Abstract:
Mass transfer in a fractured-porous carbonate reservoir is considered. Such reservoirs
have a natural system of destruction in the form of fractures and cavities. In this work, a
mathematical model of fluid redistribution between a pore-type matrix and a network of
natural fractures is proposed and studied. The resulting system of differential equations is
quasilinear and rather complicated. When solving it numerically, a number of difficulties
arises. First, the system contains a large number of unknown functions. Second, the nature of the nonlinearity of the equations is such that the corresponding linearized system
no longer possesses the property of self-adjointness of spatial differential operators. To
solve the problem, the method of splitting by physical processes and the approximations
of differential operators by the method of finite differences are used. The resulting split
grid model is equivalent to the discrete initial balance equations of the system (conservation of mass components of fluids and total energy of the system) written in divergent
form. This approach is based on a nonlinear approximation of grid functions in time,
which depends on the fraction of the volume occupied by fluids in the pores, and is easy
to implement. The work presents the results of numerical calculations, analyzes the
space-time dynamics of pressure change processes.
Keywords:mathematical modeling, differential equations, mass transfer, fractured reservoir, saturation.
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