Page 334 - Principles of Applied Reservoir Simulation 2E

Part V: Technical Supplements 319

Some of the terms in Eq. (31.1) depend on time-varying pressure and
saturation, while other factors change relatively slowly or are constant with
respect to time. We separate these terms to obtain

PI =

where the quasi-stationary factors are collected in the PID term, that is,

0.00708 J: . A

The WINB4D user is expected to provide a PID for each well connection. A
connection is a gridblock with a well perforation.

31.2 Vertical Wells

A value of the connection flow index PID for a vertical well can be
estimated from a formula derived by Peaceman [1978]:
0.007080
PID, =
(31.2)

where

2 7
r e - r o = 0.14(A* 2 + Ay )' '
for an isotropic system. With respect to permeability, an isotropic system is a
= K y).
system in which x direction and y direction permeabilities are equal, (K x
For a square well block in an isotropic system, AJC = Ay and r 0 « 0.2 AJC. The
subscript k in Eq. (31.2) denotes the &th connection. For a well in a rectangular
gridblock and an anisotropic system (that is, K x * K y), well PID is estimated
using an effective permeability

K = K K
]/ X y
and an equivalent well block radius