Search

Abstract: This is the second and final part of our digital rock physics (DRP) benchmarking study. We use segmented 3-D images (one for Fontainebleau, three for Berea, three for a carbonate, and one for a sphere pack) to directly compute the absolute permeability, the electrical resistivity, and elastic moduli. The numerical methods tested include a finite-element solver (elastic moduli and electrical conductivity), two finite-difference solvers (elastic moduli and electrical conductivity), a Fourier-based Lippmann-Schwinger solver (elastic moduli), a lattice-Boltzmann solver (hydraulic permeability), and the explicit-jump method (hydraulic permeability and electrical conductivity). The set-ups for these numerical experiments, including the boundary conditions and the total model size, varied as well. The results thus produced vary from each other. For example, the highest computed permeability value may differ from the lowest one by a factor of 1.5. Nevertheless, all these results fall within the ranges consistent with the relevant laboratory data. Our analysis provides the DRP community with a range of possible outcomes which can be expected depending on the solver and its setup. [Copyright &y& Elsevier]

Abstract: The key paradigm of digital rock physics (DRP) “image and compute” implies imaging and digitizing the pore space and mineral matrix of natural rock and then numerically simulating various physical processes in this digital object to obtain such macroscopic rock properties as permeability, electrical conductivity, and elastic moduli. The steps of this process include image acquisition, image processing (noise reduction, smoothing, and segmentation); setting up the numerical experiment (object size and resolution as well as the boundary conditions); and numerically solving the field equations. Finally, we need to interpret the solution thus obtained in terms of the desired macroscopic properties. For each of these DRP steps, there is more than one method and implementation. Our goal is to explore and record the variability of the computed effective properties as a function of using different tools and workflows. Such benchmarking is the topic of the two present companion papers. Here, in the first part, we introduce four 3D microstructures, a segmented Fontainebleau sandstone sample (porosity 0.147), a gray-scale Berea sample; a gray-scale Grosmont carbonate sample; and a numerically constructed pack of solid spheres (porosity 0.343). Segmentation of the gray-scale images by three independent teams reveals the uncertainty of this process: the segmented porosity range is between 0.184 and 0.209 for Berea and between 0.195 and 0.271 for the carbonate. The implications of the uncertainty associated with image segmentation are explored in a second paper. [Copyright &y& Elsevier]

Natural rock is heterogeneous at all scales. This challenges the digital rock physics concept since the images of natural rock are mm-sized, while the results should be applicable at much larger spatial scales. To address this challenge we subsample a digital volume and compute the permeability of its subvolumes, as well as that of the entire volume, using the lattice-Boltzmann method (LBM). We reassemble the resulting values in 3D and use Darcy's flow simulator to re-compute the permeability of the entire host volume. In spite of significant heterogeneity of the subvolume properties, the Darcy-upscaled entire-volume permeability falls very close to that LBM-computed. Next, by using random reconstructions of the subvolume permeability matrix, we obtain physically meaningful permeability versus porosity transforms that can arguably be used at a scale much greater than that of a digital CT-scan image. This simple principle "to see a trend in a grain of sand" is the novel contribution of our work. Arguably, it can be implemented using images of drill cuttings collected within an interval in a well. We discuss examples of this principle for three basic rock types: high-porosity unconsolidated sand, medium-porosity sandstone, and medium-porosity carbonate. • Permeability-porosity transforms can be obtained from a single micro-CT scan. • Elemental permeabilities are computed using the Lattice-Boltzmann method. • Upscaled transforms are produced using Darcy's flow simulation. • Process-based averaging concept enables upscaling. [ABSTRACT FROM AUTHOR]

Matrix acidizing is a well stimulation method that is applied to enhance productivity. The success of a stimulation job depends mainly on the efficiency of the acid systems that are employed. This study investigated a new and efficient acid system that is biodegradable, not corrosive, and safe to handle. The system efficiency was compared to that of HCl and chelating agents. Acid coreflooding has been applied to chalk, dolomite, and limestone carbonate rock samples to measure the efficiency in terms of injected pore volume to breakthrough (PVBT). The rock samples were characterized in terms of porosity, permeability, composition using X-ray diffraction (XRD), and pore distribution using nuclear magnetic resonance (NMR). The effluent was collected at different times and analyzed using induced coupled plasma (ICP). Medical computed tomography (MCT) was used to visualize the interior of the rock samples after acidizing. The new acid system was more efficient in terms of acid spending than straight HCl acid and chelating agents in Indiana limestone. At the optimum injection rate, chelating agents had an optimum PVBT value of about 15 compared to 0.85 for plain HCl acid. Using the new acid system resulted in an optimum PVBT value of only 0.41, which is less than half of HCl acid. A numerical wormhole simulator was implemented to match the experimental PVBT and assess the reactivity of the acid system. • A novel acid system has been identified to be better than aqueous HCl. • A modelling approach reproduces the wormholing. • Different lithologies react (systematically) different. [ABSTRACT FROM AUTHOR]

New experimental tests on a suite of tight gas sandstone samples show a strong dependence of both P- and S-wave velocities, V p and V s , on hydrostatic confining stress in the range from almost zero to 50 MPa. The Klinkenberg-corrected absolute gas permeability of these samples also exhibited a dramatic stress dependence. It decreased by one to two orders of magnitude as the stress increased. A new approach is used to consolidate the 18-sample dataset at each confining stress and arrive at the effective permeability and elastic moduli. For the former, we utilize a randomly generated permeability matrix with its elements drawn from the 18 datapoints. For the latter, we use the elastic bounds. As a result, we obtain permeability-stress, porosity-stress, and velocity-stress relations characteristic of the class of rock under examination. Theoretical simulations based on the inclusion-based differential effective medium theory mimic the experimental velocity-stress results. We also derive a permeability versus acoustic impedance and versus stress relation to be used for inferring permeability variations as a function of the measured impedance versus stress changes. This relation can serve to estimate the permeability from the elastic property variations during time-lapse monitoring, as well as during fracking of this rock. • Laboratory tests on tight gas sandstone samples measuring the elastic properties and absolute permeability. • Consolidating the 18-sample dataset. • Permeability-stress, porosity-stress, and velocity-stress relations. • Permeability versus acoustic impedance and versus stress relation. [ABSTRACT FROM AUTHOR]