On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs Page: 57 of 188
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3.3.3 Discretized multiphase flow equations
The discretized multiphase flow equations are derived in this section. The volu-
metric balance equation (3.15) is rewritten here for convenience.
V -= at B + q.
Let the subscripts o, w and g represent oil, water and gas phases, respectively,
then the three-phase volumetric balance equations are
V -g V -, =
+ Rs O + qg + R, qo.
Referring to equation (3.33), the discretized three-phase equations for triangle T
can be written as
kropg fio i
krgPg gfig i
At B n
RsBopog f"io+ ii t [Rs OiO)
CB )+ITI go,
+ - (. T
- IT Rgo.
The modified head gradients for each phase on each side of T are
f = 2hoV -qi
f = -hwV -qi
fig = hgV -qi
2T Eo (q- nj) l1,
2IT hj (q - nj 'j,
2 ITI Ehjg (qj .n) -j
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Deo, Milind D. On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs, report, August 31, 2005; Utah. (https://digital.library.unt.edu/ark:/67531/metadc877059/m1/57/: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.