Accurate and efficient localization of CO2 leakage if occurred in subsurface formations, is of significant importance in achieving secure geological carbon sequestration (GCS) projects. However, this task is inherently challenging due to the considerable uncertainties in the subsurface. In this work, we develop a novel deep learning-assisted Bayesian framework for identifying potential CO2 leakage sites based on the reservoir pressure transient behavior measured at the wellbores of injection or observation wells. The method consists of two essential steps: 1) Deep learning surrogate: This step aims to effectively replace the intensive high-fidelity simulation with an efficient deep learning surrogate. 2) Bayesian inversion: In this step, the posterior distributions of potential CO2 leakage locations are inverted, in which the surrogate serves as the forward model. The above two processes are automated using Bayesian optimization instead of a labor-intensive trial-and-error approach. The proposed framework is verified using a 3D geological model simulating CO2 sequestration into a brine-filled reservoir. The results demonstrate the Bayesian-optimized surrogate could successfully capture the underlying process of subsurface CO2-brine flow. The Bayesian inversion algorithm enables localizing CO2 leakage with high accuracy. To our knowledge, the proposed Bayesian framework is implemented for the first time to locate multiple leakage sites at the field scale. The proposed workflow provides an accurate and efficient approach to detecting possible CO2 leakage locations in a real-time manner and has promising potential for field-scale GCS applications.
Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model’s predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas.
Abstract The hydraulic fracturing process is a prominent example of fracture network evolution under stress. However, the interactions between hydraulic fractures and natural fracture networks, along with the connectivity evolution of the resultant fracture networks, require more research. This research incorporates discrete fracture networks to characterize subsurface structures and employs the Discrete Element ‐ Lattice Boltzmann Method to simulate the hydraulic fracturing process. The dynamic evolution of subsurface structures, including the initiation of hydraulic fractures and their interaction with natural fractures, is systematically investigated. Results indicate that natural fractures significantly impact fracture initiation, propagation, and connectivity evolution, which in turn affects fluid production. Fracture strength is key for the interaction, and hydraulic fractures tend to propagate along weak natural fractures with low resistance. Fracture strength variability determines the final fracture networks, with low‐strength fractures breaking due to the altered in‐situ stress and forming local clusters. High injection rates and fluid viscosity result in a large pressure buildup and exaggerate the influential region. A multi‐cluster system is thus formed during the hydraulic fracturing process, and its connectivity can be well quantified with a novel connectivity metric. In low‐permeable reservoirs, fracture clusters connected to production wells can contribute instantly, while local clusters may contribute to production from a long‐term perspective. Injection rate, fluid viscosity, fracture orientation, and clustering effects have consistent positive correlations with the total connectivity and production. Heterogeneity has a weak positive correlation with fluid production, while a moderate negative correlation with total connectivity.
Abstract Due to the scarcity and vulnerability of physical rock samples, digital rock reconstruction plays an important role in the numerical study of reservoir rock properties and fluid flow behaviors. With the rapid development of deep learning technologies, generative adversarial networks (GANs) have become a promising alternative to reconstruct complex pore structures. Numerous GAN models have been applied in this field, but many of them suffer the unstable training issue. In this study, we apply the Wasserstin GAN with gradient penalty, also known as the WGAN-GP network, to reconstruct Berea sandstone and Ketton limestone. Unlike many other GANs using the Jesnen-Shannon divergence, the WGAN-GP network exhibits a stable training performance by using the Wasserstin distance to measure the difference between generated and real data distributions. Moreover, the generated image quality correlates with the discriminator loss. This provides us an indicator of the training state instead of frequently subjective assessments in the training of deep convolutional GAN (DCGAN) based models. An integrated framework is presented to automate the entire workflow, including training set generation, network setup, model training and synthetic rock validation. Numerical results show that the WGAN-GP network accurately reconstructs both Berea sandstone and Ketton limestone in terms of two-point correlation and morphological properties.
Hydraulic properties of natural fractures are essential parameters for the modeling of fluid flow and transport in subsurface fractured porous media. The cubic law, based on the parallel-plate concept, has been traditionally used to estimate the hydraulic properties of individual fractures. This upscaling approach, however, is known to overestimate the fractures hydraulic properties. Dozens of methods have been proposed in the literature to improve the accuracy of the cubic law. The relative performance of these various methods is not well understood. In this work, a comprehensive review and benchmark of almost all commonly used cubic law-based approaches in the literature, covering 43 methods is provided. We propose a new corrected cubic law for incompressible, single-phase laminar flow through rough-walled fractures. The proposed model incorporates corrections to the hydraulic fracture aperture based on the flow tortuosity and local roughness of the fracture walls. We identify geometric rules relative to the local characteristic of the fracture and apply an efficient algorithm to subdivide the fracture into segments, accordingly. High-resolution simulations for Navier-Stokes equations, computed in parallel, for synthetic fractures with various ranges of surface roughness and apertures are then performed. The numerical solutions are used to assess the accuracy of the proposed model and compare it with the other 43 approaches, where we demonstrate its superior accuracy. The proposed model retains the simplicity and efficiency of the cubic law but with pronounced improvement to its accuracy. The data set used in the benchmark, including more than 7500 fractures, is provided in open-access.
Abstract Complex natural fracture networks typically consist of multiple clusters, whose connectivity is rarely quantified. Therefore, for each identified fracture network, we propose a connectivity metric that accounts for individual fracture clusters and their interactions. This metric evaluates contributions from all fracture clusters, considering their relative sizes and interactions among the isolated clusters, which in turn depend on the hydraulic conductance of the interconnecting rock matrix. Furthermore, we investigate how the system connectivity depends on fracture sealing, alterations of central clusters, and cluster linkage. Fracture sealing strongly impacts overall fracture connectivity, with 5 percent of sealed fractures reducing connectivity by 20 percent. The connectivity reduction is small when transitioning the central cluster from the largest to the smallest one. However, the largest cluster significantly contributes to overall connectivity, while the smallest one contributes minimally. Natural fracture networks increase connectivity by linking more clusters, with heterogeneity and anisotropy playing pivotal roles.
Abstract Hydraulic fracturing is widely used to stimulate unconventional reservoirs, but a systematic and comprehensive investigation into the hydraulic fracturing process is insufficient. In this work, a discrete element‐lattice Boltzmann method is implemented to simulate the hydro‐mechanical behavior in a hydraulic fracturing process. Different influential factors, including treatment parameters (injection rates and fluid viscosity), formation parameters (in situ stress states and natural fractures) and rock properties (heterogeneity of rock strengths and rock permeability), are considered and their impacts on the initiation and propagation of hydraulic fractures are evaluated. A higher injection rate, increased viscosity, and larger in situ stress will lead to an increase in the initiation pressure. Conversely, higher formation permeability and a greater degree of heterogeneity in bond strengths will result in a decrease in the initiation pressure. The complexity of generated fractures is significantly influenced by the injection rate and degree of heterogeneity. However, fluid viscosity, in situ stress states, and formation permeability individually do not affect the geometrical complexity. Shear displacement can occur during a hydraulic fracturing process due to increased pore pressure and variations in in situ stress caused by injected fluid. Low‐viscosity fluid with a high injection rate can have a significant pressure buildup and generate complex fracture networks in low‐permeability heterogeneous formations. Natural fractures can significantly impact the complexity of generated fractures, while more in‐depth research is required regarding complex natural fracture distributions.
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