\"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.
","abstract_html":"<p>"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.</p> <p>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.</p> <p>The RELAX+ADIP combination was found to be the best method tested for solving the pressure equation in the simulation model"--Abstract, page ii.</p>","abstract_has_math":false,"creators":["Achmad, Grufron"],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Petroleum Engineering","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:18:50Z","subjects":["Petroleum Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/234","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Achmad, Grufron"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Petroleum Engineering"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Petroleum Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/234"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"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.
"]},{"key":"dc:title","label":"Title","values":["An application of residual relaxation to mathematical simulation of petroleum reservoirs"]}]}],"canonical_facts":{"dc:creator":["Achmad, Grufron"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"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.
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/234"],"dc:subject":["Petroleum Engineering"],"dc:title":["An application of residual relaxation to mathematical simulation of petroleum reservoirs"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Petroleum Engineering"],"thesis:institution_name":["University of Missouri--Rolla"]},"updated_at":"2026-07-24T03:18:50Z"}