Some Computational Issues in Oil Reservoir Studies
In tertiary oil recovery, an inexpensive fluid is injected into the reservoir so as to mix with the hydrocarbon (oil) and then to push the resulting fluid towards the production wells. Assuming there is no volume change and the fluid is slightly compressible, the mathematical model gives rise to a coupled system of parabolic equations: one in pressure and the other one in concentration. Since the concentration equation is convection dominated and depends mainly on velocity not pressure, the following issues are addressed in , (in the list of publications) and , ,  (Submitted Manuscripts and Thesis of Mr. M. A. Mohamed Ali):
1. H1-mixed finite element method.
2. C0-interior penalty method and modified method of characteristics (exclusively for convection dominated diffusion problems).
3. Incomplete time stepping with preconditioning (to solve efficiently the resulting large system of equations).