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Recent Submissions

  • Benchmark modeling and 3D applications of solidification and macro-segregation based on an operator-splitting and fully decoupled scheme with term-wise matrix assembly

    Feng, Xiaoyu; Chen, Huangxin; Yu, Bo; Sun, Shuyu (arXiv, 2023-03-19) [Preprint]
    The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The quantitative prediction of phase change, chemical heterogeneities, and multi-phase and multi-component flows plays critical roles in many natural scenarios and industrial applications that involve many disciplines, like material, energy, and even planet science. In view of this, some scholars and research institutions have called for more contributors to join the benchmark analysis of solidification and segregation problems. Our work proposes an operator-splitting and matrix-based method to avoid non-linear systems. Also, the combination of vectorization and forward equation-based matrix assembly techniques enhances the implementability of extensions of 3D applications. Lastly, the novel scheme is well validated through a bunch of 2D and 3D benchmark cases. The numerical results also illustrate that this method can ensure accurate prediction and adequately capture the physical details of phenomena caused by the solutally and thermally driven flow, which include channel segregation, the formation of freckles, edge effect, aspect ratio effect, and 3D effect.
  • Data-Driven Machine Learning Modeling of Mineral/CO2/Brine Wettability Prediction: Implications for CO2 Geo-Storage

    Tariq, Zeeshan; Ali, Muhammad; Yan, Bicheng; Sun, Shuyu; Khan, Mohammad; Yekeen, Nurudeen; Hoteit, Hussein (SPE, 2023-03-07) [Conference Paper]
    CO2 wettability and the reservoir rock-fluid interfacial interactions are crucial parameters for successful CO2 geological sequestration. This study implemented the feed-forward neural network to model the wettability behavior in a ternary system of rock minerals (quartz and mica), CO2, and brine under different operating conditions. To gain higher accuracy of the machine learning models, a sufficient dataset was utilized that was recorded by conducting a large number of laboratory experiments under a realistic pressure range, 0 – 25 MPa and the temperatures range, 298 – 343 K. The mica substrates were used as a proxy for the caprock, and quartz substrates were used a proxy for the reservoir rock. Different graphical exploratory data analysis techniques, such as heatmaps, violin plots, and pairplots were used to analyze the experimental dataset. To improve the generalization capabilities of the machine learning models k-fold cross-validation method, and grid search optimization approaches were implemented. The machine learning models were trained to predict the receding and advancing contact angles of mineral/CO2/brine systems. Both statistical evaluation and graphical analyses were performed to show the reliability and performance of the developed models. The results showed that the implemented ML model accurately predicted the wettability behavior under various operating conditions. The training and testing average absolute percent relative errors (AAPE) and R2 of the FFNN model for mica and quartz were 0.981 and 0.972, respectively. The results confirm the accuracy performance of the ML algorithms. Finally, the investigation of feature importance indicated that pressure had the utmost influence on the contact angles of the minerals/CO2/brine system. The geological conditions profoundly affect rock minerals wetting characteristics, thus CO2 geo-storage capacities. The literature severely lacks advanced information and new methods for characterizing the wettability of mineral/CO2/brine systems at geo-storage conditions. Thus, the ML model's outcomes can be beneficial for precisely predicting the CO2 geo-storage capacities and containment security for the feasibility of large-scale geo-sequestration projects.
  • An Intelligent Safe Well Bottom-Hole Pressure Monitoring of CO2 Injection Well into Deep Saline: A coupled Hydro-Mechanical Approach

