Page 306 - Principles of Applied Reservoir Simulation 2E

Part V: Technical Supplements 291

27.4 Material Balance

Material balance is one measure of the numerical stability and accuracy
of a simulator. The WINB4D material balance calculation at time t is given by
FIP
:
Material Balance = (27 17)
OFIP - Prod + Inj l
where
FIP = fluid in place at time /
OFIP = original fluid in place
Prod = cumulative fluid produced at time /
Inj = cumulative fluid injected at time t
Based on this definition, material balance should equal one in an idealized
calculation. Actual simulator material balance may not equal one.
Material balance error reported by WINB4D is calculated using the
formula

{ OFIP - FTP + Inj 1 \ x 100% (27.18)
1
—
Prod
J
Material balance can be a sensitive indicator of error. Material balance error is
greatest in WINB4D when a gridblock undergoes a phase transition, for example,
when a gridblock passes from single phase oil to two-phase oil and gas during
a timestep.
Material balance errors can be corrected by adding or subtracting enough
fluid to reestablish an exact material balance [Nolen and Berry, 1973; Spillette,
et al., 1986], This material balance correction technique is equivalent to adding
a source/sink term to the mass conservation equations for every gridblock. These
terms are not included in the WINB4D formulation. The exercises in Parts I and
II show that the uncorrected formulation can be used with good accuracy in
many practical situations.