EPA-600/2-80-191
November 1980
NUMERICAL SIMULATION OF AERATED SLUDGE COMPOSTING
by
Robert Smith
and
Richard G. Eilers
Wastewater Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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TECHNICAL REPORT DATA
(Phase read Inumctions on the reverse before completing)
1. REPORT NO. )2.
EPA-600/2-80-191
3. RECIPIENT'S ACCESS! Of*NO.
pjtfil 12 04 46
4. TITLE AND SUBTITLE
NUMERICAL SIMULATION OF AERATED SLUDGE COMPOSTING
S. REPORT DATE
November 1980
6, PERFORMING ORGANIZATION CODE
7, AUTHORS)
Robert Smith and Richard G. Eilers
8. PERFORMING ORGANIZATION REPORT NO.
9, PERFORMING ORGANIZATION NAME AND ADDRESS
Municipal Environmental Research Lab oratory—Cin., OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
tO. PROGRAM ELEMENT N'O.
36B1C
11, CONTRACT/GRANT NO.
12, SPONSORING AGENCY NAME AND ADDRESS
Same as above
13, TYPE OF REPORT AND PERIOD COVERED
Inhouse
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Contact: Robert Smith (513)684-7624
16. ABSTRACT
ihis report describes, development of a time-dependent computerized model for
composting or wastewater treatment plant sludge with forced aeration of the pile. The
work was undertaken because, -in the past, development of the composting process for
wastewater sludge has been _almost wholly experimental and interpretation of ex-
perimental results is often difficult without a well organized scientific preception of
the phenomena believed to control the process. The model is two-dimensional because
piles are long compared to dimensions of the trapezoidal cross-section. The cross-
sectional area of the pile is divided into rectangular and triangular area! increments.
The pressure source for the forced aeration is along the longitudinal plane of symmetry
at ground level. The air flow regime is established first using an iterative solution
to Larlace s equation. Mass flow rates for water vapor, oxygen, and enthalpy are
computed around each area! increment. The biological decomposition rate is treated as
a function of temperature and moisture content of each areal increment. Finally
properties such as temperature, moisture content, and oxygen concentration are found for
each areal increment at each time point. A time interval of 15 minutes was found to give
satisfactory results, Physical properties of compost were derived from soil science
h"iited measurements made by the Los Anqeles County Sanitation
Districts. Biological properties of compost were taken from work completed for
composting of sol id-"wastes. Measurements made on mechanically aerated piles by the Los
Angeles County Sanitation Districts were used to test the validity of the model
Computed results agreed reasonably well with measurements but additional research is
recommended to maximize the usefulness of the computational approach. The movement of
moisture through the pile by capillary action was not included in the model because the
necessary measurements needed to characterize the phenomenon are not available.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b, IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
13. DISTRIBUTION STATEMENT
Release to pub-lie
19. SECURITY CLASS (This Report}
Unclassified
21, NO, OF PAGES
76
20. SECURITv CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for public-
ation. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
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s
FOREWORD
The U.S. Environmental Protection Agency was created because of in-
creasing public"and government concern about the dangers of pollution to the
health and welfare of the American people. Noxious air, foul water, and
spoiled land are tragic testimonies to the deterioration of our natural
environment. The complexity of that environment and the interplay between
its components require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem
solution, and it involves defining the problem, measuring its impact, and
searching for solutions. The Municipal Environmental Research Laboratory
develops new and improved technology and systems to prevent, treat, and
manage wastewater and solid and hazardous waste pollutant discharges from
municipal and community sources, to preserve and treat public drinking water
supplies, and to minimize the adverse economic, social, health, and
aesthetic effects of pollution. This publication is one of the products of
that research—a most vital communications link between the researcher and
the user community.
As the environmental protection movement has grown over the past
several years perception of the cost involved in control of pollution has
also grown. This has resulted in increasing interest in low cost treatment
processes such as composting of wastewater treatment plant sludge. Although
experimental research on the process has been substantial engineering
analysis has proven to be intractable compared to other wastewater treatment
processes. In response to this need this report describes development of a
first-generation computerized time-dependent model for the composting pro-
cess using forced aeration of the pile.
Francis T. Mayo
Director, Municipal Environmental
Research Laboratory
i i i
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ABSTRACT
~This report describes development of a time-dependent computerized
model for composting of wastewater treatment plant sludge with forced
aeration of the pile. The work was undertaken because, in the past, de-
velopment of the composting process for wastewater sludge has been almost
wholly experimental, and interpretation of experimental results is often
difficult without a'wel1-organized scientific perception of the phenomena
believed to control the process. The model is two-dimensional because piles
are long compared to dimensions of the trapezoidal cross-section. The cross-
sectional area of the pile is divided into rectangular and triangular area!
increments. The pressure source for the forced aeration is along the
longitudinal plane of symnetry at ground level. The air flow regime is
established first using an iterative solution to LaPlace's equation. Mass
flow rates for water vapor, oxygen, and enthalpy are computed around each
areal increment. The biological decomposition rate is treated as a function
of temperature and moisture content of each areal increment. Finally,
properties such as temperature, moisture content, and oxygen concentration
are found for each areal increment at each time point. A time interval of 15
minutes was found to give satisfactory results. Physical properties of
compost were derived,from soil science literature and from limited measure-
ments made by the Los Angeles County Sanitation Districts. Biological
properties of compost were taken from work completed for composting of solid
wastes. Measurements made on mechanically aerated piles by the Los Angeles
County Sanitation Districts were used to test the validity of the model...
Computed results agreed reasonably well with measurements but additional
research is recommended to maximize the usefulness of the computational
approach. The movement of moisture through the pile by capillary action was
not included in the model because the necessary measurements needed to
characterize the phemonemon are not available.
iv
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CONTENTS
Foreword i i i
Abstr act a*****)! iv
Figures . vi
Tables vii
1. Introduction 1
2. Conclusions and Recommendations 3
3. Description of Compost Model 4
4. Physical Properties of Air and Water 9
5. Physical Properties of Compost 12
6. Air Flow Regime 19
7. Microbiological Heat Generation 22
8. Movement and Storage of Moisture 26
9. Movement and Storage of Heat 29
10. Movement and Consumption of Oxygen 32
11. Comparison of Computed and Measured. Results 35
References ; 43
Appendix 45
v
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FIGURES
Number Page
1 Discretization scheme for numerical integration of
non-aerated composting process 5
2 Discretization scheme for numerical integration of
aerated composting process 6
3 Specific volume versus moisture content for Muck soil
and compost 13
4 Air flow velocity versus pressure gradient for sludge
compost 18
5 Rate of microbiological activity versus compost
temperature 23
6 Rate of microbiological activity versus compost solids
fraction 25
7 Diagram of LACSD aerated compost pile for wastewater
treatment sludge 36
8 Measured and computed interior compost temperatures
versus composting time for piles A&B 37
9 Measured and computed interior compost temperatures
versus composting time for piles C&D 38
10 PDK and air flow rate (cfm) versus compost solids
fraction 41
vi
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TABLES
Number * Page
., , ¦ .*/
A-l Input Variables to CMPST 46
A-2 Output Parameters from CMPST 48
A-3 FORTRAN Listing of CMPST ..... 51
A-4 Input Data to CMPST ...... 61
A-5 Printed Output from CMPST . 62
vi i
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INTRODUCTION
Windrow composting of wastewater treatment plant sludge is a promising low
cost method for land disposal of sludge. The process consists of mixing
dewatered raw or digested sludge with a bulking agent such as previously cured
sludge, wood chips, sawdust, or rice hulls and piling the mixture in long (50-
150 meters) windrows with a natural trapezoidal cross-sectional shape. The
bulking agent is used to increase porosity of the windrow, thus facilitating
flow of atmospheric air through the pile for support of aerobic microbiological
activity. Aerobic microbiological activity within the windrow pile consumes
odor producing organic material with production of heat. The heat destroys
pathogenic bacteria and evaporates a portion of the water in the pile to produce
a cured compost product which is easily handled and aesthetically acceptable as
a soil amendment.
If the porosity provided by the bulking agent is great enough .an adequate
convective flow of air through the pile can be produced by the temperature
difference between pile and atmospheric air. However, forced aeration has been
found to be advantageous, especially when raw rather than digested sludge is
used. Forced aeration is provided by laying perforated (10 cm dia) air headers
under the windrow and using an air blower to draw air through the pile or force
air out through the pile. This assures an adequate supply of atmospheric oxygen
with a reduction in curing time. Also, if air is drawn into the pile the problem
of odor emission is minimized. Since land area needed for the windrows is rela-
tively large (8 mgd/acre) protection from the weather is usually not provided.
Periodic mixing or turning of the windrows is sometimes necessary about
once every one to three days to expose all of the sludge to the higher interior
temperatures for pathogen destruction and evaporation of water. Turning of the
windrows is usually done with a commercially available diesel powered piece of
mobile equipment called a composter. Mechanically aerated windrows are usually
not turned during the composting period.
Research and development work on windrow composting of wastewater sludge
has been primarily empirical in nature. Initial research (1) on composting was
conducted by the Agricultural Research Service (ARS), U.S. Department of
Agriculture at Beltsvilie, Maryland. The use of various bulking agents was
studied to provide for adequate convective movement of atmospheric oxygen
through the windrows. A mixture of three volumes of wood chips to one volume
of digested dewatered sludge was found to give good results. Windrows (60
meters long) were laid on a 30 cm layer of wood chips and turned daily for a
period of 2-3 weeks. The trapezoidal cross-section of the windrow was 4.5 m
wide at the base and 2 m high. Temperature of 55-65 C were achieved at the
interior of the windrows and the processed compost was further cured for about
30 days in the storage area. Finally, wood chips were salvaged for reuse by
screening.
When the ARS began composting raw dewatered sludge the odor produced by
the raw sludge caused complaints from local residents. Forced aeration (2) of
the windrow was found to be the best solution to this problem. Perforated air
headers (10 cm dia) were laid in the wood chip base and atmospheric air was
drawn into the pile and out through the air headers, a water trap, the blower,
and finally through a small pile of screened cured compost. Inward flow of air
1
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was maintained for 16-21 days into the composting cycle and then reversed for
8-10 days. The 6 meter wide by 2.5 meter high windrow was also covered with a
30 cm thick layer of screened cured compost. Windrows were not periodically
mixed. Temperature and oxygen concentrations at various locations within the
windrow were measured (3) over the 28 days composting period. Temperatures
reached maximum values of about 75°C and oxygen concentrations a minimum of
about 5% at the center of the windrow. Fecal coliform and salmonella bacteria
were effectively destroyed.
Over the past several years Los Angeles County Sanitation Districts
(LACSD) has conducted extensive research, partially,supported by EPA Contract
14-12-15, into both windrow and mechanical composting methods. LACSD has
tended to adjust the initial compost porosity by mixing dry cured compost with
the dewatered sludge. Portions of the LACSD work were used in development of
the model described in this report. In an effort to generalize some of the
experimental findings of LACSD, Roger T. Haug developed (4) mass and heat
balance relationships for the composting process as a whole. This analysis
shows the relationship between available fuel and allowable moisture content
in the initial compost mixture to achieve any required moisture content in the
cured compost.
Although steady-state mass and heat balance relationships like those
developed by Haug are useful for understanding some of the limitations of the
process they cannot be used to clarify the essential time-dependent mechanisms
which govern the process. This report describes development of a first
generation time-dependent simulation model of the windrow composting process
with forced aeration.
Most of the mechanisms known to be operative in the process have been
included in the model even though reliable measurements for physical and
microbiological properties of compost are not available. Many of the
properties have been taken from the soil science literature or from other
technical disciplines. The finite difference numerical integration scheme
used is not the most efficient or the most accurate but it is simple in concept
and easily understood by sanitary engineers. The model should be useful as a
first step towards establishing a technically sound quantitative research
program for overcoming the remaining obstacles preventing widespread use of
windrow composting as a sludge disposal method.
In general, current research goals are to avoid odor and particulate
emissions from the uncovered compost windrows, to minimize or eliminate the
need for wood chips or other inert bulking media used to increase the porosity
of the pile, and to reduce the processing time while adequately stabilizing the
sludge, destroying pathogenic bacteria, and reducing the water content to a
friable level.
2
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CONCLUSIONS AND RECOMMENDATIONS
A first generation, time-dependent, numerical simulation of the aerated
composting process for wastewater treatment sludge has been developed and
tested against measurements made on the full-sized process. The model is two-
dimensional based on the assumption that the length of the trapezoidal cross-
section pile is great compared to the dimensions of the cross-section.
Measurements made by the Los Angeles County Sanitation Districts research
engineers on an obelisk shaped pile 6 meters wide at the base, 2.5 meters high,
and 12 meters long were used in validating the model. The performance of four
piles operated over a 30 day composting period were used for comparison with
computed results. Final solids and volatile fractions agreed reasonably well
between computed and measured values. Measurements of interior compost tem-
perature versus time compared less favorably with computed results. The
principal problem found in running the simulation program is the tendency of
area! increments along the air-compost boundary to become too dry. This
problem could be associated with omission of the mechanism for movement of
moisture under capillary pressure or with the assumption that water vapor
within the pile is always saturated at the local compost temperature. The
finite-difference method of numerical integration used appears to be adequate
for the simulation. Fundamental measurements of compost physical and micro-
biological characteristics are needed before the simulation model can be
upgraded to a valuable predictive tool. Additional work should be undertaken
to adapt the program for simulation of non-aerated compost windrow perform-
ance.
3
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DESCRIPTION OF CCWPOST MODEL
The trapezoidal cross-sectional area of the compost windrow is divided into
a number of rectangular and triangular areal increments one centimeter deep as
shown in Figures 1 and 2. If the length of the windrow is great compared to the
dimensions of the cross-section the end effects can be neglected and a two-
dimensional model is adequate. Also, since the trapezoidal cross-sectional shape
is symmetric about the vertical centerline only one-half of the cross-sectional
area need be studied. Air enters the aerated pile from a perforated pipe in the
longitudinal plane of symmetry at ground level.
The shape of the trapezoidal cross-section is specified by inputting the
number (NVB) of vertical blocks, the number (NBB) of blocks along the base of the
trapezoid, and the number (NTB) of blocks along the top surface of the trapezoid.
For example, in Figure 1; NBV is 10, NBB is 27, and NTB is 7. In Figure 2; NVB is
12, NBB is 29, and NTB is 5. When the width (DX) and height (OY) of the interior
blocks are supplied in centimeters as input the dimensions and division scheme for
the trapezoidal cross-section are fully determined.
Approximate dimensions of the non-aerated windrow (Figure 1) used by LACSD
are 4 ft high, 13 ft wide at the bottom, and 3.5 ft wide at the top. Therefore, by
setting DX at 0.475 ft (14.478 cm) and DY at 0.4 ft (12.192 cm) the dimensions of
the simulated cross-section are 4 ft high, 12.825 ft wide at the bottom, and 3.325
ft wide at the top. Similarly, dimensions of the aerated pile were 2.5 meters high
and 6 meters wide at the bottom with sides sloping at 45°. Thus, if both DX and
DY are set equal to 20.83 cm the dimensions of the simulated aerated pile (Figure
2) are 2.5 meters high, and 6.0407 meters wide at the bottom with slides sloping
at 45 . Thus, it can be seen that the program has the flexibility to approximate
any trapezoidal cross-sectional shape.
Areal increments (blocks) are identified by the row number (I) and the column
number (0). For example, the solids fraction of compost in the block in the 11th
row and the J'th column is written as FS(I,0), The pressure source which drives
ambient air through the pile is always located in the 2'nd row and 2'nd column.
Therefore, the number (IV) of the top row of the trapezoid is (NVB+1). Similarly,
the number (0B) of the last column on the right will be (NBB+3)/2. and the number
(OT) of the first column on the sloping boundary will be (NTB+5)/2. The area
(AREA) of the trapezoidal cross-section (excluding the pressure source is
computed as follows:
AREA = DX*DY(NVB*(NVB+NTB)-l)/2
The first phase of computation solves for the horizontal (UX) and vertical (UY)
components of air flow velocity at each of the nodal points (black circles) within
the windrow cross-section. Flow of air through the compost is assumed to be
laminar and obey Darcy's law. An iterative solution of Laplace's equation
combining conservation-of-mass and Darcy's law is used. When the blower pressure
(PBL0W) is input as a positive value air is forced out through the pile and when
PBL0W is negative air is drawn into the pile. Two hundred iterations have been
found to be adequate for convergence. The air flow pattern is assumed to persist
throughout the composting cycle. A second generation model might adjust the air
flow pattern periodically if the relationship between compost physical properties
such as moisture content and porosity and the Darcy's law coefficient is known.
4
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i i 0-4--
i
i
10 o-
I
I
9 O-
i
I
8 O-
I
I
7 O-
I
I
6 O-
I
I
5 O-
I
4 O-
'iff
2 O- 4- -
4- -•
M-
10 11 12 13 14 15
Figure 1. Discretization scheme for numerical integration of non-aerated composting process
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13
12
11
10
9
8
7
6
5
4
3
1
2
O-
i
i
o-
I
I
o-
I
I
o-
I
I
o-
I
I
o-
I
I
o-
I
I
o-
I
I
o-
I
(
o-
I
I
I
o-
h-
I"
r
r.
l-_-
L-
I--
I-
¦t
k
k
10 11 12 13 14 15 16
Figure 2. Discretization scheme for numerical integration of aerated composting process
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The overall objective of the program (CMPST) is to compute the movement and
storage or conversion of water vapor, enthalpy, and oxygen within the pile as
a function of time. Time is divided into equal increments (DT) and the number
of time increments computed times DT equals the composting period, usually less
than 30 days. A time increment of 15 minutes has been found to give good
results-. At each time point the computation begins by computing the flux of
water vapor (gm/hr), enthalpy (cal/hr), and oxygen (gm/hr) into (positive
inward} each block. The computation starts with the block in the third row of
the second column and proceeds up the second column to the IV1th row. The
columns are then considered consecutively from column 3 to column JB always
proceeding up the column from the bottom block to the top block. Four flux
values are computed for each block. For example, water vapor flux from the
left, right, bottom and top are QVL, QVR, QVB, and QVT. Similarly, enthalpy
flux values are QHL, QHR, OHB, and QHT and oxygen flux values are QOL, QOR, QOB,
and QOT.
Air within the compost pile is assumed to be saturated with water vapor at
the local compost temperature. The rate of microbiological heat generation in
each block is proportional to the concentration of volatile solids remaining
and is also a function of compost temperature and the moisture content. Water
is produced as one of the products of .combustion; 0.54 gm HgO per gm of solids
combusted. Heat produced is HCOMB cal/gm of volatile solids combusted.