    Tariq, Zeeshan; Yan, Bicheng; Sun, Shuyu (SPE, 2023-03-07) [Conference Paper]
    Geological Carbon Sequestration (GCS) in deep geological formations, like saline aquifers and depleted oil and gas reservoirs, brings enormous potential for large-scale storage of carbon dioxide (CO2). The successful implementation of GCS requires a comprehensive risk assessment of the confinement of plumes and storage potential at each storage site. To better understand the integrity of the caprock after injecting CO2, it is necessary to develop robust and fast tools to evaluate the safe CO2 injection duration. This study applied deep learning (DL) techniques, such as fully connected neural networks, to predict the safe injection duration. A physics-based numerical reservoir simulator was used to simulate the movement of CO2 for 170 years following a 30-year CO2 injection period into a deep saline aquifer. The uncertainty variables were utilized, including petrophysical properties such as porosity and permeability, reservoir physical parameters such as temperature, salinity, thickness, and operational decision parameters such as injection rate and perforation depth. As mentioned earlier, the reservoir model was sampled using the Latin-Hypercube sampling approach to account for a wide range of parameters. Seven hundred twenty-two reservoir simulations were performed to create training, testing, and validation datasets. The DNN model was trained, and several executions were performed to arrive at the best model. After multiple realizations and function evaluations, the predicted results revealed that the three-layer FCNN model with thirty neurons in each layer could predict the safe injection duration of CO2 into deep saline formations. The DNN model showed an excellent prediction efficiency with the highest coefficient of determination factor of above 0.98 and AAPE of less than 1%. Also, the trained predictive models showed excellent agreement between the simulated ground truth and predicted trapping index, yet 300 times more computationally efficient than the latter. These findings indicate that the DNN-based model can support the numerical simulation as an alternative to a robust predictive tool for estimating the performance of CO2 in the subsurface and help monitor the storage potential at each part of the GCS project.
  • Application of Image Processing Techniques in Deep-Learning Workflow to Predict CO2 Storage in Highly Heterogeneous Naturally Fractured Reservoirs: A Discrete Fracture Network Approach

    Tariq, Zeeshan; Yan, Bicheng; Sun, Shuyu (SPE, 2023-03-07) [Conference Paper]
    Naturally fractured reservoirs (NFRs), such as fractured carbonate reservoirs, are commonly located worldwide and have the potential to be good sources of long-term storage of carbon dioxide (CO2). The numerical reservoir simulation models are an excellent source for evaluating the likelihood and comprehending the physics underlying behind the interaction of CO2 and brine in subsurface formations. For various reasons, including the rock's highly fractured and heterogeneous nature, the rapid spread of the CO2 plume in the fractured network, and the high capillary contrast between matrix and fractures, simulating fluid flow behavior in NFR reservoirs during CO2 injection is computationally expensive and cumbersome. This paper presents a deep-learning approach to capture the spatial and temporal dynamics of CO2 saturation plumes during the injection and monitoring periods of Geological Carbon Sequestration (GCS) sequestration in NFRs. To achieve our purpose, we have first built a base case physics-based numerical simulation model to simulate the process of CO2 injection in naturally fractured deep saline aquifers. A standalone package was coded to couple the discrete fracture network in a fully compositional numerical simulation model. Then the base case reservoir model was sampled using the Latin-Hypercube approach to account for a wide range of petrophysical, geological, reservoir, and decision parameters. These samples generated a massive physics-informed database of around 900 cases that provides a sufficient training dataset for the DL model. The performance of the DL model was improved by applying multiple filters, including the Median, Sato, Hessian, Sobel, and Meijering filters. The average absolute percentage error (AAPE), root mean square error (RMSE), Structural similarity index metric (SSIM), peak signal-to-noise ratio (PSNR), and coefficient of determination (R2) were used as error metrics to examine the performance of the surrogate DL models. The developed workflow showed superior performance by giving AAPE less than 5% and R2 more than 0.94 between ground truth and predicted values. The proposed DL-based surrogate model can be used as a quick assessment tool to evaluate the long-term feasibility of CO2 movement in a fracture carbonate medium.
  • Numerical Investigations on the Doublet Huff and Puff Technology to Extract Heat from the Geothermal Reservoirs and Storing of CO2

