An Evaluation of Mixing Rules for the Trebble-Bishnoi-Salim Equation

3112

Znd. E n g . Chem. Res. 1995,34, 3112-3128

An Evaluation of Mixing Rules for the Trebble-Bishnoi-Salim Equation of State Paul H. Salim and Mark A. Trebble* Department of Chemical and Petroleum Engineering, The University of Calgary, 2500 University Drive N . W., Calgary, Alberta T2N 1N4, Canada

Several sets of mixing rules have been evaluated for use with the Trebble-Bishnoi-Salim equation of state (TBS EOS). Calculations for each rule have been performed on a screened Gas Processor's Association (GPA) data base which contains 137 binary systems and spans very wide ranges of temperature and pressure. Classical quadratic mixing rules are compared to Schwartzentruber-Renon mixing rules and to a new mixing rule based on the previous work of Huron and Vidal, Schwartzentruber and Renon, and Wong and Sandler. The new mixing rule preserves the quadratic nature of the predicted second virial coefficient and forces excess volumes to be zero a t infinite pressure. In order to satisfy both conditions it was necessary to include a n additional ao/uparameter in the attractive parameter of the TBS EOS which results in a quartic equation in volume. The method of Huron and Vidal was used to incorporate a Margules excess energy model into the EOS a t infinite pressure. Not surprisingly it was observed in the study that the more complex mixing rules are only of significant benefit in systems exhibiting large asymmetry or polarity effects. Classical mixing rules are shown to be adequate in most of the binaries investigated here.

Introduction Cubic equations of state are valuable tools for predicting thermophysical properties and phase equilibria for both single-component and multicomponent systems. Anderko (1990) has thoroughly reviewed the literature regarding equations of state (EOS) and their extention t o mixtures up to 1990. The following introduction will discuss only some more recent publications resulting from incorporation of excess Gibbs free energy models. Huron and Vidal(1979) introduced the incorporation of excess Gibbs (GE)models directly into equations of state using an infinite pressure boundary condition. In order to maintain a finite value of GE at infinite pressure it was necessary for them to model the covolume term as a linear combination (Le., bm = ZxlbL).The methodology suffered from two disadvantages: (1)published GE model coefficients obtained from fitting low-pressure vapor-liquid equilibria (VLE) data could not be used directly and (2) the quadratic compositional dependence of the predicted second virial coefficient was lost. The mixing rules suggested by Michelsen (1990) and Heidemann and Kokal (1990) introduce the GE model into the EOS at a zero pressure boundary condition and are consequently able to incorporate published GE model constants directly. Neither of these methodologies reproduces the quadratic compositional nature of the second virial, however. Wong and Sandler (1992) consequently introduced a method for incorporating a GE model using a lowpressure boundary condition while retaining the quadratic nature of the second virial. Their approach equated the Helmholtz energy at infinite pressure to the Helmholtz energy at low pressure. They then equated the low-pressure Helmholtz energy to the lowpressure Gibbs energy in order t o incorporate a GE

* Author t o whom correspondence should be addressed. E-mail: [email protected].

model fit to low-pressure VLE data. Wong and Sandler forced the quadratic dependence of the second virial coefficient by calculating the mixture virial as shown below:

where

(2) The disadvantage of this approach is that the mixture covolume parameter calculated from eq 1 above is temperature dependent. This will produce inconsistent predictions of derived thermodynamic properties (including negative heat capacities) at very high pressures as pointed out by Salim and Trebble (1991) and by Satyro and Trebble (1995). Another difficulty arises when applying the Wong-Sandler rules to three- or four-parameter equations of state since the calculation of the mixture b value becomes implicit. For the Trebble-Bishoi-Salim (TBS) EOS the following set of equations would have to be solved at each iteration:

A:

a,

RT

b,e,

---ln( -

2+um-Om 2+u,+e,

)-

where

0888-588519512634-3112$09.00/0 0 1995 American Chemical Society

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3113 Table 1. Additional Pure Component Parameters" component neopentane phenol toluene methylcyclohexane m-xylene p-xylene ethylbenzene ethylcyclohexane 2,2,4-trimethylpentane n-propylbenzene 1,3,5-trimethylbenzene propylcyclohexane helium-4* nitrogen" sulfur dioxide* hydrogen* carbon dioxide* propylene* n-butane* isobutane* n-pentane* a

Tc (K) 433.75 694.20 591.80 572.20 617.10 616.20 617.20 609.00 544.00 638.20 637.30 639.00 5.2 126.2 430.7 33.0 304.2 364.5 425.2 408.1 469.8

Pc(bar)

w

5 C

31.96 61.30 41.00 34.70 35.40 35.10 36.00 30.00 25.70 32.00 31.30 28.00 2.275 34.00 78.85 12.93 73.83 46.00 37.97 36.48 33.75

0.2688 0.2432 0.2633 0.2684 0.2594 0.2597 0.2624 0.2666 0.2659 0.2654 0.2534 0.2372 -0.3868 0.0350 0.2510 -0.2192 0.2250 0.1480 0.1993 0.1849 0.2516

0.2896 0.2502 0.2637 0.2734 0.2549 0.2536 0.2573 0.2487 0.2765 0.2509 0.2498 0.2623 0.3309 0.3164 0.2871 0.3249 0.2898 0.2892 0.2985 0.3030 0.2932

m 0.9157 1.2329 0.9039 0.9223 0.9752 0.9492 0.9349 0.6866 1.1376 0.9672 1.1129 0.9297 -0.4600 0.8915 1.1281 -0.0091 1.0106 0.7283 1.1524 1.1798 1.2358

d (cm3 mol-')

P 0.2320 1.7285 1.2435 1.2050 1.3206 1.3026 1.4005 1.8146 1.2401 1.4414 1.3326 2.0500 0.0000 0.1973 0.3017 0.0000 0.2367 0.1315 0.3040 0.3329 0.3492

107.05 76.33 105.33 122.67 125.33 126.33 124.67 150.00 156.00 146.67 143.00 150.00 12.48 18.80 33.58 18.99 31.18 66.77 69.84 64.71 88.44

Asterisks denote recalculated parameters.

Table 2. Comparison of Fit between Original and

(5a,b)

Recalculated Parametersa comuonent

N

xici

c, =

(7)

i=l

recalculated

%AADPs %AADOv

%AADPs %AADOv 4.16 4.85 0.47 1.84 2.54 0.34 2.45 3.78 0.99 1.12 0.40 1.82 1.71 0.75 0.37 1.66 2.11 0.83

helium-4 nitrogen sulfur dioxide hydrogen carbon dioxide propylene n-butane isobutane n-pentane

3.65 0.57 0.39 2.95 1.04 0.61 0.78 0.65 1.04

4.78 1.79 2.53 2.42 1.11 1.74 1.71 1.61 2.04

Note: %AAD Ps is percent absolute average deviation of vapor pressure; %AAD Ov is percent overall absolute average deviation.

N

d, =

origin a 1

xidi i=l

Satyro and Trebble (1995) modified the Wong-Sandler mixing rules by using a quadratic mixture covolume parameter instead of eq 1. The result is that the temperature dependence in the covolume is eliminated and the thermodynamic inconsistency is removed. Unfortunately, the quadratic nature of the second virial coefficient is not reproduced and the excess volume at infinite pressure is not zero. In this work we introduce a method of incorporating GE models directly into an equation of state while retaining the quadratic nature of the second virial compositional dependence through the use of a temperature-independent linear combination covolume parameter which forces thermodynamic consistency and a zero excess volume at infinite pressure.

avoid negative a values leads to minimal degradation of pure component PVT properties (as shown in Table o\ f5 1.

Development of a New Mixing Rule For extension of the TBS EOS to mixtures, the following formula was investigated:

a,

p=-- RT u - bm

u2

+ (b, +

+ ao/u

C,)U

- (b,c,

+ dm2) (9)

where N

b, =

xibi

(10)

xici

(11)

i=l

Pure Component Parameters Detailed information about the TBS EOS for pure components in the vapor-liquid region is given elsewhere (Salim and Trebble, 19911, and parameters are given in Table 1 for some additional components used in this study. Nevertheless, some components (with asterisks) had their parameters recalculated t o prevent ai from becoming negative at high temperature. The geometric mean of ak for a conventional mixing rule can then be evaluated without using an absolute value of ai or a, which would lead to discontinuity in the first and second derivatives of a, with respect to temperature. Regression of the TBS parameters restrained to

N

c, = i=l N

N

(12)

+

di dj d F. J = ( ~ ) (- Kd,) 1

(13)

Obviously eq 9 is quartic in volume. A cubic EOS could have been retained giving a mixing rule similar to that

3114 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 proposed by Schwartzentruber and Renon (1991):

p = - RT u - bm

a,

-

u2

+ a0/(u - b,)

+ (b, +

C,)U

- (b,c,

+ dm2) (14)

It was not possible to utilize the Wong-Sandler approach for eq 14, however, since the Helmholtz energy at infinite pressure becomes indeterminate. We can use the van der Waals EOS (1890) t o demonstrate the problem below:

Table 3. Error Comparison for Binary VLE Systems with the TBS EOS" mixing rule conventional conventional SR-1 SR-2

Hv WSHV

and its excess Helmholtz free energy would be

conventional conventional SR-1 SR-2

AE(T,x,P=low) =

Hv WSHV

c

i=N

RT(ln[u - b,] -

xi In (ui

- b,)) (16)

i=l

and,

conventional conventional SR-1 SR-2 HV

WSHv

fitted constants AADP AADY a. 53 Systems (HC-HC) Ka 3.4 1.1 Ka, Kd 3.0 1.0 Ka, L 2.6 0.9 Ka, Kd, L 2.0 0.9 Ka, C112, C122 2.0 0.6 Ka, c112, c122 2.2 0.9 b. 65 Systems (HC-NHC) Ka 6.1 1.7 4.4 1.5 Ka, Kd 4.8 1.5 Ka, L Ka, Kd, L 3.6 1.3 Ka, C112, C122 4.2 1.4 3.8 1.9 Ka, C112, C122 c. 19 Systems (NHC-NHC) 4.3 Ka 20.5 9.9 3.2 Ka, Kd 3.3 Ka, L 13.4 10.5 3.4 Ka, Kd, L 6.3 1.7 Ka, C112, C122 6.2 1.9 Ka, C112, (2122

no. of points 2131 2143 1955 1926 1817 1778 2967 2974 2667 2680 2209 2244 973 1111 877 916 851 904

a Note: AADP is absolute average deviation of all DPs; AADY is absolute average deviation of all DYs.

A~(T,x =m) ~ =

standard deviations (SD)calculated from: indeterminate (17) It is seen that AE(T,x,P= w) f AE(T,x,P=low) = GE(T,x,P=low). Therefore, Wong and Sandler's (1992) method could not be utilized with eq (14) leading to the choice of the quartic equation 9. A linear combination mixture covolume was chosen based on the fact that excess volumes a t high pressure should approach zero as argued by Huron and Vidal(1979).

Results and Discussion Volumes for mixtures in eq 9 were solved analytically with the Ferrari method (Conkwright, 1965). For root selection, the following procedure was applied. Liquid Volume Calculation. (1)Choose the smallest positive root, (2) test the mechanical stability (%'/ au 01, and (3) if step 2 is violated, pick a higher root and repeat step 2. Vapor Volume Calculation. (1)Choose the highest positive root, (2) test the mechanical stability ( W a u 0), and (3) if step 2 is violated, pick a lower root and repeat step 2. Using pure component parameters from Salim and Trebble (1991) and Table 1, we optimized the binary interaction parameters with the following objective function, utilizing a bubble point pressure flash algorithm: M

(20) where E is as defined in eq 18, M is the number of data points, 0 represents the number of parameters regressed, and K refers to the interaction parameter which has the standard deviation. The binary systems were divided into three groups according to their component types, HC (hydrocarbons) and NHC (non-hydrocarbons); HC-HC (53 binaries), HC-NHC (65 binaries), and NHC-NHC (19 binaries). NHC components included CO, C02, Hz, N2, He, HzS, SO2, H20, and phenol. The following is the discription of all mixing rules examined in this study. Use of Classical Mixing Rules. A comparison of classical mixing rules for the TBS EOS was conducted as follows:

p=-- RT u - bm

u2

+ (b, +

am C,)U

(21)

- (bmc, + dm2)

where N

N

(22)

N

b, =

xibi

(24)

i=l

k=l

N

where N

DY, = 100 y"(:

N

(26)

- yyp)

(1%) Comparisons are given in Tables 3 parts a-c for VLE data regressions of 137 binary systems described by Trebble (1990). Tables 4-9 give individual interaction parameter values for each binary as well as their

di+ d .

di, = ( i ) ( l- Kd,)

(27)

An interaction parameter was not used in the covolume

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3115 Table 4. Binary Interaction Parameters for TBS EOS (Conventional Mixing Rules) COMP(1) COMP(2)

c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2

c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6 TOL

H2S

0.0222 0.0785 0.0367 0.0307 0.6549 0.0806 0.1248 0.0230 0.1242 0.0737 0.0981 0.0345 0.0828 0.0523 0.1294 0.0805 1.0215 0.1486 0.0102 0.1308 0.0511 0.1393 0.1304 0.0453 0.0857 0.0495 0.1210 0.0130 -0.0972 0.0825 0.0688 0.0280 -0.2618 -0.0411

