Multigrid Methods for Fully Implicit Black-Oil Reservoir Simulation.

                                 H. Molenaar

In industry the black oil model is widely used for numerical reservoir
engineering.  In this model it is assumed that water, oil and gas are present
in the reservoir, and that gas can dissolve into the oil.  The standard
approach for the numerical solution of these equations is a first order upwind
space discretization, combined with an implicit time integration.  This means
that large systems of nonlinear equations have to be solved in every time
step.  Usually this is done by Newton's method.  The resulting system of
linear equations is then either solved by a direct method or by some conjugate
gradient type method.

In this talk we discuss the possibility of applying multigrid methods for the
iterative solution of the systems of nonlinear equations.  We will present two
different multigrid methods:  a linear multigrid method for the solution of
the linear systems that appear in Newton's method, and a nonlinear multigrid
method.  A simple 2D problem in which the local disappearance of the gas phase
occurs, serves as a test problem to compare these two methods.

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H. Molenaar

Faculty of Technical Mathematics and Informatics
Delft University of Technology
P.O.Box 5031
2600 GA  Delft, The Netherlands

e-mail: hansmo@twi.tudelft.nl