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Application of the hole quasi-chemical group contribution equation of state for phase equilibrium calculation in systems with association
Fluid Phase Equilibria, 66 (1991) 77- 101
77
Elsevier Science Publishers B.V.. Amsterdam
Application of the hole quasi-chemical group contribution equation of state for phase equilibrium calculation in systems with association A.I. Victorov a~1and Aa. Fredenslund b a Leningrad State University, Chemical Department, Petrodvoretz (U.S.S.R.) b Institut for Kemiteknik,
Universitetsky Prosp., 2, 198904, Leningrad
The Technical University of Denmark, DK-2800, Lyngby (Denmark)
(Received October 22, 1990; accepted in final form March 12, 1991)
ABSTRACT Victorov, A.I. and Fredenslund, Aa., 1991. Application of the hole quasi-chemical group contribution equation of state for phase equilibrium calculation in systems with association. Fluid Phase Equilibria, 66: 77-101. Hole group contribution quasi-chemical model parameters for mixtures containing methanol, water and acetone together with light and heavy alkanes, nitrogen, hydrogen sulfide and carbon dioxide are determined. A list of model parameters is given, encompassing about 30 different functional groups. The results of liquid-gas and liquid-liquid equilibrium calculations for many binary and several multicomponent mixtures at normal and elevated pressures (up to 40 MPa) are discussed.
INTRODUCTION
The topic of the present paper is the description of systems containing substances with strongly interacting molecules, such as alcohols or water, over a wide range of temperatures and pressures. These substances are capable of association via hydrogen bond formation, and their mixtures, especially with non-polar compounds, reveal rather complex concentration behavior, which cannot be described in terms of simple cubic equations of state with conventional mixing - rules. A traditional way to handle such systems is to consider the chemical equilibrium between species present in the mixture. The law of mass action for an assumed association model is ’ Author to whom correspondence 0378-3812/91/$03.50
should be addressed:
0 1991 Elsevier Science Publishers B.V. All rights reserved
78
incorporated into an equation of state, chosen to take into account the non-ideality of the chemically equilibrated mixture (Heidemann and Prausnitz, 1976). Some versions of these equations, containing the chemical equilibrium constants as additional parameters, have been proposed recently (Grenzheuser and Gmehling, 1986; Ikonomou and Donohue, 1987, 1988; Anderko, 1989a,b, 1990a,b). As a rule, satisfactory description of phase equilibria can be achieved, but the results are strongly dependent on the chosen association model. Another approach to the problem is to couple an equation of state with an excess Gibbs energy liquid solution model when deriving mixing rules (Huron and Vidal, 1979). Usually, the local composition GE models are employed, which are capable of representing complex concentration behavior of strongly non-ideal mixtures under low and normal pressures. The resulting equations for mixtures (Mollerup, 1986; Gupte et al., 1986; Danner and Gupte, 1986; Mollerup and Clark, 1989; Gani et al., 1989; Dahl et al., 1990) are flexible enough and perform impressively well. However, they are somewhat empirical in nature, owing to lack of clarity in the underlying molecular model. An alternative way to construct equations of state for complex systems is provided by lattice theories. As is the case with the above mentioned local composition GE models, the rigid lattice quasi-chemical model by Barker and its group contribution versions (Smirnova et al., 1985) can also represent the excess functions of liquid solutions for a variety of mixtures, including ones with associated components. The simplest way to obtain the equation of state from the lattice model is to allow the presence of vacant lattice sites (holes), which are not occupied by the molecular segments. Then the system volume is the sum
0) where V * is the volume of one lattice site, N, is the number of holes, Ni is the number of molecules of kind i (having ri segments), and n is the number of components. The configurational partition function can be written in the conventional form, as a product of two terms (an athermal term and a residual term) as follows: Z(T, V, N,, N;,...,N,) = Z&N,(V),
N,, N2, . . . . N,)Z,,,(T,
giving the equation of state
N,(V),
N,, Nz,...,
N,)
(2)
79
where the athermal parts (subscript “ath”) correspond to the system with purely repulsive interactions. Some practical equations of state based on hole-lattice theory have been proposed (Sanchez and Lacombe, 1976; Ishizuka et al., 1980; Costas et al., 1981; Kleintjens, 1983; Kumar et al., 1986), but none of them take into account the effects of local ordering due to the energetic inhomogeneity of molecular surfaces, e.g. hydrogen bond formation, though it was clear, that such an approach could be implemented (Panayiotou and Vera, 1981,1982). In our version of the hole model (Victorov and Smirnova, 1985; Smimova and Victorov, 1987), hereafter abbreviated as HM, the molecular surface is assumed to be energetically inhomogeneous and is divided into groups. To take into account the effects of orientational ordering (i.e. the ordering between groups) the Guggenheim quasi-chemical approximation is employed for Z,,,. The effects of the molecular size and shape are described with the aid of Staverman’s combinatorial term, Z,,. The model was previously checked for a variety of systems, including compounds of differing molecular mass and polarity, e.g. for long-chain alkanes and alcohols (Smirnova and Victorov, 1987), for typical natural gas component mixtures (Prikhodko et al., 1989), for aqueous mixtures of petroleum reservoir compounds (Victorov et al., 1990), etc. The results of phase equilibrium predictions for a wide range of temperatures (200-650 K) and pressures (even up to 100 MPa) in most cases appeared to be of satisfactory accuracy, at least for technological needs. The main aim of the present paper is to apply the model to some strongly non-ideal mixtures of practical importance, particularly ones containing methanol, acetone and water, over a wide range of pressures. Since the existing HM parameters are to be found in different literature sources, an updated parameter list, including all the estimated model parameters, is also given. In the following section a brief outline of the model is made. Then, some new applications of the HM are discussed, and the comparison with the MHV-2 model (an advanced model of the “Huron-Vidal family” (Dahl et al., 1990)) and AEOS (the modem version of a “chemical equilibrium theory” equation of state, Anderko, 1989a,b; Anderko and Malanowski, 1989) is made. THE MODEL OUTLINE
The equation of state, which comes out of eqn. (2), is n
Pathv * -=
RT
n
C xi1* -In (1 - p) + p
C
xi4i
C
xiri
1___!+-
(4) i=l
where u* is the molar volume per lattice site, x, is the mole fraction of the component i in an n-component mixture Ii = z( r,q,)/2 - ri + 1
(6)
is the molecular bulkiness factor, z is the coordination number, ri and qi are the geometrical parameters characterizing molecular size and surface area; p = u* Cy=rx,ri/u, i.e. the reduced density (u is the system molar volume), and X,, is the solution of the following set of “quasi-chemical” equations: X,
AC
C at X, exp - $ r=O
i
= 1 i
where the indices s and t denote parts of the molecular surface (groups of kind s and t), whose interaction is described in terms of interchange energies AC,, (s = 0 imply holes). In this set of equations (Y,is the surface fraction of groups of kind t in the system. Aest is believed to be temperature-dependent (Kehiaian, 1983) as follows:
Afst RT =t,++h,,(T,-
T)/T+c,,
To-
In $? - 7
T
where asr, h,, and c,~ are the interchange free energy, enthalpy and heat capacity in respectively, units of kTo (dimensionless energetic parameters of the model), and To is some arbitrary reference temperature. The equation of state, eqns. (4-S), is written in the same form for pure and for mixed fluids, and does not incorporate any postulated mixing rules for the latter. It can be reduced to the Sanchez and Lacombe (1976) equation of state for pure components consisting of chain molecules ( li = 0) under the assumption of a random distribution of the molecules upon the lattice (formally it corresponds to infinitely large values of z). The expression for Pathcoincides also with that of Costas et al. (1981), if I, = 0, but in the residual term (5) the preferential pair formation between certain kinds of groups is taken into account by means of the quasi-chemical approximation (7). The model is similar to those, discussed by Panayiotou and Vera (1982), or by Kumar et al. (1987), and is described in more detail elsewhere (Smirnova and Victorov, 1987). For the calculations to be simplified, consider vacancies as an additional component of the mixture, having mole fraction a,,, so that the equation &=I i=O
holds.
81
The chemical potential of the component by the following expression
i, pi, can, via eqn. (1) be related
(9
pi = pi - rip0
to the quantities, defined as
00)
i=O, 1,2 ,..., n
TABLE 1 The mode of subdivision of molecules into functional ters (u* = 14.244 cm3 mol-‘, z =lO) ‘s
groups and their geometrical parame-
Type of group (in molecule)
Group number
1.0 1.0865
0.0 1.0
H_OLE CH2
(1) (2)
1.9621 2.6427 0.0 0.6624 1.9144 2.6551 2.8627 3.9682 4.9728 1.1903 0.0
0.5 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
CH3 S(H2S) 2H(H2S) C(CO2) 2o(CO2) N2 Cl c2
(3) (4) (5) > (6) (7) > (8) (9) (10) (11) (12) (13) >
1.0076 0.0
0.9 0.5
2.5165 0.0
0.1 0.5
1.0318 2.7093 2.2534 2.2242 0.5 0.2142
1.0 0.5 0.5 1.5 0.5 1.5
5.0655 0.0 1.7049 0.0 2.7613 0.0
1.0 0.0 1.0 0.0 0.5 0.5
:HZO) 2H(H20) O(ALKANOL) H(ALKANOL) OH3COO H(CH3COOH) ACH CH2=CH(ENE) WE) ACCOO H(ACCOOH) =CH-(ISO)
(14) (15) >
Substances represented hydrocarbon chain: aIkanes C”( n r 4), alkanols C,( n 2 3), etc. hydrogen sulfide carbon dioxide nitrogen methane ethane propane water aIkanols C”( n 2 3)
(16) (17) 1 (18) (19) (20) (21) (22) >
acetic acid
(24)
isomeric hydrocarbon chain
=C3H6 (ACETONE) =0 (ACETONE)
I;:; >
N(NH3) 3H(NH3) MEOH(MEOH)
(27) (28) I (29) (30) >
benzene aIkenes C, (n 2 5) alkynes C,( n r 5) benzoic acid
acetone ammonia methanol
82 TABLE 2 Model energetic parameters (T, = 298.16 K). For group numbers assignment see Table 1. The absence of any pair of group numbers implies that the corresponding energetic parameters are not available
-
-
-
0.0 0.233900 0.156800 0.190900 0.190900 0.028700 0.028700 0.061600 0.096500 0.141600 0.161300 0.088400 0.088400 0.372100 0.372100 0.100600 0.100600 0.240987 0.175249 0.256104 0.091833 0.091833 0.546953 0.257853 0.401052 0.090887 0.090887 0.235115 0.235115 0.0 0.025600 0.031000 0.031000 0.079400 0.079400 0.048800 0.029400 0.016200 0.024522 0.034476 0.034476 0.016500 0.016500 0.007700
