Impact of time-dependent wettability alteration on the dynamics of capillary pressure

Kassa, Abay Molla; Gasda, Sarah E.; Kumar, Kundan; Radu, F.

doi:10.1016/j.advwatres.2020.103631

Cited by 14 publications

(22 citation statements)

References 36 publications

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“…In this article, we consider an extended capillary pressure model that captures the dynamic change of rock wettability at pore‐scale. Kassa et al 14 have introduced the dynamic term as an interpolation between the end wetting state curves. This can be described mathematically as follows,

\begin{align} P_{c} = false(1 prefix- ω false(\cdot false) false) P_{c}^{w w} + ω false(\cdot false) P_{c}^{o w}, \end{align}

where,

P_{c}^{w w}

and

P_{c}^{o w}

are end wetting (respectively, the water‐wet and oil‐wet) capillary pressure functions.…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…The dynamic coefficient

ω (\cdot)

is designed to upscale the dynamics of (pore‐scale) time‐dependent WA mechanism. In Reference 14 a fluid‐fluid contact angle (CA) change model (that changes the wettability from an arbitrary initial wetting state to the final wetting state) was introduced at the pore‐level. In Kassa et al, 14 two approaches were considered, namely, uniform and nonuniform WA .…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…In Reference 14 a fluid‐fluid contact angle (CA) change model (that changes the wettability from an arbitrary initial wetting state to the final wetting state) was introduced at the pore‐level. In Kassa et al, 14 two approaches were considered, namely, uniform and nonuniform WA . The first assumes all pores in the REV has been altered identically through exposure time to the WA agent, whereas the nonuniform WA case considers a CA change in a pore only if that particular pore is exposed to the WA agent.…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…The obtained curves and the interpolation model were combined to propose the dynamic coefficient

ω

. According to the results in Reference 14,

ω

can be represented as:

ω (S_{w}, t) = \{\begin{matrix} \frac{β_{1} χ}{β_{1} χ + 1}, normalfor normaluniform normalWA, \\ \frac{β_{2} S_{w} χ}{β_{2} S_{w} χ + 1}, normalfor normalnonuniform normalWA, \end{matrix}

where

β_{1}

and

β_{2}

are fitting parameters that have a clear relation with the pore‐scale CA change model parameter (see the details in Reference 14).…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…In our previous work, 14 we upscaled time‐dependent WA processes to Darcy‐scale phenomenon, and we have developed an interpolation‐based dynamic capillary pressure model. The proposed model is (macroscale) fluid history and time‐dependent (see Section 2.2 and Reference 14 for the details) in addition to the current wetting phase saturation. This implies that a nonlocal capillary diffusion term in time is introduced in a two‐phase flow model.…”

Section: Introductionmentioning

confidence: 99%

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Implicit linearization scheme for nonstandard two‐phase flow in porous media

Kassa

Kumar

Gasda

et al. 2020

Numerical Methods in Fluids

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SummaryIn this article, we consider a nonlocal (in time) two‐phase flow model. The nonlocality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed‐point iterative linearization scheme for the resulting nonstandard model. The scheme treats the dynamic capillary pressure functions semiimplicitly and introduces an L‐scheme type stabilization term in the pressure as well as the transport equations. We prove the convergence of the proposed scheme theoretically under physically acceptable assumptions, and verify the theoretical analysis with numerical simulations. The scheme is implemented and tested for a variety of reservoir heterogeneities in addition to the dynamic change of the capillary pressure function. The proposed scheme satisfies the predefined stopping criterion within a few number of iterations. We also compared the performance of the proposed scheme against the iterative implicit pressure explicit saturation scheme.

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\begin{align} P_{c} = false(1 prefix- ω false(\cdot false) false) P_{c}^{w w} + ω false(\cdot false) P_{c}^{o w}, \end{align}

where,

P_{c}^{w w}

and

P_{c}^{o w}

are end wetting (respectively, the water‐wet and oil‐wet) capillary pressure functions.…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…The dynamic coefficient

ω (\cdot)

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

“…The obtained curves and the interpolation model were combined to propose the dynamic coefficient

ω

. According to the results in Reference 14,

ω

can be represented as:

ω (S_{w}, t) = \{\begin{matrix} \frac{β_{1} χ}{β_{1} χ + 1}, normalfor normaluniform normalWA, \\ \frac{β_{2} S_{w} χ}{β_{2} S_{w} χ + 1}, normalfor normalnonuniform normalWA, \end{matrix}

where

β_{1}

and

β_{2}

are fitting parameters that have a clear relation with the pore‐scale CA change model parameter (see the details in Reference 14).…”

Section: Nonlocal Two‐phase Flow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Implicit linearization scheme for nonstandard two‐phase flow in porous media

Kassa

Kumar

Gasda

et al. 2020

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

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A Study of Interfacial Wettability of Glass Spreading on a Silicon Substrate

Yang

Zhang

et al. 2022

J. Electron. Mater.

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Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Lasseux

Valdés‐Parada

Wood

2021

Advances in Water Resources

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Le et al. (2020) studied the flow and transport problem of CO 2 -enhanced coalbed methane recovery also by means of the homogenization technique. They considered a multiscale model that incorporated two levels of porosity that correspond to nanopores and the cleat network. This work includes a set of numerical simulations showing that the cleat permeability decreases significantly near the injection well because of the high injection pressure. In addition, Sharmin et al. (2020) considered two-phase (or unsaturated) incompressible flow in a thin, but long, single pore (a thin strip) with a stratified distribution of the two phases and derived an effective model starting from the Navier-Stokes equations. The upscaled model was obtained using the asymptotic homogenization method. It encompasses different regimes associated to the values of the capillary number and viscosity ratio. It also accounts for surface tension variations (Marangoni effects) which may result from the transport of a solute in one of the two phases. The upscaled model was compared to direct numerical simulations of the 2D pore-scale model. Finally, Airiau and Bottaro (2020) used the adjoint homogenization method to shed new light on the derivation of upscaled models for steady and creeping flow of a shear-thinning fluid in homogeneous porous media. These authors derived a Darcy-like model, where the components of the effective permeability tensor were obtained from the solution of an associated boundary-value problem in a periodic unit cell. Due to the dependence of the viscosity on the pore-scale flow, a coupled solution approach was used that translated into a strong anisotropy of the permeability tensor, even in isotropic geometries.Not all the works corresponding to this research topic used the homogenization method to carry out their analysis. For example, Cotta et al. (2020) studied flow and transport in fractured porous media using the generalized integral transform technique to derive analytical and numerical-analytical solutions. A salient feature of this work is the treatment of multiporosity cases, by means of a single integral transformation process. This approach is illustrated with two examples in fractured media and unsaturated soils. In addition, Angot et al. ( 2020) used an asymptotic analysis to study single-phase inertial flow in the fluidporous boundary. They show that the total inertial work exerted by the fluid over the solid is always positive. Non-equilibrium modeling for transport in homogeneous and heterogeneous porous mediaThis research subject comprises stochastic modeling and upscaling of transport processes. Engdahl and Bolster (2020) proposed to use a

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Impact of time-dependent wettability alteration on the dynamics of capillary pressure

Cited by 14 publications

References 36 publications

Implicit linearization scheme for nonstandard two‐phase flow in porous media

Implicit linearization scheme for nonstandard two‐phase flow in porous media

A Study of Interfacial Wettability of Glass Spreading on a Silicon Substrate

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

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