B41oa oil and Gas Processing Section a flow Assurance Heriot-Watt University

1.7.5 K-Value Method: Vapour-Liquid-Solid Equilibrium 
However, for liquid hydrocarbons the procedure must be re-written to also 
include the vapour-liquid equilibrium constant 
i
VL
K
,
i
i
i
VL
x
y
K
=
,
……………………………………………
.(1.13)
In which 
i
x
is the mole fraction of component 
i
in the non-aqueous liquid 
phase. Thus, if the equilibrium involves a gas, a non-aqueous liquid and a 
solid hydrate, then equation (1.10) must be extended from two to three 
phases. When this is done two functions are obtained – the first 
)
,
(
1
L
V
f
and
the second 
)
,
(
2
L
V
f
are given by
(
)
(
) (
)(
)
∑
=
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
+
−
−
=
n
i
i
VL
i
i
VL
i
VL
i
VK
K
K
L
V
V
L
K
z
L
V
f
1
,
,
,
1
1
1
1
1
)
,
(
…………
(1.14)
(
) (
)(
)
∑
=
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
+
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
n
i
i
VL
i
i
VL
i
i
VL
i
VK
K
K
L
V
V
L
K
K
z
L
V
f
1
,
,
,
2
1
1
1
1
)
,
(
…
..
……
(1.15)
These two functions must be solved iteratively to find the phase fractions 
V
and 
L
such that the values of both functions are each zero. 
1.7.6 K-Value Method: Liquid-Solid Equilibrium 
For a hydrate formation with only a non-aqueous liquid, the situation is similar 
to vapour-solid equilibrium. Now the K-value equivalent to equation (1.8) is 
i
i
i
VS
i
VL
i
LS
x
s
K
K
K
=
=
,
,
,
…………………………
..
…
..
…
.(1.16)

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TOPIC 1: Gas Hydrates 
 
 
 
53 
©H
ERIOT
-W
ATT
U
NIVERSITY B41OA December 2018 v3 
The condition for hydrate formation in a non-aqueous liquid is then simply 
given by 
0
.
1
1
,
∑
=
=
n
i
i
i
LS
x
K
……………………………
.
………
..(1.17)
K
VL
values for the hydrocarbon species can be obtained from the literature or 
calculated in the usual way (see notes from B49CE). 
These are quite basic methods but have some reliability and accuracy for 
preliminary results: 
•
The gas gravity method is usually accurate to within 20% for sweet 
gases. 
•
The K-factor method is usually accurate to between 10% and 15%, 
plus the error associated with reading the chart. 
Neither method can predict which hydrate structure is formed. However, there 
are some rules of thumb that provide an indication: 
•
Type II predominates. 
•
Whenever only a small amount of type II hydrate former is present in 
the gas, the resultant hydrate is type II. 
•
Type I hydrate formers will occupy the smaller cavities in the Type II 
structure. 
A small change in gas composition can result in a big change in hydrate 
formation pressure (this is because a different hydrate structure is formed). For 
example, pure methane forms type I hydrate at 288 K and 12.8 MPa but the 
presence of 1 % propane leads to the formation of type II hydrate at 7.7 MPa 
at the same temperature. 
These methods assume that there is a large quantity of water present and 
therefore should not be used to determine hydrate forming conditions in a 
dehydrated gas.