h St
C,t
Type of groups sandt
0.0 0.234200 0.167600 0.521000 0.521000 0.392700 0.392700 0.064600 0.101300 0.144900 0.178500 0.198800 0.198800 0.620100 0.621000 0.035700 0.035700 0.262474 0.133848 0.396458 - 0.829396 - 0.829396 - 1.243084 0.354285 1.908210 0.299452 0.299452 0.332527 0.332527 0.0 0.026200 0.305200 0.305200 0.220900 0.220900 0.017900 0.016700 0.012900 0.034300 0.052595 0.052595 0.114500 0.114500 0.042000
0.0 - 0.006000 - 0.007200 0.070300 0.070300 - 0.595100 - 0.595100 - 0.016900 - 0.024800 -0.018700 - 0.025000 - 0.010400 - 0.010400 - 0.261000 - 0.261000 - 0.002700 - 0.002700 - 0.017988 - 0.106426 - 1.136340 0.0 0.0 - 0.441623 0.266898 - 5.549790 - 0.838840 - 0.838840 - 0.046180 - 0.046180 0.0 0.008100 0.0 0.0 - 0.283400 - 0.283400 - 0.092500 - 0.034500 - 0.028100 - 0.052646 0.210350 0.210350 0.040800 0.040800 0.0
HOLE-HOLE HOLE-CH2 HOLE-CH3 HOLE-S(H2S) HOLE-H(H2S) HOLE-C(C02) HOLE-G(C02) HOLE-N2 HOLE-Cl HOLE-C2 HOLE-C3 HOLE-G(H20) HOLE-H(H20) HOLE-O(ALKANOL) HOLE-H(ALKANOL) HOLE-CH3COO HOLE-H(CH3COOH) HOLE-ACH HOLE-C=C(ENE) HOLE-C=C(YNE) HOLE-ACCOO HOLE-H(ACCGGH) HOLE- =CHHOLE-“CH”(ACETONE) HOLE- =G(ACETONE) HOLE- N(NH3) HOLE- 3H(NH3) HOLE-MEOHOLE-H(MEOH) CH2-CH2 CH2-CH3 CH~-S(H~SJ CH2-H(H2S) CH2-C(C02) CH2-O(C02) CH2-N2 CH2-Cl CH2-C2 CH2-C3 CH2-O(H20) CH2-H(H20) CHZ-G(ALKANOL) CHZ-H(ALIGANOL) CH2-CH3COO
Group numbers
(l-1) (l-2) (l-3) (l-4) (l-5) (l-6) (l-7) (l-8) (l-9) (l-10) (l-11) (1-12) (1-13) (1-14) (1-15) (1-16) (1-17) (1-18) (1-19) (l-20) (1-21) (l-22) (l-24) (l-25) (l-26) (l-27) (l-28) (l-29) (l-30) (2-2) (2-3) (2-4) (2-5) (2-6) (2-7) (2-8) (2-9) (2-10) (2-11) (2-12) (2-13) (2-14) (2-15) (2-16)
83 TABLE 2 (continued)
%
h J,
Gt
Type of groups sandr
Group numbers
- 0.007700 0.004174 0.061292 - 1.588710 - 0.000896 2.070376 0.023865 0.023865 0.0 0.031000 0.031000 - 0.079400 - 0.079400 0.048800 0.029400 0.016200 0.024522 0.034476 0.034476 0.016500 0.016500 - 0.007700 - 0.007700 0.004174 0.061292 - 0.247140 - 0.000896 2.070376 0.023865 0.023865 0.0 - 0.296700 - 0.064290 - 0.064290 0.060500 0.022670 0.014500 0.027000 - 0.025300 - 0.025300 - 1.230226 - 0.023580 - 0.023580 - 0.021884 - 0.021884 0.0 - 0.064290 - 0.954400
0.042000 - 0.083863 0.157375 - 2.334519 - 0.009976 11.13251 0.003641 0.003641 0.0 0.305200 0.305200 0.220900 0.220900 0.017900 0.016700 0.012900 0.034300 0.052595 0.052595 0.114500 0.114500 0.042000 0.042000 - 0.083863 0.157375 - 2.023101 - 0.009976 11.13251 0.003641 0.003641 0.0 2.996200 0.002340 0.002340 0.344600 0.298400 0.297500 0.186200 1.003600 1.003600 - 1.514048 0.543882 0.543882 0.166459 0.166459 0.0 0.002340 6.526200
0.0 0.026822 - 1.226770 - 1 ~I05600 0.470642 - 58.82660 0.050648 0.050648 0.0 0.0 0.0 -0.283400 - 0.283400 - 0.092500 - 0.034500 - 0.028100 - 0.052646 0.210350 0.210350 0.040800 0.040800 0.0 0.0 0.026822 - 1.226770 0.0 0.470642 - 58.82660 0.050648 0.050648 0.0 - 0.338000 5.063800 5.063800 - 0.753400 - 0.429800 - 0.076800 - 0.795100 - 1.565600 - 1.565600 - 7.648420 0.0 0.0 0.0 0.0 0.0 5.063800 - 87.04500
CHZ-H(CH3COOH) CHZ-C=C(ENE) CH2-C=C(YNE) CH2- =CHCH2-“CH”(ACETONE) CH2- =qACETONE) CHZ-ME0 CHZ-H(MEOH) CH3-CH3 CH3-S(H2S) CH3-H(H2S) CH3-C(C02) CH3-qC02) CH3-N2 CH3-Cl CH3-C2 CH3-C3 CH3-qH20) CH3-H(H20) CH3-qALKANOL) CH3-H(ALKANOL) CH3-CH3COO CH3-H(CH3COOH) CHS-C=C(ENE) CH3-C==YNE) CH3- =CHCH2-“CH”(ACETONE) CH2- =qACETONE) CH3-ME0 CH3-H(MEOH) S(HZS)-S S-H(H2S) s-C(CO2) s-o(CO2) S-N2 S-Cl s-c2 s-c3 S-O(H20) S-H(H20) S- =CHS- “CH”(ACETONE) S- =qACETONE) S-ME0 S-H(MEOH) H(HZS)-H H-C(CO2) H-qC02)
(2-17) (2-19) (2-20) (2-24) (2-25) (2-26) (2-29) (2-30) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) (3-13) (3-14) (3-15) (3-16) (3-17) (3-19) (3-20) (3-24) (2-25) (2-26) (3-29) (3-30) (4-4) (4-5) (4-6) (4-7) (4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-24) (4-25) (4-26) (4-29) (4-30) (5-5) (5-6) (5-7) (continued)
84 TABLE 2 (continued)
0.060500 0.022670 0.014500 0.027000 - 0.672500 - 0.025300 - 1.230023 - 0.023580 - 0.023580 - 0.021884 - 0.021884 0.0 - 0.690900 -0.117900 - 0.095600 - 0.091200 -0.110300 1.136338 - 0.507422 - 0.155289 - 1.357070 - 0.099832 - 0.099832 - 0.267875 - 0.093518 0.0 - 0.117900 - 0.095600 - 0.091200 - 0.110300 - 0.507422 - 1.134031 -0.155289 - 1.357070 - 0.099832 - 0.377502 - 0.093518 - 1.988160 0.0 0.064280 - 0.002900 0.035800 0.11OOOo 0.11OOOo - 0.588345 0.072906 0.072906 0.027077
h S,
C*t
0.344600 0.298400 0.297500 0.186200 - 8.828700 1.003600 - 1.514048 0.543882 0.543882 0.166459 0.166459 0.0 0.648500 0.308200 0.180600 0.114600 0.150400 6.483739 - 1.549623 - 0.113199 - 2.698503 0.903197 0.903197 - 0.101255 0.267862 0.0 0.308200 0.180600 0.114600 0.150400 - 1.549623 2.023017 -0.113199 - 2.698503 0.903197 - 14.84510 0.267862 - 3.270630 0.0 - 0.130100 0.232800 - 0.029300 0.531700 0.531700 - 0.590070 0.384260 0.384260 0.188251
-
0.753400 0.429800 0.076800 0.795100 21.25270 - 1.565600 - 7.648420 0.0 0.0 0.0 0.0 0.0 - 2.797300 - 0.168100 - 0.782900 - 1.067600 - 1.017500 - 5.751650 0.421246 4.986721 - 5.558874 0.0 0.0 6.434720 - 2.701920 0.0 - 0.168100 - 0.782900 - 1.067600 - 1.017500 0.421246 - 7.918130 4.986721 - 5.558874 0.0 0.0 - 2.701920 1.227410 0.0 - 0.272500 0.837100 - 0.479500 - 1.326900 - 1.326900 - 0.010040 0.0 0.0 0.325018
Type of groups s and t
Group numbers
H-N2 H-Cl H-C2 H-C3 H-0(H20) H-H(H20) H- =CHH- “CH”(ACETONE) H- =O(ACETONE) H-ME0 H-H(MEOH) C(COZ)-c c-O(CO2) C-N2 C-Cl c-c2 c-c3 C-O(H20) C-H(H20) C-C=C(ENE) C- =CHC- “CH”(ACETONE) C- =O(ACETONE) C-ME0 C-H(MEOH) O(COZ)-0 O-N2 O-Cl o-c2 o-c3 O-O(H20) O-H(H20) 0-C=C(ENE) 0- =CH0- “CH”(ACETONE) 0- =O(ACETONE) O-ME0 0-H(MEOH) N2-N2 N2-Cl N2-C2 N2-C3 N2-O(H20) N2-H(H20) N2- -CH= N2- “CH”(ACETONE) N2- =O(ACETONE) N2-N(NH3)
(5-8) (5-9) (5-10) (5-11) (5-12) (5-13) (5-24) (5-25) (5-26) (4-29) (4-30) (6-6) (6-7) (6-8) (6-9) (6-10) (6-11) (6-12) (6-13) (6-19) (6-24) (6-25) (6-26) (6-29) (6-30) (7-7) (7-8) (7-9) (7-10) (7-11) (7-12) (7-13) (7-19) (7-24) (7-25) (7-26) (7-29) (7-30) (8-8) (8-9) (8-10) (8-11) (8-12) (8-13) (8-24) (8-25) (8-26) (8-27)
85 TABLE 2 (continued) @St
h s*
c*,
Type of groups sandt
0.027077 0.049455 0.088174 0.0 0.023360 0.016600 0.017460 0.017460 -0.911216 0.041106 0.414318 0.024410 0.024410 0.0 0.001600 0.011500 0.011500 - 0.886809 - 0.009868 3.229580 0.024443 - 1.950480 0.0 0.021960 0.021960 - 1.567438 0.025459 - 0.232589 0.013115 - 0.826218 0.0 - 4.988000 - 0.902669 - 0.002289 - 2.071404 - 0.074038 - 4.256760 0.0 - 0.902670 - 0.002289 - 4.587387 - 4.256760 - 0.074038 0.0 - 4.844100 0.287225 0.202719 0.0
0.188251 0.051214 6.369623 0.0 - 0.391860 0.052700 - 0.116800 - 0.116800 0.133408 0.000649 2.940640 0.031732 - 2.077890 0.0 0.141000 - 0.140600 -0.140600 - 1.835540 - 0.009868 3.229580 - 0.037572 - 3.446530 0.0 - 0.086400 - 0.086400 - 2.116688 0.298540 - 2.605305 0.001627 - 1.729440 0.0 - 6.972200 - 3.200302 0.072522 2.718630 - 0.374747 - 5.705090 0.0 - 3.200302 0.072522 - 0.199471 - 5.705090 - 0.374747 0.0 - 0.757470 1.139087 0.759310 0.0
0.325018 0.0 0.0 0.0 - 1.367800 0.415600 0.723900 0.723900 - 5.859100 0.0 0.0 0.0 0.0 0.0 - 0.052000 0.669200 0.669200 - 0.672725 0.0 0.0 - 0.043271 21.95800 0.0 0.761200 0.761200 - 7.573480 - 0.442213 - 5.492830 - 0.014979 0.438674 0.0 2.029000 24.81680 - 0.121601 - 1.576860 - 0.048681 2.168970 0.0 24.81680 - 0.121601 - 32.82200 2.168970 - 0.048681 0.0 - 0.218200 0.0 0.0 0.0
N2-3H(NH3) N2-ME0 NZ-H(MEOH) Cl-Cl Cl-C2 Cl-C3 Cl-O(H20) Cl-H(H20) Cl- -CH= Cl- “CH”(ACETONE) Cl- =O(ACETONE) Cl-ME0 Cl-H(MEOH) c2-c2 C2-C3 C2-0(H20) C2-H(H20) C2- =CHC2- “CH”(ACETONE) C2- --ACETONE) C2-ME0 CZ-H(MEOH) c3-c3 C3-O(H20) C3-H(H20) C3- -CH= C3-“CH”(ACETONE) C3- =O(ACETONE) C3-ME0 C3-H(MEOH) O(H20)-0 O-H(H20) 0- -CH= 0- “CH”(ACETONE) 0- =O(ACETONE) O-ME0 0-H(MEOH) H(HZO)-H H- -CH= H- “CH”(ACETONE) H- =O(ACETONE) H-ME0 H-H(MEOH) O(ALKANOL)-0 0-H(ALKANOL) 0-C=C(ENE) 0-C=C(YNE) H(ALKANOL)-H
Group numbers (8-28) (8-29) (8-30) (9-9) (9-10) (9-11) (9-12) (9-13) (9-24) (9-25) (9-26) (9-29) (9-30) (10-10) (10-11) (10-12) (10-13) (10-24) (10-25) (10-26) (10-29) (10-30) (11-11) (11-12) (11-13) (11-24) (11-25) (11-26) (11-29) (11-30) (12-12) (12-13) (12-24) (12-25) (12-26) (12-29) (12-30) (13-13) (13-24) (13-25) (13-26) (13-29) (13-30) (14-14) (14-15) (14-19) (14-20) (15-15) (continued)
86 TABLE 2 (continued) h **
%r
-
-
-
-
-
0.287225 0.202719 0.0 0.937960 0.0 0.0 0.750289 0.750289 0.053200 0.815509 0.0 0.0 0.0 7.466638 0.0 0.0 0.965361 7.514690 1.220540 1.220540 0.0 0.385174 0.~5~ 0.004540 0.0 0.004540 5.603040 0.0 1.989642 0.198847 1.827563 0.0 1.827563 0.198847 0.0 4.146474 0.0
1.139087 0.759310 0.0 - 14.06360 0.0 0.0 - 2.288639 - 2.288639 - 0.049053 - 2.420315 0.0 0.0 0.0 - 7.426928 0.0 0.0 4.015690 0.516438 - 0.287602 - 0.287602 0.0 3.166760 0.083805 0.083805 0.0 0.083805 - 0.649868 0.0 - 1.742137 - 0.204625 - 1.766863 0.0 - 1.766863 - 0.204625 0.0 - 6.601423 0.0
Type of groups sandt
Group numbers
0.0
H-C==C(ENE)
0.0 0.0
H-WE)
(15-19) (15-20) (16-16) (16-17) (17-17) (18-18) (18-21) (18-22) (18-27) (18-28) (19-19) (20-20) (21-21) (21-22) (22-22) (24-24) (24-25) (24-26) (24-29) (24-30) (25-25) (25-26) (25-29) (25-30) (26-26) (26-29) (26-30) (27-27) (27-28) (27-29) (27-30) (28-28) (28-29) (28-30) (29-29) (29-30) (30-30)
car
0.~25~ 0.0 0.0 0.0 0.0 0.976358 4.774510 0.0 0.0 0.0 0.0 0.0 0.0 138.3910 - 0.001616 0.0 0.0 0.0 - 0.547888 0.0 0.0 0.0 0.0 0.0 0.0 - 4.576230 - 1.550740 0.134267 0.0 0.134267 - 1.550740 0.0 2.583120 0.0
CH3COO-CH3COO ~H3C~-H(CH3C~~ H(CH3COOH)-H ACH-ACH ACH-ACCOO ACH-H(ACCOOH) ACH-N(NH3) ACH-3H(NH3) C=@NE)-C=C C=C(YNE)-C=C ACCOO-ACCOO ACCOO-H(ACCOOH) H(ACCOOH)-H =c- - =CH=CH- “CH”(ACETONE) ==CH- =O(ACETONE) =CH- -ME0 =CH- -H(MEOH) “CH”(ACETONE)-“CH” “CH”- ==O(ACETONE) “CIP-ME0 “CH’‘-H(MEOH) *ACETONE) - -0 =0-ME0 =o - H(MEOH) N(NH3)-N N-3H(NH3) N-ME0 N-H(MEOH) 3H(NH3)-3H 3H(NH3)-ME0 3H(NH3)-H(MEOH) MEO-ME0 MEO-H(MEOH) H(MEOH)-H
where F is the Helmholtz free energy. Notice, that the system volume is not fixed in the derivatives (lo), so the pi are exactly the quantities which play the role of chemical potentials in the lattice theories without vacancies (Smimova et al., 1985). The quantity PO for holes is closely connected with the system pressure f+=
-- v*p RT
87
Hence the condition of phase equilibrium for an n-component be written in the form pt.*’ = p(J) i-0,1,2 ,..., n I
mixture may 02)
t
which includes also the condition of mechanical equilibrium (i = 0) between phases (Yand /3. The last set of equations can be rewritten in terms of “rigid lattice activity coefficients” by means of eqn. (lo), leading us to i=O,
( CxiYi)@) = ( “Ji)@)
1,2 ,..., n
(13)
with yi determined by eqns. (14)-(18). In Y, = In Y&i + ln Yresi In Yathi= -{qi
ai = ail;:/
04)
cp. a$ in-j+ - e+l
(
I
I
+ln:-:+l I
1
05)
I
i airi i=o
(16)
e, = aiqi/ 5 aiqi
(17)
i=O In
(18)
Yresr= z C &i In (X/X,(i)) s=o
Here X, and XSCijare the solutions of eqn. (7) related to the system under consideration and to the standard state one: a hypothetical system, containing only particles of kind i (either molecules of the ith component or holes).
