Page 131 - Fundamentals of Enhanced Oil and Gas Recovery

Miscible Gas Injection Processes 119

Therefore, it can be concluded that
ig X ig
M T Pð Þ 5 x i M ðT p i Þ (4.25)
i i
i
In Eqs. (4.23) (4.25), T, P, p i , M, and M are temperature, pressure, partial pres-
sure, molar, and partial molar property, respectively. The superscript ig shows the ideal
gas. The Gibbs theorem states that the parameter M can be any thermodynamic prop-
erty in exception of the volume parameter. Application of Eq. (4.25) for estimation of
volume may lead to inaccurate results. In approximating the amount of solvent for a
specific reservoir conditions, thermodynamic calculations should be considered for
characterizing the behavior of solvent heavy oil system [59].

4.5.1.2 Diffusion Coefficient for Solvent Heavy Oil System
Injection of miscible solvent in the reservoir is an example of mass transfer process
that is governed by a diffusion coefficient. It is suggested that precise diffusion data
for this process are essential in order to calculate the following parameters as
follows [76]:
• The amount of gas flow rate for injection,
• The extent of heavy oil the its viscosity would be decreased,
• The needed time to reach to desired mobility,
• The oil production rate.
It is only possible when constant diffusion coefficient is assumed, which is in the
need of the following conditions [76]:
• Having similarity between molecular diameter and shape of molecules,
• Negligibility of intermolecular forces within diffusion mixture,
• Nonreacting environment.
In most of the reservoir situations, the solvent heavy oil system meets the third
condition, except in place where asphaltene deposition can happen and consequently,
none of the above conditions are fulfilled [77].
Chang and Chang [78] developed a finite volume approach for the inverse esti-
mation of thermal conductivity in one-dimensional domain. The method can also
be utilized to convert the differential equation governing the mass diffusion into a
system of linear equations in matrix form. The unknown diffusion coefficients are
obtained by solving the system directly. Hence, no prior information about the
functional form of the diffusion coefficient is required and no iterations in the cal-
culation process are needed. Thus, starting from Fick’s second law, which is as fol-
lows [77]:

@c @ @c
5 D (4.26)
@t @x @x