CRICONDENTHERMS AND CRICONDENBARS Their Prediction jfor Binar3, Hydrocarbon $stems E D W A R D D. S I L V E R M A N A N D GEORGE T H O D O S The Technological Institute, Xorthwestern Unzuersity, Evanston, Ill.
An empirical function has been developed relating the maximum temperature (cricondentherm) and the maximum pressure (cricondenbar) points of binary hydrocarbon systems to composition and the ratio of the absolute normal boiling points of the heavy and light constituents. The constants in the empirical function were determiiied from data for 13 systems. Except for systems containing methane, the average deviations of the calculated temperature and pressure a t the cricondentherm point were 2.1 and 4.6y0, respectively; for the cricondenbar, they were 1.9 and 5.5%, respectively.
URREKT
studies of the vapor and liquid behavior of binary
C and multicomponent systems require a complete knowledge of the behavior of these systems throughout the critical region. Several methods (2. 4, 73, 77, 20, 26) have been presented in the literature for the prediction of the critical temperature and critical pressure of a multicomponent system. These constants have recently been shown to produce more reliable results than the corresponding pseudocritical values ( 5 ) . To define completely the saturation envelope in the vicinity of the critical point, it is necessary also to establish the corresponding maximum temperature point (cricondentherm) and maximum pressure point (cricondenbar). Recently, Etter and Kay (3) have developed empirical equations for calculatioii of the pressure and temperature at the critical, cricondentherm, and cricondenbar points for multicomponent mixtures of normal paraffins. These equations are specific to each individual paraffin and require constants which can be established from a fairly complicated procedure. Although these equations appear to produce accurate cricondentherms and cricondenbars for the normal paraffins investigated, it would be desirable to obtain relationships for the prediction of the cricondentherm and cricondenbar of any aliphatic hydrocarbon mixture. Therefore, in this study an attempt has been made to develop relationships between characteristic properties of the system and the temperatures and pressures a t the cricondentherm and cricondenbar for binary hydrocarbon mixtures, utilizing statistical techniques which have recently received considerable application in chemical engineering problems. Phase Behavior of Multicomponent Systems in Critical Region
A multicomponent system of a fixed composition is characterized by the existence of a two-phase region similar to that shown in Figure 1. This region is bordered by a boundary curve consisting of a bubble point line and a dew point line, which meet at the critical point of the mixture. For a pure component, the critical point represents the maximum temperature and maximum pressure a t which two phases can exist. However, for a multicomponent system, two phases can be
present at temperatures above the critical temperature up to a maximum temperature point (the cricondentherm) and a t pressures above the critical pressure up to the maximum pressure point (the cricondenbar). These maximum temperature and pressure points are shown in Figure 1 for a mixture whose critical point is located between them. Anomalous phase behavior is exhibited by multicomponent mixtures a t temperatures between the cricondentherm and the critical point (retrograde condensation) and a t pressures between the cricondenbar and the critical point (retrograde vaporization). Retrograde condensation can be illustrated by considering the isothermal decrease of pressure of the system of Figure 1 from the conditions of state A to those of state B. Condensation begins at point a on the dew point line and continues until point e is reached. where a maximum amount of liquid is present. This formation of a heavier phase with decreasing pressure is contrary to normal behavior. At point e, normal vaporization is initiated, which continues as the pressure is decreased until the dew point line is again crossed a t point b. Similarly, retrograde vaporization is exhibited during the isobaric temperature decrease from state A to state C. Vaporization begins a t point c on the bubble point line and continues until point f is reached, where a maximum amount of vapor is present. Normally, vaporization does not occur during an isobaric temperature decrease. Kormal condensation does take place as the temperature is further decreased from point f,until point d is reached, where the system is entirely liquid. For the system of Figure 1, retrograde condensation and vaporization can occur only in the shaded regions illustrated. I n the general case, a knowledge of the cricondentherm and cricondenbar points is essential to define the regions where these retrograde processes will be exhibited.
Development of a Response Function
T o expedite the study of these complex properties, the development of this investigation was limited to binary hydrocarbon systems for which sufficient experimental data are available. The following response function was proposed to treat the available experimental data for these systems, VOL
1
NO. 4
NOVEMBER 1 9 6 2
299
I
having as parameters the composition of the system and the interactions of these compositions:
moximum pressure (cricondenbor)
\
y r
criticai point
t e!
maximum temperature
2
9 =
aini
+
22
aijnini
+
222 ailkninjnk
2222
Liquid
aijkminjnknr
+. . .
(1)
ijkl
.y
v)
ng!
+
ijk
I
1
Liquid and Vopor
where q can be the temperature or pressure a t the cricondentherm or cricondenbar points. Subscripts i, j , k, I . , = 1 represent the light component, and i, j , k , I . . . = 2 the heavy component. The expansion of Equation 1 was truncated after the fifth-order interactions, since any higher order interactions are highly improbable. If it is assumed that molecules of the same type do not inter- 022 = . . act with each other, cy11 = cy111 = . . . . -
.
L
.
Temperature +Figure 1 . Vapor-liquid behavior of a mixture in the critical region
multicomponent
.. . .
If it is also assumed that the effect of an interaction is independent of its order, the following equalities result: =
cy22222
= 0.
=
a12
0121
a112
=
a121
=
a12222
=
a21222
01211
=
0122122
=
a22212
= 0122121
When these relationships are used, Equation 1 reduces to 9 =
alnl
f am
40lllzn?na
+
+
2al2nm
6aiiznn?nB
f
+
f -t-
3 a l l ~ n h 4alzzznlni
loaiiiz2n?ni
f
3a122nlni 5allll2n:n2
1001iizzzfL?n;
+
+
+
5ai2222nin:
(2)
If a l and CYZ are defined to be either the critical temperatures or critical pressures of the components of the mixture, then alnl
A
nButone-n-Heptane
0.2
0,4
",
1.363
0.6
0.8
Figure 2. Dependence of variable composition for binary hydrocarbon systems
300
I&EC FUNDAMENTALS
I.O "I
((&,t
on
Figure 3.
l.0
