Development of a deflation based solver for 3D pressure equations in oil reservoir simulation
Joost van der Linden
Video of the internship, which Joost has done at IBM in New York.
Supervisor: Kees Vuik
Site of the project:
Schlumberger Abingdon Technology Center
Lambourn Court, Wyndyke Furlong
Abingdon Business Park
Abingdon, Oxfordshire, OX14 1UJ
start of the project: April 2013
The Master project has been finished in December 2013
by the completion of the
and a final
has been given.
For working address etc. we refer to our
Summary of the master project:
In reservoir simulation we predict the recovery of gas and oil by solving for the fluid flow in porous
Intersect (IX) is the next generation reservoir simulator developed in a joint venture of Schlumberger
and Chevron. The main development team is located at the Abingdon Technology Center (AbTC), UK.
The time-dependent, non-linear equations which underlie reservoir simulation are discretized by the
Finite Volume method and solved by the Newton-Raphson method and implicit time integration. In
every step of the Newton-Raphson method we evaluate the derivatives of the non-linear reservoir
simulation equations and solve the corresponding linear system. Typically for a simulation of N cells we
solve for Nxl unknowns, with l unknowns per cell. These are pressure, water (and gas) saturations and
molefractions. In this project we only regard isothermal cases; hence temperatures are a given constant.
Two major issues affect the performance of the evaluation of these equations. For heterogeneous
media and large differences in fluid properties we may see large jumps in the coefficients in the matrices
of the corresponding linear systems. Moreover, for large and/or fine meshes the corresponding linear
systems are very big. Both issues can lead to ill conditioned linear systems that are hard to solve.
The aim of this project is to explore the effect of a deflation based preconditioner to help
the linear solver solving the 3D pressure equations. This might be done by addition of
deflation to FGMRES. Key is the construction of the correct deflation vectors. These might be
either physics based or come from an algebraic approach.
Results of reservoir simulation
Artist impression of oil flow in a reservoir
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