    Gudala, Manojkumar; Tariq, Zeeshan; Yan, Bicheng; Sun, Shuyu (IPTC, 2023-02-28) [Conference Paper]
    In this work, we studied the implementation of huff and puff technology to extract heat from the geothermal reservoir. Two-dimensional numerical investigations were carried out using a fully coupled two-phase thermo-hydro-mechanical model with dynamic rock and fluid properties. COMSOL Multiphysics (a finite element solver) was utilized to build the model. The CO2 geofluid is injected in a supercritical state in a water-saturated geothermal reservoir. The results were showing promising for the extraction of heat and storing of CO2. In the simulation model, we designed a well pair (two-vertical wells) system with two different operating perforations in the same well with huff and puff cycle operation, and this technology is named as Doublet Huff and Puff (DHP). Injection wells operating at the top of the formation and production wells are operating at the bottom. The injection well-1 and production well-1 are operating at same time (i.e., 2 years). During this period, injection well-2 and production well-2 are ideal, and injection well-1 and production well-1 are ideal while operating injection well-2 and production well-2. This process is continued till the whole reservoir is saturated with the injected CO2 and/or the reservoir temperature reaches 60 % (i.e., geothermal reservoir life) of its original temperature. The CO2 plume expanding throughout the reservoir effectively while extracting heat from the reservoir. The sensitivity of well distance, injection temperature, injection velocity, and perforation length on the production temperature was investigated. The production temperature stays stable and high for a long time and no influence on the production temperature. Thus, the proposed technique (DHP) can be implemented for sequestering large amounts of CO2 along with heat extraction in geothermal reservoirs.
  • Three-dimensional simulation of wormhole propagation in fractured-vuggy carbonate rocks during acidization

    Liu, Piyang; Kong, Xue; Feng, Gaocheng; Zhang, Kai; Sun, Shuyu; Yao, Jun (Advances in Geo-Energy Research, Yandy Scientific Press, 2023-02-20) [Article]
    Acidization is a widely used stimulation technique for carbonate reservoirs aimed at removing formation damage, and if successful, can result in the creation of wormholes of specific lengths and conductivities around the wellbore. The formation of wormholes depends on the injection rate for a particular acid-mineral system and can be predicted through numerical simulations of the reactive phenomenon during acidization. In this paper, the commonly used two-scale continuum model is enhanced to encompass fractured-vuggy porous media. The fractures are characterized by a pseudo-fracture model, while vugs are represented by a cluster of anomalous matrices with high porosity. Moreover, a method for generating random pore-fracture-vuggy models is proposed. The governing equations are discretized by the finite volume method and are solved under three-dimensional linear and radial conditions. Sensitivity analysis of dissolution dynamics with respect to fracture and vug parameters is performed. The simulation results indicate that both fractures and vugs significantly impact wormhole development. Except for fractures perpendicular to the acid flow direction, fractures in other directions play a crucial role in determining the direction of wormhole growth.
  • Deep Multi-Input and Multi-Output Operator Networks Method for Optimal Control of Pdes

    Yong, Jinjun; Luo, Xianbing; Sun, Shuyu (Elsevier BV, 2023-02-10) [Preprint]
    Deep operator networks are widely used to solve optimal control problem due to the expressive capability of the approximate nonlinear operators. Generally, an optimal control problem is equivalent to a system of partial differential equations problem. Based on this, we propose a deep multi-input and multi-output operator neural network (MIMOONet) method. We apply the proposed MIMOONet and physically informed MIMOONet to solve the optimal control problems. It works successfully for solving the elliptic (linear and semi-linear) and parabolic optimal control problems.
  • An energy stable, conservative and bounds-preserving numerical method for thermodynamically consistent modeling of incompressible two-phase flow in porous media with rock compressibility

    Kou, Jisheng; Wang, Xiuhua; Chen, Huangxin; Sun, Shuyu (International Journal for Numerical Methods in Engineering, Wiley, 2023-02-10) [Article]
    In this paper, we consider modeling and numerical simulation of incompressible and immiscible two-phase flow in porous media with rock compressibility. Using the second law of thermodynamics, we rigorously derive a thermodynamically consistent mathematical model, which characterizes the two-phase capillarity and rock compressibility through free energies, thereby following an energy dissipation law. We also derive a general and thermodynamically consistent formulation for the effective pore fluid pressure acting on rocks, which is a fundamental problem for two-phase flow with rock compressibility. To solve the model effectively, we propose an energy stable numerical method, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and positivity of porosity and saturations. Benefiting from the newly-developed energy factorization approach and careful treatments for the effective pressure and porosity, the proposed scheme can inherit the energy dissipation law at the discrete level. The fully discrete scheme is constructed using a locally conservative cell-centered finite difference method. The implicit strategy is applied to treat the upwind phase mobilities and porosity in the phase mass conservation equations and the porosity equation so as to conserve the mass of each phase as well as pore volumes. The positivity of porosity and saturations is proved without any restrictions on time step and mesh sizes. An efficient sequential iterative method is also developed to solve the nonlinear system resulting from the scheme. Finally, numerical results are given to verify the features of the proposed method.
  • An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows

