Linear stability analysis of immiscible two-phase flow in porous media with capillary dispersion and density variation

Riaz, Amir; Tchelepi, Hamdi A.

doi:10.1063/1.1812511

Cited by 83 publications

(53 citation statements)

References 29 publications

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“…While large Ca implied that capillarity effects are macroscopically negligible, the latter does not apply at smaller length scales. On the contrary, capillarity greatly affects pore-scale interfacial dynamics within the capillary dispersion zone (CDZ) [69][70][71].…”

Section: Stable Displacement Regime: Capillary Dispersion Zonementioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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We perform pore-scale resolved direct numerical simulations of immiscible two-phase flow in porous media to study the evolution of fluid interfaces. Using a Smoothed-Particle Hydrodynamics approach, we simulate saturation-controlled primary drainage in heterogeneous, partially wettable 2D porous microstructures. While imaging the evolution of fluid interfaces near capillary equilibrium becomes more feasible as fast X-ray tomography techniques mature, imaging methods with suitable temporal resolution for viscous-dominated flow have only recently emerged. In this work, we study viscous fingering and stable displacement processes. During viscous fingering, pore-scale flow fields are reminiscent of Bretherton annular flow, that is, the less viscous phase percolates through the core of a pore-throat forming a hydrodynamic wetting film. Even in simple microstructures wetting films have major impact on the evolution of fluid interfacial area and are observed to give rise to nonnegligible interfacial viscous coupling. Although macroscopically appearing flat, saturation fronts during stable displacement extend over the length of the capillary dispersion zone. While far from the dispersion zone fluid permeation obeys Darcy's law, the interplay of viscous and capillary forces is found to render fluid flow within complex. Here we show that the characteristic length scale of the capillary dispersion zone increases with the heterogeneity of the microstructure.

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Section: Stable Displacement Regime: Capillary Dispersion Zonementioning

confidence: 99%

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Sivanesapillai

Steeb

2018

Geofluids

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“…We ignore the effects of diffusion under the assumption that they are negligible in favour of advection [6,14,15]. Therefore, our model equations will be of the form…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The volume flux in (3) depends on a relative permeability function α i (s), which we fit using a power law or Corey-type permeability [6,8,14,15,19]:…”

Section: Mathematical Modelmentioning

confidence: 99%

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Fingering phenomena in immiscible displacement in porous media flow

Moyles

Wetton

2014

J Eng Math

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Pressure-driven displacement of one fluid by another in porous media has many applications, including oil production and the removal of soil contaminants. When the displacing fluid is less viscous, an idealized flat displacement front is ill-posed with respect to the growth of transverse perturbations (Taylor-Saffman instability). In models that include relative permeabilities, a macroscopic mixing of the fluids occurs in a rarefaction wave in a displacement region with a final discontinuity (shock wave) to the pure displaced fluid (Buckley-Leverett model). This discontinuity can also suffer from Taylor-Saffman instability. The instability is regularized by capillary effects, and a most unstable wavenumber can be found. Growth of these instabilities leads to fingering of the displacing fluid. In this work, we review the appropriate models and present a robust numerical approach to computing the most unstable wave numbers for given parameters (provided they lead to a non-degenerate parabolic problem). This approach to quantitatively accurate solutions will be of use in fitting experimental results and evaluating models used in a number of applications. We show that the Buckley-Leverett shock can be stabilized due to relative permeability effects in some cases. We give a clear presentation of asymptotic results in the limit of small capillarity for this problem. These asymptotic results lead to far-field pressure conditions that greatly simplify the numerical computations. They also highlight some open mathematical questions in this area.

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“…Despite the predominant impact of the mobility ratio on viscous fingering, the stability of heavy oil displacement by gas can also be affected by capillary pressure, which can lead to an exacerbation or dampening of the viscous fingers [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

An Improved Approach to Estimate Three-Phase Relative Permeability Functions for Heavy-Oil Displacement Involving Instability and Compositional Effects

et al. 2017

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Simultaneous three-phase flow of gas, oil and water is a common phenomenon in enhanced oil recovery techniques such as water-alternating-gas (WAG) injection. Reliable reservoir simulations are required to predict the performance of these injections before field application. However, heavy oil displacement by gas or water can lead to viscous fingering due to the unfavorable mobility ratio between heavy oil and the displacing fluid. In addition, the injection of partially dissolvable gases such as CO 2 can result in compositional effects, which can bring about a significant reduction of oil viscosity and hence can cause variations of the mobility ratio. Estimations of three-phase relative permeability under such conditions are extremely complex, and using conventional techniques for the estimation can lead to erroneous results. We used the results of four coreflood experiments, carried out on a core, to estimate two-phase and three-phase relative permeability. A new history matching methodology for laboratory experiments was used that takes into account the instability and the compositional effects in the estimation processes. The results demonstrate that a simultaneous CO 2 and water injection (CO 2 -simultaneous water and gas (SWAG)) can be adequately matched using the relative permeabilities of a secondary gas/liquid and a tertiary oil/water. In heavy oil WAG injection, the injected water follows the CO 2 path due its lower resistance as a result of the CO 2 dissolution in the oil and the resultant reduction of the oil viscosity. This is contrary to WAG injection in conventional oils, where gas and water open up separate saturations paths. It is also important to include capillary pressure (Pc), even in high permeable porous media, as we observed that the inclusion of capillary pressure dampened the propagation of the viscous fingers and hence helped the front to become stabilized, leading to a more realistic simulated sweep efficiency.

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Linear stability analysis of immiscible two-phase flow in porous media with capillary dispersion and density variation

Cited by 83 publications

References 29 publications

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Fluid Interfaces during Viscous-Dominated Primary Drainage in 2D Micromodels Using Pore-Scale SPH Simulations

Fingering phenomena in immiscible displacement in porous media flow

An Improved Approach to Estimate Three-Phase Relative Permeability Functions for Heavy-Oil Displacement Involving Instability and Compositional Effects

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