IMPES and IMPLICIT

There are 2 methods for obtaining numerical solutions in the numerical reservoir simulation:

• the Implicit Pressure, Explicit Saturation formulation (IMPES),
• the fully Implicit formulation (IMPLICIT).

The solution of these equations, at finite timesteps, provides a way to estimate specific time-dependent changes in pressure, saturation, composition, and other key parameters for each cell and each well over the production period desired.

Most of commercial simulators allows both methods to solve the equations. Which method to chose?

IMPES is much faster per timestep. However, because of the explicit treatment of mobility terms and capillary pressure (evaluation at N instead of N+1 timestep), it is much less stable and requires more and smaller timesteps compare to the IMPLICIT method. The classic situations that are problematic for IMPES are small cells near wells, vertical gas percolation, and pinchouts. Each of these involve large cell throughput relative to its size over a timestep. On the contrary, IMPLICIT requires more RAM than IMPES, because of more equations are being solved. However, since it is more stable than IMPES, the simulator is able to take larger timesteps.

	IMPLES	IMPLICIT
Memory	Less	More
Stability	Less	More
Dispersion	Less	More
CPU Time / Step	Less	More
Time Steps	More	Less
Total CPU Time	Care dependent	Care dependent

External Links

http://en.wikipedia.org/wiki/Explicit_and_implicit_methods
http://digitalcommons.uconn.edu/cgi/viewcontent.cgi?article=1118&context=srhonors_theses
http://www.geophysik.uni-muenchen.de/~igel/downloads/nmgimplicitmethods.pdf