ANALYTICAL STUDY ON A ONE-DIMENSIONAL MODEL COUPLING BOTH DARCY FLOW AND LOW-VELOCITY NON-DARCY FLOW WITH THRESHOLD PRESSURE GRADIENT IN HETEROGENEOUS COMPOSITE RESERVOIRS

Wenchao Liu, Yaoyao Duan, Qitao Zhang, Zhangxin Chen, Xuemei Yan, Hedong Sun, Arash Dahi Taleghani

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In the exploitation process of unconventional tight oil reservoirs in modern times, the involved heterogeneous composite reservoirs are common; in such reservoirs, different rock compartments indicate different permeability properties. In ultra-low-permeability compartments, non-Darcy flow with a threshold pressure gradient (TPG) happens, but in relatively high-permeability compartments, Darcy flow happens. The existence of TPG introduces a nonlinear motion boundary problem, which makes a composite reservoir model coupling both Darcy flow and non-Darcy flow much more challenging. Here, a new model of one-dimensional flow in a heterogeneous composite reservoir with TPG is presented in consideration of a boundary motion process. Relying on a previous exact analytic solution for such a motion boundary problem in a homogeneous reservoir, semi-analytic solutions for the heterogeneous composite reservoir model are obtained by adopting the Laplace transformation method and mathematical arguments. Significantly, applications of Duhamel's principle in compartments with Darcy flow serve as a key procedure to analytically solve the model. And their semi-analytic versions are also validated. Finally, by relying on these solutions, the necessity of incorporating the motion boundary process is demonstrated in the mathematical modeling, and the deviation degree of the transient pressure type curves is also analyzed when the boundary motion process is neglected.

Original languageEnglish (US)
Pages (from-to)47-76
Number of pages30
JournalJournal of Porous Media
Volume25
Issue number9
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Biomedical Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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