Abstract
Recent advances in high-resolution three-dimensional X-ray CT imaging have made it possible to visualize fluid configurations during multiphase displacement at the pore-scale. However, there is an inherited difficulty in image-based curvature measurements: the use of voxelized image data may introduce significant error, which has not—to date—been quantified. To find the best method to compute curvature from micro-CT images and quantify the likely error, we performed drainage and imbibition direct numerical simulations for an oil/water system on a bead pack and a Bentheimer sandstone. From the simulations, local fluid configurations and fluid pressures were obtained. We then investigated methods to compute curvature on the oil/water interface. The interface was defined in two ways; in one case the simulated interface with a sub-resolution smoothness was used, while the other was a smoothed interface extracted from synthetic segmented data based on the simulated phase distribution. The curvature computed on these surfaces was compared with that obtained from the simulated capillary pressure, which does not depend on the explicit consideration of the shape of the interface. As distinguished from previous studies which compared an average or peak curvature with the value derived from the measured macroscopic capillary pressure, our approach can also be used to study the pore-by-pore variation. This paper suggests the best method to compute curvature on images with a quantification of likely errors: local capillary pressures for each pore can be estimated to within 30% if the average radius of curvature is more than 6 times the image resolution, while the average capillary pressure can also be estimated to within 11% if the average radius of curvature is more than 10 times the image resolution.
Highlights
The curvature computed on these surfaces was compared with that obtained from the simulated capillary pressure, which does not depend on the explicit consideration of the shape of the interface
This paper suggests the best method to compute curvature on images with a quantification of likely errors: local capillary pressures for each pore can be estimated to within 30% if the average radius of curvature is more than 6 times the image resolution, while the average capillary pressure can be estimated to within 11% if the average radius of curvature is more than 10 times the image resolution
Immiscible fluid displacement in porous media is common in a variety of industrial applications, such as hydrocarbon recovery through water injection, carbon capture and storage in the subsurface (CCS) and biological water filtration [1,2,3]
Summary
Immiscible fluid displacement in porous media is common in a variety of industrial applications, such as hydrocarbon recovery through water injection, carbon capture and storage in the subsurface (CCS) and biological water filtration [1,2,3]. The arrangement of fluid phases in contact with each other and a solid is governed by energy balance; displacements move toward local energy minima at a pore-by-pore level [4]. It is of interest to study the interfaces of the phases since the change in the interfacial energy primarily controls the change in the energy of the system [5]. The curvature of the interface can be used to estimate capillary pressure from the Young-Laplace equation [6,7]. To help frame the analysis of interfaces, it is useful to introduce some properties of the surface. At an arbitrary point on surface, two principal curvatures (κ1 and κ2 ) which are orthogonal
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