## Abstract

Reservoir simulation in the oil industry has become the standard for solving reservoir- engineering problems. Reservoir simulation combines physics, mathematics, reservoir engineering, and computer programming to develop a tool for predicting hydrocarbon reservoir performance under various production strategies. The steps involved in the development of a simulator include: derivation of the partial differential equations (PDE's) describing the recovery process through formulation, discretization of the PDE's in space and time to obtain nonlinear algebraic equations, linearization of resulting algebraic equations, solving the linearized algebraic equations numerically, and finally validation of the simulator. Developers of simulators relied heavily on mathematics in the first two steps (mathematical approach) to obtain the third step (nonlinear algebraic equations or finite-difference equations). A new approach, that derives the finite-difference equations without going through the rigor of PDE's and discretization, is presented in this paper. The new approach is called the engineering approach because it is closer to the engineer's thinking and to the physical meaning of the equations. Both the engineering and mathematical approaches treat boundary conditions with the same accuracy if the mathematical approach uses second order approximations. The engineering approach is simple and yet general and rigorous. In addition, it results in the same finite-difference equations for any hydrocarbon recovery process. Because the engineering approach is independent of the mathematical approach, it provides justification for the use of central differencing in space, and gives implications of the approximations, that are usually used in the mathematical approach, in time discretization.

Original language | English |
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Title of host publication | Nature Science and Sustainable Technology |

Publisher | Nova Science Publishers, Inc. |

Pages | 39-71 |

Number of pages | 33 |

ISBN (Electronic) | 9781536111989 |

ISBN (Print) | 9781604560091 |

Publication status | Published - Jan 1 2008 |

## ASJC Scopus subject areas

- General Engineering