Chemistry Reference
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30
C16
C10
C5
10
0
100
Te mperature/C
FIGure a.1
Variation of γ with temperature for different alkanes (C
5
:
n
-pentane; C
10
:
n
-decane; C
16
:
n
-hexadecane).
composition. The addition of gas to a liquid always decreases the value of γ . For
example, the variation of γ of the system CH
4
+ hexane is given as follows:
γ(CH
4
+ hexane) = 0.64 + 17.85 xhexane
(A.4)
It is seen that, actually by measuring γ for such a system, the concentration of CH
4
can be estimated. This fact has much relevance in oil reservoir engineering opera-
tions where CH
4
is found in crude oil.
It is well known that the corresponding states theory can provide much useful
information about the thermodynamics and transport properties of fluids. For exam-
ple, the most useful two-parameter empirical expression, which relates the surface
tension, γ, to the critical temperature, Tc, is given as
γ = ko (1−T/Tc)
k1
(A.5)
where ko and k1 are constants. Van der Waals derived this equation and showed that
k1 = 3/2, although experiments indicated that k1 = 1.23. Guggenheim (Guggenheim,
1945) has suggested that k1 = 11/9 . However, for many liquids, the value of k1 lies
between 6/5 and 5/4.
Van der Waals also found ko to be proportional to Tc
1/3
Pc
2/3
. Equation A.5, when
fitted to the surface tension, γ, data of liquid CH
4
, has been found to give the follow-
ing relationship:
γCH
4
= 40.52 (1−T/190.55)
1.287
(A.6)
where Tc = 190.55 K. This equation has been found to fit the γ data for liquid meth-
ane from 91 to −190 K, with an accuracy of “0.5 mN/m. In a recent study, the γ
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