
Kinetics Element Data:
   Rate  Coef. (Matrix): Rxn 1
   Kinetics Elem. Location & Type
Steady State Solution:
   Flow Element Mass Flow Rates
   Contaminant Excitation
Return to Interactive Mode
Command/data File
1

* Six-Zone (7-Node)  Example
*      Units:  g,  m, hr
*      Concentration  [=] g-N02/g-air
*      Generation  rate  [=] g-N02/hr
*
FLOWSYS
N=7  S=l  ID=N02
7  BC=C             < Ext."Zone"  Cone.Spec.
<                   (Air Dens.  1.2E+3 g/m3)
                      Node 1 Vol. Mass
                      Nodes 2  & 3 Vol. Mass
                      Nodes 4  & 5 Vol. Mass
                      Node 6 Vol. Mass
                      Node 7 Ext. Vol. Mass
                      Flow Element  1
                      Flow Element  2
                      Flow Element  3
                      Flow Element  4
                      Flow Element  5
                      Flow Element  6
                      Flow Element  7
                      Flow Element  8
                      Flow Element  9
                      Flow Element  10
                      Flow Element  11
1 V=1.2E+3*1.0
2,3 V=1.2E+3*40.0
4,5 V=1.2E+3*30.0
6 V=1.2E+3*0.1
7 V=1.2E+3*l.E+6
END
FLOWELEM
1
2
3
4
5
6
7
8
9
10
11
=1,2
=1,3
=7,2
=2,7
=7,3
=3,7
=2,4
=3,5
=4,6
=5,6
-6,1
END
KINELEM
K=l
0.4
<
<
<
<
<


<
<
<
<
<
<
<
<
<
<
<


<

1  1=1  K=l
6  1=6  GEN=1  K=l
END
STEADY
1,2   W=70*1.2E+3
3,6   W=20*1.2E+3
7,10  W=70*1.2E+3
11    W=140*1.2E+3

2  CG=0.11
7  CG=0.0
END
RETURN
                      Rxn  1:N02  -> products
< Node 1:  Rxn 1
< Nodes 2 to 6:   Rxn 1

<(Air Dens.l.2E+3 g/m3)
< Supply Ducts
< Infiltration
< Return Loop
< Main Return Duct

< Node 2: N02 Gen. Rate
< Node 7:Ext. N02 Cone.
   Details are given on the following pages for each CONTAM87 command.
                                     7-3

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Indoor Air  Quality Model           PART  II - CONTAM87 USERS  MANUAL
Phase  III Report                                  8.  Command  Reference
8.  Command Reference

   CONTAM87 provides two general classes of commands; Intrinsic Commands and
CONTAM Commands.
8.1  Intrinsic Commands

   The intrinsic commands are used to control the operation of the command processor
CONTAM87 and to examine arrays generated by the CONTAM87 commands.

   These intrinsic commands have been developed to  provide general  command
processor operations that, together with the general command conventions outlined
earlier, define a standard user-machine interface that may be used in the development
of other simulation software.
8.1.1  HELP

   The command  HELP, or simply H, will  produce  a  list of available intrinsic
commands, in abbreviated form.
8.1.2   ECHO

   The command ECHO-ON acts to cause computed results normally directed to the
results output file to be echoed to the screen.  The command ECHO-OFF turns this
feature off. At start-up CONTAM87 is set to ECHO-ON. Selective use of ECHO-ON
and ECHO-OFF can act to speed computation as writing results to  the screen
consumes a significant amount of time.
8.1.3  LIST

   The command LIST, or simply L,  will produce a list of all arrays currently in the
array database.
8.1.4  PRINT  A=

   The command PRINT  A= or simply P  A=  will print
array named , a one-to  four character name, to the  screen. Arrays
currently in memory are listed by name using the LIST command.
                                  8-1

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Indoor Air Quality Model           PART II -  CONTAM87 USERS MANUAL
Phase  III Report                                   8. Command  Reference
8.1.5  DIAGRAM A=

   The command DIAGRAM  A= or simply D A= will print
a diagram of array named , a one-to four character name, to the screen
indicating position of zero and nonzero terms. (Character arrays can not be diagramed.)
8.1.6  SUBMIT  F=

   The command SUBMIT  F= or simply S F= will cause the
program to switch to batch mode and read all subsequent commands from the batch file
.
8.1.7   PAUSE

   The command PAUSE  will cause the execution of CONTAM87 to pause until a
carriage return  is entered from the keyboard.  Selective use of PAUSE in a batch
command/data input file will allow the user time to view results of interim calculations.
(Note: PAUSE is a single line command and, therefore, cannot be placed within other
multiline command/data groups.)
8.1.8  RETURN

   The command RETURN returns the operation of the program from batch mode to
interactive mode. RETURN or QUIT will normally be the last command of batch
command/data input files.
8.1.9  QUIT

   The command QUIT or simply Q terminates execution of the program and returns the
user to the control of the operating system.
                                  8-2

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Indoor  Air Quality Model           PART II -  CONTAM87 USERS MANUAL
Phase III Report                                     8. Command  Reference
8.2   CONTAM87 Commands

   The  GONTAM87 Commands implement basic  contaminant dispersal analysis
operations. These operations are based upon the dimensionally homogeneous theory
presented in the first part of this report, thus, the analyst may use any dimensional units
that are convenient so long  as  a consistent set of units are employed.  Following the
underlying theory one may elect to express all quantities in terms of units of mass and
time;
   species concentration          [=] mass-species/mass-air
   species generation rate        [=] mass-species/time
   zone ("volumetric") mass       [=] mass-air
   air flow rates                  [=] mass-air/time
   kinetics rate constants         [=] 1/time
or, if consideration is limited to isothermal cases, one may  elect to use volumetric
quantities;
   species concentration          [=] volume-species/volume-air
   species generation rate        [=] volume-species/time
   zone volume                  [=] volume-air
   air flow rates                  [=] volume-air/time
   kinetics rate constants         [=] 1/time

   Using the  simple in-line arithmetic expressions allowed for numeric data, one may
easily convert from one quantity to another while maintaining a  record of the conversion
in the input command/data file for future reference. For example, the zone "volumetric"
mass (i.e., the mass of  the air within  the  volume of each zone) required by the
FLOWSYS command could be expressed in terms of zone dimensions and air density
as v=s .0*10.0*2.5*1.2  for a room that is 5 m x 10 m x 2.5 m containing  air with a
density of 1.2 kg/m3.

   The following conventions will be  used for the command definitions presented in this
section;

      ellipses,'...', indicate unlimited repetition of similar data items or data lines
      within a data subgroup

   -   square brackets, [...],  indicate optional data,

      numeric data is indicated by lower case n, as n1,n2,...,  and

   -   character data by  lower case  c, as c1.
8.2.1   FLOWSYS

   The number of the flow  system nodes and species, boundary conditions, and
volumetric masses of system nodes are defined with the following command/data group;
                                    8-3

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Indoor Air Quality  Model            PART II  - CONTAM87  USERS  MANUAL
Phase III Report                                      8.  Command  Reference
   FLOWSYS
   N=n1 S=n2 [ID=c1,c2, ...]
   n3,n4,n5 BC=c3,c4, ...
   n3,n4,n5  V=n6

   END

   where; n 1        = the number of flow nodes
          n2        = the number of contaminant species
          c1,c2, ...  = species ID's; a four character (or less) identification for each
                    species  used for labeling results; species  are identified  by
                    species-number and, optionally, by species ID given in species-
                    number order; omitted species IDs will be set to species-number
          n3,n4,n5  = first node, last node, node increment of a series of nodes with
                    identical boundary conditions
          c3,c4, ...  = boundary condition codes for each species by species number
                    order; a single character code of C for concentration prescribed
                    nodes or G , for generation prescribed nodes; (default = G),
          n6        = nodal volumetric mass; (default = 0.0)

   The direct species mass generation rate 01 the species concentration, but not both.
may be specified for each  species at each node to establish the  discrete boundary
conditions of the analysis problem being posed.

   Omitted boundary condition data will be assumed to be generation-prescribed.
Typically,  nodes associated with the outdoor environment will be assigned specific
contaminant concentrations and  nodes associated  with indoor  air zones will  be
assigned  specific  species  generation rates (a zero generation rate will  often  be
appropriate for the interior species/node combinations).

   Volumetric  mass data omitted will be assumed to be zero.  The  present version of
CONTAM  does not eliminate system variables associated with zero mass nodes.  For
time constant  analysis, and in some instances dynamic analysis, a zero nodal mass
value will result in numerical difficulties.  From a practical point of view, all nodes of a
flow system idealization will have some volume of  air associated with them, although
some may seem insignificantly small, and, therefore, to avoid numerical difficulties all of
these volumes  should be modeled with nonzero volumetric mass values.

   At the other extreme, some nodes, such as those corresponding to the outdoor
environment , may have practically infinite volumes  associated with them. The analyst
should realize practically accurate analysis results for these "infinite" nodes  if their
volumes are modeled  with  volumetric  masses several orders of magnitude larger than
that of the largest "non-infinite" node.
                                     8-4

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Indoor Air Quality Model           PART II - CONTAM87 USERS MANUAL
Phase III Report                                     8. Command Reference
8.2.2  FLOWELEM

   Presently  two types of flow  elements are available for  contaminant dispersal
analysis;

   -   a simple flow element that models fluid flow from one node to another ignoring
       the dynamic effects of diffusion and convection that result in species flow delay
       along  the flow path (i.e., flow of  a fluid  parcel in  simple flow elements is
       instantaneous) and,

   -   a convection-diffusion  flow  element that models fluid  flow from one node to
       another accounting for these  dynamic effects (presently  limited  to constant
       cross-section flow passage idealizations and lumped mass idealizations).

   To  use these elements effectively  and reliably the analyst  should be familiar with
their underlying theoretical basis and numerical  characteristics.   This is especially
important when using the convection-diffusion  element.  An inexperienced analyst is
well-advised to avoid the use of convection-diffusion elements altogether.

   Both simple flow elements and convection-diffusion flow elements may be added to
the flow system assemblage with a command/data group having unique formats of data
lines for each flow element type of the form;

   FLOWELEM
   n1  I=n2,n3  [GEN=n4]  [T=SIMP]  [E=n5,n6,...]

   or

   n1  I=n2,n3  [GEN=n4] T=CNDF  M=n7 L=n8 [D==n9,n10,...]  [F=n11]
   END

   where; n1       = the element number
          n2, n3    = the system node numbers to which the element is connected
          n4       = generation increment (default = 1)

          For Simple Flow Elements: [T=SIMP]
          n5,n6,...  = the element filter efficiency for each species being considered,
                   in species-number order, (must be > 0.0; default = 0.0),

          For Convection-Diffusion Elements: T=CNDF
          n7       = the fluid mass per unit length of the (equivalent) constant cross-
                   section element  (must be > 0.0; default = 0.0),
          n8       = the flow passage length (must be > 0.0;  default = 0.0),
          n9,n10,... = species dispersal coefficient for  each species considered, in
                                     8-5

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Indoor Air Quality Model           PART II -  CONTAM87  USERS MANUAL
Phase III Report                                     8.  Command  Reference
                   species-number order, (must be > 0.0; default = 0.0)
          n11      = upwind factor, ; where 0 <  < 1;  (default = the lower bound of
                   the stability criteria , equation (4.11))

   For assemblages consisting of only Simple flow elements the command/data group
would  consist of data  lines  of  the form  with the  type  identifier  T=SIMP.  For
assemblages consisting of only Convection-Diffusion  flow elements the command/data
group would consist of data lines of the form with the type identifier T=CNDF.  For
mixed assemblages the appropriate  mix of the two forms of data  lines would be used;
there are no special restrictions on the use of mixed assemblages.

   If the element type identifier is omitted the element will  be assumed to be of type
SIMP.

   Normally, the analyst should accept the  default upwind factor for the Convection -
Diffusion element. This default will ensure that numerical solutions to the posed problem
may be determined in an efficient and stable  manner.  (The option  to specify the upwind
parameter is provided to  allow  one to study the numerical characteristics of the
upwinding strategy rather than the practical behavior of flow systems.)

   Element data must be supplied  in numerical order.  Omitted  data is automatically
generated by incrementing the  preceding node numbers  by the current generation
increment. Generated elements will have  the properties of the current element.  If, for
example, an HVAC duct, included as part of a air flow system, was to modeled by a
series of, say, ten convection diffusion elements, as illustrated below in Figure 8-1, then
one could conveniently use the generation option  to  "generate"  the  intermediate
elements by specifying only the first and last Convection-Diffusion flow element in the
series. The portion of the input command/data file needed to implement this example  is
listed below.

   FLOWELEM

   21  1=12,15   T=CNDP  M=1.2E+03  L=l. 0
   30  1=39,42   T=CNDF  M=1.2E+03  L=1.0  GEN=3
   END
              Node Number
         12    15^  18    21
24    27   30    33    36    39    42
         f 21V f 22   23 + 24   25   26  f 27   28  + 29  f 30

           Element Number

         Figure 8-1  Hypothetical Conduction-Diffusion  Element Subassemblv
   The command FLOWELEM  may be invoked more than once to incrementally add
flow elements to the assemblage. Using this feature an analyst may consider a series of
successively more complex flow system assemblages and their response to specified
                                     8-6

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Indoor Air Quality Model            PART II  - CONTAM87 USERS MANUAL
Phase III Report                                     8. Command Reference
excitations.
8.2.3 KINELEM

   Interactive species behavior governed by first order kinetics may be accounted for
in  the model through the  assembly of kinetics elements.  A kinetics element will,
typically, model chemical, radio-chemical, or sorption kinetics between a contaminant
species  and the immediate environment or other species within a well-mixed zone.  As
such they may be associated only with those system nodes that correspond to well-
mixed zones.  These elements may be added to  the assembly with the  following
command/data group that first defines pertinent rate coefficient matrices and then
assigns  specific rate coefficient matrices to specific nodes of the system;

   KINELEM
   K=n1
   n2, n3, ...
   n4, n5, ...

   K=n1
   n2, n3, ...
   n4, n5, ...
   n6  I=n7  K= n8  [GEN=n9]
      
   END

   where; n1       = the kinetics ID of the following rate coefficient matrix,
          n2, n3, ...
          n4, n5, ..  = the rate coefficient matrix for kinetics ID n1

          n6       = the kinetics element number
          n7       = the well-mixed zone system node number at which the kinetics is
                   to be applied,
          n8       = kinetics  ID
          n9       = generation increment (default = 1),

   The  rate coefficient matrices are entered by  rows,  in species-number order, and
must be defined in terms of all species considered whether or not all of the species are
involved in a given rate expression.  Therefore, for a system involving N species all rate
coefficient matrices will be square matrices with N x N terms. If a particular species is
not  involved in  a  given rate  expression the  terms in  the columns and  rows
corresponding to this species will simply be zero values.

   Element data  must be supplied in numerical  order. Omitted data is automatically
generated by incrementing the preceding node  number by the current generation
                                     8-7

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Indoor  Air  Quality Model
Phase III Report
                         PART II - CONTAM87 USERS  MANUAL
                                          8. Command  Reference
increment.  Generated elements will have the properties of the current element.

Example

   Given a system involving three species, say, A, B, and C involved in the following
chemical reactions;

   1) a simple reversible reaction

       A <-> B

   governed by the rate expression;

       d[A]
        dt
       d[B]
        dt
       d[C]
        dt
= -0.45[A] + 0.45[B]  + 0.0[C]


= 0.45[B] - 0.45[A] + 0.0[C]


= 0.0[A] + 0.0[B] + 0.0[C]
    or, more concisely by the first order rate coefficient matrix;
              0.45-0.45  0
              -0.45 0.45   0
                000
   and,
   2) a single-step reaction

       B - products (that are of no particular interest)

   governed by the rate expression;

       d[A]
        dt
       d[B]
        dt
       d[C]
        dt
= 0.0[A]  + 0.0[B] + 0.0[C]


= 0.0[A]  - 0.35[B] +  0.0[C]


= 0.0[A]  + 0.0[B] + 0.0[C]
   or, more concisely by the first order rate coefficient matrix;
                                      8-8

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Indoor Air Quality Model
Phase III  Report
PART II  - CONTAM87 USERS MANUAL
                8. Command Reference
               000
               0  0.35  0
               000
where the first reaction occurs at system nodes 3,5,7,9 while the second reaction only
occurs at nodes 5 and 7 (e.g., due to the action of a specific catalyst at these nodes)
kinetics  elements could be added to the  contaminant dispersal system using  the
following command/data group;
KINELEM
K=l
0
-0
0
K=
0
0
0
1
4
5
6
.45 -0.
.45
 Q
2
.0
.0
.0









1=3
1=9
1=5
1=7
0.
0.

0.
0.
0.




45 0.0
45 0.0
0 0.0

0 0.
35 0.
0 0.
K=l
K=l
K=2
K=2




0
0
0

G


END
                         < Kinetics  ID 1:   A <=> 3
                         < Kinetics  ID 2:  B => products
                         < Kin Elem 1:  Node 3:   Kinetics ID 1:
                         < Kin Elems 2,3, & 4:  Nodes 5,7,& 9:  Kinetics ID 1:
                         < Kin Elem 5:  Node 5:   Kinetics ID 2:
                         < Kin Elem 6:  Node 7:   Kinetics ID 2:
   The rate expressions, above, have been written in terms of all contaminant species,
including the  nonreactive species  C,  to  emphasize the  manner  in which  rate
expressions are defined through the use of rate coefficient matrices.
8.2.4  FORM-[W]

   In some instances an analyst may wish to examine the details of the mass transport
matrix, [W].  The command FORM-[W] answers this special (and unusual) need.  This
command  is not required as an interim step to complete any of the analyses options
offered by  subsequently defined commands.

   The system mass transport matrix, [W], assembled from flow element and reaction
element matrices may be formed with the following command/data group;

   FORM-[W] [F=c1c2c3c4]
   n1,n2,n3  W=n4

   END

   where;  c1c2c3c4 = FULL or BAND; (default = FULL)
          n1,n2,n3  = first element number, last element number, element number
                   increment of a series of elements with identical mass flow rates
          n4       = element total mass flow rate
                                    8-9

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Indoor Air Quality  Model           PART II  - CONTAM87  USERS  MANUAL
Phase III Report                                    8.  Command Reference
   The matrix may be formed in its full form or compacted form (i.e., only the nonzero
band of the [W] matrix). The system mass transport matrix may be printed or diagrammed
using the intrinsic commands PRINT and DIAGRAM.
8.2.5   STEADY

   The response of the system to steady contaminant generation with steady element
mass flow may be computed with the following command/data group;

   STEADY
   n1,n2,n3 W=n4
   n5,n6,n7  CG=n8,n9,...

   END

   where; n1 ,n2,n3 = first element number, last element number, element number
                  increment of a series of elements with identical mass flow rates
         n4      = element total mass flow rate
         n5,n6,n7 = first node, last node, node increment of a series of nodes with
                  identical  excitation
         n8,n9,...  = contaminant concentration or contaminant generation  rate  for
                  each species considered,  as appropriate  to  the  boundary
                  condition of the  node/species combination specified with the
                  FLOWSYS command; (default = 0.0)

   Net total mass flow rate at each system node will be reported, but computation will
not be aborted if net mass flow is nonzero. The analyst must assume the responsibility to
check continuity of mass flow from these reported values.
8.2.6   TIMECONS

   System time constants, nominal and actual, may be computed with the following
command/data group;

   TIMECONS  [E=n1]
   n2,n3,n4  W=n5

   END

   where; n1       = optional convergence parameter, epsilon ; (default = machine
                  precision)
         n2,n3,n4 = first element number, last element number, element number
                                  8-10

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Indoor  Air  Quality Model            PART II - CONTAM87 USERS MANUAL
Phase III Report                                     8. Command Reference
                   increment of a series of elements with identical mass flow rates
          n5       = element total mass flow rate

   The nominal time constants are computed for each node as the quotient of the nodal
volumetric mass divided by the total air flow out of a zone.  The actual time constants
are computed using an eigenanalysis  routine that is  a variant of Jacob! iteration
adapted for nonsymmetric matrices [Eberlein et. al. 1971].  It should be noted that the
actual time constants are likely to be very different from the nominal time constants for
systems having well-coupled zones and the eigenanalysis of the flow system matrices is
a time consuming task.
Example


   To determine the time constants associated with the building idealization presented
earlier, in the introductory example, the following command/data group would have to
be added to the command/data file.

   TIMECONS              <  (Air Density 1.2E+3 g/m3)
   1,2   W=70*1.2E+3       <   Supply Ducts
   3,6   W=20*1.2E+3       <   Infiltration
   7,10  W=70*1.2E+3       <  Return Loop
   11    W=140*1.2E+3      <  Main Return Duct
   END
8.2.7   Dynamic  Analysis

   The response  of the system, including transients,  to general dynamic excitation,
may be computed using the command DYNAMIC.  The dynamic solution procedure
used is driven by  discrete time histories of excitation and element mass flow rate data
that must first be generated with the commands FLOWDAT and EXCITDAT.
8.2.7.1   FLOWDAT

   Discrete time histories of element mass flow  rate may be defined, in step-wise
manner, from given element mass flow data, as illustrated below;

      Data
      Value
                                                        '   Given Data Value
                                                            Time
             TIME(I)              TlhE(2)   TlhE(3)      TIME(4)

                  Figure 8-1 Arbitrarily Defined Time  History Data



                                    8-11

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Indoor Air Quality Model
Phase III  Report
              PART II  - CONTAM87 USERS  MANUAL
                              8. Command Reference
or, alternatively, discrete time histories of element mass flow data, defined in a step-wise
manner at equal time-step  intervals along  piece-wise  linear segments,  may  be
generated from given element mass flow data over a time range defined by an initial
time, TJ, a final time, Tf, and a generation time increment, AT, as illustrated below;
      Data
      Value
                                   Given Data Value

                                    Generated Value
                          AT
                                                            Time
             TIME(1)
           TIME(2)  TIME(3)
TIME(4)
             Figure 8-2 Eaual-Time-Steo-Generated Time History Data
using the following command/data group;

   FLOWDAT  [T=n1,n2,n3]
   TIME=n4
   n5,n6,n7 W=n8
   TIME=n4
   n5,n6,n7 W=n8
[additional TIME data to define the complete excitation time history]
   END

   where; n1 ,n2,n3 = initial time, final time, time step increment used for the generation
                   option
          n4       = time value for subsequent data subgroups
          n5,n6,n7 = first element number, last element number, element number
                   increment of a series of elements with identical mass flow data
          n8       = prescribed element mass flow: (default = 0.0)

   If data values n1,n2,n3 are specified, step-wise time histories will be generated from
the given data, along piece-wise linear  segments as illustrated in Fig. 7.2 above,
otherwise the given data will be used directly,  as illustrated in Fig. 7.1  above.

   At least  two "TIME" data subgroups  must be provided.  FLOWDAT writes the
generated time history to the file .WDT so that this data may subsequently be
accessed by the command DYNAMIC.
                                    8-12

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Indoor Air Quality Model            PART II -  CONTAM87 USERS MANUAL
Phase III  Report                                    8.  Command Reference
8.2.7.2   EXCITDAT

   Discrete time histories of excitation data may be defined in the two ways discussed
above for the FLOWDAT command using the following command/data group;

   EXCITDAT  [T=n1,n2,n3]
   TIME=n4
   n5,n6,n7 CG=n8,n9,...
   TIME=n4           [additional TIME data to define the complete excitation time history]
   n5,n6,n7  CG=n8,n9,...
   END

   where; n1,n2,n3  = initial time, final time, time step increment used for generation
                   option
          n4       = time value for subsequent data subgroups
          n5,n6,n7  = first node, last node,  node  number increment of a series of
                   nodes with identical excitation data
          n8,n9,...   =  prescribed   contaminant  concentration  o_r  prescribed
                   contaminant generation  rate (as appropriate to node boundary
                   condition) for each species considered: (default = 0.0)

   If data values n1 ,n2,n3 are specified, step-wise time histories will be generated, from
the given  data, along piece-wise linear segments as illustrated  in Fig. 7.2 above,
otherwise the given data will be used directly, as illustrated in Fig. 7.1 above.

   At least two "TIME" data subgroups must be provided.  EXCITDAT writes the
generated time history  to the  file .EDT so that it may subsequently be
accessed by the command  DYNAMIC.
8.2.7.3  DYNAMIC

   The response of the system to excitation defined by the EXCITDAT  command,
using the prescribed element flow data defined by the FLOWDAT command, may be
computed using the following command/data group;

   DYNAMIC
   T=n1,n2,n3 [A=n4] [Rl=n5] [PS=n6]
   n7,n8,n9  IC=n10,n11,...

   END
                                   8-13

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Indoor  Air  Quality Model
Phase III Report
PART  II -  CONTAM87 USERS  MANUAL
                 8. Command  Reference
   where; n1,n2,n3  = initial time, final time, time step increment
          n4        = integration parameter,  a, where 0.PLT, of concentration response results will be created
                    with values scaled by the factor n6
          n7,n8,n9  = first node, last node, node increment of a series of nodes with
                    identical data
          n10,n11,...= initial nodal concentration for each species in species order;
                    (default = 0.0)

   The response is computed using the. predictor-corrector method presented earlier
[Axley 1987]. With this method the system flow matrix is updated at the discrete times
used to define element flow rate time histories and the system excitation is updated at the
discrete times used to define excitation time histories, as illustrated below;
Row
Pteta
Vail 10



















I

,


<


Gene
c\ r\
rl_U


                                         '  Flow Time Step
                                                                 Time
Excitation
Data
Value

4



'


	 1



...








: Generated by
> : EXCITDAT


                                     Excitation Time Step
     Response
      Value
                       Computed by
                       DYNAMIC
                                                                "Time
                               Integration Time Step
          Figure 8-3 Flow and Excitation Driven Dynamic Solution Procedure

   The accuracy of the computed response is, therefore, dependent upon the choice of
the flow  data  time  step, the  excitation data time step, and the integration time step
chosen by the  analyst. Furthermore, the flow data and excitation data time steps may be
nonconstant.  The analyst should, therefore, consider investigating the effects of the
choice of these time constants to gain a sense of the error they induce.
                                     8-14

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Indoor  Air  Quality  Model
Phase III Report
           PART  II  - CONTAM87  USERS  MANUAL
                            8.  Command Reference
8.2.7.4   Dynamic  Analysis Example

   To provide an example of a command/data sequence needed for dynamic analysis
we  may  consider an  extension to the introductory example presented earlier; the
analysis  of the  dynamic response of the given building system,  under conditions  of
constant  air flows, to a step change in NC>2 generation.  Specifically, to consider the
case where the  kerosene heater is turned on and then turned off 133 minutes later, the
following  command/data group would have to be added to the command/data file used
in the introductory example;
   FLOWDAT
   TIME=0.0
   1,2   W=-70*1.2E+3
   3,6   W=20*1.2E+3
   7,10  W=70*1.2E+3
   11    W=140*1.2E+3

-------
Indoor  Air Quality Model
Phase III  Report
PART  II  - CONTAM87 USERS MANUAL
               9. Example  Applications
 9.  Example  Applications

   Examples of the application  of CONTAM87 to practical  problems of building
contaminant dispersal are presented  in this  section.   The reader will also  find a
discussion of the use of the convection-diffusion flow element for both steady state and
dynamic analysis of  contaminant dispersal in one-dimerisional flow paths presented in
section 4.3.
9.1 IBR Test  House  Study

   While working at the National Swedish Institute for Building Research (IBR) Kai Siren
developed a program for multi-zone contaminant dispersal analysis,  MULTIC,  and
applied it to the analysis of the dynamic behavior of the five-room test house maintained
by the IBR [Siren  1986], Figure 9-1.   Using data reported by Sir6n the building
idealization shown below, Figure 9-2,  was  formulated and  the  (dynamic)  decay
response of the idealization to an initial  concentration in the bed room, node 2,  was
computed (for steady flow conditions) and  compared to the results reported by Sir6n.  Air
flow rates, zonal volumes, and initial conditions  are reported below, Figure 9-2.
                    Figure 9-1 The IBR Five-Room Test House
                                    9-1

-------
Indoor Air Quality Model
Phase III  Report
                  PART  II -  CONTAM87  USERS  MANUAL
                                  9.  Example Applications
              13.28
                                         "exterior zone"
                                                                 9.45
    V = 55.6
    C(0) = 350
                             35.67
                             22.39
     V = 13.0
     C(0) = 350
                   V = 36.2
                   C(0) = 35C
                                               9.45
                                      V . 36.1
                                      C(0) = 2500
                                               42.89^
                                               27.40
                                                      V = 34.8
                                                      C(0) = 350
     0.33
7.80
                                   0.23
                                                          1.21
                                                      16.70
                     Figure 9-2 Idealization of IBR Test House
            (all flows [=] l/s; volumes [=] m3; initial concentrations [=] ppm)

CONTAM87 Command/Data File  The CONTAM87 command/data file  used to
complete the analysis is listed below.
* IBR5ZONE
*
*
*
FLOWSYS
N=6  S=l  ID=C02
6   BC=C
                Swedish IBR Test House:  5 Zone  Model
                Units  m, hr
                Analysis by volume rather than  mass  (i.e.
                contaminant density set  to unity).
                                       air and
1
2
3
4
5
6
END
V=55
V=36
V=36
V=34
V=13
V=l.

