Mathematical Model and Numerical Presentation of Equations for Joint Fluid Motion

Abstract

A modern analysis of the hydrocarbon field development system and forecast of production dynamics under different operating conditions is carried out using mathematical models of reservoir behavior, the effective use of which requires significant computa-tional costs. The uncertainty associated with the characteristics of the formation and its saturating fluids lead to the need for a pre-liminary hydrodynamic study of the formation's reaction to a change in the production (injection) regime in the wells. Mathematical modeling of multiphase flow in a porous medium, to a large extent, is still an open question. The main difficulty is related to its diverse nature. In fact, it is necessary to consider a multiphase flow as a problem with complex physics, i.e., when differ-ent processes prevail on different scales. Such complex behavior is not desirable to reduce to the creation of simplified mathematical models, which are a generalization of models that describe a single-phase flow well. This is especially true for a three-phase flow, which was traditionally modeled by the direct application of a two-phase description. The purpose of this paper is to develop a universal approach to the creation of a software package for the hydrodynamic modeling of oil fields, which we will simply call the simulator. This method is a network approach to creating a simulator of deposits and pro-vides a higher level of standardization than the classical method. To solve this problem, we present a mathematical model and a nu-merical representation of the equations for the joint movement of fluids .