The Mathematical Basis of the Adaptive Implicit Method

The adaptive implicit method is described which enables a reservoir simulator to choose the degree of implicitness in a grid block to guarantee stability. The mathematical procedure involves labeling the implicit/explicit mix of unknowns and then composing the matrix problem. The technique can be applied to any simulation problem involving N unknowns. The advantage is substantial reduction in computing time and storage requirements compared to fully implicit formulations. 7 refs.