Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach (Kadeethum et al., 2021d) of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn & Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in poroelastic problems.
Large-scale CO2 sequestration into geological formations has been suggested to reduce CO2 emissions from industrial activities. However, much like enhanced geothermal stimulation and wastewater injection, CO2 sequestration has a potential to induce earthquake along weak faults, which can be considered a negative impact on safety and public opinion. This study shows the physical mechanisms of potential seismic hazards along basement faults driven by CO2 sequestration under variation in geological and operational constraints. Specifically we compare the poroelastic behaviors between multiphase flow and single-phase flow cases, highlighting specific needs of evaluating induced seismicity associated with CO2 sequestration. In contrast to single-phase injection scenario, slower migration of the CO2 plume than pressure pulse may delay accumulation of pressure and stress along basement faults that may not be mitigated immediately by shut-in of injection. The impact of multiphase flow system, therefore, needs to be considered for proper monitoring and mitigation strategies.
Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 106 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.
Injecting CO2 into a deep geological formation (i.e., geological carbon storage, GCS) can induce earthquakes along preexisting faults in the earth's upper crust. Seismic survey and regional geo-structure analysis are typically employed to map the faults prone to earthquakes prior to injection. However, earthquakes induced by fluid injection from other subsurface energy storage and recovery activities show that systematic evaluation of the potential of induced seismicity associated with GCS is necessary. This study mechanistically investigates how multiphysical interaction among injected CO2, preexisting pore fluids and rock matrix alters stress states on faults and which physical mechanisms can nucleate earthquakes along the faults. Increased injection pressure is needed to overcome capillary entry pressure of the fault zone, driven by the contrast of fluids' wetting characteristics. Accumulated CO2 within the reservoir delays post shut-in reduction in pressure and stress fields along the fault that may enhance the potential for earthquake nucleation after terminating injection operations. Elastic energy generated by coupled processes transfers to low-permeability or hydraulically isolated basement faults, which can initiate slip of the faults. Our findings from generic studies suggest that geomechanical simulations integrated with multiphase flow system are essential to detect deformation-driven signals and mitigate potential seismic hazards associated with CO2 injection.
We propose the use of balanced iterative reducing and clustering using hierarchies (BIRCH) combined with linear regression to predict the reduced Young's modulus and hardness of highly heterogeneous materials from a set of nanoindentation experiments. We first use BIRCH to cluster the dataset according to its mineral compositions, which are derived from the spectral matching of energy-dispersive spectroscopy data through the modular automated processing system (MAPS) platform. We observe that grouping our dataset into five clusters yields the best accuracy as well as a reasonable representation of mineralogy in each cluster. Subsequently, we test four types of regression models, namely linear regression, support vector regression, Gaussian process regression, and extreme gradient boosting regression. The linear regression and Gaussian process regression provide the most accurate prediction, and the proposed framework yields R2 = 0.93 for the test set. Although the study is needed more comprehensively, our results shows that machine learning methods such as linear regression or Gaussian process regression can be used to accurately estimate mechanical properties with a proper number of grouping based on compositional data.
We propose the use of balanced iterative reducing and clustering using hierarchies (BIRCH) combined with linear regression to predict the reduced Young's modulus and hardness of highly heterogeneous materials from a set of nanoindentation experiments. We first use BIRCH to cluster the dataset according to its mineral compositions, which are derived from the spectral matching of energy-dispersive spectroscopy data through the modular automated processing system (MAPS) platform. We observe that grouping our dataset into five clusters yields the best accuracy as well as a reasonable representation of mineralogy in each cluster. Subsequently, we test four types of regression models, namely linear regression, support vector regression, Gaussian process regression, and extreme gradient boosting regression. The linear regression and Gaussian process regression provide the most accurate prediction, and the proposed framework yields R2 = 0.93 for the test set. Although the study is needed more comprehensively, our results shows that machine learning methods such as linear regression or Gaussian process regression can be used to accurately estimate mechanical properties with a proper number of grouping based on compositional data.
The earth texture with complex morphological geometry and compositions such as shale and carbonate rocks, is typically characterized with sparse field samples because of an expensive and time-consuming characterization process. Accordingly, generating arbitrary large size of the geological texture with similar topological structures at a low computation cost has become one of the key tasks for realistic geomaterial reconstruction and subsequent hydro-mechanical evaluation for science and engineering applications. Recently, generative adversarial neural networks (GANs) have demonstrated a potential of synthesizing input textural images and creating equiprobable geomaterial images for stochastic analysis of hydrogeological properties, for example, the feasibility of CO2 storage sites and exploration of unconventional resources. However, the texture synthesis with the GANs framework is often limited by the computational cost and scalability of the output texture size. In this study, we proposed a spatially assembled GANs (SAGANs) that can generate output images of an arbitrary large size regardless of the size of training images with computational efficiency. The performance of the SAGANs was evaluated with two and three dimensional (2D and 3D) rock image samples widely used in geostatistical reconstruction of the earth texture and Lattice-Boltzmann (LB) simulations were performed to compare pore-scale flow patterns and upscaled permeabilities of training and generated geomaterial images. We demonstrate SAGANs can generate the arbitrary large size of statistical realizations with connectivity and structural properties and flow characteristics similar to training images, and also can generate a variety of realizations even on a single training image. In addition, the computational time was significantly improved compared to standard GANs frameworks.
Kim, Sung E.; Seo, Yongwon; Hwang, Junshik; Yoon, Hongkyu; Lee, Jonghyun
Stochastic network modeling is often limited by high computational costs to generate a large number of networks enough for meaningful statistical evaluation. In this study, Deep Convolutional Generative Adversarial Networks (DCGANs) were applied to quickly reproduce drainage networks from the already generated network samples without repetitive long modeling of the stochastic network model, Gibb’s model. In particular, we developed a novel connectivity-informed method that converts the drainage network images to the directional information of flow on each node of the drainage network, and then transforms it into multiple binary layers where the connectivity constraints between nodes in the drainage network are stored. DCGANs trained with three different types of training samples were compared; (1) original drainage network images, (2) their corresponding directional information only, and (3) the connectivity-informed directional information. A comparison of generated images demonstrated that the novel connectivity-informed method outperformed the other two methods by training DCGANs more effectively and better reproducing accurate drainage networks due to its compact representation of the network complexity and connectivity. This work highlights that DCGANs can be applicable for high contrast images common in earth and material sciences where the network, fractures, and other high contrast features are important.
