A digital rock physics approach to effective and total porosity for complex carbonates: pore-typing and applications to electrical conductivity

Recent advances in micro-CT techniques allow imaging heterogeneous carbonates at multiple scales and including voxel-wise registration of images at different resolution or in different saturation states. This enables characterising such carbonates at the pore-scale targeting the optimizing of hydrocarbon recovery in the face of structural heterogeneity, resulting in complex spatial fluid distributions. Here we determine effective and total porosity for different pore-types in a complex carbonate and apply this knowledge to improve our understanding of electrical properties by integrating experiment and simulation in a consistent manner via integrated core analysis. We consider Indiana Limestone as a surrogate for complex carbonate rock and type porosity in terms of macro- and micro-porosity using micro-CT images recorded at different resolution. Effective and total porosity fields are derived and partitioned into regions of macro-porosity, micro-porosity belonging to oolithes, and micro-porosity excluding oolithes’ rims. In a second step we use the partitioning of the micro-porosity to model the electrical conductivity of the limestone, matching experimental measurements by finding appropriate cementation exponents for the two different micro-porosity regions. We compare these calculations with calculations using a single cementation exponent for the full micro-porosity range. The comparison is extended to resistivity index at partial saturation, further testing the assignment of Archie parameters, providing insights into the regional connectivity of the different pore types

Porous Structure Reconstruction Using Convolutional Neural Networks

The three-dimensional high-resolution imaging of rock samples is the basis for pore-scale characterization of reservoirs. Micro X-ray computed tomography (µCT) is considered the most direct means of obtaining the three-dimensional inner structure of porous media without deconstruction. The micrometer resolution ofµ-CT, however, limits its application in the detection of small structures such as nanochannels, which are critical for fluid transportation. An effective strategy for solving this problem is applying numerical reconstruction methods to improve the resolution of the µ-CT images. In this paper, a convolutional neural network reconstruction method is introduced to reconstruct high-resolution porous structures based on low-resolution µ-CT images and high-resolution scanning electron microscope (SEM) images. The proposed method involves four steps. First, a three-dimensional low-resolution tomographic image of a rock sample is obtained by µ-CT scanning. Next, one or more sections in the rock sample are selected for scanning by SEM to obtain high-resolution two-dimensional images. The high-resolution segmented SEM images and their corresponding low-resolution µ-CT slices are then applied to train a convolutional neural network (CNN) model. Finally, the trained CNN model is used to reconstruct the entire low-resolution three-dimensional µ-CT image. Because the SEM images are segmented and have a higher resolution than the µ-CT image, this algorithm integrates the super-resolution and segmentation processes. The input data are low-resolution µCT images, and the output data are high-resolution segmented porous structures. The experimental results show that the proposed method can achieve state-of-the-art performance

Pore-type partitioning for complex carbonates: Effective versus total porosity and applications to electrical conductivity

The pore-scale characterization of complex carbonate rock is of considerable importance in the context of optimizing hydrocarbon recovery due to structural heterogeneity, resulting in complex spatial fluid distributions. Recent advances in micro-CT techniques allow imaging such pore-systems at various scales. Here we present a workflow to determine effective and total porosity for different pore-types and apply this knowledge to improve our understanding of electrical properties by integrating experiment and simulation in a consistent manner via integrated core analysis. Defining as micro-porosity voxels in tomograms containing porosity below voxel resolution, a pore-typing technique is introduced separating microporous rims of oolithes from other types of microporosity using Indiana Limestone; about 50% of the pore space falls into the micro-porosity category for the chosen sample size of diameter (resolution) 1 inch (11um). While the rims exhibit well connected porosity in the high resolution image, they appear as a particular micro-porosity type at low resolution. Various corners are lost due to partial volume effects and imaging noise in the low resolution data. The low-resolution pore-typing allows us to derive micro-porosity specific total- to effective porosity transforms. We utilized the latter regional transforms to establish regional Archie parameters. Experimentally measured formation factor and resistivity index at partial saturation are compared with direct-image based calculations considering both the case of globally and regionally defined Archie parameters. In particular, we find reasonable agreement with the experiments for higher water saturations using global parameters

