TY - JOUR

T1 - Time asymptotics of non-darcy flows controlled by total flux on the boundary

AU - Aulisa, E.

AU - Bloshanskaya, L.

AU - Ibragimov, A.

N1 - Funding Information:
Also we would like to thank Dr. A. K. Gushin for useful recommendations. The research of this paper was supported by the NSF grant Nos. DMS-0908177.

PY - 2012/7

Y1 - 2012/7

N2 - We study the long term asymptotics of the diffusive capacity, the integral characteristic of a domain with respect to a nonlinear Forchheimer flow in porous media. Conditions on the boundary are given in terms of the total flux and constraints on the pressure trace on the boundary. We prove that, if the total flux is stabilizing, then the difference between the pressure average inside the domain and the pressure average on the boundary is stabilizing as well. This result can be used for calculating the productivity index of the well, an important characteristic of the well performance. To obtain the main theorem, a refined comparison of the fully transient pressure with the pseudo-steady state pressure (the time derivative of pressure is constant) was performed. These results can be effectively used in reservoir engineering and can also be applied to other problems modeled by nonlinear diffusive equations. Bibliography: 26 titles.

AB - We study the long term asymptotics of the diffusive capacity, the integral characteristic of a domain with respect to a nonlinear Forchheimer flow in porous media. Conditions on the boundary are given in terms of the total flux and constraints on the pressure trace on the boundary. We prove that, if the total flux is stabilizing, then the difference between the pressure average inside the domain and the pressure average on the boundary is stabilizing as well. This result can be used for calculating the productivity index of the well, an important characteristic of the well performance. To obtain the main theorem, a refined comparison of the fully transient pressure with the pseudo-steady state pressure (the time derivative of pressure is constant) was performed. These results can be effectively used in reservoir engineering and can also be applied to other problems modeled by nonlinear diffusive equations. Bibliography: 26 titles.

UR - http://www.scopus.com/inward/record.url?scp=84862664768&partnerID=8YFLogxK

U2 - 10.1007/s10958-012-0875-3

DO - 10.1007/s10958-012-0875-3

M3 - Article

AN - SCOPUS:84862664768

SN - 1072-3374

VL - 184

SP - 399

EP - 430

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 4

ER -