A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

Frette, Olav Inge; Helland, Johan Olav

doi:10.1016/j.advwatres.2010.05.002

Cited by 36 publications

(30 citation statements)

References 27 publications

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“…Following decades of remarkable developments, researchers have aimed to determine the fluid distribution using mathematical models and experimental models Frette and Helland 2010;Jamaloei et al 2010;Jia et al 2007;Piri and Blunt 2004;Van Dijke et al 2004;Van Dijke and Sorbie 2003). With the advent of computed microtomography and the development of image analysis techniques, the geometrical characterizations and channel cross sections of pores in porous media have become available (Lindquist et al 1996(Lindquist et al , 2000Sholokhova et al 2009;Wildenschild and Sheppard 2013).…”

Section: Introductionmentioning

confidence: 99%

The distribution of fluids in irregular capillary tubes: a new capillary model based on the single-corner capillary

Long

Zhang

2017

J Petrol Explor Prod Technol

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A new basic single-corner capillary model is presented. In this model, the distribution of immiscible fluids is determined by a particular threshold pressure.Additionally, we derive and analyze the interface curvature and profile of the fluid menisci in different tubes. Various polygonal cross sections are obtained by repeatedly superposing the basic single-corner capillary model. We study the relationship between the number of polygon edges and the distribution of fluids as well as the saturation of the wetting phase in equilateral polygon tubes. Furthermore, for the first time, we discuss the interaction of the corners to reveal the five stages of the fluid interfaces with various corner geometries. The dimensionless interface curvature and the radius of the circle are considered to extend our conclusions to similar cross-sectional capillary tubes of different sizes.

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Section: Introductionmentioning

confidence: 99%

The distribution of fluids in irregular capillary tubes: a new capillary model based on the single-corner capillary

Long

Zhang

2017

J Petrol Explor Prod Technol

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“…An orientation angle a is then computed in each boundary point b as the angle defined between the tangent at b and a line parallel with the abscissa . Primary drainage at uniform water-wet conditions is simulated on the basis of the algorithm developed by Frette and Helland (2010). Here, we describe the algorithm for imbibition at mixedwet conditions developed by Helland and Frette (2010) and Zhou et al (2012) and provide relevant details.…”

Section: Model Descriptionmentioning

confidence: 99%

Pore-Scale Modeling of Waterflooding in Mixed-Wet-Rock Images: Effects of Initial Saturation and Wettability

2013

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We simulate transient behavior of viscous-and capillary-dominated water invasion at mixed-wet conditions directly in scanningelectron-microscope (SEM) images of Bentheim sandstone by treating the pore spaces as cross sections of straight tubes. Initial conditions are established by drainage and wettability alteration. Constant rate or differential pressure is imposed along the tube bundle. The phase pressures vary with positions along the tube length but remain unique in each cross section, consistent with 1D core-scale models. This leads to a nonlinear system of equations that are solved for the interface positions as a function of time. The cross-sectional fluid configurations are computed accurately at any capillary pressure and wetting condition by a semianalytical model that is based on free-energy minimization. The fluid conductances are estimated by newly derived explicit expressions that are shown to be in agreement with numerical computations performed directly on the cross-sectional fluid configurations.An SEM image of Bentheim sandstone is taken as input to the developed model for simulating the evolution of saturation profiles during waterfloods for different flow rates and several mixed-wet conditions, which are established with various initial water saturations and contact angles. It is demonstrated that the simulated saturation profiles depend strongly on initial water saturation at mixedwet conditions. The saturation profiles exhibit increasingly gradual behavior in time as the contact angle, defined on the oil-wet solid surfaces, increases or the initial water saturation decreases. Front menisci associated with positive capillary pressures promote oil displacement by water, whereas for large and negative capillary pressures at small flow rates, oil displaces water because the associated front menisci retract. This results in the development of pronounced gradual saturation fronts at mixed-wet conditions. The waterfloods simulated at conditions established with a large initial water saturation and small contact angle on the oil-wet solid surfaces exhibit sharp Buckley-Leverett saturation profiles for high flow rates because the capillary pressure is small and less important. The shape of the saturation profiles is interpreted on the basis of the simulated capillary pressure curves and the corresponding fluid configurations occurring in the rock image.

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“…Primary drainage at uniform water-wet conditions is simulated first, based on the algorithm developed by Frette and Helland (2010). Capillary-controlled displacement for uniform water-wet conditions is modeled by the process in which oil displaces water.…”

Section: Semi-analytical Model For Computing Fluid Configurations Andmentioning

confidence: 99%

A Dimensionless Capillary Pressure Function for Imbibition Derived from Pore-Scale Modelling in Mixed-Wet Rock Images

2012

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It has been demonstrated experimentally that Leverett's J-function yields almost unique dimensionless drainage capillary pressure curves in relatively homogeneous rocks at strongly water-wet conditions, whereas for imbibition at mixed-wet conditions, it does not work satisfactorily because the permeability dependency on capillary pressure has been reported to be weak. The purpose of this study is to formulate a new dimensionless capillary pressure function for mixed-wet conditions, based on pore-scale modeling, which could overcome these restrictions. We simulate drainage, wettability alteration and imbibition in 2D rock images using a semi-analytical pore-scale model which represents the identified pore spaces as crosssections of straight capillary tubes. The fluid configurations occurring during drainage and imbibition in the highly irregular pore spaces are modeled at any capillary pressure and wetting condition by combining the free energy minimization with an arc menisci-determining procedure that identifies the intersections of two circles moving in opposite directions along the pore boundary. Circle rotation at pinned contact lines accounts for mixed-wet conditions. Capillary pressure curves for imbibition are simulated for different mixed-wet conditions in Bentheim sandstone samples, and the results are scaled by a newly proposed improved J-function that accounts for differences in formation wettability induced by different initial water saturations after primary drainage. At the end of primary drainage, oil-wet pore wall segments are connected by many waterwet corners and constrictions that remain occupied by water. The novel dimensionless capillary pressure expression accounts for these conditions by introducing an effective contact angle which depends on the initial water saturation and is related to the wettability measured at the core scale by means of a wettability index.The accuracy of the proposed J-function is tested on 36 imbibition capillary pressure curves for different mixed-wet conditions that are simulated with the semi-analytical model in SEM images of Bentheim sandstone. The simulated imbibition capillary pressure curves and the reproduced curves, based on the proposed J-function, are in good agreement for the mixed-wet conditions considered in this study. The detailed behavior is explained by analyzing the fluid displacements occurring in the pore spaces. It is demonstrated that the proposed J-function could be applied to mixed-wet conditions to generate a family of curves describing different wettability conditions induced by assigning different wetting properties on the solid surfaces or by varying the initial water saturation after primary drainage. The variability of formation wettability and permeability could be described more accurately in reservoir simulation models by means of the proposed J-function, and hence allow for improved evaluation of core-sample laboratory experiments and reservoir performance.In this expression, the contact angleθ was added later in an attempt to desc...

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A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

Cited by 36 publications

References 27 publications

The distribution of fluids in irregular capillary tubes: a new capillary model based on the single-corner capillary

The distribution of fluids in irregular capillary tubes: a new capillary model based on the single-corner capillary

Pore-Scale Modeling of Waterflooding in Mixed-Wet-Rock Images: Effects of Initial Saturation and Wettability

A Dimensionless Capillary Pressure Function for Imbibition Derived from Pore-Scale Modelling in Mixed-Wet Rock Images

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