A digital rock physics approach to effective and total porosity for complex carbonates: pore-typing and applications to electrical conductivity

Recent advances in micro-CT techniques allow imaging heterogeneous carbonates at multiple scales and including voxel-wise registration of images at different resolution or in different saturation states. This enables characterising such carbonates at the pore-scale targeting the optimizing of hydrocarbon recovery in the face of structural heterogeneity, resulting in complex spatial fluid distributions. Here we determine effective and total porosity for different pore-types in a complex carbonate and apply this knowledge to improve our understanding of electrical properties by integrating experiment and simulation in a consistent manner via integrated core analysis. We consider Indiana Limestone as a surrogate for complex carbonate rock and type porosity in terms of macro- and micro-porosity using micro-CT images recorded at different resolution. Effective and total porosity fields are derived and partitioned into regions of macro-porosity, micro-porosity belonging to oolithes, and micro-porosity excluding oolithes’ rims. In a second step we use the partitioning of the micro-porosity to model the electrical conductivity of the limestone, matching experimental measurements by finding appropriate cementation exponents for the two different micro-porosity regions. We compare these calculations with calculations using a single cementation exponent for the full micro-porosity range. The comparison is extended to resistivity index at partial saturation, further testing the assignment of Archie parameters, providing insights into the regional connectivity of the different pore types

Computation of Relative Permeability from Imaged Fluid Distributions at the Pore Scale

Image-based computations of relative permeability for capillary-dominated quasi-static displacements require a realistic description of the distribution of the fluids in the pore space. The fluid distributions are usually computed directly on the imaged pore space or on simplified representations of the pore space extracted from the images using a wide variety of models which capture the physics of pore-scale displacements. Currently this is only possible for uniform strongly wetting conditions where fluid-fluid and rock-fluid interactions at the pore-scale can be modelled with a degree of certainty. Recent advances in imaging technologies which make it possible to visualize the actual fluid distributions in the pore space have the potential to overcome this limitation by allowing relative permeabilities to be computed directly from the imaged fluid distributions. The present study explores the feasibility of doing this by comparing laboratory measured capillary-dominated drainage relative permeabilities with relative permeabilities computed from micro-CT images of the actual fluid distributions in the same rock. The agreement between the measurements and the fluid image-based computations is encouraging. The paper highlights a number of experimental difficulties encountered in the study which should serve as a useful guide for the design of future studies

Relative Permeability from Tomographic Images: Effect of Correlated Heterogeneity

We examine the calculation of relative permeability and residual saturation using networks derived from tomographic images of Fontainebleau sandstone previously used to successfully calculate single-phase transport properties. In contrast to electrical conductivity and permeability calculations, we find that that computed relative permeabilities and residual saturations for samples of the same sandstone display a high degree of variability. Randomizing pores and throats to remove all correlations almost completely eliminates the variability between samples and produces smooth numerical data sets. We conclude that correlations in rock microstructure, which appear to have little effect on the calculation of single fluid properties, have a major effect on computed relative permeability and residual saturation

Volume Conservation of the Intermediate Phase in Three-Phase Pore-Network Models

Quasi-static rule-based network models used to calculate capillary dominated multi-phase transport properties in porous media employ equilibrium fluid saturation distributions which assume that pores are fully filled with a single bulk fluid with other fluids present only as wetting and/or spreading films. We show that for drainage dominated three-phase displacements in which a non-wetting fluid (gas) displaces a trapped intermediate fluid (residual oil) in the presence of a mobile wetting fluid (water) this assumption distorts the dynamics of three-phase displacements and results in significant volume errors for the intermediate fluid and erroneous calculations of intermediate fluid residual saturations, relative permeabilities and recoveries. The volume errors are associated with the double drainage mechanism which is responsible for the mobilization of waterflood residual oil. A simple modification of the double drainage mechanism is proposed which allows the presence of a relatively small number of partially filled pores and removes the oil volume errors

Effect of network topology on two-phase imbibition relative permeability

In a previous study Arns et al. (2004, Transport Porous Media 55, 21-46) we considered the ro le of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. Th