On a mathematical model of the productivity index of a well from reservoir engineering

Akif Ibragimov, Dinara Khalmanova, Peter P. Valko, Jay R. Walton

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann, or third boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

Original languageEnglish
Pages (from-to)1952-1980
Number of pages29
JournalSIAM Journal on Applied Mathematics
Volume65
Issue number6
DOIs
StatePublished - 2005

Keywords

  • Diffusive capacity
  • Parabolic equation
  • Productivity index
  • Skin
  • Time-invariant

Fingerprint Dive into the research topics of 'On a mathematical model of the productivity index of a well from reservoir engineering'. Together they form a unique fingerprint.

  • Cite this