TABLE 3 The accuracy of pure component saturation pressures (6P) and liquid densities (6~) with the aid of the hole group-contribution model (HM), Anderko’s (1989) equation of state (AEOS), and the conventional form of the Peng-Robinson equation Substance
Range of T(K)
Averaged relative deviations
ww Water Methanol Decanol Hexadecanol Methane Decane Hexadecane Acetone Carbon dioxide Hydrogen sulfide
323-633 273-503 293-553 333-617 95-185 273-433 411-482 220-500 216-300 255-366
SP(W
HM
AEOS
1.3 0.8 1.6 2.7 0.8 4.1 5.4 3.2 0.4 0.8
0.8 0.3 0.7 3.1 0.5 0.3 1.7 -
PR 3.6 3.3 2.2 5.4 21.0 1.7 2.0
HM
AEOS
PR
0.5 0.8 1.2 1.5 1.8 0.5 0.6 1.6 1.2 1.7
8.0 3.9 3.4 1.1 6.7 1.3 4.5 -
26.5 24.0 8.3 6.7 9.1 5.3 5.5
88 TABLE 4 The accuracy of representation of binary liquid-gas equilibrium in the methanol and acetone containing systems by the hole group-contribution model System
NB
Conditions T(K)
MeOH-H,O
Deviations PA
SPc
(bar)
5%
10 12
298.16 373.16
11
473.16
38
6
523.16
65
0.1 3.3
0.9 ,::; (Z (:::
MeOH-acetone
12
298.16
0.3 1::;
14
328.16
1.0 1:::
12
372.79
15
423.16
3.8 (;:Z 12 ,Y:Z [0.6
10
473.16
40 ,‘,:: [1.2
MeGH-CO,
5 13
273.16 298.16
33 60
5
313.16
79
Ay* (mol%)
Reference to the experiment
1.4 0.9 1.0) = 1.0 1.2) 3.9 1.3)
Hall et al., 1979 Griswold and Wong, 1952
1.7 1.71 = 0.6 0.41 0.8 1.1) 2.1 1.8) 1.61 3.2 3.1) 3.11
Tamir et al., 1981
4.1
Freshwater and Pike, 1967 Wilsak et al., 1986 Griswold and Wong, 1952
0.1 0.11 0.4 0.51
Weber et al., 1984 Katayama et al., 1975 Ohgaki and Katayama, 1976
1.5 1.2
-
Weber, 1981
,::; 1::: MeOH-H2S
4 4
258.16 273.16
MeOH-N,
5 5 5
250 275 300
179 175 178
4.8 3.3 3.1
-
Weber et al.. 1984
MeOH-C,
11 12 12 11
250.03 273.16 290.0 330.0
414 414 414 414
6.5 5.4 5.9 5.4
0.08 0.15 0.16 0.33
Hong et al., 1987
MeGH-C,
11 5 5
273.16 298.16 373.16
23 41 60
-
Zeck and Knapp, 1986 Ma and Kohn, 1964
8 6
313.1 343.1
14 25
8
373.1
43
0.6 1.5 1.61 2.5 2.01
MeOH-Cs
5.9 10
4.4 Galivel-Solastionk et al., 1986
89 TABLE 4 (continued) System
N a
TK
P,& (bar)
Ayd (mol%)
6Pc %
Reference to the experiment
1.0
1.8
5.9
Budantseva et al., 1975
1.0 8.3 25
Pr: ‘4.6 4.2 3.5
4.9 2.5 2.7
Budantseva et al., 1975 Wilsak et al., 1987
298.16
0.3
2.3 2.21
Iguchi, 1978
308.16
0.5
Pr: 2.0 Il.9 Pr: 1.6 [1.2 2.5 [2.1 0.4
11 -
MeGH- ho-C,
11
297.15337.85
MeOH-C,
11 9 9
338-303 372.69 422.59
MeGH-C,
7 10
Acetone-H,0
Deviations
Conditions
2.5
Wolf and Hoeppel, 1968
II
17
348.16
1
473.02
18
308.16
0.4
1.5
2.0
18
373.16
3.7
18
473.16
28
1.8 (1.5 0.7 (2.7
8
523.16
63
0.9 0.6) 0.8 1.1) 2.5 0.7)
50
(::: 1.0 1.5
De Loos et al., 1988 Lieberwirth and Schuberth, 1979 Griswold and Wong, 1952
13 12
298.16 313.16
Acetone-H,S
1 1
263.16 298.16
Acetone-N,
3 2 3 1
223.16 258.16 283.16 308.16
63 63 61 55
Acetone-C,
10 12
298.16 323.16
120 120
Acetone-C,
7
298.16
Acetone-C,
4 4 4 4 3
325.16 350 375 400 425
Acetone- isoX,
3
278-318
1.0
5.3
Acetone- isoX,
10
298-330
1.0
3.1
1.6
Budantseva et al., 1981
Acetone-C,
11 12 8
258.16 298.16 372.69
0.1 0.8 6.6
Pr: 4.7 1.3 Pr: 1.2
3.4 1.4 2.2
Rall and Schaefer, 1959
Acetone-CO*
61 73 1.0 1.0
0.4 0.7
0.0 0.0
Katayama et al., 1975 Short et al., 1983
1 x100.01 0.04 0.2
Hicks and Prausnitz, 1981
3.8 2.9
0.1 0.2
Yokoyama et al., 1985
39
1.7 [2.8
0.2 0.31
Ohgaki et al., 1976
13 20 30 42 47
0.6 0.6 1.1 1.3 1.5
2.4 2.8 3.6 7.6 7.4
Gomez-Nieto and Thodos, 1978
Zhang and Hayduk, 1984
Campbell et al., 1986
90
TABLE 4 (continued) System
NB
Conditions TK
Deviations d
P&
SP”
(bar)
%
;:OF%)
Reference to the experiment
Acetone-C,
9 15 9
293.16 313.16 328.16
0.3 0.7 1.2
Pr: 4.4 Pr: 2.0 2.5
2.6 0.9 1.1
Rall and Schaefer, 1959 Kolasinska et al., 1982 Kudryavtseva and Susarev, 1963
Acetone-C,
7 8
313.16 338.16
0.6 1.4
Pr: 0.8 2.2
0.3 1.3
Acetone-C, Acetone-C,e
19 19
333.16 313.16
0.8 0.6
Pr: 1.7 Pr: 2.0
Acetone-C,, Acetone-C,,
9 15 8
338.16 333.16 333.16
1.3 1.0 1.0
,::,’ Pr: 3.8 Pr: 3.9
0.1 0.0 0.1 0.21 -
Kolasinska et al., 1982 Maripuri and Ratcliff, 1972a Kolasinska et al., 1982 Maripuri and Ratcliff, 1972b Messow et al., 1977
a Number of experimental points. b Maximum pressure in an experimental data set. ’ Average relative deviations between calculated and experimental bubble pressures. d Mean absolute deviation of vapor composition. ’ Values of deviations in square brackets and parentheses correspond to the correlations of Anderko (1989a-c) (AEOS) and Dahl et al. (1990) (MHV-2), respectively. f Pr: predicted; otherwise correlated. Equations (15) and (18) are then identical to those for the activity coefficients in the rigid lattice theory if holes are treated as a component of the mixture. The set of equations (13) determines the equilibrium parameters of any two coexistent phases (Yand /3 (vapor, liquid or supercritical fluid), and was used in the present work for phase equilibrium calculations. This set of equations has the same form for mixtures and pure substances. The model has geometrical ( r,, e) and energetic ( ast, h,,, cst) parameters, which, except for q,, were adjusted using some experimental data. The r, parameters were obtained from pure component data only. To get energetic parameters it was often necessary to apply the experimental data for the binary mixtures. The qs parameters can be calculated from r, values and eqn. (6), employed for groups, when we prescribe some value to I, factors of groups, building up the molecule. These I, values were established for every substance considered, using some simple models of the molecular structure, e.g. treating the molecule as a chain, ring, etc. (Smimova and Victorov, 1987; Prikhodko et al., 1989). From the additivity of rj and qi we get the following for the bulkiness factor of a molecule as a whole:
li =
c
(1, - 1) v,, + 1
s
where vsi is the number of groups of type s in molecule i.
(19)
91
.O 0
E:
s
8
z
z 22 Mb’
0 0
4
/
d
+o 8
8
::
6
92
As in any group-contribution approach the number of parameters depends on how we subdivide the molecule into groups. The mode of this subdivision and the available values of geometrical parameters of groups (prescribed Z, and estimated rs) are summarized in Table 1. Often it is desirable to decrease the number of energetic parameters, distinguishing only between specific and non-specific interactions in the system. For pure water, for instance, we may distinguish between H and 0 groups, but use only two interchange energies: one for hydrogen bond formation ( Aeo_u), and the other, averaged ( Ae~H20~_hole),for the remaining interactions. Thus, treating water molecules as energetically homogeneous, unless O-H contact is formed, we have: 00-hole
= WH-hole
= W(H,O)-hole
#
wO-H
Analogous relations are assumed hereafter for the h,, and c,~ parameters. Simplifications of this kind were made for mixtures as well. For example, to describe water-alkane, or water-nitrogen mixtures one averaged interchange energy was used: wH-x
= 00-x
= w(H,O)-x
CO2 37X; (a)200.00
METHANOL 323U
q
(b) 80.00
60.00
CO2 - METHANOL T=298.16U
-
0.00 0.4
0.0
xl
mol.fraction
0.8
0.0
0.4
xl
0.8
mol.fraction
Fig. 2. The predicted (a) and correlated (b) liquid-gas phase behavior for the CO2 (l)methanol(2) binary (full lines). Experimental data from: (a) Semenova et al., 1979 (*, T = 373.16 K; 0, T = 323.16 K); (b) Katayama et al., 1975.
93
where x denotes C,-C, alkane or N, molecules, or groups CH, and CH,. These latter groups were believed to be energetically equivalent with respect to the water molecules, that is W(H,O)-CH,
=
W(H,O)-CH,
=
W(H,O)-“CH,”
although in some cases we distinguish between the interactions with CH, and CH, groups, which proved to be important, e.g. when describing alkane mixtures. Further details of the interaction energy assignments for different groups can be followed from Table 2, which contains the updated list of the model energetic parameters. RESULTS OF THE CALCULATIONS
In this work the model was applied to pure methanol and acetone, and to mixtures containing these compounds, mainly with constituents of natural gases and oils (see Table 4 for the list of binaries). The model parameters for methanol and acetone (Tables 1 and 2) were estimated, fitting the experimental liquid density and saturated vapor pressure data for these pure substances. Table 3 shows the results of this fit, and
METHANE T=323.16K
xl
ACETONE
mol.fraction
Fig. 3. Liquid-gas equilibrium phase behavior in the methane(l)-acetone(2) lines). *, experiment (Yokoyama et al., 1985).
binary (full
94
some examples of the model’s performance for other compounds compared with that of the AEOS and Peng-Robinson equations are included as well. The interaction parameters for mixtures (Table 2) were estimated from binary liquid-vapor equilibrium data, selected to represent a wide range of temperatures and pressures. In Table 4 the accuracy of the binary liquid-gas equilibrium description is given. Some experimental data sets were not used in the parameter estimation, and these, serving as examples of prediction, are indicated ‘Pr:’ in Table 4. For the majority of the mixtures considered, the components are represented by individual groups, as in the methanol-carbon dioxide, methanolethane and methanol-propane systems, and for such binaries at least some experimental points are always needed to determine the interaction parameters. Some examples of calculated phase diagrams for a wide range of temperatures and pressures are given in Figs. l-4. In most cases the performance of the model is quite good (note that the data at 508 K in Fig. lb appear to be erroneous). With the aid of the HM it is often possible not
s
m
50.00
:
30.00
1
ETHANE - METHANOL 298K, 273K; 260K
\ CL 20.00 1
x1
mol.fraction
Fig. 4. Liquid-liquid-vapor equilibrium phase behavior in the ethane(l)-methanol(2) system: calculated (- - -) and experimental (. - .- 0) liquid-liquid-vapor coexistence lines; saturated liquid line (*, experimental; full line, calculated). Horizontal solid lines are the calculated liquid-liquid tie lines. Experimental data by Zeck and Knapp, 1986.
95
only to represent the experimental data (Figs. 2b and 3), but also to predict, at least in some cases, the diagrams for conditions far beyond those for which the parameters were estimated (Fig. 2a). In the case of mixtures containing n-alkanes from butane upwards, which were treated in a group contribution manner, it was sufficient to use only a few data sets for the parameter evaluation (Table 4). For the methanol-alkane family of binaries, this enables us to predict the solubility of n-butane in methanol with an average accuracy of 0.7 mol% in the temperature range 298-313 K (see Miyanov and Hayden, 1986 for experimental data), and the phase behavior of the methanol-n-alkane mixture series, as is shown in Fig. 5a-d. In agreement with experiment the model predicts limited miscibility of methanol with aIkanes (Figs. 4 and 5a), the calculated miscibility gap being somewhat wider than the experimental one. This gap disappears when the temperature is raised (Fig. 5b-d). The model reflects correctly the dependence of the upper critical consolution temperature (and of the critical composition) upon alkane chain length, but the deviations from the corresponding experimental values (Bernabe et al., 1988) are large. For example, the calculations still reveal phase splitting for the methanol-hexane system at 330 K, being almost 30 K above the experimental consolution point. The predictions are similar to those of the AEOS (Anderko and Malanovsky, 1989).
TABLE 5 Liquid-gas equilibrium predictions for multicomponent mixtures using the HM (bubble point calculations). 6(ln Kc,,) is the averaged absolute deviation for the logarithm of the component i K-value: Kc,, = y,/x, System
T, P range
6P(W)
by
Ref. a
(mol%)
a(Ln Kc,,) (1) (2)
(3)
Acetone + MeOH + C,
372.1 K 5-8 bar
5.5
1.7
0.07
0.09
0.04
1
Acetone + MeGH + H,O
330-523 K l-81 bar
‘.’
