zbMATH — the first resource for mathematics

A nonlinear dual-porosity model. (English) Zbl 0817.76087
A nonlinear dual-porosity formulation incorporating a quadratic gradient term in the governing flow equation is presented. To avoid solving the simultaneous system of equations, decoupling of fluid pressures in the matrix from the fractures is furnished by assuming a quasi-steady-state flow in the matrix with the pressure difference between matrix and fractures as a primary unknown. The nonlinear fracture flow equation is linearized using the function transformation currently adopted in the nonlinear single-porosity formulation. Analytical solutions are obtained in a radial flow domain using the Hankel transform. Both solution accuracy and efficiency are achieved by using an optimized algorithm when solving the inherent Bessel functions.

76S05 Flows in porous media; filtration; seepage
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] Barenblatt, G.I.; Zheltov, I.P.; Kochina, I.N., Basic concept in the theory of homogeneous liquids in fractured rocks, J. appl. math. mech., 24, 5, 1286-1303, (1960) · Zbl 0104.21702
[2] Warren, J.E.; Root, P.J., Behavior of naturally fractured reservoirs, Soc. pet. eng. J., 228, 245-255, (1963), Trans. AIME
[3] Chakrabarty, C.; Farouq Ali, S.M.; Tortike, W.S., Analytical solutions for radial pressure distribution including the effects of the quadratic-gradient term, Water resour. res., 29, 4, 1171-1177, (1993)
[4] Odeh, A.S.; Babu, D.K., Comparison of solutions of the nonlinear and linearized diffusion equations, SPE res. eng., 3, 4, 1202-1206, (1988)
[5] Finjord, J., Curling up the slope: effects of quadratic gradient term in the infinite-acting period for two-dimensional reservoir flow, Spe 16451, (1986), Richardson Tex
[6] Finjord, J.; Aadnoy, B.S., Effects of quadratic gradient term in steady-state and quasisteady-state solutions for reservoir pressure, SPE form. eval., 4, 3, 413-417, (1989)
[7] Wang, Y.; Dusseault, M.B., The effect of quadratic gradient terms on the borehole solution in poroelastic media, Water resour. res., 27, 12, 3215-3223, (1991)
[8] Streltsova, T.D., Well testing in heterogeneous formations, (1988), John Wiley & Sons New York
[9] Moench, A.F., Double-porosity models for a fissured groundwater reservoir with fracture skin, Water resour. res., 20, 831-846, (1984)
[10] Bai, M.; Elsworth, D.; Roegiers, J-C., Modelling of naturally fractured reservoirs using deformation-dependent flow mechanisms, 34th U.S. symp. on rock mech., (1993), Univ. of Winconsin Madison
[11] Bai, M., Ma, Q., and Roegiers, J-C. Dual-porosity behavior of naturally fractured reservoirs. Int. J. Num. Anal. Methods Geomech., (in press) · Zbl 0851.76084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.