I
BENJAMIN C.-Y. LU' and W. F. GRAYDON Department of Chemical Engineering, University of Toronto, Toronto, Can.
Prediction of Vapor-Liquid Equilibrium Data Binary H y d r o c a r b o n Systems with O n e A r o m a t i c C o m p o n e n t
A
NUMBER of methods have been proposed for predicting deviations from ideality for binary vapor-liquid equilibrium data. The minimum primary information required to make a prediction at constant pressure is (2, 3, 74, 78):
1. The boiling temperatures for the binary system as a function of liquid composition a t constant pressure, or 2. One vapor-liquid equilibrium measurement for the binary system in question at a known temperature and pressure, or 3. Partial niolal energy change of mixing. These methods have been useful for extrapolation and prediction of x - y data. T h e equations that have been developed theoretically, in general, are used empirically (2, 3, 78). I n practice, all require some measurement be made for the binary system in question. I n addition, there have been suggestions for estimating Raoult law deviations using the properties of the pure components as primary information. Ewell and others (7) discussed deviations from ideality in a qualitative way in terms of the hydrogen bonding characteristics of the pure component. Hildebrand (77) has suggested that for binary solutions the larger the difference between the internal pressures of the pure components, the greater the deviation of the vapor-liquid equilibrium data from ideality. I n the present investigation, empirical equations are used for predicting the vapor-liquid equilibrium data at 1 atm. for binary systems composed of hydrocarbons, one of which is a n aromatic 1 Present address, Department of Chemical Engineering, University of Ottawa, Ottawa, Can.
1 05 8
compound. The data required as primary information are the vapor pressures and internal pressures of the pure components. All of these systems show considerable deviation from ideality and some of the systems show a minimum boiling azeotrope. The predictions are based on the estimation of values of the constants in the equations suggested by Clark (5)
I n order that the complete vaporliquid equilibrium relations may be represented, the two hyperbolas should be tangent at a value of x between 0 and 1. The necessary condition is that, (aa')".h
f (6b')O.S = 1
(2)
where the sign of the quantities 6 , b ' and (bb ' ) 0 . 5 is taken to be the sign of the quantity 1 - (au')o,j At the tangent point (
x =
1
3
.
pressed by the physical properties of the pure components. B =E -18 1 21
C
=
El 216 :
-
(6162)0.6(A1
+ A z ) at
- ( 6 i 6 s ) 0 . 5 ; ( A ~+ A z ) at
(sa) 7'2
where 6 refers to solubility parameter as defined by Hildebrand (77). The quantities A I and A2 are constants as defined below. Empirical Arrangements for Quantity A Component A Benzene VL/ Bn Aromatic hydrocarbons (JVdMi)'(VL/V' other than benzene D (Tz- T,p.*a [MzIMi) ( V L I V H ) ~ Other hydrocarbons D (Tz - T1)O.U Where V = molal volume, ml./mole M = molecular weight T = boiling point, O C. D = unity, (" C.)*.26
Subscripts H = higher value L = lower value
5
+ (ab">"."
(3)
The constants a and Q ' of the Equations
1a and 1b may be expressed as
If the unit of 6 is taken to be (calories per milliliter)0,5 and of E, (calories per milliliter)-O.b, then E is unity. The quantity within the sign is assumed to be positive.
I
1
Evaluation of Constants b and
where Po and T refer to vapor pressure and boiling point of the pure components. The quantities, B and C, are arbitrary constants. Subscripts 1 and 2 refer to the components. The constants, B and C characteristic of a binary system, are empirically ex-
INDUSTRIAL AND ENGINEERING CHEMISTRY
(5b)
6'
After obtaining the constants a and a' using Equations 4 and 5 , two equations are required to evaluate the constants b and b'. Equation 2 provides one of the relationships. The Redlich and Kister relationship ( 7 G ) may be combined with Equations l a and l b to provide the other. By definition a = - p1 O Y 1 PZ0Y2
cients to be independent of temperature, Redlich and Kister have shown that
and L'log
dx = L'log
CY
(;$)
dx
The quantity
may be taken to be
A
a
From Equation 1
OB
06
*
and 1 - x = -___
04
x(b'
- a') +
a'
for x
