Chapter 5 - Simulation with a point-distributed grid

Abstract

Discretization process creates inherent challenges involving proper representation of natural processes. The problem is accentuated by boundaries, which create discontinuities—an absurd condition for natural systems. Historically, the petroleum engineers have identified these problems and have attempted to address many problems that emerge from discretization and boundary conditions, which must be addressed separately. Few, however, have recognized that the engineering approach keeps the process transparent and enables modelers to remedy with physically realistic solutions. This chapter presents discretization of 1-D, 2-D, and 3-D reservoirs using point-distributed grids in Cartesian and radial-cylindrical coordinate systems. This chapter describes the construction of a point-distributed grid for a reservoir and the relationships between the distances separating gridpoints, block boundaries, and sizes of the blocks represented by the gridpoints. The resulting gridpoints can be classified into interior and boundary gridpoints. While Chapter 2 derives the flow equations for interior gridpoints, the boundary gridpoints are subject to boundary conditions and thus require special treatment. This chapter presents the treatment of various boundary conditions and introduces a general flow equation that is applicable to interior gridpoints and boundary gridpoints. This chapter also presents the equations for directional transmissibilities in both Cartesian and radial-cylindrical coordinate systems and discusses the use of symmetry in reservoir simulation.