TY - JOUR

T1 - Variational principle and steady state invariants for non-linear hydrodynamic interactions in porous media

AU - Aulisa, Eugenio

AU - Cakmak, Adem

AU - Ibraguimov, Akif

AU - Solynin, Alexander

PY - 2007

Y1 - 2007

N2 - This research is
motivated by the well productivity index (PI) concept of the
reservoir engineering. It was observed by petroleum engineers that
the PI stabilizes to a constant value. The goal of this paper is
to develop a mathematically rigorous framework to prove the
existence of a certain time invariant for the transient dynamic
processes associated with a non-linear flow. Calculus of
variations is applied to estimate this invariant, which is, in
fact, the PI of the well. As a result of the developed framework,
in order to compute the PI, it is sufficient to solve an auxiliary
steady state problem. At the same time, the solution of each BVP
minimizes the energy functional in the corresponding Sobolev
space. This link between the PI and calculus of variations allows
us to estimate dependency of the PI on the geometry of the
reservoir/well system and to identify the optimal configurations
of the well without solving an auxiliary BVP.

AB - This research is
motivated by the well productivity index (PI) concept of the
reservoir engineering. It was observed by petroleum engineers that
the PI stabilizes to a constant value. The goal of this paper is
to develop a mathematically rigorous framework to prove the
existence of a certain time invariant for the transient dynamic
processes associated with a non-linear flow. Calculus of
variations is applied to estimate this invariant, which is, in
fact, the PI of the well. As a result of the developed framework,
in order to compute the PI, it is sufficient to solve an auxiliary
steady state problem. At the same time, the solution of each BVP
minimizes the energy functional in the corresponding Sobolev
space. This link between the PI and calculus of variations allows
us to estimate dependency of the PI on the geometry of the
reservoir/well system and to identify the optimal configurations
of the well without solving an auxiliary BVP.

M3 - Article

SP - 148

EP - 155

JO - Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., Advances in Dynamical Systems, suppl. S2

JF - Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., Advances in Dynamical Systems, suppl. S2

ER -