.
.
f
.
B
6
1
2
8
0
OE+06


<
<
<
<
<
<

Node
Node
Node-
Node
Node
Node

1
2
3
4
5
6

FLOWELEM
1
2
3
1=6,
1=6,
1=1,
1
2
3












                   <"Ext. Zone" Cone.  Specified
                   < Air density set to unity.
                             Vol.  Mass
                             Vol.  Mass
                             Vol.  Mass
                             Vol.  Mass
                             Vol.  Mass
                             Exterior  Vol. Mass
                                     9-2

-------
Indoor Air Quality  Model            PART  II  - CONTAM87  USERS MANUAL
Phase III  Report                                     9.  Example Applications
4
5
6
7
8
9
10
11
12
13
14
END
*
1=3,1
1=2,3
1=3,5
1=5,3
1=3,4
1=4,3
1=6,5
1=5,6
1=6,3
1-6,4
1=4,6


   *  STEADY STATE ANALYSIS: C02 generation assumed constant at 80 I/sec.
   *
   STEADY          < Flow rates - m3/sec  x 3600 sec/hr
   1   W=13.28E-03*3600
   2   W=9.45E-03*3600
   3   W=35.67E-03*3600
   4   W=22.39E-03*3600
   5   W=9.45E-03*3600
   6   W=19.52E-03*3600
   7   W=12.05E-03*3600
   8   W=42.89E-03*3600
   9   W=27.40E-03*3600
   10  W=0.33E-03*3600
   11  W=7.80E-03*3600
   12  W=0.23E-03*3600
   13  W=1.21E-03*3600
   14  W=16.70E-03*3600
   <               < Generation Rates  & Specified Concentration
   4   CG=80E-03    < Steady Generation [=]  m3-C02/hr
   6   CG=350E-06   < Exterior Concentration [=] m3-CO2/m3-air
   END
   *
   *  DYNAMIC ANALYSIS: Flow steady, C02 generation 80  I/sec for 1.0 hr.
   *
   FLOWDAT
   TIME=0.0
   1   W=13.28E-03*3600
   2   W=9.45E-03*3600
   3   W=35.67E-03*3600
   4   W=22.39E-03*3600
   5   W=9.45E-03*3600
   6   W=19.52E-03*3600
   7   W=12.05E-03*3600
   8   W=42.89E-03*3600
   9   W=27.40E-03*3600
   10  W=0.33E-03*3600
   11  W=7.80E-03*3600
   12  W=0.23E-03*3600
   13  W=1.21E-03*3600
   14  W=16.70E-03*3600
   <
   TIME=10.1
   1   W=13.28E-03*3600
   2   W=9.45E-03*3600
   3   W=35.67E-03*3600
   4   W=22.39E-03*3600
   5   W=9.45E-03*3600
   6   W=19.52E-03*3600
   7   W=12.05E-03*3600
   8   W=42.89E-03*3600
   9   W=27.40E-03*3600
                                     9-3

-------
Indoor Air Quality Model
Phase III  Report
                                 PART  II - CONTAM87  USERS  MANUAL
                                                 9.  Example Applications
       W=0.33E-03*3600
       W=7.80E-03*3600
       W=0.23E-03*3600
       W=1.21E-03*3600
       W=16.70E-03*3600
10
11
12
13
14
END
EXCITDAT
TIME=0.0
4   CG=80E-03
6   CG-350E-06

TIME=1.0
4   CG=0.0
6   CG=350E-06

TIME=10.1
4   CG=0.0
6   CG-350E-06
END
DYNAMIC
T=0,10,0.1 PS=1.0E+6
1     IC-350E-06
2     IC=2500E-06
3,6,1 IC=350E-06
END
RETURN
                      < Steady Generation [=] m3-C02/hr
                      < Exterior Concentration  [-] m3-C02/m3-air
                      < Steady Generation [=] m3-CO2/hr
                      < Exterior Concentration  [=] m3-C02/m3-air
                      < Steady Generation  [=] m3-C02/hr
                      < Exterior Concentration  [=] m3-C02/m3-air
Results  The results obtained using CONTAM87 are compared to those using Siren's
program MULTIC below, Figure 9-3.  These results are practically identical, as they
should be, as this study provides, in effect, a comparison of two numerical solutions of
the identical system of equations.  Nevertheless, the  results do  indicate that both
programs have numerical procedures that have been correctly coded.
         2500 0
         2000
  Cone.
  (ppm)
         1500
         1000
          500
                                                                 Node 1

                                                               O  Node 2

                                                                 Node 3
                                                               D  Node 4
                                                               A  Node 5
              012345678910
                                   Time (hr)

   Figure 9-3 Comparison of MULTIC Results (markers) to CONTAM87 Results (lines)
                                     9-4

-------
Indoor Air Quality Model
Phase III  Report
PART  II  - CONTAM87 USERS  MANUAL
               9. Example Applications
9.2 Carnegie-Mellon  Townhouse Study

   Borrazzo and  his  colleagues  at Carnegie-Mellon  University,  Pittsburg,
Pennsylvania, have  conducted detailed field investigations  of a two-story townhouse
measuring CO, NO, and N02 emissions characteristics of the gas appliances within the
townhouse and the dispersal of these contaminants throughout the townhouse under a
variety of different weather conditions [Borazzo et. al.  1987].  Illustrated in Figure 9-4 is
an idealization of the townhouse and the measured dynamic  emission characteristics of
the principal pollutant source, the gas range.  The instantaneous emission rate, G(t), is
plotted relative to the steady state value, Gss.  The N02 emission characteristics were
more or less constant and are, therefore, not illustrated. N02 is a  reactive contaminant
and was modeled as so using the measured reactivity of K=2.4 hr1-
O.U]
G(t)/G
2.0
1.0
0.0(
SS~





^^













^^H





^MM














(
\




2<




>




) 0.5 Time(hr) 1-
          Building Idealization
G(t)/C
1.0
0.5
0.0(
Son

^^^



(55!



	 1
VHHWt


























^<




>




) 0.5 Time(hr) 1.
Emission Characterics
   Figure 9-4 Townhouse Building Idealization and Range Emission Characteristics


CONTAM87 Command/Data File   The CONTAM87 command/data  file used  to
complete the analysis for the N02 response is listed below.
   * Borrazzo et al's. Townhouse 4-Node,  3-Zone Example
   *   Units: g, hr,  m
   *

   FLOWSYS
   N=4 S=l ID=N02
   4 BC=C                       < Node 4 is exterior node
                                    9-5

-------
Indoor Air Quality  Model
Phase III Report
                                  PART  II - CONTAM87  USERS MANUAL
                                                  9.  Example Applications
1,3V=126.5*1.2E+03
4  V=126.5E+09*1.2E+03
END
FLOWELEM
1 1=1,2
2 1=2,1
3 1=2,3
4 1=3,2
5 1=4,2
6 1=2,4
7 1=4,3
8 1=3,4
9 1=4,1
10 1=1,4
END
FLOWDAT
TIME-10.0
1,2,1  W=0.4*126.5*1.2E+03
3,4    W=7.5*126.5*1.2E+3
5,8    W-0.21*126.5*1.2E+03
9,10   W=0.21*126.5*1.2E+03
   TIME=20.0
1,2,1
3,4
5,8
9,10
END
KINELEM
K=l
2.4
          W-0,
          W=7,
4*126.5*1.2E+03
5*126.5*1.2E+3
          W=0.21*126.5*1.2E+03
          W=0.21*126.5*1.2E+03
                                < Air Density = 1.2E+03 g/m3
                                < Exterior Zone Set At Large Value
                   < ACH  bsmnt-to-first
                   < ACH  first-to-second
                   < 0.21 ACH ext-to-first &
                   < ACH  ext-to-bsmnt
                                                           second
< ACH bsmnt-to-first
< ACH first-to-second
< 0.21  ACH ext-to-first & second
< ACH ext-to-bsmnt
                                < Rxn 1: N02 => products
                                < Kinelem 1: Node 1:  Rxn 1
                                < Kinelem 2: Node 2:  Rxn 1
                                < Kinelem 2: Node 2: Rxn 1
1 1=1 K=l
2 1=2 K=l
3 1=3 K=l
END
*  Transient N02 Emission  Model  (basis :Gss = 12 (J.g/kJ
EXCITDAT
TIME=10.0
2  CG=0.0068                 
-------
Indoor Air Quality Model
Phase III Report
                                 PART  II -  CONTAM87  USERS MANUAL
                                                 9.  Example Applications
   4
   END
   RETURN
     IC=0.0206E-06
<0.013 ppm *  (46/28.98)
   The CONTAM87 command  /data files for the CO and NO analysis would  be
identical to the file listed above with the species IDs changed from N02 to CO and NO,
respectively,  the  KINELEM command removed,  and the  EXCITDAT and  DYNAM
commands replaced with those listed below. Note that in  both cases a constant pilot
light generation contribution plus a dynamically varying burner generation contribution
is accounted for.
   For CO:
   *  Transient CO Emission Model (basis:Gss  =  98 |J.g/kJ ; Igas  150  kJ/min)
   EXCITDAT
   TIME=10.0
   2  CG-0.0415                 0.0415
4  CG=0.389E-06
END
DYNAMIC
T=10, 16. 0,0.1  RI=1
     IC=0.389E-06
     IC=0.389E-06
     IC=0.389E-06
                             
-------
Indoor  Air  Quality  Model
Phase III Report
                                  PART  II -  CONTAM87 USERS MANUAL
                                                  9. Example  Applications
   For NO:
*  Transient NO Emission Model  (basis:Gss
EXCITDAT
TIME=10.0
2  CG-0.0038                 
-------
Indoor  Air  Quality Model
Phase III Report
                  PART II - CONTAM87 USERS  MANUAL
                                  9. Example Applications
exchange rate was assumed to be 0.4 ACH, and all flows were assumed to be constant.

   As may be seen, the CO response was under-predicted and the NO response was
over-predicted,  but both  are  within the  reported  uncertainty  of  the emission
characteristics (CO:  18% & NO: 6.5%).
 [CO]
 (ppm)
        10
                 Upstairs

                 Bsmnl
         O Lvng Rm

         '~ Model Bsmnt
               Kitch        n  Outside

               Model 1st Fir   Model 2nd Fir
11
12
   13
Time (hour)
       0.55
                                  Q-a--n-n-no-n-o-n-a -a-rja-n-a~n-a-a-n-
                                           13
                                       Time (hour)

        Figure 9-5 Comparison of Computed and Measured CO & NO Response

   Although, the measured  N02 data is quite suspect, because of its scatter  and
negative values,  there appears to be some agreement between this  data  and the
computed response.  Importantly,  it is  noted that the NO2 concentration can fall below
ambient levels out-of-doors due to the reactivity of this contaminant.
data, reporting an interzonal exchange  rate of 1.35 ACH.  Their method was considered to be very
poorly conditioned, thus, their results unreliable, and, therefore, the  interzonal air change rate was
assumed based upon the computed behavior of the townhouse arid past experience.
                                     9-9

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Indoor  Air Quality Model
Phase III Report
     PART II  - CONTAM87 USERS  MANUAL
                    9. Example Applications
   Inasmuch as the measured data was used to determine the reactivity constant the
agreement here may be an artifice. The basis of determination of the reactivity and the
basis of the computed response are more or less the same  as the system behaves,
practically, as a single zone system, therefore the agreement may reflect no more than
this.
 [NO2]
 (ppm)
                     11
12
   13
Time (hour)
14
15
16
          Figure 9-6 Comparison of Computed and Measured NOo Response
          ^"^**^^""^"^^~   - - *             ,__-_-._- , -, -,._-,j-r-n^ ._-_n_  - ^^.^__M*B*_i^H_
                           (NOa Reactivity = 2.4 hr -1)


9.3 NBS Office Building Study

    Infiltration and ventilation studies of a fifteen story office building are presently being
conducted by members of the Indoor Air Quality and Ventilation Group at NBS. Some of
these studies involve periodic injections of a commonly used tracer gas, SF6, into the
fresh  air supply ports  of the  building HVAC system.  Flows in the supply ducts were
measured  (with  significant  uncertainty) by  hot-wire  anemometer traverse,  SF6
concentration time histories were recorded, and  outdoor air  change rates were
estimated by tracer decay.  Using the air flow measurements the upper two floors of this
building were idealized as shown in Figure 9-7.

    As indicated by this  idealization, fresh  air was  supplied to each  floor  through a
ceiling plenum space and exhausted via an  exhaust duct to the outside.  In  Figure 9-8
we compare measured SF6 concentration time histories (measured centrally within the
"space" and at the "exhaust"  ports) to computed values of the 15th floor for two supply
flow rates: 100% and 75% of the measured flow.  In this case, the agreement between
measured and computed time histories is within the uncertainty of the measured flows
and validation is therefore indicated.
                                    9-10

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Indoor Air Quality Model
Phase III Report
              PART  II - CONTAM87 USERS MANUAL
                             9. Example  Applications
































8
rs|







E
7
*
_
3
3
? J
x L
II
T






4j





7
4d
4-




_ .  . 100% Supply
Exterior "Zone" f1 g^
(1.68 A
15th Ceiling Plenum 3 I
03 4550 c

15th Floor 9 4

 J M .
I...J I...I
0.20 ACH
14th Ceiling Plenum  5 f
06 4550 Cfi


14th Floor  6
..... .....
 y y -
0.20 ACH


Flow
fm
OH,

fm




5

Tl






Ra
M
L
2

o
Q
;
CO








te
































       Figure 9-7 Idealization of the 14th and 15th Floors of an Office Building
1000
                                                    15th "Space"-12/1/86
                                                    15th "Exhaust"- 12/1/86
                                                  Model 3 Node 4- 10095
                                                  Model 3 Node 4 - 75S5
             100
200
600
700
                           300      400     500
                                 Time (min)
Hours 9-8 Comparison of Computed and Measured Response for an Office Building
800
                                   9-11

-------
Indoor Air Quality Model
Phase III  Report                10. Summary and Directions of  Future Work
10. Summary and Directions of Future Work

   In  the first section of this report we have attempted to give clearer definition to the
emerging field of indoor air quality analysis. It has been argued that the central problem
of indoor air quality analysis is contaminant dispersal analysis and that the related
problems of inverse contaminant  dispersal analysis, flow analysis, and  thermal
analysis may be  thought to serve the needs of  contaminant dispersal analysis.
Furthermore, we have suggested that the central problem and these related problems
may be addressed  with an integrated set of computational tools based on an element
assembly formulation of the familiar well-mixed zone simplification of the macroscopic
equations of  motion for multi-zone building systems of  arbitrary complexity.  The
CONTAM family  of programs  is  presently  under development to provide one
demonstration of this integrated  approach; the first  two members  of  the  family
CONTAM86 and  CONTAM87  are presently  available  and  provide  contaminant
dispersal analysis tools.

   The noninteractive contaminant dispersal theory presented in the Phase II report of
this project [Axley 1987] has been extended in this report through:

   a)   a discussion of strategies of forming contaminant dispersal analysis equations for
       multi-zone systems involving  multiple contaminant species,

   b)   the introduction of element equations that may be used to model mass transport
       phenomena governed by first order kinetics, and

   c)   through the  introduction of element equations that  may be used to model the
       details of mass transport  driven by conduction and diffusion  processes in one
       dimensional flow paths.

CONTAM87 provides a complete computational implementation of the contaminant
dispersal theory presented earlier and that introduced here.  As such, CONTAM87
provides a set of indoor air quality analysis commands1 that are a superset of those
made  available in CONTAM86. Future members of the CONTAM family of programs will
provide additional indoor air quality  analysis commands superseding or complimenting
those  made available by earlier members of the family.

   Although it is well recognized that kinetics  plays an important role in chemical,
radio-chemical, sorption,  and settling  processes that affect contaminant dispersal
processes in buildings, the detailed knowledge  needed to apply the kinetics analysis
techniques presented here is often not available and actual  field or  experimental
measured data needed to validate any modeling effort is scarce.  The application of the

1  A command,  here,  is a set of computational procedures that  completes a basic indoor air
quality analysis task.
                                    10-1

-------
Indoor  Air  Quality  Model
Phase III Report                 10. Summary and  Directions of Future Work
kinetics techniques presented here, nominally known as source or sink modeling, has
become an area of emphasis in the direction of our future work.

   Although "good" source and sink models are essential to interactive contaminant
dispersal analysis, they introduce a source of uncertainty, as they  are inevitably based
upon empirical correlations, that is not  a  problem in noninteractive contaminant
dispersal analysis.  Therefore, while  validation of the contaminant dispersal analysis
techniques developed for noninteractive contaminant dispersal involved, primarily,  the
verification program logic (i.e., the primary assumption involved was the assumption of
conservation  of  mass), the  validation  of techniques  developed  for  interactive
contaminant dispersal analysis will, necessarily, focus on the validity of the  specific
source or sink models being employed.

   At this time the kinetics of radon decay is well understood and simple models of the
kinetics of formaldehyde emission and N02 reaction are available, yet multi-zone field
measurements needed to validate the  use of these models in the multi-zone context are
wanting.

   In the development  and  application of the one dimensional  convection-diffusion
element presented in this report, it was recognized that this element  provided one means
to model certain classes  of imperfectly mixed zones, those zones that behave as-/Ythey
were one dimensional flow  systems. Thus this mass  transport element could be
considered,  also, to be  a imperfectly-mixed  zone element.  Following  this train of
thought, a well-mixed zone, whose mass transport behavior is defined by its volumetric
mass, may be  thought to be modeled  by a  well-mixed zone element, rather than  being
considered a basic assumption of the underlying theory, and, therefore, the contaminant
dispersal  theory  presented  here may  be  generalized  to  remove the restricting
assumption of perfect mixing. Presently, an attempt is being made to recast the  element
assembly  approach to contaminant dispersal analysis in such a way as to avoid  the
limiting assumption of perfect  mixing.  In this new formulation of the theory the well-mixed
model becomes one special case  and a framework is provided for the development of
other imperfectly mixed zone elements.

   Two parallel research efforts in the areas of inverse contaminant dispersal  analysis
and  flow  analysis, respectively,  are also presently  underway,  complimenting  the
contaminant dispersal analysis  work reported here.  In the former area  integral
formulations of the multi-zone inverse  analysis problem have been  formulated and used
to develop a new multi-zone  tracer gas technique.  Field applications  of this technique
have proven the technique to be promising. In the flow analysis area, the flow elements
developed during Phase II  of this  project [Axley 1987]  have undergone further
refinement and some  additional elements  have been  formulated.  The results of first
applications  of these new flow elements have been encouraging.
                                     10-2

-------
Indoor  Air Quality  Model                                           REFERENCES
Phase III Report
REFERENCES

Axley, J.W., DTAM1: A Discrete Thermal Analysis Method for Building Energy Simulation: Part I Linear
    Thermal Systems  with DTAM1 Users' Manual. 1985 (presently under review for publication by the
    National Bureau of Standards, Building Environment Division, Center for Building Technology)

Axley, James, Indoor Air Quality Modeling: Phase II Report. NBSIR 87-3661, CBT, National Bureau of
    Standards, Gaithersburg, MO, Oct., 87

ASHRAE.  ASHRAE  Handbook 1985  Fundamentals.  SI Edition. ASHRAE, Atlanta,  GA. , 1985, pp.
    33.11-12

Bathe, K.J., Finite Element Procedures in Engineering Analysis. Prentice-Hall, Inc., 1982, pp. 702-706

Borrazzo, J.E., Osborn, J.F., Fortmann, R.C., & Davidson, C.L.,  " Modeling and Monitoring of CO,  NO
    and NO2 in a modern Townhouse", Atmospheric Environment, Vol. 21, No. 2, Pergamon Press,
    1987,  pp. 299-311

Eberlein, P.J. & Boothroyd, J., "Contribution 11/12: Solution to the Eigenproblem by a Norm Reducing
    Jacob! Type Method," Handbook for Automatic Computation: Volume II: Linear Algebra, Wilkinson,
    J.H. & Reinsch,&  Reinsch, C. - editors, Springer-Verlag, 1971

Grot,  R.A.,  Silberstein,  S., & Ishiguro, K.,  Validation of Models  for  Predicting  Formaldehyde
    Concentrations in Residences Due to Pressed Wood Products: Phase I. NBSIR 85-3255, CBT,
    NBS, Gaithersburg,  MD, Sept., 1985

Huebner, K.H. & Thornton, E.A., The Finite Element Method for Engineers. 2nd Edition. John Wiley  &
    Sons,  New York,  1982 . pp.  444-451

Hughes, T.J.R. & Brooks, A., "A Theoretical Framework for Petrov-Galerkin  Methods with Discontinuous
    Weighting Functions: Application to the Streamline-Upwind  Procedure," Finite Elements in Fluids,
    Volume 4, Edited by Gallagher et.al.. John Wiley & Sons, 1982, pp. 47-65

Matthews, T.G., Reed,  T.J.,  Daffron, C.R., & Hawthorne, A.R., "Environmental  Dependence of
    Formaldehyde Emissions from Pressed-Wood Products:  Experimental  Studies and  Modeling,"
    Proceedings. 18th International Washington State University  Particleboard/Composite Materials
    Symposium, pp. 10-23,1984

McNall, P., Walton. G., Silberstein, S., Axley. J., Ishiguro, K., Grot, R., & Kusuda, T., Indoor Air Quality
    Modeling Phase I  Report: Framework for Development of General Models. NBSIR 85-3265, U. S.
    Dept. of Commerce, National Bureau of Standards, October 1986

Moore, J.W.  & Pearson,  R.G., Kinetics and Mechanism Third Edition. John Wiley & Sons, New York,
    1981

Nauman, E.B. & Buff ham, B.A., Mixing  in Continuous Flow Systems. John Wiley & Sons, NY, 1983

Nicholas, J.E.. Chemical Kinetics:  A Modern Survey of Gas Reactions. John  Wiley & Sons, New York,
    1976
                                          Ref-1

-------
Indoor  Air  Quality  Model                                            REFERENCES
Phase III  Report
Nitschke,  I.  A., Traynor,  G.W., Wadach,  J.B., Clarkin,  M.E.,  & Clarke, W.A., Indoor Air Quality.
    Infiltration  and Ventilation in  Residential Buildings. NYSERDA Report 85-10,  N.Y. State ERDA,
    Albany. N.Y.. Mar. 1985

Sandberg, Mats, "The Multi-Chamber Theory Reconsidered from the Viewpoint of Air Quality Studies,"
    Building  and Environment, Vol. 19, No.  4, Pergamon Press, Great Britain, 1984  pp. 221-233

Sinden, F.W., "Mufti-Chamber Theory of Air Infiltration," Building and Environment, Vol. 13, Pergamon
    Press, Great Britain, 1978 pp. 21-28

Siren, Kai, A Computer Program to Calculate the Concentration Histories and Soma Air Quality Related-
    Quantities  in a Multi-Chamber System. Helsinki University of Technology, Institute of Energy
    Engineering, Otaniemi, 1986

Tezduyar, T.E. &  Ganjoo, O.K., "Petrov-Galerkin  Formulations  with Weighting Functions  Dependent
    Upon Spatial  and Temporal Discretizations: Applications  to Transient  Convection-Diffusion
    Problems," Computer Methods in  Applied Mechanics and Engineering, Vol. 59, Elsevier Science
    Publishers, North Holland, 1986, pp. 49-71

Traynor,  G.W., Allen, J.R., Apte, M.G., Girman,  J.R., & Holowell, C.D.,  "Pollution Emissions from
    Portable Kerosene-Fired Space Heaters", Environmental Science & Technology, Vol. 17. June 1983,
    pp. 369-371

Walas, S.M., Reaction Kinetics for Chemical Engineers. McGraw-Hill, New York, 1959

Walton, G.N., Estimating Interroom Contaminant Movements. NBSIR 85-3229,U.S.  DOC, NBS,
    Gaithersburg,  MD, August, 1985

Wen,  C.Y., & Fan, L.T., Models for Flow Systems and Chemical  Reactors. Marcel Dekker, Inc., NY.NY,
    1975

Yu, C.C. &  Heinrich, J.C., "Petrov-Galerkin Methods for the Time-Dependent Convective Transport
    Equation,", International Journal for Numerical Methods in Engineering, Vol.  23, John Wiley & Sons,
    1986, pp.  883-901

Zienkiewicz,  O.C. & Morgan, K., Finite  Elements and Approximation. John Wiley & Sons,  NY, 1983
                                          Ref-2

-------
Indoor   Air  Quality  Model
Phase  III  Report
   CONTAM87  FORTRAN
      APPENDIX
77   Source   Code
APPENDIX
CONTAM87 FORTRAN  SOURCE  CODE

The  FORTRAN?? source code  for CONTAM87  is
listed below. In  this listing  you will note  the  use of
the compiler directives "INCLUDE".  These directives
are commonly available in most compilers  but are not
part  of the  FORTRAN language.  They are used to
"include" code  stored  in  separate "include files" that,
here,  contain  common  block data  specifications
shared by many subroutines.  The  contents of these
include  files  are  listed  on  the  last  page  of  this
appendix.

      PROGRAM CONTAM
   PRO:CONTAM - BUILDING CONTAMINANT DISPERSAL ANALYSIS PROGRAM
               VERSION FY87

   	 Developed by James Axley
                  Building Environment Division,  NBS
                  Spring 1917
       Using;
       A) CAL-SAP Library of subroutines developed  by Ed Wilson,
         u.c. Berkeley
       B) Microsoft FORTRAN V2.2 Compiler for Apple Macintosh
         For Mac
           1. Set logical unit numbers, In SUBROUTINE INITIO, as;
                  NTR - 9  ;  NTW " 9   ;   NCMD  - 9
           2. INCLUDE statements use .INC (I.e.. without  ')
           3. In SUBROUTINE PROMPT use: WRITE(NTW,'(A,M') STRING
       4. In SUBROUTINE EIGEN2 use:  WRITE!... A.\)  at  Section 2.0
       C) IBM PC Professional FORTRAN (Ryan-McFarland)
           1. Set logical unit numbers. In SUBROUTINE INITIO. as;
                  NTR = 5  ;  NTH < 6   ;   NCMD  - 5
           2. INCLUDE statements use '.INC'  (I.e., with  ')
           3. In SUBROUTINE PROMPT use: WRITE(NTW.'(A)')  STRING
       4. In SUBROUTINE EIGEN2 don't use: WRITE!... A) at Section 2.0

       Memory for dynamically allocated/defined arrays is  located in
       vector IA(MTOT) in blank common.   To increase or decrease this
       area alter the dimension of IA. in the section 0.0  below, set
       MTOT, in section 1.0 below, equal to this new dimension, and
       recompile the code.  As Integers are 4 bytes wide,  memory
       dedicated to IA(MTOT)  Is equal to MTOT*4  bytes.

       The number of species is presently limited to MAXSP25.
       This may be changed by altering MAXSPE In the CNTCOM.INC file.
      IMPLICIT REAL'S (A-H.O-Z)
C0.0 DATA SPECIFICATIONS < COMMON STORAGE
      COMMON MTOT,NP,IA<50000)

      INCLUDE 'ARYCOM.INC1
      INCLUDE 'IOCOM.INC1
      INCLUDE 'CMDCOM.INC'
      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR
     IF(MODE.EQ.'INTER') CALL PROMPT!' CMND>'//CHAR(7))
     CALL FREE
     IF(MODE.EQ.'BATCH') CALL FREEHR(NTH)
C
C3.3 INTERPRET COMMAND LINE
C
C	GET COMMAND ( ARRAY NAMES. IF ANY
C
     CALL FREECC  ' .NCMND, 8.1)
     CALL FREEC('A',M1U),4.7)
C
c	INTRINSIC COMMANDS
C
     IFKNNCMND.EQ.'H'I .OR. (NNCMND.EO.'HELP')) THEN
       IF(MODE.ZQ.'BATCH') THEN
         CALL ALERT('ERROR: Command not defined In BATCH mode.',
    +    'S'.'S')
         CALL RETRN
       ELSE
         CALL HELP
       ENDIF

     ELSEIFI(NNCMND.EO.'ECHO-ON').OR.(NNCMND.EO.'ON')) THEN
       ECHO - .TRUE.

     ELSEIF((NNCMND.EO.'ECHO-OFF').OR.(NNCMND.EO.'OFF')) THEN
       ECHO = .FALSE.

     ELSEIF((NNCKND.EQ.*L').OR.(NNCHND.EQ.'LIST'))  THEN
       IF(MODE.EQ.'BATCH11 THEN
         CALL ALERT('ERROR: Command not defined In BATCH mode.',
    +    'S'.'S')
         CALL RETRN
       ELSE
         CALL LIST
       ENDIF

     ELSEIF((NKCMND.EQ.'P').OR.(NNCMND.EQ.'PRINT')) THEN
       CALL PRINT

     ELSEIF((NNCKND.EO.'D').OR.(NNCMND.EQ.'DIAGRAM')I  THEN
       CALL DII.GRM

     ELSEIF(NNCMND.EQ.'PAUSE') THEN
       PAUSE '   "" PAUSE: Enter  to continue.'

