Doctoral Dissertations


"Stability and convergence have long been primary concerns in the application of numerical techniques to the simulation of petroleum reservoir performance. An iterative method based on sequentially reducing the residual to zero at each grid point has been developed. It has been shown analytically that this residual relaxation method is stable, convergent, and consistent.

A three-phase areal model was developed to simulate a hypothetical homogeneous petroleum reservoir, and various computational methods were tested with this model. The residual relaxation method developed in this study (RELAX) was found to converge as rapidly as SIP, and much faster than either LSOR or LSOR+2DC. The RELAX+ADIP combination was found to converge more rapidly than SIP. No iteration parameter is needed for either RELAX or RELAX+ADIP, and both methods are easily programmed.

The RELAX+ADIP combination was found to be the best method tested for solving the pressure equation in the simulation model"--Abstract, page ii.


Arnold, Marion D., 1932-2010

Committee Member(s)

Govier, John P., 1913-1998
Harvey, A. Herbert
Carlile, Robert E.
Ho, C. Y. (Chung You), 1933-1988
Wilson, Tommie C., 1939-


Geosciences and Geological and Petroleum Engineering

Degree Name

Ph. D. in Petroleum Engineering


University of Missouri--Rolla

Publication Date



vii, 85 pages

Note about bibliography

Includes bibliographical references (pages 58-59).


© 1973 Grufron Achmad, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type




Library of Congress Subject Headings

Hydrocarbon reservoirs -- Mathematical models
Residual stresses -- Mathematical models
Stress relaxation -- Mathematical models

Thesis Number

T 2808

Print OCLC #


Electronic OCLC #


Link to Catalog Record

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