vvEPA
United States      Industrial Environmental Research EPA-600/7-80-116
Environmental Protection  Laboratory         May 1980
Agency        Research Triangle Park NC 27711

Solubilities of Acid Gases
and Nitrogen in Methanol

Interagency
Energy/Environment
R&D Program Report

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                                EPA-600/7-80-116

                                          May 1980
Solubilities of  Acid Gases
and Nitrogen in  Methanol
                    by

           J.K. Ferrell, R.W. Rousseau,
               and J.N. Matange

           North Carolina State University
         Department of Chemical Engineering
           Raleigh, North Carolina 27607
              Grant No. R804811
           Program Element No. INE825
        EPA Project Officer: Robert A. McAllister

      Industrial Environmental Research Laboratory
    Office of Environmental Engineering and Technology
          Research Triangle Park, NC 27711
                 Prepared for

      U.S. ENVIRONMENTAL PROTECTION AGENCY
         Office of Research and Development
             Washington, DC 20460

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                               CONTENTS

FIGURES
TABLES
INTRODUCTION	-	1
STATEMENT OF OBJECTIVES	4
DEVELOPMENT OF THE THERMODYNAMIC MODEL	5
     FUNDAMENTALS	-	5
     THERMODYNAMIC CORRELATIONS	—13
          Vapor Fugacity Coefficients	13
          Activity Coefficients	18
          Reference Fugacities	22
     STRUCTURE OF THERMODYNAMIC MODEL	27
          Model BUBLT—		28
          Model DEWT	32
     EVALUATION OF MARGULES PARAMETERS	33
          Summary	56
EXPERIMENTAL EQUIPMENT AND PROCEDURE	57
     REAGENTS	57
     ANALYSIS	59
     CALIBRATIONS	59
     TEST DATA:  METHANOL-C02 MIXTURES	60
     MULTICOMPONENT PROCEDURE	61
MULTICOMPONENT MEASUREMENTS AND PREDICTIONS	61
CONCLUSIONS	73
LITERATURE CITED	75

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                                   FIGURES


Number                                                                       Page


    1.  Flow chart for BUBLT	-	30

    2.  Flow chart for DEWT	31

    3.  Comparison of equilibrium experimental and predicted
        pressures for methanol-carbon dioxide mixtures	40

    4.  Comparison of equilibrium experimental and predicted
        pressures for methanol-nitrogen mixtures	43

    5.  Comparison of equilibrium experimental and predicted
        pressures for methanol-hydrogen sulfide mixtures	46

    6.  Comparison of equilibrium experimental and predicted
        pressures for carbon dioxide-nitrogen mixtures	49

    7.  Comparison of equilibrium experimental and predicted
        pressures for carbon dioxide-hydrogen sulfide mixtures	52

    8.  Comparison of equilibrium experimental and predicted
        pressures for nitrogen-hydrogen sulfide mixtures	54

    9.  Experimental apparatus	58

   10.  Comparison of experimentally determined equilibrium
        pressures with those of  Katayama et al (1975) for
        methanol-C02 mixtures at 298.15 K			62

   11.  Comparison of predicted and measured equilibrium
        pressures for four-component mixtures at 258.15 K	69

   12.  Comparison of predicted and measured equilibrium
        pressures for four-component mixtures at 273.15 K	70

   13.  Comparison of predicted and measured equilibrium
        vapor compositions for four-component mixtures at
        258.15 K	71

   14.  Comparison of predicted and measured equilibrium
        vapor compositions for four-component mixtures at
        273.15 K	72

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                                   TABLES


Number                                                                    Page

   1.  Binary interaction constants for Soave modification of
       Redlich-Kwong equations  of state	17

   2.  Critical  constants and Pitzer accentric factors	18

   3.  Constants used in Equation 21d for  calculating
       methanol  liquid molar volume	24

   4.  Comparisons of experimental  vapor-liquid equilibrium
       data with model correlations for methanol  (1)  -  car-
       bon dioxide (2) mixtures	38,  39

   5.  Comparisons of interpolated experimental vapor-
       liquid equilibrium data  with mode]  correlations
       for methanol (1) - nitrogen (2) mixtures-	42

   6.  Comparisons of experimental  vapor-liquid equilibrium
       data with model correlations for methanol  (1)  -
       hydrogen sulfide (2) mixtures	44,  45

   7.  Comparisons of interpolated experimental vapor-
       liquid equilibrium data  with model  correlations
       for carbon dioxide (1) - nitrogen (2) mixtures	48

   8.  Comparisons of experimental  vapor-liquid equilibrium
       data with model correlations for carbon dioxide (1) -
       hydrogen sulfide (2) mixtures	50,  51

   9.  Comparisons of interpolated experimental vapor-liquid
       equilibrium data with model correlations for nitrogen
       (1) - hydrogen sulfide (2) mixtures	53

  10.  Margules parameters from parameter optimization
       procedure GMAR	--55

  11.  Comparisons of experimental vapor-liquid equilibrium
       data with those of Katayama et al (1975) for methanol-
       C02 mixtures at 298.15 K	63

  12.  Experimental vapor-liquid equilibrium data for methanol-
       carbon dioxide-nitrogen-hydrogen sulfide mixtures at
       258.15 K-	64

  13.  Experimental vapor-liquid equilibrium data for methanol-
       carbon dioxide-nitrogen-hydroge'n sulfide mixtures at
       273.15 K	65

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                                   TABLES
                                   (cont.)

Number                                                                   Page


  14.  Comparison of model  predictions with experimental
       pressure and vapor composition for methanol-carbon
       dioxide-nitrogen-hydrogen sulfide mixtures at 258.15 K	67

  15.  Comparison of model  predictions with experimental
       pressure and vapor composition for methanol-carbon
       dioxide-nitrogen-hydrogen sulfide mixtures at 273.15 K	68

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                              INTRODUCTION

     Considerable attention has  been given recently to coal  gasifica-
tion in the hope that a substitute for natural  gas  and crude oil  can
be developed, thereby easing the prevailing energy  shortage.  For coal
gasification to be part of a solution to the energy shortage, prepara-
tion must be made to gasify literally millions  of tons of coal.
     Perhaps the most consistent feature of coal  is its inconsistency.
Its molecular structure is undefined; its composition and character-
istics can vary widely depending upon the geographic area, the coal
seam, and even the location within the same seam, from which it is
mined.  Thus when coal is gasified, the gas formed has a very complex
composition.  Along with the desired products,  H2, CO, hydrocarbons,
etc., there is a significant quantity of undesirables such as hLS,
C02, COS, benzene, phenol, etc.    In this environmentally con-
scious era, coal gasification would be acceptable only if the environ-
mental impact of coal gasification can be accurately assessed and
then properly handled.
     Recognizing this situation, the Environmental Protection Agency
in 1977 contracted for the design and construction of a coal gasifi-
cation-gas cleaning test facility at North Carolina State University,
to be operated by faculty and staff of the Department of Chemical
Engineering.  Construction was begun in January 1978 and the plant
was completed and turned over to the University in the summer of 1978.
     The principal components of the pilot plant are a continuous
fluidized bed gasifier, a cyclone separator and venturi scrubber for

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 removing  participates,  condensables, and water-soluble species  from
 the  raw synthesis gas,  and  absorption  and  stripping  towers and  a flash
 tank for  acid  gas removal and  solvent  regeneration.  The gasifier
 operates  at  pressures up to  100  psig (791  kPa), has  a capacity  of 50
 Ibs  coal/hr  (23  kg/hr), and  runs with  either steam-air or steam-02
 feed mixtures.   The acid gas removal system is modular in design, so
 that alternative absorption  processes  may  be evaluated.  Associated
 with the  plant are facilities  for direct digital control of all process
 systems and  for  on-line data acquisition,  logging, and graphical dis-
 play.   Facilities for sampling and exhaustive chemical analysis of all
 solid,  liquid, and gaseous feed and effluent streams are also available.
      The  overall objectives of the project are to characterize  complete-
 ly the gaseous and condensed phase emissions from the gasification-
 gas  cleaning process and to determine  how emission rates of various
 pollutants and methanation catalyst poisons depend on adjustable pro-
 cess  parameters.
      The  task of this study was to concentrate on the gas cleaning
 portion of the project.  Broadly speaking, gas cleanup systems  can
 be divided into  three groups based on  the absorbents used:  amine
 based systems, hot carbonate systems, and physical solvent systems.
      In amine based systems the most common solvents are monoethanol-
 amine (MEA) and diethanolamine (DEA).  Acid gases, H2$ and C02> react
with  the amine solution to form chemical complexes; the reactions may
 be reversed by applying heat to the solution and stripping off the
 H2S and CO^ in a regeneration tower.  Amine systems are falling into
 disfavor as they are both non-selective and suffer high vaporization

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losses.  In addition,  MEA forms stable compounds  with COS  and  C$2
which cannot be regenerated by heat.   Diglycolamine is increasingly
being employed in gas  cleanup systems due to its  lower volatility.
Another amine that is  finding use is  diisopropanol  amine.
     In hot carbonate  processes, acid gases are absorbed in a  counter-
current contactor by a carbonate solution.  The gases are  recovered
from the rich solution by flashing and steam-stripping in  a low pres-
sure regenerator.  Modern carbonate systems—such as the Benfield
Process, the Catacarb  Process, and the Giemmarco-Vetrocoke Process-
have found many applications in today's gas, chemical and  refinery
industries.  These systems employ a 20 to 30 percent water solution
of potassium carbonate, operate at between 220° and 300°F, and uti-
lize various additives to increase the rate of gas absorption  as well
as to catalyze the reactions.
     The third general method for removing acid-gas from a raw-gas
stream is by physical  absorption in an organic solvent without chemical
reaction.  The solvent can be regenerated by heat, pressure reduction,
or gas stripping, producing a concentrated stream of the absorbed  gas.
H2S and CO,, as well as minor components in the gas stream—including
COS, CS2 and mercaptans—are more soluble in many organic solvents
than fuel-gas species, especially at elevated pressure.  In addition,
some of the physical solvents are highly selective for H2S over C02.
This aspect is important in applications where a H?S rich stream has to
be generated to be sent to a Claus Plant for sulfur recovery.
     Refrigerated methanol is the solvent being used currently in  the
NCSU facility.  Methanol is also the solvent used in Lurgi's proprie-

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 tary  Rectisol  process.  After  a careful search of the literature, it
 was concluded  that  the data and correlations available to the techni-
 cal public  are not  sufficient  to analyze this system properly.  Thus
 the objective  of this study was to generate part of the data and cor-
 relations necessary for analysis of methanol-based acid gas removal
 systems.  The  particular emphasis of this study was the multicomponent
 vapor-liquid equilibrium behavior of selected constituents of crude
 coal  gas.