3.3
0.22
0.15
0.10
2,3
2.0
-
-
-
4
-
-
-
-
C,+C,+C,+N,+ + CO2 f H,S H,O+N, +CO, +C, + +c,+c,+c,+ + i.w-C4 + C,
185-236 K 27-80 bar
4 1
333-393 K 50-250 bar
42
. ’
a 1, Wilsak et al., 1987; 2, Kato et al., 1971; 3, Griswold Robinson, 1979; 5, Zuo, 1989.
5
and Wong, 1952; 4, Kalra and
96 METHANOL T= 298.16K
(a) 0.40
-
HEXANE I
HEXANE 473K;448K
METHANOL
(b)s.oo
0.30
4.00
I
2
: I
3.00
\ a
2.00
1 .oo
000
1 0.0
I
I
1
0.4
x
1 mol.fraction
I
4
0.8
0.00
’
0.4
0.0 x
HEPTANE 498K; 473K;
METHANOL 448K; 423K
b-38 00
WI8
00
0.8
mol.fraction
DECANE 498K; 473K;
METHANOL 448K; 423K
q
6.00
6.00
u
2 I
5 \4
1
\4.00
00
a
a
2.00
2.00
I !
0.0
x1
mol.fraction
I
I
0.4
x 1 mol.fraction
I
0.8
97 060
ACETON E T= 31: i.15K
7
DECANE
0 20
0.10
xl
mol.fraction
Fig. 6. The predicted phase diagram for the acetone(l)-decane(2) lines); experimental data (*) by Kolasinska et al., 1982.
system at 313.16 K (full
It should be mentioned also, that for the propane-methanol mixture at 313.1 K (Table 4) the HM predicts phase splitting which has not been observed experimentally (Galivel-Solvastionk et al., 1986), though the experimental bubble curve is rather flat, indicating the trend of the mixture towards phase splitting. Despite quite accurate description of the experimental data, an analogous result was obtained for the acetone-ethane binary at 298.16 K which is also an example of a strongly non-ideal mixture possessing a flat bubble pressure curve. Good results are obtained when predicting the azeotropic behavior of acetone-alkane and methanol-alkane mixtures (Fig. 5), but again, when the
Fig. 5. The calculated (full lines) and experimental (points) phase diagrams for the binaries of the methanol-alkane family. (a) Vapor-liquid-liquid diagram for the methanol(l)-hexane(2) system at 298.16 K. Experimental data by Iguchi, 1978 (*), and by Huang and Robinson, 1977 (0). The experimental miscibility gap is shown (- - -). (b) Vapor-liquid-equilibrium for the system hexane(l)-methanol(2) at 448.16 K and 473.16 K (experiment at data by De Loos et al., 1988 and Zawisa, 1985). (c,d) Vapor-liquid-equilibria for the heptane(l)methanol(2) and decane(l)-methanol(2) binaries, respectively, at 423.16 K, 448.16 K, 473.16 K, 498.16 K (experimental data by De Loos et al., 1988). In (c) the location of the experimental binary critical regions is sketched (- - -).
98
TABLE 6 Liquid-gas equilibrium calculations)
predictions for multicomponent T, P range
System
mixtures using the HM (P, T-flash Ref. a
a(m K,,,)
(1)
(2)
(3)
(4)
MeGH + COa + N,
273 K 50-125 bar
0.05
0.05
MeOH+C,+N,
260 K 15-75 bar
-
0.11
0.03
2
MeOH + CO2 + C,
343 K 5-22 bar
0.24
0.12
0.03
3
258-273 K 9-40 bar
0.44
0.12
0.22
0.48
4
311-450 K 48-173 bar
0.19 (0.14
0.15 0.11
0.15 0.09
0.75 b 0.19)
5
MeOH + CO2 + N, + + H,S C, +COz +H,S+H,O
(
1
’ 1, Weber et al., 1986; 2, Zeck and Knapp, 1986; 3, Gahvel-Solvastionk Rousseau et al., 1981; 5, Huang et al., 1985. b MHV-2 model.
et al., 1986; 4,
system is near the formation of a critical phase (Fig. 5c, T = 498.16 K), the type of predicted diagram could be erroneous, even though the deviations between experimental and calculated pressures are not necessarily large. In Fig. 6 a typical example of the liquid-vapor equilibrium prediction for an acetone-alkane mixture is presented. The comparison with the MHV-2 model and with the AEOS can be made (Table 4), though with the latter equation separate parameters are used for each isotherm. In the case of our model or the MHV-2 model unique parameter sets for all the temperatures were used. Nevertheless, this information allows us to conclude that all three models are of approximately the same level of accuracy for liquid-gas equilibrium calculations. The HM predictions for multicomponent mixtures seem to be reasonable (Tables 5 and 6). For the last mixture, shown in Table 6, the MHV-2 model gives somewhat better equilibrium ratios than the HM. However, as expected, the MHV-2 model in general gives much poorer liquid volume predictions than the HM model does (Prikhodko et al., 1989; Victorov et al., 1990). CONCLUSIONS
The hole group-contribution quasi-chemical model has been used to predict phase equilibria in binary and multicomponent systems containing
99
associating substances over a wide range of temperatures and pressures. The accuracy of the model has been found to be sufficient for industrial applications for a variety of mixtures (strongly polar and non-polar, light and heavy compounds). An updated model parameter list is presented, permitting predictions of phase equilibria for many mixtures of practical importance, e.g., for those of natural gas/oil components together with acetone, methanol and water.
ACKNOWLEDGMENT
The authors are thankful to Prof. P. Rasmussen for carefully reading the manuscript and for his many helpful suggestions.
REFERENCES Anderko, A., 1989a. Fluid Phase Equilibria, 50: 21-52. Anderko, A., 1989b. Fluid Phase Equilibria, 45: 39-67. Anderko, A., 1990a. Equation of state methods for the modeling of phase Equilibria. Fluid Phase equilibria, submitted for publication. Anderko, A., 1990b. Personal communication. Anderko, A. and MaIanowski, S., 1989. Fluid Phase Equilibria, 48: 223-241. Bernabe, D., Romero-Martinez, A. and Trejo, A., 1988. Fluid Phase Equilibria, 40: 279-288. Budantseva, L.S., Lesteva, T.H. and Nemtsov, M.S., 1975. Zh. Fis. Khim. (Russian), 49: 1847. Budantseva, L.S., Evstigneev, A.Yu., Lesteva, T.M., 1981. Prom-St Sint. Kauch. (Russian), 11: 7. Campbell, S.W., WiIsak, R.A. and Thodos, G., 1986. J. Chem. Eng. Data, 31: 424. Costas, M., Epstain, H.I., Sanctuary, B.C., Richon, D. and Renon, H., 1981. J. Phys. Chem., 85: 1264, 3153-3160. DahI, S., Fredeslund, Aa. and Rasmussen, P., 1990. SEP publication 9008, Institut for Kemiteknik, The Technical University of Denmark. De Loos, Th. W., Poot, W. and De Swaan Arons, 1988. Fluid Phase Equilibria, 42: 209-227. Danner, RP. and Gupte, P.A., 1986. Fluid Phase Equilibria, 29: 415-430. Donohue, M.D. and Prausnitz, J.M., 1987. AIChE J., 18: 1184-1191. Freshwater, D.C. and Pike, K.A., 1967. J. Chem. Eng. Data, 12: 179. Gahvel-Solvastionk, K.F., Langier, S. and Richon, D., 1986. Fluid Phase Equilibria, 28: 73-85. Gani, R., Tzouvaras, N., Rasmussen, P. and Fredenslund, Aa., 1989. Fluid Phase Equilibria, 47: 133-153. Gomez-Nieto, M. and Thodos, G., 1978. Chem. Eng. Sci., 33: 1589. Grenzheuser, P. and Gmehhng, J., 1986. Fluid Phase Equilibria, 25: l-29. Griswold, J. and Wong, S.Y., 1952. Chem. Eng. Progr. Symp. Ser., 48: 18. Gupte, P.A., Rasmussen, P. and Fredenshmd, Aa., 1986. Ind. Eng. Chem. Fundam., 25: 636-645. Hall, D.J., Marsh, C.J. and Pemberton, R.C., 1979. NPL Rept. Chem., January: 95.
100 Heidemann, R.A. and Prausnitz, J.M., 1976. Proc. Nat. Acad. Sci. USA, 73: 1773. Hicks, P.J. and Prausnitz, J.M., 1981. J. Chem. Eng. Data, 26: 74. Hong, J.H., Malone, P.V., Jett, H.D. and Kobayashi, R., 1987. Fluid Phase Equilibria, 38: 83-90. Huang, S.S., Len, A.D., Ng, H.G. and Robinson, D.B., 1985. Fluid Phase Equilibria, 19: 21-32. Huron, M.J. and Vidal, J., 1979. Fluid Phase Equilibria, 3: 255-271. Iguchi, A., 1978. Kagaku So&i, 20: 66. Ikonomou, G.D. and Donohue, M.D., 1987. Fluid Phase Equilibria, 33: 61-90. Ikonomou, G.D. and Donohue, M.D., 1988. Fluid Phase Equilibria, 39: 129-159. Ishizuka, I., Sarashina, E., Arai, Y. and Saito, S., 1980. J. Chem. Eng. Jpn., 13: 90-97. Lieberwirth, I. and Schuberth, H., 1979. Z. Phys. Chem. (Leipzig), 260: 669. Kaha, H. and Robinson, D.B., 1979. Fluid Phase Equilibria, 3: 133-144. Katayama, T., Ohgaki, K., Maekana, G., Goto, M. and Nagano, T., 1975. J. Chem. Eng. Jpn, 8: 89. Kato, M., Sato, T., Konishi, H. and Hirata, M., 1971. J. Chem. Eng. Jpn., 4: 311. Kehiaian, H.V., 1983. Fhtid Phase Equilibria, 13: 243-252. Kleintjens, L.A., 1983. Fluid Phase Equilibria, 10: 183-190. Kolasinska, G., GoraI, M. and Giia, J., 1982. Z. Phys. Chem. (Leipzig), 263: 151. Kudryavtseva, L.S. and Susarev, M.P., 1963. Zh. PrikI. Khim. (Russian), 36: 1471. Kumar, S.K., Suter, V.W. and Reid, R.C., 1986. Fluid Phase Equilibria, 29: 373-382. Kumar, S.K., Suter, V.W. and Reid, R.C., 1987. Ind. Eng. Chem., 26: 2532-2542. Ma, Y.H. and Kohn, J.P., 1964. J. Chem. Eng. Data, 9: 3-5. Maripuri, V.C. and Ratcliff, G.A., 1972a. J. Chem. Eng. Data., 17: 36. Maripuri, V.C. and Ratcliff, G.A., 1972b. J. Appl. Chem., 22: 899. McGlashan, M.I. and Williamson, A.G., 1976. J. Chem. Eng. Data, 21: 196. Messow, U., Doye, U., Kuntzsch, S. and Kuchenbecker, 1977. Z. Phys. Chem. (Leipzig), 258: 90. Miyanov, Y. and Hayden, W., 1986. J.-Chem. Eng. Data, 31: 77. Mollerup, J.M., 1986. Fluid Phase Equilibria, 25: 323-327. Mollerup, J.M. and Clark, W.M., 1989. Fluid Phase Equilibria, 51: 257. Ohgaki, K. and Katayama, T., 1976. J. Chem. Eng. Data, 21: 53-54. Ohgaki, K., Sano, F. and Katayama, T., 1976. J. Chem. Eng. Data, 21: 55-58. Olevsky, V.M., 1956. Trudy GIAP (in Russian), 6: 45. Panayiotou, C. and Vera, J.H., 1981. Can. J. Chem. Eng., 59: 501-506. Panayiotou, C. and Vera, J.H., 1982. Polym. J., 14: 681-694. Prikhodko, I.V., Schmeltzer, J., Victorov, A.I. and Smirnova, N.A., 1989. J. Appl. Chem. (Russian), 62: 2734-2737. RalI, W. and Schaefer, K., 1959. Z. Elektrochem., 63: 1019. Rousseau, R.W., Matange, J.N. and FerreIl, J.K., 1981. AIChE J., 27: 605-613. Sanchez, I.C. and Lacombe, R.H., 1976. J. Phys. Chem., 80: 2568-2580. Semenova, A.I., Emel’yanov, E.A., Tsimmerman, S.S. and Tsikhs, D.S., 1979. Zh. Fis. Khim. (Russian), 53: 1426. Short, I., Sahgal, A. and Hayduk, W., 1983. J. Chem. Eng. Data, 28: 63. Smirnova, N.A. and Victorov, A.I., 1987. Fluid Phase Equilibria, 34: 235-263. Smimova, N.A., Piotrovskaya, E.M. and Victorov, A.I., 1985. J. Appl. Chem. (Russian), N6, 1261-1265. Tamir, A., Apelblat, A. and Wagner, M., 1981. Fluid Phase Equilibria, 6: 113. Victorov, A.I. and Smirnova, N.A., 1985. In: Proceedings of VII Mendeleev’s discussions (in Russian). Kharkov, pp. 37-42.
101
Victorov, A.I., Fr~enslund, Aa. and Smimova, N.A., 1990. Fluid Phase Equilibria, 66: 187-210. Weber, W., 1981. Ph.D.thesis, Berlin. Weber, W., Zeck, S. and Knapp, H. 1984. Fluid Phase Equilibria, 18: 253-270. Wilsak, P.A., Campbell, S.W. and Thodos, G., 1986. Fluid Phase Equilibria, 28: 13. Wilsak, P.A., Campbell, S.W. and Thodos, G., 1987. Fluid Phase Equilibria, 33: 173-190. Wolf, H. and Hoeppel, H.E., 1968. Ber. Bunsenges. Phys. Chem., 72: 710. Yokoyama, O., Masuoka, M., Arai, K. and Saito, S., 1985. J. Chem. Eng. Data, 30: 177. Zawisa, A., 1985. J. Chem. Thermodyn., 17: 941-947. Zeck, S. and Knapp, H., 1986. Fluid Phase Equilibria, 25: 303-322. Zhang, G. and Hayduk, W., 1984. Can. J. Chem. Eng., 62: 713. Zuo, Y.X., 1989. Ph.D.thesis, Beijing Graduation School, Univ. Petrol., China.