0.0015 2.3 0.0009 1.3 0.0018 8.1 0.0005 0.9 0.0047 14.8 0.0017 5.1 0.0021 3.2 0.0014 3.8 0.0010 1.4 0.0034 1.8 0.0075 20.3 0.0011 9.1 0.0006 9.8 0.0010 5.0 0.0008 1.6 0.0016 1.6 0.0063 7.8 0.0053 8.6 0.0209 13.9 0.0011 3.2 0.0033 2.7 0.0049 9.0 0.0030 4.7 0.0023 1.7 0.0063 4.1 0.0023 2.3 0.0032 2.8 0.0051 5.5 0.0049 5.4 0.0021 2.1 0.0021 3.5 0.0023 4.6 0.0082 0.9 0.0045 7.2

1.8 0.9 1.8 0.8 4.6 1.9 0.8 0.8 1.0 2.7 0.5 0.6 0.9 1.0 1.0 1.3 1.4 1.7 4.7 1.2 1.7 2.1 1.7 2.4 1.2 2.0 1.9 1.1 2.5 2.2 1.6 1.5 0.9 1.1

H2S H20 H20 H20 H20 H20 NH3 PHENOL PHENOL PHENOL c02

0.1164 -0.6485 -0.9356 -0.0013 -0.6750 0.0058 -0.2510 -0.0280 0.0398 -0.5582 -0.0677

0.0037 0.0125 0.0279 0.0078 0.0136 0.0019 0.0012 0.0071 0.0018 0.0246 0.0033

MXYL MESI c3 NC4 IC4 NC5 c10 C3ENE CYCG TOL

MXYL MESI C3BEN C3CYC6 ClCYC6

c02 H2S H2 N2 N2

co

H2 H2S N2 c02 H20 H2 c02 NH3

co

DY PTS PTSM COMP(1) COMP(2) 0.3 125 0.5 148 0.8 140 0.9 15 0.6 117 4.5 28 1.0 154 1.9 88 0.8 18 1.4 46 1.2 42 3.0 36 0.1 23 1.1 21 1.1 22 0.6 105 1.4 83 1.7 64 1.2 14 2.5 38 3.2 26 2.2 23 1.0 21 1.6 27 1.1 25 1.7 25 1.0 27 1.0 26

c2 c2 c2 c2 c2 c3

N2

DP

0.0004 1.3 0.0004 2.1 0.0001 3.6 0.0026 1.4 0.0011 4.7 0.0118 8.5 0.0007 7.0 0.0000 4.6 0.0031 4.5 0.0050 9.5 0.0017 4.2 0.0066 11.3 0.0011 4.7 0.0060 10.4 0.0061 10.6 0.0008 1.6 0.0016 1.9 0.0024 1.6 0.0044 3.2 0.0050 7.7 0.0044 4.6 0.0025 2.6 0.0000 6.8 0.0037 7.1 0.0026 4.8 0.0038 6.8 0.0022 3.1 0.0024 3.5

c02 H2 N2 HE H2S so2

c3 c3 c3 c3 NC4 NC4 NC4 NC4 IC4 IC4 IC4 NC5 NC5 NC5 IC5 IC5 c7 c7 C8 c9

SD

0.0038 0.0161 0.0027 0.0269 0.0064 -0.0863 0.0111 -0.0410 -0.0669 -0.1491 -0.0405 -0.1761 -0.0244 -0.1111 -0.1366 -0.0021 0.0034 -0.0069 0.0040 -0.0907 -0.0313 -0.0242 -0.0262 -0.0497 -0.0616 -0.0667 -0.0402 -0.0399

c1 c1 c1 c1 c1 c1 c1

c3

Ka

co

co

co

c02 H2S HE H2 N2 c02 H2S H2 c02 H2S N2 H2S c02 N2 N2 c02 c02 H2S

co

74 102 129 176 168 86 5 26 173 27 80 97 107 21 64 78 62 46 19 89 24 93 39 61 13 31 28 42 47 29 56 39 15 10

9.5 1.5 72 37.1 7.0 18 41.2 10.2 18 33.7 8.0 11 34.4 7.5 16 19.5 3.3 54 6.9 1.6 211 3.3 0.6 10 10.2 0.5 12 55.3 0.8 18 4.6 2.0 34

a. HC-HC 150 C3 150 C3 150 C3 15 C3 117 C3 28 C3 156 C3 96 C3 20 c3 49 c3 42 NC4 36 NC4 23 NC4 21 NC4 22 IC4 157 IC4 83 NC5 72 NC5 14 NC5 44 C6 26 C6 24 C6 21 c 7 27 C8 25 C8 25 total average

NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 c7 c10 C4ENE IC4ENE C3ENE ClCYC6 CYCG ClCYC5 ClCYC5 CYCG ClCYC6 TOL C2BEN PXYL

Ka

SD

DP

-0.0020 0.0046 0.0095 -0.0246 -0.0224 -0.0807 -0.0136 -0.0281 -0.0411 -0.0288 -0.0023 0.0037 -0.0411 0.0020 0.0027 -0.0220 -0.0088 -0.0081 -0.0057 -0.0056 -0.0131 -0.0056 0.0020 -0.0059 0.0028

0.0011 0.0010 0.0009 0.0021 0.0062 0.0030 0.0012 0.0020 0.0018 0.0008 0.0007 0.0064 0.0021 0.0008 0.0010 0.0061 0.0038 0.0017 0.0013 0.0015 0.0037 0.0006 0.0010 0.0012 0.0008

1.6 1.5 0.8 2.2 1.8 4.4 1.7 3.5 3.8 2.9 0.8 1.3 2.8 0.4 0.4 3.5 1.2 0.3 0.7 0.3 0.4 0.4 0.9 1.4 0.2 182.9 3.4

ig

b. HC-NHC 75 c10 107 C10 130 C12 184 CYCG 189 CYCG 86 ClCYC6 5 ClCYC6 26 ClCYC6 192 C2CYC6 27 C2CYC6 80 C2CYC6 100 C2ENE 107 C3ENE 21 C4ENE 64 BEN 79 BEN 62 TOL 46 TOL 19 TOL 90 C3CYC6 25 MXYL 93 MXYL 39 MXYL 63 MESI 13 MESI 31 MESI 28 C1 42 C2ENE 47 C3ENE 29 C8H18 56 C16 total average 10 C. NHC-NHC 72 N2 18 H2 18 HE 17 C02 16 GO2 116 N2 215 CO 10 c 0 2 total 34 average

;E

t:

N2 c02 H2 c02 H2 c02 H2S N2 c02 N2 H2S C02 c02 c02

co

c02 c02 H2S N2 H2S c02 H2S N2 N2 H2S c02 H20 N2 N2 H2 c02

HE

co

H2 H2S H2

co

H2S N2

DY 1.2 0.7 0.8 1.3 2.7 0.6 0.9 0.9 0.7 0.5 0.4 1.0 0.7 0.2 0.3 1.2 0.5 0.7 0.2 0.3 0.5 0.2 0.2 0.6 0.3

PTS PTSM 70 64 84 32 19 20 26 29 26 24 51 6 24 14 9 18 7 7 8 7 6 9 13 27 4

70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4

57.0 2131 1.1

2272

-0.2544 0.0170 -0.3040 0.0487 0.0340 0.0679 0.0234 -0.1327 0.0287 -0.2864 -0.0308 0.0563 0.0668 0.0502 -0.0378 0.0865 0.0539 -0.0356 -0.0114 -0.0370 0.0301 -0.0453 -0.0359 -0.0422 -0.0568 0.0165 -0.2331 0.0496 -0.0208 0.0912 -0.0761

0.0069 0.0038 0.0186 0.0077 0.0100 0.0030 0.0042 0.0059 0.0041 0.0136 0.0034 0.0018 0.0033 0.0022 0.008 0.0013 0.0022 0.0030 0.0071 0.0034 0.0024 0.0045 0.0092 0.0080 0.0030 0.0026 0.0110 0.0049 0.0028 0.0077 0.0009

5.8 0.8 17 17 8.7 2.1 44 44 7.5 0.2 10 10 2.6 2.7 31 31 1.1 3.6 9 9 4.7 2.6 28 31 4.8 2.9 28 29 7.0 1.1 28 28 7.6 3.0 42 45 17.2 1.6 41 41 4.1 2.3 27 28 2.0 0.7 34 34 4.2 1.3 22 22 2.1 11 11 0.6 0.4 51 51 0.2 9 1.6 0.7 9 4.7 1.5 33 33 1.7 27 4.4 27 12.5 0.9 23 23 4.2 2.1 33 35 5.4 1.7 38 39 6.9 2.0 29 30 14.6 18 18 0.9 13.2 0.4 15 15 28 4.9 1.5 29 6.4 32 32 1.6 11 42.3 12.9 16 13 1.2 5.3 13 1.8 20 1.9 20 0.9 3.5 16 16 2.0 4.7 43 66 398.9 112.3 2967 3071 6.1 1.7

0.0605 0.0235 0.0261 0.0952 0.1148 0.0106 0.0537 -0.0680

0.1254 0.0010 0.1462 0.0008 0.0074 0.0012 0.0032 0.0012

53.1 14.4 49.9 1.2 4.1 0.4 8.8 2.5 390.1 20.5

9.6 1.9 21.7 1.2 1.9 0.2 1.5 1.4 82.4 4.3

11

147 12 153 19 8 49 100 973

223 147 149 156 20 8 50 111

1411

3116 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Table 5. Binary Interaction Parameters for TBS EOS (Conventional Mixing Rules) COMP(1)

e1 c1 c1 c1 c1 c1 c1 c1 c1 c1 e1 c1 c1 c1 c1 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2

c2

c3 c3 c3 c3 c3 c3 c3 c3 e3 c3 NC4 NC4 NC4 NC4 IC4 IC4 NC5 NC5 NC5 C6 C6 C6 c7 C8 C8 total average

c1 c1 c1 c1 c1 c1 c1 c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4

COMP(2) c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6

TOL MXYL MESI c3 NC4 IC4 NC5 c10 C3ENE CYCG

TOL MXYL MESI C3BEN C3CYC6 ClCYC6 NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 e7 c10 C4ENE IC4ENE C3ENE ClCYC6 CYC6 ClCYC5 ClCYC5 CYCG ClCYC6

TOL C2BEN PXYL

co e02 H2 N2

HE H2S so2

co

c02 H2S H2 N2 N2

co

c02 H2S HE H2 N2 c02 H2S

Ka

Kd

SD Ka

0.0137 0.0119 0.0011 0.0447 0.0091 -0.0658 0.0063 -0.0342 -0.0832 -0.0936 -0.0393 -0.1376 -0.0349 -0.1032 -0.1450 0.0070 0.0130 0.0055 0.0238 -0.0756 0.0022 -0.0205 -0.0232 -0.0428 -0.0603 -0.0526 -0.0299 -0.0268 0.0025 0.0043 0.0156 0.0060 -0.0146 -0.0576 -0.0053 -0.0139 -0.0327 -0.0270 0.1265 0.0298 -0.0346 0.0057 0.0266 -0.0206 -0.0256 -0.0102 -0.0120 0.0070 0.0059 0.0011 0.0168 0.0066 -0.0099

-0.0556 0.0182 0.0067 -0.0937 -0.0097 -0.0745 0.0352 -0.0358 0.0263 -0.0654 -0.0031 -0.0531 0.0165 -0.0097 0.0091 -0.0579 -0.0880 -0.1396 -0.1282 -0.0766 -0.1075 -0.0098 -0.0136 -0.0234 -0.0040 -0.0332 -0.0461 -0.0543 -0.0239 0.0020 -0.0455 -0.0945 -0.1506 -0.0640 -0.0328 -0.0700 -0.0304 -0.0119 -0.0875 -0.1780 -0.0338 -0.0198 -0.1115 0.0024 0.0708 0.0069 0.0220 -0.0495 -0.0677 -0.0277 -0.0456 -0.0343 0.0365

a. HC-HC 0.0004 0.0012 0.0001 0.0124 0.0018 0.0155 0.0008 0.0019 0.0156 0.0066 0.0028 0.0087 0.0020 0.0164 0.0167 0.0032 0.0028 0.0036 0.0093 0.0045 0.0130 0.0045 0.0001 0.0058 0.0040 0.0048 0.0022 0.0025 0.0045 0.0066 0.0010 0.0044 0.0075 0.0045 0.0023 0.0022 0.0028 0.0026 0.0034 0.0076 0.0057 0.0034 0.0088 0.0350 0.0077 0.0066 0.0099 0.0046 0.0040 0.0033 0.0149 0.0240 0.0146

0.0104 0.0768 0.0494 0.0276 0.7897 0.0527 0.0698 0.0080 0.1456 0.0906 0.2068 0.0156 0.0353 0.0251 0.1414 0.0770 1.2460 0.3042 -0.0348 0.1134 0.0223