     ELSEIF((NHCMNO.EQ.'S').OR.(NNCMND.EO.'SUBMIT')) THEN
       IF(MODE.EQ.'BATCH') THEN
         CALL ALERT('ERROR: Command not defined In BATCH mode.',
    +    'S'.'S')
         CALL 11ETRN
       ELSE
         CALL .'SUBMIT
       ENDIF

     ELSEIFKNHCMND.EO.'R'I.OR. (NNCMND.EQ.'RETURN') I THEN
       IF(MODE.EQ.'INTER') THEN
         WRITE(NTW,2320)
       ELSE
         CALL KETRN
       ENDIF
 2320   FORMAT!' *** ERROR: Command not defined in INTERACTIVE  mode.1)

     ELSEIF((NNCMND.EQ.'0').OR.(NNCMND.EQ.'QUIT1))  THEN
       CLOSE(NOT)
       STOP
       CONTAM COMMANDS
     ELSEIF(NNCMND.EQ.'FLOWSYS'I THEN
       CALL FLOSYS
     ELSEIF(NNCMND.EQ.'FLOWELEM')  THEN
       CALL FLOELM
C--1.0 INITIALIZE INTERNAL VARIABLES
c	
      MTOT > 50000
      CALL INITARIMTOT)
      CALL INITIO
      CALL INITCN
      ERR=.FALSE.
C2.0 WRITE BANNER
      CALL BANNER(NTW)
      CALL BANNER(NOT)
      WRITE(NOT.2200) (FNAME(1:LFNAME)//'.OUT1)
 2200 FORMAT!/1  "= RESULTS OUTPUT FILE:  ', (A) I
                                                                       ELSEIF(NNCMND.EO.'KINELEM') THEN
                                                                        CALL XINELM
                                                                       ELSEIFWCMND.EQ. 'FORM-[H| ') THEN
                                                                        CALL FORMFO
     ELSEIF(NNCMND.EQ.'STEADY') THEN
       CALL STEADY
                                                                       ELSEIF(NMCMND.EO.'TIMECONS') THEN
                                                                        CALL T1IMCON
                                                                       ELSEIF (N1ICMND.EQ. 'FLOWDAT'I THEN
                                                                        CALL F1.0DAT
     ELSEIF(NMCMND.EQ.'EXCITDAT') THEN
       CALL EXCDAT
C--3.-0 COMMAND PROCESSOR LOOP

C
C	3.1 CHECK BLANK COMMON STORAGE
C
   30 NSTOR - 
-------
Indoor  Air  Quality   Model
Phase  III  Report
                                                 APPENDIX
   CONTAM87   FORTRAN   77   Source   Code
      SUBROUTINE INITMUMTOT)
CSUB:INITAR - INITIALIZES DYNAMIC ARRAY MANAGER VARIABLES
C               IN BLANK COMMON AND LABELED COMMON /ARYCOM/

      INCLUDE 'ARYCOM.INC'

      DUMA - 0
      NEXT = 1
      IDIR " MTOT
      IP<1) - 4
      IP (2) = 8 '
      IPO) - 1
      RETURN
      END


      SUBROUTINE INITIO
CSUBUNITIO - INITIALIZES LABELED COMMON /ICCOM/
C               OPENS DEFAULT RESULTS OUTPUT FILE

      INCLUDE 'IOCOM.INC1

      NTR  =  5
      NTH  =  
      NCMD   5
      NIN  - 10
      NOT  = 11
      NPLT - 12
      ND1  = 13
      ND2  - 14
      ND3  - 15
      ND4  - 16
      FNAME = 'CONTAM'
      LFNAME = 6
      EXT = '   '
      CALL NOPENINOT,(FNAME(1:LFNAME)//'.OUT'),'FORMATTED')
      MODE - 'INTER'
      ECHO - .TRUE.
      RETURN
      END
      SUBROUTINE INITCN
 CSUBlINITCN - INITIALIZES CONTAM LABELED COMMON /CNTCOM/
      INCLUDE 'CNTCOM.INC'
 C	 INITIALIZE CONTAM CONTROL VARIABLES
                                                               IHITAR C
                                                                      C-
                                                                              (H)ELP
                                                                                                   List available Intrinsic commands.',/,
      NSNOD
      NSSPE
      NSEQ
      MS BAN
      NFELM
      NKINEL
 C	 INITIALIZE POINTERS

      MPV   =0
      MPVM  = 0
      MPF   =0
      MFC   =0
      MPE   -0
      MPKSEQ - 0
      MPNE  - 0
      MPEFF = 0
      KPDIFF= 0
      MPCENR- 0
      DO 10 N-1,9
   10 MPKIK(N)  = 0
      MPTEMP - 0

 C	INITIALIZE OTHERS

      EP   - l.OD-16

      RETURN
      END
      INCLUDE 'IOCOM.INC'
      HRITE(NTN,2000)
                         HELP LIST ~
 2000 FORMAT!/, ' -
        (H)ELP
        ECHO-(ON)
        ECHO-(OFF)
        (L)IST
        (P)RINT   A-
        (D)IAGRAM A-
             INTRINSIC COMMANDS',//,
                    List available intrinsic commands.', /,
                    Echo results to screen.',/,
                    Do not echo results to screen.'./.
                    List the directory of all arrays.',/,
                    Print array named .'./.
                    Diagram array named .',/,
(S)UBMIT F*> Read connands from  batch .',
(R)ETURN             Return to Interactive mode.',/,
(Q)UIT               Quit program.'/)
      SUBROUTINE LIST
CSUB:LIST  - LIST DIRECTORY OF ALL ARRAYS IN BLANK COMMON
C
C--HELP LIST	
C
C    .'  (L)IST                List the directory of all arrays.',/,
      COMMON HTOT.NP.IAU)
      INCLUDE  'AXYCOM.INC'
      INCLUDE  'ICCOM.INC'

      CHARACTER*! NAM(4),LOC(4,2).TYPE(9,3),STOR(13,2)
      CHARACTER*! CHK
                                                                            DATA TYPE/'I'.'N'
                                                                           1          'R'.'E'
                                                                           2          'C'.'H'
                       'T','E','G'. '', 'R'.
                       A'.'L','  '.' '.'  ',
                       'A','R'.'A','C','T',
                                                                                                                 E'.'R'/
                                                                            DATA LOC/'C','0'.'R'.'E'
      SUBROUTINE BANNER(LUN)
 CSUB: BANNER - WRITES PROGRAM BANNER TO LOGICAL UNIT LUN

      COMMON MTOT,NP,IA(1)

      HRITE(LUN,2000)  MTOT
  2000 FORMAT!//, IX, 78UH-)./.
     .'I                           C 0 N T A M 9 T.T79. 'I'./.
     .'  I          Contaminant Dispersal Analysis for Building  Systems'
     .,T79,'|'./,
     .'  I                      Version 4/87 - Jim Axley - NBS',
     .179. 'I './.IX.TBdH-) ,/,5X. 'MTOT:',19)
RETURN
END
C
C INTRINSIC COMMANDS
C



C
C
C

       SUBROUTINE HELP
 CSUB: HELP - PROVIDES ON-SCREEN HELP
 C
 CHELP LIST	.	
 C
      DATA  STOR/'S','E'.'Q'.'U'.'E'.'N'.'T','I1.'A'.'L'
     1         'D','I','R'.'E','C1.'T'.'  '.'A1,'C','C'
C
C	LIST  DIRECTORY OF ALL ARRAYS IN DATA BASE
      IF(NUMA.EQ.O) GO TO 900
C
C	WRITE HEADER FOR SCREEN  LISTING OF FILE DATA
      WRITE(NTH,1000)
C
C	START COUNT OF LINES TO  SCREEN
      IL -  5
C
      1C =  IDIR
      DO 100 I-l.NUMA
      IL -  IL t 1
      1LOC  = 1
      1ST  0
      IA6  IAUC+6)
      IA7  IA(IC*7)
      IA9 * IAdCn-91
C	CHECK FOR LOCATION AND STORAGE TYPE
      IFUA9.GT.O) ILOC-2
      IFIIA7.LT.O) ILOC-2
      IFIIA7.EQ.-1) 1ST-1
      IFdA7.EQ.-2l IST-2
      IFIIA9.GT.O) IST-3
      IPN = 1C - 1
      DO 10 J=1.4
      IPN = IPN + 1
   10 NAM(J) - CHAR(IAIIPN) I
C	WRITE DATA TO TERMINAL
      IF(IST.EQ.O) WRITE(NTH,1100)  (NAM(J),J-l.4),
     * IA(IC+4),IA(IC*5). (TYPE(K.IA6),K=1.9).  
     * (LOC(L.ILOC).L*1,4)
C
      IF(IST.EO.l) WRITE(NTW.1100)  (NAM(J) . J-l, 4) ,
     * IA(ICt4).IA(IC+5),(TYPE(K,IA6),K=1.9),
      (LOC(L.ILOC).L-1,4). , (LOC (L, ILOC), L-1,4),
      (STOR(M,2),M-l,13)
C
      1C -  1C + 10
C	CHECK FOR NUMBER OF LINES  PRINTED
      IFdL.LT.20l GO TO 100
      IFII.EO.NUMA) GO TO 100
      CALL  PROMPT!'   ** Do you  want more ? (Y/N)  ')
      READ(NTR,2200)
      IFUCHX.EO. 'n'l  .OR. (CHK.EQ. 'N')) GO TO 900
      IL -  0
      WRITE(NTW.2000]
  100 CONTINUE
C
  900 RETURN
C
 1000 FORMAT!'  LIST: ARRAY  LIST',//,
     *  Name',2X.'Number1.2X.'Number',5X,'Data'.5X.
     " 'Location',SX,'Storage',/,8X,'Rows',2X,
     * 'Columns',5X.'Type*,19X,'Type',/)
 1100 FORMAT(IX,4A1.2X,I4.4X.I4.5X.9A1,4X.4A1,4X,13A1)
                                                            Append  -2

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                            APPENDIX
             CONTAM87   FORTRAN  77   Source   Code
  1200 FORMAT (IX, 4A1, '   NI=',I4,'  NR=',I4.'  NC=',14,5X.4A1,4X.13A1)
  1300 FORMAT(IX.4A1.3X,-RECORD  LENGTH = '. 16,7X,4A1,4X,13A1)
  2000 FORMAT!)
  2200 FORMAT (1 AD
           2000 FORMAT!/' COLi ='.6112)
           2001 FORMAT(' ROM',14,6E12.S)
           2002 FORMAT!' ROH',14.6F12.S)
                END
      SUBROUTINE PRINT
CSUB:PRINT - COMMAND TO "PRINT" ARRAY TO RESULTS OUTPUT  FILE
C
CHELP LIST	
C
C     .' (P)RINT   A-    Print array named .'./.
   ' PRINT  C	
                SUBROUTINE CPRT(C,NR,NO
          CSUB:  CPRT  - PRINTS CHARACTER*! ARRAY  TO RESULTS OUTPUT FILE
      COMMON MTOT.NP.IA(l)
      INCLUDE 'ARYCOM.INC'
      INCLUDE 'IOCOM.INC'
      INCLUDE 'CMDCOM.INC'

      CHARACTER MA*4
      EQUIVALENCE (MA.Ml(D)

C	PRINT OF REAL OR INTEGER ARRAY
      CALL PROMH(l)
C	LOCATE MATRIX TO BE  PRINTED
      IF(ECHO) WRITE(NTH,2000) Ml
      WRITE(NOT, 2000)  Ml
      CALL LOCATE (Ml. NA.NR.NO
      IF(NA.EO.O) THEN
        CALL ALERTCERROR: Array '//MA//' does not exist.'.'S'
        CALL ABORT
        RETURN
      ELSEIF(NA.LT.O)  THEN
        CALL ALERTCERROR: Array '//MA//' Is out of core.','!'
        CALL ABORT
        RETURN
      ELSE
        IFWP.EQ.l)  CALL IPRT(IA(NA),NR,NC)
        IF(NP.EQ.2)  CALL RPRT (IA (NA) , NR.NC)
        IFOJP.EQ.3)  CALL CPRT (lA(NA).NR. NCI
      ENDIF
'$')
'$')
      RETURN
 2000 FORMAT!/'
      END
                     PRINT  OF  ARRAY  "',4A1,'"')
      SUBROUTINE IPRT(N,NR.NC)
CSUB: IPRT - PRINTS INTEGER ARRAY TO RESULTS OUTPUT  FILE

      DIMENSION N(NR.NC)

      INCLUDE 'IOCOM.INC'

      NUMC = 14
      DO 100 1=1.NC,NUMC
      IN  I + NUMC - 1
      IF(IN.GT.NC)  IN = NC
      WRITE(NOT.2000)     Diagram array named .'./,
               COMMON MTOT.NP.IA(l)

               INCLUDE 'IOCOM.INC'
               INCLUDE 'CMDCOM.INC'

               CHARACTER MA*4
               EQUIVALENCE  (MA. Ml(1))

    IPRT  C	PRINT OF REAL OR INTEGER ARRAY
               CALL PROMH(l)
          c	LOCATE MATRIX TO BE PRINTED
               IFIECHO) HRITE (NTH. 2000)  Ml
               HRITE(NOT,2000)  Ml
               CALL LOCATEIMl.NA.NR.NC)
               IF(NA.EQ.O) THEN
                 CALL ALERTCERBOR:  Array  '//MA//1 does not exist.','S','S')
                 CALL ABORT
                 RETURN
               ELSEIF(NA.LT.O)  THEN
                 CALL ALERTCERROR:  Array  '//MA//' Is out of core.', ' S'. ' S'l
                 CALL ABORT
                 RETURN
               ELSEIFINP.EQ.3)  THEN
                 CALL ALERTCERROR:  Array  '//MA//' Is a character array.'.
               +  'S'.'S'I
                 CALL ABORT
                 RETURN
               ELSE
                 IF(NP.EQ.l) CALL IDIAGRIIAINA).NR.NC)
                 IFINP.F.Q.2) CALL RDIAGR (IAINA) ,NR,NC)
               ENDIF
                                                                             RETURN
           2000  FORMAT!/'
                END
                                                                                          >  DIAGRAM  OF  ARRAY
                SUBROUTINE IDIAGR(N.NR.NC)
          C--SUB:  IDIAGR - "DIAGRAMS" INTEGER  ARRAY TO RESULTS OUTPUT FILE

                INTEGER N(NR.NC)
                CHARACTER*! ICON (36)

                INCLUDE 'IOCOM.INC1

          C	DIAGRAM INTEGER ARRAY
                NUMC = 36
                DO 200 1=1.NC,NUMC
                IN = I  NUMC - 1
                IFIIN.GT.NC) IN = NC
                WRITE(NOT.2000) (INT(K/10).K-I,IN)
                WRITE(NOT,2010) ((K-INT(X/10)*10),K=I,IN)
                IFIECHO) HRITE(NTH.2000)  (INT(K/10).K=I.IN)
                IFIECHO) HRITE(NTH.2010)  (
-------
Indoor   Air  Quality  Model
Phase  III  Report
      CONTAM87   FORTRAN
       APPENDIX
77  Source   Code
      SUBROUTINE RDIAGR(A,NR,NC>
CSUB: RDIAGR - 'DIAGRAMS- REAL ARRAY TO RESULTS  OUTPUT FILE

      REAL'S A(NR.NC)
      CHARACTER*! ICON(36)

      INCLUDE 'IOCOH.INC'

C	DIAGRAM INTEGER ARRAY
      NUMC - 36
      DO 200 1=1.NC. NUMC
      IN - I + NUMC - 1
      IF (IN.GT.NO  IN - NC
      WRITE(NOT,2000)  (INT(K/10) ,K-I. IN)
      WRITE(NOT.2010)  ((K-INT(K/10)10),K-I.IN)
      IF(ECHO) WRITE(NTH,2000)  (INT(K/10),K=I,IN)
      IF(ECHO) WRITE(NTS,2010)  ((K-INT(K/10)*10) , K-I, IN)
      DO 200 J-l.NR
      DO 100 K-I.IN
       ICON(K) - '*'
       IF(AIJ.K) .EO. O.ODO) ICON(K) - ' '
  100 CONTINUE
       WRITE(NOT,2020) J, (ICON (X),K-I.IN)
       IF(ECHO) WRITE(NTW.2020) J.(ICON(K),K=I,IN)
  200 CONTINUE
C
      RETURN

 2000 FORMAT(/ COLI  ,36(IX,II))
 2010 FORMAT (7X. 36 (IX. ID)
 2020 FORMAT!' ROW'. 13.36(IX.Al))
      END
      SUBROUTINE SUBMIT
CSUB: SUBMIT - SWITCHES  TO BATCH MODE AND OPENS  BATCH COMMAND FILE
C
CHELP LIST	
C
C     .' (S)UBMIT F- Read commands from  batch .',/,
C  SUB
C
C
C  BEL
C
C
C
C
C
C
C
C
C
SUBROUTINE FLOSYS
FLOSYS - COMMAND TO READ < PROCESS FLOW SYSTEM CONTROL VARIABLES
ESTABLISHES FLOW SYSTEM EQUATION NUMBERS t B.C.
FLONSYS N=nl
N-nl S=n2 ID-cl,c2, .
n3,n4,n5 BC-C3
n3,n4,n5 V=n6
END'!//,
Flowsystem control variables.'./.
. nl ** no. flow nodes; n2- no. species
cl,c2,... species IDs (4 chars)',/.
c3  boundary condition; G or C'./,
n6 * nodal volumetric mass',/,
         COMMON MTOT.NP.IA(l)

         INCLUDE  'IOCOH.INC1
         INCLUDE  'CNTCOM.INC'

         LOGICAL  ERR
         INTEGER  IJK<3)
         EXTERNAL BCDATO.VDATO

         ERR * .FALSE.
   C
   C1.0 GET NUMBER OF FLOW SYSTEM NODES, NUMBER OF SPECIES,  f  SPECIES IDS
   C
         IF (ECHO.OR.(MODE.EO.'INTER'))  WRITE(NTW.2100)
         WRITE(NOT,2100)
    2100 FORMAT (/.'  FLOWSYS:  FLOW  SYSTEM CHARACTERISTICS')

         IF(NSNOO.NE.O) CALL RESET

         IF(MODE.EQ.'INTER') CALL  PROMPT|'DATA>')
         CALL FREE
         IF (MODE. EQ.'BATCH') CALL  FREEWRtNTW)
      INCLUDE 'IOCOM.INC'
      LOGICAL FOUND

      CALL FREEC('F',FNAME.12.1)
      INQUIRE(FILE-FNAME(1:LENTRM(FNAME)),EXIST-FOUND)
      IF(FOUND)  THEN
        MODE = 'BATCH'
        NCMD  NIN
        LFNAME - LENTRM(FNAME)
        WRITE(NTW,2010) FNAME
        WRITE(NOT,*)
        WRITE(NOT,2010) FNAME
 2010   FORMAT(  CONTAM set to BATCH mode uslno  file: ',A)
        OPEN(NCMD,FILE=FNAME(1:LFNAHE).STATUS-'OLD')
        REWIND NCMD
        CLOSE(NOT)
        CALL NOPENINOT,(FNAME(1:LFNAME)//'.OUT1),'FORMATTED')
        CALL BANNER(NOT)
        WRITE(NOT.2020)  (FNAME(1:LFNAME)//'.OUT')
 2020   FORMAT(/'  RESULTS OUTPUT FILE:  '.(A))

      ELSE
        WRITE(NTW,2030)
 2030   FORMAT!'    NOTE: Submit file not  found.')
        CALL ABORT
      ENDIF

      RETURN
      END
      SUBROUTINE RETRN
CSUB:RETRN - RETURNS TO  INTERACTIVE MODE
C
CHELP LIST	
C
C     .' (R)ETURN             Return to Interactive mode.'./,
   C1.1  NUMBER OF FLOW NODES

         CALL FREEI('N',NSNOD,1)
         CALL CKIZERCthe number of flow system nodes'.NSNOD.l,'GT',ERR)
         IF(ERR) GO TO 999

         IF(ECHO) WRITE(NTW,2120)  NSNOD
         WRITE(NOT,2120)  NSNOD
    2120 FORMAT!/,1      Number of flow system nodes 	',15)

   C	1.2  NUMBER OF SPECIES

         CALL FREEH'S',NSSPE, 1)
         CALL CXIRNGCthe nunfcer of contaminant species'.NSSPE, 1,
        fO, 'LTLE' .MAXSPE.ERR)
         IF(ERR) GO TO 999

         IF(ECHO) WRITE(NTW,2140)  NSSPE
         WRITE(NOT.2140)  NSSPE
    2140 FORMAT('      Number of contaminant species ....'.15)

   C	1.3  SPECIES IDS

         CALL ZEROC(SID,4,NSSPE)
         CALL GETIDS(SID,NSSPE,'Contaminant species IDs:')
   C
   C2.0 DEFINE XSEQ ARRAY AND NUMBER EQUATIONS IN (NODE.SPECIES)  ORDER
   C
         IF (ECHO.OR.(MODE.EO.'INTER')) WRITE(NTW,2150)
         WRITE(NOT,2150)
    2150 FORMAT!/,'   = Boundary Conditions and Equation Nunfcers')

         NSEQ - NSNOD'NSSPE

         CALL DELETE('XSEQ')
         CALL DEF1NI('KSEQ',MPKSEQ,NSNOD,NSSPE)

         CALL EQNUMdA (MPKSEQ),NSNOD.NSSPE)
      INCLUDE 'IOCOM.INC'

      WRITE(NOT, *)
      WRITE(NOT. 2010)

      CLOSE(NCMD)
      CLOSE (NOT)
      FNAME - 'CONTAM'
      LFNAME - 6
      OPEN (NOT. FILE" (FNAME (1: LFNAME) //'.OUT') , STATUS-'OLD',
     +FORM-'FORMATTED')
      CALL APPEND(NOT)
      NCMD - NTR
      MODE = 'INTER1

      WRITE(NTW, 2010)
      WRITE(NOT, )
      WRITE(NOT, 2010)
  2010 FORMAT!' * CONTAM returned to INTERACTIVE node.')

      RETURN
      END
                    CONTAM  COMMAND
   C3.0 PROCESS  BOUNDARY CONDITION DATA <  REPORT EQUATION NUMBERS
   C
         CALL DATGEN(BCDATO,NSNOD,ERR)
         IF(ERR) GO TO  999

         CALL RPRTX(IA(MPKSEQ),SID,NSNOD.NSSPE)
   C
   C--4.0 GET NODAL VOLUMETRIC MASSES
   C
         IF(ECHO.OR.(MODE.EQ.'INTER'))  WRITE(NTW,2400)
         WRITE(NOT,2400)
    2400 FORMAT)/,'   = Nodal Volumetric Mass')

         CALL DELETE('V  ')
         CALL DEFINRCV  ', MPV.NSNOD, 1)
         CALL ZEROR(IA(MPV),NSNOD.l)

         CALL DATGEN(VDATO,NSNOD,ERR)
         IF(ERR) GO TO  999

         CALL RPRTNOIIA(MPV),NSNOD,'Node')
   C
   C--5.0 ORDERLY  COMPLETION: SXIP TO "END"
   C
-C   500 IF(EOC) RETURN
 C       IFIMODE.EQ.'INTER')  CALL PROMPTCEND?>')
 C       CALL FREE
 C       GO TO 500
                                                             Append  -4

-------
Indoor   Air   Quality  Model
Phase  III  Report
   CONTAIM87   FORTRAN
                                                   APPENDIX
                                            77   Source   Code
C9.0 ABORT IF ERR
C

  999 IF(ERR) THEN
        CALL DELETE CKSEQ')
        CALL DELETECV   ')
        NSNOD " 0
        NSSPE = 0
        NPKSEO = 0
        HPV - 0
        ERR - .FALSE.
        CALL ABORT
        RETURN
      ENDIF

      END
      SUBROUTINE EONUM(KSEQ.NSNOD,NSSPE)
C--SUB:EQNUM - ESTABLISHES EQUATION NUMBERS

      INTEGER KSEQ (NSNCO,NSSPE)

      NN - 0
      DO 10 N=l,NSNOD
      DO 10 Ml,NSSPE
      NN = NN+1
   10 KSEQ(N,H)  NN
      RETURN
      END
      SUBROUTINE VDATO(N.ERR)
C~SUB:VDATO -  CALLS VDAT1 PASSING ARRAYS
C
      COMMON MTCT,NP,IA(1)

      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR

      CALL VDAT1(IA(MPV),NSNOD,N,ERR)

      RETURN
      END
      SUBROUTINE BCDATO(N,ERR)
CSUB:BCDATO - CALLS BCDAT1  PASSING TEMPORARY ARRAY
C
C	POINTERARRAY	
C   MPBCBC (NSSPE) *1  : TEMPORARY STORAGE OF BC CODES


      COMMON MTOT.NP.IAIl)

      INCLUDE 'lOCOH.INC'
      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR

      CALL BCDAT1 (LMMPKSEQ) .CDATA.N, NSNOD,NSSPE. ERR)

      RETURN
      END
      SUBROUTINE BCDAT1(KSEQ,BC,N.NSNOD.NSSPE,ERR)
CSUB: BCDAT1 - PROCESSES BC DATA

      INCLUDE 'IOCOM.INC1

      INTEGER KSEQ (NSNOD, NSSPE)
      CHARACTER BC(NSSPE)*!, BCH'l
      LOGICAL ERR

      CALL FREECCC',BC(1) .1. NSSPE)

      DO 10 H-l,NSSPE
      BCM - BC(M)
      IFI(BCM.NE.'C').AND.(BCM.NE.'G1).AND.(BCM.NE.'  '))  THEN
        WRITE(NTH.2000)  BCM.N.M
        WRITE(NOT,*)
        WRITE(NOT,2000)  BCM,N,M
        ERR  .TRUE.
        RETURN
 2000 FORMAT(' ***  ERROR: Boundary condition "',A1,'- not  available.',
     +/,                 Node:',14,'   Speclea:',I4)
      ELSEIF(BCM.EO.'C') THEN
        XSEQ(N,M)  =  -KSEQ(N.M)
   10 ENDIF

      RETURN
      END

c	RPRTK
      SUBROUTINE RPRTK(KSEQ,SID,NSNOD,NSSPE)
CSUB:RPRTK - REPORTS SYSTEM EQUATION NUMBERS STORED IN  ARRAY
C              KSEQ(NSNOD,NSSPE)

      INCLUDE 'IOCOM.INC'

      INTEGER KSEQ(NSNOD,NSSPE)
      CHARACTER SID(NSSPE)<

      IF(ECHO) WRITE(NTH.2000)  (SID(M),M=1,NSSPE)
      WRITE(NOT,2000)  (SID(M),H-l,NSSPE)

      DO 10 H-l.NSNOD
      IF(ECHO) WRITE(NTH,2010)  N, (KSEQ(N, M),M=1,NSSPE)
      HRITEINOT.2010)  N,(KSEQIN.M),M-1.NSSPE)
   10 CONTINUE

      RETURN

 2000 FORMAT!/,
     .6X,'Neg. Eqtn-f *  concentration-prescribed (Independent DOF).',/.
     .fix,'Pos. Eqtn-l *>  generation-prescribed (dependent  DOF).',//,
     .13X,'Species ID:',/.
     .EX,'Node1,10I3X.A4))
 2010 FORMAT16X,14,10<3X,14)>
      END

C	VDATO
      SUBROUTINE VDAT1(V,NSNOD,N.ERR)
CSUB:VDAT1 - READS NODE VOLUMETRIC MASS DATA
C
      INCLUDE 'IOCOM.INC'

      REAL'S V(NSNOD),VDAT
      LOGICAL ERR

      CALL FREEIM'V'.VDAT, 1)
      CALL CKRZURCnodal volumetric mass',VDAT. 1. 'GE' .ERR)
      IF(ERR)  RETURN
      V(N)   VDAT

      RETURN
      END
C .................. i. mm. .... HI.. ............. ............................  ...... . ..... i-j.i  i. n FLOELM
      SUBROUTINE FLOELM
C SUB: FLOELM - COMMAND TO READ t WRITE FLOW ELEMENT DATA TO FILE *.FEL
C
C--HELP  LIST ------------------------------------------------------------
C
        FLOWELEM             Flow elements:  Simple or Conv-dlf f . ' , /.
        nl T-SIMP I=n2,n3 E=n4'./.
        or',/.
                               L=i>6 D=n7,n8,... G=n9,nlO, . . . F-nll',/,
                              nl = elera.  number;  n2,n3 a end nodes ',/,
                              n4 " filter eff.; nS = mass/length;',/,
                              n6  length;  n7,n8,...= disp. coef.',/,
                              n9.nlO = generation; nil  upwind fact.')
        nl T-CNDF  I=n2,n3
        END
      COMMON  MTOT.NP.IA(l)
                                                                             INCLUDE 'IOCOM.INC'
                                                                             INCLUDE 'CNTCOM.INC'
      LOGICAL F.RR, FOUND
      EXTERNAL FLOELO
C	VARIABLE	DESCRIPTION	
C   ERR      ERROR FLAG
C   FOUND        FILE FOUND FLAG
C   FLOELO       SUB. TO READ I WRITE FLOW ELEM DATA
C   NENOD        NUMBER OF ELEMENT NODES
C   NESTRT       FIRST ELEMENT NUMBER
C0.0 INITIALIZATION
C
      ERR = .FALSE.
      NENOD - 2

      IFIECHO.OR.(MODE.EQ.'INTER'))  WRITE(NTW,2000)
      WRITE(NOr.2000)
 2000 FORMAT!/,'  FLOWELEM: FLOW ELEMENTS')
C
C--1.0 CHECK TO  SEE  IF SYSTEM NODES I EQUATION NUMBERS ARE DEFINED
C
      CALL CKSYSd.ERR)
      IF(ERR)  THEN
        CALL ABORT
        RETURN
      ENDIF
C
C2.0 OPEN .FEL
C
      INQUIRE (FILE-FNAME(1:LFNAME)//'.FEL',EXIST-FOUND)

      IF((.NOV.FOUND).OR.(NFELM.EQ.0)) THEN
        CALL MOPEN(ND1,(FNAME(1:LFNAME)//'.FEL'),'UNFORMATTED1)
      ELSEIF(FOUND)  THEN
        WRITE(NTW,2200)
        WRITE(NOT,)
        WRITE(NOT, 2200)
 2200   FORMAT(
     +  '   *" NOTE: Additional flow elements being added to system.')
        OPEN (ND1, FILE=(FNAMEU: LFNAME)//1. FEL1 ),STATUS=' OLD',
       FORM"'UNFORMATTED')
        CALL APPEND(ND1) ~
      ENDIF
C
C3
C
     0 DEFINE TEMPORARY ARRAYS; GENERATE ELEMENT DATA;  REPORT BANDWIDTH

      CALL DELETE('EFF  ')
      CALL DELETECDIFF')
      CALL DELETECGENR')
      CALL DEFINRCGENR' .MPCENR.NSSPE, 1)
      CALL DEFINRCDIFF'.MPDIFF,NSSPE,1)
      CALL OEFINRCEFF  '. MPEFF. NSSPE, 1)

      NESTRT = NFELM+1
      CALL ELGEN(FLOELO,NENOD.NESTRT,NSNOD,ERR)
                                                             Append  -5