77
Elsevier Science Publishers B.V.. Amsterdam
Application of the hole quasi-chemical group contribution equation of state for phase equilibrium calculation in systems with association A.I. Victorov a~1and Aa. Fredenslund b a Leningrad State University, Chemical Department, Petrodvoretz (U.S.S.R.) b Institut for Kemiteknik,
Universitetsky Prosp., 2, 198904, Leningrad
The Technical University of Denmark, DK-2800, Lyngby (Denmark)
(Received October 22, 1990; accepted in final form March 12, 1991)
ABSTRACT Victorov, A.I. and Fredenslund, Aa., 1991. Application of the hole quasi-chemical group contribution equation of state for phase equilibrium calculation in systems with association. Fluid Phase Equilibria, 66: 77-101. Hole group contribution quasi-chemical model parameters for mixtures containing methanol, water and acetone together with light and heavy alkanes, nitrogen, hydrogen sulfide and carbon dioxide are determined. A list of model parameters is given, encompassing about 30 different functional groups. The results of liquid-gas and liquid-liquid equilibrium calculations for many binary and several multicomponent mixtures at normal and elevated pressures (up to 40 MPa) are discussed.
INTRODUCTION
The topic of the present paper is the description of systems containing substances with strongly interacting molecules, such as alcohols or water, over a wide range of temperatures and pressures. These substances are capable of association via hydrogen bond formation, and their mixtures, especially with non-polar compounds, reveal rather complex concentration behavior, which cannot be described in terms of simple cubic equations of state with conventional mixing - rules. A traditional way to handle such systems is to consider the chemical equilibrium between species present in the mixture. The law of mass action for an assumed association model is ’ Author to whom correspondence 0378-3812/91/$03.50
should be addressed:
0 1991 Elsevier Science Publishers B.V. All rights reserved
78
incorporated into an equation of state, chosen to take into account the non-ideality of the chemically equilibrated mixture (Heidemann and Prausnitz, 1976). Some versions of these equations, containing the chemical equilibrium constants as additional parameters, have been proposed recently (Grenzheuser and Gmehling, 1986; Ikonomou and Donohue, 1987, 1988; Anderko, 1989a,b, 1990a,b). As a rule, satisfactory description of phase equilibria can be achieved, but the results are strongly dependent on the chosen association model. Another approach to the problem is to couple an equation of state with an excess Gibbs energy liquid solution model when deriving mixing rules (Huron and Vidal, 1979). Usually, the local composition GE models are employed, which are capable of representing complex concentration behavior of strongly non-ideal mixtures under low and normal pressures. The resulting equations for mixtures (Mollerup, 1986; Gupte et al., 1986; Danner and Gupte, 1986; Mollerup and Clark, 1989; Gani et al., 1989; Dahl et al., 1990) are flexible enough and perform impressively well. However, they are somewhat empirical in nature, owing to lack of clarity in the underlying molecular model. An alternative way to construct equations of state for complex systems is provided by lattice theories. As is the case with the above mentioned local composition GE models, the rigid lattice quasi-chemical model by Barker and its group contribution versions (Smirnova et al., 1985) can also represent the excess functions of liquid solutions for a variety of mixtures, including ones with associated components. The simplest way to obtain the equation of state from the lattice model is to allow the presence of vacant lattice sites (holes), which are not occupied by the molecular segments. Then the system volume is the sum
0) where V * is the volume of one lattice site, N, is the number of holes, Ni is the number of molecules of kind i (having ri segments), and n is the number of components. The configurational partition function can be written in the conventional form, as a product of two terms (an athermal term and a residual term) as follows: Z(T, V, N,, N;,...,N,) = Z&N,(V),
N,, N2, . . . . N,)Z,,,(T,
giving the equation of state
N,(V),
N,, Nz,...,
N,)
(2)
79
where the athermal parts (subscript “ath”) correspond to the system with purely repulsive interactions. Some practical equations of state based on hole-lattice theory have been proposed (Sanchez and Lacombe, 1976; Ishizuka et al., 1980; Costas et al., 1981; Kleintjens, 1983; Kumar et al., 1986), but none of them take into account the effects of local ordering due to the energetic inhomogeneity of molecular surfaces, e.g. hydrogen bond formation, though it was clear, that such an approach could be implemented (Panayiotou and Vera, 1981,1982). In our version of the hole model (Victorov and Smirnova, 1985; Smimova and Victorov, 1987), hereafter abbreviated as HM, the molecular surface is assumed to be energetically inhomogeneous and is divided into groups. To take into account the effects of orientational ordering (i.e. the ordering between groups) the Guggenheim quasi-chemical approximation is employed for Z,,,. The effects of the molecular size and shape are described with the aid of Staverman’s combinatorial term, Z,,. The model was previously checked for a variety of systems, including compounds of differing molecular mass and polarity, e.g. for long-chain alkanes and alcohols (Smirnova and Victorov, 1987), for typical natural gas component mixtures (Prikhodko et al., 1989), for aqueous mixtures of petroleum reservoir compounds (Victorov et al., 1990), etc. The results of phase equilibrium predictions for a wide range of temperatures (200-650 K) and pressures (even up to 100 MPa) in most cases appeared to be of satisfactory accuracy, at least for technological needs. The main aim of the present paper is to apply the model to some strongly non-ideal mixtures of practical importance, particularly ones containing methanol, acetone and water, over a wide range of pressures. Since the existing HM parameters are to be found in different literature sources, an updated parameter list, including all the estimated model parameters, is also given. In the following section a brief outline of the model is made. Then, some new applications of the HM are discussed, and the comparison with the MHV-2 model (an advanced model of the “Huron-Vidal family” (Dahl et al., 1990)) and AEOS (the modem version of a “chemical equilibrium theory” equation of state, Anderko, 1989a,b; Anderko and Malanowski, 1989) is made. THE MODEL OUTLINE
The equation of state, which comes out of eqn. (2), is n
Pathv * -=
RT
n
C xi1* -In (1 - p) + p
C
xi4i
C
xiri
1___!+-
(4) i=l
where u* is the molar volume per lattice site, x, is the mole fraction of the component i in an n-component mixture Ii = z( r,q,)/2 - ri + 1
(6)
is the molecular bulkiness factor, z is the coordination number, ri and qi are the geometrical parameters characterizing molecular size and surface area; p = u* Cy=rx,ri/u, i.e. the reduced density (u is the system molar volume), and X,, is the solution of the following set of “quasi-chemical” equations: X,
AC
C at X, exp - $ r=O
i
= 1 i
where the indices s and t denote parts of the molecular surface (groups of kind s and t), whose interaction is described in terms of interchange energies AC,, (s = 0 imply holes). In this set of equations (Y,is the surface fraction of groups of kind t in the system. Aest is believed to be temperature-dependent (Kehiaian, 1983) as follows:
Afst RT =t,++h,,(T,-
T)/T+c,,
To-
In $? - 7
T
where asr, h,, and c,~ are the interchange free energy, enthalpy and heat capacity in respectively, units of kTo (dimensionless energetic parameters of the model), and To is some arbitrary reference temperature. The equation of state, eqns. (4-S), is written in the same form for pure and for mixed fluids, and does not incorporate any postulated mixing rules for the latter. It can be reduced to the Sanchez and Lacombe (1976) equation of state for pure components consisting of chain molecules ( li = 0) under the assumption of a random distribution of the molecules upon the lattice (formally it corresponds to infinitely large values of z). The expression for Pathcoincides also with that of Costas et al. (1981), if I, = 0, but in the residual term (5) the preferential pair formation between certain kinds of groups is taken into account by means of the quasi-chemical approximation (7). The model is similar to those, discussed by Panayiotou and Vera (1982), or by Kumar et al. (1987), and is described in more detail elsewhere (Smirnova and Victorov, 1987). For the calculations to be simplified, consider vacancies as an additional component of the mixture, having mole fraction a,,, so that the equation &=I i=O
holds.
81
The chemical potential of the component by the following expression
i, pi, can, via eqn. (1) be related
(9
pi = pi - rip0
to the quantities, defined as
00)
i=O, 1,2 ,..., n
TABLE 1 The mode of subdivision of molecules into functional ters (u* = 14.244 cm3 mol-‘, z =lO) ‘s
groups and their geometrical parame-
Type of group (in molecule)
Group number
1.0 1.0865
0.0 1.0
H_OLE CH2
(1) (2)
1.9621 2.6427 0.0 0.6624 1.9144 2.6551 2.8627 3.9682 4.9728 1.1903 0.0
0.5 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
CH3 S(H2S) 2H(H2S) C(CO2) 2o(CO2) N2 Cl c2
(3) (4) (5) > (6) (7) > (8) (9) (10) (11) (12) (13) >
1.0076 0.0
0.9 0.5
2.5165 0.0
0.1 0.5
1.0318 2.7093 2.2534 2.2242 0.5 0.2142
1.0 0.5 0.5 1.5 0.5 1.5
5.0655 0.0 1.7049 0.0 2.7613 0.0
1.0 0.0 1.0 0.0 0.5 0.5
:HZO) 2H(H20) O(ALKANOL) H(ALKANOL) OH3COO H(CH3COOH) ACH CH2=CH(ENE) WE) ACCOO H(ACCOOH) =CH-(ISO)
(14) (15) >
Substances represented hydrocarbon chain: aIkanes C”( n r 4), alkanols C,( n 2 3), etc. hydrogen sulfide carbon dioxide nitrogen methane ethane propane water aIkanols C”( n 2 3)
(16) (17) 1 (18) (19) (20) (21) (22) >
acetic acid
(24)
isomeric hydrocarbon chain
=C3H6 (ACETONE) =0 (ACETONE)
I;:; >
N(NH3) 3H(NH3) MEOH(MEOH)
(27) (28) I (29) (30) >
benzene aIkenes C, (n 2 5) alkynes C,( n r 5) benzoic acid
acetone ammonia methanol
82 TABLE 2 Model energetic parameters (T, = 298.16 K). For group numbers assignment see Table 1. The absence of any pair of group numbers implies that the corresponding energetic parameters are not available
-
-
-
0.0 0.233900 0.156800 0.190900 0.190900 0.028700 0.028700 0.061600 0.096500 0.141600 0.161300 0.088400 0.088400 0.372100 0.372100 0.100600 0.100600 0.240987 0.175249 0.256104 0.091833 0.091833 0.546953 0.257853 0.401052 0.090887 0.090887 0.235115 0.235115 0.0 0.025600 0.031000 0.031000 0.079400 0.079400 0.048800 0.029400 0.016200 0.024522 0.034476 0.034476 0.016500 0.016500 0.007700
h St
C,t
Type of groups sandt
0.0 0.234200 0.167600 0.521000 0.521000 0.392700 0.392700 0.064600 0.101300 0.144900 0.178500 0.198800 0.198800 0.620100 0.621000 0.035700 0.035700 0.262474 0.133848 0.396458 - 0.829396 - 0.829396 - 1.243084 0.354285 1.908210 0.299452 0.299452 0.332527 0.332527 0.0 0.026200 0.305200 0.305200 0.220900 0.220900 0.017900 0.016700 0.012900 0.034300 0.052595 0.052595 0.114500 0.114500 0.042000
0.0 - 0.006000 - 0.007200 0.070300 0.070300 - 0.595100 - 0.595100 - 0.016900 - 0.024800 -0.018700 - 0.025000 - 0.010400 - 0.010400 - 0.261000 - 0.261000 - 0.002700 - 0.002700 - 0.017988 - 0.106426 - 1.136340 0.0 0.0 - 0.441623 0.266898 - 5.549790 - 0.838840 - 0.838840 - 0.046180 - 0.046180 0.0 0.008100 0.0 0.0 - 0.283400 - 0.283400 - 0.092500 - 0.034500 - 0.028100 - 0.052646 0.210350 0.210350 0.040800 0.040800 0.0
HOLE-HOLE HOLE-CH2 HOLE-CH3 HOLE-S(H2S) HOLE-H(H2S) HOLE-C(C02) HOLE-G(C02) HOLE-N2 HOLE-Cl HOLE-C2 HOLE-C3 HOLE-G(H20) HOLE-H(H20) HOLE-O(ALKANOL) HOLE-H(ALKANOL) HOLE-CH3COO HOLE-H(CH3COOH) HOLE-ACH HOLE-C=C(ENE) HOLE-C=C(YNE) HOLE-ACCOO HOLE-H(ACCGGH) HOLE- =CHHOLE-“CH”(ACETONE) HOLE- =G(ACETONE) HOLE- N(NH3) HOLE- 3H(NH3) HOLE-MEOHOLE-H(MEOH) CH2-CH2 CH2-CH3 CH~-S(H~SJ CH2-H(H2S) CH2-C(C02) CH2-O(C02) CH2-N2 CH2-Cl CH2-C2 CH2-C3 CH2-O(H20) CH2-H(H20) CHZ-G(ALKANOL) CHZ-H(ALIGANOL) CH2-CH3COO
Group numbers
(l-1) (l-2) (l-3) (l-4) (l-5) (l-6) (l-7) (l-8) (l-9) (l-10) (l-11) (1-12) (1-13) (1-14) (1-15) (1-16) (1-17) (1-18) (1-19) (l-20) (1-21) (l-22) (l-24) (l-25) (l-26) (l-27) (l-28) (l-29) (l-30) (2-2) (2-3) (2-4) (2-5) (2-6) (2-7) (2-8) (2-9) (2-10) (2-11) (2-12) (2-13) (2-14) (2-15) (2-16)
83 TABLE 2 (continued)
%
h J,
Gt
Type of groups sandr
Group numbers
- 0.007700 0.004174 0.061292 - 1.588710 - 0.000896 2.070376 0.023865 0.023865 0.0 0.031000 0.031000 - 0.079400 - 0.079400 0.048800 0.029400 0.016200 0.024522 0.034476 0.034476 0.016500 0.016500 - 0.007700 - 0.007700 0.004174 0.061292 - 0.247140 - 0.000896 2.070376 0.023865 0.023865 0.0 - 0.296700 - 0.064290 - 0.064290 0.060500 0.022670 0.014500 0.027000 - 0.025300 - 0.025300 - 1.230226 - 0.023580 - 0.023580 - 0.021884 - 0.021884 0.0 - 0.064290 - 0.954400
0.042000 - 0.083863 0.157375 - 2.334519 - 0.009976 11.13251 0.003641 0.003641 0.0 0.305200 0.305200 0.220900 0.220900 0.017900 0.016700 0.012900 0.034300 0.052595 0.052595 0.114500 0.114500 0.042000 0.042000 - 0.083863 0.157375 - 2.023101 - 0.009976 11.13251 0.003641 0.003641 0.0 2.996200 0.002340 0.002340 0.344600 0.298400 0.297500 0.186200 1.003600 1.003600 - 1.514048 0.543882 0.543882 0.166459 0.166459 0.0 0.002340 6.526200
0.0 0.026822 - 1.226770 - 1 ~I05600 0.470642 - 58.82660 0.050648 0.050648 0.0 0.0 0.0 -0.283400 - 0.283400 - 0.092500 - 0.034500 - 0.028100 - 0.052646 0.210350 0.210350 0.040800 0.040800 0.0 0.0 0.026822 - 1.226770 0.0 0.470642 - 58.82660 0.050648 0.050648 0.0 - 0.338000 5.063800 5.063800 - 0.753400 - 0.429800 - 0.076800 - 0.795100 - 1.565600 - 1.565600 - 7.648420 0.0 0.0 0.0 0.0 0.0 5.063800 - 87.04500
CHZ-H(CH3COOH) CHZ-C=C(ENE) CH2-C=C(YNE) CH2- =CHCH2-“CH”(ACETONE) CH2- =qACETONE) CHZ-ME0 CHZ-H(MEOH) CH3-CH3 CH3-S(H2S) CH3-H(H2S) CH3-C(C02) CH3-qC02) CH3-N2 CH3-Cl CH3-C2 CH3-C3 CH3-qH20) CH3-H(H20) CH3-qALKANOL) CH3-H(ALKANOL) CH3-CH3COO CH3-H(CH3COOH) CHS-C=C(ENE) CH3-C==YNE) CH3- =CHCH2-“CH”(ACETONE) CH2- =qACETONE) CH3-ME0 CH3-H(MEOH) S(HZS)-S S-H(H2S) s-C(CO2) s-o(CO2) S-N2 S-Cl s-c2 s-c3 S-O(H20) S-H(H20) S- =CHS- “CH”(ACETONE) S- =qACETONE) S-ME0 S-H(MEOH) H(HZS)-H H-C(CO2) H-qC02)
(2-17) (2-19) (2-20) (2-24) (2-25) (2-26) (2-29) (2-30) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) (3-13) (3-14) (3-15) (3-16) (3-17) (3-19) (3-20) (3-24) (2-25) (2-26) (3-29) (3-30) (4-4) (4-5) (4-6) (4-7) (4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-24) (4-25) (4-26) (4-29) (4-30) (5-5) (5-6) (5-7) (continued)
84 TABLE 2 (continued)
0.060500 0.022670 0.014500 0.027000 - 0.672500 - 0.025300 - 1.230023 - 0.023580 - 0.023580 - 0.021884 - 0.021884 0.0 - 0.690900 -0.117900 - 0.095600 - 0.091200 -0.110300 1.136338 - 0.507422 - 0.155289 - 1.357070 - 0.099832 - 0.099832 - 0.267875 - 0.093518 0.0 - 0.117900 - 0.095600 - 0.091200 - 0.110300 - 0.507422 - 1.134031 -0.155289 - 1.357070 - 0.099832 - 0.377502 - 0.093518 - 1.988160 0.0 0.064280 - 0.002900 0.035800 0.11OOOo 0.11OOOo - 0.588345 0.072906 0.072906 0.027077
h S,
C*t
0.344600 0.298400 0.297500 0.186200 - 8.828700 1.003600 - 1.514048 0.543882 0.543882 0.166459 0.166459 0.0 0.648500 0.308200 0.180600 0.114600 0.150400 6.483739 - 1.549623 - 0.113199 - 2.698503 0.903197 0.903197 - 0.101255 0.267862 0.0 0.308200 0.180600 0.114600 0.150400 - 1.549623 2.023017 -0.113199 - 2.698503 0.903197 - 14.84510 0.267862 - 3.270630 0.0 - 0.130100 0.232800 - 0.029300 0.531700 0.531700 - 0.590070 0.384260 0.384260 0.188251
-
0.753400 0.429800 0.076800 0.795100 21.25270 - 1.565600 - 7.648420 0.0 0.0 0.0 0.0 0.0 - 2.797300 - 0.168100 - 0.782900 - 1.067600 - 1.017500 - 5.751650 0.421246 4.986721 - 5.558874 0.0 0.0 6.434720 - 2.701920 0.0 - 0.168100 - 0.782900 - 1.067600 - 1.017500 0.421246 - 7.918130 4.986721 - 5.558874 0.0 0.0 - 2.701920 1.227410 0.0 - 0.272500 0.837100 - 0.479500 - 1.326900 - 1.326900 - 0.010040 0.0 0.0 0.325018
Type of groups s and t
Group numbers
H-N2 H-Cl H-C2 H-C3 H-0(H20) H-H(H20) H- =CHH- “CH”(ACETONE) H- =O(ACETONE) H-ME0 H-H(MEOH) C(COZ)-c c-O(CO2) C-N2 C-Cl c-c2 c-c3 C-O(H20) C-H(H20) C-C=C(ENE) C- =CHC- “CH”(ACETONE) C- =O(ACETONE) C-ME0 C-H(MEOH) O(COZ)-0 O-N2 O-Cl o-c2 o-c3 O-O(H20) O-H(H20) 0-C=C(ENE) 0- =CH0- “CH”(ACETONE) 0- =O(ACETONE) O-ME0 0-H(MEOH) N2-N2 N2-Cl N2-C2 N2-C3 N2-O(H20) N2-H(H20) N2- -CH= N2- “CH”(ACETONE) N2- =O(ACETONE) N2-N(NH3)
(5-8) (5-9) (5-10) (5-11) (5-12) (5-13) (5-24) (5-25) (5-26) (4-29) (4-30) (6-6) (6-7) (6-8) (6-9) (6-10) (6-11) (6-12) (6-13) (6-19) (6-24) (6-25) (6-26) (6-29) (6-30) (7-7) (7-8) (7-9) (7-10) (7-11) (7-12) (7-13) (7-19) (7-24) (7-25) (7-26) (7-29) (7-30) (8-8) (8-9) (8-10) (8-11) (8-12) (8-13) (8-24) (8-25) (8-26) (8-27)
85 TABLE 2 (continued) @St
h s*
c*,
Type of groups sandt
0.027077 0.049455 0.088174 0.0 0.023360 0.016600 0.017460 0.017460 -0.911216 0.041106 0.414318 0.024410 0.024410 0.0 0.001600 0.011500 0.011500 - 0.886809 - 0.009868 3.229580 0.024443 - 1.950480 0.0 0.021960 0.021960 - 1.567438 0.025459 - 0.232589 0.013115 - 0.826218 0.0 - 4.988000 - 0.902669 - 0.002289 - 2.071404 - 0.074038 - 4.256760 0.0 - 0.902670 - 0.002289 - 4.587387 - 4.256760 - 0.074038 0.0 - 4.844100 0.287225 0.202719 0.0
0.188251 0.051214 6.369623 0.0 - 0.391860 0.052700 - 0.116800 - 0.116800 0.133408 0.000649 2.940640 0.031732 - 2.077890 0.0 0.141000 - 0.140600 -0.140600 - 1.835540 - 0.009868 3.229580 - 0.037572 - 3.446530 0.0 - 0.086400 - 0.086400 - 2.116688 0.298540 - 2.605305 0.001627 - 1.729440 0.0 - 6.972200 - 3.200302 0.072522 2.718630 - 0.374747 - 5.705090 0.0 - 3.200302 0.072522 - 0.199471 - 5.705090 - 0.374747 0.0 - 0.757470 1.139087 0.759310 0.0
0.325018 0.0 0.0 0.0 - 1.367800 0.415600 0.723900 0.723900 - 5.859100 0.0 0.0 0.0 0.0 0.0 - 0.052000 0.669200 0.669200 - 0.672725 0.0 0.0 - 0.043271 21.95800 0.0 0.761200 0.761200 - 7.573480 - 0.442213 - 5.492830 - 0.014979 0.438674 0.0 2.029000 24.81680 - 0.121601 - 1.576860 - 0.048681 2.168970 0.0 24.81680 - 0.121601 - 32.82200 2.168970 - 0.048681 0.0 - 0.218200 0.0 0.0 0.0
N2-3H(NH3) N2-ME0 NZ-H(MEOH) Cl-Cl Cl-C2 Cl-C3 Cl-O(H20) Cl-H(H20) Cl- -CH= Cl- “CH”(ACETONE) Cl- =O(ACETONE) Cl-ME0 Cl-H(MEOH) c2-c2 C2-C3 C2-0(H20) C2-H(H20) C2- =CHC2- “CH”(ACETONE) C2- --ACETONE) C2-ME0 CZ-H(MEOH) c3-c3 C3-O(H20) C3-H(H20) C3- -CH= C3-“CH”(ACETONE) C3- =O(ACETONE) C3-ME0 C3-H(MEOH) O(H20)-0 O-H(H20) 0- -CH= 0- “CH”(ACETONE) 0- =O(ACETONE) O-ME0 0-H(MEOH) H(HZO)-H H- -CH= H- “CH”(ACETONE) H- =O(ACETONE) H-ME0 H-H(MEOH) O(ALKANOL)-0 0-H(ALKANOL) 0-C=C(ENE) 0-C=C(YNE) H(ALKANOL)-H
Group numbers (8-28) (8-29) (8-30) (9-9) (9-10) (9-11) (9-12) (9-13) (9-24) (9-25) (9-26) (9-29) (9-30) (10-10) (10-11) (10-12) (10-13) (10-24) (10-25) (10-26) (10-29) (10-30) (11-11) (11-12) (11-13) (11-24) (11-25) (11-26) (11-29) (11-30) (12-12) (12-13) (12-24) (12-25) (12-26) (12-29) (12-30) (13-13) (13-24) (13-25) (13-26) (13-29) (13-30) (14-14) (14-15) (14-19) (14-20) (15-15) (continued)
86 TABLE 2 (continued) h **
%r
-
-
-
-
-
0.287225 0.202719 0.0 0.937960 0.0 0.0 0.750289 0.750289 0.053200 0.815509 0.0 0.0 0.0 7.466638 0.0 0.0 0.965361 7.514690 1.220540 1.220540 0.0 0.385174 0.~5~ 0.004540 0.0 0.004540 5.603040 0.0 1.989642 0.198847 1.827563 0.0 1.827563 0.198847 0.0 4.146474 0.0
1.139087 0.759310 0.0 - 14.06360 0.0 0.0 - 2.288639 - 2.288639 - 0.049053 - 2.420315 0.0 0.0 0.0 - 7.426928 0.0 0.0 4.015690 0.516438 - 0.287602 - 0.287602 0.0 3.166760 0.083805 0.083805 0.0 0.083805 - 0.649868 0.0 - 1.742137 - 0.204625 - 1.766863 0.0 - 1.766863 - 0.204625 0.0 - 6.601423 0.0
Type of groups sandt
Group numbers
0.0
H-C==C(ENE)
0.0 0.0
H-WE)
(15-19) (15-20) (16-16) (16-17) (17-17) (18-18) (18-21) (18-22) (18-27) (18-28) (19-19) (20-20) (21-21) (21-22) (22-22) (24-24) (24-25) (24-26) (24-29) (24-30) (25-25) (25-26) (25-29) (25-30) (26-26) (26-29) (26-30) (27-27) (27-28) (27-29) (27-30) (28-28) (28-29) (28-30) (29-29) (29-30) (30-30)
car
0.~25~ 0.0 0.0 0.0 0.0 0.976358 4.774510 0.0 0.0 0.0 0.0 0.0 0.0 138.3910 - 0.001616 0.0 0.0 0.0 - 0.547888 0.0 0.0 0.0 0.0 0.0 0.0 - 4.576230 - 1.550740 0.134267 0.0 0.134267 - 1.550740 0.0 2.583120 0.0
CH3COO-CH3COO ~H3C~-H(CH3C~~ H(CH3COOH)-H ACH-ACH ACH-ACCOO ACH-H(ACCOOH) ACH-N(NH3) ACH-3H(NH3) C=@NE)-C=C C=C(YNE)-C=C ACCOO-ACCOO ACCOO-H(ACCOOH) H(ACCOOH)-H =c- - =CH=CH- “CH”(ACETONE) ==CH- =O(ACETONE) =CH- -ME0 =CH- -H(MEOH) “CH”(ACETONE)-“CH” “CH”- ==O(ACETONE) “CIP-ME0 “CH’‘-H(MEOH) *ACETONE) - -0 =0-ME0 =o - H(MEOH) N(NH3)-N N-3H(NH3) N-ME0 N-H(MEOH) 3H(NH3)-3H 3H(NH3)-ME0 3H(NH3)-H(MEOH) MEO-ME0 MEO-H(MEOH) H(MEOH)-H
where F is the Helmholtz free energy. Notice, that the system volume is not fixed in the derivatives (lo), so the pi are exactly the quantities which play the role of chemical potentials in the lattice theories without vacancies (Smimova et al., 1985). The quantity PO for holes is closely connected with the system pressure f+=
-- v*p RT
87
Hence the condition of phase equilibrium for an n-component be written in the form pt.*’ = p(J) i-0,1,2 ,..., n I
mixture may 02)
t
which includes also the condition of mechanical equilibrium (i = 0) between phases (Yand /3. The last set of equations can be rewritten in terms of “rigid lattice activity coefficients” by means of eqn. (lo), leading us to i=O,
( CxiYi)@) = ( “Ji)@)
1,2 ,..., n
(13)
with yi determined by eqns. (14)-(18). In Y, = In Y&i + ln Yresi In Yathi= -{qi
ai = ail;:/
04)
cp. a$ in-j+ - e+l
(
I
I
+ln:-:+l I
1
05)
I
i airi i=o
(16)
e, = aiqi/ 5 aiqi
(17)
i=O In
(18)
Yresr= z C &i In (X/X,(i)) s=o
Here X, and XSCijare the solutions of eqn. (7) related to the system under consideration and to the standard state one: a hypothetical system, containing only particles of kind i (either molecules of the ith component or holes).
