Page 158 - Principles of Applied Reservoir Simulation 2E

Part II: Reservoir Simulation 143

enlarged to include position-dependent effects by modifying the grid represent-
ing the reservoir architecture. Thus, a single block material balance calculation
in a reservoir simulation model can be expanded with relative ease to Include
flow in one, two, or three spatial dimensions. This procedure is used in the case
study presented in Part III.
Most reservoir simulators assume reservoirs are produced under
isothermal conditions. They also assume complete and instantaneous phase
equilibration in each cell. Thus, most simulators do not account for either
temperature gradients or the time it takes a mixture to reach equilibrium. They
assume, instead, that reservoir temperature remains constant throughout the life
of the field and that equilibration is established instantaneously. These are often
reasonable assumptions.
Momentum conservation is modeled using Darcy' s Law. This assumption
means that the model does not accurately represent turbulent flow in a reservoir
or near the wellbore. Some well models allow the user to model turbulent flow,
especially for high flow rate gas wells. Turbulent flow models relate pressure
change to a linear flow term, as in Darcy's Law, plus a term that is quadratic in
flow rate. This quadratic effect is not usually included in the reservoir model,
only in the well model.

15.2 Flow Equations

The general equations for describing fluid flow in a porous medium are
shown in Table 15-1 and associated nomenclature is presented in Table 15-2.
The molar conservation equation includes a dispersion term, a convection term,
a source/sink term representing wells, and the time varying accumulation term.
The dispersion term is usually neglected in most workhorse simulators such as
black oil and compositional simulators. Neglecting dispersion simplifies program
coding and is justified when dispersion is a second-order effect. In some
situations, such as miscible gas injection, physical dispersion is an effect that
should be considered. Further discussion of dispersion is presented in Chapter
16.