-------
Indoor   Air   Quality   Model
Phase  III  Report
                                         CONTAM87   FORTRAN
                                                   APPENDIX
                                            77  Source   Code
      CALL DELETE('EFF ')
      CALL DELETE('DIFF')                                                C-	 READ ELEMENT DATA
      CALL DELETE('GENR')                                                        CALL ZEROR(EFF,NSSPE.1)
                                                                                CALL FREERCE'.EFFU),NSSPE)
      IF(ERR) THEN                                                              CALL CXRZERCfilter offIclency'.EFF.NSSPE,'GE'.ERR)
        CALL ABORT                                                              IF (ERR)  GO TO 999
        RETURN
      ENDIF                                                             C	UPDATE SYSTEM BANDWIDTH
                                                                                DO 30 N=l,NSSPE
      IF(ECHO) WRITE(NTH.2300)  MSBAN                                              LS(l)  = N
      WRITE(NOT,")                                                         30   CALL ELBAN(KSEQ.NSNOD,NSSPE,LN.NENOD.LS.NESPE.MSBAN)
      WRITE(NOT.2300)  MSBAN
  2300 FORMAT!'    NOTE:  Current system bandwidth la:', IS)             C	WRITE ELEM.  DATA TO ND1
C                                                                              WRITE(ND1) TYPE
C4.0 ORDERLY COMPLETION: CLOSE FILE ND1;  SKIP TO 'END-                         WRITE(NDl) LN(1), LN(2),  (EFF (N) ,11-1, NSSPE)
C
      CLOSE(ND1)                                                        C	UPDATE  ELEMENT COUNT
                                                                                NFELM -  NEL
      IF(HCOE.EQ.'INTER')  RETURN
   500 IF(EOC) RETURN                                                    C	REPORT ELEMENT DATA
        CALL FREE                                                               WRITE(NOT,2030) NEL,TYPE, LN (1),  LN(2),  SID(1),EFF(1)
      GO TO 500                                                                 IF(NSSPE.GE.2) WRITE(NOT,2032)  (SID(N),EFF(N),N=2.NSSPE)
                                                                                IF(ECHO)  THEN
      END                                                                         WRITE(NTW,2030) NEL,TYPE, LN(1), LN (2),  SID(l),  EFF(l)
                                                                                  IF(NSSPE.GE.2) WRITE(NTW. 2032)   (SID (N) , EFF (N) .N-2,NSSPE)

      SUBROUTINE FLOELO(NEL,LN,ERR)                                       2030 FORMAT(2X,14,1X.A4,214,2X.A4,1X.G11.4)
C--SUB:FLOELO - CALLS  FLOEL1  PASSING ARRAYS                              2032 FORMAT!(21X.A4,1X.G11.4) I

      COMMON MTOT,NP,IA(1)                                              C
                                                                        C4.0 CONVECTION-DIFFUSION ELEMENTS
      INCLUDE 'CNTCOM.INC'                                              C
                                                                              ELSEIF(TYPE.EO.'CNDF') THEN
      LOGICAL ERR
      INTEGER LN(2)                                                     C	READ ELEMENT DATA

      CALL FLOEL1(IA(MPKSEQ),IA(MPFF).IA(MPDIFF).IA(MPGENR),NEL,LN,ERR)          MASSL -  O.ODO
                                                                                CALL FREEH CM', MASSL, 1)
      RETURN                                                                    CALL CXRZER('mass/lengtn',MASSL,1,'GE'. ERR)
      END                                                                       IF(ERR)  GO TO 999

c	FLOEL1          LENGTH - O.ODO
      SUBROUTINE FLOEL1(KSEO.EFF.DIFF,GENR,NEL,LN.ERR)                           CALL FREER)'L',LENGTH,1)
CSUB:FLOEL1 - READS  FLOW ELEMENT PROPERTY DATA,                                CALL CXRZER('flow passage length'.LENGTH,1,'GT',ERR)
C              UPDATES SYSTEM BANDWIDTH MSBAN,                                  IF(ERR)  GO TO 999
C              WRITES FLOW ELEMENT DATA TO LOGICAL UNIT ND1,  AND
C              REPORTS ELEMENT DATA TO RESULTS OUTPUT FILE                      CALL ZEROR(DIFF,NSSPE,1)
                                                                                CALL FREERCD'.DIFFd),NSSPE)
      INCLUDE 'IOCOM.INC'                                                        CALL CXRZER('dispersal coe.',DIFF,NSSPE,'GE'.ERR)
      INCLUDE 'CNTCOM.INC'                                                      IF(ERR)  GO TO 999
      REAL'S EFF(NSSPE),  DIFF(NSSPE),  GENR(NSSPE).MASSL.LENGTH,FACTOR
      INTEGER KSEO (NSNOD. NSSPE), LN (2) , LS (1), NEL.
      CHARACTER TYPE*4,TYPEON4
      LOGICAL ERR
      SAVE TYPEON
C	VARIABLE	DESCRIPTION-
    TYPE*4       :  ELEMENT TYPE:  'SIMP' OR  'CNDF'
    TYPEON*4 :  CURRENT ELEMENT TYPE "ON" OR ACTIVE
    MASSL        :  MASS PER UNIT  LENGTH -  'CNDF' ELEMENTS.
    LENGTH       :  FLOW PASSAGE LENGTH -  'CNDF' ELEMENTS.
    FACTOR       :  UPWIND FACTOR  - 'CNDF' ELEMENTS.
    ERR      :  ERROR  FLAG
                                      C       CALL ZEROR (GENR, NSSPE, 1)
                                      C       CALL FREER('G',GENR(1), NSSPE)

                                              FACTOR - l.ODO
                                              CALL FREERCF'.FACTOR.l)
                                              CALL CKRRNGC upwind  factor' , FACTOR, 1. 0. 000. 'LELE' . 1 . ODO, ERR)
                                              IF (ERR) GO TO 999
                                              IF(NOOATA)  FACTOR -  -l.ODO
                                                                               UPDATE SYSTEM BANDWIDTH
                                              DO 40 N-l. NSSPE
                                                LS(1)  - N
                                              CALL ELBAN (KSEO, NSNOD, NSSPE, LN.NENOD, LS.NESPE, MSBAN)
 C0.0 INITIALIZATION
 C
      NESPE - 1
      NENOD - 2
 C
 C1.0 GET ELEMENT TYPE
 C
      TYPE = 'SIMP1
      CALL FREECCT'.TYPE,4,1)
                                             	 WRITE ELEM. DATA TO ND1
                                              WRITE(ND1)  TYPE
                                              WRITE(ND1)  LN(1),LN(2),MASSL.LENGTH,FACTOR.
                                              (DIFF(N),N=1,NSSPE)
                                                                             	 UPDATE ELEMENT COUNT
                                              NFELM = NEL
                                          -UNDEFINED ELEMENTS
      IF((TYPE.NE.'SIMP').AND.(TYPE.NE.'CNDF')) THEN
        ERR   .TRUE.
        CALL ALERT(
     +   'ERROR: Flow element type '//TYPE//'  15 not available',
     +   'S'.'S')
        GO TO  999
      ENDIF
 C
 C2.0 REPORT  TABLE HEADER IF NECESSARY
 C
      IF((NEL.EQ.NESTRT).OR.(TYPE.NE.TYPEON))  THEN
        TYPEON = TYPE
                                                 SIMPLE ELEMENTS
        IF(TYPEON.EQ.'SIMP')  THEN
          IF(ECHO) WRITE(NTW,2020)
          WRITE(NOT.2020)
        ELSEIF(TYPEON.EQ.'CNDF')  THEN
          IF(ECHO) WRITE(NTH,2022)
          WRITE(NOT,2022)
        ENDIF
      ENDIF
                                              CONV-DIFF ELEMENTS
  2020 FORMAT(/,3X,'Num Type   I
  2022 FORMAT!/,3,'Num Type   I
     +Fact   Spec  Dlsp.Coef.',/)
C3.0 SIMPLE ELEMENTS
C
      IF(TYPE.EQ.'SIMP')  THEN
J  Spec   Fllt.Eff',/)
J  M/Length   Length
                       Upw.
c	REPORT ELEMENT DATA
        IF(FACTOR.NE.-l.ODO) THEN
          WRITE(NOT, 2040) NEL,TYPE, LN(1),LN(2),MASSL,LENGTH,
         FACTOR,SID(l),DIFF(l)
        ELSE
          WRITE(NOT,2041) NEL,TYPE, LN(1),LN(2),MASSL,LENGTH,
     +    '   default   '.SID(1),DIFF(1)
        ENDIF
        IF (NSSPE.GE.2)
     *    WRITE(NOT,2042)  (SID(N).DIFF(N).N-2.NSSPE)
        IF(ECHO)  THEN
          IF(FACTOR.NE.-l.ODO) THEN
            WRITE(NTW.2040) NEL.TYPE.LN(1).LN(2).MASSL,LENGTH.
     +      FACTOR,SID(1),DIFF(1)
          ELSE
            WRITE (NTW,2041) NEL,TYPE,LN(1),LN(2),MASSL,LENGTH,
     +      '   default  '.SID(1),DIFF(1)
        ENDIF
          IF (NSSPE.GE.2)
     *      WRITE(NTW,2042)  (SID(N),DIFF(N).N=2.NSSPE)
        ENDIF
 2040 FORMAT(2X,14.IX,A4,214.3(Gil.4),IX,A4.1(Oil.4))
 2041 FORMAT(2X,14.IX,A4.214.2(Gil.4),A11,IX,A4,1(Gil.4))
 2042 FORMAT((53X,A4,1(G11.4)))

      ENDIF

      RETURN

  999 CALL ALERT(
     ^'WARNING: All  flow element data has  been deleted.'.'S','S')
      NFELM  - 0
      CLOSE(ND1.  STATUS-'DELETE')
      RETURN
      END
                                                              Append  -6

-------
Indoor   Air  Quality  Model
Phase  III  Report
                                                  APPENDIX
   CONTAM87   FORTRAN   77   Source   Code
      SUBROUTINE KINELM
C SUB: KINELM - COMMAND
C
C
C
C .
C
C
C
C .
C
C
C .
C
KINELEM
K=nl
n2,n3,...
M,n5....

K=nl* , /,
'/
<
n6 I=n7 Kn8

C . END' )
TO READ ft WRITE KIN ELEMENT DATA TO FILE *.KIN

Kinetics elements:',/.
nl ** rate coefficient matrix ID number',/,
n2,n3,...B lat row rate coef. matrix',/,
n4,n5,...s 2nd row rate coef. matrix'./.
additional rows as necessary',/.


end of rate coef. matrices subgroup',/.
n6 = elera, number; n7 = node number',/.
n8 = rate coefficient matrix ID number',/.

      COMMON MTOT.N?,IAU)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOH.INC'

      INTEGER NK
      LOGICAL ERR,FOUND
      EXTERNAL KINELO
C	VARIABLE-
                     -DESCRIPTION	
C   ERR     ERROR FLAG
C   FOUND        FILE FOUND FLAG
C   KINELO        SUB. TO READ t WRITE KIN  ELEM DATA
C   NK      KATE COEF.  MATRIX  ID NUMBER
C   NENOD        NUMBER OF ELEMENT NODES
C   NESPE        NUMBER OF SPECIES PER ELEMENT (CURRENTLY=NSSPE)
C   NESTRT        FIRST ELEMENT NUMBER
C0.0 INITIALIZATION
C
      ERR = .FALSE.
      NENOD - 1

      IF(ECHO.OR.(MODE.EQ.'INTER'))  HXITE(NTH,2000)
      WRITE(NOT,2000)
 2000 FORMAT!/,' ===== KINELEM: KINETICS ELEMENTS')
C
C~1.0 CHECK TO SEE IF SYSTEM NODES  C  EQUATION NUMBERS ARE DEFINED
C
      CALL CXSYSU.ERR)
      IF(ERR)  THEN
        CALL ABORT
        RETURN
      ENDIF
C
C2.0 OPEN .KIN
C
      INQUIRE (FILE=FNAME(1:LFNAME)//'.KIN',EXIST=FOUND)

      IF((.NOT.FOUND).OR.(NKINEL.EQ.0))  THEN
        CALL NOPEN(ND1,(FNAME(1:LFNAME)//'.KIN'),'UNFORMATTED')
      ELSEIF(FOUND) THEN
        WRITE(NTH.2200)
        HRITEINOT,")
        WRITE(NOT,2200)
 2200   FORMAT I
     +  '    ""  NOTE: Additional kin.  elements being added to system.')
        OPEN(ND1,FILE-(FNAME(1:LFNAME)//'.KIN').STATUS-'OLD',
     +  FORM-'UNFORMATTED')
        CALL APPEND(ND1)
      ENDIF
C
C--3.0 GET RATE COEFFICIENT ARRAYS
C
      CALL DELETE('TEMP')
      CALL OEFINR('TEMP'.MPTEMP.NSSPE.l)

   30 CALL FREE
      IF (ECO)  GO TO 40
      NK - 0
      CALL FREEICK'.NK, 1)
      CALL CKIRNGCrate coef. matrix ID', NK. 1, 0, ' LTLE', 9. ERR)
      IF(ERR)  GO TO 999
      CALL DELETE('KIK'//CHAR(NK+48))
      CALL DEFINR!'KIK'//CHAR(NK+48), MPKIK(NK).NSSPE.NSSPE)
      CALL GETKIK(IA(MPKIK(NK)),IA(MPTEMP),NK,ERR)
      IF(ERR)  GO TO 999
      GO TO 30
C
C4.0 GENERATE ELEMENT DATA; REPORT BANDWIDTH
C
   40 WRITE(NTW,2400)
      HRITEINOT.2400)
 2400 FORMAT!/,'    Kinetics Elements'.//.6X.'Elem
      IF(ECHO) WRITE(NTW,2410)  MSBAN
      HRITE(NOT.)
      HRITEINOT,2410) MSBAN
 2410 FORMAT!'    "" NOTE: Current  system bandwidth Is:1,  IS)
C
C--5.0 ORDERLY COMPLETION: CLOSE FILE ND1; SKIP TO "END"
C
      CLOSE (HDD

      IFIMOOE.EC.'INTER') RETURN
  500 IF(EOC) RETURN
        CALL FREE
      GO TO 500
C
C ABORT COMMAND
C
  999 CALL ALERT<
     ('WARNING:  All kinetics element data has been deleted.','$','$')
      NKINEL=0
      CLOSE (ND1,  STATUS*>'DELETE')
      DO 900 NK-1,9
  900 CALL DELETE('KIK'//CHAR(NK+48) )
      CALL DELETECTEMP')
      CALL ABORT
      RETURN
      END
      SUBROUTINE GETKIK(XIK,TEMP,NK, ERR)
CSUB:GETKIK - READS AND REPORTS  KINETICS RATE COEF.  ARRAYS

      INCLUDE 'CNTCOM.INC1
      INCLUDE 'IOCOM.INC'

      REAL'S KIK(NSSPE.NSSPE),  TEMP(NSSPE)
      INTEGER NK
      LOGICAL ERR

      IF (ECHO) HRITE(NTW,2000)  NK
      WRITE(NOT,2000) NK
 2000 FORMAT!/,'   = Kinetics  Rate Coef. Matrix:  KlnlD  =',13)
C
C1.0 READ  IK)
C
      DO 110 1-1,NSSPE
        IF(MODE.EQ.'INTER')  WRITE(NTW,2100) I
 2100    FORMAT('    Enter terms In row number: '.14)
        CALL FREE
        IF(EOD) THEN
         CALL ALERT!
     +    'ERROR: Data expected. Data subgroup terminator found.',
     +    'S'.'S'I
         ERR ' .TRUE.
         RETURN
        ENDIF
        CALL FKEERC ', TEMP,NSSPE)
        DO 100 J=l. NSSPE
  100   KIK(I.J) = TEMP(J)
  110 CONTINUE
C
C2.0 REPORT FIVE COLUMNS AT A TIME
C
      DO 200 J1<=1,NSSPE,5
        J2 = MIN(NSSPE,Jl+4)
        IF(ECHO) WRITE(NTH, 2200)  (SID(J),J-J1,J2)
        RITE(NOT,2200)  (SID(J) , J=J1,J2)
 2200   FORMAT!/, 12X, 5 (:3X,A4.6X

        DO 200 1=1,NSSPE
          IF(ECHO) WRITE(NTW,2210)  SID (I) , (KIK (I. J) . J-J1. J2)
         HRITEINOT, 2210) SID(I), (KIK (I, J) , J-J1, J2)
  200 CONTINUE
 2210 FORMAT(6X,A4,2X,S(:G11.3,2X)|
      RETURN
      END
      SUBROUTINE KINELO(NEL,LN,ERR)
CSUB:KINELO  - READS ADDITIONAL KINETICS ELEMENT DATA,
C              WRITE KINETICS ELEMENT DATA TO FILE ND1,
C              UPDATES SYSTEM BANDWIDTH, AND REPORTS ELEMENT DATA

      COMMON MTOT,NP,IA(1)

      INCLUDE  'IOCOM.INC'
      INCLUDE  'CNTCOM.INC1

      LOGICAL  ERR
      INTEGER  LN(1), NK

      NENOD -  1
      NESPE =  NSSPE
                                                      Node   KlnlD')
                                                                       C
C	'TEMP' STORES  SPECIES CONNECTIVITY ARRAY, LS (NSSPE),  USED BY  ELBAN  C1.0 GET RATE COEFFICIENT MATRIX ID
      CALL DELETE('TEMP')
      CALL DEFINICTEMP',MPTEMP.NSSPE,1)
      DO 42 N-l, NSSPE
   42 IAIHPTEMP+N-1) = N

      NESTRT  NKINEL+1
      CALL ELGEN(KINELO,NENOD.NESTRT.NSNOD,ERR)
      IF(ERR)  THEN
        CALL ABORT
        RETURN
      ENDIF

      CALL DELETE I'TEMP'I
      CALL FREEI CK'.NK, 1)
      IFIMPKIXINK).EQ.0) THEN
       .CALL ALERTI'ERROR: Rate coefficient matrix not defined',
     *  'S'.'S')
        ERR = .TRUE.
        RETURN
      ENDIF

  -2.0 WRITE DATA  TO ND1

      HRITEIND1) LN(l),  NX

  -3.0 UPDATE SYSTEM BANDWIDTH (NOTE:  IA(MPTEMP)=LS(NSSPE)  )
                                                            Append  -7

-------
Indoor  Air  Quality   Model
Phase  III  Report
                                                                    CONTAM87   FORTRAN
                                                 APPENDIX
                                           77   Source   Code
      CALL ELBAN(IA(MPKSEQ),NSNOD.NSSPE,LN.NENOD,IA(HPTEMP).NESPE.MSBAN)
 C
 C4.0 REPORT DATA
 C
      IF(ECHO)  WRITE(NTH,2000) NEL,  LN(1), NK
      KRITE (NOT. 2000) NEL. LN(1).  NX
                                                                        CALL ABORT
                                                                        RETURN
                                                                      ENDIF

                                                                      CLOSE(N01)
                                                                      IF(NKINEL.GT.O)  CLOSE(ND2)
2000 FORMAT(6X,I4,4X,I4,4X,I4)
NKINEL = NEL
RETURN
END
SUBROUTINE FORMFO
C  SUB:FORHFO - COMMAND TO FORM CONTAM. DISPERSAL MASS TRANS ARRAY [N]
C
C .' FORM- [Ml Fceee Form (F| , cccc - FULL or BAND',/,
C .' n2,n3,M WnS n2,n3,n4 = elem: first, last, Incr.1,/,
C .' ... n5  element flow rate',/.
C .' END')
C
IMPLICIT REALM (A-H.O-Z)
COMMON MTOT. NP.IA(l)
INCLUDE 'IOCOM.INC1
INCLUDE 'CNTCOM.INC'
LOGICAL ERR
C
C 5.0 DELETE ARRAYS
C
CALL DELETE (' TEMP '
CALL DELETE CCONT'
CALL DELETE ('VCD '
CALL DELETE ('EFF '
CALL DELETE ('DIFF'
CALL DELETE COENR'
CALL DELETE ('HE '
RETURN
END
SUBROUTINE STEADY
C SOLUTION (C) IS WRITTEN OVER (E)
C
C
C . STEADY Steady state solution.'./.
C . ... n4 H element flow rate',/,
C . ...  n8,n9, . . . *> spec. cone, or gen. rate* , /,
C . END',//,
      ERR - .FALSE.
 C
 C0.0 WRITE HEADER  AND READ ARRAY FORM
 C
      WRITE(NOT. 2000)
      IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTW,2000)
 2000 FORMAT)/,
     t, a== FORM-IW]: FORM MASS TRANSPORT MATRIX  [W] ')

      FORM = 'FULL'
      CALL FREECCF'.FORM,4,1)
      IF(FORM.EQ.'FULL') THEN
        IF (ECHO) WRITE (NT*. 2002)
        WRITE(NOT,*)
        WRITE(NOT,2002)
 2002   FORMATC   * NOTE: [W] being formed In FULL form.')
      ELSEIF(FORM.EQ.'BAND') THEN
        IF (ECHO) WRITE(NTW,2004)
        WRITE(NOT,)
        WRITE(NOT,2004)
 2004   FORMAT!'   ** NOTE: (W| being formed In BAND form.')
      ELSE
        CALL ALERT('ERROR: '//FORM//' not defined.','$'.S')
        CALL ABORT
        RETURN
      ENDIF
 C
 C--1.0 CHECK IF  FLOW SYSTEM AND ELEMENT DATA ARE DEFINED
 C
      CALL CKSYS(2,ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF
 C
 C2.0 DEFINE AND  INITIALIZE ARRAYS
      CALL DELETE('TEMP'
      CALL DELETE CCONT'
      CALL DELETE!'VCD  '
      CALL DELETE!'EFF  '
      CALL DELETE('DIFF1
      CALL DELETE I'GENR'
      CALL DELETE CHE   '
      CALL DELETE('W   '
      IF (FORM.EQ.'FULL') CALL DEFINRCW
      IF (FORM.EQ.'BAND') CALL DEFINRCW
      CALL DEFINRCWE   ' , MPWE.NFELM, 1)
      CALL DEFINR COENR', MPGENR. NSSPE. 1)
      CALL DEFINR CDIFF'.MPDIFF, NSSPE, 1)
      CALL DEFINRCEFF  ',MPEFF.NSSPE,1)
      CALL DEFINR('VCD  ',MPVCD,NSNCO,1)
      CALL DEFINRCCONT',MPCONT,NSNOD,1)
                                                                       IMPLICIT REAL*8(A-H, 0-Z)
                                                                       COMMON MTOT.NP.IAd)

                                                                       INCLUDE 'IOCOH.INC'
                                                                       INCLUDE 'CMDCOM.INC'
                                                                       INCLUDE 'CNTCOM.INC'

                                                                       COMMON /STDCOM/ MPEDAT

                                                                       LOGICAL ERR

                                                                       ERR - .FALSE.

                                                                       WRITE(NOT,2000)
                                                                       IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTW, 2000)
                                                                  2000  FORMAT!/,'  -= STEADY: STEADY STATE SOLUTION')

                                                                 C
                                                                 C1.0 CHECK IF FLOW SYSTEM AND ELEMENT DATA ARE DEFINED I AVAIL
                                                                 C
                                                                       CALL CKSYSI2.ERR)
                                                                       IF(ERR) THEN
                                                                        CALL ABORT
                                                                        RETURN
                                                                       ENDIF
                                                                 C
                                                                 C2.0 DEFINE AND INITIALIZEARRAYS
                                                                 C
                                   ',MPF,NSEQ,NSEQ>
                                   1,MPF.NSEQ. 2'MSBAN-l)
CALL DELETE CEDAT'
CALL DELETE CCONT 
CALL DELETE!' VCD '
CALL DELETE! 'EFF '
CALL DELETE! 'DIFF'
CALL DELETE!' GENR'
CALL DELETE CE
CALL DELETE CHE '
CALL DELETE CF '
CALL DEFINR ('F '
CALL DEFINRCWE '
CALL DEFINRCE '
CALL DEFINR ('GENR'
CALL OEFINRCDIFF'
CALL DEFINR I ' EFF '
CALL DEFINR C VCD '
CALL DEFINR CCONT'
CALL DEFINR CEDAT'
)
)
)
)
)
)
)
)
>
,MPF,NSEQ,2*MSBAN-1)
.KPWE.NFELM, 1)
, MPE.NSEQ, 1)
.MPGENR, NSSPE, 1)
.MPOIFF, NSSPE, 1)
, HP EFF, NSSPE. 1)
.HPVCD, NSNOD. 1)
, HP CONT, NSNOD, 1)
.MPEDAT, NSSPE, 1)
 C
 C--3,
 C
 C
 C4.
 C
0 GET ELEMENT FLOW RATES (WE)

 CALL ZEROR(IA(MPWE),NFELM.1)
 CALL READWE(ERR)
 IF(ERR)  THEN.
   CALL ABORT
   RETURN
 ENOIF

0 FORM (W|

 OPEN (FNAME (1: LFNAME) //'.KIN') ,STATUS='OLD',
+FORH-'UNFORMATTED')
 ENDIF

 CALL FORMFIIA(MPKSEQ),IA(MPF).IA(MPHE),FORM,ERR)
 IF(ERR)  THEN
C
C3.0 GET ELEMENT FLOW RATES  (WE)
C
      CALL ZEROR(IA(MPWE),NFELM,1)
      CALL README(ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF
C
C--4.0 FORM  (F)
C
      OPEN(N01,FILE=(FNAME(1:LFNAME)//'.FEL'),STATUS='OLD'
     +FORM-'UNFORMATTED')

      IF (NKINEL.GT.O)  THEN
      OPEN(ND2,FILE"(FNAME(1:LFNAME)//1.KIN'),STATUS-'OLD'
     +FORM-'UNFORMATTED'I
      ENDIF
                                                                            CALL FORMF(IA(MPKSEO),IA(MPF),IA(MPWE),
                                                                            IF(ERR)  THEN
                                                                              CALL ABORT
                                                                              RETURN
                                                                            ENDIF

                                                                            CLOSE(ND1)
                                                                            IFINXINEL.GT.O) CLOSE (ND2)
                                                                                                                  'BAND',ERR)
                                                            Append  -8

-------
Indoor   Air  Quality  Model
Phase  III  Report
                                                                                                                         APPENDIX
                                                                         CONTAM87   FORTRAN   77   Source   Code
c
C6.
C

c
C--7.
C
c
C--5.0 FORM (E)
C
      CALL ZEROR(IA(HPE),NSEQ, 1)
      CALL FORMEX(ERR)
      IF(EKR)  THEN
        CALL ABORT
        RETURN
      ENDIF

     0 MODIFY  (E) AND  [F] FOR PRESCRIBED CONCENTRATIONS

      CALL MODIF(IA(MPKSEQ),IA(MPF),IA(MPE))

     0 SOLVE

      CALL FACTCA(LMM?F),NSEQ,MSBAN,ERR)
      IF(ERR)  THEN
        CALL ABORT
        RETURN
      ENDIF
      CALL SOLVCA (IA (MPF) . IA (MPE) . NSEQ. MSBAN, ERR)
      IF (ERR)  THEN
        CALL ABORT
        RETURN
      ENDIF
C
C8.0 REPORT  SOLUTION
C
      IF(ECHO) WRITE(NTH.2800)
      WRITE(NOT.2800)
 2800 FORMAT!/,'   == Response: Node Concentrations')

      CALL RPRTEN(IA(MPE),IA(MPKSEO))
C
C9.0 DELETE  ARRAYS
C
      CALL DELETE CEDAT1)
      CALL DELETE('CONT')
      CALL DELETE('VCD  ')
      CALL DELETE('EFF  ')
      CALL DELETE('DIFF')
      CALL DELETE CGENR')
      CALL DELETE CE    ')
      CALL DELETE ('HE   ')
      CALL DELETECF    ')

      RETURN
      END

c	FORMEX
      SUBROUTINE FORMEX(ERR)
CSUB:FORMEX  - READS I REPORTS NODAL CONTAMINANT EXCITATION DATA

      COMMON MTOT.NP.IAU)

      INCLUDE  'IOCOM.INC'
      INCLUDE  'CNTCOM.INC'

      LOGICAL  ERR
      EXTERNAL EXDATO

      WRITE(NOT,2100)
      IF(ECHO.OR.(MODE.EQ.'INTER'))  WRITE(NTH.2100)
 2100 FORMAT!/,
     +'     Excitation: Contaminant Concentration or Generation')

      CALL DATGEN(EXDATO,NSNOD,ERR)

      CALL RPRTEN (IA (MPE) , IA (MPKSEQ) )

      RETURN
      END
      SUBROUTINE EXDATO(N.ERR)
CSUB:EXDATO - CALLS  EXDAT1 PASSING ARRAYS
C
      COMMON MTOT.NP.IAd)

      INCLUDE 'CNTCOM.INC'

      COMMON' /STDCOM/  MPEDAT
      LOGICAL ERR

      CALL EXDAT1(IA (MPE).IA(MPKSEQ),IA(MPEDAT) ,N. ERR)

      RETURN
      END
        ELSE
          WRITE(NTH,2000) N
          NRITE(NOT,)
          WRITE(NOT,2000) N
  000     FORMAT(' "* ERROR:  Node  ',15,'
          ERR -  .TRUE.
          RETURN
        ENDIF
   10 CONTINUE

      RETURN
      END
                                                                                                                Is not a defined  flow node.')
                                                                             SUBROUTINE MODIF(XSEQ,F. E)
                                                                       CSUB:MODIF - MODIFIES [F|  AND (E) FOR C-PRESCRIBED DOFS

                                                                             INCLUDE 'CNTCOM.INC'

                                                                             REAL'S F(NSEQ,2*MSBAN-1),E(NSEQ)
                                                                             INTEGER KSEQ(NSNOD,NSSPE)

