A total of around ~2 trillion barrels of viscous crude oil is held in a
carbonate reservoir. The heavy oil held in a Fractured Carbonate Reservoir (FCR)
encompasses an enormous potential to contribute to the world's oil needs.
Continuous steam flooding Enhanced Oil Recovery (EOR) is used as a tertiary
method to increase recovery from these complex classes of reservoirs. The
mathematical perspective of modelling these reservoirs involves the inclusion of
three flow equations (oil, water, and steam) and one heat balance equation. In
recent studies, for modelling FCR, flow equations are defined for two different
sub-domains, namely fracture and matrix. Both the grid blocks possess high
porosity and permeability contrast, in which fracture has high transmissibility
and the matrix has a high storage capacity of hydrocarbons. In this study, an
attempt is made to derive flow equations (partial differential equation) for all
phases in two dimensions, including gravity effect with the help of Darcy's law.
The presence of pressure and saturation terms in flow equation for steam, oil,
and water makes the modelling of steam flooding EOR in FCR more challenging. The
derivation of fluid flow equations (oil, water, and steam) involves deriving of
the continuity equation first, followed by combining it with Darcy's law. An
under-saturated reservoir considered in this case, where the reservoir pressure
is always higher than the bubble-point pressure, and hence, the fluid of
interest is of aqueous phase only in the absence of any phase changes between
steam and liquid. The present study is aimed at deducing an improved
mathematical model by considering the reservoir fundamental parameters, namely,
porosity, permeability, and compressibility, as a function of petrophysical
parameters associated with a dual-continuum system. The correlations used in the
derivation of the fluid flow equation incorporate separate equations defined
mathematically for fracture and matrix porosity and permeability, respectively.
Also, porosity is considered as a variable coefficient which changes with change
in pressure. This work will help in modelling fractured reservoirs more
efficiently by solving fluid flow equations with more ease.
Keywords: fractured carbonate reservoir, partial differential equation,
correlations, improved mathematical model, implicit pressure and explicit