                        STATEMENT OF OBJECTIVES

      The purpose of this study was to develop a thennodynamic model
 for the system methanol-carbon dioxide-nitrogen-hydrogen sulfide.
 To check the validity of the model  predictions it was necessary to
have experimental vapor-liquid equilibrium data for the four compo-
nent system.  As these data could not be found in the literature,
another objective of this research was to develop an experimental
apparatus to obtain multicomponent vapor-liquid equilibrium data for
mixtures of these components.   The objective of the experimental pro-
gram was to obtain the multicomponent vapor-liquid equilibrium data
with the system pressure in the range of five to forty atmospheres
and system temperature in the range of 0°C to -20°C.

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                DEVELOPMENT OF THE THERMODYNAMIC MODEL

FUNDAMENTALS
     The main objective of this research was development of a  thermo-
dynamic model for prediction of vapor-liquid equilibria for a  multi-
component system containing the principal components in an acid gas
removal system.   The multicomponent system chosen for study consisted
of mixtures of methanol, carbon dioxide, nitrogen and hydrogen sul-
fide.  The structure of the thermodynamic model  was made flexible to
facilitate future inclusion of additional components into the model.
     This work was a continuation of that by Bass (19781.  In the
interest of continuity, the next few paragraphs  trace the thermody-
namic model development from its inception to its current
status.
     Development of any phase equilibrium model  begins with a considera-
tion of the fundamentals of phase equilibria.  Since phase equilibria
is a vast subject, the intent here will be to discuss that segment
which applies to the thermodynamic model.  Since the model
was based on one liquid phase in equilibrium with a vapor phase, the
phase equilibria discussion also focuses on this situation.
     For liquid and vapor phases to be  in equilibrium with each other
it is necessary that the system be in a  state of equilibrium with
respect to  the three processes of heat  transfer, boundary displacement,
and mass transfer.  Equality  of temperature and of  pressure between  the
two  phases  assures equilibrium for heat transfer and  boundary  displace-

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 merit processes.   Unfortunately,  the  conditions  necessary  for establish-
 ing  mass  transfer equilibrium  cannot be  expressed  in  a  similar  straight-
 forward fashion.   At  a  strictly  mathematical  level, Gibbs  provided  a
 guide  by  defining the chemical potential  function, v; for  mass trans-
 fer  equilibrium,  the  chemical  potential  of  each component  must  be in-
 variant from  phase  to phase.   Thus for a  system comprised  of N  compo-
 nents, equilibrium  with  respect  to the processes mentioned earlier  is
 indicated by  the  following equalities:

              TVap  =  TLiq                              (1)
                                     (1 - 1 to N)         (3)
     To establish equilibrium between the two phases  it  is clear that
temperature and pressure of the two phases must be equal .  However
what is necessary to obtain the equality of chemical  potentials is
not clear.  What is needed is an expression relating  chemical potential
(an abstract quantity), to composition, temperature and  pressure
(measurable quantities).
     G. N. Lewis obtained the following expression for a pure ideal
gas at constant temperature:
                  v - n  = RT In  -                     (4)
                                 P°
where

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     u   =  chemical  potential of  the  ideal  gas  at  system  temperature  T
     y° =  chemical  potential of  the  ideal  gas  at  arbitrary  reference
          conditions
     R   =  gas constant
     T   =  temperature of the ideal gas
     P   =  pressure  of the ideal  gas  at  system  temperature,  T
     P° =  pressure  of the ideal  gas  at  the arbitrary reference   con-
          ditions at which v   is evaluated
Equation 4 represents an important simplification         in it the
abstract chemical  potential  function is expressed in terms of a mea-
surable quantity,  pressure.   However, this is possible only under
pure ideal gas conditions.  To remove this constraint, Lewis introduced
the function fugacity through the definition
                               f.
               y.  - v°. = RT In ~                       (5)
                               f°

where
     p. = chemical potential of component i at system temperature and
          pressure
     u? = chemical potential of component i at arbitrary reference
          conditions
     f • = fugacity of component i at system temperature T and pressure
     f? = fugacity of component i at the arbitrary reference condition
          at which \i. is evaluated

The concept of fugacity is akin to  that of pressure; under ideal
gas conditions, fugacity and pressure are the same.  Prausnitz (1969),
for example, refers  to fugacity as  a "corrected  pressure."   It should

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 be noted that Equation 5 does not refer to a  particular phase and,
 therefore, applies to gases, liquids and solids.
      It can be shown that equality of fugacity of each component in
 every  phase is equivalent to the corresponding equality of chemical
 potentials.  Thus the condition for mass transfer equilibrium can now
 be written as
                                                                 (6)

where
     f.   = fugacity of component i  in  the  vapor  phase

     f-   = fugacity of component i  in  the  liquid phase
     Equation 6 is a significant improvement  on Equation 3 as the
abstract chemical  potential  term is  replaced  by fugacity, a term simi-
lar to pressure.  Equation 6 is  the  fundamental thermodynamic rela-
tionship to be used. for phase equilibria.   It now remains to develop
expressions relating fugacity to composition,  temperature and pressure.
     There are two basic methods for calculating  the fugacities.  The
first utilizes the exact relationship
                    • TIT  l" «&•>   ,     -  "w -'» or
                                 i   ' »n                n
where
     R = gas constant
     T = temperature

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     P  = total  pressure
     V  = total  volume
     n^ = moles  of component i
     f.j = fugacity of component i

A single equation of state is used for both the vapor and the liquid
phase.  This equation of state is used to solve the partial derivative
in Equation 7.
     The use of Equation 7 to evaluate f.. requires utilization of a
pressure explicit equation of state that describes P-V-T properties
of the system over the limits of integration.  While such calculations
are indeed possible for many single-component substances and for a limited
number of mixtures, it is not expected that the components encountered
in acid gas removal systems could be handled in this manner.
      In the second method, liquid and vapor phases are treated inde-
pendently.  To obtain fugacities in the vapor phase the following
expression is used:
                                                                 (8)
              i       i  i

where
     . = fugacity coefficient of component i
     y. = vapor phase mole fraction of component i
     P  = total pressure

The fugacity coefficient, ., is the measure of the deviation from
                                   9

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ideal behavior of component i in the vapor phase.
     Either of the following two equations can be used to calculate
the fugacity coefficient of component i, $ . :
              In *. -JL/" [(|f-)       -S!]dV - In z           (9)
                  1   RT V    8ni T,V,n,   V
                                       J

                                   i T,P,n.
                                          O
     z s pv/RT = compressibility factor

     To obtain the fugacity coefficient from Equation 9 a pressure
explicit equation of state is necessary, while Equation 10 requires
a volume explicit equation of state.  Since most equations of state
are in the pressure explicit form, Equation 9 is used more easily
than Equation 10.
     Liquid fugacities are obtained from the definition
                                                                 (11)

where
     Y.:   = activity coefficient of component i
     x..   = liquid mole-fraction of component i
      Ref
     f?   = reference state fugacity for component i

Although the choice of the reference state is arbitrary, the activity

                                 10

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coefficient, which is a measure of deviation from ideal  solution be-
havior, depends on the composition temperature and the choice of the
reference state.  There are two choices for the reference fugacity:
one leading to an ideal solution in the sense of the Raoult's law and
the other to an ideal solution in the sense of the Henry's law.
     For an ideal solution at constant temperature and pressure, the
fugacity of each component is proportional  to its liquid mole frac-
tion.  Thus for component i in an ideal solution,
                           = V-                                (12)
where C. is a proportionality constant dependent on temperature and
pressure but independent of the mole fraction of component i.
     If Equation 12 holds over the entire range of composition, from
x- = 0 to x.j = 1, then the solution is ideal in the Raoult's law sense.
In this case, it is evident from the boundary condition  at x-  = 1  that
the proportionality constant, C.. , is equal to the fugacity of pure
liquid i at the temperature and pressure of the solution.
     If on the other hand, Equation 12 holds over a small range of
x.., with x.. being close to zero, then the solution is ideal in the
Henry's law sense.  In this case, the constant C.. is not equated to
the fugacity of pure liquid i, but to the fugacity of i in an infinite-
ly dilute solution.
     A comparison of Equations 11 and 12 shows that activity coeffi-
cients of all the components are equal to unity in an Ideal solution.
In nonideal solutions, the term normalization of a component is often
                                  11

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used.  Normalization of a component refers to the conditions which
will  lead  to  ideal behavior for that component.  When the reference
state of component i is chosen in the Raoult's law sense, normaliza-
tion for component i implies
                 Y.J  •>  1.0      as      x..  ->•  1.0
On the other hand, if the reference state for component i is chosen
in the Henry's law sense, normalization for component i is

                 •y.  -»  1.0      as      x.j  •*  0.0

     If all components of a solution are normalized in the same way,
either in Raoult's law sense or in the Henry's law sense, normaliza-
tion is said to follow the symmetric convention.  If some components
are normalized in the Raoult's law sense and others in the Henry's
law sense, the normalization follows the unsymmetric convention.
     Using Equations 6, 8 and 11 to express equilibrium conditions
results in the relationship
                                                                 (13)
     As mentioned in the beginning of this section, the multicomponent
system  being modelled consists of methanol -carbon dioxide-nitrogen-
hydrogen sulfide.  Since methanol is a polar compound, and methanol
and carbon dioxide are known to associate in the vapor phase (Hemma-
                                  12

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plardh and King, 1972), the thermodynamic model  developed in this study
was based on the second method of calculating the fugacities; i.e.
Equation 13.  The temperature and pressure range for which the thermo-
dynamic model was developed suggested the symmetric convention for
normalization.  Furthermore, as pointed out by O'Connell (1977), severe
difficulties exist in using Henry's law for the reference state basis
when the solvent consists of more than one component.  Since it was
believed that more flexibility would result from defining reference
liquid state conditions by the Raoult's law convention, particularly
in regard to adding components to the system model, this approach
was chosen.

THERMODYNAMIC CORRELATIONS
     A foundation for the thermodynamic model was found in the final
form of the fundamental relationship of phase equilibria (Equation 13).
The next step was development of a structure for using  the model.  The
building blocks for this structure were thermodynamic correlations to
calculate fugacity coefficients, activity coefficients  and reference
state fugacities for each component in the multicomponent system  methanol-
carbon dioxide-nitrogen-hydrogen sulfide.

