### Abstract

The evolution of a sharp interface between two immiscible fluids in a randomly heterogeneous porous medium is investigated analytically using a stochastic moment approach. The displacing fluid is taken to be at constant saturation and to have a much larger viscosity than does the displaced fluid, which is therefore effectively static. Capillary pressure at the interface is related to porosity and permeability via the Leverett J-function. Whereas porosity is spatially uniform, permeability forms a spatially correlated random field. Displacement is governed by stochastic integro-differential equations defined over a three-dimensional domain bounded by a random interface. The equations are expanded and averaged in probability space to yield leading order recursive equations governing the ensemble mean and variance of interface position, rate of propagation and pressure gradient within the displacing fluid. Solutions are obtained for one-dimensional head- and flux-driven displacements in statistically homogeneous media and found to compare well with numerical Monte Carlo simulations. The manner in which medium heterogeneity affects the mean pressure gradient is indicative of how it impacts the stability of the mean interface. Capillary pressure at the interface is found to have a potentially important effect on its mean dynamics and stability.

Original language | English (US) |
---|---|

Pages (from-to) | 3331-3341 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 15 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2003 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*15*(11), 3331-3341. https://doi.org/10.1063/1.1612944

**Immiscible front evolution in randomly heterogeneous porous media.** / Tartakovsky, Alexandre M.; Neuman, Shlomo P; Lenhard, Robert J.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 15, no. 11, pp. 3331-3341. https://doi.org/10.1063/1.1612944

}

TY - JOUR

T1 - Immiscible front evolution in randomly heterogeneous porous media

AU - Tartakovsky, Alexandre M.

AU - Neuman, Shlomo P

AU - Lenhard, Robert J.

PY - 2003/11

Y1 - 2003/11

N2 - The evolution of a sharp interface between two immiscible fluids in a randomly heterogeneous porous medium is investigated analytically using a stochastic moment approach. The displacing fluid is taken to be at constant saturation and to have a much larger viscosity than does the displaced fluid, which is therefore effectively static. Capillary pressure at the interface is related to porosity and permeability via the Leverett J-function. Whereas porosity is spatially uniform, permeability forms a spatially correlated random field. Displacement is governed by stochastic integro-differential equations defined over a three-dimensional domain bounded by a random interface. The equations are expanded and averaged in probability space to yield leading order recursive equations governing the ensemble mean and variance of interface position, rate of propagation and pressure gradient within the displacing fluid. Solutions are obtained for one-dimensional head- and flux-driven displacements in statistically homogeneous media and found to compare well with numerical Monte Carlo simulations. The manner in which medium heterogeneity affects the mean pressure gradient is indicative of how it impacts the stability of the mean interface. Capillary pressure at the interface is found to have a potentially important effect on its mean dynamics and stability.

AB - The evolution of a sharp interface between two immiscible fluids in a randomly heterogeneous porous medium is investigated analytically using a stochastic moment approach. The displacing fluid is taken to be at constant saturation and to have a much larger viscosity than does the displaced fluid, which is therefore effectively static. Capillary pressure at the interface is related to porosity and permeability via the Leverett J-function. Whereas porosity is spatially uniform, permeability forms a spatially correlated random field. Displacement is governed by stochastic integro-differential equations defined over a three-dimensional domain bounded by a random interface. The equations are expanded and averaged in probability space to yield leading order recursive equations governing the ensemble mean and variance of interface position, rate of propagation and pressure gradient within the displacing fluid. Solutions are obtained for one-dimensional head- and flux-driven displacements in statistically homogeneous media and found to compare well with numerical Monte Carlo simulations. The manner in which medium heterogeneity affects the mean pressure gradient is indicative of how it impacts the stability of the mean interface. Capillary pressure at the interface is found to have a potentially important effect on its mean dynamics and stability.

UR - http://www.scopus.com/inward/record.url?scp=0345330825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345330825&partnerID=8YFLogxK

U2 - 10.1063/1.1612944

DO - 10.1063/1.1612944

M3 - Article

AN - SCOPUS:0345330825

VL - 15

SP - 3331

EP - 3341

JO - Physics of Fluids

JF - Physics of Fluids

SN - 0031-9171

IS - 11

ER -