0.0627 0.0152 -0.0383 0.0197 -0.1942 0.0971 0.1387 0.0858 -0.1546 -0.0722 -0.1660 0.1428 0.1453 0.0812 -0.0855 0.0230 -0.2077 -0.2040 0.2807 0.0798 0.1984

b. HC-NHC 0.0052 0.0013 0.0048 0.0012 0.0047 0.0053 0.0228 0.0027 0.0037 0.0134 0.0818 0.0009 0.0020 0.0057 0.0034 0.0066 0.0134 0.0129 0.0321 0.0030 0.0115

SD Kd

DP

DY

PTS

PTSM

0.0002 0.0046 0.0001 0.0639 0.0052 0.0314 0.0024 0.0050 0.0247 0.0082 0.0052 0.0098 0.0028 0.0188 0.0162 0.0192 0.0242 0.0332 0.0562 0.0134 0.0445 0.0102 0.0001 0.0131 0.0088 0.0080 0.0067 0.0078 0.0242 0.0412 0.0037 0.0124 0.0735 0.0112 0.0076 0.0085 0.0082 0.0080 0.0197 0.0448 0.0259 0.0182 0.0474 0.2330 0.0286 0.0211 0.0363 0.0148 0.0148 0.0141 0.0448 0.0675 0.0429

1.2 2.0 3.6 1.1 4.6 7.4 5.0 3.8 4.4 8.2 4.1 10.1 3.8 10.5 10.3 1.5 1.8 1.6 3.1 4.8 3.9 2.8 6.6 6.2 4.8 5.6 1.7 2.6 1.6 1.5 0.8 1.2 1.6 3.3 1.4 2.0 3.4 2.7 0.6 0.9 2.5 0.4 0.2 3.4 1.0 0.3 0.6 0.1 0.2 0.3 0.9 1.3 0.1 159.4 3.0

0.3 0.5 0.8 0.8 0.6 4.0 1.0 1.8 0.9 1.2 1.2 2.8 0.1 1.1 1.1 0.6 1.3 1.3 1.2 2.6 3.2 2.2 1.0 1.6 1.1 1.8 1.0 0.9 1.2 0.7 0.8 1.1 2.3 0.6 0.8 0.8 0.7 0.5 0.5 0.5 0.6 0.2 0.4 1.2 0.4 0.7 0.2 0.2 0.1 0.1 0.2 0.7 0.3 53.8 1.0

126 148 140 15 117 28 154 88 18 49 42 36 23 21 22 111 83 66 14 38 26 23 21 27 25 25 27 26 70 64 84 32 20 20 26 29 26 24 51 6 24 14 9 17 7 7 8 7 6 9 13 27 4 2143

150 150 150 15 117 28 156 96 20 49 42 36 23 21 22 157 83 72 14 44 26 24 21 27 25 25 27 26 70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4 2272

0.0293 0.0077 0.0133 0.0087 0.0075 0.0160 0.0569 0.0148 0.0248 0.0520 0.1235 0.0047 0.0060 0.0167 0.0226 0.0443 0.0120 0.0164 0.1161 0.0131 0.0798

2.0 1.3 8.0 0.8 8.6 4.5 1.9 2.5 1.2 1.2 20.3 3.1 4.4 3.0 1.5 1.6 3.5 5.0 12.4 2.9 1.9

1.9 1.0 1.6 0.8 2.4 2.3

72 102 129 176 178 86 5 26 175 27 80 97 107 21 64 71 62 46 19 89 24

75 107 130 184 189 86 5 26 192 27 80

1.1

0.8 0.9 2.5 0.5 0.7 0.6 1.1

0.8 1.3 1.1 0.8 4.8 1.2 1.9

100

107 21 64 79 62 46 19 90 25

Ind. Eng. Chem. Res., Vol. 34,No. 9, 1995 3117 Table 5 (Continued) COMP(1) NC4 IC4 IC4 IC4 NC5 NC5 NC5 IC5 IC5 c7 c7 C8 c9 c10 c10 c12 CYCG CYCG ClCYC6 ClCYC6 ClCYC6 C2CYC6 C2CYC6 C2CYC6 C2ENE C3ENE C4ENE BEN BEN TOL TOL TOL C3CYC6

MXYL MXYL MXYL MESI MESI MESI

c1

C2ENE C3ENE C8H18 C16

COMP(2) H2 c02 H2S N2 H2S e02 N2 N2 e02 e02 H2S

co

H2S e02 N2 H2 c02 H2 c02 H2S N2 c02 N2 H2S e02 c02 c02

co

c02 c02 H2S N2 H2S c02 H2S N2 N2 H2S e02 H20 N2 N2 H2 e02

Kd

SD Ka

0.2384 0.0989 0.0607 0.0273 0.0633 0.1065 -0.0057 -0.0848 0.0760 0.0666 0.0132 -0.1564 -0.1172 -0.0066 -0.3039 -0.0371 0.0697 0.0907 0.0662 -0.0062 -0.1551 0.0265 -0.3355 -0.0416 0.0922 0.1275 0.0624 -0.0446 0.0808 0.0427 -0.0587 -0.0101 -0.0413 0.0227 -0.0882 0.0894 -0.1066 -0.0872 0.0087 0.7389 0.0300 -0.0254 0.1294 -0.0759

-0.1181 0.2245 -0.0984 0.1937 -0.0633 0.0967 0.0424 -0.0142 0.0182 0.0092 0.0543 -0.1167 0.1019 0.0489 0.0250 -0.0862 -0.1187 -0.0294 0.0213 0.0874 0.0194 0.0059 0.0301 0.0208 -0.2122 -0.1888 -0.0387 0.0128 0.0321 0.0419 0.0612 -0.0015 0.0109 0.0216 0.1010 -0.1062 0.0653 0.0586 0.0199 -1.6404 0.2164 0.0205 -0.0203 0.0037

b. HC-NHC 0.0114 0.0073 0.0115 0.0160 0.0060 0.0053 0.0130 0.0117 0.0051 0.0001 0.0050 0.0362 0.0154 0.0060 0.0300 0.0377 0.0080 0.0608 0.0056 0.0077 0.0239 0.0065 0.0469 0.0075 0.0072 0.0152 0.0080 0.0069 0.0017 0.0022 0.0057 0.0201 0.0068 0.0036 0.0070 0.0288 0.0237 0.0050 0.0042 0.0356 0.0034 0.0051 0.0281 0.009

0.1222 1.1004 1.1669 0.3352 1.4320 0.1568 -0.2443 -0.1627 0.0267 -0.1792 -0.0802 0.4644 0.0080 -0.2107 0.0846 0.1846 0.0317 0.0112 -0.0672

-0.0113 -2.1160 -1.5137 -0.8206 -2.6509 -0.3901 -0.0457 -0.0400 0.0420 -0.5099 0.0765 -0.2516 0.0768 0.0330 0.0571 -0.1120 -0.1454 0.0881 0.0342

Ka

DP

DY

PTS

PTSM

0.0128 0.0463 0.0643 0.0430 0.0235 0.0264 0.0267 0.0115 0.0107 0.0001 0.0150 0.0355 0.0200 0.0098 0.0140 0.0119 0.0285 0.0245 0.0117 0.0177 0.0194 0.0099 0.0261 0.0121 0.0420 0.0424 0.0232 0.0128 0.0078 0.0045 0.0131 0.0220 0.0147 0.0060 0.0132 0.0236 0.0229 0.0081 0.0064 0.0611 0.0218 0.0127 0.0134 0.0022

7.2 4.7 1.6 1.5 2.3 2.6 5.1 5.3 1.8 3.5 3.8 0.5 3.1 7.6 5.3 3.1 2.5 2.6 4.3 2.9 6.7 7.6 16.2 3.8 1.7 3.3 1.9 0.4 0.5 2.6 3.0 12.5 4.2 4.3 5.1 10.6 11.6 3.2 5.4 10.6 1.6 1.2 3.4 4.5 288.8 4.4

1.2 2.0 2.2 1.4 2.0 1.9 1.2 2.5 2.3 1.6 1.4 0.5 0.8 2.3 0.8 0.1 1.8 0.9 2.6 3.0 1.3 2.9 1.8 2.3 0.6 1.4 0.8 0.2 0.7 1.4 1.7 0.9 2.1 1.7 1.9 0.8 0.9 1.5 1.5 2.2 1.0 2.0 0.8 2.0 97.0 1.5

93 37 61 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 28 28 28 42 41 27 34 22 11 51 9 33 27 23 33 38 29 18 15 28 32 16 13 20 16 43 2974

93 39 63 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 31 29 28 45 41 28 34 22 11 51 9 33 27 23 35 39 30 18 15 29 32 16 13 20 16 66 3071

0.0319 0.1028 0.0261 0.0722 0.1603 0.0001 0.0191 0.0119 0.0098 0.0233 0.0162 0.0087 0.0001 11.7439 0.0001 0.0218 0.0547 0.0249 0.0164

9.7 12.4 5.8 10.3 13.7 14.3 6.8 2.8 9.0 22.9 3.5 13.0 13.2 36.2 0.9 3.0 0.2 8.5 2.4 188.6 9.9

1.4 1.8 0.7 1.5 2.4 7.5 1.6 0.4 0.6 0.8 2.0 2.5 2.9 29.0 1.4 1.2 0.2 1.8

72 18 18 11 16 109 211 10 12 19 34 101 146 5 154 19 8 49 99

72 18 18 17 16 116 215 10 12 19 34 223 147 149 156 20 8 50

1111

1411

SD Kd

total average C.

N2

co H2 H2S N2 c02 H20 H2 e02 NH3

co

N2 H2 HE c02 c02 N2

co

c02 total average

H2S H20 H20 H20 H20 H20 NH3 PHENOL PHENOL PHENOL c02 HE

co

H2 H2S H2

co

H2S N2

NHC-NHC 0.0170 0.0840 0.0348 0.0300 0.1265 0.0001 0.0030 0.0355 0.0034 0.0194 0.0042 0.0029 0.0001 4.9036 0.0001 0.0152 0.0076 0.0130 0.0044

1.6 61.3 3.2

111

3118 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Table 6. Binary Interaction Parameters for TBS EOS (SR-1 Mixing Rules) COMP(1)

COMP(2)

Ka

L

c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1

c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6

0.0096 0.0163 0.0021 -0.0067 0.0091 -0.1088 0.0153 -0.0380 -0.0261 -0.1041 -0.0337 -0.1309 -0.0332 -0.0372 -0.0830 0.0002 0.0050 -0.0096 0.0112 -0.0881 -0.0196 -0.0269 -0.0203 -0.0438 -0.0576 -0.0569 -0.0389 -0.0389 0.0028 0.0093 0.0125 -0.0205 -0.0213 -0.0679 -0.0084 -0.0237 -0.0345 -0.0257 -0.0010 0.0058 -0.0364 0.0031 0.0062 -0.0178 -0.0075 -0.0076 -0.0066 -0.0030 -0.0092 -0.0035 0.0048 -0.0041 0.0030

0.6855 -0.1292 -0.0207 -4.0972 0.9823 -0.7265 -1.4223 2.9270 8.1063 10.0420 1.2076 6.7821 -1.5146 8.6880 6.7441 0.3496 0.6777 -1.2532 3.0754 7.4928 2.1884 -0.7098 2.3097 2.6638 1.7723 3.7584 2.0812 1.0148 1.6744 2.1588 1.4465 1.4933 2.7218 6.6235 2.0785 5.3232 3.9181 2.6645 -0.5583 4.4116 6.1774 0.4195 1.4059 8.7496 -2.4670 -0.4276 - 1.1235 2.0607 4.2743 1.4364 1.5356 -3.4416 -0.8563

SD Ka a. HC-HC 0.0005 0.0006 0.0008 0.0280 0.0004 0.0588 0.0007 0.0015 0.0088 0.0049 0.0027 0.0058 0.0017 0.0119 0.0127 0.0011 0.0018 0.0036 0.0043 0.0031 0.0048 0.0060 0.0048 0.0046 0.0029 0.0040 0.0013 0.0021 0.0014 0.0012 0.0010 0.0030 0.0063 0.0018 0.0014 0.0011 0.0017 0.0016 0.0010 0.0060 0.0016 0.0010 0.0032 0.0053 0.0022 0.0018 0.0015 0.0008 0.0010 0.0005 0.0011 0.0011 0.0045

0.0249 0.0831 0.0526 0.0331 0.6171 0.0898 0.2836 0.0269 0.1259 0.0880 0.1216 0.0548 0.0950 0.0598 0.1336 0.0864 1.0215 0.1576 0.0122 0.1370 0.0579

