**Numerical Simulation in
Reservoir Engineering: **

**An Overview**

**A. S. Harouaka and H.
Menouar**

**CPM/Research Institute **

**King Fahd
University of Petroleum & Minerals **

**Abstract **

Reservoir simulation has been
recently defined as the art, science and engineering of the modeling of flow in
petroleum reservoirs by solving relevant equations using modern computers.

Specifically, we seek the
solution to a system of highly nonlinear partial differential equations (PDE),
describing a single or multiphase fluid flow in one two or three dimensions.
The procedure most commonly used and accepted is to approximate the PDE by
finite difference.

The discretisation
process leads to a matrix A whose entries are mainly zeros. This matrix can be
extremely large for reservoir engineering problems of a practical size. The
solution technique needed to solve the matrix A is by far the most important
part of any reservoir simulator and for large simulation problems, iterative
solutions techniques have been preferred to direct ones.

The main objectives of this
discussion are: 1) Present a brief description of a reservoir simulator; 2)
show the different models currently being used and 3) describe how reservoir
simulators are considered the primary tools for reservoir management.