TY - JOUR

T1 - Convergence of a dual-porosity model for two-phase flow in fractured reservoirs

AU - Yeh, Li-Ming

PY - 2000/6/1

Y1 - 2000/6/1

N2 - A dual-porosity model describing two-phase, incompressible, immiscible flows in a fractured reservoir is considered. Indeed, relations among fracture mobilities, fracture capillary pressure, matrix mobilities, and matrix capillary pressure of the model are mainly concerned. Roughly speaking, proper relations for these functions are (1) Fracture mobilities go to zero slower than matrix mobilities as fracture and matrix saturations go to their limits, (2) Fracture mobilities times derivative of fracture capillary pressure and matrix mobilities times derivative of matrix capillary presure are both integrable functions. Galerkin's method is used to study this problem. Under above two conditions, convergence of discretized solutions obtained by Galerkin's method is shown by using compactness and monotonicity methods. Uniqueness of solutions is studied by a duality argument.

AB - A dual-porosity model describing two-phase, incompressible, immiscible flows in a fractured reservoir is considered. Indeed, relations among fracture mobilities, fracture capillary pressure, matrix mobilities, and matrix capillary pressure of the model are mainly concerned. Roughly speaking, proper relations for these functions are (1) Fracture mobilities go to zero slower than matrix mobilities as fracture and matrix saturations go to their limits, (2) Fracture mobilities times derivative of fracture capillary pressure and matrix mobilities times derivative of matrix capillary presure are both integrable functions. Galerkin's method is used to study this problem. Under above two conditions, convergence of discretized solutions obtained by Galerkin's method is shown by using compactness and monotonicity methods. Uniqueness of solutions is studied by a duality argument.

UR - http://www.scopus.com/inward/record.url?scp=0034204527&partnerID=8YFLogxK

U2 - 10.1002/1099-1476(200006)23:9<777::AID-MMA132>3.0.CO;2-Z

DO - 10.1002/1099-1476(200006)23:9<777::AID-MMA132>3.0.CO;2-Z

M3 - Article

AN - SCOPUS:0034204527

VL - 23

SP - 777

EP - 802

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 9

ER -