TOPIC 1: Gas Hydrates
56
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ERIOT
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ATT
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NIVERSITY B41OA December 2018 v3
In which the sum in both equations (1.22) and (1.23) is over all the
j
components in the gas mixture. The pressure
j
P
is the partial pressure of the
component
j
in the gas mixture.
All components are included because the gas molecules compete for cavities
to occupy, so as a cavity becomes occupied
the probability that a gas
molecule can enter the hydrate is reduced.
Parrish and Prausnitz also replaced the partial pressure with fugacity in order
to deal with any non-ideal behaviour in the gas phase, so that equation (1.23)
becomes
j
ij
j
K
i
i
K
f
c
f
c
Y
ˆ
1
ˆ
,
∑
+
=
…………………………………
.(1.24)
Ng and Robinson (1977) extended the model further to include liquid phase
hydrocarbons and calculated the fugacities from the Peng-Robinson equation
of state. Any other relevant equation of state
can be used with minor
modifications to the equations. To do the calculations equation (1.25), shown
below, must be solved.
0
=
−
α
µ
µ
H
………………………………………
..(1.25)
This requires that the chemical potential of water in the aqueous phase must
be equal to that of the water in the hydrate phase. This is iterative and for a
single component gas is straightforward because the type of hydrate formed is
known.
For
a gas mixture, where the hydrate structure formed is not necessarily
known, the calculation must be done for EACH of the possible hydrate
structures:
•
If the results is a difference GREATER than zero for the first hydrate
structure, this is the stable structure and the calculation ends.
•
If the difference is LESS than zero, the calculation must be performed
until the chemical potentials are identical for the other structure.
Commercially available software is available to do these calculations.
•
EQUI-PHASE Hydrate from D.B. Robinson and Associates.
•
HWHYD from Heriot-Watt University.
•
CSMHYD from the Sloan group at the Colorado School of Mines.
•
The process
modelling software Hysys, Aspen and Prosim all contain
hydrate prediction tools.
TOPIC 1: Gas Hydrates
57
©H
ERIOT
-W
ATT
U
NIVERSITY B41OA December 2018 v3
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