Trifluoromethane과 propane의 고압 기-액 상평형

양웅조, 임종성, 이병권, 이윤우, 김재덕

한국과학기술연구원 CFC대체연구센터

High-pressure vapor-liquid equilibrium of trifluoromethane + propane

Woong-Jo Yang, Jong Sung Lim, Byung Gwon Lee

Youn-Woo Lee, Jae-Duck Kim

CFC Alternatives Research Center, KIST

Introduction

Hydrofluorocarbons(HFCs) and hydrocarbons(HCs) have been considered as promising alternative refrigerants in place of chlorofluorocarbons(CFCs) since their ozone depletion potentials and global warming potentials are low.  HFCs are stable but very expensive, on the other hand, hydrocarbons are flammable but very cheap. The mixtures of the two compounds may have good potential for alternative refrigerants. The thermodynamic modeling of phase equilibrium is a core concern in chemical process design. The design and operation are based on a knowledge of phase equilibria coexisting phases and phase equilibrium information is also essential in the development of new chemical processes. In this work, vapor-liquid equilibria(VLE) of the mixture composed of trifluoromethane(R-23) and propane(R-290) was studied in the temperature range between 273.15 and 293.15K, using a recirculation apparatus in which both phases are continuously recirculated. The phase compositions at equilibrium were measured by gas chromatography and the experimental data were regressed with the Peng-Robinson equation of state using the Wong and Sandler mixing rule [1] within the uncertainty of ±1.0%.

Experimental

The experimental apparatus used in this work is the same that used in our previous work [2] and briefly summarized here.  The VLE measurements were carried out in a stainless steel equilibrium cell equipped with Pyrex glass windows of 20-mm thickness and duplex high pressure pump for recirculating vapor and liquid phases. A stirrer rotated with variable speeds by an external magnet was installed to accelerate the attainment of the equilibrium state and reduce any concentration gradient in both phases. The mixture in the cell was stirred continuously by the magnetic stirrer for over 1 hour. Both vapor and liquid phases were recirculated by the high-pressure pump until the equilibrium state was established. It is believed that 1 hr or more is sufficient to obtain thermal equilibrium between the cell fluid and the thermostated bath.  After then, pressure was measured and vapor and liquid samples were taken from the recycling lines by the vapor and liquid sampling valves, respectively. The composition of the phases was determined by gas chromatography which is connected on-line to the VLE cell. The gas chromatography was calibrated with pure components of known purity and with mixtures of known composition that were prepared gravimetrically. The uncertainty of the liquid and vapor phase composition is estimated to be within ±0.5 mol%, including the uncertainty of the calibration curve.

Results and Discussion

The experimental results for the VLE were correlated with the Peng- Robinson equation of state (PR). The PR is expressed as follows [1]

[eqn: P= {RT} over {v-b}- {a(T) } over {v(v+b)+b(v-b) }]	(1)

with

a(T)=(0.457232R2Tc2/Pc)□(T)	(2)

b=0.0077796RTc/Pc	(3)

□(T)=[1+□ (1-T□0.5)]2	(4)

□=0.37464+1.54226□-0.26992□2	(5)

and where the parameter a is a function of temperature, b is constant, □ is a constant characteristic of each substance, □ is the acentric factor. The Wong-Sandler mixing rule [2] was used in this work to obtain equation of state parameters for a mixture from those of the pure components. This mixing rule for a cubic equation of state can be written as

[eqn: {b}_{m}= { SUM from { i } SUM from { j } { x}_{i }{ x}_{j }{(b-a/RT) }_{ ij}} over {(1- {A }`_{∞} ^{E }/CRT- SUM from { i } { x}_{i } { a}_{i }/RT { b}_{i } ) }]	(6)

with

(b-a/RT)ij=[eqn: { 1} over {2 }][(b-a/RT)i+(b-a/RT)j](1-kij)	(7)

and

[eqn: { {a }_{m } } over { {b }_{ m} } = SUM from { i } {x }_{ i}{ {a }_{i } } over { {b }_{ i} }+ { { A}`_{∞ } ^{E } } over {C }]	(8)

and where C is a numerical constant equal to [eqn: ln( SQRT { 2} -1)/SQRT { 2}] for the PR equation used in this work. Also, [eqn: { A}`_{ inf } ^{E }] is an excess Helmholtz free energy model at infinite pressure which can be equated to a low-pressure excess Gibbs free energy model; in this study we use the NRTL model[2] given by

[eqn: { { A}`_{∞ } ^{ E} } over {RT } = SUM from { i } { x}_{i } { SUM from { j } { x}_{j} { G}_{ji} {tau }_{ji}} over { SUM from { k } { x}_{k} { G}_{ki} }]	(9)

with

Gji=exp(-□ij□ji)  and □ij = Aij/RT	(10)

where Gji is the local compositon factor for NRTL model, □ij is the NRTL model binary interaction parameter, Aij=(gij - gji) and gij is an interaction energy parameter of the i-j, □ij is a non-randomness parameter and R is the universal gas constant (8.314 JK-1mol-1). We have set the non-randomness parameter,□ij, equal to 0.3 for all the binary mixtures studied here.

