Page 272 - Fundamentals of Enhanced Oil and Gas Recovery

260 Alireza Keshavarz et al.

increases, by an enriched N 2 mixture, although, the quality of the produced gas is still
of concern due to the quick N 2 breakthrough. The best performance was obtained by
a mixture of 13% CO 2 and 87% N 2 . Sayyafzadeh et al. claimed that the performance
of mixture gas injection can be improved by applying a varying composition strategy,
throughout a continuous injection of N 2 /CO 2 mixture [4]. A series of sensitivity
analyses were performed to find an optimal scenario. The best scenario was the one
that starts by injecting a mixture with less CO 2 and continues by a sequential rise in
the CO 2 fraction.
The optimal gas composition depends on the petrophysical, geomechanical, and
sorption characteristics of the coal. Hence, it is suggested to conduct a sensitivity anal-
yses or an optimization using numerical simulation to find an operationally and eco-
nomically viable scenario. Sayyafzadeh and Keshavarz used a genetic algorithm to
optimize well controls and injectant composition to maximize the revenue from a
semisynthetic coalbed model [109].

8.5.2.1 The Governing Equations for Modeling ECBM
A set of partial differential equations (PDEs) should be solved to model and simulate
fluid flow in an enhanced coalbed recovery process. This allows us to predict adsorbed
gas content (V i ), mole fraction in cleats (y i ), pressure (p l ), saturation (s l ), well flow rate
(q i ), and well bottomhole pressure (p wf )inspace andtime(x, y, z, t). i and l denote
component and phase, respectively. The PDEs are derived based on the following laws
and equations, including mass conservation law, Darcy’s law, Fick’s law, a sorption model
(typically extended Langmuir isotherm), a permeability model and equations of state.

8.5.2.1.1 Mass Continuity Equations
In coalbed, there are typically two phases (water and oil). By writing molar mass bal-
ance for each component in each phase on a representative elementary volume (REV)
through Eulerian formulation, the below equations for cleats will be achieved. The
Ð
flow from matrix to cleats or from cleats to matrix ( @Ω j i :~nds) can be seen as a sink/
source term for the following equations in an isotherm state:
@
ð ð ð ð
y i g g ~ g ~ndA 1 y i g g φS g dV 2 ~ q dV 2 ~ j i ~ndA 5 0 (8.27)

b
u
b
ig
@Ω Ω @t Ω @Ω
ð ð ð

y i w w ~ w ~ndAÞ 1 @ y i w w φS w dV 2 ~ q dV 5 0 (8.28)
b
b
u
ð
iw
@Ω Ω @t Ω
is the mole fraction of component i in
where b l is the molar density of each phase, y i l
phase l, ~q is the molar rate production/injection of component i from phase l per
il
unit volume, j i is the molar flux rate of component i from matrix to cleats or from
cleats to matrix, ~ l is phase l fluid velocity, φ is cleats porosity, S l is phase saturation,
u