                                                                             DO 10 N-l,NSNOD
                                                                             DO 10 M=l, NSSPE
                                                                               NEQ - KSEOIN.M)
                                                                               NNEQ - ABS(NEQ)
                                                                               IF(NEO.LT.O) THEN
                                                                                 FINKEQ.MSBAN) - F(NNEQ,MSBAN)!.OD15
                                                                                 E(NKEO)  E(NNEQ)*F(NNEQ,MSBAN)
                                                                               ENDIF
                                                                          10 CONTINUE
                                                                             RETURN
                                                                             END
                                                                             SUBROUTINE TIMCON
                                                                          SUB:TIMCON - COMMAND TO FORM CCNTAM. DISPERSAL EIGENVALUE PROBLEM
                                                                       C
                                                                       C
                                                                       C
                                                                       C
                                                                       c
                                                                       c
                                                                       c
                                                                       c
                                                                       c
                                                                       c
                                                                       CHELP  LIST
                                                                       C
                                                                       C
                                                                       c
                                                                       c
                                                                       c
                                                                       c-
                                                                       c
                                                                       c
                                                                       c
              [[V|-1[F| - (1/THIHE) =  (0)

             IIHERE: [V|  - FLOW VOLUMETRIC MASS MATRIX (DIAGONAL)
                    [F|   FLOW SYSTEM  FLOW MATRIX
                    (E)  - (RIGHT)  EIGENVECTORS
                     T   = CONTAM.  DISPERSAL TIME CONSTANTS

               TO EVALUATE TIME CONSTANTS. EIGENVECTORS ARE NOT FOUND.
        TIMECOHS E=nl
        n2,n3,n4 W=n5
        END')
Time constant solution, nl  epsllon',/,
 n2.n3.n4   elem: first, last,  Incr.'./,
 nS - element flow rate',/.
    MPTC TC (NSEQ) TEMPORARY ARRAY FOR STORAGE OF TIME CONS
      IMPLICIT REAL'S(A-H.O-Z)

      COMMON MTOT.NP.IAd)

      INCLUDE 'IOCOM.INC1
      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR

      ERR =  .FALSE.
C
C0.0 WRITE HEADER AND READ PRECISION
C
      NRITE(NOT,2000)
      IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTH,2000)
 2000 FORMAT!/.
     +' ran riMECONS: TIME CONSTANTS - CONTAMINANT DISPERSAL  SYSTEM ')

      EP1 = El'
      CALL FREERCE'.EPl.l)
      HRITE(NOT.2010) EP1
      IF (ECHO) HRITE (NTH, 2010)  EP1
 2010 FORMAT(/'   Ba Convergence parameter, epsllon: ',  G10.3)
C
ci.o CHECK :;F FLOW SYSTEM AND ELEMENT DATA ARE DEFINED
c
      CALL CK!iYS(2.ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF
      SUBROUTINE EXDAT1(E,KSEQ.EDAT.N, ERR)
CSUB:GDAT1 - READS CONTAMINANT EXCITATION DATA
C
      COMMON MTOT.NP.IAd)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'

      REAL'S E(NSEQ).  EDAT (NSSPE)
      INTEGER KSEQ(NSNOD,NSSPE)
      LOGICAL ERR

      CALL ZEROR(EDAT.NSSPE,1)
      CALL FREER I'G',EDAT, NSSPE)

      DO 10 M=l,NSSPE
        NEQ = ABS (KSEQ (N, M))
        IFfNEQ.NE.O) THEN
          E(NEQ) - EDAT(H)
                                                                       C2.0 DEFINE ARRAYS
                                                                       C
                                                                            CALL DELETE('TEMP
                                                                            CALL DELETE ('CONT
                                                                            CALL DELETE)'VCD
                                                                            CALL DELETE I'EFF
                                                                            CALL DELETE CDIFF
                                                                            CALL DELETE CGENR
                                                                            CALL DELETE('TC
                                                                            CALL DELETE CVM
                                                                            CALL DELETE CHE
                                                                            CALL DELETE)'F
                                                                            CALL DEFINRCF
                                                                            CALL DEFINRCWE
                                                                            CALL DEFINRCVM
                                                                            CALL DEFINRCTC
                                                                            CALL DEFINR CGENR
                                                                            CALL DEFINR CDIFF
                                                                            CALL DEFINRCEFF
                                                                            CALL DEFINRCVCD
                       . MPF, NSEQ.NSEQ)
                       ,MPWE.NFELM, 1)
                       .MPVM.NSEQ. 1)
                       ,MPTC.NSEQ, 1)
                       ,MPGENR,NSSPE. 1)
                       ,MPDIFF.NSSPE,1)
                       ,HPEFF.NSSPE,1)
                       ,HPVCD.NSNOD,1)
                                                             Append  -9

-------
Indoor   Air  Quality  Model
Phase  III  Report
   CONTAM87   FORTRAN
                                                  APPENDIX
                                           77   Source   Code
      CALL DEFINRCCONT'.MPCONT.NSNOO.l)
 C
 C3.0 GET ELEMENT FLOW RATES  {ME)
 C
      CALL ZERORUA(MPNE).NFELM,1)
      CALL README(ERR)
      IF(ERR) THEM
        CALL ABORT
        RETURN
      ENOIF
 C
 C4.0 FORM  [F|
 C
      OPEN(NDl,FILE-(FNAME(l:LFNAME)//'.FEL'),STATUSa'OLD',
     +FORM-'UNFORMATTEO')

      IF(NKINEL.GT.O)  THEN
      OPEN(ND2,FILE-(FNAHE(1:LFNAHE)//'.KIN'),STATUS-'OLD',
     +FORM-'UN FORMATTED')
      ENDIF

      CALL FORMF (IA (HPKSEQ), IA (MPF), IA (HFWE) , ' FULL'. ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENOIF

      CLOSE (HDD
      IF(NKINEL.GT.O)  CLOSE(ND2)
 C
 C5.0 FORM VOLUMETRIC MASS MATRIX
 C
      CALL ZEROR(IA(MPVM),NSEQ.l)
      CALL FORHVM (IA (MPKSEQ), IA (M?V). IA (HPVCD). IA (MPVM))
 C
 C6.0 COMPUTE i REPORT NOMINAL TIME CONSTANTS
 C
      IF(ECHO) WRITE(NTH,2600)
      MRITE(NOT.2600)
 2600 FORMAT!/.1    Nominal  Tims Constanta')
      CALL ZEROR(IA(MPTC),NSEQ,1)
      CALL NOMTC (IA (MPKSEO), IA (MPVM) , IA (MPF) . IA (MPTC))
      CALL RPRTEN(IA(MPTC).IA.HDT

OPTIONALLY EQUAL STEP TIME HISTORIES MAY  BE GENERATED
        FLONDAT  [T-nl,n2,n3l  Generate element Clow time histories.',/,
        TIME=nl                nl = time'./.
        nl,n2,n3 N=n4          nl,n2,n3  node: first, last, Incr.',/,
        ...                    n4  element  mass  flow rate.',/.
        :'./,
        END',//,
      IMPLICIT REAL*8(A-H, 0-Z)

    CAL-SAP:  DATA I COMMON STORAGE

      COMMON  MTOT.NP.IAd)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'
c




C FLODAT: DATA t COMMON STORAGE
C
C    D I C T
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c

I 0 N A 1
POINTER VARIABLE


TIME (3)
MPNE ME (NFELM)

TIME

DAT(l)





DAT (2)



HIST





DESCRIPTION

! START TIME, ENDTIME, TIMESTEP
: CURRENT ELEMENT MASS FLOH VALUES

O R  DATA

* - - - Time histories of excitation data
I defined as step-wise functions of









are
time
*- using arbitrary values or, optionally.
1
*_
1
- - *-
TM(2)

MPTDAT TDATI2)
MPHDT1 HDT1 (NFELM)
MPNDT2 NDT2 (NFELM)
generated Intermediate values of
equal step size.

1 _ 	 	
TM(1)

: CURRENT ARBITRARY TIME VALUES
: ELEM. FLOH DATA AT TDAT(l)
: ELEM. FLOH DATA AT TDAT(l)









                                                            Append  -10

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                  APPENDIX
   CONTAM87   FORTRAN  77   Source   Code
      COMMON /FLODT/ MPTDAT.MPHDT1.MPHDT2
      REAL'S TIME(3)
      LOGICAL ERR

      ERR  .FALSE.
      WRITE(NOT.2000)
      IF(ECHO.OR.(MODE.Ed.'INTER')) WRITE(NTH,2000)
 2000 FORMAT!/,'   FLOMDAT: ELEMENT FLOW TIME HISTORY DATA')
C
C1.0 CHECK TO SEE IF PERTINENT DATA HAS BEEN DEFINED
C
      CALL CKSYS(2,ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF
C
C2.0 GET DATA GENERATION  CONTROL DATA
C
      TIME(l) - O.ODO
      TIME(2) - O.ODO
      TIME(3) - O.ODO
      CALL FREER CT', TIME (1) , 3)
      CALL CKIZERCtlme step', TIME (3) . 1,'GE', ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ELSEIF(TIME(3).GT.O.ODO) THEN
        IF (TIME (2) .LT.TIME(D) THEN
          CALL ALERT(
     +    'ERROR: Final time  must be greater than Initial time.',
     +    '$','$')
          CALL ABORT
          RETURN
        ENDIF

        IF (ECHO)  WRITE (NTH, 2220)
        WRITE(NOT,2220)
 2220   FORMAT!/,'    = Generation Control Variables')
        IF (ECHO)  WRITE (NTH, 2230)  (TIME (I) , 1=1, 3)
        WRITE(NOT,2230)  (TIME(I),1=1,3)
 2230   FORMAT(/,
     .'      Initial time	  '.G10.3,/,
     .'      Final  time 	  '.G10.3,/,
     .'      Time step increment 	  *,G10.3)
      ENDIF
C
C3.0 OPEN .WDT
C
      CALL NOPENIND1, (FNAMEU :LFNAME) //' .WDT'), 'UNFORMATTED')
C
C4.0 READ < GENERATE FLOW DATA
C
      WRITE(NOT,2400)
      IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTH,2400)
 2400 FORMAT!/,'     Element  Mass Flow Time History Data')
C
C	4.1 DEFINE t  INITIALIZE ARRAYS
C
      CALL DELETE CTDAT')
      CALL DELETE CWDT1')
      CALL DEFINR('HDT1',MPHDT1,NFELM,1)
      CALL DEFINR('TDAT',MPTDAT,1,2)
      CALL ZEROR(IA(MPHDT1),NFELM,1)
      CALL ZEROR(IA(MPTDAT),1,2)
      IF(TIME(3).GT.O.ODO)  THEN
        CALL DELETE('HDT2')
        CALL DELETE CHE  )
        CALL DEFINRCHE  ' .MPHE.NFELM, 1)
        CALL DEFINR('WDT2',MPWDT2,NFELM,1)
        CALL ZEROR(IA(KPNDT2),NFELM, 1)
        CALL ZEROR(lA(MPNE),NFELM,1)
      ENDIF
C
C4.2 GENERATE VALUES ( WRITE TO .HDT
C
      IF(TIME(3).GT.O.ODO)  THEN
        CALL GENWD1(IA(MPHE),IA(MPTDAT),IA(MPHDT1),IA(MPHDT2),TIME,ERR)
        IF(ERR)  THEN
          CALL ABORT
          RETURN
        ENDIF
      ELSE
        CALL GENHD2 (IA (MPTDAT). IA (MPWDT1) , ERR)
        IF(ERR)  THEN
          CALL ABORT
          RETURN
        ENDIF
      ENDIF
C--5.0 DELETE ARRAYS,  CLOSE ELEMENT FLOB DATA FILE,  SKIP TO -END"
C
      CALL DELETE CHE  ')
      CALL DELETE CHDT2')
      CALL DELETE CHDT1'I
      CALL DELETE CTDAT')

      CLOSE (ND1)

      IF(MODE.EQ.'BATCH')  THEN
   500   IF(EOC) RETURN
        CALL FREE
        GO TO SOO
      ENDIF

      RETURN
      END

c	GENWD1
      SUBROUTINE GENWD1(HE,TDAT.HDTl,WDT2.TIME, ERR)
CSUB:  GENWD1  - GENERATES ELEMENT MASS  FLOW DATA, AT EQUAL TIME STEP
C               INTERVALS, FROM GIVEN ARBITRARY DISCRETE TIME DATA

      IMPLICIT  REAL*8(A-H,O-Z)

      INCLUDE  'ICCOM.INC'
      INCLUDE  'CNTCOM.INC'
C
C	FLOHDAT:  DATA t COMMON STORAGE
C
      COMMON /FLODT/ MPTDAT,HPWDT1,HPKDT2
      LOGICAL ERR

   - GENHD1: DATA I COMMON STORAGE

      REAL'8 NF. (NFELM), TDAT (2), WDT1 (NFELM) ,HDT2 (NFELM) , TIME (3)

   1.0 GET FIRST TWO TIME HISTORY RECORDS

       CALL  GEl'TDT(TDAT)
       IF(EOC)  THEN
         CALL ALERT('ERROR: Insufficient data.','$','S')
         ERR -  .TRUE.
         RETURN
       ENDIF
       CALL  GETWDT(WDT1,HDT2.ERR)
       IF(ERR)  RETURN

       CALL  GETTDT(TDAT)
       IF(EOC)  THEN
         CALL ALERT('ERROR: Insufficient data.'. 'S', 'S')
         ERR -  .TRUE.
         RETURN
       ELSEIF(TDATIl).LT.TDAT(21) THEN
         CALL ALERT('ERROR: Time data out  of sequence.','$','$')
         ERR -  .TRUE.
         RETURN
       ENDIF
       CALL  GETWDT(WDT1,WDT2.ERR)
       IF(ERR)  RETURN

   2.0 GENERATION TIME  LOOP

      DO 200 T-TIME(1),TIME(2).TIME<3)

  2.1  UPDATE  FLOW TIME HISTORY DATA IF NEEDED

   20 IF(T.GT.TDAT(D)   THEN
        CALL GETTDT(TDAT)
        IF(EOC) THEN
          CALL  ALERT('ERROR: Insufficient  data.','$','$')
          ERR = .TRUE.
          RETURN
        ELSEIF(TDATd) .LT.TDAT(2)|  THEN
          CALL  ALERTCERROR: Time data out  of sequence. '.'S'.'S'l
          ERR = .TRUE.
          RETURN
        ENDIF
        CALL GETWDT(WDT1,WDT2.ERR(
        IF(ERR) RETURN
        GO TO 20
      ENDIF

   -2.2  COMPUTE INTERPOLATION FRACTION

      XT = (T--TDAT(2))/(TDAT(1)-TDAT(2)(

   2.3  COMPUTE (WE(T) )

      DO 23  N'-l,NFELM
      HE(N)  - HDT2(N) -f XT* (HDT1 (N)-HDT2 (N) )
   23 CONTINUE
C
C	2.4  WRITE TIME, I WE (TM TO ND1
C

      WRITE (HDD T
      WRITE(ND1)  (WE(I),1=1,NFELM)
  200 CONTINUE

  3.0 WRITE ONE  ADDITIONAL TIME VALUE TO DISK

      WRITE(ND1)  T

    '  RETURN
      END
                                                                             SUBROUTINE OETWDT(WDT1,HDT2,ERR)
                                                                         SUB: GETHDT - UPDATES ELEMENT  FLOW DATA VALUES
      INCLUDI! 'CNTCOM.INC'

      LOGICAL ERR
      REAL'S WDT1(NFELM), HDT2(NFELM)
      EXTERNAL WDATO
C
C1.0 UPDAT1! 'OLD' DATA VALUES; INITIALIZE 'NEW'  DATA VALUES
C
      DO 10 N=l.NFELM
        WDT2 (N)  - HDT1 (N)
        WDT1(N)  a 0.ODO
   10 CONTINUE
C
C2.0 READ NEW VALUES
C
      CALL DATGENIHDATO,NFELM,ERR)
      IF(ERR)  RETURN
                                                            Append  -1  1

-------
Indoor  Air  Quality  Model
Phase   III   Report
                                                 APPENDIX
   CONTAM87   FORTRAN   77   Source   Code
CALL RPRTNO(HDTKl), NFELM, 'Elem')
RETURN
END
SUBROUTINE NOATO (N , ERR)
C  SUB:NDATO - CALLS WDAT11 PASSING ARRAYS
C
COMMON MTOT.NP.IAU)
INCLUDE 'CNTCOM.INC'
COMMON /FLODT/ MPTDAT, MPNDT1 , MPHDT2
LOGICAL ERR
CALL WDAT1 (IA (MPWDT1 ) , NFELM, N)
RETURN
END
SUBROUTINE WDAT1 (WDT1, NFELM, N)
C SUB:DAT1 - READS ELEMENT MASS FLOW RATE TIME HISTORY DATA
C
REAL'S NDTI (NFELM)
CALL FREER('W',WDTl(N).l)
RETURN
END
SUBROUTINE GENWD2 (TDAT, WDT1, ERR)
C SUB: GENWD2 - GENERATES ELEMENT MASS FLOW DATA. AT GIVEN TIME STEP
C INTERVALS, FROM GIVEN DISCRETE TIME DATA
IMPLICIT REAL'S (A-H.O-Z)
INCLUDE 'ICCOM.INC'
INCLUDE 'CNTCOM.INC'
I 0 0 0 0 1



.' :'./.
.' END'.//.
IMPLICIT REAL'S (A-H.O-Z)
COMMON MTOT.NP.IA(l)
INCLUDE 'ICCOM.INC'
INCLUDE 'CNTCOM.INC'

POINTER VARIABLE DESCRIPTION
TIME (3) : START TIME, ENDTIME, TIMESTEP
MPE E (NSEQ, NSSPE) : CURRENT EXCITATION VALUES
TIME HISTORY DATA
1 defined as atop-wise functions of time
*- using arbitrary values or. optionally,
t generated Intermediate values of
*- equal step size.
1
DAT (2) - - -
TM(2) TM(1)
MPTDAT TDAT(2) : CURRENT ARBITRARY TIME VALUES
MPEDT1 EDT1 (NSSPE, NSNOD) : EXCITATION DATA AT TDAT(l)
MPEDT2 EDT2 (NSSPE. NSNOD) : EXCITATION DATA AT TDATI2)
COMMON /EXCDT/ MPTDAT, MPEOT1, MPEDT2
REAL'S TIME (3)
LOGICAL ERR
ERR - .FALSE.
WRITE (NOT. 2000)
 C	 FLOHDAT:  DATA t COMMON STORAGE
 C
      COMMON /FLODT/ MPTDAT,HPWDT1.MPWDT2
      LOGICAL ERR
      EXTERNAL HDATO
 C  
 C	GENHD2: DATA I COMMON STORAGE
 C
      REAL'S TDAT(2),MDT1(NFELM)
 C1.0 GET FIRST TIME HISTORY RECORD  ( TDAT(l),  WDT1 (NFELM) )
 C
      CALL GETTDT(TDAT)
      IF(EOC)  RETURN
      TDAT(2)  - TDAT(l)
      CALL ZEROR(WDT1,NFELM,1)
      CALL DATGENIMDATO,NFELM,ERR)
      IF(ERR)  RETURN
      CALL RPRTNO(WDT1(1),NFELM,'Elem')
      WRITE(ND1)  TDAT(l)
      WRITE(NDl)  (WDTKIl.I'l.NFELM)
 C
 C2.0 GET ADDITIONAL TIME HISTORY  RECORDS
 C
   20 CALL GETTDT(TDAT)
      IF(EOC)  GO TO 300
      IFITDAT(l).LT.TDAT(2))  THEN
        CALL ALERTCERROR:  Time data  out of sequence.','$','S')
        ERR - .TRUE.
        RETURN
      ENDIF
      TDAT(2)  - TDAT(l)
      CALL ZEROR(WDT1,NFELM. 1)
      CALL DATGEN(WDATO.NFELM,ERR)
      IF(ERR)  RETURN
      CALL RPRTNO(HDT1(1),NFELM,'Elem')
      WRITE(ND1)  TDAT(l)
      WRITE (NOD  (WDTKI) ,1=1. NFELM)
      GO TO 20
                                                                           IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTW.2000)
                                                                       2000 FORMAT!/, '  EXCITDAT:  EXCITATION TIME HISTORY DATA')
C
C1,
c
c
C2.
C
0 CHECK TO SEE IF FLOW SYSTEM HAS BEEN DEFINED

 CALL CKSYS(l.ERR)
 IF (ERR)  THEN
   CALL ABORT
   RETURN
 ENOIF

0 GET DATA GENERATION CONTROL DATA

 TIME(l)  - O.ODO
 TIME(2)  - O.ODO
 TIME(3)  = O.ODO
 CALL FREERCT'.TIME(l) ,3)
 IF(TIME(3).LT.O.ODO) THEN
   CALL ALERTCERROR: Tim  step may not be negative.',1?1
   CALL ABORT
   RETURN
 ELSEIF(TIME(3).GT.O.ODO) THEN
   IF(TIME(2).LT.TIME(1)) THEN
    CALL ALERT!
+   'ERROR:  Final time must be greater than initial time.
+   'S'.'S'I
     CALL ABORT
     RETURN
   ENDIF

   IF(ECHO)  WRITE(NTW,2220)
   WRITE(NOT,2220)
I   FORMAT!/,'   = Generation Control Variables')
   IF(ECHO)  WRITE(NTW,2230)  (TIME(I),1-1,3)
   WRITE(NOT.2230) (TIME(I),1=1,3)
I   FORMAT)/,
.'      Initial time 	 '.G10.3./.
.'      Final tlrao 	 '.G10.3,/,
.'      Time step increment 	 '.G10.3)
 ENDIF
 C--3.0 WRITE ONE ADDITIONAL TIKE VALUE TO DISK
 C
 300  WRITE(ND1)  TDAT(l)

      RETURN
      END
      SUBROUTINE EXCDAT
 CSUB:EXCDAT - COMMAND TO READ EXCITATION DATA I GENERATE STEPWISE
 C               TIME HISTORIES OF EXCITATION VALUES,  EINSEQ).AND
 C               WRITES TIME HISTORIES  IN FORMAT;
 C
 C          TIME
 C                  .EDT
 CHELP LIST	
 C
 C     .' EXCITDAT [Tanl.n2.n3) Generate excitation time histories.',/.
 C     .' TIME-nl               nl  time'./.
 C     .' nl.n2,n3 CG*n4,n5....  nl,n2,n3 = node: first, last, incr.',/.
C3.0 OPEN .EDT
C
      CALL NOPEN(ND1.(FNAME(1:LFNAME)//'.EOT'),'UNFORMATTED')
C
C4.0 READ < GENERATE EXCITATION DATA
C
      WRITE(NOT,2400)
      IF(ECHO.OR.(MODE.EQ.'INTER')) WRITE(NTH,2400)
 2400 FORMAT!/,   = Nodal Excitation Tim-  History Data')
c
C	4.1 DEFINE  ( INITIALIZE ARRAYS
C
      CALL DELETE!TDAT')
      CALL DELETE('EDT1')
      CALL DELETE!'E   ')
      CALL DEFINRCE   ' , HPE.NSEQ, 1)
      CALL DEFINR('EDT1',HPEDT1,NSSPE,NSNOD)
      CALL DEFINRCTDAT',MPTDAT.1,2)
      CALL ZERORIIA(MPE).NSEQ.1)
      CALL ZEROR(lA(MPEDTl).NSSPE.NSNOD)
      CALL ZEROR(IA(MPTDAT).1.2)
      IF(TIME(3).GT.O.ODO) THEN
        CALL DELETECEDT2')
        CALL DEFINR('EDT2'.MPEDT2,NSSPE.NSNOD)
                                                           Append  -12

-------
Indoor  Air  Quality  Model
Phase   III   Report
                                                APPENDIX
   CONTAM87  FORTRAN   77   Source   Code
        CALL ZEROR(IA(MPEDT2),NSSPE,NSNOD)
      ENDIF
C
C	4.2 GENERATE VALUES t WRITE TO .EDT
C
      IF(TIME(3) .GT.O.ODO)  THEN
        CALL GENED1(IA(MPKSEO),IA(MCE),IA(MPTDAT),IA(HPEDT1).IA(HCEDT2),
     *  TIME.ERK)
        IF(ERR) THEN
          CALL ABORT
          RETURN
        ENDIF
      ELSE
        CALL GENED2 (IA (MPKSEQ) . IA (MCE) . IA (MPTDAT) . IA (MPEDT1) , ERR)
        IF(ERR) THEN
          CALL ABORT
          RETURN
        ENDIF
      ENDIF
C
C5.0 DELETE ARRAYS, CLOSE ELEMENT FLOW DATA  FILE, SKIP TO "END"
C
      CALL DELETECEDT2')
      CALL DELETE('TDAT')
      CALL DELETE CEDT1')
      CALL DELETE CE   ')

      CLOSE(ND1)

      II- (MODE. EQ. 'BATCH') THEN
   500   IF(EOC) RETURN
        CALL FREE
        GO TO SOO
      ENDIF
       NEQ - ABS(KSEO(N,M)>
       IF(NEQ.NE.O) E(NEQ) - EDT2(M,N) + XT"(EDT1(M.N)-EDT2(M,N))
   23  CONTINUE
C
C	2.4 WRITE TIME, (E(TH TO ND1
C
      HRITE(NDl)  T
      WRITE(ND1)  
  200 CONTINUE

  -3.0 WRITE ONE ADDITIONAL TIME VALUE TO DISK

      WRITE(ND1) T

      RETURN
      END
      SUBROUTINE GETEDT(KSEO,E.EDT1.EDT2,ERR)
  -SUB:  GETEDT - UPDATES EXCITATION  DATA VALUES
      COMMON MTOT.NP.IAd)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'
C
C GETEDT: DATA I COMMON STORAGE
C
      LOGICAL ERR
      REAL'S EINSEOI,EDT1(NSSPE.NSNOD), EDT2(NSSPE.NSNOD)
      INTEGER KSEQ(NSNOD,NSSCE)
      EXTERNAL EDATO






RETURN
END

SUBROUTINE GENED1 (KSEO. E, TDAT, EDT1 . EDT2 , TIME , ERR)
C
C 1.
c


C  SUB: GENED1 - GENERATES EXCITATION DATA, AT EQUAL TIKE STEP
C
C






C
c 	
C


c
C--1.
c








INTERVALS, FROM GIVEN ARBITRARY TIME DATA

IMPLICIT REAL'S (A-H.O-Z)

INCLUDE 'IOCOM.INC'
INCLUDE 'CNTCOM.INC'

LOGICAL ERR

GENEDI: DATA < COMMON STORAGE

REAL'S E (NSEQ) , TDAT (2) , EDT1 (NSSPE.NSNOD) , EDT2 (NSSPE. NSNOD) , TIKE (3)
INTEGER KSEQ (NSNOD, NSSPE)

0 GET FIRST TWO TIME HISTORY RECORDS

CALL GETTDT(TDAT)
IF(EOC) THEN
CALL ALERTCERROR: Insufficient data. ' , ' S ' , ' S ' )
ERR a .TRUE.
RETURN
ENDIF
CALL GETEDT (KSEQ, E.EDT1.EDT2, ERR)
IF (ERR) RETURN
CALL GETTDT(TDAT)
10
C--2.
C


c
C3.
C




30








0 UPDATE 'OLD' DATA VALUES; INITIALIZE 'NEW' DATA VALUES

DO 10 N-l.NSNOO
EDT2(H,N) - EDTl(M.N)
EDTKM.N)  O.ODO
CONTINUE
0 READ NEW VALUES

CALL DATSEN (EDATO, NSNOD, ERR)
IF (ERR) RETURN

0 REPORT. VALUES

DO 30 N-l, NSNOD
DO 30 K=l. NSSPE
NEQ = ABS(KSEQ(N,M)I
IF(NEQ.NE.O) E(NEQ) = EDTKM.N)
CONTINUE

CALL RPRTENIEd) . IA (MPKSEQ))

RETURN
END

SUBROUTINE EDATO (N, ERR)
C SUB: EDATO - CALLS EDAT1 CASSING ARRAYS
C



COMMON MTOT.NP.IAd)
INCLUDE 'CNTCOM.INC'
       IF(EOC)  THEN
         CALL ALERTCERROR: Insufficient data.'.'$'.'$)
         ERR =  .TRUE.
         RETURN
       ELSEIF(TDATd) .LT.TDATI2)) THEN
         CALL ALERTCERROR: Tine data out of sequence. '.'S'.'S')
         ERR =  .TRUE.
         RETURN
       ENDIF
       CALL GETEDT(KSEQ. E.EDT1.EDT2, ERR)
       IF(ERR)  RETURN

  2.0 GENERATION TIME LOOP

      DO 200 T=TIHE(1),TIME(2),TIME<3)

  	2.1 UPDATE  EXCITATION TIME HISTORY DATA IF NEEDED

    20 IF(T.GT.TDATd)) THEN
       CALL GETTDT(TDAT)
       IF(ECC)  THEN
         CALL ALERTCERROR: Insufficient data.'.'$','S')
         ERR -  .TRUE.
         RETURN
       ELSEIF(TDATd) .LT.TDAT(2 THEN
         CALL ALERTCERROR: Time data out of sequence. ','S'.'S')
         ERR =  .TRUE.
         RETURN
       ENDIF
       CALL GETEDT(KSEQ.E.EDT1.EDT2,ERR)
       IF(ERR)  RETURN
       GO TO 20
      ENDIF

  	2.2 COMPUTE INTERPOLATION FRACTION

      XT -  (T-TDAT(2))/(TDAT<1)-TDAT(2))

  	2.3 COMPUTE (EIT))

      DO 23 N-l,NSNOD
      DO 23 M-l,NSSPE
      COMMON /EXCDT/ MPTDAT.MPEDT1, MPEDT2
      LOGICAL ERR

      CALL EDST1(lA(MPEDTl),N)

