On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs Page: 78 of 188
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Table 5.1: Fracture properties available from oil field.
Fracture No. Start End Permeability width 1
f1 (X, y1) (X, Y1) ki _
f2 (X2, y2) (X, y2) k2 W2
The width of fractures is not always available.
by its starting and ending points. Fracture permeability kf is given as a scalar
which represents the permeability along the fracture line. The width of fractures
is sometimes but not always available as shown in the last column of Table 5.1.
5.3 Single-Porosity Model
When the width information of fractures is available, the most straightforward
and accurate approach to fracture simulation is the single porosity model. In
this model, fractures are represented by very tiny or very thin two-dimensional
Consider a square domain with one fracture as shown in Figure 5.6. To put
the width of fractures into consideration, the line is replaced by a rectangle and
is shown is Figure 5.7. It important to note that the width and the length of the
fracture in Figure 5.7 are not in proportion; the width has been enlarged in order
to be visible. In general the ratio of length to width of fractues is in the range of
four to six orders. The triangular mesh of this single fracture domain is shown in
Figure 5.8. It is clear that a trimendous amount of triangles is required by the
single-porosity model even for a single, disproportional fracture. Consequentlly,
the single-porosity model will need a lot more elements for a real fracture (a
fracture that is in correct proportion) than the disproportional fracture.
5.4 Discrete-Fracture Model
In view of the limited fracture information that is available and the difficulty
(requires too many elements) involved in the single porosity model, it is natural
to consider the use of line elements to approximate fractures in two-dimensional
Consider the same square domain with one fracture as discussed in section 5.3.
Without the introduction of fracture width, the domain is directly triangulated
and the result is shown in Figure 5.9. Comparing Figure 5.8 with Figure 5.9,
the number of triangular elements required by the single-porosity for a single
disproportional fracture is about five times of that required by the discrete-fracture
model. When the number of fracture increases and real fracture geometry is used
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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/m1/78/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.