Vapor Fugacity  Coefficients
     To obtain  the correlation for the fugacity coefficient, it was
decided to  use  Equation 9 with a pressure explicit  equation  of  state.
                                   13

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        in  *, =     /[(-)        -]dV - In z                 (9)
            1    Kl  V    8ni T,V,n.      V
                                J
 There are  many  equations of  state, including Redlich-Kwong, the
 Soave modification of the Redlich-Kwong , Benedict-Webb-Rubin and
virial.
     The Redlich-Kwong  equation is commonly considered one of the best
 two  parameter equations of state and was the first equation of state
 used in the present therinodynamic model.  Subsequently, it was deter-
 mined that the  Soave modification of the Redlich-Kwong equation of state
 provided a  significant  improvement in accuracy; it was used in the
 remainder  of this work.  The Soave modification of the Redlich-Kwong
 equation of state is given by
                                   aa
where
    v   = vapor molar volume
    a,b = constants in the Soave modification of the Redlich-Kwong
          equation of state
    a   - function of temperature and acentric factor, u

For any pure component, constants a, b and a are obtained from
                a = 0.42747 R2 T2 / P                            (14a)
                                \f    \t
                                  14

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                 b  =  0.08664  R  T   /  Pr                            (14b)
                               c     c
   a = [1  + (0.48508 + 1.55171u>  -  0.15613to2}  {1  -  (-)}]2         (14c)
where
     T  = critical  temperature

     P  = critical  pressure

     0)  = Pitzer acentric factor
     For a mixture, constants a and b are obtained by the mixing rules


                         N
                     b - I  y.b.                                 (14d)
                          N   N
                     «a " I   I   y
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 Equation  14  can  also  be  expressed as
           Pv3 -  RTv2  + (a  -  RTb  -  Pb2)v  - ab = 0                 (15)
 The largest  root  of Equation  15  is  the vapor phase molar volume.
      Substitution of Equation 14  into Equation 9 yields the following
 equation  for fugacity coefficient of component i

                           bi
                    In *  =     (z-1) - In (z-B)
where
                      A = 2f»                                   (16a)
                          irr
                                                                 (16b)
     Fugacity coefficients were calculated for the component of interest
from Equation 16.  Binary interaction constants, K.., are presented  in
Table 1.  Of the six binary interaction constants required by the model,
three were found in the literature, while the other three were cal-
culated using experimental binary x-P-T data.  The criterion used to
obtain these constants was the minimization of the bubble point pressure
variance.  Generally the binary interaction constants are small and
on the order of 0.00 to 0.25 (Graboski and Daubert, 1978).  The sum  of
                                 16

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the squares of the deviations  between pressure predicted by the model
and experimental  pressure was  calculated for several  values of K-.  in
                                                    '            ' J
the range 0.00 to 0.25.   Using quadratic interpolation the optimum
value of K.. was  taken as that minimizing the sum of the square of  the
          ' 0
deviations for each of the three binaries for which literature values
were unavailable.  Critical constants and Pitzer  acentric factors
used in the model are given in Table 2.
                                TABLE 1
          Binary Interaction Constants for Soave Modification
                  of Redlich-Kwong Equation of State.
    System                 K..                     Source
 lethanol - C02            0.0628                      a
 lethanol - N2             0.080                       b
 lethanol - H2S           -4.000                       c
 02 - N2                 -0.022           Graboski and Daubert  (1978)
 :02 - H2S                 0.102           Graboski and Daubert  (1978)
   - H~S                  0.140           Graboski and Daubert  (1978)
     Calculated from x-P-T data found in literature  (Yorizane et al.,
 1969;  Katayama et al., 1975).
       Calculated from x-P-T data found by Weber and Knapp  (unpublished
 data,  Dechnische Universitat, Berlin, Fachdereich 10, Berfahrenseechink,
 Institut  fiir  Thermodynarnik and Anlagentechm'k, 1978).
     Calculated from x-P-T data found in literature  (Yorizane et al.,
 1969).
                                  17

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                               TABLE 2
                Critical Constants and Pitzer  Acentric
                     Factors  (Reid et al., 1977).
Component
Methanol
co2
N2
H2S
]c
512.6
304.2
126.2
373.2
Pc
(atm)
79.9
72.8
33.5
88.2
vc
(cc/mole)
118.0
94.0
87.5
98.5
00
0.559
0.225
0.040
0.100
Activity Coefficients
     A number of correlations are available for activity coefficients.
Prominent among them are the Wohl equation, the Wilson equation, and
the UNIQUAC equation.  Adler et al (1966) have recommended a special
case of the Wohl equation, the four-suffix Margules equation, as the
best choice for calculating activity coefficients in systems of the
type under study here.   Based on this recommendation, the four-suffix
Margules equation was selected to calculate activity coefficients in
the model.  It should also be mentioned that the Wilson equation was
examined, but convergence problems associated with estimation of model
parameters reinforced the decision to use the Margules equation.
     Truncating the original Wohl polynomial (1953) to include only
the terms up to the fourth power and assuming equal molal volumes
for the components, the following expression for the activity coef-
                                 18

-------
ficient of component i  in a mu Hi component solution can be obtained:
                            N   N   N

                log Y. = 4  I   I   I  x.x.x 8..

                     1     j=l  k=l £=1   J k * 1J
                        N   N   N   N


                                                                  (17)
where B. ,.,, are related to binary Wohl constants, A.., A., and D..
                                                   i J   j i      i j »
and a ternary constant C* (to be discussed in subsequent paragraphs).


     Depending on the values of the integers i, j, k, and £,



is determined by the following rules:


If i = j = k = £,
If i  = j  = k ^ i,




                                                   A

           Pijk£= Biii£=





If 1  = j  f k = i,
                                                      .
                                                  + Ak. - D1|£)    (17c)





 If i = j t k j« £,
           6ijk£ = eiik£ = 6ik£i =  •


                                  19

-------
              1/12 [(Ak. + A£. + A.k£) - CVik£]                 (17dconfd)
If 1 t j ? k
                                Aik£
where
                   Aik + \i + AU + A*i * \£ + A£k,
           C*. ..   = ternary constant for component i in the ik



                     ternary mixture.







     Adler et al.  (1966) studied the effect of C* on the deviation



of the predicted  vapor composition from the experimental vapor com-



position for a number of ternary systems.  Their study indicated that



for all systems the value of C* can be expected to be very near zero.



This implies that  the term in the series expansion of the excess



free energy owing  to clusters of three molecules, all different, is



not exceptionally  important.  In fact, the expected population of



such clusters seems to be about equal to the average of the popula-



tions expected for triple clusters from the binary data.  Based on



this the value of C* was taken as zero in the model.



     To calculate values for B-JJ^. it is necessary to know the con-



stants A.., A., and D.. for all binary mixtures that can be formed
         ' J   J I      IJ


by the system components.  Unfortunately, solution  theory  1s  not



at a point where these constants can be calculated a priori from pure




                                 20

-------
component properties;  they must be estimated from binary experimental
vapor-liquid equilibrium data.
     A total of six binaries result from the combinations of the com-
ponents of the multicomponent system, methanol-carbon dioxide-nitro-
gen-hydrogen sulfide.   They are methanol-carbon dioxide, methanol-
nitrogen, methanol-hydrogen sulfide, carbon dioxide-nitrogen, carbon
dioxide-hydrogen sulfide, and nitrogen-hydrogen sulfide.  For each of
these binaries, extensive equilibrium data were collected from  the
literature.
     For a binary system, the four-suffix Margules equation simplifies
to

     log YI - xj [A.. + 2(A.. - AIJ - D.-Jx. + 30.^]            (18)

The binary constants  A..., A., and D..  were evaluated from the binary
experimental x-P-T data using a number of techniques.  The constants
which were finally used in the model were evaluated by the technique
which resulted in the smallest deviation between the predicted  pressure
and the experimental pressure.  The details of this technique will be
discussed in the section dealing with parameter evaluation.
      It should be noted that the binary constants, A..,  A., and D..,
                                                     I J   J »       IJ
are evaluated for a fixed temperature and pressure.  The effect of
pressure on the liquid phase is usually small and the pressure  depend-
ence of the constants was neglected.  For the temperature  dependence,
a simple inverse  relationship with  respect  to temperature  has been sug-
gested  (Adler et  a!., 1966).  Assumptions of A.., A... and  D.. to  be
                                               1J   J 1       IJ
                                   21

-------
 inversely  proportional  to absolute temperature were used in the para-
 meter evaluation  techniques.  For the binary mixtures involving nitrogen,
 use of the  inverse temperature dependence for the constants was found
 to give unsatisfactory  results.  A number of alternatives were tested
 to obtain  the constants for these binaries.  The one which was most
 successful  involved the interpolation of experimental binary x-P-T
 data.  System pressure  P was evaluated for a number of values of the
 liquid mole fraction x  at the temperatures of interest using linear
 interpolation of  the experimental system pressure with respect to the
 temperature.  These interpolated x-P-T data  then were used to obtain
 the binary constants at the temperatures of interest.

 Reference Fugacitles
     Reference states for all  the components were chosen as the pure
 liquid at the temperature and pressure of the system.

