Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis

Schmid, Karen Sophie; Alyafei, Nayef; Geiger, Sebastian; Blunt, Martin J.

doi:10.2118/184393-pa

Cited by 68 publications

(53 citation statements)

References 27 publications

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“…This model can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett, 1942) model given the corresponding capillary pressure and relative permeability curves. Recently Schmid et al (2016) compared their calculated results with the experimental measurements of saturation profiles for a water-wet medium, which yielded some good matches. Further reviews can be found in the work by Meng et al (2017).…”

Section: Introductionmentioning

confidence: 91%

“…Recently, Bjørnarå and Mathias (2013) improved the solution using a pseudospectral Chebyshev differentiation matrix. Schmid et al (2011Schmid et al ( , 2013Schmid et al ( , 2016 only focused on spontaneous imbibition and the forced imbibition was not presented in their works.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we propose a self-similar analytical solution of spontaneous and forced imbibition by introducing the capillary fractional flow function (Chen et al, 1990;McWhorter and Sunada, 1990;Schmid et al, 2016). Corresponding concise algorithms for solving the analytical solution are also proposed using the combination of Runge-Kutta and Bisection methods.…”

Section: Introductionmentioning

confidence: 99%

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A self-similar analytical solution of spontaneous and forced imbibition in porous media

Wang

Sheng

2018

Adv. Geo-Energy Res.

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Citation:Wang, X., Sheng, J.J. A self-similar analytical solution of spontaneous and forced imbibition in porous media. Both viscous and capillary forces control the two-phase flow in porous media. The Buckley Leverett solution for viscous flow in porous media has been proposed for over a half century. While the corresponding studies of capillary dominated solutions are mainly based on the capillary tube based models. The continuum solutions are just prevail in recently years. The analytical solution of the combination of both effects is rarely investigated. A self-similar analytical solution of spontaneous and forced imbibition in porous media is proposed in this work and the corresponding concise algorithms are presented. The proposed solution successfully solves this typical non-linear partial differential equation by introducing a transformation variable and the capillary fractional flow function analog to the fractional flow function of Buckley Leverett solution. Finally, the case study is performed, which demonstrates the feasibility and accuracy of this proposed solution to a general two-phase flow condition.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A self-similar analytical solution of spontaneous and forced imbibition in porous media

Wang

Sheng

2018

Adv. Geo-Energy Res.

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“…Table provides the initial and boundary conditions for equation . Schmid et al () used the similarity variable ω = x / √ t and presented a general solution in terms of the derivative of a capillary‐driven fractional flow function ( F ) as follows:

ω ((), S_{w}) = \frac{2 C}{φ} \frac{\partial F}{\partial S_{w}},

…”

Section: Derivation Of Semi‐analytical Modelmentioning

confidence: 99%

“…

F_{1} = - B F_{2} - 0.5 F_{3} + \sqrt{B^{2} F_{2}^{2} + 0.25 F_{3}^{2} + B F_{2} F_{3} - \frac{1}{(1 - A)} true(A F_{2} F_{3} - 2 A F_{2}^{2} + \frac{φ_{t}}{2 {C^{'}}^{2}} D ((),, S_{w}, σ^{'}) {Δ S}_{w}^{2}},

where

A = \frac{S_{w} ln ((), φ_{t} / φ_{i})}{{Δ S}_{w}}

and

B = \frac{((), 3 A - 2)}{2 ((), 1 - A)}

are simplifying parameters. Classical approaches, which neglect porosity change ( φ t = φ i ), employ A = 0 and B = − 1; this reduces equation to the definition of capillary‐driven fractional flow term presented by Schmid et al (). In equation , F 1 , F 2 , and F 3 refer to F ( S w ), F ( S w + Δ S w ), and F ( S w + 2Δ S w ), respectively.…”

Section: Derivation Of Semi‐analytical Modelmentioning

confidence: 99%

New Semi‐Analytical Insights Into Stress‐Dependent Spontaneous Imbibition and Oil Recovery in Naturally Fractured Carbonate Reservoirs

Haghi

Chalaturnyk

Geiger

2018

Water Resources Research

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Fluid injection and withdrawal in a porous medium create changes in pore pressure that alter effective stresses within the medium. This leads to pore volume changes, which can be described by the poroelastic theory. These changes in pore volume can influence fluid flow processes, such as capillary diffusion and imbibition, potentially altering multiphase flow characteristics in subsurface reservoirs with a focus on oil recovery in the naturally fractured carbonate reservoirs. In this study, a semi‐analytical model is developed to analyze the impact of stress‐dependent spontaneous imbibition. The model allows us to study the influence of stress‐dependent effects on porosity, absolute permeability, relative permeability, and capillary pressure on the imbibition and oil recovery mechanisms of both intact rock and fracture in naturally fractured carbonate reservoirs. In order to capture the geomechanical interactions involved, pure compliance poroelastic definitions and nonlinear joint normal stiffness equations are used to assess the deformation of intact rock and fracture, respectively. The model shows that increasing effective confining stress shifts the imbibition capillary pressure curve upward, resulting in improved absorption of the wetting phase into the smaller pores and enhanced extraction of the nonwetting phase. Model calculations provide a rationale for how and why irreducible water saturation increases during compression of mixed‐wet carbonates and decreases in the case of initially strong water‐wet carbonates. It is also shown how higher relative permeability of the wetting phase leads to a greater diffusion of the wetting phase and improved oil recovery for the less deformed mixed‐wet rock.

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Parameter estimation from spontaneous imbibition into volcanic tuff

Kuhlman

Mills

Heath

et al. 2022

Vadose Zone Journal

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Two‐phase fluid flow properties underlie quantitative prediction of water and gas movement, but constraining these properties typically requires multiple time‐consuming laboratory methods. The estimation of two‐phase flow properties (van Genuchten parameters, porosity, and intrinsic permeability) is illustrated in cores of vitric nonwelded volcanic tuff using Bayesian parameter estimation that fits numerical models to observations from spontaneous imbibition experiments. The uniqueness and correlation of the estimated parameters is explored using different modeling assumptions and subsets of the observed data. The resulting estimation process is sensitive to both moisture retention and relative permeability functions, thereby offering a comprehensive method for constraining both functions. The data collected during this relatively simple laboratory experiment, used in conjunction with a numerical model and a global optimizer, result in a viable approach for augmenting more traditional capillary pressure data obtained from hanging water column, membrane plate extractor, or mercury intrusion methods. This method may be useful when imbibition rather than drainage parameters are sought, when larger samples (e.g., including heterogeneity or fractures) need to be tested that cannot be accommodated in more traditional methods, or when in educational laboratory settings.

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Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis

Cited by 68 publications

References 27 publications

A self-similar analytical solution of spontaneous and forced imbibition in porous media

A self-similar analytical solution of spontaneous and forced imbibition in porous media

New Semi‐Analytical Insights Into Stress‐Dependent Spontaneous Imbibition and Oil Recovery in Naturally Fractured Carbonate Reservoirs

Parameter estimation from spontaneous imbibition into volcanic tuff

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