All ETDs from UAB

Advisory Committee Chair

Ian Knowles

Advisory Committee Members

Marius Nkashama

Shan Zhao

S S Ravindran

Hemant K Tiwari

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences


Inverse problems involving partial differential equations have many physical applica- tions. One of the most important applications is in petroleum reservoir modeling. The estimation of petroleum reservoir properties is an essential component in predicting reservoir behavior. Generally, oil and water are present together in petroleum reservoirs and the resulting reservoir model consists of two nonlinear partial differential equations. Much research deals with two phase flow in porous media assuming incompressibility, but a few researchers consider the weakly compressible case which generally applies when the reservoir model does not include a gas phase. In this thesis we assume the weakly compressible case, in which the oil and water compressibilities are assumed to be small, and constant throughout the oilfield. We are adapting a method that has been successfully used to estimate the values of the parameters of the single phase groundwater flow equation, depending on the minimization of convex functionals. This kind of minimization was first presented in 1995 by Knowles and Wallace, and applied in the groundwater field in 2002 by Knowles,Yan and Le. This method of minimization initially failed for the two phase weakly compressible model because of the presence of delta functions in the right hand side of the model equations. We introduce a successful technique for modifying the functionals by locally removing the delta functions representing the location of the production wells. We use a Neuberger gradient to minimize the functional. Simulation results using synthetic data shows that we recover the absolute perme- ability coefficient function with very few iterations.



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