Page 160 - Principles of Applied Reservoir Simulation 2E

Part II: Reservoir Simulation 145

The molar flow equations were derived using the conservation laws
introduced in Chapter 15.1. An energy balance equation can be found in the
thermal recovery literature [Prats, 1982]. The energy balance equation is more
complex than the flow equations because of the presence of additional nonlinear
terms. Energy loss to adjacent non-reservoir rock must also be computed. The
resulting complexity requires substantial computation to achieve an energy
balance. In many realistic systems, reservoir temperature variation is slight and
the energy balance equation can be neglected by imposing the isothermal
approximation. The result is a substantial savings in computation expense with
a reasonably small loss of accuracy.
Several supplemental - or auxiliary - equations must be specified to
complete the definition of the mathematical problem. There must be a flow
equation for each modeled phase. Commercial black oil and compositional
simulators are formulated to model up to three phases: oil, water, and gas. The
inclusion of gas in the water phase can be found in some simulators, though it
is neglected in most. The ability to model gas solubility in water is useful for
CO 2 floods or for modeling geopressured gas-water reservoirs. Some black oil
simulator formulations include a condensate term. It accounts for liquid yield
associated with condensate reservoir performance.
In addition to modeling reservoir structure and PVT data, simulators must
include rate equations for modeling wells, phase potential calculations, and rock-
fluid interaction data such as relative permeability curves and capillary pressure
curves. Saturation-dependent rock-fluid interaction data are entered in either
tabular or analytical form. More sophisticated simulators let the user represent
different types of saturation change processes, such as imbibition, drainage, and
hysteresis. Applying such options leads to additional computation and cost,

15.3 Well and Facilities Modeling

Well and surface facility models are simplified representations of real
equipment [Williamson and Chappelear, 1981]. The well model, for example,
does not account for flow in the wellbore from the reservoir to the surface. This
effect can be taken into account by adding a wellbore model. The wellbore model