From computed microtomography images to resistivity index calculations of heterogeneous carbonates using a dual-porosity pore-network approach: influence of percolation on the electrical transport properties

A general-purpose tool for modeling multifunctional thin porous media (POREnet): From pore network to effective property tensors

POREnet, a novel approach to model effective properties of thin porous media, TPM, is presented. The methodology allows the extraction of local effective property tensors by volume averaging from discrete pore networks, PNs, built on the tessellated continuum space of a TPM. The gradient theorem is used to describe 3D transport in bulk tessellated space, providing an appropriate metric to normalize network fluxes. Implemented effective transport properties include diffusivity, permeability, solid-phase conductivity, and entry capillary pressure and contact angle under two-phase conditions, considering multi-component materials with several solid phases and local contact resistances. Calculated property tensors can be saved on 3D image stacks, where interfacial and sub-CV scale features can be added before exporting data to CFD meshes for simulation. Overall, POREnet provides a general-purpose, versatile methodology for modeling TPM in an ample range of conditions within a single CFD framework. Among other advantages, coupling of PN and continuum models at TPM-channel interfaces is simplified, interfacial contact resistances can be included using robin boundary conditions, and transient multiphysics simulations can be implemented more easily using CFD. The code is tested against a miscellaneousness of examples extracted from electrochemical applications.

Study on Rock-Electric Characteristics of Cracked Porous Rocks by the Novel Multifactor Conductivity Model

Due to the influence of multiple factors on the conductive properties of rocks, the Archie's formula, considering only a single factor, makes it difficult to reasonably explain rock-electric characteristics of cracked porous rocks. In order to better describe the conductive mechanism of cracked porous rocks, a generalized multifactor conductivity model was proposed by considering and introducing multiple influencing factors such as the series-parallel structure, conductive matrix, cracks, and fluids, which is conducive to more accurate research on the conductive mechanism of rocks. It should be noted that the developed model is not only applicable to cracked porous rocks but also useful for porous rocks. Through the study and analysis of various influencing factors, it is demonstrated by the simulation results that both the conductive matrix and cracks improve the conductive ability, which are crucial factors resulting in the non-Archie behavior and low-resistivity pay zone, and rock conductivity is more sensitive to the conductive matrix and cracks in tight reservoirs with porosity below 10%. Furthermore, experimental data are available to validate the novel multifactor conductivity model, and the comparison results show its advantages in predicting and explaining the conductive properties of cracked porous rocks.

A Triple Pore Network Model (T-PNM) for Gas Flow Simulation in Fractured, Micro-porous and Meso-porous Media

In this study, a novel triple pore network model (T-PNM) is introduced which is composed of a single pore network model (PNM) coupled to fractures and micro-porosities. We use two stages of the watershed segmentation algorithm to extract the required data from semi-real micro-tomography images of porous material and build a structural network composed of three conductive elements: meso-pores, micro-pores, and fractures. Gas and liquid flow are simulated on the extracted networks and the calculated permeabilities are compared with dual pore network models (D-PNM) as well as the analytical solutions. It is found that the processes which are more sensitive to the surface features of material, should be simulated using a T-PNM that considers the effect of micro-porosities on overall process of flow in tight pores. We found that, for gas flow in tight pores where the close contact of gas with the surface of solid walls makes Knudsen diffusion and gas slippage significant, T-PNM provides more accurate solution compared to D-PNM. Within the tested range of operational conditions, we recorded between 10 and 50% relative error in gas permeabilities of carbonate porous rocks if micro-porosities are dismissed in the presence of fractures.

Improved method for effective rock microporosity estimation using X-ray microtomography

Petrophysical analysis using X-ray microtomography provides key textural and compositional information, useful to investigate porous media characteristics of hydrocarbon and geothermal reservoirs. Several approaches, used for rock porosity estimation from tomography data, rely mainly on visual or mathematical segmentation algorithms that attempt to obtain thresholding values to segment a phase solved by pixel analysis resolution. Therefore, porosity is evaluated using only pores above pixel resolution (macroporosity), and dismiss pores sized less than the pixel resolution (microporosity) that can be essential to characterize permeability conditions of geothermal reservoirs. Here we propose an improved method to calculate the total effective porosity and simulate the absolute permeability of rock samples. This method combines the analysis of X-ray computed microtomography (μCT) with the interpretation of data using a powerful thresholding method that is based on the greyscale interclass variance. The 3D volume is segmented into three domains: solid, pores above resolution and, an intermediate region where each pore below resolution is linearly combined with solid matrix resulting in a grey scaled pixel equal to this combination. For the intermediate region, the microporosity was calculated employing a Matlab code that provides a new thresholding value containing pores, both above and below resolution (total porosity). Finally, by using this new calculated thresholding value the total effective porosity was obtained and an absolute permeability simulation was implemented only to the connected pores. Our results show that micropores contribute for nearly 50 percent of the total porosity and that microporosity plays a key role in estimating effective porosity, and assessing the geothermal potential of a rock reservoir.

Universal Stochastic Multiscale Image Fusion: An Example Application for Shale Rock

Spatial data captured with sensors of different resolution would provide a maximum degree of information if the data were to be merged into a single image representing all scales. We develop a general solution for merging multiscale categorical spatial data into a single dataset using stochastic reconstructions with rescaled correlation functions. The versatility of the method is demonstrated by merging three images of shale rock representing macro, micro and nanoscale spatial information on mineral, organic matter and porosity distribution. Merging multiscale images of shale rock is pivotal to quantify more reliably petrophysical properties needed for production optimization and environmental impacts minimization. Images obtained by X-ray microtomography and scanning electron microscopy were fused into a single image with predefined resolution. The methodology is sufficiently generic for implementation of other stochastic reconstruction techniques, any number of scales, any number of material phases, and any number of images for a given scale. The methodology can be further used to assess effective properties of fused porous media images or to compress voluminous spatial datasets for efficient data storage. Practical applications are not limited to petroleum engineering or more broadly geosciences, but will also find their way in material sciences, climatology, and remote sensing.

Numerical homogenization of electrokinetic equations in porous media using lattice-Boltzmann simulations

We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.

Re-examining Archie's law: Conductance description by tortuosity and constriction

In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g., brine), usually described using the Archie cementation exponent. We show how the electrical conductance depends on changes in the drift velocity and the length of the electric field lines, in addition to the porosity and the conductance of the electrolyte. We characterize the length of the electric field lines by a tortuosity and the changes in drift velocity by a constriction factor. Both the tortuosity and the constriction factor are descriptors of the pore microstructure. We define a conductance reduction factor to measure the local contributions of the pore microstructure to the global conductance. It is shown that the global conductance reduction factor is the product of the tortuosity squared divided by the constriction factor, thereby proving that the combined effect of tortuosity and constriction, in addition to the porosity and conductance of the electrolyte, fully describes the effective electrical conductance of a porous medium. We show that our tortuosity, constriction factor, and conductance reduction factor reproduce the electrical conductance for idealized porous media. They are also applied to Bentheimer sandstone, where we describe a microstructure-related correlation between porosity and conductivity using both the global conductance reduction factor and the distinct contributions from tortuosity and constriction. Overall, this work shows how the empirical Archie cementation exponent can be substituted by more descriptive, physical parameters, either by the global conductance reduction factor or by tortuosity and constriction.