    Feng, Xiaoyu; Qiao, Zhonghua; Sun, Shuyu; Wang, Xiuping (Journal of Computational Physics, Elsevier BV, 2023-02-10) [Article]
    Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes–Cahn–Hilliard (NSCH) model in the Eulerian framework, while few investigations have been made in the Lagrangian framework. Smoothed particle hydrodynamics (SPH) is a popular mesh-free Lagrangian method for solving complex fluid flows. In this paper, we present a pioneering study on the energy-stable SPH discretization of the NSCH model for incompressible two-phase flows. We prove that this SPH method inherits mass and momentum conservation and the energy dissipation properties at the fully discrete level. With the projection procedure to decouple the momentum and continuity equations, the numerical scheme meets the divergence-free condition. Some numerical experiments are carried out to show the performance of the proposed energy-stable SPH method for solving the two-phase NSCH model. The inheritance of mass and momentum conservation and the energy dissipation properties are verified numerically.
  • Spatial–temporal prediction of minerals dissolution and precipitation using deep learning techniques: An implication to Geological Carbon Sequestration

    Tariq, Zeeshan; Yildirim, Ertugrul Umut; Gudala, Manojkumar; Yan, Bicheng; Sun, Shuyu; Hoteit, Hussein (Fuel, Elsevier BV, 2023-02-08) [Article]
  • Deep Learning Models for the Prediction of Mineral Dissolution and Precipitation During Geological Carbon Sequestration

    Tariq, Zeeshan; Yildirim, Ertugrul Umut; Yan, Bicheng; Sun, Shuyu (SPE, 2023-01-24) [Conference Paper]
    In Geological Carbon Sequestration (GCS), mineralization is a secure carbon dioxide (CO2) trapping mechanism to prevent possible leakage at later stage of the GCS project. Modeling of the mineralization during GCS relies on numerical reservoir simulation, but the computational cost is prohibitively high due to the complex physical processes. Therefore, deep learning (DL) models can be used as a computationally cheaper and at the same time, reliable alternative to the conventional numerical simulators. In this work, we have developed a DL approach to effectively predict the dissolution and precipitation of various important minerals, including Anorthite, Kaolinite, and Calcite during CO2 injection into deep saline aquifers. We established a reservoir model to simulate the process of geological CO2 storage. About 750 simulations were performed in order to generate a comprehensive dataset for training DL models. Fourier Neural Operator (FNO) models were trained on the simulated dataset, which take the reservoir and well properties along with time information as input and predict the precipitation and dissolution of minerals in space and time scales. During the training process, root-mean-squared-error (RMSE) was chosen as the loss function to avoid overfitting. To gauge prediction performance, we applied the trained model to predict the concentrations of different mineral on the test dataset, which is 10% of the entire dataset, and two metrics, including the average absolute percentage error (AAPE) and the coefficient of determination (R2) were adopted. The R2 value was found to be around 0.95 for calcite model, 0.94 for Kaolinite model, and 0.93 for Anorthite model. The R2 was calculated for all trainable points from the predictions and ground truth. On the other hand, the average AAPE for all the mappings was calculated around 1%, which demonstrates that the trained model can effectively predict the temporal and spatial evolution of the mineral concentrations. The prediction CPU time (0.2 seconds/case) by the model is much lower than that of the physics-based reservoir simulator (3600 seconds/case). Therefore, the proposed method offers predictions as accurate as our physics-based reservoir simulations, while provides a huge saving of computation time. To the authors' best knowledge, prediction of the precipitation and dissolution of minerals in a supervised learning approach using the simulation data has not been studied before in the literature. The DL models developed in this study can serve as a computationally faster alternative to conventional numerical simulators to assess mineralization trapping in GCS projects especially for the mineral trapping mechanism.
  • Physics Informed Surrogate Model Development in Predicting Dynamic Temporal and Spatial Variations During CO2 Injection into Deep Saline Aquifers

