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Chapter 32
The IMPES Formulation
The following section from Fanchi, et al. [1982] shows how the flow
equations for a black oil simulator can be recast in a form that is suitable for
solution by a numerical technique. The numerical technique is based on the
formulation originally presented by Sawyer and Mercer [1978].
32.1 Flow Equations and Phase Potentials
The form of the Darcy velocities (Eqs. (4.10) through (4.12)) may be
simplified by defining the potential €> p of phase p as
$ = p - _Z ( 32> i)
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and we have used the assumption that g=g c. In this notation, including x, y, and
z directional permeabilities and unit vectors i, j, k, the Darcy velocities may
be written as
v = -K (32.2)
dx y By z dz
K • A...VO... = -A. (32.3)
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