Page 166 - Principles of Applied Reservoir Simulation 2E

Part II: Reservoir Simulation 151

formulation, and the "-" sign applies to IMPES. Notice that an increase in A?
um
in the fully implicit formulation increases D" while it decreases D Hum when
the IMPES technique is used. Indeed, it appears that a judicious choice of Al-
and A/ could eliminate D num altogether in the IMPES method. Unfortunately,
um
the combination of AJC and A t that yields D" = Q violates a numerical stabi lity
criterion. In general, IMPES numerical dispersion is not as large as that
associated with fully implicit techniques.
As a rule of thumb, timestep sizes in folly implicit calculations should
not exceed a quarter of a year, otherwise numerical dispersion can dominate front
modeling. By contrast, the maximum timestep size in an IMPES simulator can
be estimated by applying the rale of thumb that throughput in any block should
not exceed 10% of the pore volume of the block. Throughput is the volume of
fluid that passes through a block in a single timestep. IMPES timestep sizes are
often on the order of a month or less. An example of a throughput calculation
is given in Chapter 22.
The IMPES timestep limitation is less of a problem than it might other-
wise seem, because it is very common to have production data reported on a
monthly basis. The reporting period often controls the frequency with which well
control data is read during a history match. Thus, during the history match phase
of a study, simulator timestep sizes are dictated by the need to enter historical
data. Large timestep sizes reduce the ability of the model to track variations of
rate with time because historical data must be averaged over a longer period of
time. As a result, the modeler often has to constrain the fully implicit simulator
to run at less than optimum numerical efficiency because of the need to more
accurately represent the real behavior of the physical system.
Fully implicit techniques represent the most advanced simulation
technology, yet IMPES retains vitality as a relatively inexpensive means of
modeling some problems. Unless a folly implicit model is readily available, it
is not always necessary nor cost-effective to employ the most advanced
technology to solve every reservoir simulation problem. The wise modeler will
recognize that you do not have to use a sledge hammer to open a peanut!
Simulators also differ in their robustness, that is, their ability to solve
a wide range of physically distinct problems. Robustness appears to depend as