Prediction of Reservoir Behavior Using Numerical Simulators
Authors: Schwabe Klaus , Brand Jack 
Published: December 2007

American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The rather complex set of partial differential equations which describes multiphase flow of fluids in reservoirs has long been studied by research engineers and mathematicians but has been of limited value to the reservoir engineer or manager attempting to determine how best to operate his reservoir. During the post decade, finite difference techniques for solution of these equations have been developed, tested, and proven with the assistance of large high-speed digital computers. It is now a routine matter to solve a set of these equations in two- or three-dimensional space in a matter of minutes for a reservoir divided into thousands of segments.
Data requirements and methods for defining the physical characteristics of a reservoir are presented. The paper explains techniques used to link the reservoir capacity in the vicinity of each well at some instant in time with the physical characteristics of the well and its production mechanism. Overall reservoir management criteria such as pipeline capacity and demand in foreign areas, and proration rules in local areas are also included.
Even though the actual work is done on a high speed electronic computer, the description of the work done by the computer is explained from the reservoir engineer's point of view. The description of the approach forms a valuable outline for making a reservoir study even if numerical simulators are not used.

Introduction
The engineer responsible for the operation of a reservoir is aware of the importance of o good reservoir study to the efficient development and exploitation of an oil or gas reservoir. He is also faced with the pressing every day operational problems which tend to place the reservoir study into the background. With the current shortage in manpower, he finds it more and more difficult to allocate a sufficient amount of man time for reservoir studies.
In response to the need for detailed studies, the numerical reservoir simulator has emerged as an extremely useful tool for the solution of reservoir problems and individual well problems. Mathematical techniques employed in the construction of these numerical simulators have been well documented in the SPE literature and in mathematical and chemical engineering journals. The complexity of the mathematics and the tremendous volume of computer programs required for a practical solution prohibit the construction of a numerical reservoir simulator for a single reservoir study. This created the need for generalized numerical reservoir simulators capable of handling and interpreting directly the reservoir data supplied by the practicing engineer.
Experience gained from the application of specialized reservoir simulators led to the development of the generalized simulators available today.