Physical properties of compost in the 11th row and J'th column are density (W-
gm/cc), solids fraction (FS(I,J)), volatile fraction of the solids (FV-
(I,J)}, and fraction of volatile solids biodegradable (FB(I,J)). The increment
of moisture (DH20, gm/cc) content lost over DT is computed as follows:
DH2Q = -(QVL+QVR+QVB+QVT)*DT/DA - DV0L*0.54
DA = incremental volume, cm^
DVOL = incremental volatile solids combusted, gm/cc
Relationships used for computing the local microbiological generation of
heat (HEAT, (cal/hr)/cc) are given later in this report but DVOL is simply
HEAT*DT/HC0M3. Oxygen used (1.6 gm Og/gm VSS) is also a function of the rate
of heat generation. Volumetric heat capacity (VHC, (cal/cc)/ C) is computed
from compost physical properties and the change in compost temperature can then
be expressed as follows:
T2(I,J) = Tl(I,J) + DT*(QHL+QHR+QHB+QHT)/VHC/DA + HEAT*DT/VHC
For interior blocks mass transfer of water and oxygen is by advection and
diffusion. No mass transfer of water or oxygen is allowed across the soil
boundary hut loss of water vapor from the boundary with ambient air is computed
using a relationship from soil science. Heat transfer within the pile is by
conduction and movement of water vapor. Convective heat loss from the bound-
ary with ambient air is computed from heating, ventilating, and air condition-
ing technology. -Heat loss to the soil is computed using anaerobic digester
design relationships. Dummy nodes shown by the open circles in column 1 of
7
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Figure 1 are used to provide for symmetry about the vertical center!ine in the
numerical integration. A running mass balance for water and heat is incorpo-
rated in the program as a check on the computations. .For example, WOUT is the
grams of water lost from the boundary with ambient air and WIN is the water
entering the pile with the forced aeration. The difference between WOUT and
WIN must equal the water lost (WLOST) from the pile. Similarly, the
microbiological heat generated (HUSED) must equal the heat lost from the
boundaries with soil and ambient air (HOUT) plus the heat stored in the pile
(HSTOR) minus the heat entering with the forced aeration (HIN). The average
physical properties of the compost pile are computed at each time point and
logic to completely mix the pile at equally spaced time intervals is provided.
8
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PHYSICAL PROPERTIES OF AIR AND WATER
Accurate values for density (gm/cm3) and enthalpy (gcal/gm) of saturated
water vapor can be found in the steam tables (5). s However, for ease of
computation closed form expressions were derived by fitting the steam table
values over the 20-70 C range of interest for compost modeling. The following
relationship was found to fit the data over the required range to within about
1%.
saturated water vapor density, gm/cc * e$-84726 - 4925.89/T (j)
T = temperature, degrees Kelvin
Steam table values are shown below with estimates made using equation (1):
Percent
Temperature, C Water vapor density, gm/1iter Error
True
Estimated
20
0.01730
0.01730
0.0
30
0.03040
0.03014
-0.86
40
0.05121
0.05066
-1.08
50
0.08313
0.08246
-0.80
60
0.13036
0.13036,
0.0
70
0.19833
0.20065
+1.17
80
0.29349
0.30139
+2.70
90
0.42355
0.44267
+4.50
Enthalpy of saturated water vapor above the enthalpy of liquid water at
0 C can be very accurately approximated by the following relationship:
saturated water vapor enthalpy, gcal/gm = 597,44 + 0.4306 T (2)
T = temperature, degrees Celsius
9
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Enthalpy values given in the steam tables are shown below with estimates made
using equation (2).
Temperature °C Water vapor enthalpy, gcal/gm
True
Estimated
0
597.55
597.44
20
606.22
606.05
40
614.83
614.66
60
623.28
623.28
80
631.44
631.89
The error can be seen to be less than 0.1% over the range shown.
According to modern kinetic theory of gases (6) diffusivity of a binary gas
mixture is directly proportional to the 1.5 power of the abolute gas temperature
and inversely proportional to absolute pressure. The following relationship for
diffusivity of water vapor in the air was used by Philip and DeVries (7) in their
paper on movement of moisture through porous media.
o -4
air-water diffusivity, cm^/sec = 4.42 x 10 T /P (3)
T = gas temperature, degrees K
P = absolute pressure, mm Hg
At 25°C the above equation would estimate a value of 0.285 em^/sec for air-
water diffusivity. Reid and Sherwood (6) reported a measured value at 25 C of
0.260 cm^/sec. The error incurred in linearizing equation (3) is only
about 0.5% over the 20-80 C range. The linearized form expressed as
cm2/hr for use in the program is shown below:
air-water diffusivity, cm^/hr = 803.0 + 8.81 T (4)
T = temperature, degrees C ¦
A comparison of diffusivity values found using equations (3) and (4) are shown in
the following table.
Temperature, °C Philip & DeVries Linearized Form
20 987.9 979.2
40 1149.9 1155.4
60 1326.0 1331.6
80 1516.3 1507.8
10
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Since the error using the linearized form is a maximum of about 0.5% the line-
arized form was used in the program.
At zero degrees Celsius, diffusivity of oxygen in air was measured as 0.175
cm2/sec and oxygen in nitrogen as 0.181 cm2/sec. according to Re id and Sherwood
(6). Thus, if air-oxygen diffusivity is assumed to be directly proportional to
the 1.5 power of absolute temperature the following relationship is found:
air-oxygen diffusivity, cm^/hr = 0.13967 (5)
T = gas temperature, degrees K
Within the 2Q-70°C range equation (5) can be linearized as follows:
air-oxygen diffusivity, cm^/hr = 625.8 + 3.74 T (6)
Equation (6) was used in the program.
To calculate the advective flow of enthalpy associated with dry air into
each block air density and air enthalpy must both be expressed as a function of
air temperature. Using the perfect gas law, air density can be expressed as
follows:
gas density, gm/cc = MW/82.05/(T + 273) (7)
Since the molecular weight (MW) of air is usually taken as 28.970 the density
of dry air at 20 C can be calculated as 0.001205 gm/cc. Specific heat at con-
stant pressure for air has an average value of 0.2391 gcal/gm per degree
Celsius (above 0 C) over the 20-80 C temperature range from the air tables (8).
Thus, enthalpy of air can be expressed as 0.2391 T where T is measured in de-
grees Celsius. Advective flow of enthalpy associated with dry air (gcal/hr) is
the product of mass flow and enthalpy per gram. Mass flow is the product of air
velocity, air density, and area normal to the velocity. The product of mass
flow and unit enthalpy can then be expressed as follows-;
enthalpy flux, gcal/hr » (28.97 x 0.239/82.05)(A-U-T)/(T + 273) (8)
A = area normal to velocity, cm2
U = air velocity, cm/hr
T = air temperature, °C
The value of the constant in equation (8) is 0.08442
For engineering purposes atmospheric air can be taken as 79% nitrogen and
21* oxygen by volume. Therefore, using a molecular weight of 32 for oxygen in
equation (7) and multiplying the result by 0.21 gives an estimate of 0.0002795
gm/cm3 for the concentration of oxygen in atmospheric air at 20°C.
11
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PHYSICAL PROPERTIES OF COMPOST
From soil science literature it is known that the specific volume (cm^/gr) of
soil is least when the soil is either very wet or very dry and has a maximum value
at some intermediate moisture content. This relationship for a muck soil taken
from the work of Patten (9) is shown in Figure 3. Measurements of specific volume
for wet sludge cake and dry cured compost are given in the March, 1978 progress
report (10) from LACSD. Five measurements were made on each material and these are
shown by the circled points in Figure 3. Dry cured compost has the greater
specific volume. The solid line through the two sets of points can be tentatively
taken as the correct relationship between moisture content and specific volume for
mixtures of wet sludge cake and dry cured compost. The starting blend of compost
used by LACSD ranged from 2 to 3 volumes of dry cured compost per single volume of
wet sludge cake. Solids content of the blend can, therefore, be computed as
follows where the mixing ratio (R) varies from 2 to 3:
FSO = (R*WD*FSD + WW*FSW)/(R*WD + WW) (9)
FSO = solids fraction of blend, fraction
R = volumes of dry compost/volume of wet cake
WD = density of dry cured compost, gm/cm^
FSD = solids fraction of dry compost, fraction
WW = density of wet cake, gm/cm^
FSW = solids fraction of wet cake, fraction
Five measurements of solids fraction and volatile fraction of the solids were
given in the LACSD progress report (11} for April, 1978. Average values are
shown below:
Solids fraction Volatile fraction
Wet sludge cake 0.2562 0.4782
Dry cured compost 0.6430 0.3062
Dry solids and moisture mass fractions computed from equation (9) using 2, 2-1/2,
and 3 for R are shown below;
R FSO 1 - FSO
2 0.496 0.504
2-1/2 0.516 0.484
3 0.531 0.469
12
-------
I
I
Specific volume versus moisture content
for Muck soil and compost.
Figure
1.6
1.5
cn
co
1.4
1.3
1.2
1.0
.9
.8
.7
.6
Percent moisture content, by mass
.5
0
70
80
-------
Expected densities of the starting compost blend can be read from Figure 3
at the points marked by the triangles with the following results:
2-1/2
3
R
2
blend density, gm/cm3
0,8711
0,8673
0.8621
In the simulation program compost is characterized by the density (W,
gm/crn3), the solids fraction (FS), the moisture fraction (1 - FS), the
fraction of solids which are volatile or organic (FV), and the fraction of
volatile solids which are biodegradable (FB). Thus, the density (gm/cc) of
biodegradable solids can be computed as W*FS*FV*FB. Similarly, the mineral
mass fraction is W*FS*(1-FV), the organic mass fraction is W*FS*FV, and the
water mass fraction is W*(1-FS). Volume fractions for mineral (XM), organic
or volatile (XV), water (XW), and air (XA) can be computed from the density
of the mineral, organic, and water components, compost density, and the
solids and volatile mass fractions. For soils DeVries (12) gives the following
commonly used values for density of the components.
Using these values for density of the components, the following relationships
for computing volume fractions can be derived:
Using the theory of DeVries (12) for soils the volume fractions computed for
gompost can now be used to estimate the volumetric heat capacity (goal/cm3/
C) by means of the following linear relationship:
mineral density 2.65 gm/cm3
organic density 1.30 gm/cm3
water density 1.0 gm/cm3
air density 0.00125 gm/cm3
XM = FS(1 - FV)W/2.65
XV = FS FV W/1.3
XW = W(1 - FS)/I.0 .
XA = 1 - XM - XV - XW
(10)
VHC = 0.46 XM + 0.60 XV + 1.0 XW + 0.0003 XA
3 o
VHC = volumetric heat capacity, gcal/cm / C
(11)
14
-------
This relationship is used in the program to compute the local volumetric heat
capacity of compost. This method of estimation gives values of 0,859 gca 1/
cm3/°c for wet cake, 0.448 for dry cured compost and 0.541 for a 2-1/2 to
1 blend.
Thermal conductivity expresses the capacity of compost to transmit sensi-
ble heat and is measured in gm-calories transmitted per square centimeter per
hour across a temperature gradient of one degree Celsius per centimeter. An
earlier method for synthesizing electrical conductivity of heterogeneous
material from measured electrical conductivity of the components was adapted
by DeVries (12) to the problem of estimating thermal conductivity of soil.
Thermal conductivity measurements for components of soil and compost such as
air, water, and mineral and organic substances are available in the literature.
Thermal conductivity of air and water are slightly temperature dependent but
thermal conductivity of mineral and organic substances are independent of ,
temperature.
The DeVries theory hypothesizes that one of the four components, called the
medium will be the principal heat transmitter and treats" the other three
components as though they are granules suspended in the medium. For compost,
water is taken as the medium. If the ratio of the temperature gradient in each
suspended component divided by the temperature gradient in the medium (water) is
called H (HM for mineral, HV for volatile, and HA for air) the thermal con-
ductivity of compost can be computed as follows:
TC =
TW*XW
+ TM*XM*HM h
- TV*XV*HV + TA*XA*HA
XW +
XM*TM + TV*XV
+ TA*XA
TC =
: thermal
conductivity
of compost, mcal/cm/sec/°C
TW =
: thermal
conductivity
of water, mcal/cm/sec/°C
TV =
: thermal
conductivity
of organics, meal/cm/sec/°C
TA =
: thermal
conductivity
of air, mcal/cm/sec/°C
TM =
= thermal
conductivi ty
of mineral, mcal/cm/sec/°C
Values of 7.0 mcal/cm/sec/ C for mineral material and 0.60 meal/cm/sec/ C for
volatile org ani cs are given by DeVries (12) as representative. The following
relationships were developed from thermal conductivity measurements given by
McAdams (13) for air and water.
TA = 0.05788 + 0.000182 T (13)
TW = 1.4179 + 0.002219 T
T = temperature, degrees
Celsius
15
-------
In the DeVries theory suspended granules are assumed to be ellipsoidal in shape
with three descriptive parameters ga, and gc. These three parameters depend
on the shape of the granules and their sum must equal one. For example, if
granules are assumed to'be spherical all three parameters have a value of 1/3.
If the granules are assumed to be long circular cross-section rods both ga and
gt> equal 0,5 and the value of gc is zero.
In computing the thermal conductivity of compost, spherical granules were
assumed. The'multiplier (H) in the DeVries theory can then be computed as fol-
) lows:
1/HI = 1 + (TI/TW - 1)/3 (A)
HI = HM, HV, and HA
TI = TM, TV, and TA
Using a value of 7.0 mcal/cm/sec/ C for the mineral or non-volatile component
of compost, a value of 0.60 mcal/cm/sec/ C for the volatile or organic component
and equations (13) for air and water thermal conductivity the following estimates
of thermal conductivity for wet cake,, dry compost, and the 2.5/1 blend were
found:
20
40
60°C
Wet Cake
1,
.338
1.374
1.410
2-1/2/1 blend
0,
.9565
0.9803
1.004
dry compost
0,
.8894
0.9103
0.9310
Thermal conductivity expressed as mca1/cm/sec/°C
The variation in thermal conductivity over the 20-60°C temperature range is
only about 5% while the variation between the starting blend and the dry
cured compost is about 7-8%. ¦ Because of the obvious weakness of the theory,
the volume of computation required, and the relatively small contribution
of sensible heat transfer in the mechanics of the process a constant value of
1.0 mcal/cm/sec/ C was used in the simulation of windrow composting. Dividing
this value of thermal conductivity by 1000 to convert from meal to gcal and
multiplying by 3600 to convert from sec to hours gives a constant value of
3.6 cal/cm/hr/ C for TC used in the simulation program.
The pressure drop caused by air flowing through porous compost has never
been measured carefully. However, a limited series of measurements on a 10 ft
cube of compost were reported in the October, 1978 progress report (14) on
composting research at LACSD. Although there is some evidence .that the pressure
drop per unit length versus air flow velocity is non-linear the measurements
are too scattered to justify use of a non-linear relationship for fitting the
data. Thus, Darcy's law which assumes a linear relationship between air flow
16
-------
velocity and pressure drop has been used. Darcy's law also provides for the
pressure drop to be inversely proportional to viscosity of the air. This
refinement has not been included in the simulation but can be added when
careful ly measured pressure-drop properties of compost are known. The LACSD
measurements of pressure drop versus air flow velocity are shown plotted in
Figure 4. The simplified form of Darcy's law used to fit the data is shown
below:
U = PDK(PD/DL) (15)
U = air flow velocity, cm/hr
PD = pressure drop over DL, mbar
DL = incremental distance, cm
2
PDK = Darcy's Law constant, cm /mbar/hr
When measurements of pressure drop versus air flow velocity are available
for varying viscosities (air temperatures) PDKO/air viscosity can be sub-
stituted for PDK. The value of PDK which fits the straight 1ines shown
in Figure 4 are 39,708 cm2/mbar/hr for compost with 53% solids and 50,462
for compost with 46% solids. In the simulation program atmospheric air
pressure is 1000 mbar at the top of the windrow pile and the pressure
maintained at the pressure source at the pile center is -6.14 mbar or
2.5 inches of water (1 mbar = 0.4071 in H2O).
17
-------
Figure 4. Air flow velocity versus pressure
gradient for sludge compost
pressure gradient, mbar/m
18
-------
AIR FLOW REGIME
Horizontal and vertical components of air flow velocity within the windrow
are found by applying Darcy's law and the con ser vat ion-of-mass law to each block
in the cross-section. Individual blocks or nodes are identified by the row
number (I) and the column number (J). Thus, horizontal air flow velocity is
UX(I,J) and vertical velocity is UY(I,J). Air flow velocity across any block
boundary is associated with the node below or to the left of the boundary. Thus,
conservation-of-mass is .expressed as follows:
DY*(UX(I,J-l) - UX(I,J)) = DX*(UY(I,J) - UY(1-1,J)) (16)
Notice that air density has been omitted from the equation. Thus, variations
in air density due to temperature differences within the. pile are neglected.
Air flow velocity across the boundary with the soil is assumed to be zero so
for the bottom row of blocks UY(1,J) is set equal to zero.
The computation begins by assigning an initial value for atmospheric
pressure at each of the nodal points. Since only pressure differences are
used in the computation, atmospheric pressure at the top surface of the
windrow is assigned a value of zero. Gravity force causes the initial pres-
sure to increase linearly with distance down from the top surface to the
nodal point. Air density (gm/cm^) is expressed as the molecular weight of
air (28.97) divided by the product of the gas constant (82.05) and the
air temperature (273 + TAIR) in degrees Kelvin. Multiplying air density
by acceleration of gravity.(981 cm/sec2) and noting that 1000 dynes/cm2
equals one mbar gives the following expression for change in atmospheric
air pressure with altitude: mbar/cm = 0,3464/(TAlR + 273). Thus, if air
temperature is 20 C initial pressure along the second row is 0.001182*
DY*(IV - 1.5) mbar. Initial pressure at each of the other rows is assigned
in a similar way. In the program the constant 0.3464 is called G.
Darcy's law for flow of air through porous media provides that air flow
velocity is directly proportional to the pressure gradient (pressure drop per
unit length along the flow path) and inversely proportional to air viscosity.
For the initial simulation of windrow composting the effect of viscosity was
neglected. Therefore, air flow velocities between nodes can be computed as
follows:
UX(I,J) = PDK*(P(I,J) - P(I,J+1))/QX (17)
UY(I,J) = PDK*(P(I,J) - P(1+1)J))/DY - PDK*G/(273 + TAIR) (18)
It can be seen that UX is positive to the right and UY is positive when
directed upward. Thus, when the pressure source (P8L0W, mbar) is equal to
atmospheric pressure at the second row the gradient (P(I,J) - P(I+1,J))/DY
equals G/(273 + TAIR) and both horizontal and vertical velocity components are
zero at al1 nodes.
PDK can be evaluated experimentally by pumping air through compost mate-
rial at a known rate and measuring the pressure drop. Some experiments of this
sort using a 10 ft cube of compost were reported in the October, 1978 progress
report (14) on composting from LACSO. These data are shown plotted' in Figure 4.