    Tariq, Zeeshan; Yan, Bicheng; Sun, Shuyu (SPE, 2023-01-24) [Conference Paper]
    Geological Carbon Sequestration (GCS) in deep geological formations, like saline aquifers and depleted oil and gas reservoirs, brings enormous potential for large-scale storage of carbon dioxide (CO2). The successful implementation of GCS requires a comprehensive risk assessment of the confinement of plumes at each potential storage site. The accurate prediction of the flow, geochemical, and geomechanical responses of the formation is essential for the management of GCS in long-term operations because excessive pressure buildup due to injection can potentially induce fracturing of the cap-rock, or activate pre-existing faults, through which fluid can leak. In this study, we build a Deep Learning (DL) workflow to effectively infer the storage potential of CO2 in deep saline aquifers. Specifically, a reservoir model is built to simulate the process of CO2 injection into deep saline aquifers, which considers the coupled phenomenon of flow and hydromechanics. Further, the reservoir model was sampled to account for a wide range of petro-physical, geological, and operational parameters. These samples generated a massive physics-informed simulation database (about 1500 simulated data points) that provides training data for the DL workflow. The ranges of varied parameters were obtained from an extensive literature survey. The DL workflow consists of Fourier Neural Operator (FNO) to take the input of the parameterized variables used in the simulation database and jointly predict the temporal-spatial responses of pressure and CO2 saturation plumes at different periods. Average Absolute Percentage Error (AAPE) and coefficient of determination (R2), Structural similarity index (SSIM), and Peak Signal to Noise Ratio (PSNR) are used as error metrics to evaluate the performance of the DL workflow. Through our blind testing experiments, the DL workflow offers predictions as accurate as our physics-based reservoir simulations, yet 300 times more efficient than the latter. The developed workflow shows superior performance with an AAPE of less than 5% and R2 score of more than 0.99 between actual and predicted values. The workflow can predict other required outputs that numerical simulators can typically calculate, such as solubility trapping, mineral trapping, and injected fluid densities in supercritical and aqueous phases. The proposed DL workflow is not only physics informed but also driven by inputs and outputs (data-driven) and thus offers a robust prediction of the carbon storage potential in deep saline aquifers with considering the coupled physics and potential fluid leakage risk.
  • Deep-Learning-Based Surrogate Model to Predict CO2 Saturation Front in Highly Heterogeneous Naturally Fractured Reservoirs: A Discrete Fracture Network Approach

    Tariq, Zeeshan; Xu, Zhen; Gudala, Manojkumar; Yan, Bicheng; Sun, Shuyu (SPE, 2023-01-24) [Conference Paper]
    Naturally fractured reservoirs (NFRs), such as fractured carbonate reservoirs, are ubiquitous across the worldwide and are potentially very good source to store carbondioxide (CO2) for a longer period of time. The simulation models are great tool to assess the potential and understanding the physics behind CO2-brine interaction in subsurface reservoirs. Simulating the behavior of fluid flow in NFR reservoirs during CO2 are computationally expensive because of the multiple reasons such as highly-fractured and heterogeneous nature of the rock, fast propagation of CO2 plume in the fracture network, and high capillary contrast between matrix and fractures. This paper presents a data-driven deep learning surrogate modeling approach that can accurately and efficiently capture the temporal-spatial dynamics of CO2 saturation plumes during injection and post-injection monitoring periods of Geological Carbon Sequestration (GCS) operations in NFRs. We have built a physics-based numerical simulation model to simulate the process of CO2 injection in a naturally fractured deep saline aquifers. A standalone package was developed to couple the discrete fracture network in a fully compositional numerical simulation model. Then reservoir model was sampled using the Latin-Hypercube approach to account for a wide range of petrophysical, geological, reservoir, and operational parameters. The simulation model parameters were obtained from extensive geological surveys published in literature. These samples generated a massive physics-informed database (about 900 simulations) that provides sufficient training dataset for the Deep Learning surrogate models. Average Absolute Percentage Error (AAPE) and coefficient of determination (R2) were used as error metrics to evaluate the performance of the surrogate models. The developed workflow showed superior performance by giving AAPE less than 5% and R2 more than 0.95 between ground truth and predictions of the state variables. The proposed Deep Learning framework provides an innovative approach to track CO2 plume in a fractured carbonate reservoir and can be used as a quick assessment tool to evaluate the long term feasibility of CO2 movement in fractured carbonate medium.
  • Molecular Simulation Study of Montmorillonite in Contact with Ethanol

    Cui, Ronghao; Nair, Arun Kumar Narayanan; Yang, Yafan; Sun, Shuyu (Industrial & Engineering Chemistry Research, American Chemical Society (ACS), 2023-01-24) [Article]
    Molecular simulations were performed to explore the adsorption and transport mechanism of ethanol and ions in Na– and Ca–montmorillonite clays. Our results show that the uptake of ethanol by montmorillonite increases with increasing relative pressure (RP)/basal d-spacing, consistent with experimental observations. The basal d-spacing of montmorillonite grows in the presence of ethanol to about 13.0 Å with a monolayer arrangement of ethanol (1L). Further uptake of ethanol allows the basal d-spacing to grow to about 16.5 Å with a bilayer arrangement of ethanol (2L). For a given solvation state, the amount of ethanol uptake is almost independent of RP and the type of the counterion. The stable basal d-spacings of the montmorillonite + ethanol system are larger than those of the montmorillonite + water system. Also, the swelling transitions are relatively shifted to higher RP values in the montmorillonite + ethanol system. This may be because the clay has a weaker affinity for the less polar ethanol molecules as compared with water. The mobility of ethanol and ions in the interlayers increases with increasing RP due to the associated swelling of montmorillonite. For a given solvation state, the mobility of these species is almost unaffected by changes in RP, as in the case of adsorption. The mobility of ethanol and ions in the 1L and 2L states is about 3 orders of magnitude lower than that in the bulk. The species mobility in the montmorillonite + ethanol system is generally much lower than those in the montmorillonite + water system. This may be attributed to the higher steric hindrance in the alcohol molecules. However, the mobility of the Ca2+ ion in the 1L state is almost similar in both the montmorillonite + ethanol and the montmorillonite + water systems. This is possibly due to the stronger Ca2+–clay interactions in the 1L state.
  • Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics

    Zhang, Yuze; Yang, Xuguang; Zhang, Lei; Li, Yiteng; Zhang, Tao; Sun, Shuyu (Journal of Computational Physics, Elsevier BV, 2023-01-14) [Article]
    With the increasingly accurate modeling and simulation demands and techniques, obtaining the knowledge of the multi-component phase equilibrium states holds the bottleneck challenge in the study of multi-phase fluid flow. In order to resolve the shortages in computational efficiency and stability in the conventional iterative flash calculation, a new phase equilibrium prediction method is proposed by solving the saddle point of the multi-phase system. In this paper, the HiSD (High order saddle point dynamic) algorithm is used for the first time to calculate the saddle points on the energy landscape of the two-phase two-component NVT flash model based on the Peng-Robinson equation of state, and the up-down search algorithm of HiSD is applied to generate the solution landscape of the flash system. The Rosenbrock-Euler ETD (exponential time differencing) format is involved to reduce the interference of system rigidity to the calculation. It can be referred from the numerical analysis that there are at most the 1st-order saddle points in the energy landscape of the two-component two-phase NVT flash system, and all these saddle points are located on one straight line of the hyperplane, where the energy is equal everywhere. All these 1st-order saddle points can converge to the same or equivalent local minima, which indicates that the two-component two-phase flash system is a system with only one single solution with physical meanings. In addition, the saddle points also obey a linear relationship and the energy remains the same at different temperatures. Therefore, using the method proposed in this paper, the conventional two-step efforts of phase stability test and phase separation calculation can be simplified. The 1st-order saddle points of the system can be directly calculated, reducing the need for an initial guess. The local minima can be directly searched through the downward direction of the saddle point, which greatly reduces the calculation amount of phase equilibrium calculations. Furthermore, the minimum states at different temperatures can be calculated in batch by using one certain initial value, which significantly improves the adaptability and reliability for complex engineering problems with drastic temperature changes.
  • A fast method to infer Nuclear Magnetic Resonance based effective porosity in carbonate rocks using machine learning techniques

