By Jun Yao, Zhao-Qin Huang
This ebook solves the open difficulties in fluid circulate modeling in the course of the fractured vuggy carbonate reservoirs. Fractured vuggy carbonate reservoirs often have complicated pore buildings, which comprise not just matrix and fractures but additionally the vugs and cavities. because the vugs and cavities are abnormal match and range in diameter from millimeters to meters, modeling fluid circulate via fractured vuggy porous media remains to be a problem. the prevailing modeling idea and strategies will not be compatible for such reservoir. It begins from the concept that of discrete fracture and fracture-vug networks version, after which develops the corresponding mathematical types and numerical tools, together with discrete fracture version, discrete fracture-vug version, hybrid version and multiscale types. in response to those discrete porous media versions, a few an identical medium types and techniques also are mentioned. the entire modeling and techniques shared during this ebook supply the most important contemporary ideas into this area.
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Additional resources for Fractured Vuggy Carbonate Reservoir Simulation
78) with Gauss divergence theorem, we obtain ZZ ZZ Z @Sw @pw þ /Sw Cw / dA À ðkw rpw Þ Á ndC À @t @t X C qw dA ¼ 0; ð2:79Þ X where C is boundary of control volume element CVi; n is unit outward normal vector on boundary C. The water saturation of the matrix and fractures can be connected with each other by Eq. 71), the ﬁrst term of the left side of Eq. 79) can be approximately expressed as ZZ m @Sw @pw @Sw @pw þ /Sw Cw þ Sw C w / dA % A/i ; @t @t @t @t X ð2:80Þ where Aui ¼ t X k¼1 uk Ak um k þ s X dSf w l¼1 dSm w el jLl jufl ; ð2:81Þ where A/i is pore volume of CVi ; t is the number of Delaunay triangle element which takes node i as vertex; uk is triangle k’s area radio to Delaunay triangle k in control volume element CVf ; Ak is the area of Delaunay triangle k; /m k is porosity of f the matrix system in triangle k; s is the number of fracture in CVf ; /l , el , and jLl j are porosity, aperture, and length of fracture l in control volume element CVi, respectively.
So, the equation is as follows: ( vFm;E þ vFm;E0 ¼ QFf P vif;F ¼ QFf þ qFf ð2:111Þ i Where vFm:E , vFm:E0 , respectively, are exchange to fracture from matrix elements P E and E′; qFf represents sources/sinks; i vif:F in the second line of above equations corresponds to equation of continuity of fracture element. (2) If F is flow barrier, it will be processed in accordance with impermeable barrier. At the moment, Eqs. 3 ÀCm 0 0 0 0 D 0 0 ÀCf 0 0 0 ÀCfT Bf DTf 32 3 2 3 0 mm gm 6 7 6 7 0 7 7 6 pm 7 6 qm 7 7 6 7 6 0 76 pm 7 ¼ 6 Àqf 7 7 D f 5 4 m f 5 4 gf 5 0 pf 0 ð2:112Þ The Solution of the Saturation Equation (1) The calculation format of ﬁnite volume method In this work, we use the IMPES (implicit pressure, explicit saturation) method, which used to be quite popular in the industry.
The ﬁrst term of the right side of Eq. 82) represents quantity of flow through control volume element CVi’s boundary; the second term represents quantity of flow through every fracture in CVi The value of saturation comply with upstream standard, where superscript up represents upstream value. For the flow in fractures can viewed as 1-D, @pfw @n can be estimated by the following equation: dpfw pj À pi ; ¼ dn 2 j Ll j ð2:83Þ where pi , pj represent pressure of 1-D adjacent element. The third term of the left side of Eq.