19
-------
It can be seen that the points do not seem to fall on a straight line through the
origin as demanded by Darcy's law. This could be due to the measurement
technique or the velocity versus pressure drop relationship could be non-
linear.' An appreciable pressure drop was measured (2.75 in H2O at 60 cfm) across
the empty 10 ft cube used to hold compost material and this was apparently sub-
tracted from the pressure drop across both apparatus and compost to estimate the
drop across the compost alone. Details are not given but the data is clearly only
a rough estimate of the pressure drop versus flow velocity relationship. The
slope of the two lines shown in Figure 4 can be used as a first estimate of PDK.
Pressure existing at steady-state flow conditions can be expressed for all
nodes except those in the 2 'nd and top row and those along the sloping boundary
by substituting equations (17) and (18) into equation (16). In this way the
following relationship is found:
P(I,J) = CY*(P( I, J+l) + P( 15 J-l)) + CX*(P(I+1,J5 + P(I-M)} (19)
CY = DY2/{DX2+DY2)/2
CX = DX2/(DX2+DY2)/2
DX2 = DX*DX
DY2 = DY*DY
To provide for zero air flow velocity across the soil boundary the following
relationship is used to compute the pressure at steady-state conditions instead
of equation (19).
P(2,J) = (DY2*(P(2,J+l)+P(2,J-l))+DX2*(P(3,J)+DPAIR))/(2.*DY2+DX2) (20)
DPAIR = DY*G/(TAIR+273)
Also, since the steady-state air pressure at the top surface of the pile must be
kept at zero and the length of the vertical flow path above nodes in the top row
is DY/2 instead of DY the following relationship is used for computing pressure
at nodes in the top row except for the single node on the sloping boundary.
P(IV,J) = (DY2*(P(IV,J-l)+P(IV,J+l))+DX2*P(IV-l,J))/(2.*DY2+3.*DX2) (21)
Equations 19-21 are applied iteratively to all nodes except the nodes on the
sloping boundary until the values for pressure converge to the steady-state
values. Two hundred iterations have been found to be adequate for achieving
convergence.
Air flow velocities between all interior blocks are then computed using equ-
ations (17) and (18). Vertical air flow velocities across the upper boundary of
blocks in the IV'th row are computed from conservation-of-mass as follows:
UY(IV,J) = UY(IV-1,J) - DY*(UX(IV,J) - UX(IV,J-l))/DX (22)
20
-------
Similarly, the vertical and horizontal components of velocity across the
sloping boundry of the windrow are computed from conservation-of-mass as
follows:
All velocities are computed as cm/hr and used in the program with these
units. However, when printed out they are converted to ft/min. When
PBLGW is input as a positive value both vertical and horizontal components
of air flow velocity will be positive, that is, directed up and to the
right. If, on the other hand, PBLOW is input as a negative value air will
flow-into the pile from the ambient atmosphere and both vertical and horizontal
components of air flow velocity will be negative. The- constant K used in
mass transfer relationships is set equal to zero when PBLOW is positive
and equal to 1 when BPLOW is negative.
UX(I5J) = DY*(DY*UX(I,J-l) + DX*UY(I-1,J))/(QX2 + DY2)
UY(I,J) = UX(I,J)*DX/DY
(23)
(24)
21
-------
MICROBIOLOGICAL HEAT GENERATION
Aerobic microbiological activity within the compost pile consumes oxygen
and volatile solids and produces heat, water vapor, and carbon dioxide. Wiley
(15) measured microbiological heat production using municipal refuse in a
laboratory composter and reported 10,000-12,000 Btu/lb (5500-6500 cal/gm) of
volatile solids destroyed. It will be shown later in this report that if water
and volatile solids balances are made on the LACSD results with aerated compost
piles these heats of combustion are too low. Therefore, in simulating the
LACSD aerated pile performance the high heat of combustion (HCOMB) was set at
the value of 9300 cal/gm of volatile solids destroyed given by Wiley for
lipids. Oxygen consumed was estimated as 1.6 gm of 0? per gm of volatile solids
destroyed and water produced at 0.54 gm H2O per gm of volatile solids
destroyed.
Rate of microbiological activity is generally agreed to be proportional
to the concentration of volatile solids (or biodegradable volatile solids)
present. However, compost temperature and moisture content are variables
which have a profound effect on the rate of microbiological activity. Jeris
and Regan (16) studied the effect of temperature on microbiological activity
expressed as mi 11 imoles of oxygen used per day per gram of volatile solids
present. Activity measurements made by Jeris and Regan on mixed refuse using
a laboratory composter are shown by the circled points in Figure 5. Solids
fraction of the compost was in the 0.35-0.4 range. It can be seen that the rate
peaks at about 57°C and falls off sharply at greater or lesser temperatures.
Earlier Schulze (17) investigated composting efficiency within the 35-60°C
temperature range and found the log-linear relationship shown by the dashed
line in Figure 5.
Measurements by Arditi (18) using a mixture of 50% straw and 50% grass at
55-60% moisture for compost are shown by the squared points in Figure 5. The
Arditi data suggest that the effect of temperature is more pronounced at
temperatures above the peak than at temperatures below the peak. Andrews (19)
used a temperature versus activity relationship of this kind in modeling the
thermophilic aerobic digestion process. A temperature versus activity
relationship which peaks at 55°C is also reported by Sne11 (20) but the details
of the experiment are not given. The temperature versus oxygen consumption
rate relationship is not known for wastewater sludge compost but the shape of
the curve is probably similar to those measured for other types of compost. The
peak rate probably occurs around 57°C. EMAX used in the program is the peak
value for oxygen consumption rate expressed as mmoles 02/day per gram
biodegradable volatile solids. EM IN is the minimum rate found to be necessary
at long composting time to prevent the pile temperature from approaching the
wet bulb temperature of ambient air rather than the observed 30-40 C range.
The form of the relationship used in CMPST is parabolic on semi-log paper which
is the same as the normal probability density equation.
22
-------
10 10
Figure 5
Rate of microbiological activity
versus compost temperature
Regan et al
y = , 7 „"{T-57) /254
Arditl
Temperature, degrees Celsius
23
-------
The second important controlling variable on microbiological rate is
moisture content of the compost. For mixed refuse the peak microbiological
rate occurs at about 30% solids. The rate tends to fall off when the solids
fraction is above or below this value. Regan et al (21) made composting rate
measurements on mixed refuse over the 50-90% moisture range holding tempera-
ture fixed. These data points are shown by the circled points in Figure 6.
Schulze (22) also investigated the effect of moisture content on oxygen uptake
rate using finished refuse compost at 20°C. The initial refuse was a
standardize garbage. A peak rate of 0.567 mmoles O2 per day per gm of volatile
solids was observed at a moisture content of 60.4%. Since the refuse used by
Regan et al and Schulze was not the same and the temperature used by Regan et
al was not given the Schulze measurements were arbitrarily multiplied by a
factor to bring them within the range of the Regan et al data for comparison of
the shapes of the two relationships. The adjusted Schulze measurements are
shown by the squared points in Figure 6. The relationship between rate and
moisture content is not known for wastewater sludge compost so the relationship
shown in Figure 6 has tentatively been used in the simulation computer program.
The following equation .is ustd in the program for computing oxygen consumption
rate:
E = EMA'X e-(T-57)2/254 e-10.973(FS-0.3)2 (25)
E = oxygen use rate, mmoles 02/day per gm
biodegradable VSS
T = compost temperature, °C
FS = solids fraction
Oxygen consumption rate (E) is converted to grams of volatile solids destroyed
per day * per gram of biodegradable volatile solids by dividing by 50. This
assumes 1.6 grams of oxygen used per gram of volatile solids destroyed.
Multiplying the volatile solids use rate by the heat of combustion (HCCMB) and
dividing by 24 hr/day gives calories/hr per gram of biodegradable volatile
solids present as E*HCCMB/12QQ. Since the concentration gm/cm3 of biode-
gradable volatile solids can be computed as W(I,J)*FS(I,J)*FB(I,J) the heat
produced (cal/hr/cm^) called HEAT in the program is computed as E*HCCMB/12Q0.
*W(I,j;*FS(I,J)*FV(I,J)*FB(I,J). If the value computed for E is less than the
input parameter EM IN, E is set equal to EM IN. The program also contains logic
to set HEAT equal to zero if the ratio of oxygen concentration in the block
divided by ambient oxygen concentration is less than the input value of CCMIN.
The counter HOFF shows the number of blocks in which E has been set equal to
zero in any single DT interval, A value of 0.25, has been used for COMIN.
24
-------
nrm i i .1 u ,
Oxygen consumption
i <\liTTTj 11 i I i! iiliFriilllilMPI ^/OTITriTU
rate, millimoles O^/day per gm VSS
ii',1 L'Il
- U LL
< TO
ro Qj
tn id
-------
MOVEMENT AND STORAGE OF MOISTURE
Moisture moves- through the aerated compost pile by advection and dif-
fusion and evaporates from the pile surface exposed to atmospheric air.
Transfer of moisture across the soil-compost boundary is assumed to be negli-
gible and is set equal to zero in the simulation. Movement of moisture
resulting from differing capillary pressures within the compost was not
included in the simulation because the required empirical relationships are
not available. Capillary action could be an important mechanism in movement of
moisture. Water vapor concentration in advective air is assumed to be
saturated at the local compost temperature. Four moisture flux rates (gm/hr)
are computed for each block at each time point. Flux rates from the left (QVL),
right (QVR), bottom (QVB), and top (QVT) are positive when moisture is moving
into the block and negative when moving out. For an interior block in the 11th
row and J1th column the four flux rates are computed as follows:
QVL = DY*(UX(I,J-l)*V(I,J-l+K) + DV*(V(I,J-l) - V(I,J))/DX)
QVR = DY*(-UX(I,J)*V(I,J+K) + DV*(V(I,J+1) - V(I,J))/DX) (26)
OVB = DX*(UY(I-1,J)*V(I-l+K,iJ) + DV*(V(I-1,J) - V(I,J))/DY)
QVT = DX*(-UY(I,J)*V(I+K,J) + DV*(V(I+1,J) - V(I,J))/DY)
The symbol DV is the product of mean compost porosity (XW) supplied as
input and mean diffusion coefficient for water vapor in air expressed as
cm^/hr. For example, DV used in the equation for QVL is computed as XAM*(803.
+ 8.31*(T1(I,J) + Tl(I,J-l))/2.}. In the other three equations DV is computed
in the same way except the temperatures used are contiguous to the diffusing
surface. K is zero when PBLOW is positive and one when PBLOW is negative.
Moisture entering or leaving the pile advectively is computed crossing
the boundaries of block (2,2). A small amount of moisture (0.54 gm H20/gm VSS)
also enters each block as a result of combustion of volatile solids. Moisture
flux across the top boundary of block (2,2) is called WTOP (gm/hr) and moisture
flux across the right-hand boundary of block (2,2) is called WRGT. The
following equations are used to compute the advective and diffusive flux into
or out of block (2,2).
DV = (803. + 8.81*(T1(3,2) + Tl(2,2))/2.)*XW
WTOP = DX/2.*(UY(2,2)*V(2,2) + DV*(V(2,2)-V(3,2))/DY) (27)
DV = (303. + 8.81*(T1(2,3) + T1(2,2))/2.)*XAM
WRGT = DY*(UX(2,2)*V(2,2+K) + DV*(V(2,2) - V(3,2))/DX)
26
-------
When PBLOW is positive (K=0) moisture enters the pile through block (2,2)
so T1(2,2) is set equal to TAIR and V(2,2) is set equal to VAIR. When PBLOW is
positive both WTOP and WRGT will be positive. When PBLOW is negative (K=l) both
WTOP and WRGT will be negative and both Tl(2,2) and V(2,2) must be computed from
WTOP and WRGT values from the last time step. V(2,2) is computed from a water
balance written as follows:
V(2,2)' = (WTOP+WRGT)/(DX/2.*UY(2,2) + DY*UX(2S2)> (28)
The enthalpy balance used to compute Tl(2,2) is given in the next section of
this report. Advective moisture entering or leaving through block (2,2) is
summed over the entire composting period and expressed as W22 grams of water
computed as follows:
W22 = W22 + {WTOP+WRGT)*DT (29)
Evaporation of water from a moist surface such as soil has been studied
extensively as shown by Taylor and Ashcroft (23) but for rough calculations
evaporation of water from a free water surface is often taken as the first
approximation. The Meyer relationship given in Chow's Handbook of Applied
Hydrology (24) was used in the simulation to estimate evaporation of water from
a free water surface. The Meyer equation is expressed as follows:
EVAP = CVE*(PW - PA)*(l+WIND/10. ) (30)
EVAP - evaporation rate, inches water/30 days
CVE = an empirical constant between 11 and 15
PW = saturation vapor pressure for free water, in Hg
PA = water vapor pressure in ambient air, in Hg
WIND - wind velocity in ambient air, miles/hr
Since moisture at the surface of the .compost pile is always assumed to be
saturated at the compost temperature the known vapor density (gm/cm^) can be
used to compute vapor pressure by assuming water vapor acts like a perfect gas.
For example, from the steam tables the ratio of saturated vapor pressure to
vapor density (psi/(lb/ft3) equals 1.071(°C + 273) with little error.
Converting to in- Hg/(gm/cm3) the ratio equals 136.64( C + 273). Since cm of
water evaporated is equivalent to gm/cm^ and 30 days is equivalent to 720 hrs
equation (30) can be converted to the following form used in the simulation
program.
EVAP = 0.482*CVE*DX*(VAIR*(TAIR+273.)-V(I,J)*(Tl(I,J)+273.))
*(l+WIND/10) (31)
EVAP = water evaporation rate, gm/hr
27
-------
For blocks along the top horizontal boundary with the atmosphere EVAP computed from
equation (31) can be added to the advective moisture flux (-UY(I,J)*V(I+K,J)*DX) to
compute QVT. For blocks along the sloping boundary with the atmosphere the factor
(2.*CX)**0.5 must be included in equation (31) to compute QVT where CX equals
DX2/{DX2+DY2)/2. A similar modification is necessary to compute QVR for sloping
boundary blocks. A value of 3.0 for CVE has been found to give reasonable agreement
with observations.
The change in moisture content (DH20) and the change in volatile solids
content (DVOL) in grams over each time increment are computed where DT is the time
increment in hours and DA is the area of the block (cm^) one,-centimeter deep. The
following relationships are used:
* DH20 = -(QVL+QVR+QVB+QVT)*DT/DA - DVOL*0.54
DVOL = HEAT*DT/HCCMB
Mass fractions for compost components are then computed at each time point for each
of the blocks as follows:
FB = (W*FS*FV*FB-DVOL)/(W*FS*FV-DVOL)
FV = (W*FS*FV-DVOL)/(W*FS-DVOL
FS = (W*FS-DV0L)/(W-DVOL-DH2O)
W = W-DVOL-DH20
A running moisture balance around the aerated pile is computed as a check on
accuracy of computation. For example, the initial water in the one centimeter
slice is computed and added to the total water which would be produced if all
biodegradable volatile solids are combusted to find the parameter WPILE. After
each DT computation the total moisture in the pile is summed and added to the
remaining biodegradable solids times the water to fuel ratio (WRF). This sum is
subtracted from WPILE to find the total water lost (WLOST) from the pile at each
point in the computation. Water lost from the compost-air boundary is summed over
the composting period and called WOUT. The parameter WSTAR is computed as W0UT-W22
and this should equal WLOST for the water balance to be correct. Typical errors
are 0.03-0.5% over a 30 day composting period.
28
-------
MOVEMENT AND STORAGE OF HEAT
Heat (enthalpy) moves within the aerated pile by conduction of sensible
heat and by advection of dry air and water vapor. Heat is stored in the pile
as sensible heat. Heat moves over the soil boundary by conduction arid over the
boundary with ambient air by advection, convection, and evaporation of water
from the surface. Heat enters the pile through block (2,2) when P8L0W is
positive and leaves through block (2,2) when PBLOW is negative.
Conductive heat transfer between blocks is computed as the product of
compost thermal conductivity, cross-sectional area normal to flow of heat, and
the temperature gradient ( C/cm) normal to the cross-sectional area. Since
thermal conductivity of compost (TC) is relatively independent of compost
characteristics a mean value of 3.6 cal/hr per cm per unit temperature
gradient (C/cm) was used in the simulation. To estimate conductive heat loss
across the soil boundary a method recommended by the ASCE MOP 36 (25) for design
of anaerobic digesters was used. In this method the soil temperature gradient
is assumed linear extending 10 ft into the soil from the compost surface
temperature to the ambient soil temperature (TSOIL) taken as 4.5 C. Soil
thermal conductivity was estimated at 16 Btu/hr per square foot per unit
temperature gradient ( F/inch) for wet soil and 8.0 for dry soil. The
following'relationship was used to?compute heat flux over the soil boundary
with a value of 0.0651 cal/hr per cm per degree Celsius temperature difference
for wet soil and one-half the value for dry soil.
QHB = HSQIL*(TSQIL-T1(2,J))*DX (32)
Heat transfer between interior blocks involves conduction of sensible heat and
advection of water vapor and dry air. Air temperature is taken as the local
compost temperature and water vapor concentration is taken as the saturation
value at the local compost temperature. Enthalpy (cal/gm) of water vapor is
approximated as a linear function (597.44 + 0.4306*T) of temperature (T=°C).
The previously computed water vapor flux values (QVL, QVR, QVB and QVT) can be
multiplied by the enthalpy of water vapor to find the enthalpy flux associated
with advection of water vapor. Enthalpy flux associated with advection of dry
air is the product of dry air mass flow (gm/hr) and dry air enthalpy (cal/gm).
Dry air mass flow is the product of dry air density (gm/cm^), flow velocity
(cm/hr),and cross'-sectional area (cm*?). Dry air density is computed as the
molecular weight of air (28.97) divided by the gas constant (82.05) and divided
by the gas temperature ( K). Dry air enthalpy is taken as 0.2391 times gas
temperature in degrees Celsius. Thus, for internal blocks the enthalpy flux
from the left, right, bottom, and top into the (I,J) block is computed as
follows:
QHL = TC*(T1(I,J-1)-T1(1,J))*DY/DX + QVL*(597.-44+.4306*Tl(I,J-l+K))
+ UX(I,J-l)*.08442*0Y*T1(I,J-l+K)/(Tl(l,J-l+K)+273.)
QHR = TC(T1(I,J+1)-T1(I,J))*DY/DX + QVR*(597.44+.4306*T1(J,J+K))
-UX(I,J)*.08442*DY*Tl(I,J+K)/(Tl(I,J*K)+273.) (33)
29
-------
QHB = TC*(T1(I-1,J)-T1(I,J))*DX/DY + QVV*(597.44+.4306*T1(I-l+K,J))
+ UY(• I -1, J')*. 08442*DX*T1 (I -1+K, J)/ (T1 (I -1+K, J) +273.)
