On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs Page: 21 of 188
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Figure 1.2: A control volume with its boundaries across several triangular ele-
Figure 1.3: Decomposition of a control volume into several subvolumes.
in Figure 1.2. A more convenient approach is then to use an element-by-element
method to add up the contributions from subvolumes b,m = b n tin. Figure 1.3
shows this concept. The residual function for the control volume b, in Figure 1.2
can then be obtained by
Pi = EFm. (1.15)
The partial residual function F, represents the part of F which is contributed
by bi,m and is defined as
F = jpv n ds + O(S)dx, (1.16)
where F L = F n tm.
1.6.3 Formulation of partial residual functions
As shown in Figure 1.4, the partial residual function F; of b2,m is derived in this
section. The same procedure can be applied to obtain F4 and Fe.
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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/m1/21/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.