On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs Page: 42 of 188
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Figure 2.2: A tetrahedron element with associated control volumes
2.3 Three-Dimensional, Two-Phase Control
The governing equation for two-phase flow may be generalized as follows:
-V-ul = 5( 01si + ql (2.18)
where 1 = o,w (oil and water phases, respectively). In subsequent development,
the subscript will be omitted for abbreviation.
For the control volume formulation, both the fluid potential and saturation
values are defined on tetrahedron vertices. The fluid potential value in a tetrahe-
dron is interpolated as described in section 1. As for fluid saturation, it is defined
as constant within each control volume.
Referring to Figure 2.2, only the residual function FO for the control volume
surrounding node 0 is derived and similar procedures can be applied to obtain F1,
F2 and F3.
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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/m1/42/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.