QHT = TC*(T1 (1+1, J)-T1 (I, J) )*DX/DY + QVT*(597.44+.4305*T1 (I+K, J) )'•
-UY(I,J)*.08442*DX*T1(I+K,J)/(Tl(I+K,J)+273.)
Heat enters the air-compost boundary by adsorption of solar energy and by
advection of air and water vapor when P3L0W is negative. Heat leaves the
surface by convection, by evaporation of water from the surface, and by
advection when PBLQW is positive. Adsorbed solar energy (SOLAR) is expressed
as calories/hr per square centimeter of surface. Solar energy adsorbed at the
compost pile boundary has never been measured but measurements (23) of daily
average solar energy adsorbed by soil cropped with Bermuda grass in North
Carolina ranged from 2-17 cal/hr per cm^ depending on the month of the year.
SOLAR also is known to depend on latitude.
Convective heat loss from the pile surface is estimated in the simulation
using the concept of surface conductance (HAIR) from HVAC literature (26).
Convective heat loss (cal/hr) is the product of surface area, surface
conductance (HAIR), and the temperature difference (°C) between ambient air
and the compost surface. Surface conductance is expressed as a linear function
(HAIR=HAIRO+K*WIND) of wind velocity (WIND) in miles/hr. For building
materials HAIRQ has a value of about 1.0 and K has a value of around 0.15. The
empirical equation for estimating evaporation of water from the surface was
discussed in the previous section so the moisture flux rate can be multiplied
by the enthalpy of water vapor to find the heat flux associated with
evaporation of moisture from the surface. Heat flux (QHT, cal/hr) over the
boundary of rectangular blocks in the top row is computed as follows:
QHT = (HAIR*(TAIR-T1(I, J) )+S0LAR)*DX + QVT*(597.44+.4306*T2(I+K,J))
- UY( I, J)*.08442*DX*T1( I+K, J)'/(T1( I+K, J)+273.) (34)
For triangular blocks along the sloping boundary QHT and QHR are computed in a
similar way except the factors (2.*CX)**.5 for QHT and (2.*CY)**.5 for QHR must
be included in the first term.
Heat also enters the pile through block (2,2) when PBLQW is positive and
leaves through block (2,2) when PBLQW is negative. Heat crossing the top
boundary of block (2,2) (HTOP) and the right boundary (HRGT) are computed as
follows:
30
-------
HTOP = DX/2.*(.08442*UY(2,2)*Tl(2+K,2)/(Tl(2+K,2)+273.))
+ WT0P*(597.44+.4306*T1(2+K,2)) (35)
HRGT = DY*(.08442*UX(2,2)*Tl(2+K,2)/(Tl(2+K,2)+273.))
+ WRGT*(597.44+.4306*Tl(2,2+K))
Heat entering or leaving through block (2,2) is summed over the composting
period as H22=H22+(HT0P+HR6T)*DT/1QQ0. Thus, H22 is the total heat passing
through block (2,2) over the composting time expressed as kilocalories. When
PBLOW is positive (K=0) Tl(2,2) is set equal to TAIR. However, when PBLOW is
negative T1(2,2) must be computed from an enthalpy, balance using the
parameters from the previous time period. The following equations are used:
TEMP = (T1(3,2)+Tl(2,3))/2. + 273. (36)
A = HTOP+HRGT-(WTQP+WRGT)*597.44
B = .4306*(WTOP+WRGT) +.08442*(DX/2.*UY(2,2)+DY*UX(2,2))/TEM P
Tl(2,2) = A/B
Heat is generated within each block by microbiological activity and the
compost temperature in each block at the end of any time increment (DT) is
computed as follows where T2 is the temperature ( C) at the end of the time'
increment and T1 is the initial temperature.
T2 = T1 + DT*(QHL+QHR+QHB+QHT)/VHC/DA + HEAT*DT/VHC
A check on the accuracy of the computations is provided by a running enthalpy
balance around the one centimeter thick slice of compost. The total heat of
combustion of all fuel (biodegradable volatile solids) within the slice is
computed initially and at each time point along the composting period. Heat
produced by combustion up to any time point is computed using HCCMB and the
remaining mass of biodegradable volatile solids and called HUSED in kcal.
Total heat crossing the boundaries with air and soil (positive out, negative
in) is summed and printed out at each time point as HOUT in kcal. Sensible
heat stored in the compost is computed and called HSTOR as kcal. Heat
entering or leaving through block (2,2) is summed (positive in, negative out)
and called H22 in kcal. The enthalpy balance then requires that HUSED = HOUT
+ HSTOR - H22. The terms on the right of this equation are summed and printed
out as HSTAR. The typical error between HUSED and HSTAR is in the range of
0.2-0.65b over a 30 day composting period.
31
-------
MOVEMENT AND CONSUMPTION OF OXYGEN
Atmospheric oxygen moves through the pile by advection and diffusion and is
consumed within the pile as a result of microbiological destruction of volatile
solids. Volume or mole fractions for the two principal components of air are
taken as 0.21 for oxygen and 0.79 for nitrogen. The perfect gas law is then used
to compute the density (gm/cm^) of oxygen in ambient air as 0.0819/(273.+TAIR).
The diffusion coefficient for oxygen in air has been measured. (6) as 0.175
cm^/sec. at zero degrees Celsius. Since theory predicts that the diffusion
coefficient will increase with temperature directly proportional to the 3/2
power of absolute gas temperature, the following linear relationship can be used
to approximate the diffusion coefficient over the 20-75°C interval.
/¦
Diffusion Coefficient, cm^/hr = 625.8 + 3.74*T (37)
T ~ gas temperature, °C
An average value for porosity (XAM) is used and the temperature used to compute
the diffusion- coefficient (DO) is the average temperature of the two contiguous
blocks between which diffusive mass transfer occurs. When the diffusion
coefficient is expressed in this way the flux of oxygen (gm/hr) entering each
block from the left, right, bottom, and top is computed as follows for internal
blocks:
, Q0L = DY*(UX(I,J-1)*C01(I,J-1+K) + D0*(C01{I,J-l)-C01(I,J))/DX)
Q0R = DY*(-liX( I ,J)*C01(I, J+K) + DO*(CGI (I, J+l) -C01 (I, J))/DX) (38)
Q0B = DX*(UY(1-1,J)*C01(I-1+K,J) + DO*(C01(1-1,J)-C01(I,J))/DY)
QOT = DX*(-UY(I,J)*C01(I+K,J) + DO*(C01{1+1,J)-C01(I,J))/DY)
The constant K has a value of zero when PBLOW is positive and a value of 1.0 when
BLOW is negative.
The approach used in computing the change in oxygen concentration within
each block over the time interval DT is to treat the block as a stirred vessel
with a constant oxygen flux entering and a flux out of the block directly
proportional to the concentration of oxygen within the block. Thus, if the
oxygen concentration within the block is C (gm/cm3), volume of the block is DA
(cm3), flux entering the block is QOIN (gm/hr), rate of oxygen used in biological
activity- is QOH (gm/hr) and volume of air leaving is QOUT (cm^/hr) the following
differential equation can be integrated over the time interval DT.
DA(dC/dt) = QOIN - QOH - C(QOUT) (39)
Equations (38) for the flux rates into each internal block can be divided into
flux into the block and flux out of the block by first defining the following
terms with the dimensions of cm3/hr.
32
-------
DOL = DY*(625.8 + 3.74*(T1(I,J) + Tl(I,J-l))/2*XAM/DX
DOR = DY*(625.8 + 3,74*(T1(I,J) + Tl(I,J+l))/2)*XAM/DX*RBf (40)
DOB = DX*(625.8 + 3.74*(T1(1,J) + Tl(1-1,J))/2)*XAM/DY
DOT = DX*(625.8 + 3.74*(T1(I,J) + Tl(1+1,J))/2)*XAM/DY*TBF
Oxygen flux due to biological activity is independent of the direction of air
flow and can be calculated simply as QQH = HEAT*DA*L6/HC0HB assuming 1.6 gm
02 used per gm solids combusted. The diffusive inward flux is also indepdendent
of air flow direction and can be-written as follows:
qDOlN, grn/hr = D0L*C01(I,J-l) + D0R*C01(I,J+l) (41)
, + D0B*C01(1-1,J) + D0T*C01(1+1,J)
Sirnilarly,'outward diffusive flux is proportional to C and is written simply
as C*(DOL+DOR+DOB+DOT). When the flow of air is outward (K=0) the inward flux
of oxygen is therefore expressed as follows:
QOIN = DY*UX( I, J-l )*CQ1( I,J-l) + DX*UY( 1-1, J)*C01 (I'-l, J) + QDOIN
When the flow of air is outward (K=l) QOIN'is computed as follows:
QOIN = QDOIN - DY*UX(I,J)*C01(I,J+l) - DX*UY(I,J)*C01(1+1,J) (42)
The term QOUT is defined as follows when the flow of air is outward (K=0).
QOLJT = DY*UX( I, J) + DX*UY( I, J) + DOL + DOR + DOB + DOL (43)
When the flow of air is inward (K=l) QOUT is computed as follows:
QOUT = DOL + DOR + DOB + DOT - DY*UX(I,J-1) - DX*UY(I-1,J) (44)
When .the parameter A is defined as (QOIN-QOH)/DA and a second parameter B is
defined as QOUT/DA equation (39) can be expressed as dC/dt = A - B*C and inte-
grated over the time interval DT with the following result:
CQ2(I,J) = A*(1 - l./EXP(B*DT))/S + C01(I,J)/EXP(B*DT) (45)
This relationship is used to compute the oxygen concentration at the end of the
time period DT from the concentration at the beginning of the time period and the
oxygen flux values for each internal block.
Some modifications are necessary for the boundary blocks in the IV'th row
and along the sloping boundary. For blocks in the top row the only modification
necessary is substituting DY/2 for the diffusing distance instead of DY. This is
done by assigning a value of 2.0 to the parameter TBF and a value of 1.0 to RBF.
For blocks along the sloping boundary the diffusing distance is taken as the
distance from the surface to the centroid computed as (DX2*DY2/3)/(DX2+DY2)**0.5
and the surface area normal to the diffusion flux is (DX2+DY2)**0.5. Using these
33
-------
expressions for the diffusing distance and normal area the sum of diffusive mass
transfer rates across the boundary; QDOT vertical and QDOR horizontal can be
computed' as follows:
QDOT + QDOR = D0*(DX/DY + DY/DX)*(COAIR - C01(I,J))*3. (46)
However the sum of the diffusive portions of QOR and QOT can be taken from
equation (38) and written as follows:
• QDOT + QDOR = D0*(DX/DY + QY/DX)*(COAIR - C01(I,J)) (47)
Since these expressions, equations (46) and (47), differ only by a factor of 3
equations (40) can be used for the sloping boundary provided both RBF and TBF are
assigned a value of 3. Logic is provided in the simulation program to assign a
value of 2 to TBF or a value of 3 to both TBF and RBF depending on whether the
boundary block is on the top row or on the sloping boundary.
34
-------
COM PARI SON OF COMPUTED AND MEASURED RESULTS
In June, 1978 LACSD research engineers constructed four obelisk shaped
aerated compost piles 'and measured the internal temperature over the 30 day
composting period. A diagram of the piles which were 2.5 meters high, 6.0 meters
wide at the base and 12 meters long is shown in Figure 7. Measurements of average
internal compost temperature reported in the July, 1978 LACSD progress report (27)
are shown in Figure 8 for piles A&B and in Figure 9 for piles C&D. Temperature
measurements were made along the vertical plane of symmetry at a depth of one-half
the pile height. Five separate measurements were made and averaged; three near
the center of the pile and one on each end of the pile. In the simulation the
measured temperature was computed as TAVG = (T2(7,2)+T2(8,2))/2.
In the experiments, atmospheric air was drawn continuously into all four
piles except for the last 9-10 days of the composting periods of piles A&D when the
air flow direction was reversed in the hope of promoting drying. Air flow rate
through the piles was set at a nominal rate of one cubic foot per minute per cubic
yard of compost in the pile. Neglecting end effects this is equivalent to 2.22
cm3/hr per cubic centimeter of compost. The pressure drop across the pile was
measured as 2.5 inches of water or 6.14 mbar and this value was used in the
simulation. The ratio (PDK) of air flow velocity to pressure gradient (mbar/cm)
decreases as solids fraction (FS) increases so that the volume of air drawn
through the piles probably decreased throughout the composting period.
Average solids fraction and volatile fraction was measured for all four piles
initially and at the end of the composting period. These reported measurements
are shown in the following table.
Start End
Pile
A
FSI
=
0.573
FSE
=
0.723
FVI
=
0.299
FVE
=
0.281
Pile
B
FSI
=
0.574
FSE
=
0.686
FVI
_
0.309
FVE
=
0.271
Pile
C
FSI
" s
0.515
FSE
=
0.653
>
FVI
=
0.328
FVE
=
0.318
Pile
D
FSI
0.522
FSE
.
0.653
FVI
'=
0.322
FVE
=
0.300
In the table FSI and FVI are the initial solids and volatile fractions and FSE and
FVE are the solids and volatile fractions at the end of the composting period.
Since non-volatile solids will be unaffected by the composting process a mass
balance for non-volatile solids will show the ratio (R) of pile mass before and
after composting. Let VI and WI equal the initial pile volume (VI, cm3) and
initial pile density (WI, gm/cm3) while VE and WE are the corresponding values at
the end of the composting period. A mass balance for non-volatile solids is written
as follows;
VI*WI*FSI*(1-FVI) = VE*WE*FSE*(1-FVE)) (48)
R = (VI*WI)/(VE*WE) » (FSE*(1-FVE))/(FSI*(l-FVl))
35
-------
Figure 7. Diagram of LACSD aerated compost pile
for wastewater treatment sludge.
-------
i
i
t
f
i
!
Figure 8. Measured and computed interior compost
temperatures versus composting time for
piles A&B.
c/)
c/)
¦o
i
l/> :
40
Composting time, days
i
-------
Figure 9. Measured and computed interior compost
temperatures versos cempesting time for
piles C&D.
m
65
l
Composting time, days
-------
The ratio R has the following values for piles A, B, C, & D.
Pile A
R = 1.2942
Pile B
R = 1.2608
Pile C
R = 1.2868
Pile D
R = 1.2915
These values are relatively consistent between piles and average 1.2834. Thus,
it appears that the mass of the piles was reduced by about 22% over the com-
posting period. Partition of this decrease between volume and density cannot
be made from available data. However, it seems likely that the density of the
initial blend is nearer dry compost than wet cake so that most of the value of
R is probably associated with a change in pile volume. If all of the change is
associated with volume the linear dimensions of the pile would be changed by
the cube root of R or by about 8.7%. Additional measurements of solids and
volatile fractions were given in the April, 1978 progress report (11) and using
these measurements a value of 1.2445 is found for R. In the March, 1978 pro-
gress report (10) five density measurements for wet cake and dry compost were
given. Average cake density was 1.044 gm/cm^ and average dry compost density
was 0.85 gm/cm3. The ratio is 1.228 which further supports the presumption
that most of the R ratio is associated with a volume change.
Using the computed R values for each of the four piles the fraction of
initial liquid water lost, the fraction of initial volatile solids lost, and
the ratio of mass of water lost to mass of volatile solids lost can be computed.
The fraction of water lost is computed as 1.0 - (1-FSE)/(1-FSI)/R and computed
values are 0.499 for pile A, 0.415 for pile B, 0.444 for pile C and 0.438 for
pile D. The average over the four piles was 44.9% of the initial water lost
during the composting period. The fraction of volatile solids lost is computed
as 1.0 - FSE*FVE/FSI/FVI/R and computed values are 0.0837 for pile A, 0.168 for
pile B, 0.0447 for pile C, and 0.0976 for pile D. Grams of water lost divided
by grams of volatile solids lost is computed as (R*{1-FSI)-(1-FSE))/(R*FSI*-
FVI-FSE*FVE) and this ratio is 14.847 for pile A, 5.914 for pile B, 28.517 for
pile C, and 12.756 for pile D. The average of the four values is about 15 mg
of water lost per gram of volatile solids lost; a surprisingly high value.
Heat of combustion of volatile sludge solids is usually taken as 10,000
Btu/lb or 5500 cal/gm. However, if the water lost/volatile solids lost ratio
is taken as 15 the enthalpy available for evaporation of the water is 5500/15
or 367 cal/gm. If the temperature of the liquid water is 25 C initially the
enthalpy change (cal/gm) needed to exhaust the water at temperature T C is
597.44 + 0.4306(T - 25.) or 572.44 + 0.4306T. Clearly, the heat of combustion
must be greater than 5500 cal/gm. If it is assumed that the lipids are first
to combust in the composting process the heat of combustion of lipids (9300
cal/gm) can be used in simulating the process. This assumption was made in
simulating the behavior of piles A and D. No attempt was made to simulate
piles B&C because the water lost/volatile solids lost ratios differed from
those computed for piles A&D by roughly a factor of 2.
39
-------
In the June-July, 1978 LACSD experiments with aerated compost piles the
reported pressure drop across the compost was 2-1/2 inches of water or 6.14 rnbar.
Measured air flow rates through the four piles were given in cfm and these
measurements are shown plotted versus the initial solid fractions in. Figure 10. In
the simulation program the air flow through the pile (ARATE, hr" ) is directly
proportional to the constant PDK when PBLOW is fixed. Therefore, slopes of the two
regression lines; one relating air flow rate to FS and one relating PDK to FS,
should be equal on semi-log paper. These two regression lines with equal slopes
are shown in Figure 10. The assumption was, therefore, made that PDK can be
estimated using the relationship: PDK = 243,743/EXP(3.4237*FSA). A more precise
method would have been to compute a local value of PDK dependent on the local
solids fraction but this degree of precision seemed to be unjustified. In
simulating the performance of piles A&D the air flow rate was corrected at each
time point using the relationship fo(| PDK given above. For example, for pile A the
initial value for ARATE was 2.43 hr" and this decreased as FSA increased over the
30 day composting period to a value of 1.40 hr" . the initial ARATE for pile D
was 2.89 hr" and this value decreased to 1.54 hr" at the end of the 30 day
composting period. The value for PBLOW was held at 6.14 mbar throughout the
composting period but a more precise method would have been to allow PBLOW to
increase as the pressure drop gradient increased according to the blower map
characteristics. In general, the simulation of the air flow regime seems adequate
but better measurements are needed to fully test the linear simulation.
A time interval of 0.25 hours was used in both simulations and the composting
period was set at 30 days; thus NT was 2881. Ambient atmospheric air was assumed
to have the reported average temperature of 21 C and an average relative humidity
of 70%. The relationship between rate of microbiological activity and compost
temperature used was the one marked Regan et al in Figure 5. EM IN was set at 0.2
mmole O^/day per gm of VSS. .Actually, in the program the concentration of
biodegradable volatile solids was used rather than the concentration of volatile
solids. Initial compost temperature (TMIX) was set at 25 C,
The biodegradable fraction of volatile solids decreased from an initial
value of FB0 = .55 to .49 for pile A and to .47 for pile D. These changes are small
compared to the uncertainty associated with the temperature versus biological
rate relationship.