0.3225 0.2345 3.8622 0.1924 7.3707 0.4982 10.5920 0.5979 0.0109 1.5771 33.6458 4.0603 6.2866 3.3128 1.7775 3.9299 26.0212 11.0109 -0.0500 4.3057 3.9483

b. HC-NHC 0.0020 0.0016 0.0026 0.0007 0.0058 0.0170 0.0704 0.0022 0.0014 0.0060 0.0078 0.0013 0.0018 0.0030 0.0011 0.0019 0.0081 0.0087 0.0664 0.0013 0.0036

c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4 NC4 IC4 IC4 NC5 NC5 NC5 C6 C6 C6 c7 C8 C8 total average

c1 c1 c1 c1 c1 c1 c1

c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4


TOL MXYL MESI E3BEN C3CYC6 ClCYC6 NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 c7 c10 C4ENE IC4ENE C3ENE ClCYC6 CYCG ClCYC5 ClCYC5 CYCG ClCYC6 TOL C2BEN PXYL

co c02 H2 N2 HE H2S so2

co

c02 H2S H2 N2 N2

co


SD L

DP

DY

PTS

PTSM

0.0639 0.0931 0.0997 3.3774 0.1696 0.4974 0.1184 0.3359 1.7660 0.9554 0.3878 0.6583 0.2390 1.4054 1.5669 0.2778 0.5209 0.9446 1.1237 0.9908 0.9153 1.2401 1.0553 0.9832 0.7264 0.9144 0.4581 0.6300 0.5099 0.5266 0.4557 0.8628 3.1537 0.7001 0.4802 0.5680 0.6514 0.6133 0.5119 1.7237 1.0274 0.3320 0.7695 1.5800 0.7566 0.6676 0.8642 0.6320 0.8618 0.4274 0.7717 0.9613 1.8403

1.1 2.2 3.8 1.1 4.4 7.1 5.0 3.2 3.2 5.6 3.6 6.6 3.7 7.4 9.0 1.7 1.7 1.1 3.3 3.9 4.1 2.6 6.1 6.7 4.6 5.7 1.5 2.8 1.6 1.3 0.8 1.6 1.2 2.1 1.0 1.6 2.7 2.2 0.8 0.8 1.9 0.3 0.2 1.2 0.8 0.2 0.4 0.2 0.4 0.3 0.7 1.0 0.1 148.7 2.6

0.3 0.5 0.7 1.0 0.7 4.4 0.9 1.6 0.7 0.7 1.1 1.8 0.1 0.6 0.8 0.7 1.4 1.6 0.9 1.6 3.1 2.2 0.1 0.8 0.7 1.0 0.7 0.5 1.2 0.8 0.8 0.8 2.5 0.2 0.7 0.6 0.7 0.4 0.5 0.8 0.5 0.2 0.4 1.6 0.3 0.6 0.2 0.2 0.1 0.1 0.2 0.5 0.2 47.4 0.9

106 139 125 15 111 18 152 77 18 44 41 34 23 21 22 97 73 54 13 28 26 22 17 19 23 20 21 21 70 63 83 25 17 18 24 25 24 22 51 6 22 14 9 14 7 7 8 7 6 9 13 27 4 1955

150 150 150 15 117 28 156 96 20 49 42 36 23 21 22 157 83 72 14 44 26 24 21 27 25 25 27 26 70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4 2272

0.3107 0.0834 0.9499 0.0804 7.5628 0.9460 4.6993 0.3517 0.1879 0.6767 4.2334 0.3890 0.9716 1.3758 0.4179 0.7202 20.5312 5.7423 5.3308 0.6597 1.6086

2.3 1.2 5.2 0.9 12.8 4.9 2.8 3.5 1.4 1.1 19.7 4.0 7.8 3.6 1.2 1.4 6.1 6.8 14.4 2.5 2.3

1.9 1.0 3.5 0.9 4.5 1.8 0.4 0.9

69 96 70 168 115 86 5 26 176 27 79 79 96 21 63 76 57 37 17 87 24

75 107 130 184 189 86 5 26 192 27 80 100 107 21 64 79 62 46 19 90 25

1.0

2.5 2.7 0.6 1.0 1.1

0.9 1.6 2.2 2.0 5.0 1.2 1.7

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3119 Table 6 (Continued) COMP(1)

COMP(2)

NC4 IC4 IC4 IC4 NC5 NC5 NC5 IC5 IC5 c7 c7 C8 c9 c10 c10 c12 CYCG CYCG ClCYC6 ClCYC6 ClCYC6 C2CYC6 C2CYC6 C2CYC6 C2ENE C3ENE C4ENE BEN BEN TOL TOL TOL C3CYC6

H2


c1

C2ENE C3ENE C8H18 C16 total average

c02 H2S N2 H2S c02 N2 N2 c02 c02 H2S

co

H2S c02 N2 H2 c02 H2 c02 H2S N2 c02 N2 H2S c02

c02 c02

co


Ka

L

0.1459 0.1425 0.0516 0.0907 0.0515 0.1298 0.0025 -0.1189 0.0860 0.0670 0.0436 -0.2673 -0.0445 0.0164 -0.2458 -0.0176 0.0402 0.0076 0.0700 0.0292 -0.1559 0.0176 -0.3154 -0.0242 0.0614 0.0625 0.0461 -0.0378 0.0922 0.0643 -0.0264 -0.0568 -0.0354 0.0308 -0.0222 -0.1490 0.0186 -0.0393 0.0222 -3.2103 0.0695 -0.0206 0.0510 -0.0760

4.6825 7.1777 2.6098 8.4388 1.3095 4.2593 -6.2104 -8.7778 1.4190 -0.8807 8.2922 -23.1370 -6.6894 -0.3990 7.0490 -18.9527 -4.2981 -7.4669 0.3378 2.9051 -15.5629 -3.3349 -14.8785 3.4732 0.6407 -1.8244 -1.9416 1.2929 1.8177 2.6695 4.3869 -13.5298 1.0422 0.0206 11.2523 -34.1636 17.6562 10.1551 1.3192 -128.1851 3.9836 -0.0837 - 13.9951 0.0036

0.1691 -2.1435 18.8378 -0.3751 -2.4792 -0.0298 -0.0246 0.4371 0.0384 -0.3744 -0.0550 0.0534 0.0256 -0.0473 0.0952 0.1044 0.0181 0.0902 -0.0569

1.7687 -43.5297 311.5039 -26.3789 -49.5581 -0.4796 1.1918 18.5346 -0.8398 38.4383 0.0127 -0.4723 0.0124 -0.1285 -0.1522 -0.9421 0.1799 1.3285 -0.6388

SD Ka

b. HC-NHC 0.0077 0.0040 0.0039 0.0065 0.0030 0.0041 0.0087 0.0064 0.0032 0.0030 0.0032 0.0026 0.0105 0.0081 0.0109 0.0172 0.0063 0.0108 0.0040 0.0057 0.0100 0.0064 0.0233 0.0039 0.0022 0.0045 0.0029 0.0009 0.0016 0.0023 0.0032 0.0179 0.0042 0.0033 0.0064 0.0157 0.0452 0.0039 0.0040 0.3802 0.0040 0.0029 0.0091 0.0015

C.

N2

co

H2 H2S N2 c02 H20 H2 c02 NH3

co

N2 H2 HE c02 c02 N2

co

c02 total average


co

H2 H2S H2

co

H2S N2

NHC-NHC 0.0062 0.0659 0.8999 0.2423 0.0843 0.0207 0.0018 0.1764 0.0024 0.1036 0.0165 0.1290 0.0091 3.1149 0.0016 0.0044 0.0016 0.0742 0.0028

SD L

DP

DY

PTS

PTSM

2.5373 1.8030 1.1466 7.7718 1.6769 1.5000 4.0767 2.0475 1.2671 1.2433 1.5493 5.0434 16.1537 4.7708 8.3449 1.1882 4.1489 3.2869 1.3424 2.7006 5.4517 1.8958 8.7983 1.8162 0.4138 1.1954 0.9140 2.6769 0.4513 0.5144 1.1198 4.6027 2.2413 0.8099 2.7892 4.0377 13.4232 1.9681 1.1979 16.2598 2.7879 0.9760 2.3756 0.4804

7.2 4.6 1.1 3.3 1.8 2.7 5.6 4.5 2.0 3.6 3.1 0.5 7.1 8.8 5.6 1.4 2.2 3.0 5.2 4.5 6.3 8.8 17.7 3.6 2.0 3.9 1.9 0.4 0.7 3.6 3.8 10.4 3.5 5.5 6.7 7.0 10.4 4.0 6.5 7.4 2.5 1.7 2.4 5.1 309.7 4.8

2.1 1.7 2.3 1.8 1.7 2.0 0.9 1.7 2.2 1.2 1.1 0.1 1.1 1.9 0.8 0.1 1.9 0.7 1.8 2.6 0.4 2.3 1.0 1.4 0.7 1.3 0.7 0.2 0.7 1.2 1.2 1.3 0.8 1.6 1.6 0.8 0.8 1.2 1.0 3.0 1.6 1.7 0.5 0.3 95.3 1.5

77 32 55 12 28 27 42 47 28 50 35 15 10 43 17 10 25 9 24 26 28 35 41 24 34 22 11 51 9 31 25 23 26 34 27 18 12 26 27 3 10 18 16 30 2667

93 39 63 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 31 29 28 45 41 28 34 22 11 51 9 33 27 23 35 39 30 18 15 29 32 16 13 20 16 66 3071

2.0994 1.8788 14.2486 17.6345 2.2642 1.1042 0.4155 4.5627 0.8147 2.2259 0.5056 222.9418 0.1314 6.7693 0.1415 2.1934 0.0948 2.7494 0.0320

8.8 10.6 10.4 26.9 10.6 20.9 7.1 3.0 10.1 20.7 4.0 55.0 14.2 36.9 1.3 2.6 0.5 8.7 2.6 254.8 13.4

1.6 3.2 4.4 3.8 3.2 2.7 1.5 0.1 0.5 0.5 1.7 9.2 1.6 22.7 1.2 1.1 0.3 1.8 1.3 62.5 3.3

72 18 18 14 16 36 208 10 12 17 29 12 91 8 153 13 8 49 93 877

72 18 18 17 16 116 215 10 12 19 34 223 147 149 156 20 8 50 111 1411

3120 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Table 7. Binary Interaction Parameters for TBS EOS (SR-2Mixing Rules) COMP(1) COMP(2) Ka L Kd SDKa SDL

c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c2 c2

c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4 NC4 IC4 IC4 NC5 NC5 NC5 C6 66 C6 c7 C8 C8 total average


c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6


TOL MXYL MESI C3BEN C3CYC6 ClCYC6 NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 c7

c10 C4ENE IC4ENE C3ENE ClCYC6 CYCG ClCYC5 ClCYC5 CYCG ClCYC6

TOL C2BEN PXYL

co c02 H2 N2 HE H2S SO2

co

c02 H2S H2 N2. N2

co


0.0104 0.0116 -0.0029 0.0012 0.0039 -0.2080 0.0105 -0.0439 -0.0685 -0.1307 -0.0367 -0.1350 -0.0283 -0.0516 -0.1021 0.0067 0.0130 0.0115 0.0155 -0.0974 0.0052 -0.0247 -0.0327 -0.0605 -0.0689 -0.0614 -0.0329 -0.0227 -0.0032 -0.0124 0.0117 0.0097 -0.0137 -0.0759 -0.0075 -0.0216 -0.0417 -0.0340 0.0142 0.0220 -0.0548 0.0052 -0.0338 -0.0249 -0.0029 0.0028 0.0143 -0.0081 -0.0046 -0.0052 0.0051 0.0360 0.0345

0.0102 0.0816 0.0581 0.0322 0.7804 0.0329 0.1796 -0.0220 0.1435 0.0907 0.2815 0.0124 0.0288 -0.0572 0.1469 0.0846 1.2435 0.3266 0.0234 0.1240 0.0303

0.6436 0.3697 2.3168 -5.7210 5.0048 1.7199 -0.6813 7.5587 14.2525 30.4992 5.7684 17.8022 -4.9439 18.5853 21.9740 0.0926 -1.0095 -3.0933 2.3356 12.7097 -0.0811 -1.5258 10.2471 16.8178 10.4962 6.7788 0.1985 -3.0377 2.2506 3.1367 1.6085 -1.5637 -1.2953 10.2204 1.8037 4.4175 8.0942 7.7214 -0.0569 1.9291 12.3688 0.3850 3.9984 9.0112 -2.9934 - 1.9246 -3.0013 2.5899 3.4344 1.7060 1.5122 -4.9083 -2.3046

-0.1530 0.3305 3.7509 0.1600 0.6928 -0.6491 6.9136 -2.8240 0.3981 1.1796 25.3870 -0.0011 -1.6872 -15.0269 1.8350 4.1762 14.1736 9.6679 -6.8689 2.8964 2.9688

a. HC-HC 0.0017 -0.0059 0.0014 0.0312 0.0020 0.0606 -0.1158 0.0247 0.0710 0.0020 0.3562 0.0959 0.0174 0.0019 0.0021 0.0712 0.1174 0.0062 0.1564 0.0034 0.0658 0.0021 0.117 0.0044 0.0039 -0.0391 0.1206 0.0056 0.1517 0.0026 -0.0460 0.0037 0.1016 0.0034 -0.2637 0.0044 -0.0394 0.0115 0.0611 0.0062 -0.1130 0.0199 -0.0144 0.0096 0.0051 0.1350 0.1782 0.0017 0.0983 0.0031 0.0335 0.0055 0.0024 -0.0365 -0.0756 0.0027 0.0391 0.0046 0.1491 0.0064 0.0080 0.0035 -0.1166 0.0057 -0.1720 0.0129 0.0419 0.0043 0.0021 -0.0058 -0.0141 0.0027 90.0512 0.0026 0.0632 0.0019 -0.0863 0.0041 0.0259 -0.1105 0.1269 0.0062 -0.0111 0.0040 0.0070 0.2818 0.0478 0.0450 0.0298 -0.0190 -0.0396 0.0135 -0.0819 0.0318 0.0214 0.0096 0.0174 -0.0184 0.0077 0.0064 -0.0008 0.0107 0.0105 -0.1059 -0.0911 0.3282

b. HC-NHC 0.0714 0.0074 0.0276 0.0018 -0.0085 0.0136 0.0055 0.0021 -0.1869 0.0135 0.1237 0.0184 0.1213 0.0530 0.1962 0.0058 -0.1169 0.0038 -0.0262 0.0111 -0.2457 0.1207 0.1494 0.0033 0.1565 0.0050 0.2522 0.0188 -0.0921 0.0044 0.0196 0.0078 -0.2025 0.0103 -0.2193 0.0136 0.3987 0.0632 0.0497 0.0050 0.1747 0.0202

