### 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 language | English (US) |
---|---|

Pages (from-to) | 300-317 |

Number of pages | 18 |

Journal | Journal of Fluid Mechanics |

Volume | 860 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 860, pp. 300-317. https://doi.org/10.1017/jfm.2018.874

}

TY - JOUR

T1 - Fundamental equations for primary fluid recovery from porous media

AU - Jin, Yan

AU - Chen, Kangping

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - low-Reynolds-number flows

KW - Navier-Stokes equations

KW - porous media

UR - http://www.scopus.com/inward/record.url?scp=85057750802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057750802&partnerID=8YFLogxK

U2 - 10.1017/jfm.2018.874

DO - 10.1017/jfm.2018.874

M3 - Article

AN - SCOPUS:85057750802

VL - 860

SP - 300

EP - 317

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -