By Jun Yao, Zhao-Qin Huang
This e-book solves the open difficulties in fluid circulate modeling in the course of the fractured vuggy carbonate reservoirs. Fractured vuggy carbonate reservoirs often have advanced pore buildings, which comprise not just matrix and fractures but additionally the vugs and cavities. because the vugs and cavities are abnormal fit and differ in diameter from millimeters to meters, modeling fluid movement via fractured vuggy porous media remains to be a problem. the present modeling concept and techniques usually are not compatible for such reservoir. It starts off from the concept that of discrete fracture and fracture-vug networks version, after which develops the corresponding mathematical types and numerical equipment, together with discrete fracture version, discrete fracture-vug version, hybrid version and multiscale types. in line with those discrete porous media versions, a few identical medium types and strategies also are mentioned. the entire modeling and techniques shared during this ebook supply the foremost contemporary suggestions into this area.
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Extra info for Fractured Vuggy Carbonate Reservoir Simulation
The saturation at interface of fractures and the matrix system is not always continuous, as shown in Fig. 8. Herein, the water phase saturation equation of fractures needs special treatment in above superposing process. For the flow potential of water is continuous, the capillary force potential and the capillary pressure are both continuous. Combining Fig. 8, the saturation of fractures and the matrix system meet the equation as follows: & k up ¼ ki if Ui ! Uj kj if Ui \Uj ð2:24Þ For fractures, Eq.
89). Pkc ¼ ÀBk lnSkw ; ð2:89Þ where superscript k ¼ 1 Á Á Á nm is the index of media in control volume element. The relationship between different media’s saturations can be established based on the concept of capillary pressure continuation. For example, as far as fracture media: f À m f Á Sm B w Sw ¼ exp ÀB 42 2 Discrete Fracture Model The maximum of Bk in Eq. 89) is chosen as reference media in here. Based on Eq. 88) and compound function derivation method, we obtain Z @Sw @pw þ /Sw Cw dA ¼ / @t @t m X dSkw k k /A dSwþ k¼1 A !
14 Velocity distribution in single fracture. a Realistic velocity, b equivalent velocity (a) (b) f (1D) f (2D) fra ctu a re m(2D) matrix sim p fra lified ctu re m(2D) matrix Fig. 15 Schematic of discrete fracture model. 3 Control Volume Method Numerical Simulation 33 Considering the 2-D porous media region in single fracture, the whole area is X, 0 and the matrix area is Xm , the fracture area is Xf in single fracture model and is aXf in discrete fracture model. So based on the discrete fracture model, the whole region of reservoir can be expressed as 0 X ¼ Xm þ aXf ð2:60Þ where a is fracture aperture.