0.1087 0.1628 0.3770 2.8468 0.6111 15.5059 0.3189 0.8651 1.9328 1.5083 0.7006 1.5629 2.3768 1.3021 0.7576 0.3281 0.6977 0.4836 2.1664 2.7746 1.6363 1.8618 2.2216 2.5422 1.4088 2.3517 0.9280 0.9499 0.6520 0.5594 0.7746 0.8557 5.3734 1.8980 0.7790 1.1749 1.4097 1.0513 0.4346 4.1230 2.3234 0.3649 0.8304 2.7408 3.2616 2.7983 2.2911 1.0252 2.2783 1.1074 2.6158 0.9035 0.9342

0.4043 0.0700 0.6136 0.0988 1.2852 1.0906 3.2855 0.4808 0.1988 1.2075 13.8895 0.5037 1.0875 3.6876 0.3291 0.8434 2.2346 1.7537 6.9437 0.9262 2.7043

SDKd

DP

DY

PTS

0.0127 0.0082 0.0119 0.0868 0.0117 0.2290 0.0074 0.0111 0.0185 0.0107 0.0089 0.0147 0.0272 0.0124 0.0061 0.0251 0.0342 0.0470 0.0951 0.0306 0.0842 0.0314 0.0330 0.0294 0.0147 0.0242 0.0120 0.0143 0.0297 0.0475 0.0364 0.0208 0.1809 0.0201 0.0116 0.0150 0.0153 0.0113 0.0235 0.1733 0.0396 0.0211 0.0594 0.2821 0.1152 0.0540 0.1144 0.0408 0.0634 0.0297 0.1363 0.0269 0.8224

1.1 2.1 3.6 0.8 3.8 5.9 5.0 2.8 1.1 2.6 2.1 3.8 3.7 3.4 1.2 1.6 1.6 1.1 3.2 4.0 3.8 2.6 4.8 4.3 3.0 6.0 1.2 1.7 1.6 1.3 0.8 0.9 1.3 1.9 1.1 1.5 2.4 1.7 0.6 0.8 1.0 0.3 0.1 1.1 0.8 0.2 0.4 0.2 0.3 0.3 0.7 0.6 0.1 105.0 2.0

0.3 0.4 0.8 1.o 0.5 5.2 0.9 1.4 0.8 0.7 1.2 1.4 0.1 0.5 0.6 0.7 1.4 1.2 0.9 1.7 3.1 2.2 0.8 0.8 0.6 1.1 0.6 0.9 1.3 0.8 0.8 1.1 2.0 0.3 0.7 0.6 0.6 0.4 0.5 0.6 0.8 0.2 0.2 1.6 0.3 0.4 0.2 0.2 0.1 0.2 0.2 0.4 0.2 46.5 0.9

106 138 118 15 103 14 150 69 18 42 41 30 23 21 22 98 76 60 13 28 26 22 16 15 19 19 22 23 69 64 83 31 17 18 24 25 23 21 51 6 22 14 9 14 7 7 8 7 6 9 13 27 4 1926

2272

2.0 1.1 5.0 0.9 8.2 4.8 1.5 2.0 1.2 1.0 19.5 2.7 4.0 2.2 1.0 1.3 2.8 3.5 13.4 2.6 1.6

2.1 1.0 3.6 0.9 2.0 2.6 0.8 0.7 0.9 2.4 1.5 0.7 0.7 1.1 0.8 1.6 0.8 1.3 4.6 1.2 1.9

67 94 72 168 137 76 5 26 178 27 80 89 104 21 63 74 62 41 17 85 24

75 107 130 184 189 86 5 26 192 27 80 100 107 21 64 79 62 46 19 90 25

0.0385 0.0088 0.0307 0.0130 0.0172 0.0196 0.0393 0.0237 0.0276 0.0732 0.1822 0.0104 0.0104 0.0405 0.0266 0.0505 0.0953 0.0171 0.1648 0.0180 0.1176

PTSM 150 150 150 15 117 28 156 96 20 49 42 36 23 21 22 157 83 72 14 28 26 24 21 27 25 25 27 26 70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3121 Table 7 (Continued) COMP(1)

COMP(2)


H2 c02 H2S N2 H2S c02 N2 N2 c02 c02 H2S

Ka

L

Kd

SDKa

0.3193 0.0816 0.0678 0.0228 0.0719 0.1113 -0.2141 -0.2397 0.0741 0.0166 0.0374 -0.2151 -0.1560 -0.1620 -1.0362 -0.0248 0.0456 0.0358 0.0021 -0.0419 -0.4013 -0.1229 -1.2995 -0.0658 0.1136 0.2046 0.0469 -0.0482 0.0746 0.0427 -0.0720 -0.3750 -0.1070 -0.0234 -0.1481 -0.5191 -0.4122 -0.1092 -0.1126 0.7370 0.0329 -0.0024 -0.0418 -0.1238

12.7492 0.4614 2.6765 -3.0246 3.9339 1.6352 -58.6868 -29.3006 -0.3962 -15.1811 6.9632 -14.9511 -34.9917 -72.7607 -194.4117 -22.9030 -4.8664 -4.9725 -17.1641 -11.7587 -65.3822 -39.5627 -232.8755 -5.1982 -0.9802 2.4817 -1.8564 0.4436 -1.2881 1.5259 -2.3349 -66.9278 -19.7849 -11.5991 -16.9046 -97.8101 -58.5676 -6.1245 -37.2592 -0.0278 0.2232 5.5612 -23.8683 -25.4640

-0.1716 0.3476 -0.1011 0.2034 -0.0733 0.0856 0.3172 0.0856 0.0226 0.0924 0.0131 -0.0560 0.1304 0.1767 0.3021 0.0216 -0.0212 -0.0102 0.1032 0.1465 0.1571 0.1380 0.4310 0.0515 -0.3400 -0.3392 -0.0020 0.0198 0.0501 0.0428 0.0870 0.2059 0.1138 0.0701 0.1811 0.1904 0.1902 0.0843 0.1341 -1.6387 0.2005 -0.0328 0.0356 0.1019

0.2341 -2.6228 3.5737 -0.3333 -3.8041 0.1420 -0.0972 0.2744 0.0068 -0.2856 -0.0557 0.0773 0.0244 -0.200 1 0.0857 0.1652 -0.0176 0.0225 -0.0645

2.9168 -51.4250 40.3722 -37.3522 -69.2815 -0.3372 11.1713 13.1329 7.3569 19.4204 0.0110 -0.5172 0.0000 -0.7337 -0.0796 -0.0091 0.3791 0.4025 -0.9590

-0.0592 0.2587 -1.3961 -0.4999 0.7639 -0.3729 -0.5932 -0.0157 0.1536 -0.2574 0.0018 0.0068 0.0028 -0.4366 0.0555 -0.0867 0.3009 0.0873 0.0264

SDL

SDKd

DP

DY

PTS

PTSM

b. HC-NHC


c1


co

H2S c02 N2 H2 c02 H2 c02 H2S N2 c02 N2 H2S c02 c02 c02

co


C.

N2

co H2 H2S N2

c02 H20 H2 c02 NH3

co

N2 H2 HE c02 c02 N2

co

c02 total average


co

H2 H2S H2

co

H2S N2

0.0144 0.0143 0.0153 0.0216 0.0124 0.0126 0.0371 0.0267 0.0149 0.0114 0.0152 0.0126 0.0143 0.0179 0.1268 0.0163 0.0120 0.0895 0.0182 0.0146 0.0373 0.0284 0.1514 0.0200 0.0086 0.0195 0.0231 0.0084 0.0136 0.0054 0.0122 0.0771 0.0112 0.0134 0.0189 0.1155 0.0502 0.0146 0.0181 0.0760 0.0050 0.0379 0.0288 0.0110

1.4172 3.8212 0.9858 6.4786 2.5827 2.7936 10.2672 5.0404 2.9365 3.4523 3.4633 4.6119 7.8837 8.9144 40.0582 3.0872 5.3543 9.3389 5.3025 3.9266 8.6581 9.0078 43.3360 5.2433 0.3270 0.5444 2.4101 2.1172 2.5121 0.9137 2.5434 14.9837 3.8072 3.1395 5.6059 23.3912 102.7199 4.0014 6.0636 1.9010 3.1865 3.3298 3.7777 5.8936

0.0132 0.0754 0.0797 0.0529 0.0356 0.0461 0.0536 0.0183 0.0225 0.0201 0.0308 0.0132 0.0151 0.0157 0.0480 0.0157 0.0471 0.0312 0.0262 0.0256 0.0232 0.0280 0.0650 0.0299 0.0504 0.0364 0.0558 0.0158 0.0404 0.0084 0.0203 0.0484 0.0203 0.0156 0.0256 0.0581 0.2184 0.0169 0.0175 0.0739 0.0281 0.0609 0.0104 0.0231

4.6 4.2 1.3 1.6 1.5 2.7 3.6 3.3 1.8 3.4 3.1 0.3 1.9 5.0 2.2 1.5 2.2 2.8 4.0 2.3 2.8 8.0 9.5 3.0 1.4 2.2 1.9 0.4 0.4 2.6 2.4 6.2 2.8 4.5 4.4 5.0 10.9 2.7 4.2 10.8 1.3 2.2 1.8 4.0 232.9 3.6

2.1 1.8 2.2 1.0 1.8 1.9 1.8 1.4 2.1 1.0 1.1 0.1 0.8 0.4 0.6 0.1 1.8 1.0 1.6 2.4 1.0 1.0 1.9 1.3 0.8 1.5 0.7 0.2 0.7 1.0 1.2 2.4 0.7 1.0 1.4 1.0 0.3 1.2 0.7 2.1 1.0 3.1 0.4 0.1 84.4 1.3

86 29 57 13 29 26 42 47 28 41 35 15 10 43 17 10 25 9 21 25 28 29 41 23 34 22 11 51 9 29 24 23 24 28 25 18 15 26 26 15 10 13 16 22 2680

93 39 63 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 31 29 28 45 41 28 34 22 11 51 9 33 27 23 35 39 30 18 15 29 32 16 13 20 16 66 3071

NHC-NHC 0.0794 0.6724 2.7716 0.3093 1.5974 0.0316 0.0056 0.2912 0.0022 0.0441 0.0192 1.0990 0.0119 58.9054 0.0039 0.0237 0.0125 0.0675 0.0047

2.3796 8.8600 48.5030 17.7403 18.6057 0.8450 0.3540 8.8026 0.9897 8.1330 0.5319 224.5538 0.1057 212.3582 0.1754 1.5819 0.1156 2.2557 0.3635

0.0405 0.4553 0.2296 0.1459 1.1716 0.0392 0.0168 0.0207 0.0114 0.1090 0.0210 2.5645 0.0243 88.2633 0.0188 0.0314 0.1176 0.0249 0.0166

9.1 9.2 3.8 7.1 9.8 14.6 3.9 2.9 1.8 18.2 3.9 52.0 14.0 33.6 1.0 3.0 0.4

2.3 3.4 1.7 1.3 3.5 6.4 1.9 0.1 0.5 0.5 1.7 8.5 1.7 24.7 1.3 0.8 0.4 1.5 1.4 63.8 3.4

72 16 16 14 12 95 208 10 11 17 13 13 92 7 153 16 8 49 94 916

72 18 18 17 16 116 215 10 12 19 34 223 147 149 156 20 8 50 111 1411

8.6

2.0 199.1 10.5

3122 Ind. Eng. Chem. Res., Vol. 34,No. 9, 1995 Table 8. Binary Interaction Parameters for TBS EOS (HV Mixing Rules) COMP(1)

COMP(2)

Ka

c112

C122

SDKa

SDC112

SDC122

DP

DY

PTS

PTSM

c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1

c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6 TOL MXYL MESI c3 NC4 IC4 NC5 c10 C3ENE CYCG TOL MXYL MESI C3BEN C3CYC6 ClCYC6 NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 c7 c10 C4ENE IC4ENE C3ENE ClCYC6 CYCG ClCYC5 ClCYC5 CYCG ClCYC6