      RETURN
      END

c	EDAT1
      SUBROUTINE EDAT1(EDT1,N)
  -SUB:EDATO - READS EXCITATION TIME HISTORY DATA
      INCLUDE 'CNTCOM.INC'

      REAL"8 S;DT1 (NSSPE. NSNOD)

      CALL FRKERCG'.EDTKI.N),NSSPE)

      RETURN
      END
      SUBROUTINE GENED2(KSEQ.E.TDAT.EDT1.ERR)
  -SUB:  GENED3 - GENERATES EXCITATION DATA FROM GIVEN TIME DATA
      IMPLICIT REAL*8(A-H.O-Z)

      COMMON MTOT.NP.IAd)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR
      EXTERNAL EDATO
C
C	 GENE02: DATA ( COMMON STORAGE
C
      REAL'S TDAT (2), EOT1 (NSSPE.NSNOD),  E (NSEQ)
      INTEGER KSEQ(NSNOD.NSSPE)
                                                          Append  -13

-------
Indoor  Air  Quality  Model
Phase  II!  Report
   CONTAM87   FORTRAN
       APPENDIX
77  Source   Code
C1.0 GET FIRST TIME HISTORY RECORD ( TDAT(l), EDT1 (N3SPE. NSNOD)  )
C
      CALL GZTTDT(TDAT)
      IF(EOC) RETURN
      TDAT(2) - TDAT(l)
      CALL ZERORIEDT1.NSSPE.NSNOO)
      CALL OATGENIEDATO. NSNOD. ERR)
      IF(ERR) RETURN

      DO 10 N-l,NSNOD
      DO 10 M-l.NSSPE
        NEQ - ABS(KSEO(N,M))
        IFINEQ.NE.O)  E(NEQ) - EDTKM.N)
   10 CONTINUE

      CALL RPRTEN(E(1),IA(KPKSEQ))

      WRITE')
      CALL FREE
      IF (MODE.EQ.'BATCH') CALL FREEHR (NTW)
      TIME(l) - O.ODO
      TIKE(2) - O.ODO
      TIKE(3) - O.ODO
      CALL FREERCT',TIME(1),3)
      IF(TIME(3).LE.O.ODO) THEN
        CALL ALERTCERROR: Tims step must be greater than  O.'.'S'.'S'I
        CALL ABORT
        RETURN
      ELSEIF(TIME(2).LT.TIME(1))  THEN
        CALL ALERT!
     +  'ERROR: Final time must be greater than Initial time.',
     +  '$','$')
        CALL ABORT
        RETURN
      ENDIF

      ALPHA - 0.7SDO
      CALL FREER CA', ALPHA, 1)
      CALL CKRRNGC alpha', ALPHA, 1, O.ODO, 'LELE*. 1. ODO, ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF

      PINT - 1
      CALL FREEK'I'.PINT, 1)
      CALL CKIZERCresults print Interval',PINT, 1,'GT',ERR)
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF

      PSCALE = O.ODO
      CALL FREERCS',PSCALE, 1)

      IF(ECHO) WRITE(NTH,2250)  (TIME(I) , 1=1, 3).ALPHA,PINT
      HRITE(NOT,2250) (TIME(I), 1=1, 3).ALPHA.PINT
 2250 FORMAT!/.
     .'     Initial time 	 '.G10.3,/,
     .'     Final time 	 '.G10.3,/.
     .'     Time step Increment 	 ',G10.3,/,
     .'     Integration parameter: alpha .... ',G10.3,/,
     .'     Reaulta print Interval  	 ',16)
      IF(PSCALE.NE.O.ODO) THEN
        IF(ECHO) WRITE(NTW. 2260)  PSCALE
        WRITE(NOT,2260)  PSCALE
      ENDIF
 2260 FORMAT!'      Reaulta plot-file scale factor .. \G10.3)
                                                                       C
                                                                       C--3.
                                                                       C
     0 DEFINE AND INITIALIZE SYSTEM ARRAYS
      IMPLICIT REAL'S(A-H.O-Z)

      COMMON MTOT.NP.IAU)

      INCLUDE 'IOCCH.INC'
      INCLUDE 'CNTCOM.INC'

      COMMON /DYNM/ THDAT,TEDAT,MPCDAT
      LOGICAL ERR,  FOUND
      REAL'S TIME(3),  PSCALE
      INTEGER PINT
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
 D I C T




TIME (3) START TIME, END TIME, TIME INCREMENT
TWDAT
TEDAT
PINT
PSCALE

P 0 I N

MPFS
MPC
MPCD
MPCDD
MPCDAT
KPE
MPID
TIME OF NEXT ELEMENT FLOW RATE RECORD
TIME OF NEXT EXCITATION RECORD
RESPONSE RESULTS PRINT INTERVAL
RESULTS PLOT FILE SCALE FACTOR

TERS TO BLANK COMMON LOC






A T I 0 N S

FS (NSEQ. 2'MSBAN-l) : [F*l DYNAM ALG. MATRIX (ASYM-COMPACT)
C(NSEO) CURRENT (C)
CD(NSEQ) CURRENT d(C)/dt
CDDINSEQ) CURRENT d/dt (d|C)/dt)
CDAT(NSSPE) TEMP. STORAGE OF INITIAL
E(NSEQ) CURRENT (E)
IDCNID) LIST OF INDEPENDENT DOF



CONDS. DATA

EQUATION NOS.
CALL DELETE C TEMP ')
CALL COUNTKIA(MPKSEQ) ,NID)
CALL DELETE ('ID
CALL DELETE CFS
CALL DELETE ('CD
CALL DELETE CCDD
CALL DELETE! 'COAT
CALL DELETE I 'CONT
CALL DELETE ('VCD
CALL DELETE CEFF
CALL DELETE CDIFF
CALL DELETE CGENR
CALL DELETE ('WE
CALL DELETE CC
CALL DELETE) 'E
CALL DELETE! 'F
CALL DELETE ('VM
CALL DEFINRCVM
CALL DEFINRCF
CALL DEFINRCE
CALL DEFINRCC
CALL DEFINRCWE
CALL DEFINR CGENR
CALL DEFINR CDIFF
CALL DEFINR CEFF
CALL DEFINR! 'VCD
CALL DEFINR! 'CONT
CALL DEFINR CCDAT
CALL DEFINR ( 'COD
CALL DEFINR! 'CD
CALL DEFINR CFS
CALL DEFINICID















, HPVM.NSEQ, 1)
, KPF. NSEO. 2*MSBAN-1)
.MPE.NSEO, 1)
.MPC.NSEQ.l)
.MPHE.NFCLM.l)
.MPGENR.NSSPE.l)
. MPDIFF.NSSPE.il
.MPEFF.NSSPE.l)
.MPVCD, NSNOD. 1)
.MPCONT, NSNOD. 1)
, MPCDAT, NSSPE.l)
, MPCDD.NSEQ. 1)
, MPCD.NSEQ. 1)
, MPFS.NSEO. 2'MSBAN-l)
.MPID.NID.l)
      ERR - .FALSE.

      HRITE(NOT.2000)
                                                                       C
                                                                       C 4
                                                                       C
     0 GET NODAL  INITIAL CONCENTRATIONS
      CALL ZEROR(IA(KPC).NSEQ. 1)
      CALL CETIC(ERR)
                                                            Append  -14

-------
Indoor   Air  Quality  Model
Phase  III  Report
                                                  APPENDIX
   CONTAM87   FORTRAN   77   Source   Code
      IF(ERR) THEN
        CALL ABORT
        RETURN
      ENDIF
C
C--5.0 OPEN ELEMENT,  FLOW AND EXCITATION DATA FILES, ( PLOT FILE
C
      OPEN(ND1,FILE"(FNAME(1:LFNAME)//'.FEL'),STATUS-'OLD',
     +FORM-'UNFORMATTED)

      IF(NKINEL.GT.O)  THEN
        OPEN(ND2,FILE-(FNAME(1:LFNAME)//'.KIN'),STATUS-'OLD'.
     +  FORM-'UNFORMATTED')
      ENDIF

      OPEN
-------
Indoor   Air   Quality  Model
Phase  III  Report
   CONTAM87   FORTRAN
       APPENDIX
77  Source   Code
C              (I.E.. TDOF EQUATION NUMBERS)
C    X(NEQN.2*MBAN-1) :  [K] MATRIX: ASYM-BANDED COMPACT-STORED
C   KSINEQN, 2'MBAN-l) :  IK'I  = [C|  + aDT[K| MATRIX  (SCALED FOR NEC ID)
C   C(NEQN)       :  CURRENT (C]  (ORDERED BY EQTN I)
C   E(NEQN)       :  CURRENT (E)  (ORDERED BY EQTN I)
C   TINEQN)       :  CURRENT (T)  (ORDERED BY EQTN I)
C   TD(NEQN) :  CURRENT 
ERROR: Can not compute for step change In', + ' dependent variable number:'.IS) ERR - .TRUE. RETURN ELSE roil) - O.ODO ENDIF c 'E'-DOF: FORM [E|-[K1(T) WHERE [K] IS IN COMPACT STORAGE ELSE TEMP - Ed) Kl - MAXd.MBAN-I+l) K2 - MIN(2'MBAN-l,MBAN+NEQN-I) DO 20 KK-K1.K2 J - I * KK - MBAN TEMP - TEMP - K(I,KK)T(J) 20 CONTINUE C SOLVE TO (I) - TEMP/C (I) 22 ENDIF C C3.0 COMPUTE TAYLOR'S TIMESTEP CHECK C IF(ECHO) WRITE(NTW. 2300) WRITE(NOT.2300) 2300 FORHAT
-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                                                                                        APPENDIX
                                                                        CONTAM87   FORTRAN   77   Source   Code
      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'

      COMMON /DYNM/ TWDAT, TEDAT, MPCDAT
      REAL'S KINSEQ,2'MSBAN-l), C(NSEQ).TM,  TWDAT,  TEDAT
      LOGICAL ERR.  KUPDAT
C
C1.0 UPDATE ELEMENT FLOH RATES IFITH.GE.TNDAT)
C
      CALL UPDAT .'  Time:  ',010.3)
        CALL RPRTEN(E,IA(MPKSEQ)>
      ENDIF
      RETURN
      END
  ------------------------------------------------------------------ UPDAT
       SUBROUTINE UPDAT (LUN. T. TD, D. ND, UPDATE. ERR)
  SUB: UPDAT
        SEARCHES A SEQUENTIAL DATA RECORD, ON UNIT LUN, OF THE FORM:
            TD
             (D (I) ,1=1, NO)
            TD
        TO UPDATE DATA VALUES  TO CURRENT TIME.  "T" .  IF DATA VALUES ARE
        UPDATED LOGICAL -UPDATE" IS SET TO TRUE.
                     :  DISCRETE  TIME VALUE
                     :  UPDATED TO NEXT VALUE
                     :  CORRESPONDING DISCRETE DATA VALUES
         TD

         DID

       UPDAT MUST BE "PRIMED" BY READING FIRST TD VALUE TO MEMORY


     INCLUDE 'IOCOM.INC'

     REAL'S D(ND).T,TD
     LOGICAL ERR, UPDATE

     UPDATE =  .FALSE.
  10 IF(T.GE.TD) THEN
	UPDATE DISCRETE DATA VALUES
       READ(LUN, ERR-800, END=900I  (D(I).1=1,NDI
       IF(ERR) RETURN
       UPDATE  o  .TRUE.
	GET NEXT DISCRETE TIME
       READ (LUN. ERR=800. END=900)  TD
       IF (ERR) RETURN
       GO TO 10
     ELSE
       RETURN
     ENDIF

 800 ERR = .TRUE.
     CALL ALERTCERROR: Time historydata file read error. ','$'.' $')
     RETURN

 900 ERR = .TRUE.
     CALL ALERT (
    +'ERROR: EOF encountered on time  history data file.',
    +'Insufficient tlras history data.'.'$')

     RETURN
     END
      IMPLICIT REAL'S (A-H.O-Z)

      REAL'S  T (NEON) ,TD (NEQN) ,E (NEQN).K(NEON,2-MBAN-lI.
     +KS(NEON,2MBAN-1)
      INTEGER ID (NID)
      LOGICAL TDOF

      DO 20 I..I.NEQN
C	SCALE BV DIAGONAL FOR TEMP PRESCRIBED NODES
      IF(TDOF(I,ID, NID))  THEN
        TO (I)  TD(I)*KS(I,MBAN)
C	FORM (EI-tKUT) WHERE IK|  IS IN COMPACT STORAGE
      ELSE
        TEMP   E(I)
        IO. -  HAXU.MBAN-I+1)
        K2 -  IN(2MBAN-1.MBAN+NEQN-I)
        DO 10 KXK1,K2
        J - I + KK - MBAN
        TEMP  '- TEMP - K(I,KK)*T(J)
   10   CONTINUE
        TD(I) - TEMP
      ENDIF
   20 CONTINUE
      RETURN
      END


      FUNCTION TDOF(N,ID,NID)
C-FUN:TDOF -  DETERMINES IF EQUATION NUMBER N IS A TEMPERATURE DOF
      LOGICAL TDOF
      INTEGER ID(NID)
      TDOF -  .FALSE.
      DO 10 NN-l.NID
       IFID(NN).EQ.N))  THEN
         TDOF -  .TRUE.
         RETURN
       ENDIF
   10 CONTINUE
      RETURN
      END
                                                                                                                                       RESULT
      SUBROUTINE FORMKS(ID,K.KS.C.ALPHA. DT,NID,NEQN,MBAN)
   -SUB:FORMXS - FORMS;
                       [K*| =  [Cl + aDT(K|

                SCALES  [K] =  [K*1*1.0D15 FOR 'T'-DOF

      IMPLICIT REAL'S(A-H.O-Z)

      REAL'S K(NEON.2*KBAN-1),KS(NEQN,2'MBAN-l).C(NEQN)
      INTEGER ID(NID)
      SUBROUTINE RESULT(T)
CSUB:RESULT - REPORTS RESPONSE RESULT VECTOR  (T)

      COMMON MTOT.NP.IA(l)

      INCLUDE 'CNTCOM.INC'

      REAL'S T(NSEQ)

      CALL RPRTENIT,IAIMPKSEQ))

      RETURN
      END

C			*-<'-< '  ' ^===0=. RESET
      SUBROUTINE RESET
CSUB:RESET - COMMAND TO RESET CONTAM  BY RE-INITIALIZING POINTERS AND
C            COUNTERS AND DELETES ARRAYS LEFT BY CONTAM IN BLANK COMMON
C--HELP  LIST	
C     .'  RESET                 Reset  CONTAM for new problem.'
c	

      INCLUDE 'IOCOM.INC'

      LOGICAL FOUND
      CHARACTER BINEXT(4)*3
      INTEGER NBIN

      DATA BINEXT/'FEL','KIN'.'WDT','EOT'/, NBIN/4/
C
C1.0 RE-INITIALIZE CONTAM CONTROL VARIABLES t DELETE CONTAM  ARRAYS
C
      CALL ::NITCN
      CALL DELETE! '0   ')
      CALL DELETE('VM  ')
      CALL DELETECC   ')
      CALL DELETE!'F   ')
      CALL DELETE('WE  ')
      CALL DELETE!'V   ')
      CALL DELETE CKSEO'I
                                                            Append  -17

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                                          CONTAM87   FORTRAN
                                                   APPENDIX
                                            77   Source   Code
      DO 100 NK=1.
   100 CALL DELETE('KIK'//CBAR(NK+48))
      CALL DELETE ('TEMP')
      CALL DELETE CCONT')
      CALL DELETE ('VCD ')
C
C  2.0 DELETE CONTAM BINARY FILES
C
      DO 20 N-l.NBIN
      INQUIRE (FILE-FNAME (1 :LFNAME) //BINEXT 

      RETURN
      END

c	 READWE
      SUBROUTINE READWE(ERR)
CSUB:README -  READS I REPORTS ELEMENT  TOTAL MASS FLOW  RATE DATA
C
      COMMON MTOT.NP.IAU)

      INCLUDE 'IOCOM.INC'
      INCLUDE 'CNTCOM.INC'

      LOGICAL ERR
      EXTERNAL NEDATO

      IF(ECHO.OR.(MODE.EQ.'INTER'))  HRITE(NTH,2000)
      HRITE(NOT.2000)
 2000 FORMAT!/,'   -= Element Mass Flow  Rates')
      CALL DATGENIHEDATO.NFELM.ERR)
      IF(ERR) RETURN

      CALL RPRTNO(IA(MPHE),NFELM,'Elem')

      RETURN
      END
                                                                              SUBROUTINE HEDATO(N,ERR)
                                                                        CSUB:HEDATO - CALLS HEDAT1 PASSING  ARRAYS
                                                                        C
                                                                              COMMON MTOT.NP.IAd)

                                                                              INCLUDE 'CNTCOM.INC'
                                                            Append  -18

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                                                                                     APPENDIX
                                                                      CONTAM87   FORTRAN  77   Source   Code
      DO 100 NX-1,9
  100 CALL DELETE('XIX'//CHAR 0.',
     +  'FLOHSYS command must be executed.','$')
        ERR - .TRUE.
        RETURN
      ENDIF

      CALL LOCATE('KSEQ',MPXSEQ.NR,NO
      IF(MPKSEQ.EQ.O) THEN
        CALL ALERT!
     +  'ERROR: System equation number army "KSEQ" not found.',
     +  'FLOHSYS command must be executed.','$')
        ERR - .TRUE.
        RETURN
      ENDIF

      CALL LOCATE CV   '.MPV.NR.NO
      IF(MPV.EQ.O) THEN
        CALL ALERT('ERROR: Nodal volumetric mass array ~V"  not found.
     +  'FLOHSYS command must be executed.','$')
        ERR - .TRUE.
        RETURN
      ENDIF
C
C 2
C
  IF(NOPT.EQ.l)  RETURN

  0 FLOHELEM I XINELEM DATA VERIFICATION

  IF((NFELM.EQ.O).AND.(NKINEL.EQ.0))  THEN
    CALL ALERT!
 +  'ERROR:  Number of flow t kinetics elements both = 0.',
 +  'FLOHELEM C/or KINELEM must be executed.'.'$')
    ERR = .TRUE.
    RETURN

  ELSEIF(NFELM.EQ.O) THEN
    CALL ALERTCERROR: Number of flow elements - 0.',
 +  'FLOHELEM must be executed.'.'$')
    ERR - .TRUE.
    RETURN

  ELSEIF(NKINEL.EO.O) THEN
    IF (ECHO)  WRITE (NTH, 2210)
    WRITE(NOT.)
    WRITE(NOT,2210)
0   FORMAT(
 +  '    * NOTE: Number of kinetics elements - 0.')
  ENDIF

  INQUIRE(FILE-(FNAME(1:LFNAME)//'.FEL'),EXIST-FOUND)
  IF(.NOT.FOUND) THEN
    CALL ALERT(
 +  'ERROR:  Data file '//FNAME(1:LFNAME)//'.FEL not found.1,
 +  'FLOHELEM command must be executed.'.'$')
    ERR - .TRUE.
    RETURN
  ENDIF

  IF(NKINEL.ST.0) THEN
    INQUIRE(FILE-(FNAME(1:LFNAME)//'.KIN'),EXIST-FOUND)
    IF(.NOT.FOUND) THEN
                                                                             CALL ALERT!
                                                                        +    'ERROIl: Data file '//FNAME(1:LFNAME)//'.KIN not found.'
                                                                        +    'KINELEM command must be executed.','$')
                                                                             ERR -  .TRUE.
                                                                             RETURN
                                                                           ENDIF
                                                                           ERR - .TRUE.
                                                                           DO 200 IIK-1,9
                                                                             CALL LOCATE('XIX'//CHAR(48+NK), MPKIK(NK), NR.NC)
                                                                           IF(MPKIIUNK).NE.O) ERR- .FALSE.
                                                                           IF(ERR) CALL ALERT(
                                                                        +  'ERROR: Kinetics rate coefflcent  arrays not found.',
                                                                        +  'KINELEM command must  be executed.','$')
                                                                           RETURN
                                                                         ENDIF

                                                                         IF(NOPT.EQ.2) RETURN
C 3.0 FLOHDAT DATA VERIFICATION
C
      INQUIRE(FILE-(FNAME(1:LFNAME)//'.TOT'),EXIST-FOUND)
      IF(.NOT.FOUND) THEN
        CALL AlERTI
     +  'ERROR: Data file '//FNAME(1:LFNAME)//'.HOT not found.',
     +  'FLONDAT  command must be executed.','$')
       ERR  -  .TRUE.
       RETURN
      ENDIF
C
C 4.0 EXCITDAT  DATA VERIFICATION
C
      INQUIRE(FILE-(FNAME(1:LFNAME)//'.EOT').EXIST-FOUND)
      IF!.NOT.FOUND) THEN
        CALL ALERT!
     +  'ERROR: Data file '//FNAME(1:LFNAME)//'.EOT not found.',
     +  'EXCITDAT command must be executed.','$')
       ERR  -  .TRUE.
       RETURN
      ENDIF

      IF(NOPT.EO.3) RETURN

      RETURN
      END
                                                                         SUBROUTINE  GETIDS(IDS,NIDS,LABEL)
                                                                   CSUB: GETIDS  -  GETS CHARM IDS FROM COMMAND/DATA LINE
                                                                   C                SETS ID" NUMBER FOR BLANK IDS

                                                                         INCLUDE 'IOCOM.INC'

                                                                         CHARACTER IDS (NIDS) M, LABEL*!*),  HEADER* (*)
                                                                         PARAMETER (HEADER-'Nun.  ID')

                                                                         CALL FRLEC('D',IDS<1),4,NIDS)

                                                                         DO 10 N-l.NIDS
                                                                         IF (IDS () .EQ.'     ') THEN
                                                                           NCENT - N/100
                                                                           NTENS - (N - NCENT*100)/10
                                                                           NONES - N - NCENTMOO - NTENSMO
                                                                           IDS(N)  -  ' '//CHAR(NCENT+48)//CHAR(NTENS+48)//CHAR(NONES+4e)
                                                                      10 ENDIF
        NCOLS - MIN(NIDS.S)
        IF(ECHO)  THEN
          WRITE(NTH,2000)  LABEL,  (HEADER,N-l,NCOLS)
          HRITE(NTH,2010)  (I, IDS(I),I-l.NIDS)
        ENDIF
        WRITE(NOT,2000)  LABEL,  (HEADER,N-l,NCOLS)
        WRITE(NOT,2010)  (I,IDS(I),1-1,NIDS)
   2000 FORMAT!/,'      ', (A),//.8X.5(: (A),3X))
   2010 FORMAT((8X,5(:I3,2X,A4,2X)))

        RETURN
        END


        SUBROUTINE  README(ERR)
  CSUB:README - READS  <  REPORTS ELEMENT TOTAL  MASS FLOW RATE DATA
  C
        COMMON MTOT.NP.IAU)

        INCLUDE 'IOCOM.INC'
        INCLUDE 'CNTCOM.INC'

        LOGICAL ERR
        EXTERNAL HEDATO

        IF(ECHO.OR.(MODE.EO.'INTER'))  WRITE(NTH.2000)
        WRITE(KOT,2000)
   2000 FORMAT(/,'      Element Mass Flow Rates')
        CALL DJiTGEN(HEDATO,NFELM, ERR)
        IF(ERR)  RETURN

        CALL RI'RTNO(IAIMPHE),NFELM,'Elem')

        RETURN
        END
                                                                             SUBROUTINE HEDATO(N, ERR)
                                                                       CSUB:HEDATO - CALLS HEDAT1 PASSING ARRAYS
                                                                       C
                                                                             COMMON MTOT.NP.IA(l)

                                                                             INCLUDE 'CNTCOM.INC'
                                                            Append  -18

-------
Indoor   Air  Quality  Model                                                                              APPENDIX

Phase  III  Report                                              CONTAM87   FORTRAN   77   Source   Code




      HIN - MAX                                                        C  NSP      :  (CURRENT) SPECIES NUMBER
      DO 10 I-l.NENOD                                                  C  FORM     :  FORM OF SYSTEM ARRAY 'FULL1 OR 'BAND-
      CD 10 J-l.NESPE                                                  C  CONT(NSNOD)  : NODAL MASS  CONTINUITY ACCUMULATOR
        NN - ABS(KSEQ(LN(I),LS(J)                                     C  LN       :  (LOCATION) NODE Of KINETICS ELEMENT
        IF(NN.GT.MAX)  MAX-NN                                            C	
        IFINN.LT.MIN)  MIN-NN
   10 CONTINUE                                                         C
C                                                                      C0.0  INITIALIZE SYSTEM ARRAYS
C2.0 COMPUTE ELEM.  BADWIDTH AND COMPARE TO CURRENT MAX SYST. BANDWIDTH  C
C                                                                           IF(FORM.EO.'BAND') CALL  ZEROR(F.NSEQ,2*MSBAN-1)
      MEBAN - MAX-MINtl                                                      IF (FORM.EQ.'FULL') CALL  ZEROR(F.NSEQ. NSEQ)
      IF(MEBAN.GT.MSBAN)  MSBAN-MEBAN                                    C
      RETURN                                                           C1.0  PROCESS FLOH ELEMENTS
      END                                                              C
                                                                       C	1.1  FORM AND ASSEMBLE ELEMENT ARRAYS

      SUBROUTINE RPRTNO(X,NX,LABEL)                                          REWIND (ND1)
C~SUB:RPRTNO - REPORTS REAL VECTOR(X) BY INDEX NUMBER                        CALL ZEROR(IA (MPVCD) ,NSNOD. 1)
                                                                            CALL ZEROR(IA(MPCONT),NSNOD.l)
C	VARIABLE	DESCRIPTION	       DO  10 NEL-1.NFELM
C   X(NX)     VECTOR OF REAL VALUES ORDERED BY INDEX NUMBER                    READ(ND1, ERR-900, END-900)  TYPE
C   LABEL    TABLE LABEL CHARACTER**
C	       IF(TYPE.EQ.'SIMP') THEN
                                                                              CALL SIMP(NEL.WE,lA(MPEFF).KSEQ.F.IA(MPCONT).FORM.ERR)
      IMPLICIT REAL'S(A-H.O-Z)                                                 IF(ERR) RETURN
                                                                            ELSEIF(TYPE.EO.'CNDF') THEN
      INCLUDE 'IOCOM.INC'                                                      CALL CNDFINEL.HE, lA(MPDIFF) . lA(MPGENR) .KSEO.F.IA(MPVCO) ,
                                                                            +  IA(MPCONT).FORM.ERR)
      REAL'S X(NX)                                                             IF(ERR) RETURN
      CHARACTER LABEL'4                                                      ELSE
                                                                              GO TO  900
        WRITE (NOT. 2000)  (LABEL.N-1.4)                                      10 ENDIF
        IF(ECHO) WRITE(NTH,2000)  (LABEL.N-1.4)                           C
        WRITE (NOT. 2010)  (N, X(N), N-l.NX)                               C	1.2  REPORT NET TOTAL MASS FLOW
        IF (ECHO) WRITE (NTW, 2010)  (N, X(N),  N-l.NX)                       C
                                                                            WRITE(NOT,2200)
 2000 FORMAT!/,6X.4I2X.A4,'    Value'. 3X1)                                    IF (ECHO) WRITE (NTW, 2200)
 2010 FORMAT((6X,1(I6.1X,G11.3)H                                        2200 FORMAT(/.'    Nee Total  Mass  Flow')
                                                                            CALL RPRTNO(IA(MPCONT),NSNOD,'Node')
      RETURN                                                           C
      END                                                              C2.0  PROCESS KINETICS ELEMENTS
                                                                       C '

      SUBROUTINE RPRTEN(X.KSEQ)                                         C	'TEMP' STORES SPECIES CONNECTIVITY ARRAY,  LM(NSSPE)
CSUB:RPRTEN - REPORTS(X)IN NODE ORDER SEQUENCE FOR EACH SPECIES
                                                                            CALL DELETE('TEMP')
C	VARIABLE	DESCRIPTION	       CALL DEFINR ( TEMP', MPTEMP, NSSPE, 11
C   X(NSEQ)       VECTOR  OF VALUES ORDERED BY EQUATION NUMBER