TABLE 3 The accuracy of pure component saturation pressures (6P) and liquid densities (6~) with the aid of the hole group-contribution model (HM), Anderko’s (1989) equation of state (AEOS), and the conventional form of the Peng-Robinson equation Substance
Range of T(K)
Averaged relative deviations
ww Water Methanol Decanol Hexadecanol Methane Decane Hexadecane Acetone Carbon dioxide Hydrogen sulfide
323-633 273-503 293-553 333-617 95-185 273-433 411-482 220-500 216-300 255-366
SP(W
HM
AEOS
1.3 0.8 1.6 2.7 0.8 4.1 5.4 3.2 0.4 0.8
0.8 0.3 0.7 3.1 0.5 0.3 1.7 -
PR 3.6 3.3 2.2 5.4 21.0 1.7 2.0
HM
AEOS
PR
0.5 0.8 1.2 1.5 1.8 0.5 0.6 1.6 1.2 1.7
8.0 3.9 3.4 1.1 6.7 1.3 4.5 -
26.5 24.0 8.3 6.7 9.1 5.3 5.5
88 TABLE 4 The accuracy of representation of binary liquid-gas equilibrium in the methanol and acetone containing systems by the hole group-contribution model System
NB
Conditions T(K)
MeOH-H,O
Deviations PA
SPc
(bar)
5%
10 12
298.16 373.16
11
473.16
38
6
523.16
65
0.1 3.3
0.9 ,::; (Z (:::
MeOH-acetone
12
298.16
0.3 1::;
14
328.16
1.0 1:::
12
372.79
15
423.16
3.8 (;:Z 12 ,Y:Z [0.6
10
473.16
40 ,‘,:: [1.2
MeGH-CO,
5 13
273.16 298.16
33 60
5
313.16
79
Ay* (mol%)
Reference to the experiment
1.4 0.9 1.0) = 1.0 1.2) 3.9 1.3)
Hall et al., 1979 Griswold and Wong, 1952
1.7 1.71 = 0.6 0.41 0.8 1.1) 2.1 1.8) 1.61 3.2 3.1) 3.11
Tamir et al., 1981
4.1
Freshwater and Pike, 1967 Wilsak et al., 1986 Griswold and Wong, 1952
0.1 0.11 0.4 0.51
Weber et al., 1984 Katayama et al., 1975 Ohgaki and Katayama, 1976
1.5 1.2
-
Weber, 1981
,::; 1::: MeOH-H2S
4 4
258.16 273.16
MeOH-N,
5 5 5
250 275 300
179 175 178
4.8 3.3 3.1
-
Weber et al.. 1984
MeOH-C,
11 12 12 11
250.03 273.16 290.0 330.0
414 414 414 414
6.5 5.4 5.9 5.4
0.08 0.15 0.16 0.33
Hong et al., 1987
MeGH-C,
11 5 5
273.16 298.16 373.16
23 41 60
-
Zeck and Knapp, 1986 Ma and Kohn, 1964
8 6
313.1 343.1
14 25
8
373.1
43
0.6 1.5 1.61 2.5 2.01
MeOH-Cs
5.9 10
4.4 Galivel-Solastionk et al., 1986
89 TABLE 4 (continued) System
N a
TK
P,& (bar)
Ayd (mol%)
6Pc %
Reference to the experiment
1.0
1.8
5.9
Budantseva et al., 1975
1.0 8.3 25
Pr: ‘4.6 4.2 3.5
4.9 2.5 2.7
Budantseva et al., 1975 Wilsak et al., 1987
298.16
0.3
2.3 2.21
Iguchi, 1978
308.16
0.5
Pr: 2.0 Il.9 Pr: 1.6 [1.2 2.5 [2.1 0.4
11 -
MeGH- ho-C,
11
297.15337.85
MeOH-C,
11 9 9
338-303 372.69 422.59
MeGH-C,
7 10
Acetone-H,0
Deviations
Conditions
2.5
Wolf and Hoeppel, 1968
II
17
348.16
1
473.02
18
308.16
0.4
1.5
2.0
18
373.16
3.7
18
473.16
28
1.8 (1.5 0.7 (2.7
8
523.16
63
0.9 0.6) 0.8 1.1) 2.5 0.7)
50
(::: 1.0 1.5
De Loos et al., 1988 Lieberwirth and Schuberth, 1979 Griswold and Wong, 1952
13 12
298.16 313.16
Acetone-H,S
1 1
263.16 298.16
Acetone-N,
3 2 3 1
223.16 258.16 283.16 308.16
63 63 61 55
Acetone-C,
10 12
298.16 323.16
120 120
Acetone-C,
7
298.16
Acetone-C,
4 4 4 4 3
325.16 350 375 400 425
Acetone- isoX,
3
278-318
1.0
5.3
Acetone- isoX,
10
298-330
1.0
3.1
1.6
Budantseva et al., 1981
Acetone-C,
11 12 8
258.16 298.16 372.69
0.1 0.8 6.6
Pr: 4.7 1.3 Pr: 1.2
3.4 1.4 2.2
Rall and Schaefer, 1959
Acetone-CO*
61 73 1.0 1.0
0.4 0.7
0.0 0.0
Katayama et al., 1975 Short et al., 1983
1 x100.01 0.04 0.2
Hicks and Prausnitz, 1981
3.8 2.9
0.1 0.2
Yokoyama et al., 1985
39
1.7 [2.8
0.2 0.31
Ohgaki et al., 1976
13 20 30 42 47
0.6 0.6 1.1 1.3 1.5
2.4 2.8 3.6 7.6 7.4
Gomez-Nieto and Thodos, 1978
Zhang and Hayduk, 1984
Campbell et al., 1986
90
TABLE 4 (continued) System
NB
Conditions TK
Deviations d
P&
SP”
(bar)
%
;:OF%)
Reference to the experiment
Acetone-C,
9 15 9
293.16 313.16 328.16
0.3 0.7 1.2
Pr: 4.4 Pr: 2.0 2.5
2.6 0.9 1.1
Rall and Schaefer, 1959 Kolasinska et al., 1982 Kudryavtseva and Susarev, 1963
Acetone-C,
7 8
313.16 338.16
0.6 1.4
Pr: 0.8 2.2
0.3 1.3
Acetone-C, Acetone-C,e
19 19
333.16 313.16
0.8 0.6
Pr: 1.7 Pr: 2.0
Acetone-C,, Acetone-C,,
9 15 8
338.16 333.16 333.16
1.3 1.0 1.0
,::,’ Pr: 3.8 Pr: 3.9
0.1 0.0 0.1 0.21 -
Kolasinska et al., 1982 Maripuri and Ratcliff, 1972a Kolasinska et al., 1982 Maripuri and Ratcliff, 1972b Messow et al., 1977
a Number of experimental points. b Maximum pressure in an experimental data set. ’ Average relative deviations between calculated and experimental bubble pressures. d Mean absolute deviation of vapor composition. ’ Values of deviations in square brackets and parentheses correspond to the correlations of Anderko (1989a-c) (AEOS) and Dahl et al. (1990) (MHV-2), respectively. f Pr: predicted; otherwise correlated. Equations (15) and (18) are then identical to those for the activity coefficients in the rigid lattice theory if holes are treated as a component of the mixture. The set of equations (13) determines the equilibrium parameters of any two coexistent phases (Yand /3 (vapor, liquid or supercritical fluid), and was used in the present work for phase equilibrium calculations. This set of equations has the same form for mixtures and pure substances. The model has geometrical ( r,, e) and energetic ( ast, h,,, cst) parameters, which, except for q,, were adjusted using some experimental data. The r, parameters were obtained from pure component data only. To get energetic parameters it was often necessary to apply the experimental data for the binary mixtures. The qs parameters can be calculated from r, values and eqn. (6), employed for groups, when we prescribe some value to I, factors of groups, building up the molecule. These I, values were established for every substance considered, using some simple models of the molecular structure, e.g. treating the molecule as a chain, ring, etc. (Smimova and Victorov, 1987; Prikhodko et al., 1989). From the additivity of rj and qi we get the following for the bulkiness factor of a molecule as a whole:
li =
c
(1, - 1) v,, + 1
s
where vsi is the number of groups of type s in molecule i.
(19)
91
.O 0
E:
s
8
z
z 22 Mb’
0 0
4
/
d
+o 8
8
::
6
92
As in any group-contribution approach the number of parameters depends on how we subdivide the molecule into groups. The mode of this subdivision and the available values of geometrical parameters of groups (prescribed Z, and estimated rs) are summarized in Table 1. Often it is desirable to decrease the number of energetic parameters, distinguishing only between specific and non-specific interactions in the system. For pure water, for instance, we may distinguish between H and 0 groups, but use only two interchange energies: one for hydrogen bond formation ( Aeo_u), and the other, averaged ( Ae~H20~_hole),for the remaining interactions. Thus, treating water molecules as energetically homogeneous, unless O-H contact is formed, we have: 00-hole
= WH-hole
= W(H,O)-hole
#
wO-H
Analogous relations are assumed hereafter for the h,, and c,~ parameters. Simplifications of this kind were made for mixtures as well. For example, to describe water-alkane, or water-nitrogen mixtures one averaged interchange energy was used: wH-x
= 00-x
= w(H,O)-x
CO2 37X; (a)200.00
METHANOL 323U
q
(b) 80.00
60.00
CO2 - METHANOL T=298.16U
-
0.00 0.4
0.0
xl
mol.fraction
0.8
0.0
0.4
xl
0.8
mol.fraction
Fig. 2. The predicted (a) and correlated (b) liquid-gas phase behavior for the CO2 (l)methanol(2) binary (full lines). Experimental data from: (a) Semenova et al., 1979 (*, T = 373.16 K; 0, T = 323.16 K); (b) Katayama et al., 1975.
93
where x denotes C,-C, alkane or N, molecules, or groups CH, and CH,. These latter groups were believed to be energetically equivalent with respect to the water molecules, that is W(H,O)-CH,
=
W(H,O)-CH,
=
W(H,O)-“CH,”
although in some cases we distinguish between the interactions with CH, and CH, groups, which proved to be important, e.g. when describing alkane mixtures. Further details of the interaction energy assignments for different groups can be followed from Table 2, which contains the updated list of the model energetic parameters. RESULTS OF THE CALCULATIONS
In this work the model was applied to pure methanol and acetone, and to mixtures containing these compounds, mainly with constituents of natural gases and oils (see Table 4 for the list of binaries). The model parameters for methanol and acetone (Tables 1 and 2) were estimated, fitting the experimental liquid density and saturated vapor pressure data for these pure substances. Table 3 shows the results of this fit, and
METHANE T=323.16K
xl
ACETONE
mol.fraction
Fig. 3. Liquid-gas equilibrium phase behavior in the methane(l)-acetone(2) lines). *, experiment (Yokoyama et al., 1985).
binary (full
94
some examples of the model’s performance for other compounds compared with that of the AEOS and Peng-Robinson equations are included as well. The interaction parameters for mixtures (Table 2) were estimated from binary liquid-vapor equilibrium data, selected to represent a wide range of temperatures and pressures. In Table 4 the accuracy of the binary liquid-gas equilibrium description is given. Some experimental data sets were not used in the parameter estimation, and these, serving as examples of prediction, are indicated ‘Pr:’ in Table 4. For the majority of the mixtures considered, the components are represented by individual groups, as in the methanol-carbon dioxide, methanolethane and methanol-propane systems, and for such binaries at least some experimental points are always needed to determine the interaction parameters. Some examples of calculated phase diagrams for a wide range of temperatures and pressures are given in Figs. l-4. In most cases the performance of the model is quite good (note that the data at 508 K in Fig. lb appear to be erroneous). With the aid of the HM it is often possible not
s
m
50.00
:
30.00
1
ETHANE - METHANOL 298K, 273K; 260K
\ CL 20.00 1
x1
mol.fraction
Fig. 4. Liquid-liquid-vapor equilibrium phase behavior in the ethane(l)-methanol(2) system: calculated (- - -) and experimental (. - .- 0) liquid-liquid-vapor coexistence lines; saturated liquid line (*, experimental; full line, calculated). Horizontal solid lines are the calculated liquid-liquid tie lines. Experimental data by Zeck and Knapp, 1986.
95
only to represent the experimental data (Figs. 2b and 3), but also to predict, at least in some cases, the diagrams for conditions far beyond those for which the parameters were estimated (Fig. 2a). In the case of mixtures containing n-alkanes from butane upwards, which were treated in a group contribution manner, it was sufficient to use only a few data sets for the parameter evaluation (Table 4). For the methanol-alkane family of binaries, this enables us to predict the solubility of n-butane in methanol with an average accuracy of 0.7 mol% in the temperature range 298-313 K (see Miyanov and Hayden, 1986 for experimental data), and the phase behavior of the methanol-n-alkane mixture series, as is shown in Fig. 5a-d. In agreement with experiment the model predicts limited miscibility of methanol with aIkanes (Figs. 4 and 5a), the calculated miscibility gap being somewhat wider than the experimental one. This gap disappears when the temperature is raised (Fig. 5b-d). The model reflects correctly the dependence of the upper critical consolution temperature (and of the critical composition) upon alkane chain length, but the deviations from the corresponding experimental values (Bernabe et al., 1988) are large. For example, the calculations still reveal phase splitting for the methanol-hexane system at 330 K, being almost 30 K above the experimental consolution point. The predictions are similar to those of the AEOS (Anderko and Malanovsky, 1989).
TABLE 5 Liquid-gas equilibrium predictions for multicomponent mixtures using the HM (bubble point calculations). 6(ln Kc,,) is the averaged absolute deviation for the logarithm of the component i K-value: Kc,, = y,/x, System
T, P range
6P(W)
by
Ref. a
(mol%)
a(Ln Kc,,) (1) (2)
(3)
Acetone + MeOH + C,
372.1 K 5-8 bar
5.5
1.7
0.07
0.09
0.04
1
Acetone + MeGH + H,O
330-523 K l-81 bar
‘.’
