Abstract

Primary fluid recovery from a porous medium is driven by the volumetric expansion of the in situ fluid. For production from a petroleum reservoir, primary recovery accounts for more than half of the total amount of recovered hydrocarbon. The primary recovery process is studied here at the pore scale and the macroscopic scale. The pore-scale flow is first analysed using the compressible Navier-Stokes equations and the mathematical theory for low-Mach-number flow developed by Klainerman & Majda (Commun. Pure Appl. Maths, vol. 34 (4), 1981, pp. 481-524; vol. 35 (5), 1982, pp. 629-651). An asymptotic analysis shows that the pore-scale flow is governed by the self-diffusion of the fluid and it exhibits a slip-like mass flow rate, even though the velocity satisfies the no-slip condition on the pore wall. The pore-scale density equation is then upscaled to a macroscopic diffusion equation for the density which possesses a diffusion coefficient proportional to the fluid's kinematic viscosity. Darcy's law is shown to be inapplicable to primary fluid recovery and it should be replaced by a new mass flux equation which depends on the porosity but not on the permeability. This is in stark contrast to the classical result and it can have important implications for hydrocarbon recovery as well as other applications.

Original languageEnglish (US)
Pages (from-to)300-317
Number of pages18
JournalJournal of Fluid Mechanics
Volume860
DOIs
StatePublished - Jan 1 2018

Fingerprint

Porous materials
recovery
porosity
Recovery
Fluids
fluids
Hydrocarbons
slip
hydrocarbons
Petroleum reservoirs
Asymptotic analysis
mass flow rate
Navier Stokes equations
Mach number
crude oil
Mass transfer
Navier-Stokes equation
Porosity
Flow rate
Viscosity

Keywords

  • low-Reynolds-number flows
  • Navier-Stokes equations
  • porous media

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Fundamental equations for primary fluid recovery from porous media. / Jin, Yan; Chen, Kangping.

In: Journal of Fluid Mechanics, Vol. 860, 01.01.2018, p. 300-317.

Research output: Contribution to journalArticle

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