The principal difficulty experienced in running the program was the tendency
of the blocks along the air-compost boundary to become too dry. This could be
caused by omission of the mechanism for moisture movement as a result of capillary
pressure or by the assumption that moisture leaving any block is saturated at the
block temperature. Correction of this problem should be first priority in the
second generation composting model. In running the program this problem was
avoided by setting the value of CVE to 3.0, WIND to zero, SOLAR to zero, and HAIR0
to 1.25.
The average compost temperature for blocks (7,2) and (8,2) was computed and
printed out as the temperature (TAVG) measured in the aerated compost pile
experiments. Computed values for TAVG are shown plotted by the solid lines in
Figures 8 and 9. The general shape of the curves are similar to the measured
points but the agreement is not adequate for predictive purposes. Measurements of
fundamental compost characteristics are needed to improve the agreement between
measured and computed results.
40
-------
1000
o
jCl.
100
Figure 10. PDK and air flow rate (cfm) versus
compost solids fraction.
compost solids fraction
0.6
0.5
0.7
0.4
41
-------
Other comparisons between computed arid measured results are shown in
the following table for piles A and D.
Computed Measured
Pile A:
final solids fraction 0.735 0.723
final volatile fraction 0.272 0.281
moisture lost fraction 0.500 0.499
water lost/VSS lost 11.7 14.8
Pile D:
final solids fraction 0.706 0.653
final volatile fraction 0.272 0.300
moisture lost fraction 0.539' 0.438
Water lost/VSS lost 11.8 12.8
These comparative values suggest that the simulation program is doing a
reasonably good job of simulating the aerated composting process. However,
more detailed measurements of compost properties over the compost period and
from various parts of the compost pile will be required to properly assess
the validity of the program.
A complete description of the program including the listing and de-
finitions of variables used is given in the appendix.
42
-------
1
2
3
4
5
6
7
8
9
10
11
12
13
REFERENCES
Epstein, E. and G. B. Willi son 1974, Composting Sewage Sludge. In:
Proc. National Conference on Municipal Sludge Management, Pittsburgh,
Pa.
Epstein, E. and G. B. Willison 1975. Composting Raw Sludge. In: Proc.
National Conference on Municipal Sludge Management, Anaheim, CA.
Epstein, E. et al 1976 A Forced Aeration System for Composting Waste-
water Sludge. Jour. Water Pollution Control Federation, Vol. 48, (1976)
pp 688-694.
Haug, Roger T. 1979. Engineering Principles of Sludge Composting.
Jour. Water Pollution Control Federation Vol. 51 (1979) pp 2189-2206.
Keen an, J, H. et al,, Steam Tables. John Wiley and Sons, Inc. New York
(1969).
Re id, R. C. and T. K. Sherwood 1958. The Properties of Gases and Liquids.
McGraw-Hill Book Co., Inc. New York.
Philip, J. R. and D. A. DeVries 1957. Moisture Movement in Porous
Materials Under Temperature Gradients. American Geophysical Union
Trans. Vol. 38 pp 222-232.
Keenan, J. H. and Joseph Kaye 1948. Gas Tables. John Wiley and Sons,
Inc. New York.
Patten, Harrison E., 1909. Heat Transference in Soils. U.S. Department
of Agriculture, Bureau of Soils Bulletin No. 59, U.S. Government Printing
Office.
Los Angeles County Sanitation Districts and Environmental Protection
Agency Joint Research Project Progress Report for March, 1978, EPA
Contract No. 14-12-15.
LACSD and EPA Joint Research Project Progress Report, April, 1978 EPA
Contract No. 14-12-15.
DeVries, D. A., 1963. Thermal Properties of Soils. In: W. R. Van
Wiejk' (ed) Physics of Plant Environment. North-Holland Pub. Co. Amsderdam.
McAdams, William H., 1954. Heat Transmission. McGraw-Hill Book Co.
43
-------
14
15
16
17
18
19
20
21
22
23
24
25
26
27
LACSD and EPA Joint Research Project Progress Report, October, 1978 EPA
Contract No. 14-12-15.
Wiley, John S., 1957. Progress Report on High-Rate Composting Studies.
Proc. 12'th Industrial Waste Conference (Purdue) pp 596-603.
Jeris, J. S. and Raymond W. Regan, 1973. Controlling Environmental
Parameters for Optimum Composting. Compost Science Jan-Feb 1973 pp 10-.
1'5.
Schulze, K. L,, 1962. Continuous Thermophilic Composting. Compost
Science Spring, 1962 pp 22-31.
Arditi, A. 1967 M.Sc. thesis University of Pirmingham In: Review of
Composting Part 2-The Practical Process. Process Biochemistry, October
1971.
Andrews, John F. and Kawi Kambhu, 1971. Thermophilic Aerobic Digestion
of Organic Solid Wastes. Environmental Systems Engineering Dept. Clemson
University, South Carolina.
Snell, John R., 1957. Some Engineering Aspects of High-Rate Composting.
ASCE Jour. Sanitary Engineering' Div. February, 1957 paper 1178.
Regan, R. et al., 1973. Cellulose Degradation in Composting, USPHS
Solid Waste Program Res. Grant UI 00508 PB 215,722 NT1S
Schulze, K. L., 1961. Relationship between Moisture Content and Activity
of Finished Compost. Compost Science Summer 1961, pp 32-34.
Taylor, S. A. and G. L. Ashcroft 1972. Physical Edaphology. W. H.
Freeman and Co., San Francisco
Chow, Ven Te, 1964. Handbook of Applied Hydrology. McGraw-Hill Book
Co., New York.
Joint Committee of ASCE and Water Pollution Control Federation, 1959
Sewage Treatment Plant Design. ASCE Manual of Practice No. 36.
ASHRAE Handbook of Fundamentals 1972. American Society of Heating,
Refrigerating, and Air-Conditioning Engineers.
LACSD and EPA Joint Research Project Progress Report, July, 1978
EPA Contract No. 14-12-15.
44
-------
APPENDIX
Using the Compost Model Computer Program
The compost model computer program is called CMPST and can be used to
compute the time-dependent performance of windrow composting of wastewater
treatment plant sludge over a specified period of time. NT is the number of time
increments of length DT (hours) which the program calculates. The shape of a
trapezoidal cross-section is determined by the input variables NVB (number of
vertical blocks), NBB (number of base blocks), and NTB (number of surface
blocks). DX and DY define the width and height of each interior block of the
cross-section. All of these input variables provide the basis for the numerical
integration.
Several variables are input to CMPST in order to control what output is
printed and how much of it. IT is the number of the time increment at which the
program begins to print out the computations; a value of zero begins the printing
at time zero. LP specifies the number of time increments that are to be skipped
between each print command. IPRNT determines whether the printed output is in
fixed or floating decimal format. ITURN defines the number of time increments
between the points at which periodic mixing of the compost pile occurs. The input
vector IP(I) determines which cross-sectional outputs are printed for each'time
step. It is possible to obtain a printing of cross-sectional calculations for up
to 12 different program output parameters. An input value of zero will suppress
the printing of individual parameters. For each parameter that is selected, the
computed value of it in each block of the trapezoidal cross-section is printed
out at each time increment that is specified. The form of the printout resembles
the right half of the compost pile cross-section having I rows and J columns. The
left half of the compost pile would be the identical mirror image of the right
half. As with any time-dependent computation over a period of time, CMPST is
capable of calculating a tremendous amount of output, but the program user can
selectively print only the information of interest by setting IT, LP, IPRNT,
ITURN, and IP(I) appropriately.
The input variables to CMPST are defined in Table A-l. The FORTRAN names
appear in the order in which they are input to the program. Table A-2 gives the
definitions of the output parameters that are calculated and printed out by
CMPST. Other parameters that are computed and only used internally by the
program are also defined in Table A-2. The FORTRAN names appear in the order in
which they are printed out by the program. The FORTRAN source code listing for
CMPST is given in Table A-3. Sample data for input to the program is shown in
Table A-4. Table A-5 gives the respective program output for the data case listed
in Table A-4.
CMPST is written completely in FORTRAN and uses no required subroutines or
functions. Standard input/output files are used. The computer program was
written for a 32K PDP-11/70 computer, but can be easily converted to other
systems that have FORTRAN compilers. Since this time-dependent model requires an
large amount of intermediate calculations in order to compute the compost pile
performance over several days, the program running time is significant. A typical
30-day simulation uses 13.5 minutes of CPU time on the PDP-11/70 computer. A 15-
day run would take about half that amount of CPU time, and so on.
45
-------
Table A-l
INPUT VARIABLES TO CMPST
NCASE number of data cases to be run
LIST alpha-numeric identification of each data case
NT the number of time increments to be computed by the program
IT number of the time increment at which the program will begin
printing output
LP the number of time increments that the program skips between
each print command
IPRNT program control: 0 prints the program output in F format
(fixed decimal point, 1 prints the program output in
E format (floating decimal point)
ITURN the number of time increments that the program skips between
each mixing of the compost pile
NBB number of bottom base blocks in a trapezoidal cross-section
of compost pile
NTB number of top surface blocks in a trapezoidal cross-section
of compost pile
NVB number of vertical blocks in a trapezoidal cross-section
of compost pile
DT length of time increment, hrs
DX width of areal increment, cm
DY height of areal increment, cm
TSOIL ambient soil temperature at a depth of 10 ft, C
TAIR ambient air temperature, °C
TMIX initial temperature of the compost, °C
TWET ambient air wet bulb temperature, °C
RH relative humidity of ambient air, fraction
WIND ambient wind velocity, miles/hr
W0 initial compost density, gnn/cm^
46
-------
initial compost solids mass fraction, fraction
initial volatile fraction of compost solids, fraction
initial biodegradable fraction of compost volatile solids,
fraction
compost thermal conductivity, cal/(cm2)(hr)(°C/cm)
constant used in biological rate versus compost solids
fraction relationship
constant in relationship for surface water evaporation
minimum oxygen concentration below which biological
activity ceases, gm/cm^
pressure maintained in pressure source, mbar above or
below atmospheric pressure
atmospheric pressure change per cm per degree Kelvin, mbar
average compost porosity, fraction
surface conductance at soil-compost boundary, (cal/hr)/cm2
composting efficiency, mmole Oj/Cday) (gui VSS)
minimum composting efficiency, inmole 02/(day){gm VSS)
gm water produced per gm fuel combusted
solids fraction at which biological activity peaks, fraction
high heat of combustion, cal/grn
adsorbed solar energy, cal/(hr)/(cm2)
surface convective heat loss coefficient for wind = 0,
tcal/hr)/(cm2)(°C)
if
IP
(1)
= 1
print
output
for
T1(I,J)
if
IP
(2)
= 2
print
output
for
T2(I,J)
if
IP
(3)
= 3
print
output
for
C01(I,J)/C0AIR
if
IP
(4)
= ¦ 4
pr'i nt
output
for
C02(I,J)/C0AIR
if
IP
(5)
= 5
pri nt
output
for
V(I,J)/VAIR
if
IP
(6)
= 6
print
output
for
P(M)
if
IP
(7)
= 7
print
output
for
UX(I,J)/6Q./30
if
IP
(8)
= 8
print
output
for
UY(I,J)/60./30
if
IP
(9)
= 9
print
output
for
W(I,J)
if
IP(10)
= 10
print
output
for
FS(I,J)
if
IPC
11)
= 11
print
output
for
FV(I,J)
if
IP{
12)
= 12
print
output
47
for
FB(I,J)
-------
Table A-2
OUTPUT PARAMETERS FROM CMPST
COAIR oxygen cencentration in ambient air, gm/cm3
AREA compost windrow cross-sectional area, cm2
WPHE initial water content in one cm thick cross-sectional area, grn
HFUEL initial fuel value in one cm thick cross-sectional area, kcal
PDK pressure drop constant from Darcy's law, cm2/(mbar)(hr)
XBLKS number of blocks in compost half cross-section
I nodal row number
J nodal column number
T1(I,J) local compost temperature at start of DT, °C
T2(I,J) local compost temperature at end of DT, °C
C01{I,J) local oxygen concentration at start of DT, gm/cm3
C02(I,J) local oxygen concentration at end of DT, gm/cm^
V(I,J) local water vapor density, gm/cm3
P(I,J) local air pressure, mbar above atmospheric pressure
UX(I,J) local horizontal air flow velocity positive to right, cm/hr
UY(I, J) local vertical air flow velocity positive upward, cm/hr
W(I,J) local compost density, gm/cm^
FS{I,J) local compost solids mass fraction
FV(I,J) local compost volatile mass fraction
F8(I,J) local compost biodegradable volatile mass fraction
TPILE average pile temperature, C
WA average compost density, gm/cm^
FSA average compost solids fraction, fraction
48
-------
FVA
average compost volatile fraction, fraction
FBA
average compost biodegradable fraction, fraction
QHUP
heat,lost across compost-air boundary, kcal
QHOWN
heat lost across compost-soil boundary, kcal
QVUP
water lost across compost-air boundary, gm
f
WSTAR
WOUT - ,%'22, gm
WLOST
water lost from compost one cm slice, gm
W22
water entering pile through block (2,2) gm
WOUT
water lost over air-compost boundary, gm
ARATE
aeration air supplies, (cm3/hr)/cm3
TAVG
average temperature for blocks (7,2) and (8,2), °C
HMIN
HEAT computed with EMIN cal/(hr)(cm3)
SHMIN
counter showing number of blocks with HEAT = HMIN
HSTAR
HOUT + HSTOR - H22, kcal
HUSED
heat produced by biological activity, kcal
H22
heat entering pile through block (2,2), kcal
HOUT
heat lost over soil and air boundaries, kcal
HSTOR
heat stored in one cm compost slice, kcal
HOFF
number of blocks in which heat = 0 because of lack
of oxygen
WLOST/WPILE fraction of initial pile water lost, fraction
WLOST/HUSED gm water lost per gm VSS lost
internal program parameters that are calculated but not printed
CQAIR oxygen concentration in ambient air, gm/cm3
FUEL0 initial concentration of biodegradable organic material, gm/cin^
HAIR surface conductance at air-compost boundary, (cal/hr)/cm2
49
-------
VMIX
saturated water vapor density at TMIX, gm/cn3
DPAIR
change in atmospheric pressure over DY, inbar
VAIR
.water vapor density in ambient air, gm/cm^
XM
local compost mineral volume fraction
XV
local compost volatile volume fraction
xw
local compost water volume fraction
XA
local compost air volume fraction (porosity)
VHC
local compost volumetric heat capacity, (cal/cm3)/°C
QHL,
QHB,
QHR
QHT
flux of enthalpy entering any block from the left, right,
bottom, and top positive into the block, cal/hr
QVL,
QVB,
QVR,
QVT
flux of water vapor entering any block fro,n the left, right,
bottom, and top positive into the block, g;n/hr
QOH
oxygen usage rate in any block, gin/hr
HEAT
heat production by microbiological activity, (cal/hr)/cm3
OA
incremental cross-sectional area, cm?
SPH
heat stored in pile- over initial heat, cal
50
-------
Table A-3
FORTRAN LISTING OF CMPST
c windrow composting process model (cmpst) 3»26-i9S0
c Richard c„ filers -¦ march i98d
c
DIMENSION Tif20,20),T?r20,20),C01f20,20),C02(20,20),
V(20,20),®r?0,20)»UXf20,20),UY(20,20),W(20,20),
FS{20,2Q)»FVf20,?0>,VAR{20»20),FB(20,20),
LIST(40),TPf12)
OPEN TUNITBJ,NA«e«»CmP8T,DAT» ,TYPE.'OLD',FORM.»FORMATTED*,READONLY)
CALL FRRSETffeJi.TRUF,,,FALSE.,.FALSE.!.FALSE.,500)
CALL FRRSETf72,.TRU?., .FALSE.,. FALSE.#. FALSE. ,500)
CALL FRRSET C 7 3 #,TRUF.,.FALSE.,.FALSE.*.FALSE,,500)
TNsl
10*4
READ fIN f 5) NC ASF
5 FOPWATfl?)
DO 1000 111«1#NCASE
RE*DfIN,10) LIST
10 FORMAT(40A3)
READfIN, 15) XNT,XT,*T#PRNT,TURN,XNBBfXNTB,XWB
READCIN, 151 DT,DX,D*,TSOlL,TAIR,TMJXf-TWET,WFP
READf IN, 15) RH, WIND»WC<, p*Sfl »FVO, FEO,TC#SPEED
READfTN,15) CVE,COMTN,PpLOW,G,XAM,HSOIL,EMAX,EMIN
READ f TNf15) FSPK,HC"MP#SOtAR,HAlPO
15 FORMaT ftFlO.O)
READfIN,201 tlPf,12)
20 FORMAT(1715)
nt«xnt
TTsXT
LPsPT
IPRNTbPPNT
ITURNsTUBN
• fclB«XNBB
MP3XNTB
NVBaXNVR
XBLKSbvUvW* ( xNTp* t . ) /?" + (xNvB#»24xNv^5/2,«! ,
jb*nbb/2'.*i .5
TV*NVP*l".
jT*NTB/2>2.5
FUFLOeWO«FSO»FV0*Fif>
APEA»D**DY«(NVB«rNVfi+l»TB)-l . )/2.
PDK»24 37 4 3./EXPf3,4?3^#FS0)
TK »2 7 3 . +TM T X
HAIR»HAIpO+, 1 674*WI*'D
VMIX»FXPf5.14726-4925.89/ftMIXf273.))
DPAlR*DY*G/CTAlR+273.}
VAIRbRH#FXP(5,I4726-4<'25.99/(TAIR*273 t ) )
HFUEL*FUELC*AREA *HCr,MP /1000.
WPILE»f WO»fi »-FS0)+wFR*FUEt«0 3*APEA
C0AlR».0Bl9/f 273.+TM")
F S A s F S 0
IF tPBLOW) 21,22*22
2} K« 1
51
-------
Table A-3 (continued)
GO TO 23
22 K*0
2J CONTINUE
c
c Zfrd all subscripted vapTaeLfs
c
DO 25 111#20
DO 25 J«l# 20
T1fI,J)«TAIP
T2fI»J)*TAIH
C01tI,JJbCOAIP
C02(I#J)sC0AIR
V(I,J)«VUR
p(i»,n*o".
uxr
WCf ,
FSf
rvfI,j)«o.