0.0016 0.0205 0.0132 0.0242 0.0199 0.1087 0.0215 -0.0132 0.0580 0.1033 0.0344 0.0309 -0.0578 0.0597 0.0622 -0.0068 -0.0046 0.0066 -0.0045 -0.0561 -0.0051 -0.0254 0.0061 -0.0017 -0.0173 0.0140 -0.0256 -0.0359 -0.0140 -0.0095 -0.0081 -0.03 12 -0.0020 -0.0509 -0.0175 -0.0233 -0.0327 -0.0243 -0.0030 -0.0226 -0.0298 -0.0043 -0.0113 -0.0004 -0.0026 -0.0108 -0.0081 -0.0128 -0.0199 -0.0095 -0.0121 -0.0087 -0.0079

0.0682 0.0651 0.0284 -0.0352 0.0247 -1.0879 0.0162 -0.0461 -0.3062 -0.5289 -0.0670 -0.3661 0.0642 -0.1826 -0.3212 -0.0104 0.0156 -0.0174 0.0677 -0.0950 0.1217 0.0005 0.0659 0.0048 -0.0584 -0.1205 -0.0501 -0.0278 -0.0141 0.0161 0.0232 0.0398 0.0114 -0.0802 0.0854 0.0194 0.0517 0.0493 -0.0025 0.0098 -0.0164 0.0246 0.0392 0.0965 0.0165 0.0451 0.0062 0.0368 0.0597 0.0364 0.0780 0.0443 0.0573

-0.0082 -0.0225 -0.0540 0.0162 -0.0646 -0.0407 -0.0041 -0.0915 -0.1519 -0.3198 -0.1539 -0.3483 0.1049 -0.3049 -0.3088 0.0159 0.0134 -0.0114 -0.0152 -0.1312 -0.1184 0.0159 -0.1340 -0.1768 -0.1298 -0.2319 -0.0527 -0.0169 0.0241 0.0202 0.0443 0.0142 -0.0900 -0.0968 -0.0064 -0.0739 -0.0751 -0.0533 0.0057 0.0155 -0.0724 0.0178 0.0249 -0.0280 0.0166 0.0430 0.0310 0.0299 0.0378 0.0263 0.0942 0.0874 0.0893

a. HC-HC 0.0019 0.0020 0.0021 0.0807 0.0041 0.0607 0.0000 0.0055 0.0172 0.0180 0.0100 0.0134 0.0225 0.0263 0.0102 0.0026 0.0039 0.0056 0.0138 0.0081 0.0188 0.0070 0.0144 0.0144 0.0103 0.0317 0.0033 0.0075 0.0024 0.0022 0.0016 0.0044 0.0101 0.0044 0.0036 0.0029 0.0065 0.0058 0.0018 0.0158 0.0039 0.0029 0.0019 0.0172 0.0120 0.0013 0.0020 0.0015 0.0147 0.0020 0.0068 0.0024 0.0012

0.0055 0.0055 0.0049 0.2041 0.0095 0.2559 0.0047 0.0118 0.0546 0.0455 0.0176 0.0286 0.0378 0.0572 0.0226 0.0091 0.0093 0.0127 0.0282 0.0204 0.0641 0.0245 0.0222 0.0237 0.0177 0.0644 0.0076 0.0141 0.0086 0.0072 0.0046 0.0180 0.0274 0.0105 0.0102 0.0064 0.0132 0.0118 0.0037 0.0434 0.0098 0.0034 0.0023 0.0248 0.0601 0.0068 0.0096 0.0047 0.0213 0.0072 0.0203 0.0084 0.1951

0.0092 0.0096 0.0085 0.1233 0.0124 0.0636 0.0039 0.0098 0.0162 0.0180 0.0187 0.0193 0.0528 0.0417 0.0156 0.0101 0.0134 0.0190 0.0432 0.0190 0.0479 0.0236 0.0512 0.0460 0.0311 0.0813 0.0103 0.0290 0.0073 0.0056 0.0054 0.0140 0.0522 0.0129 0.0170 0.0136 0.0298 0.0261 0.0046 0.0318 0.0170 0.0038 0.0031 0.0258 0.0410 0.0057 0.0070 0.0044 0.0224 0.0037 0.0078 0.0082 0.0177

1.3 3.2 3.8 1.4 4.4 5.3 5.8 2.7 1.3 2.4 2.0 2.4 3.6 3.8 1.7 1.6 1.6 1.4 3.3 3.3 4.6 2.6 5.7 6.1 3.8 5.7 1.6 3.3 1.4 1.2 0.6 1.3 1.9 1.8 1.1 1.3 2.8 2.4 0.8 0.6 1.6 0.4 0.2 1.4 0.8 0.2 0.4 0.2 0.4 0.3 0.8 0.6 0.1 103.3 2.0

0.4 0.4 0.8 0.6 0.8 3.3 1.0 0.7 0.2 0.4 0.6 0.4 0.2 0.6 0.4 0.6 1.4 1.2 1.0 1.0 1.6 2.0 0.8 0.9 0.9 1.0 0.3 0.5 0.8 0.3 0.6 1.0 1.5 0.2 0.7 0.5 0.7 0.4 0.4 0.6 0.3 0.1 0.1 1.2 0.3 0.4 0.2 0.2 0.3 0.2 0.2 0.4 0.2 33.9 0.6

104 139 129 15 105 14 147 60 14 28 28 19 21 13 14 93 72 54 13 23 26 22 16 16 16 9 17 20 69 63 82 24 17 17 24 24 23 22 51 6 22 14 9 1.5 7 7 8 7 6 9 13 27 4 1817

150 150 150 15 117 28 156 96 20 49 42 36 23 21 22 157 83 72 14 44 26 24 21 27 25 25 27 26 70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4 2272

0.0152 0.0447 -0.0135 0.0125 0.2664 0.0806 0.1803 0.0206 0.0447 0.0258 -0.2699 0.0674 0.1251 0.1068 0.0641 0.0243 0.7558 -0.0007 0.1150 0.0681 0.0060

0.0572 0.3701 0.1600 0.0872 0.4021 0.2545 0.5330 -0.0528 0.2877 0.3223 0.5687 -0.0480 -0.0782 -0.1914 0.1851 0.2205 0.1673 0.1492 -0.3042 0.1942 0.1443

0.0862 0.1263 -0.1009 0.1394 0.5908 0.0572 -0.1797 0.3159 0.4075 0.3671 -0.9795 0.1309 -0.0722 0.3934 0.4609 0.4438 0.2127 0.2135 -0.0138 0.3576 0.3064

b. HC-NHC 0.0059 0.0080 0.0207 0.0026 0.0397 0.0087 0.2948 0.0087 0.0047 0.0092 0.1055 0.0084 0.0031 0.0074 0.0051 0.0098 0.0379 0.0239 0.1437 0.0071 0.0108

0.0225 0.0232 0.0378 0.0102 0.0454 0.0695 0.4466 0.0411 0.0087 0.0485 0.1367 0.0305 0.0139 0.0297 0.0176 0.0215 0.0270 0.0263 0.2732 0.0252 0.0291

0.0231 0.0257 0.0469 0.0089 0.3479 0.0338 1.0184 0.0249 0.0098 0.0372 0.3835 0.0133 0.0168 0.0247 0.0127 0.0269 0.0627 0.0492 0.1668 0.0168 0.0251

2.6 2.6 2.7 1.7 7.0 4.4 0.9 5.8 2.7 5.1 20.8 6.2 5.3 2.1 3.0 3.7 3.0 3.4 13.7 5.5 3.3

2.4 0.9 1.9

67 67 56 155 50 72 4 25 117 27 71 97 104 20 58 67 54 37 14 77 21

75 107 130 184 189 86 5 26 192 27 80

c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4 NC4 IC4 IC4 NC5 NC5 NC5 C6 C6 C6 c7 C8 C8 total average

c1

c1 c1 c1 c1 c1 c1

c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4

TOL C2BEN PXYL


co

c02 H2S H2 N2 N2

co


1.1

3.0 3.6 0.4 0.8 1.1 2.3 1.3 3.3 3.3 0.9 1.1

1.7 1.3 1.9 6.5 1.2 2.0

100

107 21 64 79 62 46 19 90 25

Ind. Eng. Chem. Res., Vol. 34,No. 9, 1995 3123 Table 8 (Continued) COMP(1)

COMP(2)


H2 c02 H2S N2 H2S c02 N2 N2 c02 c02 H2S


c1


co


co


Ka

c112

C122

SDKa

0.0451 0.0460 0.0043 0.0706 0.0097 0.0441 0.2848 0.0641 0.0486 0.0045 -0.0572 -0.1590 0.0411 0.2371 -0.0409 -0.1832 0.0425 0.1628 0.0576 0.0238 0.0927 0.0315 0.2894 -0.0503 0.0059 0.0310 0.0089 -0.0108 0.0322 0.0433 -0.0302 0.3841 -0.0490 0.0266 -0.0440 0.0473 0.1349 -0.0509 0.0290 -0.7741 0.0221 -0.0058 0.4496 0.2050

0.0680 0.3052 0.1338 0.0671 0.0957 0.1889 -0.2884 -0.2103 0.0966 0.0249 0.2362 -0.0695 -0.1342 -0.3601 -0.1708 -0.1134 0.0005 -0.0548 -0.0031 0.0224 -0.2435 -0.0246 -0.5792 0.0745 0.1382 0.0822 0.0906 -0.0156 0.1661 0.0588 0.0366 -0.2876 0.0224 0.0144 0.0782 -0.2116 -0.1652 0.0179 -0.0228 10.4968 0.1426 0.0626 -0.1901 -0.4499

0.1308 0.3356 0.3812 -0.2183 0.3102 0.3241 -0.4451 -0.1262 0.1960 0.3759 0.3615 -0.0209 -0.3551 -0.6054 -0.2587 0.0872 -0.0019 -0.2723 0.1387 0.0520 -0.0859 0.1184 -0.1309 0.0675 0.2180 0.2956 0.2615 -0.1110 0.2457 0.0888 -0.0817 -1.9702 0.0928 0.0775 -0.1233 0.2356 -0.2774 -0.0894 0.0473 2.1719 0.0306 0.0958 -0.2901 -0.8501

0.1082 - 1.1156 -2.6529 -0.2152 -1.2614 -0.2231 -0.1709 -0.2325 0.1534 -0.1382 -0.0914 0.2921 -0.0235 0.2179 0.0637 0.1786 0.0046 0.0648 -0.0917

0.8372 10.5095 -1.3331 -0.9623 25.9471 3.3728 -0.4452 0.6638 0.0427 -0.1612 0.0820 0.1394 0.3007 0.9210 0.2380 -0.0673 0.0538 0.0816 0.0714

0.0104 1.3064 2.6502 1.3428 1.5627 0.8476 -0.2103 -0.0553 -0.3021 -2.7440 0.1273 -0.0185 0.1632 0.3390 0.1643 -0.3774 0.0343 0.0134 0.3260

b. HC-NHC 0.0342 0.0133 0.0056 0.0268 0.0051 0.0127 0.0448 0.0403 0.0108 0.0129 0.0073 0.0024 0.0361 0.0084 0.0222 0.0649 0.0114 17.8578 0.0110 0.0141 0.0134 0.0180 0.1199 0.0108 0.0057 0.0157 0.0074 0.0114 0.0053 0.0080 0.0068 0.2055 0.0108 0.0074 0.0123 0.0296 0.0144 0.0061 0.0151 0.0230 0.0050 0.0047 0.0779 0.0292

C.

