IMPES and Fully Implicit

Part 12, Chapter 12: Running a Simulation, History Matching, and Forecasting

Two Ways to Step Forward

A simulator advances in time by one of two schemes. IMPES (implicit pressure, explicit saturation) solves the pressure field implicitly each step but updates saturation with an explicit formula, so each step is cheap.

IMPES and fully implicitCFLIMPESfully implicittimestep (days) ->total cost (log)IMPES is cheaper for small steps but floors out at the CFL limit; fully implicit takes big steps at Newton cost and wins beyond the crossover (here 20 days).

The Explicit Limit

The explicit saturation update is stable only below a timestep limit, the CFL condition, so a large step must be chopped into many small ones. IMPES therefore floors out: it cannot run cheaper than the CFL-limited step count.

Fully Implicit

Fully implicit solves pressure and saturation together by Newton iteration. Each step costs several linear solves, but it is stable at any size. Beyond the crossover, taking big implicit steps beats running many small explicit ones, which is why field-scale runs are usually fully implicit.

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