VAR(IfJ)«0,
FB(IfJ)»0,
25 eONfjNUF
WP JTe(TO * 30 ) LIST
3d FOPMftTf//,20X,40»2,/)
WPITE(I0,32) NT,IT,TP,IPPNT,ITURN,NBB#NTi,NVB
3? F0PM1T(9X,'NT',10X,' IT »,J OX,•LP',7X,'IPRNT•,7X,»ITUPN•,*X,• NBB1,
, 9X , • NTP ¦ # 9X, »NVB',/,»I12,/)
wPTTFf TO, 35) DTfnx,^Y»TSOII,f TAJR, TMIX»TWEJ,WFP
35 FOpMiTftX*»DT»#10X,*DV»f10X#»DY'»7X»•TSOIL»#8X»
. tT&IB•,fiX,'TMIX'#8X,* TWET*,9X,•WFR« #'#8F12,4,/)
WRTTFfTO.40> PH,WlNr,Wo,FsO,FV0«FB0,TC»5PPED
40 FORMAT(9*,' RH • » R X »•hIwD~,tOX,tW0»,9X,«FsOi#9X,IFV0',9X»»FBO»,
, 10X,»TC'»7X»»SP*Et>,«'»8Fl?.4,/)
WRTTE(TO» 45) CVF,C0WTv,pPLOW,G,XAM,HsOIL,FMAx,EM IV
45 FORMATf§X,"CVE',7X,'COmINSTXi~PPlO*'#11X,•G•# 9X »•XAm * # 7X »
. 'HSOIL'.ex,»EMftX',RX,lEMIN',/,8F!2,4,/)
WRTTf(TO,50) FSpK,HCO»B#SOLAR#HATRO
50 FORMITf7X#»FSPK>,7*f»WfDyS* #?X,'SOLAR 1 »7X, •HA IPO'#/,4Fl2.4,/)
WRITE £ TO,55) fIP(I)»I*1,12)
55 FQRMlT( 9X #'Tl',9X,»T2',PX,'CO!• ,8x.*C02»,10X,
, 'V«, 10X, • p « ,9X, IUX»,<*X, «UY» ,10X, iw»,9x, 'FS'»9X# »FV ,9*, * FB » ,
. / # 6x» «T5EG C'#6X»'DF(J f i#2X# ,COl/qOAIR,»2X,«c02^CO*IR,»
. 5X # 'V/V|IR"«7X, 'MHR» P5X, •FT'MIN I # 5X# » Ff/MIN » ,
. 6X, iGM/CC' #7X, I'aS/Wi ,6x, »VSS/W«#gX» »ViS/W',/,i2lH,/)
WRTTff IO#60) C0aIR**PfA#wP1LiE#HFUeL»PDK»XbLKS
bO F0PM6TC6X# »COAlP«#8X,• AREA'#7X,~KPILE'»7X,»HFUEL»,9X,'PpK',
. 7X, ' XPLKS',/,Fl2.7,5F12.4,//)
WPTTFfTO,65)
65 FORMatmx# 'I ¦ ROW NUWBEP '«/#1X# ' J ¦ COLUMN NUMBER')
C
C INITIALIZE ALL SUBSCRlpTFD VARIABLES
C
TND1«J1-I
IND2«JT-J
52
-------
Table A-3 (continued)
DO 95 J«1 ,*J1
IF CJ-JTJ 70,75,75
70 NPbIV+1
GO TO 80
75 NPbNR-1
*0 DO 95 I«1»NR
IF (I-n 05,90,85
85 P £ I , J )aDPAIP* ClV"l4,5J
CO!(IfJ)»COftIR
C02 (T » J1«CO*IP
T1(I, J)bTMIX
T2CI,J)«TMIX
V(|»J)»VWIX
W CIrJ)*W0
fs(I#j)bfso
FVfI,J)*FV0
FB(I,J)bFBO
GO TO 95
90 T1(I, J JbTSOIL
T2a,Ji»TS0IL
95 CONTINUE
TH2,2)*TMIX
T2f2,2)*TMIX
V(2,2 5 *VMIX
n¥2»DY*DY
DX2»DX»DX
CY«nY2/fPX2+PV2)/2.
CX»DX2/(DX2+DY2j/2.
P(2,2)*PlL0W
DO 155 ,200
DO 100 I»1 ,IV
P(I,1JePf1,3)
1 00 CONTTNI'F
NPT*TV
DO 150 Jb2,TND1
NRB"?
IF fJ-JT) 110,105,J"5
IO5 NPTBNRTwj
JiO IF (J-2) 125,120,12*
120 NPB»1
125 Do 150 IsNPB,NPT
IF f1-2J 5 35, 1 10,115
130 P(2,J)«DY2»(P(2,J*1 UPf2,J-m/(2.«DY2*DX2)*nx2«
£P(3,J)*dPAIc)'(2««DY2+DX2)
GO TO 150
135 IF (I.TV) 145,140,1<5
J40 PCIV,J)«0Y2«CP(IV,J*1UP(TV,J4l)5/C2.»DY2*1,#DX2>~
PX2#P(IV-1 2.«0Y24 3.#DX2)
GO TO 150
145 PCI,J)«CY»fPCI,J*11*PfI,J-l))*CX#fPC|4l,J)+P(I»l,J5)
l5f> CONTTNtlE
1&5 CONTIMUF
NPT«IV
nO 170 J«2,IND1
NPp*2
53
-------
Table A-3 (continued)
TF (J-JT) 165,160,160
160 NRT«NRT»1
lb5 DO 170 laNPBfN"T
Uy(I,J5«PDK#(P(l,Jj»PfT+l|J))/D¥«PDK#DPAIP/DY
UX(IfJ)sPDK*fP(T»JJ-P'1.J*1>>'DX
I'O CONTINUE
UXCIV,1)«-UX(IV,2J
DO 175 J«2, IND2
tm iv, ji«uy(ivi#j>-cuxcivlj)-uxciv,j-i))»Dy/DX
1?5 CONTINUE
no IPO
UX(If.J1«fDY#UXCI,a-1UDX»UYCl-l#J))»DY/(DX2+DY2}
uY(l,J)«nxfi,J)«r>x/py
180 CONTINUE
C
c ppint values or ux,uy
c '
DO 194 11*1,2
DO 186 I«1,20
DO 186 J*1»20
GO TO f 1B2#184),II '
182 VAPf I,,n»UX(I,J)/6O./^O.4 0
IVAR1»»UX«
TVAR?*' '
GO To 196
I 8 4 VAF (I ,«J)»UY(I ,J)/60,/'0,4S
lV*Rls»OY»
TV*P2s» »
1»6 CONTINUE
L1«IV
NCOLbJT-I
WRITE(10,224) IVAR1 , IVAP2
DO 192 Ts1,IV
NCOLbNCOI. +1
WRITE(I0« 22§) il,(VRRfLl#J)»J«2iNCOL)
TF fNCOt-JBI 190,IS8,181
188 NCOLbJR-1
190 LlsIV-T
192 CONTINUE
194 CONTINUE
WRITECT0,195)
195 FORMAT f///)
C
c print initial values p* dimensioned variables
c
IMIXbO
OHUPbO,
OHOWNeO,
OVUPbO.
AIRUPbO.
W22»0.
H 2 2 b 0 .
RH20l»o,
54
-------
Table A-3 (continued)
DH202S0.
DO 500 JI»1,NT
IF (IT-IT) 290.290,196
19$ TIME.fIT.l)*nT
DAYS»TIME/24,
ITbIT+LP
WRITE(10,198) TlME,PftYs
198 FORMATC//,IX,"TIME ¦ ' ,F7,1,IX,«H0UR5'»2XiF7,2,IX,'DAYS'5
TVARl*' 1
*
DO 2fO KK«1,!2
IF ClPCKKl) 280,230,200
200 DO 220 1*1,20
DO 220 Jat,20
GO TO r20t,202,203,*04,205,206,207,208,209,210,211,2125,IPCKK)
201 VAP(l,J1sT1CI,J)
iVAPls'Tf «
IV A R 2 * • »
CO TP 220
202 VAP(I,J)sT2(X«J)
jVAR1««T2'
IV A R 2 ¦ • 1
GO TO 220
20J VARfl,J)«C01(I,j)/CaATB
IVARIb'CO'
TV AR2» M •
GO TO 220
204 VAR(T,J)«C02tT,J)'C0ATp
iVARis'Cn'
IV 8 R 2 = • 2 1
GO TO 220
205 VARtI,JlaVfI.J)/VAI»
IV A R1 * ' V '
IV A R 2 » ' '
GO TO 220
206 VARtT,J1»PCI,JJ
f V A R 1 « 1 P «
IVAR2*' »
GO TO 220
207 vAp(T,d>»UX
-------
Table A-3 (continued)
lVAR2a' "
GO TO 220
211 VABCI,
ivarib'fv'
IVAR2«» '
GO TO 220
212 VAPCl,J)«FBfI»J! - -
IVARl«»ri'
IVAR2»' «
220 CONTINUE
UR TTF f Tfl „ 29 4 1 TVAR1 , TVAR2
22 4 FORMATf//#1X,2A2,' I' , IX, • J«2•»7X,•J'r7X,•4•»7X,'5'i7X, • 6 ' ,7X,»7» ,
. 7X, «8'»7X, • 1 1 * »6X, '12«»6X, '13»,6X, 1 J4«,6X* » S 5 • #
, 6X# M fih
Lt*rv
NCOLbJT-1
DO 260 Tb1 , IV
NCOLbNCOL*1
IF CTPPUT) 230,226,210
226 WRITfC10,228) L1,tV*R'LI•J J«J*2,NCOL)
22 8 FOPM^TfIft,16F8.4)
GO TO 235
2l0 WPITe fJO,232^ L!,CV»RfI I,J),Js2,NC0L1
232 F0*M#T(I6#16F8.2)
2^5 IF(NCOL-JB) 250,240,240
240 NfOL«JP-1
250 t1»IV•I
2b0 CONTINUE
2^0 C0NTIN11F
WrITF(IO,285) TPILF» W ® ,FS* ,F*VA,fBA,QHUP ,QHDWW,QVUP,
WSTAP,WT nST,V)2 2,WOUT, ARATF,TAVG,HMlN,SHHlN,
HsTAR,Hti$ED,w22,H0UT,HST0P#HOFF,WP,HR
2»5 FORMATf/,9x,»TPILE'«I4X,'WA» »13X,»FSA» »llX,*FVA»,13X,'FBAi,I2X,
. ' QHUP , 1 IX, 'QHBWH'iI?X, « CVUP » , / , §F16 , 5 , / , 9Xf I WSTftR I , 11X ,
. 'W L D S T1.13x,* W 2 2 *,12*,•WOUT',I1X,' APATE',12X,«TAVG»,12X.
, 'HMINi,J IX,ISHMIN',/»8F16.5#/,9X,'HSTAP',1IX,IHUSED"illXf
, »H22»,I2X,'HOUT',i 'X,tHSTOR',12X,«HOFF »#5X,tWLOST/WPILF•,
, 5X,»WL0ST/HUSEP»,/»8*16,5J
C
c initialize left §oundry wooes
c
TIV*IV4l
290 00 300 T»3,IIV
V (I» 1 )bV(1,2 )
T1fI,l)»TlCI,2)
UX(I,1)«.UXCT,?>
UY f1, 1 1»UY(1,2)
COi(1,1)BC02tI,23
30n continue
c
c solve for all variable* *t later tiwe
c
gPHBO.
SVHCsO.
56
-------
Table A-3 (continued)
WGT»0,
SOL*0,
PH2DbO.
VSOLbO.
VBSOLbO.
HOFFbQ,
SHMlNaO,
0)tD¥»nx«n¥
NRT*IV
AIRINany«UXt2,2)*DX«nVf 2,2 V?.
ARATFbAIPIN/AREA
IF CPlLOW) 304,302#*02
102 Tir2,2l«TAIP
V(2#?)bV»IR
104 DV«CB03.+B.81«ff 1 Cl»2HTi (2,2»/2.)«XA*
WTOP«OX/2.*(UYf2,2i«Vr2+K,2)-DV»(V(3,2)-V(2,2)J/CYJ
OVBteOS. + B.flUKTl C2#3Uf 1 C2«2))/2.5*XAM
WpGTB!jy*(UX(2,2)#Vf 2»2**l-TlV»fV(2,3)-Vt2#2})/DX)
W22»W22*CWT0P*WrGT)«DT
Hf OP »dX/2.*(.08442#" Y'?,25#Tl (2+K , 2 ) / £ T1 C 2 + K , 2 U27 3 . ) J ~
WTOP»(S97.44+.«j06#Tt(2+K#2))
HPGT«pY#£.08442*UXr?,?UTt f2,2*K)/(Tl (2,2*K)*273.) )~
WPGf#e597.4 4*,43fl6#Tl(2,2+Kn
h22»H22+CHTOP4HPGT)«DT/|000.
DO 400 Js2,JB
Np§s 2
IF fJ-JT> 3?5,3j5,j05
305 NRTsnrT-1
315 IF fJ-2) 325, 320,32''
320 N P B * 3
325 DO 400 T«NRB,NPT
DA«DXDY
XMbFSCI,J)*C1,-FV(I»J))»W0/2t65
XV.FSU ,J]»FV(I, J)»W0/1 .3
XWbC1.»FS(I,J))«W0
X»«l,-XM-XV-XW
VHC«#46»XM*.§»XV+XW
TF (C01 (I, J)/C0JUR-€0MIN J 330,330,312
330 HFATbQ.
HOFFbHOFF*!,
GD TO 336
332 HWIN«HCOHB/1200,#EMTN»V)(I,J)*FSCIfJ)*FVfI,J)#FiClfJ)
HEaT»HC0!«B/1200,«EM8X«wel, J)#FS(I, J ) #FV(I,J3#FB(I,J)~
FXP((T1fIiJ>-57,5«#2/254,)/IXPCSPRED#CFS(I,Jl*FSPK)#»25
333 IF (HEAT-HMIN) 335,13?,336
335 HEATbHMIN
SHMlN«SHMlN*l,
3 36 DVB C80 3. + 8, 81« Cf i (I /2,)#XAM
OVOLbHEAT«DT/HCO*B
OVL«OY#(UXfI,J-I)«vrirj.i+K)tDV«(VfX»J-l)-V(XtJ))/DX)
DVB(RO3.*0,81»(Tl(TfLJUTlCI»J*l))/2,)*XAM
QVRbOY»C-UXCI,J)«VfTf.HK)*OV»CV(I,J + J)"V(I,JJ )/DX )
OVsf80 3,*8.81»(Tl(T*JWt1(I-1»iJ>)/2.)*XAM
GV*Bnx«(UY(I-l ,JJ«VfI-WK,vn+DV«fVCI-l # )/DY)
57
-------
Table A-3 (continued)
OV* (803.^8.81 «(T1 (I»JUTi (J + i , J))/2,5#XftM
QVT®DX«f-UYCl#J)«VtT+K,j)*Dv*(V(I+l#J)-V(I,J))/DY)
PBF®\.
TBF»1. '
j4q If tl-NPT) 348,342,14®
l«2 IF (J-JT1 344,346# 3*6
344 TBF«2•
GO To 345
346 RBF«1.
TBF»3«
348 DOL«DY«(625.i+3.74»fT'CI.J5+T1CX,J-1}3/2,J#XAM/DX
DOPHDY« C625,8 + 3,74# fT'fI,J3+T1(I,J + l)3'2«)«XAM/DX»PBF
DOP«DX«f625,8*3,14#fTlCI,J)*Ti(1-1»J3 3/2,)«XAM/D¥
DOTBDX*(625.8+3,7 4#fT'(I,J)+T1 (Ul»JJ3*1•3*X**/DY«TBF
QDOlN»naL*COl (I, j-l H"OP*Cf>1 f I» d+1 3 4-DOB»CO» (T-l, J3*Dof*COi CT + i , J)
00HSHFAT«DR»1,6/HCOmP
IF fPBLDW) 349,350,350
3«9 QDIN»QD0IN-DY#UXCI,J)«C01CI#J*13-DX*UY*CTUl,J3*27 3 , 3 3#DX-UYCT,J3«Vn + K,Jl#DX
0VP».48 2#CVE«rI.~WTND/10,)«(2.#CY)«#.5«(V*IR#fTAIP+273,>»
VCI,J)*CT1(T»J1*273,)>«DY-UXCI,J)»VCI,J+K)*DY
359 OHt.«TC*CTl CI,J-1 5-T1 t T , J 5 ) #OY/DX+QVl» ( 597 , 4 4# . 4 306#T 1 CI » J* I ~* 3
, wuxn,j«l )« ,aM4?#ny«Ti Cl,J-l«-K3'(Tl(i,j-1+K 3 + 273.)
OHP»TC«Cf t CI I J+13-T* {T,J3)#DY/dX*QVR«(597,44+,4306«TI(I»J4K3
, 3-UXf I, J)«.08442#rfY«Tl CI>J*K3/CT1 (I»J+K3*273,)
QHB»TC»CTl (1-1 # J)*T' {*,J3 3«OX/D¥+QVB»C597,44 +,4306«T1
3+»JY(I-l ,J3*.0f442#Dx«f 1 (I-l+K, J3 /(Tl CI-14K, J)+271, )
0HT*TC«CT1(1 + 1*J3-T'(TfJ 33fDX/DY + QVT#(597,44 +.4106#Ti(I+K,J3
)»UYCl,J)«,0844?#riX«TlCI*K,J3/(Tl (I+K,J 3+273.3
IF Cl.NPl) 372,362,17?
3^2 IF Cj-33 364,366» 370
3«>4 OHB*HTOP*2,
GO TO 372
366 OHL«HRGT
370 OHB»HSOIL*CTSOIL-TJfl»J31«DX
OHDWNsOHD«»N-OHB«DT
372 IF (I-NRT) 384,375,184
375 IF (J.JT3 380,382,3*2
360 OHT*CHiIP« fTAIR-Tt f 7,t1 J ) + S0LftR5*DX+QVT« C597,44+,4306«7i (I*K, J3
3-UYf I, J)«,0844'#*X*T1 (I + K, J3/f 273,+T1 fl + K, J3 )
58
-------
Table A-3
(continued)
QH1JP«QWUP-QH1«DT
OVUPbOVUP-OVT#DT
GO TP 30 4
, 3^2 IR«CT»IP-T1 j+SOLAR5*DX*C2»)•».5+0VT« {597,44+,4306#
f 1 (I + KlJ))-u¥C!»J)f.0i442«DX«Tl CI+K#J 5/(273,m (I+K(tJ) J
OHR»(H»IB«fTAXP-Tl f Tr.J) )+a0L*P)«O*#{2.«C*)«#,,5 + OVB#C59T;444,4 J0$«
T1 fl,J + Kn-UX(T'J^«.0844 2#DY«Tl (JiJ + K)/(27 3, + Tl (IiJ+K))
0HUP«QHUP-(0Ht + (5HR)»DT
QVUP»QVUp-fOVT+QVR)«DT
nA*DXr)Y/2 .