The Marquardt algorithm was applied to obtain the parameters with the following objective function:

objective function =[eqn: { { 1} over {N } SUM from {j} to {n} LEFT [ LEFT ( { { P}_{j,exp}-{ P}_{j,cal} } over {{ P}_{j,exp} } RIGHT ) TIMES 100RIGHT ] }^{ 2}]	(11)

We measured VLE for R-23+ R-290 systems. The experimental results are shown in Fig. 1 on a pressure-composition diagram. In this figure, the dashed lines are the calculated values using PR equation of state with Wong-Sandler mixing rule. There is an evident positive deviation from Raoult's law at all temperatures. For this mixture, the present data show an azeotrope, but is nearly a tangent azeotrope[3, 4]. In Fig. 2, the deviations between measured and calculated pressures (△P/P(%)) and vapor compositions (△y) were compared point by point. Table 1 is a comparison of measured vapor pressures of pure R-23 and R-290 with those calculated from the database REFPROP 6.01[5] which is considered to be reliable for the pure compounds. The average deviation (|△P|/P) between measured and calculated values from the data of REFPROP 6.01 is 0.883% for R-23, 0.304% for R-290.

Table 1. Comparison of the Measured Pure Components Vapor Pressures with           the Calculated values from the Database REFPROP 6.01 (1998)

component	T/K	P/MPa		△Pa/MPa	△P/Pb/(%)
		measd	calcd
R-23	273.15	2.5616	2.5190	0.0426	1.691
	283.15	3.2890	3.2740	0.0150	0.458
	293.15	4.2230	4.2020	0.0210	0.500
R-290	273.15	0.4769	0.4743	0.0026	0.548
	283.15	0.6364	0.6365	0.0001	0.016
	293.15	0.8392	0.8363	0.0029	0.347

a△P=[eqn: LEFT | { P}_{exp}- { P}_{cal } RIGHT |], and b△P/P=[eqn: LEFT |LEFT({P}_{exp}- {P}_{cal}/ {P}_{exp} RIGHT) RIGHT| times 100]

Table 2 lists the interaction parameters of binary mixtures for each isotherm, the binary parameters of the NRTL model with the Wong-Sandler mixing rules, and the average absolute deviations of pressure (□P) and vapor phase composition (□y) between measured and calculated values.  As can be seen in Table 2, the average deviations of pressures are 0.753% for the R-23 + R-290  system  and those of vapor phase compositions are 0.0079 for the R-23 + R-290 system. This value of vapor phase composition is far below ±0.02 that can be considered as the limit to state the thermodynamic consistency between the experimental data and the model used for the correlation. The kij values for the R-23 + R-290 system decrease with temperature. From these figures and the low average deviations of pressure and vapor phase compositions in Table 2, we conclude that the values calculated with the PR equation of state and Wong-Sandler mixing rule give comparatively good agreement with experimental data.

Table 2. Values of Binary Parameters and Average Deviations of P and y

System	T/K	NRTL parameters/kJ·mol-1			□Pc/(%)	□yd
R-23/R-290	273.15	kij=0.459	Aij=0.681	Aji=0.364	0.978	0.0088
	283.15	kij=0.425	Aij=0.706	Aji=0.378	0.695	0.0072
	293.15	kij=0.412	Aij=0.731	Aji=0.364	0.585	0.0077

c□P=[eqn: { 1} over {N } SUM LEFT | LEFT ( { P}_{exp }- { P}_{cal } RIGHT )/{ P}_{exp } RIGHT | TIMES 100], and d□y=[eqn: { 1} over {N } SUM LEFT | { y}_{exp } - { y}_{ cal} RIGHT |]

Literature Cited

1. Jong Sung Lim, Ji-Young Park, J. Chem. Eng. Data. 2000, 45, 734-737.

2. H. Orbey, S. I. Sandler., Modeling Vapor-Liquid Equilibria-cubic equation     of state and their mixing rules. Cambridge University Press, 1998, 1-74.

3. S. Bobbo, R. Camporese, J. Chem. Thermodynamics. 1998, 30, 1041-1046.

4. S. Bobbo, L. Fedele, R. Camporese, R. Stryjek,  Fluid Phase Equilibria. 2000, 174, 3-12.

5. M. O. McLinden, S. A. Klein, E. W. Lemmon, A. P. Peskin, REFPROP Version 6.01, NIST. Thermophysics Division, 1998.