      IMPLICIT REAL'8(A-H.O-Z)                                               DO  200 NEL=1.NKINEL
                                                                              READ(ND2.  ERR-950. END-950) LN,  NK
      INCLUDE 'IOCOM.INC'                                                200 CALL KINELX (LN, KSEQ, IA(MPKZK(NK)), F. IA (MPTEMP). IA (MPV). FORM)
      INCLUDE 'CNTCOM.INC'
                                                                            CALL DELETECTEMP')
      REAL'S X (NSEQ), XX M)
      INTEGER KSEQ (NSNOD, NSSPE)                                               RETURN
      CHARACTER FLG(4)*1                                                C
                                                                       C3.0  READ ERROR  TERMINATION
      WRITE(NOT,2000)                                                  C
      IF(ECHO) WRITE(NTW,2000)                                            900 ERR = .TRUE.
 2000 FORMAT!/,                                                              CALL ALERT(
      .13X,'V - independent DOFa       "U" - undefined DOFa.'l              +'ERROR:  Read error or EOF In file '//FNAME//'.FEL','$','$')
                                                                             RETURN
      DO 100 M-l,NSSPE
        WRITE(NOT.2010)  SID(M)                                            950 ERR - .TRUE.
        IF (ECHO) WRITE (NTW, 2010)  SID (M)                                      CALL ALERT (
 2010   FORMAT!/,8X,'Species:  '.A4,/.                                        *'ERROR:  Read error or EOF In file '//FNAME//'.KIN','$','$')
      *  6X,4(2X,'Node    Value',3X1)                                          RETURN
      DO 100 N=l,NSNOD,                                                      END
        NN = MIN(N3, NSNOD)
        DO 10 I-N.NN.l                                                 C	  SIMP
          NEQ - KSEQII.M)                                                    SUBROUTINE  SIMP (NEL,WE, EFF, KSEO.F.CCNT, FORM.ERR)
          NNEO * ABS(NEO)                                              CSUB:SIMP -  FORMS AND ASSEMBLES SIMPLE FLOH ELEMENT EQUATIONS
          IF(NEQ.LT.O) THEN                                            C             FOR  ALL SPECIES  CONSIDERED
            XXd-N+1)  - X(NNEQ)
            FLG(I-N*1) -  '"                                                  INCLUDE  'IOCOM.INC'
          ELSEIF(NEQ.EQ.O)  THEN                                               INCLUDE  'CNTCOM.INC'
            XXU-N+1)    O.ODO
            FLGd-N+1) -  'U'                                                 REAL'S WE (NFELM), EFF (NSSPE) ,F (NSEQ, 1) ,CCNT(NSNOD) , ELFI2, 2) ,W
          ELSE                                                               INTEGER  KSEO(NSNOD.NSSPE).LN(2>,  LM(2)
            XX(I-N-l-l)  - X(NNEQ)                                              CHARACTER  FORM'4
            FLG(I-N1) -  '  '                                                 LOGICAL  ERR
          ENDIF
   10   CONTINUE                                                       C	VARIABLE	DESCRIPTION	
        IF(ECHO) WRITE(NTH,2020)  (I,FLG(I-Ntl),XX(I-N+1). I=N, NN|         C  NEL     :  (CURRENT) ELEMENT NUMBER
        WRITE(NOT,2020)  (I.FLO(I-N+1).XX(I-N+1),I=N,NN)                  C  FORM     :  FORM OF SYSTEM  ARRAY 'FULL'  OR 'BAND'
 2020   FORMAT((6X,4(K,1A1,G11.3)))                                    C    CONT(NSNOD)  : NODAL MASS  CONTINUITY ACCUMULATOR
   100 CONTINUE                                                         C    EF (NENOO, NENOD)  :  ELEMENT  (F| ARRAY
                                                                       C  W       :  ELEMENT TOTAL MASS FLOW RATE
      RETURN                                                           C  LN(2)         : ELEMENT NODE LOCATION/CONNECTIVITY
      END                                                              C  NSP     :  (CURRENT) SPECIES NUMBER
                                                                       C  LM(2)         : SYSTEM DOF  CORRESPONDING  TO  EACH ELEMENT DOF

      SUBROUTINE FORMF(KSEQ,F.WE.FORM,ERR)
C~SUB:FORMF - FORMS  SYSTEM FLOW  MATRIX AND CONDF CONTRIBUTION TO [V]     C
C              ARRAY  CONT(NSEQ) USED TO CHECK NODAL MASS FLOH CONTINUITY  C1.0  GET ELEMENT DATA
                                                                       C
      COMMON MTOT.NP.IA(l)                                                   READ(ND1. END=900, ERR=900)  LNU) .LN (2), (EFF(I) , 1-1,NSSPE)
                                                                            W = HE (NEL)
      INCLUDE 'IOCOM.INC'                                               C
      INCLUDE 'CNTCOM.INC'                                              C2.0  FORM ELEMENT ARRAYS
                                                                       C
      REAL'S F(NSEQ,1), HE (NFELM)                                            IF (W. GT. 0 . ODO) THEN
      INTEGER KSEQ(NSNOD.NSSPE).  MPCONT                                        ELF(1.1) W
      LOGICAL ERR,  LN                                                .         ELF(1,2) - O.ODO
      CHARACTER FORM4,  TYPE*4        ,                                         ELFI2.2)   O.ODO
                                                                              CONT(LNU)) = CONT(LNd))  + H
C	VARIABLE	DESCRIPTION	         CONT(LN(2 -CONT(LN(2  -W
C   NEL      :  (CURRENT)  ELEMENT NUMBER                                      ELSEIF(H.LT.0.ODO) THEN
                                                            Append  -20

-------
Indoor   Air  Quality  Model
Phase  III  Report
                                                                                                                  APPENDIX
                                                                    CONTAM87   FORTRAN   77   Source   Code
  ELF(1,1)  -  O.ODO
  ELF(2,1)  -  O.ODO
  ELF(2,2)  -  -W
  CONT(LNU)) - CONT(LNU))  + W
  CONT(LN(2)I - CONT(LN(2))  - W
ELSE
  ELFU.l)  -  O.ODO
  ELF(1,2)  -  O.ODO
             O.ODO
             O.ODO
        ELF(2.1)
        ELFI2.2)
      ENDIF
                                                                          10 CONTINUE

                                                                            RETURN

                                                                         900 ERR - .TRUE.
                                                                            CALL ALERT!
                                                                           ('ERROR: Read error or EOF In file //FNAHE//'.FEL'.'S'
                                                                            RETURN
                                                                            END
                                                                                                                           '$>
C	2.1 LOOP OVER SPECIES FOX NONZERO OFF-DIAGONAL TERM
C
      DO 10 NSP-1,NSSPE
        LH(1) - ABS(XSEQ(LN(1),NSP))
        LM(2) - ABS(KSEQ(LN(2).NSP))
        IF(W.GT.O.ODO) THEN
          ELF(2,1)  - -(!.ODO-EFFfliSP))
        ELSEIFW.LT. O.ODO) THEN
          ELF (1.2)  - NMl.ODO-EFF(NSP))
        ENDIF
                                                                      SUBROUTINE KJNELK(LN,XSEO,XIX,F,LM,V,FORM)
                                                                C~SUB:XINELX - FORMS KINETICS ELEMENT ARRAY  FROM KIN RATE COEF.  MATRIX
                                                                C
                                                                    LN       :  (LOCATION) NODE OF KINETICS
                                                                    XIK(NSSPE.NSSPE): KINETICS RATE COEF. MATRIX
                                                                    FINSEQ,1)     :  SYSTEM FLOW MATRIX
                                                                    LM(NSSPE)     :  SYSTEM DOF CORRESPONDING TO EACH ELEMENT DOF
                                                                    V(NSNOO)  : NODAL VOLUMETRIC MASSES
                                                                    FORM     : TORM OF [F]:  'FULL'  OR  'BAND'
C
C	2.
C
 2 ASSEMBLE ELEMENT ARRAYS
      CALL ADDA(ELF,2,F.NSEQ.HSBAN.LM,1.ODD,FORM)

   10 CONTINUE

      RETURN

  900 ERR - .TRUE.
      CALL ALERT!
     + 'ERROR:  Read  error  or EOF In file '//FNAME//'.FEL', '$','$)
      RETURN
      END
      SUBROUTINE CNOF(NEL,HE,DIFF,GENR,KSEQ,F,VCD,CCNT,FORM,ERR)
CSUB:CNDF - FORMS AND ASSEMBLES CONV-DIFF FLCH  ELEMENT EQUATIONS
C             FOR ALL SPECIES CONSIDERED
      INCLUDE
      INCLUDE
        'IOCOM.INC'
        'CNTCOM.INC'
                                                                      INCLUDE 'CNTCOM.INC'

                                                                      REAL'S laK (NSSPE. NSSPE), F(NSEQ.l),  V(NSNOD), SCALE
                                                                      INTEGER 1.M (NSSPE) , LN, KSEQ (NSNOO. NSSPE)
                                                                      CHARACTER FORUM

                                                                      DO 100 Nl,NSSPE
                                                                 100  LM(N) - ABS(KSEQ(LN,N))
                                                                      SCALE - V(LN)
                                                                      CALL ADDA(KIK,NSSPE,F,NSEQ,MSBAN,LM,SCALE,FORM)

                                                                      RETURN
                                                                      END


                                                           CNDF       SUBROUTINE ADDA (AE.NEDOF, AS,NSDOF.MSBAN.LM, SCALE, FORM)
                                                                 CSUB:ADDA - ADDS SCALED ELEMENT ARRAY,  SCALE*[AEI, TO SYSTEM ARRAY, AS
                                                                 C
                                                                      REAL'S AE(NEDOF.NEDOF), AS(NSDOF,1). SCALE
                                                                      INTEGER LM(NEDOF)
                                                                      CHARACTER FORM'4
      IMPLICIT REAL*8(A-H.O-Z)
      REAL*! HE(NFELM),DIFF(NSSPE),GENR(NSSPE),F(NSEQ,1),VCD(NSNOD),
     +CONT(NSNOD),ELF(2,2),H,MASSL,LENGTH,FACTOR
      INTEGER KSEQ(NSNOO.NSSPE).LN(2),LM(2)
      CHARACTER FORM*4
      LOGICAL ERR
 C	VARIABLE	DESCRIPTION	
 C   NEL      :  (CURRENT) ELEMENT NUMBER
                                                                 C	VARIABLE	DESCRIPTION	
                                                                 C   AE(NEDOF.NEDOF)  : ELEMENT ARRAY
                                                                 C  NEDOF        :  NUMBER OF ELEMENT DOFS
                                                                 C  AS(NSDOF,2'MSBAN-l)    :  (COMPACTED) BANDED ASYM. SYSTEM ARRAY
                                                                        OR --
                                                                     AS (NSDOF, NSDOF)  : FULL ASYM. SYSTEM ARRAY
                                                                    LM (NEDOF)     :  SYSTEM DOF  CORRESPONDING TO EACH ELEMENT DOF
                                                                    SCALE        :  SCALAR FACTOR
                                                                    FORM     :  FORM OF SYSTEM ARRAY  'FULL' OR  'BAND'
C
c
c
c
c
c
c
c
c
c
FORM : FOR
CCNT (NSNOD)
ELF(NENOD,NE>
N : ELE
LN(2)
NSP : (CU
LM(2)
MASSL
LENGTH
FACTOR
M OF SYSTEM ARRAY 'FULL' OR 'BAND'
NODAL MASS CONTINUITY ACCUMULATOR
CO) : ELEMENT [F| ARRAY
MENT TOTAL MASS FLOW RATE
ELEMENT NODE LOCATION/CONNECTIVITY
RXENT) SPECIES NUMBER
SYSTEM DOF CORRESPONDING TO EACH ELEMENT DOF
AIR MASS PER UNIT LENGTH - CNDF ELEMENTS
FLOH PASSAGE LENGTH - CNDF ELEMENTS
UPWIND FACTOR - CNDF ELEMENTS
c
C 1.0 GET ELEMENT DATA
C
                                                                             DO 20 Il.NEDOF
                                                                               II - LM(I)
                                                                               DO 10 J-l. NEDOF
                                                                                IF(FORM.EQ.'BAND')  JJ = MSBAN - II + LM(J)
                                                                                IF(TORM.EQ.'FULL')  JJ-LM(J)
                                                                                ASCII,JJ) = AS(II.JJ) + SCALE'AEd, J)
                                                                          10   CONTINUE
                                                                          20 CONTINUE
                                                                             RETURN
                                                                             END
      REAO(ND1.END-900,ERR=900) LN (1) ,LN (2) .MASSL. LENGTH. FACTOR.
     +   (DIFF (N).N-l, NSSPE)

      W - WE (NEL)
C
C 2.0 FORM ELEMENT ARRAYS
C
      IF (W.LT. O.ODO)  THEN
        LNTEMP  - LNI2)
        LN(2)  - LNU)
        LN(1)   LNTEMP
      ENDIF
C
C ---- 2.1 FORM ELEMENT LUMPED VOLUMETRIC MASS  TERMS
C
VCD(LN(1))  - VCD(LNU))
VCD (LN (2)1  = VCD(LN(2)I
                               MASSL*LENGTH*0.50DO
                               MASSL'LENGTH'O . 50DO
C
C ---- 2.2 ACCUMULATE MASS FLOW RATES FOR CONTINUITY CHECK                 C-
C
      CONT(LNIl))  -CONT(LNU)) + W                                     C-
      CONT(LN(2)  -CONT(LN(2)I -W                                     C
C
C ---- 2.3 LOOP OVER SPECIES TO FORM ELEM MASS  TRANSPORT MATRIX 4 ASSEMBLE
C
      DO 10 NSP-1, NSSPE                                                 C
        LM(l)  = ABS(XSEQ(LN(1),NSP)I                                     C-
        LM(2)  = ABS(KSEQ(LN(2) ,NSP))                                     C

        COEF - MASSL'DIFF (NSP) /LENGTH                                   C
        IF(FACTOR.EQ.-l.ODO) FACTOR>MAX (0. ODO. 1 .ODO-COEF/W)               c-
        ELF(l.l)  = (W/2)*< 1 + FACTOR)  + COEF                           c
        ELF (1,2)  = (W/2)*( 1 - FACTOR)  - COEF                           c.
        ELFI2.1)   (W/2)*(-l - FACTOR)  - COEF
        ELF (2, 2)  - (W/2JM-1 * FACTOR)  + COEF
   -2.2 ASSEMBLE ELEMENT FLOW ARRAYS

        CALL ADDA(ELF,2,F.NSEQ,MSBAN,LM,1.ODO,FORM)
                                                                      SUBROUTINE FORMVM(KSEO,V,VCD,VM)
                                                                   -SUB:FORMVM - FORMS VOLUMETRIC MASS MATRIX (A DIAGONAL ARRAY)

                                                                      INCLUDE 'CNTCOM.INC'

                                                                      REAL'S V(NSNOD) , VM (NSEQ), VCD (NSNOD) ,VN
                                                                      INTEGER KSEQ(NSNOD.NSSPE)

                                                                      CALL ZEROR(VM,NSEQ,1)

                                                                      00 10 N-l,NSNOD
                                                                        VN - (N)  +  VCD(N)
                                                                      DO 10 M-l,NSSPE
                                                                        NEQ - ABSIKSEQ(N.M))
                                                                        IF(NEQ.NE.O)  VM(NEQ) - VN
                                                                    10 CONTINUE

                                                                      RETURN
                                                                      END
                                                                      SUBROUTINE GETTDT(TDAT)
                                                                   -SUB: GETTCO - UPDATES  TIME DATA VALUES

                                                                      INCLUDE 'IOCOM.INC'

                                                                      REAL'S TDATI2)

                                                                   -1.0 UPDATE OLD VALUES

                                                                      TDATI2) = TDAT(l)

                                                                   -2.0 READ NEW VALUE

                                                                    CHECK TOR END-OF-COMMAND "END"
                                                                      IF(EOC) THEN
                                                                        EOD  .TRUE.
                                                                        RETURN
                                                                      ENDIF
                                                                      IFIHODK.EQ.'INTER') CALL PROMPT('TIME>')
                                                                      CALL FREE
                                                                      IFIMOOE.EQ.'BATCH') CALL FREEWR(NTW)
                                                           Append   -21

-------
Indoor  Air  Quality  Model                                                                              APPENDIX
Phase  III  Report                                             CONTAM87   FORTRAN  77   Source   Code



C ---- CHECK FOR END-OF-COMMAND "END"                                         CALL FREEIC  '.NR,1)
      IF(EOC)  THEM                                                           GO TO 100
        EDO - .TRUE.                                                   C
        RETURN                                                          200 IF(NC.GT.O) GO TO 900
      ZNDIF                                                                 CALL PROMPT C    " Enter number of  columns: ')
      CALL FREER('E',TDAT(1),1)                                              CALL FREE
C ---- REPORT                                                                CALL FREEIC  '.NC,D
      IF (ECHO) WRITE (NTH, 2020) TDAT(l)                                        GO TO 200
      WRITE (NOT, 2020) TDAT(l)                                          C
 2020 FORMAT!/,'    Tina:  '.G10.3)                                     900 RETURN
                                                                            END
      RETURN
      END                                                             C ----------------------------------------------------------------- ABORT
                                                                            SUBROUTINE ABORT
                                                                      C  SUB: ABORT - ABORTS  COMMAND AND RETURNS TO INTERACTIVE MODE
C                                                                   C
C        COMMAND   PROCESSOR   UTILITIES         C       INCLUDE 'IOCOM.INC'
C                                                                   C
C+-M-++++++++++-M-M * * ' * M+-f+4--f-M--f-f+-f-f-M"f-f-M"f+-M"f-f+-H"--*-f4"f-f+-f+-M-f-f-M-4"fC       WRITE (NTW, 2000)
                                                                            WRITE (NOT, ")
C -------------------------------------------------------------- NOPEN       WRITE (NOT, 2000)
      SUBROUTINE NOPEN (LUN.FNAME. FRM)                                    2000 FORMAT!'  *** COMMAND ABORTED')
C  SUB: NOPEN - OPENS A FILE AS A NEW FILE WHETHER IT EXISTS  OR NOT            IF (MODE. EQ. 'BATCH' ) CALL RETRN
C                LUN > LOGICAL UNIT NUMBER
C                FNAME - FILENAME                                           RETURN
C                FRH - FORM; 'UNFORMATTED' OR  'FORMATTED'                     END
      INTEGER LUN                                                     C+++-f++++4-+++4^++-
      CHARACTER FNAME* (), FRM(>                                      C                                                                   C
      LOGICAL FOUND                                                    C                CALSAPX   LIBRARY                       C
                                                                      C                                                                   C
      INQUIRE (FILE-FNAME.EXIST-FOUND)                                   C         AN EXTENSION OF "CAL-SAP" LIBRARY OF SUBROUTINES            C
      IF (FOUND)  THEN                                                   C              DEVELOPED BY ED WILSON,  U.C. BERKELEY                  C
        OPEN (LUN, FILE=FNAME.STATUS='OLD',FORM=FRM)                      C*+++++++++++++++-M++++++-M.+-M-++++++t+++-M.++++++<-f++-H-++++C

          WRITE (LUN, 2000) LUN                                          C 1.0 FREE-FIELD INPUT SUBROUTINES
 2000     FORMAT (1 6)                                                   C+++^++^+++^++4+++4>++^++^++^++4^++^++^++4+++4+++^++^+++-*-++-t~K:
        ELSEIFIFRM.EQ. 'UNFORMATTED')  THEN                               C ---------------------------- - ------------------------------------- FREE
          WRITE (LUN)  LUN                                                     SUBROUTINE FREE
        ENDIF                                                         C~SUB:FREE - READ  LINE OF FREE FIELD DATA
        CLOSE(LUN,STATUS-'DELETE')                                      C             COMMENTS LINES ECHOED TO SCREEN
        OPEN (LUN, FILE-FNAME. STATUS-'NEW' , FORM-FRM)
      ELSE                                                                  INCLUDE 'IOCOM.INC'
        OPEN (LUN. FILE-FNAME, STATUS-'NEW', FORM=FRM)                            INCLUDE 'FRECOM.INC'
      ENDIF                                                           C
                                                                      C-O.O-INITIALIZE VARIABLES
      RETURN                                                          C
      END                                                                   EOD - .FALSE.
                                                                            EOC - .FALSE.

      SUBROUTINE APPEND(LUN)                                              3  LINE(I)-' '
 C--SUB: APPEND - POSITIONS  'OLD' FILE AT LAST  RECORD SO ADDITIONAL       C
 C                RECORDS  MAY BE APPENDED                               C-1.0 GET LINE OF DATA
 C                LUN  - LOGICAL UNIT NUMBER                             C

      INTEGER LUN                                                           II- 80
                                                                            READ(NCD.1000.ERR=100>  (LINE (KX) .XK-I.II)
      REWIND LUN
   10  READ(LUN,*,END-20)                                               C ----- CHECK FOR ADDITIONAL LINE
      GO TO 10
   20  BACKSPACE (LUN)                                                         JJ - LENTRM(LLINE)
      RETURN                                                                DO 12 K-I.JJ
      END                                                                     IF(LINE(K).EQ. '\'( THEN
                                                                                I - K
 c --------------------------------------------------------------- PROMPT           11= K+79
      SUBROUTINE PROMPT (STRING)                                                  READINCMD, 1000, ERR-100)  (LINE (KK) , KK=I, II)
 C SUB:PROMPT - INLINE PROMPT                                           1000     FORMAT (80A1)
                                                                                GO TO 14
      INCLUDE 'IOCOM.INC'                                                      ENDIF
                                                                         12 CONTINUE
      CHARACTER STRING*!*)
                                                                      C ----- CHECK FOR COMMENT
      WRITE (NTW, ' (A) ' )  STRING
      RETURN                                                             14 IF(LINEU).EO.'*') THEN
      END                                                                     IF (MODE. EQ. 'BATCH') CALL FREEHR (NTW)
                                                                              CALL FREEWR(NOT)
 c --------------------------------------------------------------- PROMH         GO TO 10
      SUBROUTINE PROMH (N)                                                    ENDIF
 C SUB: PROMH - "HOLLERITH PROMPT"                                      C
                                                                      C-2.0 DETERMINE LENGTH-OF-INFORMATION
      COMMON MTOT.NP.IAU)                                             C
                                                                            JJ - LENTRM(LLINE)
      INCLUDE 'IOCOM.INC'                                              C
      CHARACTER*! NCMND, M                                              C-3.0 DETERMINE LENGTH-OF-DATA AND CONVERT  DATA TO UPPER CASE
      COMMON /CMND/ NCMND(6) , M(4, 7)                                    C
                                                                            ISP - ICHARC  ')
 C ----- PROMPT FOR ARRAY NAMES                                                 IA  - ICHAR('a')
      IF (MODE. EQ.' BATCH') GO TO 900                                          DO 30 I-l.JJ
      DO 200 1=1, N                                                             IF(LINE(I).EQ.'
-------
Indoor  Air  Quality  Model
Phase  III  Report
                                                                                                          APPENDIX
                                                           CONTAM87  FORTRAN   77   Source   Code
      SUBROUTINE FREEWR(LUN)
CSUBlFREEWR - WRITE COMMAND/DATA LINE TO FILE LUN
C               LUN - LOGICAL UNIT NUMBER  TO WRITE TO
      INCLUDE
      INCLUDE
'lOCOM.INC'
 FRECOM.INC'
      WRITE(LUN.2000)  (LINE(I),1=1,JJ)
 2000 FORMAT (IX,BOA!)
      RETURN
      END
      SUBROUTINE FREEFN(SEP,NC,FOUND)
CSUB:FREEFN - FINDS NEXT NC-CHARACTER SEPARATOR IN INPUT FILE
C                SEP (NO M - CHARACTER STRING
      INCLUDE
      INCLUDE
'lOCOM.INC'
'FRECOM.INC'
      CHARACTER*!  SEP(NC)
      LOGICAL FOUND

      FOUND = .FALSE.

   50 CALL FREE
      IF(NC.LE.II) THEN
        DO 60 N-l.NC
   CO   IF(SEP(N).NE.LINE(N  GO TO 50
        FOUND = .TRUE.
        RETURN
      ELSE
        GO TO SO
      ENDIF
      Y=0
      IS-1
      xx=o.o
      IF(LINE(I+1).EQ.'-')  THEN
        IS1
        1=1+1
      ELSEIF 'LELE'  :  (RMIN < RVALUE (N) <= RMAX)  IS O.K.
          OPT - 'LTLE1  :  (VMIN <  RVALUE(N) <= RMAX)  IS O.K.
          OPT - 'LELT'  :  (RMIN <= RVALUE(N) <  RMAX)  IS O.K.
          OPT = 'LTLT'  :  (RMIN <  RVALUE(N) <  RMAX)  IS O.K.

          STRING - SINGULAR  NOUN DESCRIBING RVALUE
      INCLUDE 'IOCOM.INC1

      CHARACTER STRING*(), OPT4
      REAL'S RVALUE(NUH).RMAX.RMIN.RVAL
      LOGICAL ERR

      DO 500 N-l.NUM
      RVAL - RVALUE(N)

      IF(OPT.EQ.'LELE')  THEN
        IF(.NOT.((RMIN.LE.RVAL).AND.(RVAL.LE.RMAX)))  THEN
          ERR = .TRUE.
          WRITE(NTH.2000) STRING,RMIN,' <=  value  <= ',RMAX, RVAL
          WRITE(NOT.*)
          WRITE(NOT. 2000) STRING. RMIN.' <=  value  <- '.RMAX,RVAL
          RETURN
        ENDIF
      FORMAT!
     ' *** ERROR: The value of , IX, A, IX,'la limited Co the range:',/,
     H2X.G11.4.A.G11.4./.
     f'             The given or generated value ls:f,G11.4)

      ELSEIF(OPT.EQ.'LELT'I THEN
        IF(.NOT.((RMIN.LE.RVAL).AND.(RVAL.LT.RMAX)))  THEN
          ERR - .TRUE.
          WRITE(NTW,2000) STRING,RMIN,' <=  value  <  '.RMAX,RVAL
          WRITE(NOT.*)
          WRITE(NOT,2000) STRING,RMIN,' <=  value  <  ',RMAX,RVAL
          RETURN
        ENDIF

      ELSEIF(OPT.EQ.'LTLE') THEN
        IF(.NOT.((RMIN.LT.RVAL).AND.(RVAL.LE.RMAX)))  THEN
          ERR = .TRUE.
          WRITE (NTH. 2000) STRING. RMIN, ' <  value  <=  ', RMAX. RVAL
          WRITE (NOT. )
          WRITE (NOT. 2000) STRING, RMIN, ' <  value  <-  ', RMAX. RVAL
          RETURN
        ENDIF

      ELSEIFIOPT.EQ.'LTLT') THEN
        IFI.NOT.((RMIN.LT.RVAL).AND.(RVAL.LT.RMAX)))  THEN
          ERR = .TRUE.
          WRITE(NTW,2000) STRING,RMIN,'  <  value  < '.RMAX,RVAL
          WRITE(NOT,*)
          WRITE(NOT,2000) STRING,RMIN,'  <  value  < '.RHAX,RVAL
          RETURN
        ENDIF

      ELSE
        ERR - .TRUE.
        WRITE(NTW,2040)
        WRITE(NOT. )
        WRITE(NOT,2040)
        RETURN
      ENDIF

 2040 FORMAT!' *** ERROR: Call to CKRRNG passed an undefined option.')

  500 CONTINUE

      RETURN
      END

C   	-CKIRNG
      SUBROUTINE CKIRNG(STRING,IVALUE,NUM,IMIN.OPT.IMAX,ERR)
CSUB:CKIRNG - CHECKS INTEGER VALUE RANGE
C              RETURN ERR-.TRUE.  IF NOT O.K.
C              VALUE IS A VECTOR OF DIMENSION IVALUE (NUM)
C
C              OPT - 'LELE' : (IMIN <-  IVALUE(N) <- IMAX)  IS O.K.
C              OPT - 'LTLE' : (IMIN <  IVALUE(N) <- IMAX)  IS O.K.
C              OPT - 'LELT' : (IMIN <-  IVALUE(N) <  IMAX)  IS O.K.
C              OPT " 'LTLT' : (IMIN <  IVALUE(N) <  IMAX)  IS O.K.
C
C              STRING - SINGULAR NOUN DESCRIBING IVALUE


      INCLUDE 'IOCOM.INC'

      CHARACTER STRING*!*),  OPT*4
      INTEGER IVALUE(NUM),IMAX,IMIN, IVAL
      LOGICAL ERR

      DO SOO N-l.NUM
      IVAL - IVALUE (N)

      IF(OPT.EQ.'LELE1) THEN
        IF(.NOT.((IMIN.LE.IVAL).AND.(IVAL.LE.IMAX))) THEN
          ERR - .TRUE.
          WRITE(NTW,2000) STRING,IMIN,'  <-  value   ',IMAX,IVAL
          WRITE(NOT.*)
          WRITE (NOT, 2000) STRING. IMIN,'    value  <= MHAX.IVAL
          RETURN
        ENDIF
 2000 FORMAT!
     +'  * ERROR: The value of'.IX.A,IX,'Is limited to the range:',/,
     +12X,I6,A.16,/,
     + '             The given or generated value is:',16)

      ELSEIFIOPT.EQ.'LELT')  THEN
        IF(.NOT.((IMIN.LE.IVAL).AND.(IVAL.LT.IMAX))) THEN
          ERR " .TRUE.
          WRITE(NTW,2000) STRING,IMIN,'  <-  value  <  ',IMAX,IVAL
          WRITE(NOT,*)
          WRITE(NOT, 2000) STRING,IMIN,'  <=  value  <  ',IMAX,IVAL
          RETURN
        ENDIF

      ELSEIF(OPT.EQ.'LTLE')  THEN
        IF(.NOT.((IMIN.LT.IVAL).AND.(IVAL.LE.IMAX))) THEN
          ERR  .TRUE.
          WRITE(NTW,2000) STRING,IMIN,'  <  value  <=  '.IMAX,IVAL
          WRITE(NOT,*)
          WRITE(NOT,2000) STRING,IMIN,'  <  value  <=  ',IMAX,IVAL
          RETURN
        ENDIF

      ELSEIF(OPT.EQ.'LTLT')  THEN
        IFI.NOT.((IMIN.LT.IVAL).AND.(IVAL.LT.IMAX))) THEN
          ERR = .TRUE.
          WRITE(NTW,2000) STRING,IMIN,'  <  value  < '.IMAX.IVAL
          WRITE(NOT.*)
          WRITE(NOT,2000) STRING,IMIN,'  <  value  < ',IMAX,IVAL
          RETURN
        ENDIF

      ELSE
        ERR  .TRUE.
        WRITE(NTH,2010)
        WRITE(NOT,*)
        WRITE(NOT,2010)
        RETURN
      ENDIF
 2010 FORMATC  **** ERROR: Call to CKIRNC passed an undefined option.')