384 ir (J-25 386,385,3P*
38§ OVL«OVR
QHL»OHP
3»6 T2fl»J)«T1(I,J)+DT«fOHL+OHP*OHB+OHT)/VHC/DA*HEAT«nT/VHC
DH20»-(OVL+QVP+OVB*flVT)#DT/nA-DVOL««FR
IF (T2tI,J)-TWET) 1*7,393,393
387 T2(I,J5»TWET
39| TK«T2fI,J5+273, *
VfiMp*fXPC5,0472-4925.89/TK)
f5VQL«WEAT«nf/HCOMB
FBf I, Jj.FVf J)-DVOL)/
-------
Table A-3 (continued)
HOUT»(OHUP+QMDWN)/! *0",
HSTAp«HGUTtHSTDP-H??
HUSED»fri}ELO-FUFLft)»ft"ift«HCOMB/iOOOi
WOUTbQVUP
WL0STaWP|tE-PH20"VB50r»WFB '
fPILE»SPH/SVHC4fMTX
TK«TPTLE*273
Vft«EXP(5".l47 26-4925,P^/TK)
HBbWLOST#HCDMB/(HOsFD-HST0P5/1000,
WPbWLOST/WPIIE
WSTftP*WOUT"W22
T6VGsfT2(7,2)*T?(8,2)1/2.
V12'» 2)¦ (WTOP + WflGT) / f DX«uY (2 # 2) / 2 ,*DY#UX (2»2) )
TEHP«(T1f3,2)*Tl(2,3))/2.*273.
ftaHTOP+HpSf-CWfOP+W^GT1»S97,44
B»,4 306»fMTOP+WPGT)+.0 8442»(DX/2.«UY(2#2)+DY«UX(2,2 3)/TeWP
T1(2,2)«I/B
UF«1. /EXPf 3,421"?»DrSjO
UXf2»2)sUXC2f 2)*UF
UY(2,?)*tlYf 2,?>«UF
C
c initialize all subscripted variables to earlier tine
c
NPT«IV
DO 490 Ja2,JB
NRB®2
IF (J-JT5 415,415,410
410 NBT»NPT-I
415 IF CJ-21 430,420,430
420 NRB*3
4*0 DO 490 J*NRB»NRf
IF tlfURN-lMlX) 440,4*0,450
440 FS(I,J1«FSft
F V f I, J ) «F V A
FB(I,J1«FBR
W(I,J)aW#
T1 fI,J)«TPILE
C01Cf,J5»C0*IR
V
-------
Table A-4
INPUT DATA TO CMPST
COMPOST MODEL - TILE D" 3-26-1900
2P81. 0. 4«0. 0. 4000. 29. 5. 12.
.25 20.83 2 0.8 3 4.5 21, 25. 17. .54
.7 0. .8665 .5220 .3 220 .5500 3.6 10.97 3
3. .25 -6.14 .3467 .45 .0651 3.7 .2
.3 9300. 0. 1.25
10 0000000 10 00
-------
Table A-5
PRINTED OUTPUT FROM CMPST
COMPOST MOorL - *PIl.E. 0"
3-26-1980
NT
2881
OT
0.2500
RH
o.'ooo
CVE
3.0000
TT
OX
20.8)00
wrNn
o.oooo
COMTN
0.2500
l.p
480
nY
20.8100
wo
0.8665
pntnw
•6.1400
JPRNT
TSOIL
4.5000
rso
0.5220
G
0.3467
tTUPN
4000
TAIR
21 .0000
FVO
0.3220
XAM
0.4500
npr
21
TMIX
25.0000
TBO
0.5S00
H80IL
0.0651
NTB
TWET
17.0000
TC
3,6000
EMAX
3.7000
NVB
12
wrp
0.5400
BpRED
10.9730
chin
0.2000
FSPK
O.IOOO
HCOMB
<1300.0000
flOLAR
0.0000
HAIRO
1 .2500
T1
DEC C
1
T2
C01
C02
dec c co'/rnaiR co2/coair
0 0 0
V
V/VAIP
0
p
mbar
0
ux
FT/MTN
0
UY
Ft/HIN
0
H
GM/CC
0
rs
flS/H
10
rv
VA8/H
o
FB
VB8/H
0
COAIR
0,0002786
AREA WPILE HFUEL PDK
44039.7227 20145.6855 33808.4102 40810.6445
XBLKS
113.0000
Ol
ro
UX
ROW NUMBER
COLUMN NUMBER
I
«J»2
3
4
5
6
7
8
9
10
11
12
1* 14 15
16
13
.0.0044
-0.0182
-0,04"4
-0,0797
12
-0.0114
.0.0365
-0.06°2
-0,1101
•0.1280
11
-0.0195
-0.0472
•0,OgOp
"0,1151
-0,1460
•0,1590
10
-0.01?9
-0.0562
-0.0916
-0*1237
-0,1507
-0,1720
-0.1798
9
.0.0230
-0.0670
-0.105?
-0,1373
-0,1613
-0,1778
•0,1875
.0.1892
8
-0.0292
.0.0832
-0.12*9
-0.1586
-0,1792
•0.1904
•0.1939
.0,1909
-0.1864
7
-0.0397
.0.1096
-0,1601
-0,1911
-0.2066
-0.2107
•0,2068
.0.1968
-0.1819
-0,1721
6
-0.0599
.0.1553
-0.9198
-0,2392
-0.2452
-0,2390
-0,2257
.0,2078
-0.1866
•0.1623
• 0-, 1407
•0 j1191
5
-0.1044
.0.2390
-0.29*6
-0,3077
-0.2961
-0,2746
•0.2492
-0,2222
-0.1943
-0,1653
-0,1350
4
-0.2233
-0.3997
-0,«267
•0,3990
-0,3568
•0.3140
-0,2742
-0,2375
•0.2030
-0,1696
-0,1366
.0,1032 -0,0863
3
-0.6124
.0.7096
•9.6H 7
-0.5048
-0.4182
-0.3504
•0,2961
-0.2506'
•0.2106
-0.173?
-0,1384
-0,1038 -0,0693 -0,0520
2
-2.1290
.1.2148
-0."056
-0,5904
-0.4607
•0.3735
-0.3093
-0.2583
-0.2150
-0.1761
-o;i3««
-0'1043 .0,0694 -0,0347
•0,0174
1
0.0000
0.0000
0>000
0.0000
0.0000
0.0000
0,0000
0.0000
0.0000
0.0000
o.oooo
0.0000 0,0000 0.0000
0,0000
UY
I
J"2
3
4
5
6
7
8
9
10
11
13
•0.1449
-0.1)50
-0,0987
-0,0797
12
•0.1547
-0.1483
•O.120g
-0.1101
.0.1280
11
-0.1775
•0.17J4
-0.16?6
-0.1510
.0.1460
-0.1590
10
-0.2086
-0.2051
-0.19«2
-0.1854
.0.1768
-0.1720
-0.1798
9
-0.2465
-0.2424
-0.2316
-0,2175
-0.2038
-0.1933
-0.1875
-0.1892
8
-0.2926
-0.2864
-O.'703
-0.2491
-0.2278
-0,2098
-0.1972
-0.1909
-0,1864
7
-0.3510
-0.3405
-0.*1"1
-0.2809
-0.2484
-0.2210
-0.2008
-0.1879
-0.1819
-0.1721
6
-0.4J05
-0.4104
-0.1647
-0.3120
-0.2639
-0,2252
-0.1969
-0.1779
-0.1670
•0.1623
5
-0.5504
.0.5059
-0.42'9
-0 . 3 3(|4
-0.2699
-0.2191
-0.18"
-0.1601
-0.1457
-0.1300
4
-0.7594
.0.6405
.0.4798
-0,3406
-0.7583
-0.1976
-0,1582
-0.1331
-0.1178
-0.1091
3
.1.2060
-0.8169
-0,*0"»0
-0.3220
-0.2162
-0*. 1548
-0.1184
-0.0965
-0.0833
-0.0758
2
-2.4109
-0.9142
-0.40Q1
-0.2152
-0.1296
-Of0871
-0.0641
-0.0510
-0.0433
-0.0389
1
0.0000
0.0000
O.nono
O.OOOO
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
12
13
14
15
16
-0'1487
-0,1350 -0'. 1191
•0,1048 .0.1032 -0.0863
-0,0717 . 00 6 9 9 .0.0693 -0.0520
-0,0365 .0.0353 .0.0348 -0.0347 .0,0174
o.oooo o'.oooo o.oooo 0.0000 o.oooo
-------
Table A-5 (continued)
time
0.00 HOURS
0,00 DAYA
T1
I J"2
U 25.0000
>2 25.0000
H 25,0000
10 25,0000
<» 25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
4.5000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
29,0000
25.0000
25.0000
25.0000
4.5000
25.0000
25."000
25.OOOfl
25 Oono
29.n0°0
25.0000
2"J.O0O0
25.0000
25.O0O0
25.0000
2 50 0 0 o
2 50 o 0 o
4. 5000
to
25.0000
25.0000
25.0000
25,0000
25.0000
25.0000
29.0000
25.0000
25,0000
25,0000
25,0000
25,0000
4.5000
11
12
1)
14
15
16
25.0000
25.0000
25.0000
25,0000
25.0000
25.0000
25,0000
25,0000
25.0000
25.0000
25.0000
4.5000
25^0000
25,0000
25.0000
25,0000
25.0000
25.0000
35,0000
25,0000
25.0000
25.0000
4.5000
25.
25.
25.
25.
25.
25.
25.
25.
25.
4.
0000
0000 25
0000 25".
0000 25.
0000 25.
0000 25,
0000 25.
0000 25.
0000 25'
5000 4.
0000
0000 25.0000
0000 25.0000 25,0000
0000 25.0000 25.0000 25^0000
0000 25.0000 25^0000 25 0000 29,0000
0000 25.0000 25,0000 25,0000 25,0000 25.0000
0000 25.0000 25.0000 25,0000 25.0000 29.0000 25.0000
nnnn 25.0000 25,0000 25,0000 29^0000 25.0000 25.0000 29.0000
4.5000 4.5000 4.9000 4.5000 4.9000 4.5000 4.5000
0000
5000
ra
I
J"2
3
4
5
6
7
8
9
10
11
13
0.5220
0.5220
0.5220
0,5220
12
0.5220
0.5220
0.9220
0,5220
0.9220
11
0.5220
0.5220
0.5270
0.5220
0.5220
0/220
10
0.5220
0.5220
0.5220
0.5220
0.5220
0.5220
0.5220
9
0.9220
0.5220
0,"220
0,5220
0,5220
0,5220
0.9220
0'9220
0
0,9220
0,5220
0,5270
0,5220
0,5220
0,5220
0.9220
0,5220
0.5220
7
0.9220
0.5220
0,'2?0
0,5220
0.5220
0,9220
0.9220
0,5220
0.5220
0,5220
6
0.5220
0.5220
0.5220
0,9220
0,5220
0,9220
0.9220
0,5220
0.5220
0.5220
5
0.9220
0,5220
0,9270
0,9220
0.5220
0,5720
0,5220
0,9220
0.5220
0,5220
4
0.9220
0.5220
0 9j?o
0.9220
0,9220
0.5220
0,9220
0 9220
0.5220
0.9220
3
0.5220
0.5220
0,5220
0,9220
0.5220
0.5220
0.9220
0.5220
0.9220
0.5220
2
0.9220
0.5220
0/270
0,9220
0.9220
0/220
0.5220
0,9220
0.5220
0,9220
1
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Tt>ne
PSK
rv*
fba
0.00000
O.oOnoO
O.922O0
0.00000
0.00000
WflTUR
H22
WOIIT
aratf.
0.00000
o.ooooo
0.00000
.0.00000
0.00000
HST»P
n»srr>
H22
HOOT
HSTOR
0.00000
0.0^000
0.00000
0.00000
0.00000
13
is
14
15
16
o'saao
0,5220
0,5220
0,5220
0,9220
0.0000
OHUP
0,00000
.T»V0
OtOOOOO
HOFr
0,00000
0*,S220
0,5220
0.5220
0,9220
0.0000
0.9220
0.5220
0,5220
0,0000
OHDHN
0.00000
hmin
0.00000
fLOST/fPlLR
0.00000
0.9220
0.5220 0.5220
0.0000 0.0000
OVUP
0.00000
SHHXN
0,00000
HLOST/HUflED
0,00000
TIME ¦ 120.00 HOUPS
5.00 days
T1
I J»2
13 23.1334
12 33.0883
H 54.2017
10 63.6475
9 68.2401
8 70.0062
72.33*3
73.1892
'3.49oO
73.3048
72.8329
72.2801
4.5000
23.0130
3 2 , 0 ? ' 7
49.8196
f 1.10)6
66,2144
60.9442
70.4747
71,2*08
71.5481
71.5888
71.7664
71.9488
4.5000
22.56q3
29/647
19,200?
51.500b
60.4941
64.15*0
66.7176
67,4si<»
68.1419
69.1110
70.6890
71 .•>70)
4'.50Ofl
5
2"'.85ll
26,0596
30,9322
30.2465
48,1641
55,2555
59.4280
62,3282
64.8589
6 7,4113
70.1104
71,5229
4.5000
10
11
12
11
14
15
16
20,
24.
20.8591
25.5375
29.6099
34.0642 28.
40.5289 31.
48.4567 37.
55.3426 46.
61.0599 56.
65.7814 64.
69.62*2 68.
71.1688 7o.
4.5000 4.
6692
8158 20.
3249 24.
8457 27.
1444 11.
3159 37.
6914 51.
0099 61.
8700 67.
4220 69.
5000 4
5291
3828 20.
7fl51 24.
4133 27.
98)7 32.
0564 43.
5802 57,
5228 65.
0843 66.
5000 4.
4674
2912 20.4049
9253 24.5260 20.5796
442® 28.7527 25,0887 ?0^7456
0158 15.4347 30.2038 25.9fl90 20.9596
6207 50.5586 39,2061 3l"48l8 26.7057 21.1584
1393 60.8006 52.1840 3B.2480 31.3169 26.8637 21.1650
7584 62.4496 53.3240 37*6324 31.3649 28.1495 24.6146 20,4607
5000 4.5000 4.5000 4.5oOO 4.5000 4.9000 4,5000 4.5000
-------
Table A-5 (continued)
Fs T
J»7
1
4
5
6
7
8
9
10
11
12 13
14 15
16
13
0.5791
0.5793
0.579b
0,5546
>7
0.5201
0.5280
0.5277
0.5283
0.5612
11
0.5116
0.5316
0.57*6
0.5286
0.5297
0.5644
10
0,549(1
0.5*77
0,«3"5
0,5296
0.5295
0.5102
0.5664
9
0.5512
0.5533
0.5509
0,5358
0.5296
0.5298
0.5105
0,5673
8
0.5403
0.5524
0,5561
0.5466
0.5320
0.5296
0.5 300
0.5305
0.5671
7
0.5448
0.5503
0.5574
0.5551
0.5393
0.5106
0.5296
0.5299
0.5304
0.5657
6
0.5423
0.5487
0.557 4
0,5600
0.5508
0.5174
0,5309
0.5295
0.5297
0,5 301
0*5634
5
0.5412
0.5483
0.55^0
0.5614
0.5595
0.5517
0.5411
0,5327
0.5294
0,5292
0,5295 0,5604
4
0.5418
0.5*86
0.5553
0.55 85
0.5590
0.5574
0.5536
0.5463
0.5355
0.5289
0,52®1 0 5283
0.5567
3
0.5441
0,5474
O.'SOO.
0,550l
0.5497
0.5494
0.5491
0.5476
0.5423
015319
0,5265 0.5262
0.5264 0,5520
2
0.5720
0.5322
0.5312
0,5329
0.5325
0.5330
0.5338
0,5338
0,5312
0,5743
0,5319 0.5223
0.5226 0.5228
0.5439
1
0.0000
0.0000
0.0000
O.OOOO
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0000 0.0000
0.0000
tpiu
"A
• FS*
FVA
FBA
QHUP
ohdmn
OVUP
47,66945
0.83)00
0,53950
0.31597
0.53734
-139290.61719 73070.13281
•91,27114
WSTAR
WTO'T
U22
HOUT
ARATE
TaVO
HMIN
8HMIN
1481.75452
1482.59583
-
1575.02563
-93.27H4
-2.72543
71.57077
0.12171
43.00000
HSTRR
H"S»T>
H22
HOUT
H3T0R
HorF NLOST/NPUe HLOST/HUSeD
1637,69470
1632.1'oi'
-
1172,22510
-56,22049
521.69006
0.00000
0.07359
13.4161S
TIME a 240.00 HOURS
10.00 DAYS
T1
CTl
-P>
I
J"3
3
4
13
25.7327
75.60
9
«4;754J
12
56.0941
55.64
5
51.7970
11
64.9705
64.13
8
60.1377
lo
69.1696
68.0202
64,7561
9
71.6060
70.22
9
66.*513
8
73.1278
71.56
2
67,8053
7
74.0562
72.31
3
69.6375
6
74,5214
72.62
4
69,1534
5
74.5586
73.59
1
69.'9'7
4
74,1834
72,43
4
70,I161
3
73.6756
72.58
3
7I.-M72
2
73.2322
72.9"
9
72.9987
1
4.5000
4.5000
4.SOOO
21^5925
3J.9*22
49.7168
58.4122
60,0141
63-2692
#1.9056
«s;3Jio
66.988*
68"9269
71*554 1
73.2561
4.5000
10
11
13
1)
14
IS
16
21.7990
30.9462
40.66^8
49.4175
54.6190
59.3447
*1,5375
64.6813
69.0982
71.6501
73.4295
4.5000
.2748
,7668
.9770
,7892
• 213"
^6215
,77*8
4788
.6833
.4235
.5000
20,8984
26.1576 20,7532
31,8943 25,9151 20.8082
4l.52<>6 32.6997 26.9057 2|'.°'M
53,0007 46,6325 37,5616 j9;7432 3l'«566
60.8123 58,3366 54.6026 47.8145 14,19*8 JJ.6992
66.7679 65,7275 64.0805 61,2643 55,8o58 43,1169 23.9368
71,4951 71 0056 70.1342 68 7108 66,*882 61,5324 49.4204 23.4242
73.2290 72.8466 72.2584 71.3960 7o,0530 67,5925 61.4899 33.3*48 21,1178
4.5000 4,5000 4.5000 4'.S000 4.5q00 4,5000 4.5000 4,5000 4,5000
rs
1
13
12
11
10
9
8
7
6
5
4
3
2
1
J»2
0.5378
0.5771
0.6096
0.6065
0.5961
0,5857
0.5778
0.5730
0.5715
0,5740
0.5807
0.5720
O.OOOO
TPTI1E
56.08520
WSTAR
4498.64649
HSTaP
4014.4431?
3
0.5379
0.5 709
0.6081
0.6120
0.6056
0.5978
0.5920
0.5893
0.5895
0,59l3
0.5900
0.5*89
0.0000
4
0 , * 18 7
0.55»7
0 . * 9 5
0.6174
0,*212
0,*194
0,6166
0,61*8
0.«1>9
0,60"6
0.5967
0.5 4 0 7
o.nooo
»A
0.76007
mo'T
«*89.6'207
H'laFn
401*„o0o«9
0,
0.
