Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects

A micro-hydromechanical model for granular materials is presented. It combines the discrete element method (DEM) for the modeling of the solid phase and a pore-scale finite volume (PFV) formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the DEM-PFV coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions.Comment: accepted in Int. Journal for Numerical and Analytical Methods in Geomechanic

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

A two-pressure model for slightly compressible single phase flow in bi-structured porous media

Abstract Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy's law at a larger scale. In this work, we develop an alternative model to Darcy's law that can be used to describe slightly compressible single phase flow within bi-structured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy's laws for velocities. Contrary to classical dual-media models, the averaging process is applied directly to Stokes problem and not to Darcy's laws. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behavior of these equations for model porous media and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem

Pore-Scale Modeling: Stochastic Network Generation and Modeling of Rate Effects in Waterflooding

Pore scale network modeling has been used to predict transport flow properties for multiphase flow successfully. The prediction is based on having geologically realistic networks that are computationally expensive to generate and normally represent only a very small section of the rock sample. We present a new method to generate stochastic random networks representing the pore space of different rocks with given input pore and throat size distributions and connectivity – these distributions can be obtained from an analysis of pore-space images. The stochastic networks can be arbitrarily large and hence are not limited by the size of the original image. The basic assumption made in the prediction of transport flow properties using most pore-scale models is that the flow is capillary dominated. This implies that the viscous pressure drop is insignificant compared to the capillary pressure. However, at the field scale, gravity and viscous forces dominate displacement processes. We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase pressure and which allows wetting layer swelling near an advancing flood front. We propose a new time-dependent algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number and mobility ratio on imbibition displacement patterns, saturation and velocity profiles. We also investigate the effects of capillary number and mobility ratio on the water fractional flow curve, cumulative oil production and residual oil saturation for water-wet and mixed-wet systems. By using large networks we reproduce Buckley-Leverett profiles directly from pore-scale modeling thereby providing a bridge between pore-scale and macroscale transport

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

A correct statistical model of soil pore structure can be critical for understanding flow and transport processes in soils, and creating synthetic soil pore spaces for hypothetical and model testing, and evaluating similarity of pore spaces of different soils. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. Simple fractal models such as fractional Brownian motion that have been proposed to capture the complex behavior of soil spatial variation at field scale rarely simulate irregularity patterns displayed by spatial series of soil properties. The objective of this work was to use CT data to test the hypothesis that soil pore structure at the horizon scale may be represented by multifractal models. X-ray CT scans of twelve, water-saturated, 20-cm long soil columns with diameters of 7.5 cm were analyzed. A reconstruction algorithm was applied to convert the X-ray CT data into a stack of 1480 grayscale digital images with a voxel resolution of 110 microns and a cross-sectional size of 690 × 690 pixels. The images were binarized and the spatial series of the percentage of void space vs. depth was analyzed to evaluate the applicability of the multifractal model. The series of depth-dependent macroporosity values exhibited a well-defined multifractal structure that was revealed by singularity and Rényi spectra. The long-range dependencies in these series were parameterized by the Hurst exponent. Values of the Hurst exponent close to one were observed indicating the strong persistence in variations of porosity with depth. The multifractal modeling of soil macropore structure can be an efficient method for parameterizing and simulating the vertical spatial heterogeneity of soil pore space

Petrographic characterization to build an accurate rock model using micro-CT: Case study on low-permeable to tight turbidite sandstone from Eocene Shahejie Formation

Pore scale flow simulations heavily depend on petrographic characterizing and modeling of reservoir rocks. Mineral phase segmentation and pore network modeling are crucial stages in micro-CT based rock modeling. The success of the pore network model (PNM) to predict petrophysical properties relies on image segmentation, image resolution and most importantly nature of rock (homogenous, complex or microporous). The pore network modeling has experienced extensive research and development during last decade, however the application of these models to a variety of naturally heterogenous reservoir rock is still a challenge. In this paper, four samples from a low permeable to tight sandstone reservoir were used to characterize their petrographic and petrophysical properties using high-resolution micro-CT imaging. The phase segmentation analysis from micro-CT images shows that 5-6% microporous regions are present in kaolinite rich sandstone (E3 and E4), while 1.7-1.8% are present in illite rich sandstone (El and E2). The pore system percolates without micropores in El and E2 while it does not percolate without micropores in E3 and E4. In El and E2, total MICP porosity is equal to the volume percent of macrospores determined from micro-CT images, which indicate that the macropores are well connected and microspores do not play any role in non-wetting fluid (mercury) displacement process. Whereas in E3 and E4 sandstones, the volume percent of micropores is far less (almost 50%) than the total MICP porosity which means that almost half of the pore space was not detected by the micro-CT scan. PNM behaved well in El and E2 where better agreement exists in PNM and MICP measurements. While E3 and E4 exhibit multiscale pore space which cannot be addressed with single scale PNM method, a multiscale approach is needed to characterize such complex rocks. This study provides helpful insights towards the application of existing micro-CT based petrographic characterization methodology to naturally complex petroleum reservoir rocks