N2

co H2 H2S N2 c02 H20 H2 c02 NH3

co

N2 H2 HE c02 c02 N2

co

c02 total average


co

H2 H2S H2

co

H2S N2

NHC-NHC 0.0203 0.0175 0.0449 0.0088 0.0188 0.0126 0.0112 0.0524 0.0805 0.0437 0.0139 0.1478 0.0045 0.0134 0.0044 0.1714 0.0029 0.0277 0.0192

SDC112

SDC122

DP

DY

PTS

PTSM

0.0302 0.0453 0.0204 0.0287 0.0208 0.0358 0.0470 0.0458 0.0315 0.0345 0.0234 0.0014 0.0895 0.0169 0.0186 0.0234 0.0138 10.7872 0.0418 0.0446 0.0134 0.0482 0.1189 0.0350 0.0078 0.0459 0.0313 0.0084 0.0246 0.0289 0.0246 0.2294 0.0365 0.0248 0.0429 0.0259 0.0231 0.0213 0.0384 4.9470 0.0112 0.0140 0.0380 0.0484

0.0347 0.0309 0.0142 0.1356 0.0208 0.0291 0.0866 0.1234 0.0241 0.0389 0.0201 0.0004 0.1121 0.0281 0.0233 0.0584 0.0814 17.4662 0.0214 0.0332 0.0395 0.0347 0.2960 0.0304 0.0056 0.0324 0.0150 0.0538 0.0057 0.0137 0.0169 1.7109 0.0300 0.0130 0.0304 0.0714 0.0298 0.0159 0.0333 0.0838 0.0267 0.0279 0.0830 0.0889

5.6 5.9 2.2 1.8 2.2 4.5 4.3 3.5 4.2 7.1 3.4 0.4 1.6 2.8 1.7 0.8 2.2 0.8 8.1 7.5 1.2 10.6 13.0 5.3 1.0 3.3 1.8 0.4 0.9 5.4 3.2 4.7 5.5 7.2 6.0 3.5 1.2 3.0 7.6 5.5 1.0 1.3 1.6 2.3 272.4 4.2

2.3 2.0

71 26 48 10 27 22 42 19 22 32 31 14 8 24 14 8 27 3 21 27 10 28 16 22 24 22 11 46 9 22 25 5 22 30 26 11 6 23 21 16 9 17 12 20 2209

93 39 63 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 31 29 28 45 41 28 34 22 11 51 9 33 27 23 35 39 30 18 15 29 32 16 13 20 16 66 3071

0.1569 5.8885 4.8911 0.3901 8.1916 0.2868 0.0490 0.1625 0.0224 0.0914 0.0502 0.1938 0.0299 0.2407 0.0135 0.2390 0.0074 0.2854 0.0447

0.0454 0.0421 0.0649 0.0582 0.0441 0.0464 0.0606 0.0414 0.2387 0.2793 0.0352 0.8240 0.0157 0.0332 0.0102 0.6551 0.0058 0.0824 0.0432

12.5 6.4 3.7 4.2 6.4 3.0 13.0 2.0 11.4 18.0 3.1 5.2 7.2 7.2 2.4 1.4 0.5 8.9 3.5 120.0 6.3

2.3 1.0 2.8 2.8 1.0 3.8 1.9 0.4 1.3 1.9 1.0 1.9 2.6 2.2 1.2 0.8 0.2

55 18 18 15 16 38 208 10 12 19 22 15 82 71 128 5 8

72 18 18 17 16 116 215 10 12 19 34 223 147 149 156 20 8

1.0

40

1.5 31.6 1.7

71 851

50 111

1.1

0.9 2.0 2.3 2.4 1.0 1.2 0.7 1.7 0.4 1.8 0.7 0.2 0.2 2.0 0.6 0.9 1.5 0.2 0.7 1.1 1.4 0.4 1.3 0.7 0.4 0.7 0.8 0.9 3.2 0.6 0.8 1.2 0.8 0.5 0.8 0.4 3.1 1.2 1.6 1.0 0.1 91.8 1.4

1411

3124 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Table 9. Binary Interaction Parameters for TBS EOS (WSHVMixing Rules) COMP(1)

c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c2 c2 c2 c2 c2 c2 c2

c2 c2 c2 c2 c2 c2 c3 c3 c3 c3 c3 c3 c3 c3 c3 c3 NC4 NC4 NC4 NC4 IC4 IC4 NC5 NC5 NC5 C6 C6 C6 c7 C8 C8 total average


COMP(2) c2 c3 NC4 IC4 NC5 IC5 C6 c7 C8 c10 CYCG C2CYC6 TOL MXYL MESI c3 NC4 IC4 NC5 c10 C3ENE CYCG TOL MXYL MESI C3BEN C3CYC6 ClCYC6 NC4 IC4 NC5 IC5 c7 c10 CYCG C3CYC6 C3BEN MESI IC4 c7 c10 C4ENE IC4ENE C3ENE ClCYC6 CYCG ClCYC5 ClCYC5 CYCG ClCYC6 TOL C2BEN PXYL


co

c02 H2S H2 N2 N2

co


Ka

c112

C122

SDKa

0.1431 0.3074 0.4141 0.4595 0.4937 0.6090 0.5967 0.6498 0.6614 0.7264 0.5655 0.6292 0.5546 0.6240 0.6618 0.0450 0.1538 0.1474 0.2563 0.5447 0.0296 0.2663 0.3603 0.4210 0.4686 0.4518 0.4819 0.3407 0.0152 0.0118 0.0936 0.0582 0.2600 0.3909 0.1267 0.3271 0.2904 0.3093 -0.0025 0.1001 0.2778 -0.0040 -0.0131 0.0283 0.0270 -0.0058 -0.0026 -0.0125 -0.0202 -0.0068 -0.0077 -0.0042 -0.0059

0.0598 0.0629 0.0673 0.0031 0.1730 -1.0557 0.0464 -0.0144 0.1221 0.0399 0.0136 0.0472 0.1689 0.1603 0.0793 -0.0110 0.0150 -0.0183 0.0711 -0.0789 0.1198 -0.0080 0.0694 0.0069 -0.0341 0.0082 -0.0407 -0.0416 -0.0154 0.0158 0.0228 0.0338 0.0122 -0.0840 0.0721 0.0112 0.0368 0.0411 -0.0025 -0.0096 -0.0220 0.0247 0.0392 0.0963 0.0158 0.0457 0.0066 0.0368 0.0596 0.0367 0.0778 0.0449 0.0567

0.0071 0.0422 0.0658 0.0326 0.1361 0.0343 0.0452 -0.0018 0.1148 -0.0280 0.0490 -0.0500 0.2298 0.0038 0.0046 0.0161 0.0145 -0.0085 -0.0076 -0.0563 -0.1171 0.1297 -0.0841 -0.0895 -0.0407 -0.0530 0.0382 0.0760 0.0250 0.0203 0.0445 0.0188 -0.0846 -0.0487 0.0193 -0.0316 -0.0196 -0.0079 0.0058 0.0379 -0.0456 0.0179 0.0249 -0.0279 0.0182 0.0428 0.0308 0.0299 0.0381 0.0261 0.0942 0.0888 0.0890

a. HC-HC 0.0018 0.0013 0.0018 0.0632 0.0032 0.0352 0.0010 0.0023 0.0269 0.0047 0.0048 0.0103 0.0148 0.0083 0.0066 0.0028 0.0040 0.0063 0.0139 0.0035 0.0202 0.0109 0.0060 0.0040 0.0023 0.0061 0.0052 0.0102 0.0026 0.0024 0.0016 0.0053 0.0094 0.0032 0.0051 0.0037 0.0037 0.0024 0.0020 0.0122 0.0025 0.0031 0.0022 0.0194 0.0165 0.0015 0.0022 0.0017 0.0164 0.0022 0.0076 0.0026 0.0034

0.0530 0.1251 0.4802 0.0658 0.7796 0.1883 0.3453 0.2790 0.0666 0.0312 0.5885 0.3274 0.4808 0.4585 0.1869 0.0980 0.9500 0.7372 0.7983 0.2970 0.1837

0.0727 0.3683 0.2626 0.1131 0.6475 0.2580 0.5092 0.1668 0.2879 0.3226 0.6335 0.1989 0.3148 0.1486 0.1859 0.2199 0.4983 0.3768 -0.1289 0.2035 0.1440

0.0752 0.1301 -0.0598 0.1258 1.1421 0.1150 0.0790 0.2214 0.4072 0.3667 -0.5914 0.1340 0.2276 0.1935 0.4587 0.4442 1.3354 0.4620 -0.1144 0.3733 0.3063

b. HC-NHC 0.0059 0.0072 0.0152 0.0025 0.0106 0.0050 0.1754 0.0038 0.0054 0.0102 0.0294 0.0021 0.0015 0.0077 0.0050 0.0103 0.0084 0.0077 0.3958 0.0043 0.0104

SDC112

SDC122

DP

DY

PTS

PTSM

0.0053 0.0057 0.0069 0.2335 0.0159 0.2280 0.0039 0.0114 0.2240 0.0437 0.0202 0.0647 0.0664 0.0505 0.0450 0.0093 0.0095 0.0138 0.0301 0.0191 0.0642 0.0416 0.0126 0.0112 0.0082 0.0223 0.0236 0.0276 0.0088 0.0072 0.0046 0.0197 0.0284 0.0126 0.0145 0.0112 0.0104 0.0076 0.0037 0.0345 0.0086 0.0033 0.0023 0.0246 0.0761 0.0071 0.0095 0.0046 0.0216 0.0074 0.0208 0.0087 0.8685

0.0086 0.0082 0.0101 0.1345 0.0162 0.0626 0.0072 0.0129 0.0899 0.0143 0.0186 0.0378 0.0729 0.0316 0.0270 0.0104 0.0139 0.0210 0.0489 0.0174 0.0486 0.0450 0.0289 0.0202 0.0129 0.0318 0.0287 0.0534 0.0076 0.0056 0.0056 0.0166 0.0546 0.0144 0.0229 0.0235 0.0209 0.0135 0.0046 0.0285 0.0140 0.0038 0.0031 0.0258 0.0481 0.0054 0.0069 0.0044 0.0226 0.0038 0.0078 0.0095 0.0806

1.4 2.9 3.4 2.5 4.7 4.3 5.2 4.4 1.8 3.0 2.8 4.0 4.2 3.2 2.6 1.6 1.7 1.4 3.5 3.2 4.7 3.0 3.1 2.5 1.8 4.8 5.0 5.2 1.4 1.2 0.6 1.5 2.2 2.0 1.1 2.7 2.7 1.8 0.8 0.7 1.3 0.4 0.2 1.4 0.9 0.2 0.4 0.2 0.4 0.3 0.8 0.7 0.1 117.9 2.2

0.3 0.8 1.4 1.2 1.8 2.0 0.9 1.8 2.1 1.1 1.9 2.2 0.2 1.8 1.8 0.6 1.4 1.4 1.3 1.6 1.6 3.2 0.7 0.4 0.3 0.9 1.0 1.5 0.8 0.3 0.7 1.0 1.7 0.4 0.8 0.7 0.6 0.5 0.4 0.6 0.6 0.2 0.1 1.2 0.3 0.4 0.2 0.2 0.3 0.1 0.2 0.5 0.2 50.2 0.9

104 129 103 15 76 12 141 60 17 39 35 25 16 19 22 91 71 54 13 24 26 18 17 16 18 19 18 17 69 63 82 22 17 17 23 23 22 21 51 5 22 14 9 15 7 7 8 7 6 9 13 27 4 1778

150 150 150 15 117 28 156 96 20 49 42 36 23 21 22 157 83 72 14 44 26 24 21 27 25 25 27 26 70 66 84 38 20 25 26 29 26 25 51 6 27 14 9 22 7 7 8 7 6 9 13 27 4 2272

0.0195 0.0189 0.0411 0.0085 0.0309 0.0469 0.4116 0.0223 0.0088 0.0477 0.0958 0.0098 0.0120 0.0520 0.0169 0.0217 0.0302 0.0284 0.9614 0.0183 0.0289

0.0204 0.0204 0.0874 0.0077 0.2950 0.0202 0.7044 0.0148 0.0098 0.0367 0.2958 0.0085 0.0159 0.0347 0.0127 0.0270 0.1301 0.0688 1.4992 0.0144 0.0250

2.5 2.7 3.1 1.4 8.0 3.3 1.0 3.1 2.7 5.1 19.5 2.7 4.2

2.2 0.8 3.1 1.0 4.6 2.3 0.7

66 67 54 154 109 66 4 26

75 107 130 184 189 86 5 26 192 27 80 100 107 21 64 79 62 46 19 90 25

1.5

2.8 3.7 5.5 4.2 14.6 4.1 3.3

1.1 1.1

2.3 1.6 1.0

2.4 2.0 1.3 1.7 2.9 2.9 6.8 1.4 2.1

118

27 77 71 71 20 59

67 55 33 8 77 21

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3125 Table 9 (Continued) COMPU)

COMP(2)

NC4 IC4 IC4 IC4 NC5 NC5 NC5 IC5 IC5 c7 c7 C8 c9 c10 c10 c12 CYCG CYCG ClCYC6 ClCYC6 ClCYC6 C2CYC6 C2CYC6 C2CYC6 C2ENE C3ENE C4ENE BEN BEN TOL TOL TOL C3CYC6 MXYL MXYL MXYL MESI MESI MESI

H2 c02 H2S N2 H2S c02 N2 N2 c02 c02 H2S

c1


co


co


Ka

c112

C122

SDKa

0.7805 0.2647 0.1636 0.6396 0.2854 0.3816 0.7244 0.6721 0.3785 0.5271 0.4010 0.9154 0.5472 0.6826 0.7821 0.9065 0.4926 0.8439 0.5036 0.4224 0.7164 0.5592 0.7605 0.4372 0.0087 0.1355 0.2262 0.7418 0.3786 0.4755 0.3588 0.8091 0.4911 0.5222 0.4235 0.7342 0.8049 0.4724 0.5728 -0.3831 0.3233 0.5165 0.8982 0.7967

0.3423 0.3042 0.1334 0.2084 0.0936 0.2204 0.0669 0.0515 0.1224 0.0065 0.2358 -0.1520 -0.0425 -0.0942 0.1823 0.0475 0.0166 0.2442 0.0310 0.0088 0.1526 -0.0173 -0.0139 0.1336 0.1379 0.0894 0.0906 0.1335 0.1781 0.1097 0.0495 0.0388 0.0363 0.0777 0.0904 0.1810 0.0860 0.0871 0.0403 10.6137 0.1763 0.0940 0.1638 -0.2419

0.6190 0.3378 0.3813 0.0249 0.3157 0.3398 0.1205 0.3699 0.2076 0.2684 0.3648 -0.2430 -0.2001 -0.1447 0.5087 0.4937 -0.0132 0.3989 0.1814 0.0699 0.5067 0.1732 0.2684 0.1159 0.2179 0.2944 0.2615 0.0709 0.2442 0.1031 -0.0789 -0.3824 0.1258 0.1596 -0.1150 0.7182 0.2114 -0.0898 0.1133 2.1351 -0.0192 0.0338 0.4444 -0.4256

0.3073 -0.4011 -0.0058 -0.1622 -0.4314 -0.1643 -0.1409 0.8310 0.4849 0.2937 0.1463 0.7145 0.3792 0.4778 0.0814 0.7455 0.0066 0.2617 0.2050

1.3554 9.7888 -2.5339 -0.4673 25.5185 1.8618 -0.4424 1.0240 0.1399 -0.1622 0.0914 0.4312 0.2612 0.9780 0.2394 0.0066 0.0538 0.5343 0.0950

0.3805 2.0923 1.7729 1.1916 2.3979 1.0288 -0.2137 0.0631 0.0732 -2.7346 0.1656 2.0183 0.2039 0.4637 0.1652 0.0661 0.0343 0.3083 0.2556

b. HC-NHC 0.0108 0.0109 0.0053 0.0002 0.0042 0.0089 0.0184 0.0202 0.0068 0.0041 0.0045 0.0171 0.0065 0.0031 0.0063 0.0062 0.0086 0.1175 0.0060 0.0065 0.0169 0.0051 0.0184 0.0064 0.0066 0.0172 0.0067 0.0272 0.0040 0.0028 0.0048 0.0843 0.0049 0.0030 0.0064 0.0148 0.0063 0.0035 0.0025 0.0172 0.0163 0.1009 0.0161 0.0073

C.