  SOO CONTINUE

      RETURN
      END

C	CKRZER
      SUBROUTINE CKRZER(STRING, RVALUE.NUM.OPT.ERR)
CSUB:CKRZER - CHECKS REAL VALUE RELATIVE TO ZERO
C              RETURNS ERR-.TRUE.IF NOT O.K.
C              WHERE VALUE IS A VECTOR  OF DIMENSION RVALUE(NUM)
C
               OPT - 'LT' : RVALUE(N)  .LT. 0.ODD IS O.K.
               OPT = 'LE' : RVALUE(N)  .LE. O.ODO IS O.K.
               OPT - 'GE' : RVALUE (N)  .GE. O.ODO IS O.K..
               OPT = 'GT' : RVALUE(N)  .GT. O.ODO IS O.K.
               OPT - 'NE' : RVALUE(N)  .NE. O.ODO IS O.K.
                                                            Append  -24

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                  APPENDIX
   CONTAM87   FORTRAN  77   Source   Code
                STRING - SINGULAR NOUN DESCRIBING RVALUE
      INCLUDE 'IOCOM.INC'

      CHARACTER STRING*!*).  OPI-2
      REAL*8 RVALUE(NUM).RVAL
      LOGICAL ERR
      DO SOO N-l.NUH
      RVAL - RVALUE(N)

      IFIOPT.EQ.'LT')  THEN
        IF(.NOT.(RVAL.LT.O.ODO)) THEN
          ERR - .TRUE.
          WRITE(NTH,2000)  STRING,'must be < O.'.RVAL
          WRITE (NOT, )
          WRITE (NOT, 2000)  STRING, 'must be < O.'.RVAL
          RETURN
        ENDIF
 2000 FORMAT!' ""* ERROR:  the value of',1X,A.1X.A,/.
     + '             The Qlven or generated value la:',Gil.4)

      ELSEIF(OPT.EQ.'LE')  THEN
        IF(.NOT.(RVAL.LE.O.ODO)) THEN
          ERR * .TRUE.
          HRITE(NTH,2000)  STRING,'muat be < O.'.RVAL
          WRITE (NOT. *)
          WRITE(NOT.2000)  STRING,'must be <- O.'.RVAL
          RETURN
        ENDIF

      ELSEIFIOPT.EQ.'GE')  THEN
        IF(.NOT.(RVAL.GE.O.ODO)) THEN
          ERR = .TRUE.
          WRITE(NTW,2000)  STRING,'must be >- O.'.RVAL
          WRITE(NOT,)
          NRITE(NOT,2000)  STRING, 'mat be >- O.'.RVAL
          RETURN
        ENDIF

      ELSEIF(OPT.EQ.'GT')  THEN
        IF(.NOT.(RVAL.GT.0.000)1 THEN
          ERR = .TRUE.
          WRITE (NTW, 2000)  STRING,'muat be > O.'.RVAL
          WRITE (NOT, ")
          WRITE(NOT.2000)  STRING,'muat be > O.'.RVAL
          RETURN
        ENDIF

      ELSEIFIOPT.EQ.'NE')  THEN
        IF(RVAL.EQ.O.ODO)  THEN
          ERR - .TRUE.
          WRITE(NTW,2000)  STRING,'must not - O.'.RVAL
          WRITE(NOT. )
          WRITE(NOT.2000)  STRING.'must not " O.'.RVAL
          RETURN
        ENDIF

      ELSE
        ERR - .TRUE.
        WRITE(NTH.2010)
        WRITE(NOT.)
        WRITE(NOT.2010)
        RETURN
      ENDIF
      ELSEIF(OPT.EQ.'LE') THEN
        IFI.NOT. (IVAL.LE.O))  THEN
          ERR '  .TRUE.
          WRITE, (NTW. 2000) STRING,'muat be <= O.'.IVAL
          WRITE. (NOT, )
          WRITE. (NOT, 2000) STRING.'muat be <= O.'.IVAL
          RETURN
        ENDIF

      ELSEIF(OCT.EO.'GE') THEN
        IFI.NOT.(IVAL.GE.O))  THEN
          ERR -  .TRUE.
          WRITE; (NTW, 2000) STRING,'must be >> O.'.IVAL
          WRITE(NOT,*)
          WRITE(NOT,2000) STRING,'muat be >= O.'.TVAL
          RETURN
        ENDIF

      ELSEIF(OFT.EQ.'GT') THEN
        IF(.NOT.(IVAL.GT.0))  THEN
          ERR <  .TRUE.
          WRITE:(NTW,2000) STRING,'must be > O.'.IVAL
          WRITE; (NOT, 
          WRITi: (NOT. 2000) STRING,'muat be > O.'.IVAL
          RETURN
        ENDIF

      ELSEIF(OFT.EQ.'NE') THEN
        IF(IVAL.EQ.O)  THEN
          ERR "  .TRUE.
          WRITE;(NTW,2000) STRING,'muat not = O.'.IVAL
          WRITE(NOT.*)
          WRITE;(NOT,2000) STRING,'muat not - O.'.IVAL
          RETUP.N
        ENDIF

      ELSE
        ERR - .TRUE.
        WRITE(NTH, 2010)
        WRITE(MOT,)
        WRITE(MOT,2010)
        RETURN
      ENDIF
 2010 FORMAT!' ** ERROR: Call to CKIZER paaaed an undefined option.')

  500 CONTINUE

      RETURN
      END

 2010 FORMAT(' *** ERROR:  Call to CKRZER paaaed an undefined option.')   2001 FORMAT!1  *  '. (A))
      SUBROUTINE ALERT(LINE1,LINE2,LINE3)
CSUB:  ERRMSG - WRITES ALERT MESSAGE TO TERMINAL AND OUTPUT FILE
C               LINE1 IS ALWAYS WRITTEN'
C               LINE2 IS WRITTEN IF LINE2(1:1).NE.'S'
C               LINE3 IS WRITTEN IF LINE3(1:1).NE.'S'


      INCLUDE 'IOCOM.INC'

      CHARACTER LINE1*!*), LINE2*<).  LINE3* ()

      WRITE(NTW,2001) LINE1
      WRITE(NOT,*)
      WRITE(NOT,2001) LINE1
   500 CONTINUE
      RETURN
      END
      SUBROUTINE CXIZER(STRING,IVALUE.HUM,OPT,ERR)
CSUB:CKIZER - CHECKS INTEGER VALUE RELATIVE TO ZERO
C               RETURNS ERR".TRUE.IF NOT O.K.
C               WHERE VALUE IS A VECTOR OF DIMENSION IVALUE(HUM)
C
      IF(LINE2(1:1).NE.'S') THEN
        WRITE(NTW.2002) LINE2
        WRITE(HOT.2002) LINE2
      ENDIF
 2002 FORMAT (UX. (A))

      IFILINE3(1:1).NE.'S') THEN
        WRITE(UTW,2003) LINE3
        WRITE(NOT. 2003) LINE3
      ENDIF
 2003 FORMAT(13X,(A))
C
C
C
C
C


OPT
OPT
OPT
OPT
S
B
a
-




LT'
LE'
'GE'
GT'
: IVALUE (N)
: IVALUE (N)
: IVALUE (N)
: IVALUE (N)

SINGULAR NOUN


.LT.
.LE.
.GE.
.GT.
0
0
0
0
IS 0
IS O
IS 0
IS O





.X.
.K.
.X.
.K.







C 3



RETURN
END

. 0 DYNAMIC &RRAY MANAGEMENT ROUTINES







       INCLUDE 'IOCOM.INC'

       CHARACTER STRING*!*),  OPT*2
       INTEGER IVALUE(NUM),IVAL
       LOGICAL ERR
      DO 500 N=1.NUM
      IVAL - IVALUE(N)

      IFIOPT.EQ.'LT')  THEN
        IFI.NOT.(IVAL.LT.O))  THEN
          ERR = .TRUE.
          WRITEINTW.2000)  STRING,'muat be < O.'.IVAL
          WRITE(NOT,)
          WRITE(NOT.2000)  STRING,'muat be < O.'.IVAL
          RETURN
        ENDIF
  2000 FORMAT)' **** ERROR: The value of',IX,A,IX,A,/,
     +'             The given or generated value Is:',16)
      SUBROUTINE DEFINR(NAME, NA.NR.NC)
CSUB:DEFINR -  DEFINE DIRECTORY AND RESERVE STORAGE
C               FOR  REAL ARRAY IN DATABASE
C               NAME - NAME OF ARRAY
C               NA   - BLANK COMMON POINTER TO ARRAY  (RETURNED)
C               NR     NUMBER OF ROWS
C               NC     NUMBER OF COLUMNS

      COMMON MTOT,NP.IA(1)
      CHARACTER*! NAME(4)
      NP - 2
      CALL DEFIN(NAME,NA.NR.NC)
      RETURN
      END
      SUBROUTINE  DEFINI(NAME.NA,NR.NC)
CSUB:DEFINI  - DEFINE DIRECTORY AND RESERVE  STORAGE
C              FOR INTEGER ARRAY IN DATABASE
C              NAME = NAME OF ARRAY
C              NA   o BLANK COMMON POINTER TO ARRAY  (RETURNED)
                                                            Append  -25

-------
Indoor  Air  Quality  Model
Phase  III  Report
                                                                                                                  APPENDIX
                                                                   CONTAM87   FORTRAN   77   Source   Code
                NR   - NUMBER OF ROWS
                NC   - NUMBER OF COLUMNS
      COMMON MTOT.NP.IAd)
      CHARACTER*! NAME(4)
      HP > 1
      CALL DEFIN(NAME,NA,NR,NC)
      RETURN
      END


      SUBROUTINE DEFIN(NAME, NA. NR, NC)
c	DEFINE AND RESERVE STORAGE FOR ARRAY	
                                                                  100 CALL ICON(NAME.IA(I))
                                                                      IAU + 4)    NR
                                                                      IA (1+51    NC
                                                                      IA (1+61    NP
                                                                      IAd+7)    ISTR
                                                                      IA(I + 8I    0
                                                                      IA(I+9)    0
                                                                 900  RETURN
                                                                 2000 FORMAT!
                                                                      .... ERROR: Insufficient blank COMMON storage.',/,
                                                                                 Storage required  MTOT -Ml./,
                                                                     *'            Storage available MTOT =',I7)
                                                                      END
      COMMON MTOT.NP.IAd)
      INCLUDE 'ARYCOM.INC'
      INCLUDE 'IOCOM.INC'

      CHARACTER*1  NAME(4)
c	DEFIN VARIABLES	
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c-
c
c
c
c
c
c
c
c
c
NC '
MTOT
NUMA
NEXT
IDIR
IP
LENR
  NAME - NAME OF ARRAY - 4 LOGICALS MAXIMUM
  NA - LOCATION OF ARRAY IF IN BLANK COMMON
  NR - NUMBER OF RONS
      ' NUMBER OF COLUMNS
         END OF DIRECTORY
         NUMBER OF ARRAYS IN DATA BASE
         NEXT AVAILABLE STORAGE LOCATION
         START OF DIRECTORY IN BLANK COMMON
         NUMBER OF LOGICALS CONTAINED IN DATA TYPE
         NUMBER OF LOGICALS IN PHYSICAL RECORD
  NP - TYPE OF DATA
     - 1 INTEGER DATA
     - 2 REAL DATA
     - 3 LOGICAL DATA
-DIRECTORY DEFINITION FOR CORE OR SEQUENTIAL FILES
 IDIR(l.N) - NAME OF ARRAY  - INAME  (4 CHAR.)
 IDIR(S.N) - NUMBER OF RONS    - NR
 IDIRI6.N) - NUMBER OF COLUMNS - NC
 IDIR(7,N) - TYPE OF DATA      - NP
 IDIRI8.N) - INCORE ADDRESS    - NA
          - -1 IF SEQUENTIAL FILE ON DISK
          - -2 IF DIRECT ACCESS ON DISK
            SIZE OF ARRAY
           - 0 IF IN CORE STORAGE
                                                                     SUBROUTINE LOCATE (NAME, NA.NR.NC)
                                                               CSUB:LOCATE - LOCATE ARRAY "NAME" AND RETURN
                                                               C               NA - POINTER TO LOCATION IN  BLANK COMMON
                                                               C               NR = NUMBER OF RONS
                                                               C               NC - NUMBER OF COLUMNS

                                                                     COMMON MTOT.NP.IAd)
IDIRI9.N)  
IDIR(IO.N)
                                                                     CHARACTER*! NAME
                                                                     DIMENSION NAME(4),INAME<4)
                                                               c	LOCATE AND RETURN PROPERTIES ON ARRAY
                                                                     NA - 0
                                                                     CALL ICON(NAME.INAME)
                                                                     I - IFIND(INAME,0)
                                                                     IF(I.EQ.O)  GO TO 900
                                                               C	RETURN ARRAY PROPERTIES	
                                                                     NA - IA(I+7)
                                                                     NR - IAd + 4)
                                                                     NC - IAd+5)
                                                                     NP - IAd+6)
                                                                 900 RETURN
                                                                     END
C	DIRECTORY DEFINITION FOR DIRECT ACCESS FILES	
C      IDIR(S.N)  - NUMBER OF INTEGERS
C      IDIR(6,N)  = NUMBER OF REAL WORDS
C      IDIR(7,N)  - NUMBER OF LOGICALS
C      IDIRie.N)  - NUMBER OF LOGICAL RECORDS
C      IDIR(9,N)  - LOGICAL RECORD NUMBER
C      IDIR(IO.N)   - LUN IF ON LOGICAL UNIT LUN

c	EVALUATE STORAGE REQUIREMENTS	
      NSIZE = (NR*NC*IP(NP) -1)/(IP(1)*2)
      NSIZE - NSI2E*2 + 2
      NA - NEXT
      NEXT - NEXT + NSIZE
C	SET UP NEW DIRECTORY	
      NUMA = NUMA + 1
      IDIR - IDIR - 10
      I  IDIR
C	CHECK STORAGE LIMITS	
      IF(I.GE.NEXT)  GO TO 100
      I - NEXT - I + MTOT - 1
      WRITE(NTW.2000) I,MTOT
      WRITE(NOT,*)
      WRITE(NOT,2000) I,MTOT
      PAUSE
      STOP
  100 CALL ICON (NAME. IA(I) )
      LAd+O   NR
      IAd+5)   NC
      IAd+6)   NP
      IAd+1)   NA
      IAd+8)   NSIZE
      IAd+9)   0
 900  RETURN
 2000 FORMAT<
     ' ** ERROR:  Insufficient blank COMMON storage.'./,
     '             Storage required  MTOT -',I7,/,
     '             Storage available MTOT -M7)
      END
      SUBROUTINE DEFDIR(NAME,NR.NC,ISTR)
CSUB:OEFDIR - DEFINE DIRECTORY FOR OUT-OF-CORE  FILE
C               NAME - NAME OF ARRAY
C               NR   ' NUMBER OF RONS
C               NC   = NUMBER OF COLUMNS
C               ISTR - OUT OF CORE FLAG (=-1)
                                                                    SUBROUTINE DELETE(NAME)
                                                               CSUB:DELETE - DELETE ARRAY "NAME- FROM DATABASE

                                                                    COMMON MTOT.NP.IAd)
                                                                    INCLUDE 'ARYCOM.INC'
                                                                    INCLUDE 'IOCOM.INC'

                                                                    CHARACTER*! NAME
                                                                    DIMENSION NAME (4), INAME (4)
                                                               C	DELETE ARRAY FROM  STORAGE 	
                                                                 100 CALL ICON(NAME,INAME)
                                                                    I - IFIND(INAME,0)
                                                                    IF(I.EQ.O)  GO TO 900
                                                               C	CHECK ON STORAGE LOCATION	
                                                                 200 NSIZE - IAII+8)
                                                               C	SET SIZE OF ARRAY	
                                                                  '  NEXT = NEXT - NSIZE
                                                                    NUMA - NUMA - 1
                                                                    NA    IAd+7)
                                                               C	CHECK IF OUT OF CORE OR DIRECT ACCESS	
                                                                    IF(NA.GT.O) GO TO  500
                                                                    WRITE(NTH,1000) NAME
                                                                    WRITE(NOT,)
                                                                    WRITE(NOT.1000) NAME
                                                                    GO TO SOO
                                                                 500 IF(NA.EQ.NEXT)  GO  TO 800
                                                               C	COMPACT STORAGE	
                                                                    II   - NA + NSIZE
                                                                    NNXT = NEXT - 1
                                                                    DO 700 J=NA,NNXT
                                                                    IA(J)  IAIII)
                                                                 700 II - II + 1
                                                               C	COMPACT AND UPDATE DIRECTORY 	
                                                                 600 NA - I - IDIR
                                                                    IDIR - IDIR + 10
                                                                    IF(NA.EQ.O) GO TO  900
                                                                    NA - NA/10
                                                                    DO 860 K-l.NA
                                                                    II - I + 9
                                                                    DO 850 J=l,10
                                                                    IA(II) = IAdI-10)
                                                                 850 II - II - 1
                                                                    IF(IA(I7).LE.O) GO TO 860
                                                                    IF(IA(I+9).EQ.O)  IA(I+7)  - IA(I+7) - NSIZE
                                                                 860 I  I - 10
                                                               C
                                                                 900 RETURN
                                                               1000 FORMAT!'    Name '.4A1.' la being used for
                                                                   *  ' OUT-OF-CORE file.1,/)
                                                                    END
      COMMON MTOT.NP.IAd)
      INCLUDE 'ARYCOM.INC'
      INCLUDE 'IOCOM.INC'

      CHARACTER*1 NAME(4)
C	EVALUATE STORAGE REQUIREMENTS
      IF(NP.EQ.O) NP  - 2
C	SET UP NEW DIRECTORY	
      NUMA  - NUMA +  1
      IDIR - IDIR - 10
      I - IDIR
C	CHECK STORAGE LIMITS	
      IF(I.GE.NEXT) GO TO 100
      I - NEXT - I   MTOT - 1
      WRITE(NTW.2000)  I,MTOT
      WRITE (NOT.  I
      WRITE (NOT. 2000)  I, MTOT
      PAUSE
      STOP
                                                                      SUBROUTINE ICON (NAME. INAME)
                                                                      CHARACTER*! NAME(4)
                                                                      DIMENSION INAME(4)
                                                                 C	CONVERT LOGICALS  TO  INTEGER DATA
                                                                      DO 100 1=1.4
                                                                   100 INAME (II  - ICHAJU NAME(I) )
                                                                 C
                                                                      RETURN
                                                                      END
                                                                      FUNCTION IFIND(INAME.LUN)
                                                                 CFUN: IFIND - FIND
                                                                      COMMON MTOT.NP.IAd)
                                                                      INCLUDE 'ARYCOM.INC'
                                                                      DIMENSION INAME(4)
                                                                c	FIND ARRAY LOCATION
                                                                      I m IDIR
                                                           Append  -26

-------
Indoor   Air   Quality  Model
Phase  III  Report
                                                  APPENDIX
   CONTAM87   FORTRAN  77   Source   Code
      DO 100 N-l.NUMA
      IF(LUN.NE.IA(I+9))  GO TO 100
      IF (INAMEU) .NE.IAII  )) GO TO 100
      IF (INAHEI2).NE.IAII*!)) GO TO 100
      IF (INAMEO).NE.IA(H-2)) GO TO 100
      IF 0    :  generate right, [Tl.  transformations
    Eigenvectors  of real eigenvalues occurr  as rows (cols)  of [T|-l
    ((T)).   Eigenvectors for a complex eigenvalue pair aj.l  laj,j+1
    may be formed by tj  ltj+1 where  t}, tj+1 are the corresponding
    rows  (cols) of  [T|-l (IT|)

    Iterations  are limited to 50 maximum. On exit from the procedure
    TMX records the number of iterations performed. Failure to
    converge is indicated by TMX50 or. if  all transformations in
    one Iteration are the identity matrix, by  TMX<0.

    The machine dependent variable EP  is set to IE-OS and should be
    reset for machine precision available.

 :	DICTIONARY  OF  VARIABLES  	
	VARIABLI:-
  --INPUT
     A(N.N)
     N
     TMS
  OUTPUT
     T(N,N)
     TMX
  LOCAL
                        DESCRIPTION
                Array to be analyzed.
                System size
                Control parameter

                Array to receive eigenvectors.
                Iteration count/iteration flag
      EP
            Precision
      IMPLICIT  REAL*8(A-H,O-Z)
      REAL-8  MN.N) ,T(N,N) ,EP
      INTEGER N.TMX
      LOGICAL MARK, LEFT, RIGHT
C
C0.0 INITIALIZE CONTROL VARIABLES
C
      IFIEP.LI1.O.ODO) EP - l.OD-9
      EPS - SQRT(EP)
      LEFT -  .FALSE.
                                                            Append  -27

-------
Indoor  Air  Quality  Model
Phase   III  Report
                                                                                                                  APPENDIX
                                                                     CONTAM87   FORTRAN  77   Source   Code
      RIGHT - .FALSE.
      IF(TMX.LT.O) THEN
       LEFT - .TRUE.
      ELSEIF(TMX.OT.O) THEN
       RIGHT - .TRUE.
      ENDIF
      MARK - .FALSE.
C
C--1.0 INITIALIZE [T| AS IDENTITY MATRIX
C
      IF(THX.NE.O) THEN
       DO 10 I-l.N
         T(I,I)  - l.ODO
       DO 10 J-I+l.N
         TII.J)   O.ODO
         TIJ.I)  - O.ODO
   10  CONTINUE
      ENDIF
C
C2.0 MAIN LOOP
C
C-MAC WRITE!*,MSX.A.M') ' '
      DO 26 IT-1,50
  MAC WRITE!*,'(A,\)') '+'

  -2.1 IF MARK IS SET
         TRANSFORMATIONS OF PREVIOUS ITERATION WERE OMITTED
         PROCEDURE WILL NOT CONVERGE

      IF(MARK)  THEN
       TMX - 1-IT
       RETURN
      ENDIF
C
C2.2 COMPUTE CONVERGENCE CRITERIA
C
      DO 20 I-l.N-1
       All - All,I)
      DO 20 J-l+l.N
       AIJ - A(I.J)
       AJI - AIJ,I)
       IF((ABS(AIJ+AJI).GT.EPS) .OR.
     +   ((ABS(AIJ-AJI). GT.EPS). AND. (ABS (AII-AU, J)) . GT.EPS))) THEN
         GOTO 21
       ENDIF
   20 CONTINUE
      TMX - IT -1
      RETURN
C
C2.3 BEGIN NEXT TRANSFORMATION
C
   21 MARK = .TRUE.
      DO 25 K-l.N-1
      DO 25 M-K-H.N
       B > O.ODO
       G = O.ODO
       HJ - O.ODO
       YH - 0.000
       DO 22 I-l.N
         AIK - A(I,K)
         AIM = Ad,HI
         TE  - AIK*AIK
         TEE - AIM-AIM
         YH  = YH + TE - TEE
         IFIII.NE.K) .AND. (I.NE.MM  THEN
                                                                            CHY -  l.ODO
                                                                            SHY   O.ODO
                                                                          ELSE
                                                                            CHY   1.0DO/SQRTI1.0DO - TANHY*TANHY)
                                                                            SHY -  CHY*TANHY
                                                                          ENDIF
C
C




C
C

PUT
Cl - CHY*CX - SHY*SX
C2  CHY*CX + SHY*SX
SI  CHY*SX + SHY*CX
32 - -CHYSX + SHY*CX

  APPLY TRANSFORMATION IF WARRANTED
                                                                          IF((ABS(SI).GT.EP).OR.(ABSIS2).GT.EP))  THEN
                                                                            MARK -  .FALSE.
                                                                     	 TRANSFORMATION  ON THE LEFT
                                                                            DO 23 I-l.N
                                                                              AKI - AIK, I)
                                                                              AMI - AIM. I)
                                                                              A(K.I) - Cl'AKI + SI-AMI
                                                                              AIM,I)  32AKI + C2*AMI
                                                                              IF(LEFT)  THEN
                                                                                TKI - T(K,I)
                                                                                TMI - KM, I)
                                                                                T(K,I)   Cl'TKI + S1*TMI
                                                                                T(M,I)  - S2*TKI + C2*TMI
                                                                              ENDIF
                                                                      23     CONTINUE
                                                                     	 TRANSFORMATION  ON THE RIGHT
                                                                            DO 24 I-l.N
                                                                              AIK - A(I,K)
                                                                              AIM - A(I.M)
                                                                              A(I,K)  C2*AIK - S2AIM
                                                                              Ad.MI i -Sl'AIK * Cl'AIM
                                                                              IF(RIGHT) THEN
                                                                                TIK - TII.K)
                                                                                TIM - T(I,M)
                                                                                TII.K)  - C2TIK - S2*TIM
                                                                                TII.M)  - -Sl'TIK + C1TIM
                                                                              ENDIF
                                                                      24     CONTINUE
                                                                          ENDIF
                                                                      25 CONTINUE
                                                                      26 CONTINUE
                                                                        TMX -  50

                                                                        RETURN
                                                                        END
           AKI
           AMI
           H
           TEP
           TEN
           G
           HJ
         ENDIF
       CONTINUE
             H
        D
        AXM
        AMK
        C
        E
                AIK, I)
                AIM. I)
                H + AKI*AMI - AIK'AIM
                TE + AMI"AMI
                TEE * AKI'AKI
                G  TEP + TEM
                BJ - TEP + TEM
                 H
             A(K.K) - A(M.M)
             A(K.M)
             A(M.K)
             AKM + AMK
             AKM - AMK
        COMPUTE ELEMENTS OF (Ri|

        IF(ABSIC).LE.EP) THEN
         CX = l.ODO
         SX = O.ODO
        ELSE
         COT2X  D/C
         SIG - SIGN(1.ODO.COT2X)
         COTX - COT2X + (SIG'SQRT(l.ODO  + COT2XCOT2X)I
         SX = SIG/SQRT(l.ODO + COTX'COTX)
         cx = sx-corx
        ENDIF

        IFIYH.LT.O.ODO) THEN
         TEM m CX
         CX = SX
         SX - -TEM
        ENDIF
        COS2X - CX*CX - SX*SX
        SIN2X  2.0DO*SXCX
        D  D*COS2X + C*SIN2X
        H - H*COS2X - HJ'SIN2X
        DEN " G * 2.0DO*IE*E + D'DI
        TANHY = (E*D - H/2.0DOI/DEN

        COMPUTE ELEMENTS OF [SI]

        IF IABS(TANHY).LE.EP)  THEN
                                                        Append -28

-------
Indoor  Air  Quality   Model                                                                             APPENDIX
Phase  III   Report                                            CONTAM87  FORTRAN   77  Source   Code

 Include Files
                                                                      C CALSAPX  FR HE-FIELD   INPUT                  SFRECOM.INC

C CALSAPX  ARRAY   MANAGEMENT                  $ARYCOM.INC       CHARACTER LINE'l. LLINE*10
c
                                                                           COMMON /CLINE1/ LINE (160)
      COMMON /ARYCOM/ NUMA.NEXT. IDIR. IP <3)                                   COMMON /CLINE2/ II. JJ
C   MTOT    SIZE OF BLANK COMMON VECTOR IA
C   NP      CURRENT DATA TYPE: 1-INTEGER:  2-REAL; 3-CHAR.                c ____ VARIABLE _________ DESCRIPTION
C   IA
-------
NBS.114A (REV. 2-aci
    U.S. DEPT. OF COMM.

   BIBLIOGRAPHIC DATA
  SHEET (See instructions)
I. PUBLICATION OR
  REPORT NO.
   NBSIR 88-3814
2. Performing Organ. Report No.
                                                                    3. Publication Date
                            JULY 1988
 4. TITLE AND SUBTITLE
  Progress  Toward a General Analytical Method  for Predicting  Indoor Air Pollution in
  Buildings -  Indoor Air Quality Modeling Phase III Report
 5. AUTHOR(S)
            James Axley
6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions;

  NATIONAL BUREAU OF STANDARDS
  U.S. DEPARTMENT OF COMMERCE
  GATTHERSBURG, MD 20899
                                             7. Contract/Grant No.
                                             8. Type of Report & Period Covered
 9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

  National  Bureau of Standards
  Building  Environment Division 747
  Center  for Building Technology
  ftaithersbure. MD 20899	
10= SUPPLEMENTARY NOTES
   [  | Document describes a computer program; SF-185, FIPS Software Summary, is attached.
11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant
   bibliography or literature survey, mention it here) This interim report  presents  the  results of Phaselll
of  the NBS General  Indoor Air Pollution Concentration  Model Project.   It describes;
a)a general element-assembly formulation of multi-zone contaminant dispersal analysis
theory that provides  a  general framework for the development of detailed (element)
models of mass transport  phenomena that may affect contaminant dispersal in buildings.
b)an approach to modeling the dispersal of interactive contaminants involving con-
taminant mass transport phenomena governed by basic principals of kinetics and intro-
duces a linear first  order kinetics element to achieve this end,  c)an approach to
modeling the details  of contaminant dispersal driven by  convection-diffusion processes
in  one-dimensional  flow situations  (e.g., HVAC ductwork)  and introduces  a convection-
diffusion flow element  to achieve this  end, and d) the features and use  of CONTAM87, a
program that provides a computational implementation of  the theory and methods discussed
The theory and methods  presented are based upon a slight generalization  of the building
idealization employed earlier  (Axley, 1987).  Here, building air  flow systems are
idealized as assemblages  of mass transport elements, rather than  simply  flow elements a
used previously, connected to discrete  system nodes corresponding to  well-mixed air
zones within the building and its HVAC  system.  Equations governing contaminant dis-
persal in the whole building air flow system due to air  flow and  reaction or sorption
mass transport phenomena  are formulated by assembling  element equations, that character-
ize  a  specific instance of mass transport in the building air flow  system, in such a
manner that the fundamental requirement  of conservation of mass is  satisfied in each
                                                                                           ZOTl
12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)
contaminant dispersal analysis, inverse  contaminant dispersal analysis,  tracer gas
techniques, building  simulation
13. AVAILABILITY

   [JQ Unlimited
   |  | For Official Distribution.  Do Not Release to NTIS
   |  | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.
      20402.

   [y~] Order From National Technical Information Service (NTIS), Springfield, VA. 22161
                                                      14. NO. OF
                                                         PRINTED PAGES

                                                            124
                                                      15. Price
                                                                                 $18.95
                                                                              USCOMM-DC 0043-P80

-------