S'
Of
0.
0.
0.
I'
6.
0,
0.
5
5914
5380
5613
5990
6204
6312
6351
6'*9
6299
6181
5968
5*78
0000
10
11
12
13
14
15
16
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
6070
5*11
5*93
5756
6061
6284
6396
6379 0.
6223 0
5954 0
5*74 0
0,
0.
0.
0.
0.
0.
0000 0.
6136
5407
5437
5565
5899
6250
6372
6738
5949
5487
0000
rs#
0.59217
U22
-4640.61719
H22
-3319.53735
0.6172
0.5401
0.5423
0.5533
0.5957
0.6291
0.6237
0.5960
0.5514
0.0000
rv*
0.30691
HOOT
¦151.97047
HOUT
0.11602
0,6199
0 .5400
0.5428
0.56*"
0.6135
0,6215
0.5980
0,5552
0.0000
0.6194
0.5404
0.6160
0.5459
0.5*13
O'6131
0.599*
0.5590
0.5418 0.6065
0.6150
0.6006
0,5751 0,5417
0.5990
0.5992
0.596*
0 5864 0.5657
0.5339 0.5861
0.5589
0.5609
0,5597 0.5501
0.5316 0,5226
0,5675
0.0000
0.0000
0.0000 0.0000
0.0000 0.0000
0,0000
FBA
OHUP
OHDWN
GVUP
0.51736
-199706.92912 199822.8*375
151 ,97047
URATE
TAVG
HHXN
8HMIN
-2.35510
73.59202
0.11930
23.00000
hstdr
HnFr wfjnST/wpiLE "lost/hosed
674.78073
0,00000
0,22706
12.42955
-------
Table A-5 (continued)
TIME a 160.no M0UR8
15.On n*K9
T1
I J"2
U 24.1052
1 2 <1 .5714
If * 4 . 01 <>4
10 ft 1 .4J64
• 65.8(161
68.6128
70.3008
71. 1 p 10
71.39??
70.9933
70.3696
70.3039
4.5000
91.9671
40.5769
5 2.4626
59.5699
63.8235
66.4039
67.19(9
6 8.5869
6 8 . 7 0 B 6
68.6152
69.0221
70.2452
4.5000
21.3654
36.'760
47.5414
54.276J
58.<805
61.1217
6?.7437
63.7219
64.4839
65.&709
67.9708
70.«l'3
4.50f>0
21.2877
30.3755
39.2535
46.0232
50.7618
54,0899
56,5268
58.5574
60.7745
63.8423
67.9525
71,2604
4.5000
10
11
12
13
14
15
16
21 .5378
29.4076 21
36.3887 27
43.2319 33
46.8267 39
50.5B84 45
54.01)80 50
58.0236 55
62.9024 62
68.3008 68
71.7279 71
4.5000 4
.2526
.7080
.24 20
.5238
,112 3
.2720
,8621
.2667
.5434
.9253
'.5000
21 .0048
26.6348 20.8964
32.1438 26.4715 20.9470
39, 167B 32.7326 27.2931 21.1764
46.4000 41.7798 35.0029 29,3225 2l'63<4
53,6861 50.9813 47.2309 41.6862 32,9668 22.6511
61.4791 60.2630 58.3875 55,48j2 50,7o46 41,9831 24.2837
68.4842 68,0631 67.2472 65.9473 63,8836 60,2333 52.1926 25,8099
71.8755 71 .6145 71.1624 7o'.5050 69 5478 68.0048 65.0536 57,6865 23,3532
4.5000 4.5000 4.5O00 4.5000 4.5oOO 4,5000 4.5000 4,5000 4,5000
FS
at
CJl
1
13
12
H
10
9
8
7
6
5
4
3
2
1
J"2
0.5470
0.6358
0.676?
0.6630
0.6427
0.6254
0.6130
O.6O57
0.6037
0.6084
O.6195
0.5220
0.0000
0.5478
0,6?83
0.6760
0.6712
0.6570
0.6441
0.6354
0.6318
0.6328
0.6365
0,6352
0.5672
0,0000
TPILF
52,17630
W8TAR
7018,33154
HSTrP
5864,56104
4
0.5488
0.5991
0.6679
0,«838
0,68'8
0.6777
0,6731
0.670#
0,66*8
0.6633
0.64^1
0.*659
O.nono
0,6338
0,55 31
0,6150
0,6677
0,6909
0.6996
0,7017
0.6999
0,6930
0,6763
0.6436
0.5614
O.OOOO
0.7004®
WLOfT
7019,?7 J46
5910.694 34
0.
0.
0,
0.
0.
0,
0.
0,
0,
0.
0.
0.
6617
5564
5841
6361
6764
6998
7092
7042
6812
6398
5592
0000
0.
0'.
0.
°r
0.
0,
0,
0.
0.
0.
6717
5539
5636
6007
6574
697?
7055
6827
6375
5597
0000
FSA
0,62512
H22
-7|77.82373
H22
-5lSB.19824
0,6768
0,5515
0,5587
0.5942
0,6659
0,6998
0,6815
0.6378
0,5624
0,0000
0,6790
0.551 1
0,5604
0.6193
0.6864
0,6836
0,6403
0.5666
0,0000
FVA
0,29966
WOUT
-159,49232
HOUT
172,62325
10
0.6785
0.5529
0.5741
0.6605
0,6810
0,6433
0.5713
0,0000
11
12
13
14
15
16
0,6757
0.5567
0,6138
0,6719
0,6444
0.5754
0,0000
O'6710
0,5614
0,6472
0^6412
0.5776
o'.oooo
0',6641
0.5866
0,6306
0,5772
0.0000
FB A
0,50051
APATC
-2,03301
HSTOR
553,73969
OHUP
-167681,68750
tavq
69,46680
HOFF
0.00000
0,6493
0.5905
0.5718
0,0000
0,6264
0.5403
0,0000
QHDWN
340104,93750
HMIN
0,11694
NL08T/NPILE
0.34843
0.5927
0,0000
QVUP
-159,49232
SHMIN
26,00000
NL0ST/HU8ED
12.18588
TImE ¦ 480.00 HOURS
20,00 DAYS
T1
I
J*2
)
4
13
22,8851
22,8259
22
.5259
12
31.2347
30.9409
29
."921
11
37.5098
16.7683
34
."5*2
10
43.5l?j
41.8558
38
.7944
9
49.8520
47.H70
42
.'738
8
55.2416
51.6854
45
.4801
7
59,0460
54.9617
48
.0196
6
61 .3036
56.8699
49
."561
5
62.1915
57.6"»49
51
,*61J
4
61,9450
50.1056
54
"0106
3
61.4939
59.7166
58
.9769
2
62.8175
63.6357
65
.76*1
1
4.5000
4.5000
4
.50Ofl
10
1 1
21,0132
27,1617
31,6999
35.2615
38^1886
40.6420
42.7215
44.782?
47,5480
52.4066
59.9245
66.9316
1.5000
12
13
14
15
16
21.
26.
31.
34.
37.
39.
41.
45.
52.
61 .
68.
4.
1804
9465 21.
1880 26.
4315 30,
0890 33.
4429 36.
9291 39.
5433 44.
1050 51.
1271 61.
0208 68.
5000 4.
0412
3670 20,9239
5203 25,9995 20,8742
8357 30.2320 25.9732 20.9064
7317 33.9275 30,5832 26.3817 21.0398
7992 37.6463 35,0998 11.8460 27 4326 2l'3227
1430 4?.6659 40.7789 38.2158 34,6759 29,6l70 21.8417
9420 51.3661 50.1403 40.0939 44.9892 40,3966 33,5«19 22.7942
8886 62.0331 61.5445 6O.4OI9 58.4822 55.4091 5O.252I 4O.9I8B 23.0365
5349 68.5910 68.2738 67.6136 66.5669 64'9442 62.2162 56.9302 44.0605 22.1592
5000 4.5000 4.5000 4.5000 4.5000 4.5000 4.5000 4.5000 4.5000 4.5000
-------
1abIe A-b (continueu)
fs r
13
»2
n
io
9
n
7
6
5
4
3
2
1
J = 7
0.5371
0.6522
0.7099
0.71J2
0.7ot5
0.6944
0.6694
0.6575
O.6540
0.6607
0.6759
0.5720
0.0000
TPTLC
44.07999
WSTAP
9902.11291
HSTAR
7111 .01320
0.5571
0.6O?
0.7072
0.7192
0.7145
0.7054
0.6969
0.6929
0.6944
0.7001
0.6990
0.6010
o.ooon
4
.55*3
.6104
.69'0
.72<*5
.71O0
,71?,
.711*
.73?2
. 7 3 * 4
. 7 3 " 3
. 7 0 ® 6
,5q<6
.O0«0
0.6790
0,9612
0.6304
0^6926
0.7241
0,7396
0,7475
0.7515
0'7512
0,7 399
0.7023
,0,5942
0.0000
0.65954
HT.qSt
9903.57930
H"SJT>
7173.97676
0.7207
0.5664
0.5983
0.6575
0.7047
0.7345
0.7510
0.7554
0.7409
0.6943
0.5788
0.0000
0,7363
0.5639
0.5761
0,6192
0.6941
0.7324
0.7520
0,7399
0.6992
0.5774
0'onoo
FSA
0.66024
W22
-8962.27441
H22
-6423.52979
8
9
1 0
11
0.7445
0.5613 0
1.7491
0.5708 0,5610
0.7474
0.6129 0
.5731
0.5612
0.7432
0.6956 0
.6422
0.5995
0.5693
0.7425 0
'.7249
0.6930
0,6372
0.7389 0
.7373
0.7125
0,7194
0.6880 0
,69ol
0.6936
0.6962
0.5794 0
.9937
0.5994
0,3954
0.0000 0.0000
0.0000
0.0000
FVA
FBA
0.29469
0.48949
-15!
HOUT
arate
160.14142
-1 .90253
HOUT
hstor
319.78543
367,71796
12
13
14
15
16
O'7366
0,5750
0,6956
0,6981
o,6oll
0.0000
0.7275
0,6069
0,6932
0,6062
0.0000
0.7079
0.6234
O.6O7I
0.0000
0,6743
0.5652
0,0000
0.6206
0.0000
QHUP
>39,37500
TAVG
57,14380
ho rr
0.00000
OHDHN
479424.8,230
hhin
0,11462
MLOST/MPILE
0.43699
OVUP
-160.14142
SHMIN
95,00000
WLOST/HUSED
12.02914
TIME v 600.00 HOURS
25.0" DAYS
T1
cr>
cr>
I J"?
>3 22.7715
12 30.6132
H 35.9579
10 39.9,77
9 43.3341
8 46.7053
7 49.6730
51.8965
53.1267
9 3.47po
53.9625
56.7764
4.5000
22.7252
10.4297
35.5490
39.2693
42,2139
44.9610
47.2917
49.9944
50.0706
51 .OO73
53.2890
59.4710
4.5OOO
22,^590
29.«0«5
34,204,
37.571,
40,'B<2
42.?9B9
44.0097
45.439,
46."4«5
49.0307
93,7o7l
60.94*4
4.5000
5
21,0134
27.0986
31^5019
34.8597
37^3199
19.6716
41,4798
41 1500
45,1145
*8,4414
54,9574
62,9924
4.5000
10
11
12
1)
14
1?
16
21.2005
26.9943
31.2<>23
34.3740
36.9311
39.1305
41.2703
43,8987
4».20Sl
56.0148
64.1899
4.9000
21,0912
26.5129 20.9768
30,6991 26.1990 20*9311
33,9910 30.4618 26,1607 20.9561
36,7391 34.0378 JO,7077 26.4719 21,0607
39.4150 37.3303 34 7975 31.5638 27,2116 2112579
42,6740 41.1735 39,2212 36.6526 33,2230 28,4986 21,9329
47.7'e' 46,p2ee 45.3175 43.1514 40.092b 35.9442 29.9904 21.7610
56^4495 56.1196 54,9394 52.8010 49,4458 44*5246 38,0181 30.2®27 21.6086
64,5937 64.3197 63.3554 61.9599 59,4943 93,2164 44.4118 33.9017 26.33*0 20.9908
4.3000 4.5000 4.5000 4.5n°0 4.5000 4.5000 4.5000 4.5000 4.5OOO 4.5000
21.7616
F8
I
J"2
3
4
9
6
7
9
9
10
11
12
13
14
19
13
0.5662
0.9663
0,5677
0,7296
12
O.66I7
0.6922
0.6177
0.9674
0.7882
11
0.7233
0.7202
0,7017
0,6402
0.5744
0,81 13
10
0.7302
0.7143
0.7333
0.7060
0.6083
0.5726
0.8242
9
0.7279
0.7373
0.74*1
0,7403
0.6706
0,5962
0.5701
0,9299
a
0.7226
0.7379
0.7313
0,7992
0.7206
0.631 J
0.5909
0.5699
0.9289
7
0.7152
0.7374
0.73*9
0.7694
0.75^9
0.6996
0.6251
0.5935
0.5724
0^9223
6
0.7o94
0.7 39 3
0,764o
0.7751
0.7722
0.7518
0.7127
0.6565
0.6010
0.9779
o",®1 21
5
0.706?
0.7430
0.7704
0.7800
0.7913
0.7766
0.7659
0.7465
0.7119
0.6519
0 5953
0,7999
4
0.7139
0.7920
0,77^3
0,7793
0.7782
0,776?
0.7739
0.7 702
0.7623
0,7451
0,709ft
0.6189
0.7722
3
0.7302
0.7960
0.7611
0.7519
0.7427
0.7169
0.7131
0.7363
0.7187
0.7392
0.7332
0.7109
0.6338
0.7272
2
0.9220
0.6429
0,*2*4
0,6118
0 . 60 36
0,6012
0 . 60 31
0,6084
0.6160
0^25,
0^6339
0",6J73
0.6299
0.9690
1
0.0000
0.0000
0.°000
0.0000
0.0000
0.0000
n.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
16
TPlLr
40.10994
wStar
9974.15117
HSTAR
7999.61769
"a.
0.6*091
KTO'T
9976 . 0*44 5
W'SfC
9067.31.4iMv
FSa
0.68570
W22
-10134.38770
H22
-7291.70557
FVA
0.29113
WOUT
-160.23677
HOUT
429.07631
FUR
0.47962
; ARATp
-1.65202
HSTOR
. 292.83569
OhUP
¦169967.46875
T*VG
49.189,4
hoff
0,00000
QHDWN
594943.68750
HHIN
0.11239
WLOST/WPIlE
0,49520
0.69J7
0.0000
OVUP
-160.23677
SHMTN
73,00000
"LOST/HUSFD
11,91795
-------
Table A-5 (continued)
TIME a 720.00 HOURS
30.00 OAYS
T1
I J"?
13 72.7491
12 30.7562
11 36.1553
10 40.0991
9 42."»¦>«?
0 45.5524
47.7300
49.3701
SO.3147
*0.6941
SI .oon
52.9175
4.5000
22.7043
30.5772
35.7703
39.4760
42.2427
44.4235
46.2399
47 .5(11 4
40.4590
49.1305
5«>.4003
54.0763
4.5000
22.4
29.7
34.4
37,"
40.4
42.4
44.0
45.3
46.4
47.B
50.50?
55.00"
4.90f>0
5
1.0202
7P 24 I 7 21,
1,7629 27,
5,2067 31,
7.9154 34,
0.0077 37,
1.8722 39,
3^4264 4»,
3,0026 43,
7,»°l4 46,
0.820'' 50,
7'. 105* 57,
4.5000 4,
10
2392
1972 21.1294
5266 26.7100 21.0290
7«3l 3l.O«07 26.4249 20.9032
3077 34.4000 30.7976 26.3715 21.0016
5761 J7.14P0 34.3741 30.9500 26.6064
5657 39.6313 37.4410 34.0059 31.4893
6602 42,2200 40.5010 30,3624 35.6670
3036 45,4U7 44.0190 42,10s" 39.654?
0150 50.1106 40.6225 46.2406 43.2535
4540 56'.6609 54.5030 50,9749 45.0203
5000 4.5000 4.5000 4.5000 4.5000
11
12
13
14
15
16
21 .0035
27 1018 2l',2l56
32.2339 27,7243 21.3454
36,5479 32,7259 27,900* 21,1702
39.7515 35.9248 J1.776J a6.96i7 2l.l«60
39,9377 34,9042 31.0358 27,33*6 23,6697 20,1702
4.5000 4.5O00 4.5000 4.5000 4,5000 4,5000
FS I
J"2
3
4
5
6
7
0
9
13
0.5757
0.5750
0.5775
O',7077
12
0.6700
0.6606
0.6?4#
0,5733
0.0684
11
0.7356
0.7322
0 . 7 1 4 8
0,6496
0.5023
0,9023
10
0.7439
0,7403
0,749J
0,7189
0.6105
0.5012
0.9213
9
0,7435
0.7526
0.76M
0,7557
0.6835
0.5961
0.5790
0.9290
0
0,7435
0*7565
0.7716
0.7755
0-7362
0.6434
0.5910
0,5780
7
0.7414
0.7601
0.7700
0.7872
0.7707
0.7140
0.6372
0.5938
6
0.7307
0.7645
0.7051
0,7956
0.7921
0.7703
0.7291
0.6701
5
0.7307
0.7715
0 . 7 9 4 J
0,8031
0.8041
0.7907
0.7069
0.7657
4
0.7479
0.7035
0,8o<0
0,8070
0.8O55
0,0031
0.7998
0,7946
3
0.7649
0.7935
0.7975
0.788§
0.7006
0.7752
0.7727
0.7716
2
0.5220
0.6703
0 . ® 5 ? 7
0,6395
0.6326
0,6317
0.6353
0.6417
1
0.0000
0.0000
o.nooo
0.0000
0.0000
0.0000
0.0000
0.0000
TPILE
*A
F»A
FVA
37,07100
0.61013
0.70630
0,28836
W8TAR
WT,0«T
W22
WOUT
10054,94141
10857.35645
-11010,41797
155,47701
H8T*B
H"sro
H22
HOUT
8689,11914 1
8756,81641
7954,85937
504,97405
10
0,9282
0.5013
0.6119
0.7284
0.7046
0.7696
0.6479
0.0000
FBA
0.47257
APATE
-1 ,53946
HSTOP
229,28505
11
12
1)
14
15
16
0.9181
0.5069
0,6647
0,7642
0.7641
0,6310
0.0000
O"9024
0,5942
0,7j00
0,7511
0,6494
0.0000
0,8817
0.6271
0,7225
0,6432
0.0000
QHUP
•189448,54687
T#VG
46,64561
Horr
0,00000
0,8436
0.6416
0,6277
0.0000
0,7826
0.5693
0.0000
QHDWN
694423,37500
HM IN
0,11013
hlost/hpjle
0.51894
0,6063
0,0000
OVUP
-155,47701
8HMIN
86,00000
HLOST/HtlSEO
11,84087
------- |