다양한 혼합법칙을 통한 혼합냉매의 기액평형 예측

박지영, 임종성, 이병권, 이윤우, 김재덕

한국과학기술연구원 환경공정연구부

Prediction of Vapor-Liquid Equilibria for refrigerant mixture

with various mixing rules

Ji-Young Park, Jong Sung Lim, Byung-Gwon Lee, Youn Woo Lee, Jae-Duck Kim

Environment and Process Technology Division, KIST

Introduction

Many mixtures of interest in the chemical industry exhibit strong nonideality, greater than that describable by regular solution theory.  Models for describing and predicting the phase behaviour have been continuously developed.  Among many models, a very attractive route for developing better mixing rules is to combine an EOS with activity coefficient models.[2]

In this study, we measured isothermal vapor-liquid equilibria for binary systems of 1,1,1,2,3,3-Hexafluoropropane (HFC-227ea) + iso-butane at 303.15, 313.15 and 323.15 K.  The experimental data were correlated with six mixing rules combined with the Peng-Robinson-Stryjek-Vera equation of state and the NRTL excess free energy model.  These mixing rules are HV-O(Huron Vidal-Original), MHV1(Modified Huron-Vidal 1st order), MHV2(Modified Huron Vidal 2nd order), LCVM(Linear Combination of Huron Vidal and michelsen), HVOS(Huron Vidal modified by Orbey and Sandler), WS(Wong

-Sandler) models[1] and the NRTL parameters obtained by these mixing rules were presented.

Theory

The VLE experimental data were correlated with the Peng-Robinson-Stryjek-

Vera (PRSV) equation of state.  The Peng-Robinson-Stryjek-Vera(PRSV) equation of state expressed as follows.

The Peng-Robinson-Stryjek-Vera (PRSV) equation of state

Here, we use the temperature dependence of the □ term proposed by Stryjek and Vera.

where the k1 is specific constant for each pure compound. k1 of the PRSV equation is obtained by fitting pure component saturation pressure(Pvap) versus temperature data.  The stryjek-Vera modification of □ takes care of the inaccuracies in temperature dependence of the term at low temperature.

These mixing rules have been developed that combine excess free-energy models (NRTL model in this study) with a cubic EOS (PRSV EOS in this study).  Various mixing rules based on this concept are expressed as follows.[2]

Mixing rules

The Huron-Vidal (Original) Mixing Rules (HVO)

The Modified Huron-Vidal 1st order Mixing Rules (MHV1)

The Modified Huron-Vidal 2nd order Mixing Rules (MHV2)

The Linear Combination of Huron-Vidal and Michelsen Models (LCVM)

The Orbey-Sandler Modification of Huron-Vidal mixing rules (HVOS)

The Wong-Sandler Mixing Rules (WS)

Table 1. Optimum k1 values of pure component in the PRSV equation of state

	Temperature range (K)	k1	Data source
Iso-Butane	303.15 ~ 323.15	-0.1426	REFPROP 6.0 [3]
HFC-227ea	303.15 ~ 323.15	0.1394	PEFPROP 6.0 [3]

EOS-Gex Model NRTL parameters
	HV-O	MHV1	MHV2	LCVM	HVOS	WS
303.15 K
A12	464.166	347.81	308.993	383.348	460.835	674.710
A21	678.727	566.863	565.703	602.963	676.483	59.815
P12	0.770	0.577	0.512	1.000	0.756	1.120
P21	1.126	0.941	0.939	1.703	1.122	0.099
313.15 K
A12	407.679	299.952	263.761	332.696	401.967	572.508
A21	683.110	578.132	569.493	611.323	682.731	62.229
P12	0.655	0.480	0.423	0.534	0.645	0.920
P21	1.097	0.929	0.915	0.982	1.097	0.100
323.15 K
A12	307.674	264.481	183.163	242.8838	368.037	124.225
A21	765.819	584.210	630.573	687.122	377.885	294.898
P12	0.479	0.411	0.285	0.378	0.573	0.193
P21	1.192	0.909	0.982	1.070	1.055	0.459

Table 2. Values of NRTL parameters in PRSV EOS-Gex (NRTL) model

* The unit of A12 and A21 is cal/mol and P12(A12=RT) and P21(A21=RT) is

dimensionless

In this study we use the NRTL model as excess free-energy model and  set the nonrandomness parameter, aij, equal to 0.3 for binary mixture studied here.

Results and discussion

The VLE of HFC-227ea/isobutane system were predicted using various mixing rules combined with NRTL excess free energy models and the PRSV equation of state.  k1 of the pure components (isobutane and HFC-227ea) in the range of 303.15~323.15 K were listed in Table 1 and all the binary parameters of the NRTL model with six mixing rules were listed in Table 2.  These mixing rules combined with PRSV equation of state and an activity coefficient model (NRTL) for the Gex term show very good correlations for the vapor-liquid equilibria of refrigerant mixtures within the uncertainty of ±1.0 %.  The AAD(%) of this system were listed in Table 3.

In this system, there exist azeotropes.  The azeotropic points change with temperature and they were x1 = 0.599 (mole fraction), P = 6.659bar at 303.15 K, x1 = 0.608, P = 8.458bar at 313.15 K and x1 = 0.614, P = 10.815bar at 323.15 K for HFC-227ea(1)/isobutane(2) system, respectively.

Table 3. AAD(%) of P by various mixing rules

AAD(%)
	HV-O	MHV1	MHV2	LCVM	HVOS	WS
303.15 K	0.606	0.702	0.617	0.629	0.655	1.334
313.15 K	0.293	0.306	0.327	0.301	0.355	0.818
323.15 K	0.273	0.411	0.284	0.276	0.460	0.616

Literature Cited

1. D. S. H., Wong and S. I., Sandler, AIChE J., 38(5), 671-680, (1992)

2. H. Orbey., S. I. Sandler., "Modeling Vapor-Liquid Equilibria-cubic equation

of state and their mixing rules", 19-74, (1998)

3. M. Huber, J. Gallagher, M. O. McLinden, G. Morrison, □Thermodynamic

Properties of Refrigerants and Refrigerant Mixtures Database(REFPROP)

V.5.0□, NIST, (1996)