N2

co

H2 H2S N2 c02 H20 H2 c02 NH3

co

N2 H2 HE c02 c02 N2

co

c02 total average


co

H2 H2S H2

co

H2S N2

HNC-NHC 0.0226 0.0117 0.0094 0.0076 0.0119 0.0095 0.0113 0.0089 0.0121 0.0296 0.0063 0.0421 0.0014 0.0067 0.0049 0.0296 0.0033 0.0234 0.0090

SDC112

SDC122

DP

0.0361 0.0412 0.0200 0.0181 0.0207 0.0341 0.0499 0.0605 0.0269 0.0223 0.0228 0.0366 0.0316 0.0135 0.0283 0.0236 0.0212 0.3417 0.0375 0.0325 0.0582 0.0254 0.0689 0.0336 0.0079 0.0493 0.0313 0.0568 0.2496 0.0175 0.0255 0.2378 0.0295 0.0159 0.0360 0.0437 0.0403 0.0194 0.0142 4.9336 0.0394 0.2381 0.0503 0.0463

0.0728 0.0314 0.0140 0.3214 0.0204 0.0311 0.1040 0.1615 0.0243 0.0195 0.0198 0.1294 0.0454 0.0269 0.0452 0.0659 0.1215 0.6174 0.0219 0.0284 0.1014 0.0206 0.1231 0.0301 0.0056 0.0340 0.0150 0.1762 0.0059 0.0087 0.0157 1.4973 0.0265 0.0133 0.0268 0.1482 0.0577 0.0188 0.0106 0.0721 0.0390 0.2314 0.1146 0.0931

6.7 5.6 2.2 1.6 1.9 3.5 5.7 4.9 3.0 5.3 3.0 1.2 1.3 2.4 2.9 0.8 2.4 2.4 4.0 6.0 2.6 4.8 10.3 3.8 1.0 3.5 1.8 2.2 0.7 2.4 2.6 3.7 4.2 2.3 5.1 5.9 4.3 2.5 3.0 5.6 1.0 4.9 2.5 2.8 249.3 3.8

0.3913 5.5427 4.1211 0.3588 7.6034 0.0984 0.0476 0.1997 0.0163 0.0932 0.0537 0.1138 0.0385 0.1173 0.0132 0.0556 0.0074 0.4389 0.0297

0.0755 0.0449 0.0369 0.0476 0.0465 0.0350 0.0589 0.0414 0.0656 0.2847 0.0205 1.0231 0.0069 0.0184 0.0098 0.2971 0.0058 0.0832 0.0325

10.8 6.1 3.5 4.2 6.2 8.0 13.0 2.5 7.1 18.3 3.5 3.5 6.0 7.3 2.4 2.4 0.5 10.1

2.8 118.2 6.2

DY 6.5 2.1 1.1

1.9 2.1 2.8 2.4 4.1 2.3 0.9 1.7 0.6 0.7 0.5 1.3 0.6 1.9 2.3 2.0 1.7 3.4 1.6 1.8 1.7 0.4 1.4 0.7 1.3 0.7 1.3 1.3 2.5 0.7 1.4 1.5 4.0 2.5 1.4 1.1 3.0 1.2 2.1 2.4 0.1 124.3 1.9 2.4 2.1 2.1 2.4 1.1 6.4 1.9 0.7 1.2 1.9 2.3 1.1 2.7 2.6 1.2 0.9 0.2 2.4 0.9 36.5 1.9

PTS

PTSM

69 26 48 9 27 21 36 25 24 37 30 13 8 23 17 8 24 6 19 28 18 28 37 20 24 22 11 42 9 24 24 17 22 23 26 18 15 26 20 16 8 11 15 20 2244

93 39 63 13 31 28 42 47 29 56 39 15 10 44 17 10 31 9 31 29 28 45 41 28 34 22 11 51 9 33 27 23 35 39 30 18 15 29 32 16 13 20 16 66 3071

67 18 18 15 16 82 208 10 12 19 24 10 71 74 127 8 8 39 78 904

72 18 18 17 16 116 215 10 12 19 34 223 147 149 156 20 8 50 111

1411

3126 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 term since this generally leads to unreasonably large predictions of excess volume as discussed by Huron and Vidal (1979) and by Trebble (1991). Results for fits of the screened GPA data base are given in Table 4 parts a-c and Table 5 parts a-c. Comparisons of fits for the TBS EOS against the Peng-Robinson EOS (Peng and Robinson, 1976) and the Soave-Redlich-Kwong EOS (Soave, 1972) have been presented elsewhere (Trebble, 1990). Obviously for HC-HC systems it is generally sufficient to use a single interaction parameter in the attractive parameter am in order to get a good fit of VLE data. Even for HC-NHC pairs the classical rules appear to be reasonably good although the second interaction parameter in d m becomes necessary. For NHC-NHC pairs it is evident that the classical mixing rules are unable to represent the VLE data adequately. Use of Schwartzentruber-Renon (SR) Mixing Rules. Use of Schwartzentruber and Renon (SR)mixing rules for the TBS EOS was examined as follows:

a , - b d m / ( v- b,)

p=-- RT u - bm

u2

+ ( b , + C,)U

- (b,cm

Use of Huron-Vidal (HV) Mixing Rules with Linear Covolume. The rules developed by Huron and Vidal (1979) were applied as follows:

p=-- RT u - bm

a, u2

+ (b, +

+ ao/u

C,)U

- (b,~,

+ dm2) (37)

where N N

(38)

+ dm2) (28)

where

N

N

N

(41)

(29)

N

b, =

xibi

(31)

i=l

xici

c, =

c N

N

(32)

b, =

(33)

c, =

xibi

(43)

C xici

(44)

i=l

i=l

N

N N

i=l

+

d, dj d i#J. . = ( ~ ) (- Kd,) 1

N

d, =

(34)

xidi

(45)

i=l

(35) Xi=j=k

Xl=jk

Results for fits of the screened GPA data base are given in Table 8 parts a-c and are summarized in Table 3 parts a-c. For all pairs, the HV mixing rules converged fewer VLE points than did the conventional mixing rules. However, for NHC-NHC as well as HC-NHC pairs, it is observed that HV mixing rules excelled in aqueous binaries, eg., Cl-H20, CO-H20, H2-H20, H2SH20, and N2-H20. Also, the HE-H2 binary which was poorly represented by the conventional mixing rules (even with regressed Ka and Kd) was better fitted with the HV rules. Use of H v Mixing Rules with Wong-Sandler (WS) Rules for Second Virials. Combining the HV rules with a Wong-Sandler type covolume parameter results in the following:

where

Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3127 v = molar volume

Subscripts m = mixture

N

N

N

(50)

N

b, =

xibi

(52)

xici

(53)

xidi

(54)

i=l

c c N

c, =

i=l N

d, =

i=l

Results for fits of the screened GPA data base are given in Table 9 parts a-c and are also summarized in Table 3 parts a-c. Again, as observed for HV mixing rules, the WSHV mixing rules in general failed to converge as many points as the conventional mixing rules. Fits of aqueous binaries along with the HE-H2 binary were again predicted much better, however.

Concluding Remarks In general, the regression results utilizing conventional mixing rules were equivalent to those obtained using GE model incorporation. This is not unexpected for a data base of this type which contains relatively ideal systems. There was an apparent benefit to GE based models in matching some of the more polar systems; in particular the HV and WSHV mixing rules excelled in correlating the HE-H2 binary as well as aqueous binaries such as Cl-H20, CO-H20, H2H20, H2S-H20, and N2-H20. Nomenclature a = attractive parameter b = covolume parameter c = equation of state parameter d = equation of state parameter C112,C122 = adjustable parameters in eqs 42 and 51 Ka = adjustable parameter in eqs 23, 30, 39, and 48 Kd = adjustable parameter in eqs 27 and 34 L = adjustable parameter in eq 36 N = number of components P = absolute pressure PTS = number of converged data points PTSM = maximum number of experimental data points R = gas constant T = absolute temperature

Component Indices BEN = benzene CO = carbon monoxide C 0 2 = carbon dioxide CYC6 = cyclohexane C1 = methane ClCYC5 = methylcyclopentane ClCYC6 = methylcyclohexane C2 = ethane C2BEN = ethylbenzene C2CYC6 = ethylcyclohexane C2ENE = ethylene C3 = propane C3BEN = n-propylbenzene C3CYC6 = propylcyclohexane C3ENE = propylene C4ENE = 1-butene C6 = n-hexane C7 = n-heptane C8 = n-octane C8H18 = trimethylpentane C9 = n-nonane C10 = n-decane C12 = dodecane C16 = hexadecane HE = helium H2 = hydrogen H 2 0 = water H2S = hydrogen sulfide IC4 = isobutane IC5 = isopentane IC4ENE = isobutylene MESI = mesitylene MXYL = m-xylene NC4 = n-butane NC5 = n-pentane NEOC5 = neopentane NH3 = ammonia N2 = nitrogen PHENOL = phenol PXYL = p-xylene SO2 = sulfur dioxide TOL = toluene

Literature Cited Anderko, A. Equation-Of-State Methods for the Modelling of Phase Equilibria. Fluid Phase Equilib. 1990,61, 145-225. Conkwight, N. B. Introduction to the Theory of Equations; Blaisdell Publishing Co.: New York, 1965;p 78. Heidemann, R. A,; Kokal, S. L. Combined Excess Free Energy Models and Cubic Eauations of State. Fluid Phase Equilib. 1990,56, 17. Huron, M. J.;Vidal, J. New Mixing Rules in Simple Equations of State for ReDresenting Vapor-Liauid Esuilibria of Strongly Nonideal Mixtures. Fruid Phase Equilib: 1979,3,255-2711: Michelsen, M. L.A Modified Huron-Vidal Mixing Rule for Cubic Equations of State. Fluid Phase Equilib. 1990,60, 42,213. Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Znd. Eng. Chem. Fundam. 1976,15 (11,59-64. Salim, P. H.; Trebble, M. A. A Modified Trebble-Bishnoi Equation of State: Thermodynamic Consistency Revisited. Fluid Phase Equilib. 1991,65, 59-71. Satyro, M. A,; Trebble, M. A. On the Applicability of the SandlerWong Mixing Rules for the Calculations on Thermodynamic Fluid Phase Equilib. Excess Properties - VE,HE, SE, 1996,in press. Schwartzentruber, J.; Renon, H. Equations of State: How to Reconcile Flexible Mixing Rules, the Virial Coefficient Constraint and the Michelsen-Kirstenmacher Syndrome for Multicomponent Systems. Fluid Phase Equilib. 1991,67,99-110.

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3128 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27 (61, 1197-1203. Trebble, M. A. An Evaluation of Multiple Binary Interaction Parameters in Cubic Equations of State. Can. J . Chem. Eng. 1990,68,487-492. Trebble, M. A. The Impact of Asymmetric Equation of State Mixing Rules on Thermodynamic Property Prediction for Normal Alkanol-Hexane Binaries. Fluid Phase Equilib. 1991,65,7388. van der Waals, J. H. On the Continuity of the Gaseous and Liquid State. Dissertation, Leiden, 1873. Physical Memoirs, English Translation by Threlfall and Adair, Phys. SOC.1890,I , iii, 333.

Wong, D. S. H.; Sandler, S. I. A Theoretically Correct Mixing Rule for Cubic Equations of State. AIChE J . 1992,38, 671-680

Received for review December 12, 1994 Accepted May 8, 1995@ IE940732Y

Abstract published in Advance A C S Abstracts, August 1, 1995. @

An Evaluation of Mixing Rules for the Trebble-Bishnoi-Salim Equation

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