3.3
0.22
0.15
0.10
2,3
2.0
-
-
-
4
-
-
-
-
C,+C,+C,+N,+ + CO2 f H,S H,O+N, +CO, +C, + +c,+c,+c,+ + i.w-C4 + C,
185-236 K 27-80 bar
4 1
333-393 K 50-250 bar
42
. ’
a 1, Wilsak et al., 1987; 2, Kato et al., 1971; 3, Griswold Robinson, 1979; 5, Zuo, 1989.
5
and Wong, 1952; 4, Kalra and
96 METHANOL T= 298.16K
(a) 0.40
-
HEXANE I
HEXANE 473K;448K
METHANOL
(b)s.oo
0.30
4.00
I
2
: I
3.00
\ a
2.00
1 .oo
000
1 0.0
I
I
1
0.4
x
1 mol.fraction
I
4
0.8
0.00
’
0.4
0.0 x
HEPTANE 498K; 473K;
METHANOL 448K; 423K
b-38 00
WI8
00
0.8
mol.fraction
DECANE 498K; 473K;
METHANOL 448K; 423K
q
6.00
6.00
u
2 I
5 \4
1
\4.00
00
a
a
2.00
2.00
I !
0.0
x1
mol.fraction
I
I
0.4
x 1 mol.fraction
I
0.8
97 060
ACETON E T= 31: i.15K
7
DECANE
0 20
0.10
xl
mol.fraction
Fig. 6. The predicted phase diagram for the acetone(l)-decane(2) lines); experimental data (*) by Kolasinska et al., 1982.
system at 313.16 K (full
It should be mentioned also, that for the propane-methanol mixture at 313.1 K (Table 4) the HM predicts phase splitting which has not been observed experimentally (Galivel-Solvastionk et al., 1986), though the experimental bubble curve is rather flat, indicating the trend of the mixture towards phase splitting. Despite quite accurate description of the experimental data, an analogous result was obtained for the acetone-ethane binary at 298.16 K which is also an example of a strongly non-ideal mixture possessing a flat bubble pressure curve. Good results are obtained when predicting the azeotropic behavior of acetone-alkane and methanol-alkane mixtures (Fig. 5), but again, when the
Fig. 5. The calculated (full lines) and experimental (points) phase diagrams for the binaries of the methanol-alkane family. (a) Vapor-liquid-liquid diagram for the methanol(l)-hexane(2) system at 298.16 K. Experimental data by Iguchi, 1978 (*), and by Huang and Robinson, 1977 (0). The experimental miscibility gap is shown (- - -). (b) Vapor-liquid-equilibrium for the system hexane(l)-methanol(2) at 448.16 K and 473.16 K (experiment at data by De Loos et al., 1988 and Zawisa, 1985). (c,d) Vapor-liquid-equilibria for the heptane(l)methanol(2) and decane(l)-methanol(2) binaries, respectively, at 423.16 K, 448.16 K, 473.16 K, 498.16 K (experimental data by De Loos et al., 1988). In (c) the location of the experimental binary critical regions is sketched (- - -).
98
TABLE 6 Liquid-gas equilibrium calculations)
predictions for multicomponent T, P range
System
mixtures using the HM (P, T-flash Ref. a
a(m K,,,)
(1)
(2)
(3)
(4)
MeGH + COa + N,
273 K 50-125 bar
0.05
0.05
MeOH+C,+N,
260 K 15-75 bar
-
0.11
0.03
2
MeOH + CO2 + C,
343 K 5-22 bar
0.24
0.12
0.03
3
258-273 K 9-40 bar
0.44
0.12
0.22
0.48
4
311-450 K 48-173 bar
0.19 (0.14
0.15 0.11
0.15 0.09
0.75 b 0.19)
5
MeOH + CO2 + N, + + H,S C, +COz +H,S+H,O
(
1
’ 1, Weber et al., 1986; 2, Zeck and Knapp, 1986; 3, Gahvel-Solvastionk Rousseau et al., 1981; 5, Huang et al., 1985. b MHV-2 model.
et al., 1986; 4,
system is near the formation of a critical phase (Fig. 5c, T = 498.16 K), the type of predicted diagram could be erroneous, even though the deviations between experimental and calculated pressures are not necessarily large. In Fig. 6 a typical example of the liquid-vapor equilibrium prediction for an acetone-alkane mixture is presented. The comparison with the MHV-2 model and with the AEOS can be made (Table 4), though with the latter equation separate parameters are used for each isotherm. In the case of our model or the MHV-2 model unique parameter sets for all the temperatures were used. Nevertheless, this information allows us to conclude that all three models are of approximately the same level of accuracy for liquid-gas equilibrium calculations. The HM predictions for multicomponent mixtures seem to be reasonable (Tables 5 and 6). For the last mixture, shown in Table 6, the MHV-2 model gives somewhat better equilibrium ratios than the HM. However, as expected, the MHV-2 model in general gives much poorer liquid volume predictions than the HM model does (Prikhodko et al., 1989; Victorov et al., 1990). CONCLUSIONS
The hole group-contribution quasi-chemical model has been used to predict phase equilibria in binary and multicomponent systems containing
99
associating substances over a wide range of temperatures and pressures. The accuracy of the model has been found to be sufficient for industrial applications for a variety of mixtures (strongly polar and non-polar, light and heavy compounds). An updated model parameter list is presented, permitting predictions of phase equilibria for many mixtures of practical importance, e.g., for those of natural gas/oil components together with acetone, methanol and water.
ACKNOWLEDGMENT
The authors are thankful to Prof. P. Rasmussen for carefully reading the manuscript and for his many helpful suggestions.
REFERENCES Anderko, A., 1989a. Fluid Phase Equilibria, 50: 21-52. Anderko, A., 1989b. Fluid Phase Equilibria, 45: 39-67. Anderko, A., 1990a. Equation of state methods for the modeling of phase Equilibria. Fluid Phase equilibria, submitted for publication. Anderko, A., 1990b. Personal communication. Anderko, A. and MaIanowski, S., 1989. Fluid Phase Equilibria, 48: 223-241. Bernabe, D., Romero-Martinez, A. and Trejo, A., 1988. Fluid Phase Equilibria, 40: 279-288. Budantseva, L.S., Lesteva, T.H. and Nemtsov, M.S., 1975. Zh. Fis. Khim. (Russian), 49: 1847. Budantseva, L.S., Evstigneev, A.Yu., Lesteva, T.M., 1981. Prom-St Sint. Kauch. (Russian), 11: 7. Campbell, S.W., WiIsak, R.A. and Thodos, G., 1986. J. Chem. Eng. Data, 31: 424. Costas, M., Epstain, H.I., Sanctuary, B.C., Richon, D. and Renon, H., 1981. J. Phys. Chem., 85: 1264, 3153-3160. DahI, S., Fredeslund, Aa. and Rasmussen, P., 1990. SEP publication 9008, Institut for Kemiteknik, The Technical University of Denmark. De Loos, Th. W., Poot, W. and De Swaan Arons, 1988. Fluid Phase Equilibria, 42: 209-227. Danner, RP. and Gupte, P.A., 1986. Fluid Phase Equilibria, 29: 415-430. Donohue, M.D. and Prausnitz, J.M., 1987. AIChE J., 18: 1184-1191. Freshwater, D.C. and Pike, K.A., 1967. J. Chem. Eng. Data, 12: 179. Gahvel-Solvastionk, K.F., Langier, S. and Richon, D., 1986. Fluid Phase Equilibria, 28: 73-85. Gani, R., Tzouvaras, N., Rasmussen, P. and Fredenslund, Aa., 1989. Fluid Phase Equilibria, 47: 133-153. Gomez-Nieto, M. and Thodos, G., 1978. Chem. Eng. Sci., 33: 1589. Grenzheuser, P. and Gmehhng, J., 1986. Fluid Phase Equilibria, 25: l-29. Griswold, J. and Wong, S.Y., 1952. Chem. Eng. Progr. Symp. Ser., 48: 18. Gupte, P.A., Rasmussen, P. and Fredenshmd, Aa., 1986. Ind. Eng. Chem. Fundam., 25: 636-645. Hall, D.J., Marsh, C.J. and Pemberton, R.C., 1979. NPL Rept. Chem., January: 95.
100 Heidemann, R.A. and Prausnitz, J.M., 1976. Proc. Nat. Acad. Sci. USA, 73: 1773. Hicks, P.J. and Prausnitz, J.M., 1981. J. Chem. Eng. Data, 26: 74. Hong, J.H., Malone, P.V., Jett, H.D. and Kobayashi, R., 1987. Fluid Phase Equilibria, 38: 83-90. Huang, S.S., Len, A.D., Ng, H.G. and Robinson, D.B., 1985. Fluid Phase Equilibria, 19: 21-32. Huron, M.J. and Vidal, J., 1979. Fluid Phase Equilibria, 3: 255-271. Iguchi, A., 1978. Kagaku So&i, 20: 66. Ikonomou, G.D. and Donohue, M.D., 1987. Fluid Phase Equilibria, 33: 61-90. Ikonomou, G.D. and Donohue, M.D., 1988. Fluid Phase Equilibria, 39: 129-159. Ishizuka, I., Sarashina, E., Arai, Y. and Saito, S., 1980. J. Chem. Eng. Jpn., 13: 90-97. Lieberwirth, I. and Schuberth, H., 1979. Z. Phys. Chem. (Leipzig), 260: 669. Kaha, H. and Robinson, D.B., 1979. Fluid Phase Equilibria, 3: 133-144. Katayama, T., Ohgaki, K., Maekana, G., Goto, M. and Nagano, T., 1975. J. Chem. Eng. Jpn, 8: 89. Kato, M., Sato, T., Konishi, H. and Hirata, M., 1971. J. Chem. Eng. Jpn., 4: 311. Kehiaian, H.V., 1983. Fhtid Phase Equilibria, 13: 243-252. Kleintjens, L.A., 1983. Fluid Phase Equilibria, 10: 183-190. Kolasinska, G., GoraI, M. and Giia, J., 1982. Z. Phys. Chem. (Leipzig), 263: 151. Kudryavtseva, L.S. and Susarev, M.P., 1963. Zh. PrikI. Khim. (Russian), 36: 1471. Kumar, S.K., Suter, V.W. and Reid, R.C., 1986. Fluid Phase Equilibria, 29: 373-382. Kumar, S.K., Suter, V.W. and Reid, R.C., 1987. Ind. Eng. Chem., 26: 2532-2542. Ma, Y.H. and Kohn, J.P., 1964. J. Chem. Eng. Data, 9: 3-5. Maripuri, V.C. and Ratcliff, G.A., 1972a. J. Chem. Eng. Data., 17: 36. Maripuri, V.C. and Ratcliff, G.A., 1972b. J. Appl. Chem., 22: 899. McGlashan, M.I. and Williamson, A.G., 1976. J. Chem. Eng. Data, 21: 196. Messow, U., Doye, U., Kuntzsch, S. and Kuchenbecker, 1977. Z. Phys. Chem. (Leipzig), 258: 90. Miyanov, Y. and Hayden, W., 1986. J.-Chem. Eng. Data, 31: 77. Mollerup, J.M., 1986. Fluid Phase Equilibria, 25: 323-327. Mollerup, J.M. and Clark, W.M., 1989. Fluid Phase Equilibria, 51: 257. Ohgaki, K. and Katayama, T., 1976. J. Chem. Eng. Data, 21: 53-54. Ohgaki, K., Sano, F. and Katayama, T., 1976. J. Chem. Eng. Data, 21: 55-58. Olevsky, V.M., 1956. Trudy GIAP (in Russian), 6: 45. Panayiotou, C. and Vera, J.H., 1981. Can. J. Chem. Eng., 59: 501-506. Panayiotou, C. and Vera, J.H., 1982. Polym. J., 14: 681-694. Prikhodko, I.V., Schmeltzer, J., Victorov, A.I. and Smirnova, N.A., 1989. J. Appl. Chem. (Russian), 62: 2734-2737. RalI, W. and Schaefer, K., 1959. Z. Elektrochem., 63: 1019. Rousseau, R.W., Matange, J.N. and FerreIl, J.K., 1981. AIChE J., 27: 605-613. Sanchez, I.C. and Lacombe, R.H., 1976. J. Phys. Chem., 80: 2568-2580. Semenova, A.I., Emel’yanov, E.A., Tsimmerman, S.S. and Tsikhs, D.S., 1979. Zh. Fis. Khim. (Russian), 53: 1426. Short, I., Sahgal, A. and Hayduk, W., 1983. J. Chem. Eng. Data, 28: 63. Smirnova, N.A. and Victorov, A.I., 1987. Fluid Phase Equilibria, 34: 235-263. Smimova, N.A., Piotrovskaya, E.M. and Victorov, A.I., 1985. J. Appl. Chem. (Russian), N6, 1261-1265. Tamir, A., Apelblat, A. and Wagner, M., 1981. Fluid Phase Equilibria, 6: 113. Victorov, A.I. and Smirnova, N.A., 1985. In: Proceedings of VII Mendeleev’s discussions (in Russian). Kharkov, pp. 37-42.
101
Victorov, A.I., Fr~enslund, Aa. and Smimova, N.A., 1990. Fluid Phase Equilibria, 66: 187-210. Weber, W., 1981. Ph.D.thesis, Berlin. Weber, W., Zeck, S. and Knapp, H. 1984. Fluid Phase Equilibria, 18: 253-270. Wilsak, P.A., Campbell, S.W. and Thodos, G., 1986. Fluid Phase Equilibria, 28: 13. Wilsak, P.A., Campbell, S.W. and Thodos, G., 1987. Fluid Phase Equilibria, 33: 173-190. Wolf, H. and Hoeppel, H.E., 1968. Ber. Bunsenges. Phys. Chem., 72: 710. Yokoyama, O., Masuoka, M., Arai, K. and Saito, S., 1985. J. Chem. Eng. Data, 30: 177. Zawisa, A., 1985. J. Chem. Thermodyn., 17: 941-947. Zeck, S. and Knapp, H., 1986. Fluid Phase Equilibria, 25: 303-322. Zhang, G. and Hayduk, W., 1984. Can. J. Chem. Eng., 62: 713. Zuo, Y.X., 1989. Ph.D.thesis, Beijing Graduation School, Univ. Petrol., China.