Answer to Question #255937 in Mechanical Engineering for Gani

Question

A slightly compressible oil is flowing in a volumetric, homogeneous reservoir. The oil has a viscosity of 2 cp, compressibility of 5 x 10-5psi -1 and formation volume factor of 1 RB/STB. The reservoir is represented by a three-gridblock system as shown: T The dimensions and the properties of all gridblocks are Ax=200 ft, Ay=100 ft, Az=20 ft, kx= 100 mD, and p=0.20. The initial reservoir pressure is 3,000 psia. The well in gridblock 3 is produced so that the well block pressure is maintained at 1,500 psia for all time >0. All the boundaries are closed. Find the pressure of gridblocks 1 and 2 at t=10 days with the implicit finite difference formulation and the time step At=10 days.

Answer 1

Development of a reservoir simulator for different types of reservoir-well systems and recovery processes requires a substantial background in mathematics and applied science, which starts with establishing the finite difference equations of a mathematical model for fluid flow in a certain type of reservoir-well system, then followed by numerical modeling and computer programming, and generates simulation software

The principles and procedures of the finite difference method are first discussed for the system of a single-phase slightly compressible fluid based on the theoretical basis of the Taylor series. For the system of a single-phase compressible fluid, the finite difference equations are built on the individual grid blocks rather than discretization of the diffusivity equation,

The heterogeneity of reservoirs, irregular size of grid blocks, and non-linearity of equations caused by pressure-dependent properties are considered in the finite difference equations.