Methanol.   The reference state  fugacity for methanol  was obtained
from the  following exact thermodynanric relationship:
                                    jf  viiq*   = vapor phase fugacity coefficient of saturated i
                                  22

-------
     v-10' = liquid molar volume
The vapor pressure for methane!  was calculated from the Antoine equa-
tion:
        log1Q P*(mmHg) = 7.87862 - |(k)-43.247                   {20)
Antoine constants were determined from experimental  vapor pressure data
of Eubank (1970) for temperatures from -40°C to +30°C.   Molar volumes
of methanol  were calculated from a corresponding states correlation of
Chueh and Prausnitz (Reid et al, 1977)
                                                                 (2D
      Ny = (1.0 - 0.89w) [exp(6.9547 - 76.2853 Tr + 191.3060
                       - 203.5472 ij + 82.7631 ij)]              (21a)
                        bjTr + CjTr + djTr + ej/Tr
                                                                 (21b)
                           PC = 1/VC                             (21c)
                               ln(l-Tr)                           (21d)

                                  23

-------
where
     z  = critical compressibility factor
     u  = Pitzer  acentric factor
     T  = reduced temperature = T/T
     VG = critical volume

Constants for Equation 21d are given in Table 3.  Using the above
correlation for the liquid molar volume and evaluating the integral
in Equation 19, the following expression is obtained for the reference
fugacity of methanol:
(22)
                                                   -)   -1]}
                            .    .
                                TABLE 3
                  Constants Used in Equation 21d for
               Calculating Methanol Liquid Molar Volume
                                 Cj
0
1
2
0.
0.
-0.
11917
98465
55314
0
-1
-0
.009513
.60378
.15793
0
1
-1
.21091
.82484
.01601
-0.
-0.
0.
06922
61432
34095
0
-0
0
.07480
.34546
.46795
-0.084476
0.087037
-0.239938
                                 24

-------
Carbon Dioxide and Hydrogen Sulfide.  Fugacities for pure carbon dioxide



and hydrogen sulfide were determined from a three-parameter reduced



states correlation (Robinson and Chao, 1979).
                       fo


                   log -J- = log v    + ulog v                    (23)
                log v(0) = B0 + B1 Pr + B2 P^ - log Pp           (23a)
            BQ = -20.651608 + 84.517272 Tr - 15.376424
                 + 152.65216 Tj| - 84.899391 ij + 24.84688
                 - 2.9786581 T                                   (23b)
If 0.8 > Tr ^0.3    B1 = (j>* 3QJJ T )        '                     (23c)

                            *     r





If 0.9 > Tr >_ 0.8    B1 = 0.321895 Tr - 0.184316                  (23d)







If 1.8 > T  > 0.9    B, = 58.16962 - 326.54444 T
       ~  r —~          i                         r




                          + 775.11716 T^ - 1006.8122 T^





                          + 773.32667 tj - 351.56938 T^





                          + 87.677429 T*j - 9.2617986 T^           (23e)
                                  25

-------
If 0.8 > Tr ^0.3        B2 = 0                                  (23f)
If 0.9 > T  > 0.8        B, = 0.0549369 (0.8 - T )               (23g)
          r —             £                     i
If 1.0 > Tr >_ 0.9        B2 = 0.673344 x TO"3 - 0.685226 x 10"2 Tr  (23h)
If Tr >_ 1.0              B£ = 0.72203901 - 2.7182597 Tr





                              + 3.984423 T2 - 2.8712448 T3





                              + 1.0202739 lAr - 0.14314712 TJJ     (231)






log v
-------
Nitrogen.  The Chao-Seader equation with adjusted parameters was used
to obtain the reference fuqacity of nitrogen.
                 log -±  = 2.7365534 - 1.9818310/Tr

                          - 0.51487289 Tr + 0.042470988 T*

                          - 0.002814385 TJJ + (-0.029474696

                          + 0.021495843 Tf) Pf - log Pr + ^     (24)
STRUCTURE OF THERMODYNAMIC MODEL
     Starting from the fundamental  thermodynamic relationship of phase
equilibria (Equation 13), two routes are available for phase equili-
bria calculations.  One is the bubble point calculational procedure
and the other is the dew point calculational procedure.
     Input data for the bubble point calculations are the pure com-
ponent constants, T , P , V , and u, the Margules constants for all
                   c   c   c
the binaries in the system and the liquid mole fractions of all the
components in the system.  One more piece of information is necessary
and that could be either the system temperature or the system pres-
sure.  Thus within the bubble point calculational procedure itself
there are two options.  In the first, the system temperature 1s chosen
as the last input variable.  In this case the output of the calcula-
tional procedure is the system pressure and the vapor mole fraction
of the system components.  In the second, it is the system pressure

                                 27

-------
 that  is the last  input variable and the output variables are the sys-
 tem temperature and the vapor mole fractions of the system components.
      Also, for the dew point calculational procedure either the sys-
 tem temperature or the system pressure can be made an input variable.
 The other data necessary for this procedure are the pure component
 constants, the Margules constants for all the binaries in the system,
 and the vapor mole fractions for all the components in the system.
 The output from this procedure includes the liquid mole fractions and
 either the system pressure (if temperature was the input variable) or
 the system temperature (if the pressure was the input variable).
      Of the four calculational procedures the isothermal bubble point
 calculational  procedure (temperature is an input variable) is the sim-
 plest and models based on this procedure require the least amount of
 computer time to yield a solution.  With this in mind the thermodynamic
 model developed was based on the isothermal bubble point calculational
 procedure and was called BUBLT.  Figure 1 shows the flow chart for model
 BUBLT.  Later, another model was developed to perform the isothermal
 dewpoint calculations and was called DEWT.  The flow chart for model
 DEWT is shown in Figure 2.  Complete listings of programs for BUBLT
and DEWT are given by Matange (1980).
Model  BUBLT
     The flow chart for model BUBLT is shown in Figure 1.  The program
starts by reading critical constants and Pitzer  acentric factors
 (Tc,  PC, Vc, and to) for all  system components.   Margules constants
(A.-,  A..,  and D. .) for all  binary combinations are read next, fol-
  ' J    J '        ' J
lowed by an input of system temperature and liquid mole fractions for

                                  28

-------
all components.   In the first iteration an initial  guess of the sys-
tem pressure is  made.  Convergence is not significantly affected by
the initial value of the pressure, but an initial  guess of zero or
some very high pressure (supercritical) is unacceptable.  Arbitrarily,
two atmospheres  was chosen as the initial guess.
     Since the system temperature and liquid mole fractions are known,
the activity coefficients, y.j» of all system components are calculated
next using the Margules equation in subroutine WOHL.  The iterative
procedure begins with the next step.
     Subroutine  REFSTS is called to calculate reference fugacities,
 Ref
f?  , of all components using expressions developed in  the previous section.
The vapor mole fraction of each component is then calculated using
the relationship
                                 ,
                        v  -
                        yi ~

SUMY is set equal to the sum of all yj and system pressure is obtained
from the expression
                                                                 (26)
                                +1
The pressure calculated by Equation 26 is compared to the previous
value, which on the first iteration is 2.0 atmospheres.  If the dif-
ference between these two values is greater than 0.01 atmosphere,
values of vapor mole fractions, y^, are normalized and vapor fugacity
                                 29

-------
Subroutine VFUGCS
       y^SUMY
                                BUBLT
                           Read TC,PC,VC,o>
                        Read Margules Consts
                           Read T, all x.
                              P = 2 atm
                              *-  = 1.0
                          Subroutine  WOHL
                         Subroutine
                        y, -
                            SUMY =
= IYI-XI
                      Subroutine VFUGCS
                  Figure 1 Flow Chart for BUBLT
                               30

-------
      c
DEWT
    Read TC, PC, VC, u>
    Read Margules Consts
    Read T, all y
           P = 1.0
             « 1.0
              1
      Subroutine REFSTS
         ^(T,
          SUMX
,y)
e VFUGCS

/ViRef
1

MX^-^^
St?^^>
TYes
•^^^
latiort^^^
ging7x^>
TNO
J">-^No


Change P


Figure 2 Flow Chart for DEWT
             31

-------
 coefficients,  .,  are calculated by calling subroutine VFUGCS.   The
 reference state fugacity is  recalculated   in the next iteration  using
 the pressure calculated  from Equation  26  and the next iteration  is
 begun.
      When an unchanging  value of pressure is achieved (tolerance being
 0.01  atmosphere) the  stoichiometric check SUMY = 1.0  is made  (tolerance
 being 0.0001).   If SUMY  is not equal to unity, vapor  composition is
 normalized, the vapor fugacity coefficients are recalculated  and the
 program  loops  back to the step where the  reference  fugacities were
 calculated.
      If  SUMY is equal  to unity convergence has been achieved  and
 system pressure and vapor composition  are printed.

 Model DEWT
      Figure 2  shows the  information  flow  chart for  the computer  model
 DEWT.  As  mentioned earlier,  this model performs the  isothermal  dew
 point calculation.
      Model DEWT begins by reading in critical  constants and Pitzer
 acentric   factors  for  all system components.   This  is  followed by
 reading in Margules constants,  A.., A..,  and  D..t   for all binaries
 in  the system,  system  temperature and  vapor  compositions.
      Calculations  begin  by initializing the  system  pressure and  the
                                                                 Rpf
activity coefficients  to unity.  Next  the reference fugacities,  fv  ,
and the vapor fugacity coefficients, <*.,  are  calculated.  The liquid
mole  fractions, x^, are calculated and SUMX  is  set  equal to the  sum
of all x..

                                 32

-------
     If SUMX is not constant (tolerance 0.0001),  the  program loops
back.  Subroutine WOHL is called and the activity coefficients are
recalculated and the control is transferred back  to the point where
x- is calculated.  When SUMX is a constant, the program moves ahead.
     In the next step, a check is made to see if  the calculations are
diverging.  This is necessary because it is possible to specify a
vapor composition and a temperature for which no  equilibrium solution
exists and which would give rise to diverging behavior.  If diverging
behavior is encountered, the best results obtained so far are normal-
ized and output; otherwise, normal calculations continue.  Next,
a check is made to verify is SUMX is equal to unity (tolerance being
0.0001).  If not, system pressure is adjusted using a Newtonian inter-
polation method, working from successive values of SUMX.  If SUMX is
equal to unity, convergence has been achieved and the system pressure
and  the liquid composition are output.

