Page 309 - Principles of Applied Reservoir Simulation 2E

294 Principles of Applied Reservoir Simulation

if we write irreducible water saturation as S wr, the relative permeability constraint
k mw (1 - S wr) = k rog (S 0 + S w = 1.0) must be satisfied since S g = 0 in both cases.

28.2 Transmissibility

The simulator offers no-flow boundary conditions, which lets you stop
flow between specified gridblocks in chosen directions. The no-flow conditions
are implemented by setting transmissibilities at boundary interfaces to zero. The
Transmissibility Modifications section in Chapter 24.3.3 describes the directional
conventions for transmissibility in the model,
Flow between neighboring blocks is treated as a series application of
Darcy's law. A transmissibility term at the interface between two blocks is
defined using the product of average values of relative permeability k^ of phase
0, absolute permeability K of each block at the interface, and cross-sectional
area A c of each block at the interface, divided by the product of viscosity jl e and
formation volume factor B% of the phase in each block. The transmissibility to
each phase is determined using a harmonic average calculation of the product
of absolute permeability and cross-sectional area at the interface between
neighboring blocks. An arithmetic average of phase viscosities and formation
volume factors is used. The average relative permeability is determined using
an upstream weighted averaging technique. The resulting Darcy transmissibility
is
Air 2(KA C
A' rt( upstream)
-"•
B u
and the finite difference transmissibility A tii. ]/2 for phase <! between block / -1
and block / used in the simulator is

+ *-t ; I/O •*••• a ;.. i

where they, k indices are suppressed and the spatial differences are
Ax — x (— _ }, Ax = X M - x i
x f