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Fundamental equations for primary fluid recovery from porous media

Published online by Cambridge University Press:  04 December 2018

Yan Jin  and
Kang Ping Chen Open the ORCID record for Kang Ping Chen [Opens in a new window]
Yan Jin
Affiliation:
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum–Beijing, Beijing 102249, China
Kang Ping Chen*
Affiliation:
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287-6106, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 300 - 317
Copyright
© 2018 Cambridge University Press 

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