EVALUATION OF MARGULES PARAMETERS
     Earlier work with the  thermodynamic model made it quite clear
that the  success of the model  hinges heavily on  the accuracy of the
Margules  constants.   This has  been  the  impetus to  investigate thorough-
ly the  process of obtaining these constants.
     As mentioned earlier,  the  four-suffix Margules equation was used
to calculate activity coefficients  for  binary mixtures.  Three Mar-
gules  constants, A.., A..,  and  D..,  are required for each binary mix-
                   1 J   J 1        I J
ture.   The  four  components  of  interest  are methanol, carbon dioxide,
nitrogen, and  hydrogen sulfide.   They  can  be combined  to give a  total

                                   33

-------
of six binary systems:  methanol -carbon dioxide, methanol-nitrogen,
methanol -hydrogen sulfide, carbon dioxide-nitrogen, carbon dioxide-
hydrogen sulfide and nitrogen-hydrogen sulfide.  Thus, a total of
eighteen Margules constants had to be evaluated.
     A number of parameter estimation techniques were investigated.
With few exceptions, the basis of these techniques was a program called
GMAR, which is a nonlinear parameter search program written by G. W.
Westley of the Computing Technology Center of Union Carbide Corpora-
tion in Oak Ridge, Tennessee.  This program was modified by Dr. R. M.
Felder of the Chemical Engineering Department, North Carolina State
University.  Typically, input data to program GMAR consist of m data
points for any given function f (x1 , x2> .... x^; b1 , b^ ..... b ) =
f(x_, b_), where x, , . .., x  are the variables and b, , ...» b  are the
parameters.  Program GMAR calculates the values of the parameters b, ,
..., b  which minimize the weighted sum of squares of the residual,
where
                      m                             *
           Residual = I  (WE^-Cdata point - ffx^.bj],           (27)
where (WE)., is a weighting factor assigned to the 1   data point.
Also necessary to run program GMAR are the derivatives of the function
f(x,b) with respect to the parameter b, , .... b -  These derivatives
  --                                  i        p
were provided to GMAR by writing a subroutine called FUNC.  Listings
of program GMAR and all necessary subroutines are given by Matange,
(1980).
                                 34

-------
     The original approach to evaluation of Margules parameters used
the Margules expression for activity coefficients as the function
f(x_,b) in the program GMAR.  Experimental values of the activity co-
efficients were obtained using binary x-y-P-T data and the following
equation:
                                  i
The fugacity coefficient, 4.^, was obtained from subroutine VFUGCS
                             Ref
and the reference fugacity, f .  , from subroutine REFSTS.  The Mar-
gules parameters were thus obtained for all six binaries.  The Mar-
gules parameters of each binary were then used in the model BUBLT
to predict the pressure and the vapor composition for that binary.
It was found that the predicted variables compared well with the ex-
perimental data for all the binaries.
      The  Margules  expression for  the activity coefficients was not
 the only  available choice for the function f(x.,b.)  used in program
                                   2
 GMAR.  The expression for log(y.j/Yj) was also tried and was found to
 improve the accuracy of the Margules constants.   Even further improve-
 ment was  achieved  when the Margules constants were obtained using a
 Fletcher Powell  search procedure in the program FPOW which minimizes
 the residual given by
                 Residual =  I  E^ic^lD*2 + (Y2C-Y2D)2]         (29)
                                  35

-------
 where
     Y1C'Y2C  =  ca^culatecl  values  of y^  and y2>  from  Equation  18,
     Y1D'Y2D  =  va^ues of "h and Y2 obtai'ned  from experimental data

     Although these efforts were  rewarded by  improvement in the fit
 to  experimental  data, there is a  scarcity of  reliable data in the
 x-y-P-T form.   However, several sets of data  were found of the form
 x-P-T; i.e. vapor compositions were not measured in  the reported
 experimental  programs.  Data  in this form were  found for all  six of
 the binary combinations.
     A program  for evaluating Margules  parameters from x-P-T  equili-
 brium data was  developed.  This program, called GMAIN, used bubble
 point calculation procedures  in conjunction with GMAR to calculate
 the Margules  constants.  Values of Margules parameters are adjusted
 until the difference between  the  system pressure calculated by the
model and the experimental pressure was minimized.
     Another advantage of the above technique was the flexibility it
allowed in using data at different temperatures.  For the methanol-
carbon dioxide, the methanol-hydrogen sulfide and the carbon dioxide-
hydrogen sulfide systems, it was  found  that assuming the Margules
parameters to be inversely proportional to the absolute temperature
was quite satisfactory.   For these binaries, a simple modification
of program GMAR made it possible  to obtain the optimum Margules para-
meters using data at all temperatures.  This significantly improved
the accuracy of the constants.  For binary mixtures  involving nitro-
gen, the inverse temperature relationship for the Margules parameters

                                  36

-------
was unacceptable.  For these systems Margules parameters at each tem-
perature of interest were obtained.

Methanol-COo.  The optimum values of the Margules parameters for the
methanol-carbon dioxide system were obtained by using data by Katayama
et al. (1975) at 298.15 K and data by Yorizane et al. (1969) at 258.15
K and 243.15 K.  Margules parameters were evaluated using the three
data sets and assuming the parameters to be inversely proportional to
temperature.  Table 4 compares model predictions to experimental data
for methanol-carbon dioxide mixtures.  Since vapor compositions were
available for the data at 298.15 K, both system pressures and vapor
compositions have been compared in Table 4 for this data set.  Vapor
composition data were not available at 258.15 K and 243.15 K and hence
only the system pressures are compared at these temperatures.  Figure
3 compares the predicted pressures with the experimental pressures
at 298.15 K, 258.15 K and 243.15 K.  Excellent agreement was obtained
between predicted and experimental values of the vapor mole fractions
of carbon dioxide at 298.15 K.  Good agreement was obtained between
the predicted and experimental system pressures for all three tempera-
tures.
Methanol-No.  Data provided by Knapp and Weber  were used to evaluate
Margules parameters for methanol-nitrogen mixtures.  As  indicated
     1H. Knapp and W. Weber.  Unpublished data.  Dechnische Unlversitat,
Berlin.  Fachdereich 10.  Berfahrenseechink.   Institut  ftir Thermody-
namik and Anlagentechnlk. (1978).
                                  37

-------
                                Table 4
         Comparisons of  Experimental Vapor-Liquid Equilibrium
Data with Model Correlations for Methanol  (l)-Carbon Dioxide (2)-Mixtures


x2
0.015
0.041
0.070
0.131
0.256
0.361
0.450
0.610
0.662

exp
(atm)
2.16
5.58
9.39
17.08
29.62
40.80
46.97
53.88
55.77

Pcalc
(atm)
2.17
5.46
8.90
15.66
28.66
39.12
46.94
54.60
54.79
298.15
DP
(atm)
0.01
-0.12
-0.49
-1.42
-0.96
-1.68
-0.03
0.72
-0.98
K
y2
exp
0.9202
0.9685
0.9797
0.9878
0.9917
0.9928
0.9930
0.9929
0.9922

calc
0.9221
0.9679
0.9796
0.9875
0.9920
0.9931
0.9934
0.9931
0.9931

Dy
0.0019
-0.0006
-0.0001
-0.0003
0.0003
0.0003
0.0004
0.0002
0.0009
DP - P       P     • nv = v       - v
     'calc    exptl' u    ^.calc   •/2,exptl
Average percent deviation for pressure = 3.0
Average percent deviation for y~ = 0*06

Experimental data by Katayama et al.  (1975)

258.15 K

X2
0.072
0.145
0.219
0.333
0.471
exp
(atm)
4.0
8.0
12.0
16.0
20.0
Pcalc
(atm)
4.95
8.96
12.49
17.11
20.81
DP
(atm)
0.95
0.96
0.49
1.11
0.81
DP = Pcalc - Pexptl
Average percent deviation for pressure = 10.2

Experimental data by Yorizane et al. (1969)
                                                     (continued)

                                 38

-------
Table 4
(continued)

243.15°K
xz
0.048
0.107
0.172
0.240
0.327
0.426
0.550
0.789
exp
(atm)
2.0
4.0
6.0
8.0
10.0
12.0
13.0
13.7
Pcalc
(atm)
2.54
5.05
7.35
9.41
11.60
13.35
14.21
12.86
DP
(atm)
0.54
1.05
1.35
1.41
1.60
1.35
1.21
-0.84
DP = Pcalc - Pexptl
Average percent deviation for pressure = 17.0
Experimental data by Yorizane et al. (1969)
                                 39

-------
   60
   50   -
   40   —
   30   —
   20   —
    10   —
                    O : MIA  OF KATAYAMA

               A Q : DATA  OF YORIZANE
                       .•MODEL PREDICTION
        00
0.2
0.4
0.6
0.8
                     MOl FRACTION C02  IN LIQUID,  X
1.0
Figure 3.   Comparison of Equilibrium Experimental  Predicted Pressures
           for Methanol  - Carbon Dioxide Mixtures.

-------
earlier the inverse temperature relationship for the Margules para-
meters does not work and values were obtained at each temperature.
Since the multicomponent model  was to be tested at 273.15 K and 258.15 K
equilibrium pressure and liquid compositions for methanol-nitrogen
mixtures at 273.15 K and 258.15 K were obtained by linear interpo-
lation of experimental pressure with respect to temperature at a num-
ber of values of the liquid mole fraction.  Data at each temperature
(273.15 K and 258.15 K were used separately in GMAR to obtain optimum
values of the Margules parameters at specific temperatures.  Table 5
and Figure 4 compare the system pressure predicted by the model and
the experimental pressure for the methanol-nitrogen system.  Excellent
agreement between the predicted and experiment pressure was obtained.

Methanol-I^S.  Optimal Margules parameters for the methanol-hydrogen
sulfide system were obtained using data by Yorizane et al. (1969) at
273.15 K, 258.15 K and 248.15 K.  The Margules parameters for this sys-
tem were found to be inversely proportional to temperature so that
the optimal parameters were based on data at all three temperatures.
As shown in Table 6 and Figure 5, good agreement was found between
the system pressure predicted by the model and the experimental pres-
sure.

CCL^Ng.-   The carbon dioxide-nitrogen system followed the pattern  set
by the methanol-nitrogen system:  Margules parameters were not  in-
versely proportional to temperature.  Data of  Zenner and Dana  (1969)
and Kaminishi et al.  (1966) were  interpolated  to  obtain  x-P  values at
                                  41

-------
 Table  5   Comparisons  of Interpolated Experimental  Vapor-Liquid
          Equilibrium  Data  with Model Correlations  for Methanol
          (1)  -  Nitrogen (2)    Mixtures
                                 273.15  K
X2
0.0000
0.0025
0.0050
0.0058
0.0118
0.0165
Pexptl
(atm)
0.00
10.00
20.00
24.20
50.30
74.00
Pcalc
(atm)
0.04
9.91
20.25
23.66
50.90
74.47
DP
(atm)
0.04
-0.09
0.25
-0.54
0.60
0.47
 DP =  Pcalc  "  Pexptl

 Average  percent deviation  for  pressure  =  1.2

 Experimental  data obtained by  interpolation of  data  by  Knapp  and  Weber3


                               258.15 K
x2
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
Pexptl
(atm)
0.00
10.00
20.00
31.30
42.50
53.00
66.20
78.00
Pcalc
(atm)
0.01
10.09
20.49
31.25
42.38
53.93
65.92
78.39
DP
(atm)
0.01
0.09
0.49
-0.05
-0.12
0.93
-0.28
0.39
np = P     - P
UK    calc    exptl

Average percent deviation for pressure = 0.9

Experimental data obtained by interpolation of data by Knapp and Weber3


     aKnapp and Weber. Unpublished data.  Dechnische Uniyersitat,
Berlin.  Fachdereich 10.  Berfahrenseechink.  Institut fiir Thermody-
namik and Anlagentechnik (1978).
                                 42

-------
   80
   70
  60
   50    -
   40
          I               I

Q:  INTERPOLATED  DATA (273.15 K)  FROM
     DATA  OF KNAPP
     INTERPOLATED  DATA (258.15 K)  FROM
     DATA  OF KNAPP
     MODEL PREDICTION

                         273.15 K
   30  5
        00
                                           SCALE CHANGED
                                                           258.15 K
                       I
                          I
        0.005
0.010
0.015
                     MOL FRACTION  N2 IN LIQUID,  X
OJ020
Figure 4.  Comparison of Equilibrium  Experimental  and Predicted Pressures
           for Methanol-Nitrogen  Mixtures.
                                     43

-------
 Table  6    Comparisons of  Experimental  Vapor-Liquid  Equilibrium
           Data with Model Correlations  for  Methanol  (1)  -
           Hydrogen Sulfide  (2) Mixtures.

xz
0.092
0.199
0.329
0.453
0.484
0.608
0.7*3
0.840
273.1
Pexptl
(atm)
2.0
4.0
6.0
7.5
8.0
9.1
9.8
10.0
5 K
Pcalc
(atm)
2.16
3.83
5.72
7.45
7.83
8.98
9.44
9.48

DP
(atm)
0.16
-0.17
-0.28
-0.05
-0.17
-0.1?
-0.36
-0.52
DP = P     - P
UK   "calc   Hexptl

Average percent deviation for pressure =3.7

Experimental data by Yorizane et al. (1969)


x2
0.165
0.231
0.298
0.367
0.403
0.490
0.585
0.662
258,15
Pexptl
(atm)
2.0
3.0
3.4
4.2
4.4
5.0
5.4
5.8
K
Pcalc
(atm)
2.26
2.90
3.54
4.19
4.52
5.23
5.79
6.04

DP
(atm)
0.26
-0.10
0.14
-0.01
0.12
0.23
0.39
0.23
DP = Pcalc - PexPtl
Average percent deviation for pressure = 4.9

Experimental data by Yorizane et al. (1969)
                                                     (continued)
                                  44

-------
Table 6  (continued)
                               248.15 K
x2
0.203
0.290
0.3?7
0.465
0.582
0.733
_.. 	
exptl
(atm)
2.0
2.5
3.0
' 3.4
4.0
4.3
Pcalc
(atm)
1.96
2.57
2.8?
3.71
4.22
4.43
DP
(atm)
-0.04
0.07
-0.18
0.31
0.22
0.13
DP = Pcalc - Pexptl
Average percent deviation for pressure = 4.7
Experimental data by Yorizane et al. (1969)
                                 45

-------
    10
                     I            I            T
             O A El •"  DATA OF YORIZANE
     8
  r  6
£
     4   —
     2   —
         0.0
                    MODEL  PREDICTION
0.2
0.4
                                  ^   o
                                                 248.15 K
0.6
0.8
TO
                     MOL  FRACTION H2S IN LIQUID, X
Figure 5.   Comparison of Equilibrium Experimental and Predicted Pressures
           for the Methanol-Hydrogen Sulfide Mixtures.
                                     46

-------
273.15 K and 258.15 K.  Optimal values of the Margules parameter were
obtained for the two temperatures using the interpolated data in GMAR.
Model predictions based on optimal Margules parameters are compared
to experimental values in Table 7 and Figure 6.  The comparison between
predicted pressure and experimental pressure is excellent.

C_0_o - H?S.  Sobocinski and Kurata  (1969) have reported data for carbon
dioxide-hydrogen sulfide mixtures at 288.71 K, 266.48 K and 244.26 K.
Since the inverse temperature relationship was found to be acceptable
for this system, optimal values of Margules constants were obtained
using data at  all three temperatures.  Table 8 compares system
pressure and vapor composition with the corresponding experimental
data for carbon dioxide-hydrogen  sulfide mixtures.  Comparisons be-
tween predicted pressure and experimental  pressure  for this system
is shown graphically  in Figure 7.

NplUgS.*  Data  °f Robinson and  Besserer  (1972) were  interpolated as
described earlier to  obtain equilibrium x-P values  at 273.15  K and
258.15  K.   Interpolated data were used to  evaluate  optimal Margules
parameters  at  273.15  K and 258.15 K using  GMAR.   Comparisons  between
experimental and model-predicted  equilibrium  pressures are shown  in
Table 9 and  Figure  8; Agreement  is excellent.
                                  47

-------
 Table 7    Comparisons of Interpolated Experimental  Vapor-Liquid
           Equilibrium Data with Model Correlations  for Carbon
           Dioxide (1) - Nitrogen (2)  Mixtures

x2
0.000
0.025
0.050
0.075
0.100
273.15
Pexptl
(atm)
34.20
47.20
60.00
71.40
82.40
K
Pcalc
(atm)
31.19
46.79
59.20
70.07
80.53

DP
(atm)
-3.01
-0.41
-0.80
-1.33
-1.87
DP =  Pcalc "  Pexptl

Average percent deviation for  pressure =  3.0

Experimental  data obtained by  interpolation of data by  Zenner and Dana
(1963) and Kaminishi et al.  (1966).
                               258.15 K
X2
0.000
0.025
0.050
0.075
0.100
Pexptl
(atm)
21.50
35.80
49.00
62.00
74.60
Pcalc
(atm)
20.69
35.33
48.72
61.25
73.26
DP
(atm)
-0.81
-0.47
-0.28
-0.75
-1.34
DP = P     - P
UK   Kcalc   pexptl

Average percent deviation for pressure = 1.7

Experimental data obtained by interpolation of data by Zenner and
Dana (1963) and Kaminishi et al. (1966).
                                  48

-------
     95
     80
GO
GO
     65
     50
     35
     20
T
 I
I
                    INTERPOLATED FROM DATA OF ZENNER  ET  AL
                    & TORIUMI  ET  AL
                    MODEL  PREDICTION
           0.0
                                     273.15 K
0.2
0.4
0.6
0.8
                       MOL  FRACTION  N? IN LIQUID,  X
1.0
  Figure 6.  Comparison  of  Equilibrium Experimental and Predicted  Pressures
             for  the  Carbon Dioxide-Nitrogen Mixtures.
                                         49

-------
 Table  8    Comparisons  of  Experimental  Vapor-Liquid  Equilibrium
           Data with Model  Correlations for  Carbon Dioxide  (1) -
           Hydrogen Sulfide (2)  Mixtures
                              288.71°K
x2
0.948
0.815
0.640
0.419
Pexptl
(atm)
20.41
27.22
34.02
40.83
Pcalc
(atm)
19.99
27.46
34.00
41.69
DP
(atm)
-0.42
0.24
-0.02
0.86
y2,exptl
0.770
0.540
0.395
0.272
y2,calc
0.748
0.531
0.395
0.261
Dy
-0.022
-0.009
0.000
-0.011
DP = Pcalc - Pexptl

Dy = y2,calc - y2,exptl

Average percent deviation for pressure = 1,3
Average percent deviation for y^ = 2.1

Experimental data of Sobocinski and Kurata  (1969)
                              266.48°K
0.887
0.630
0.164
13.61
20.41
27.22
14.19
19.97
26.47
0.58
-0.44
-0.75
0.590
0.340
0.095
0.573
0.356
0.128
-0.017
0.016
0.033
   = p     . p
     Kcalc   pexptl
Dy = y2,calc " y2,exptl

Average percent deviation for pressure = 3.1
Average percent deviation for y2 = 14.1

Experimental data of Sobocinski and Kurata (1969)
                                                         (continued)

                                  50

-------
Table 8  (continued)

244.26°K
x2
0.915
0.235
Pexptl
(atm)
6.80
13.61
Pcalc
(atm)
6.95
13.52
DP
(atm)
0.15
-0.09
y2,exptl
0.572
0.120
y2,calc
0.563
0.144
Dy
-0.009
0.024
np = P     - p
UP    calc    exptl
Dy = y2,calc " y2,exptl
Average percent deviation for pressure = 1.4
Average percent deviation for y^ - 10.8
Experimental data of Sobocinski and Kurata (1969)
                                  51

-------
     60
     50
     40
 ae  30
 §
 LU
 £
     20
     10
      I            I            T
O A EH  : DATA OFSOBOCINSKI
           : MODEL  PREDICTION
        0.0
                    I
                 I
I
I
     0.2          0.4          0.6          0.8
     MOL FRACTION C02  IN LIQUID, X
                      1.0
Figure 7.   Comparison of Equilibrium Experimental and Predicted Pressures
           for Carbon Dioxide-Hydrogen Sulfide Mixtures.
                                     52

-------
Table 9   Comparisons of Interpolated Experimental Vapor-Liquid
          Equilibrium Data with Model Correlations for Nitrogen
          (1) - Hydrogen Sulfide (2) Mixtures


xl

0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
273.1
Pexptl
(atm)
10.7
14.0
18.5
23.0
28.0
33.5
39.0
44.4
50.0
55.7
61.4
66.8
72.3
5°K
Pcalc
(atm)
10.05
14.11
18.54
23.30
28.36
33.68
39.21
44.89
50.67
56.47
62.22
67.87
73.32

DP
(atm)
-0.65
0.11
0.04
0.30
0.36
0.18
0.21
0.49
0.67
0.77
0.82
1.07
1.02
DP = Pcalc * PexPtl
Average percent deviation for pressure =1.5
Experimental data interpolated from data of Robinson and Besserer  (1972)


0.000
0.004
0.008
0.012
0.016
0.020
0.024
258.1
6.2
16.4
29.4
43.8
58.3
72.8
85.7
5CK
6.47
16.85
29.54
43.93
59.10
73.85
86.88

0.27
0.45
0.14
0.13
0.80
1.05
1.18
DP = Pcalc *  Pexptl
Average percent deviation  for  pressure  -  1.7
Experimental  data  interpolated from  data  of Robinson and Besserer (1972)
                                   53

-------
     100
      80
      60
CO
e/5
£    40
      20
          I            I            I


O A :  INTERPOLATED  FROM DATA OF ROBINSON

   	:  MODEL  PREDICTION
                                         258.15 K
                       I
                      I
  I
           OO       0.005
                   0.010
0.015
                                                          273.15 K
  I
0.020     0.025
                        MOL FRACTION  N2  IN LIQUID,  X
   Figure 8.   Comparison of Equilibrium Experimental and Predicted

              Pressures for Nitrogen-Hydrogen Sulfide Mixtures.
                                         54

-------
Summary
     Margules parameters for six binary mixtures have been determined
from vapor-liquid equilibrium data found in the literature.  Consti-
tuents of these mixtures are taken from the group methanol, hydrogen
sulfide, carbon dioxide and nitrogen.  Parameters for the three nitro-
gen-free binary mixtures were found to be inversely proportioned to
temperature, while parameters for the three nitrogen containing mix-
tures did not follow such a relationship.  Since the model is to be
tested against multicomponent equilibrium data taken at 273.15 K and
258.15 K.  Margules parameters for each of the six binary mixtures
were evaluated at these temperatures and are given in Table 10.  The
fits of binary equilibrium data to that predicted using these para-
meters are excellent.
                                   55

-------
Table 10   Margules parameters from Parameter Optimization
           Procedure GMAR
Binary
A12
A21
D12
273.15°K
Methanol
Methanol
Methanol
co2(i) -
co2(i) -
N2(l) -
(1) - C02(2)
(1) - N2(2)
(1) - H2S(2)
N2(2)
H2S(2)
H2S(2)
1.3395
5.2000
1.0758
2.1228
0.5705
0.8115
0.6427
1.1446
0.5374
0.3023
0.5777
-66.5928
0.6940
2.2000
0.9891
3.1223
0.5793
-72.8469

258.15°K
Methanol
Methanol
Methanol
co2(i) -
co2(i) -
N2(D -
(1) - C02(2)
(1) - N2(2)
(1) - H2S(2)
N2(2)
H2S(2)
H2S(2)
1.4174
11.0000
1.1383
0.6328
0.6037
0.8990
0.6800
1.1657
0.5686
0.2849
0.6113
-114.3787
0.7342
8.7000
1.0466
0.7872
0.6130
-123.1370
                                  56

-------
                 EXPERIMENTAL EQUIPMENT AND PROCEDURE

     The experimental  apparatus used to obtain multicomponent vapor
liquid equilibrium data was a modification of the system used by
Bass (1978).  A schematic diagram of the apparatus is shown in Figure
9.  The stainless steel cell had a volume of 1084 ml  and was equipped
with internal baffles.  Valves used in the recycle line as well as
those used for sampling and gas charging were teflon packed and rated
for use at high pressure.  Liquid in the cell was recirculated using
a microflo pulsafeeder metering pump, model L20-S-3, manufactured by
the Interpace Corporation.  The diaphragm used in this pump eliminated
any possibility of contamination.  Pressure in the equilibrium cell
was measured using a 16-inch Heise gauge graduated in 0.5 psi incre-
ments up to 1250 psia.  The gauge had a guaranteed accuracy of 0.1
percent of the full scale.  An Ashcroft type 1327 portable dead weight
tester was used to confirm calibration of the gauge.  Temperatures
were measured using a copper-constantan thermocouple and a digital
temperature indicator calibrated against  known temperatures.  The
entire high pressure apparatus was housed in a Harris industrial
freezer which provided the  refrigeration.  A Thermistemp temperature
controller, a fan and a heater controlled the temperature in  the cell
within 0.1°C.

REAGENTS
     Methanol was Fisher  Spectranalyzed(R)with a  stated purity  of
99.95 percent.  Carbon dioxide and nitrogen  used  in  the research  had
                                  57

-------
en
CO
       CO,
                         - way valve
/
                                          temperature

                                          controller
digital

thermocouple
                                                                                  pressure gauge
N2

' \
H2S
Mix
                            heater
                                capillary

                                tubing
                                                                                         equilibrium cell

                                                                                         magnetic stirrer
                  Figure  9,  Experimental  Apparatus.

-------
a stated purity of 99.99 percent and 99.999 percent, respectively.
These gases were supplied by Airco Inc.   A mixture of 15.1  percent
hydrogen sulfide in nitrogen, supplied by Air Products, was used.

ANALYSIS
     Analyses of liquid and vapor samples taken during a run were done
on a Tracer model 550 gas chromatograph equipped with a thermal con-
ductivity detector, a temperature programmer and a heated gas sampling
valve.  Component separation was achieved in a stainless steel column,
3 meters in length and 3.2 mm in diameter, packed with Porapak QS.
The signal from the gas chromatograph was analyzed using Southern
Analytical's Supergrator-3 digital integrator and a Leeds and North-
rup strip chart recorder.

CALIBRATIONS
     Calibration of the gas chromatograph-supergrator  combination
was done by injecting known amounts of components into the gas chroma-
 tograph and noting the  corresponding  areas  integrated  by the  super-
 grator.  For each amount  of every component  the corresponding area
was obtained for  at  least five  replicate  injections.   The mean and
 the standard deviation  were calculated for  the replicate areas.  The
mean area  was  the response of the gas chromatograph-supergrator  for
 the amount of  the particular component under consideration  and became
 part of the calibration data for that component.  The  percent stan-
 dard deviations  of the  replicate areas provided a measure  of  the pre-
 cision of  the  replicate areas obtained.   The percent standard devia-
                                   59

-------
 tion of the replicate areas  was calculated  at each  calibration  point
 for all four components.   The average of these values  is  reported  as
 the average percent standard deviation for  area for each  component
 in the following  paragraphs.   Calibration data in the  form of g-moles
 of a component  and  the  corresponding  area integrated by the gas chroma-
 tograph-supergrator combination were  fit with linear equations  for
 all  four components.  Determination of unknown compositions were
 performed using these linear equations for  the four components.
      For methanol calibration,  different concentrations of methanol
 in distilled, deionized water were prepared.   Varying  amounts of
 samples at each concentration were injected into the gas  chromatograph.
 Sample injections were done  using a Hamilton  microliter syringe.
 All  injections  involved a  sample volume  greater than 2 microliters.
 The  smallest graduation on the  syringe was  0.1  microliter.  It was
 observed that for methanol the  average percent standard deviation
 for  the area was less than 0.6.  For  the calibration of carbon di-
 oxide,  nitrogen and hydrogen  sulfide,  gaseous  injections  at various
 pressures  were  made using  the gas sampling  valve.   The pressure gauge
 used for  this purpose had  a least count of  0.034 atm.  The average
 percent standard deviations for  the area for  carbon  dioxide, nitrogen
 and  hydrogen sulfide were  0.49,  0.53 and 1.79,  respectively.

 TEST DATA:   METHANOL - C02 MIXTURES
     For  the purpose of verifying the  proposed  experimental procedure,
 vapor-liquid equilibrium data were taken for methanol-carbon dioxide
mixtures at  298.15 K.  On  the basis of excellent comparison of these

                                  60

-------
data with those of Katayama et al.  (1975),  the experimental  apparatus
and procedure were judged sound.   The comparison is shown in Figure
10 and Table 11.  The average deviation of  COg mole fraction of car-
bon dioxide between the two sets  of data was 5.4%.

MULTICOMPONENT PROCEDURE
     The first step in taking multicomponent vapor-liquid equilibrium
data was to fill the equilibrium cell with  about 390 ml of methanol.
The refrigeration system was turned on to achieve the desired tempera-
ture in the cell, and the three gases were added to generate the de-
sired overall composition and pressure.  Liquid in the cell was re-
circulated for six hours and then allowed to sit unagitated for at
least twelve hours prior to sampling.  Samples were allowed to ex-
pand through the capillary tubing into the evacuated sample containers.
Sampling was done quickly and the cell pressure was seldom disturbed
by more than 0.48 atm.  The vapor sample container was pressurized to
approximately 1.36 atm with helium and then both containers were
monitored to insure that the methanol  in the samples did not approach
the point of condensation.  The contents of each container were analyzed
a minimum of five times using the gas  chromatograph.

              MULTICOMPONENT MEASUREMENTS AND  PREDICTIONS
     Multicomponent vapor-liquid equilibrium data were taken for
methanol-carbon  dioxide-nitrogen-hydrogen sulfide mixtures  at  258.15  K
and 273.15  K.   Data are given in Tables  12  and 13.   Four data  points
were taken  at  258.15  K and four more were obtained  at  273.15 K.   At
                                  61

-------
UJ
OC
D
UJ
OC
Q.
     60
     SO
     40
     30
     20
     10
             • DATA OF  KATAYAMA
             • THIS STUDY
        O.O     O.2
0.4
0.6
0.8
1.0
             MOL FRACTION CO - IN LIQUID
                                      2
Figure  10.  Comparison of  Experimentally Determined Equilibrium
           Pressures with Those of Katayama et al. (1975)  for
           Methanol-C02 Mixtures at 298.15 K.
                              62

-------
Table 11    Comparison of Experimental  Vapor-Liquid  Equilibrium
           Data with Those of Katayama et  al.  (1975)  for  Methanol-
           C02 mixtures  at 298.15 K.
p
(atm)
9.39
29.62
46.97
*2
0.070
0.256
0.450
*2b
0.065
0.250
0.420
      Note:  Average percent deviation for x« = 5.4.
      aData of Katayama et al.  (1975).
       Data from this investigation.
each data point, vapor and liquid compositions were determined by gas
chromatographic analysis; five repetitions were conducted on each of
the vapor and liquid samples.  The gas chromatographic analysis pro-
vided the absolute amounts for the four components in the system.
Since it was the composition that was being sought, replicates of every
analysis were normalized so that each replicate indicated the same
amount of carbon dioxide.  Carbon dioxide was chosen for this role
because, over the entire data set, it was the component that was most
significant in both the liquid and the vapor phases.  After normali-
zation, percent deviations for all the other components were calculated.
For liquid sample analysis over the entire data set, the average
percent standard deviation for methanol, nitrogen and hydrogen sul-
                                  63

-------
           Table 12   Experimental  Vapor-Liquid  Equilibrium Data  for  Methanol-
                      Carbon Dioxide-Nitrogen-Hydrogen Sulfide  Mixtures  at  258.15  K
P.atm
9.34
20.75
29.64
40. 1C
XCH3OH
0.9081
0.7680
0.6462
0.7419
Xco2
0.0736
0.2100
0.3312
0.2346
xw
N2
0.0029
0.0031
0.0052
0.0078
XH2S
0.0153
0.0189
0.0209
0.0157
yCH3OH
N.D.a
N.D.a
N.D.a
N.D.a
yco2
0.5400
o.em
0.5892
0.4580
yN
N2
0.4000
0.3654
0.4004
0.5420
yH2S
0.052
0.0235
0.0104
N.D.a
aN.D. = not detected.

-------
en
                               Table  13   Experimental  Vapor Liquid Equilibrium Data for
                                          Methanol-Carbon Dioxide-Nitrogen-Hydrogen Sul-
                                          fide Mixtures at 273.15 K
P.atm
9.2
21.2
29.0
39.8
XCH3OH
0.8997
0.7433
0.6961
0.6872
Xco2
0.0850
0.2339
0.2832
0.2849
xw
N2
0.0019
0.0018
0.0033
0.0074
XH2S
0.0134
0.0211
0.0175
0.0204
yCH3OH
N.D.a
N.D.a
N.D.a
N.D.a
yco2
0.6853
0.8007
0.7720
0.5847
y»2
0.2839
0.1648
0.2026
0.3760
yH2S
0.0308
0.0345
0.0218
0.0393
              aN.D. = not detected

-------
 fide was  0.8,  5.1  and  3.0,  respectively.   In  the  vapor  samples,  the
 amount of methanol  present  was  too  small  to be  detected.   In  the
 vapor sample analysis,  the  average  percent standard deviation for
 nitrogen  and hydrogen  sulfide was 0.7 and  5.1,  respectively.
      The  experimental  temperature and liquid  phase composition were
 used in program  BUBLT  to  predict equilibrium  system pressure  and
 vapor composition.   Comparisons of  predicted  and  experimental results
 at  258.15 K and  273.15  K  are given  in Tables  14 and 15, respectively.
 Over the  entire  data set, the average deviation of pressure was  7.9%
 and the average  deviations  for mole fractions in  the vapor were  7.1%
 for carbon dioxide,  11.7% for nitrogen  and 24.8%  for hydrogen sulfide.
 All  percent deviations  used experimental values as a basis.   The high
 percent deviation obtained  for hydrogen sulfide was partly due to
 the relative insensitivity  of the thermal conductivity  detector  in
 the gas chromatograph to  hydrogen sulfide, especially at low  concen-
 tration.
      Figures 11  and  12  compare the  system pressure predicted  by the
 model  and the experimental  pressure at 258.15 K and 273.15 K, respec-
 tively.   Figures 13 and 14  compare  the predicted  vapor  composition
 and  the experimental vapor  composition at 258.15  K and  273.15 K,
 respectively.  These figures show excellent agreement between model
 predictions and  experimental data.
     Clearly,  the model satisfies  many of the  objectives of this
research project.  Namely, it is now possible  to predict equilibrium
behavior for mixtures of CC^-^S-N,,  and  methanol over  a  limited
temperature range.   Additional  research  1s needed to expand
the range  of the model, to adapt it  to general bubble
                                 66

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                         Table 14   Comparison of Model Predictions with Experimental
                                    Pressure and Vapor Compositions for Methanol
                                    Carbon Dioxide-Nitrogen-Hydrogen Sulfide Mixtures
                                    at 258.15 K
en
         P
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                       Table  15    Comparison of Model  Predictions with  Experimental
                                  Pressure  and Vapor  Compositions for Methane!-Carbon
                                  Dioxide-Nitrogen-Hydrogen Sulfide Mixtures  at
                                  273.15  K
            P(atm)           yCH.OH               yC0
                                                     n
       exptl  model   DPa   exptl  model   Dy   exptl   model      Dy    exptl   model      Dy    exptl  model     Dy


        9.2   12.05   2.85 N.D.C  0.0037   -   0.6853  0.6414  -0.0439  0.2839  0.3227   0.0388  0.0308 0.0322   0.0014

       21.2   22.14   0.94 N.D.C  0.0023   -   0.8007  0.8284   0.0277  0.1648  0.1385  -0.0263  0.0345 0.0308  -0.0037

»      29.0   30.77   1.77 N.D.C  0.0019   -   0.7720  0.7357  -0.0363  0.2026  0.2442   0.0416  0.0218 0.0183  -0.0035

       39.8   39.11  -0.69 N.D.C  0.0017   -   0.5847  0.6286   0.0*39  0.3760  0.3561  -0.0199  0.0393 0.0136  -0.0257
             DP " Pmodel  " Pexptl


             Dy = ymodel  " yexptl
            CN.D.  = not detected

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     50
I           I
                T= 258.15 K
     40
     30
     20
i
      10
                    10
                                          o>
           20
30
40        50
                           PRESSURE, EXPTl,  ATM
   Figure 11.  Comparison of Predicted and Measured Four-Component Mixtures
              at 258.15 K.
                                      69

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    50
    4O   —
    30
    20   —
    10
                          PRESSURE, EXPTL, ATM
Figure  12.  Comparison  of Predicted and Measured Pressures  for
           Four-Component Mixtures at 273.15 K.
                                 70

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   10

   08


   0.6
   0.4

   01


  0.08


  006



  Qj04
  O02
  001
I- ?5B 15 K

0: co2
A- N2
Q: H2s
                                                        I
                                                    I	I
     001      002       004   006  008 0.1        O2


                          VAPOR COMPOSITION,  EXPTL
                                              CM   06  0.8 10
Figure  13.   Comparison of Predicted and  Experimental  Vapor Compositions  for
             Four-Component Mixtures at 258.15 K.
                                 71

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    1.0
    0.8


    0.6
   0.4
B 02
    01

   0.08


   0.06



   004
   0.02
   O.O1
                    I    I
I =273.15 K

O:  co2
A:  N2
D :  HZS
                                               I
                                                                I	I
              OO2        004   006  OO8 0.1        O2

                           VAPOR COMPOSITION, EXPTL
                                              04    0.6  0.8 1.0
Figure  14.   Comparison  of Predicted and  Experimental Vapor Compositions
             for Four-Component  Mixtures  at 273.15 K.
                                 72

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    point,  dewpoint and  flash  calculations,  and  to  include  additional  key
    constituents  of crude coal  gas.

                                 CONCLUSIONS
1.  A thermodynamic model was  developed which successfully  correlated
    vapor-liquid  equilibrium data for the six binary mixtures that can be
    formed from carbon dioxide, hydrogen sulfide,  nitrogen  and methanol.
    The model  uses the Soave modification of the Redlich-Kwong equation
    of state to describe the gas phase, the  four-suffix Kargules equation
    to express activity coefficients, and pure liquids at the temperature
    and pressure  of the system as reference  states.  Margules parameters
    were evaluated from a parameter search procedure known as GMAR.  These
    parameters were found to be functions of temperature, with the func-
    tionality varying according to the binary mixture.
2.  An experimental equilibrium cell, complete with sampling devices and
    gas chromatographic analysis capabilities, was constructed.  The
    apparatus was checked by a favorable comparison of experimentally
    measured equilibrium data to literature data.
3.  Experimental  vapor-liquid equilibrium data were obtained for methanol-
    carbon dioxide-nitrogen-hydrogen sulfide mixtures at 258.15 K and
    273.15 K.  Pressures in these experiments ranged from 6 to 40 atm.
4.  A multicomponent version of the vapor-liquid equilibrium model was
    used to predict vapor compositions and equilibrium pressures based
    on measured liquid compositions and system temperature.  There was
    excellent agreement  between experimental and predicted pressures and
    carbon dioxide and nitrogen vapor mole fractions.  There was fair

                                     73

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agreement between experimental and predicted hydrogen sulfide mole
fractions; this was believed due to poor chromatograph sensitivity to
low hydrogen sulfide concentrations.
                                74

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                                 78

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                                TECHNICAL REPORT DATA
                         (Please read {nUructions on the reverse before completing)
1. REPORT NO.

     -6PP/7-8(bll6_
                     IZ
4. TITLE AND SUBTITLE
Solubilities of Acid Gases and Nitrogen in Methanol
 7 AUTHOFUS)
 J.K. Ferrell, R. W.Rousseau, and J. N. Matange
                                                     3. RECIPIENT'S ACCESSION NO.
                                                      5. REPORT DATE
                                                       May 1980
                                                      6. PERFORMING ORGANIZATION CODE
                                                     8. PERFORMING ORGANIZATION REPORT NO.
 9. PERFORMING ORGANIZATION NAME AND ADDRESS
 North Carolina State University
 Department of Chemical Engineering
 Raleigh, North Carolina 27607
                                                      1O. PROGRAM ELEMENT NO.
                                                     INE825
                                                     11, CONTRACT/GRANT NO.

                                                     Grant R804811
 12. SPONSORING AGENCY NAME AND ADDRESS
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC 27711
                                                     13. TYPE OF REPORT AND PERIOD COVERED
                                                     Final; 9/79-4/80
                                                     14. SPONSORING AGENCY CODE
                                                       EPA/600/13
 15 SUPPLEMENTARY NOTES jERL-RTP project officer is Robert A. McAllister, Mail Drop
 61, 919/541-2160.
 16. ABSTRACT
           The report describes  a thermodynamic model, developed to predict the
 equilibrium behavior of carbon dioxide, hydrogen sulfide,  nitrogen, and methanol
 mixtures. The model uses the four-suffix Margules equation to describe liquid-phase
 nonidealities and the Soave modification of the Redlich-Kwong equation of state to
 describe the gas phase. Model parameters were obtained from previously published
 binary vapor/liquid equilibrium  data. Vapor/liquid equilibrium data were obtained
 experimentally for CO2/H2S/N2/methanol mixtures at temperatures of 258.15 K and
 273.15 K and pressures of 6-40 atm. Model predictions of equilibrium pressure and
 vapor compositions from specifications of temperature and liquid compositions com-
 pared favorably with experimentally measured values.
                             KEY WORDS AND DOCUMENT ANALYSIS
                DESCRIPTORS
 Pollution
 Carbinols
 Solubility
 Gases
 Nitrogen
 Thermodynamics
                    Mathematical Models
                    Carbon Dioxide
                    Hydrogen Sulfide
                                          b.IDENTIFIERS/OPEN ENDED TERMS
                                                                  c.  COS AT I field/Group
                                         Pollution Control
                                         Stationary Sources
                                         Acid Gases
13B
07C
07D

07B
20M
12A
 3. DISTRIBUTION STATEMENT

 Release to Public
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                                                                  21. NO. OF PAGES

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