    Tariq, Zeeshan; Gudala, Manojkumar; Yan, Bicheng; Sun, Shuyu; Mahmoud, Mohamad (Geoenergy Science and Engineering, Elsevier BV, 2023-01-11) [Article]
    A better estimation of the effective porosity of the reservoir rock is a critical task for petrophysicist and well logs analyst. A majority of the current approaches to estimate the effective porosity of the reservoir rocks from well logs are based on the information of the Density-Neutron logs. These approaches usually resulted in the inaccurate estimation of the rock porosity particularly in the naturally fractured carbonates or dolomite rocks. The Nuclear Magnetic Resonance (NMR) based effective porosity is independent of the rock matrix and mineralogy, on contrary it depends on the number of hydrogen nuclei in the pore spaces of the rock. In this study, we have used six machine learning (ML) techniques to predict the NMR based effective porosity in carbonate rocks. The ML models to predict the effective porosity includes deep neural networks (DNN), random forest regressor (RF), decision trees (DT), K-Nearest Neighbors algorithm (KNN), extreme gradient boosting (XGB), and adaptive gradient boosting (AdaBoost). These models were trained on the geophysical well logs such as Gamma ray log (GR), caliper log (Cali), neutron porosity log (NPHI), photoelectric factor log (PE), and bulk density log (RHOB). A total of 4002 data points were obtained from the five wells located in the carbonate field. The tuning of ML models hyperparameters were conducted using a ‘GridSearchCv’ method. Furthermore, the K-fold cross-validation criterion was implemented to improve the accuracy of the ML models. The ML models performances were evaluated using multiple graphical and goodness of fit tests including prediction cross-plots, average absolute percentage error (AAPE), root means square error (RMSE), and coefficient of determination (R) methods. The prediction results showed that the DNN, RF, and XGB models performed better than the other implemented ML techniques. These methods resulted in a significantly low error and high (R). The achieved accuracy was above 85% when validated on a blind dataset. This study also offered an empirical model that can be used to quickly estimate the NMR based effective porosity using afore-mentioned well logs. The model can also be used as a standalone package that can be coupled with any logging software for quick evaluation of NMR based effective porosity.
  • Molecular Perspectives of Interfacial Properties in the Water+Hydrogen System in Contact with Silica or Kerogen

    Yang, Yafan; Nair, Arun Kumar Narayanan; Zhu, Weiwei; Sang, Shuxun; Sun, Shuyu (arXiv, 2022-12-27) [Preprint]
    Interfacial behaviours in multiphase systems containing H2 are crucial to underground H2 storage but are not well understood. Molecular dynamics simulations were conducted to study interfacial properties of the H2O+H2 and H2O+H2+silica/kerogen systems over a wide range of temperatures (298 - 523 K) and pressures (1 - 160 MPa). The combination of the H2 model with the INTERFACE force field and TIP4P/2005 H2O model can accurately predict the interfacial tensions (IFTs) from the experiment. The IFTs from simulations are also in good agreement with those from the density gradient theory coupled to the PC-SAFT equation of state. Generally, the IFTs decrease with pressure and temperature. However, at relatively high temperatures and pressures, the IFTs increase with pressure. The opposite pressure effect on IFTs can be explained by the inversion of the sign of the relative adsorption of H2. The enrichment of H2 in the interfacial regions was observed in density profiles. Meanwhile, the behaviours of contact angles (CAs) in the H2O+H2+silica system are noticeably different from those in the H2O+H2+kerogen system. The H2O CAs for the H2O+H2+silica and H2O+H2+kerogen systems increase with pressure and decrease with temperature. However, the effect of temperature and pressure on these CAs is less pronounced for the H2O+H2+silica system at low temperatures. The behaviours of CAs were understood based on the variations of IFTs in the H2O+H2 system (fluid-fluid interaction) and adhesion tensions (fluid-solid interaction). Furthermore, the analysis of the atomic density profiles shows that the presence of H2 in between the H2O droplet and the silica/kerogen surface is almost negligible. Nevertheless, the adsorption of H2O on the silica surface outside the H2O droplet is strong, while less H2O adsorption is seen on the kerogen surface.
  • Physics-Informed Machine Learning for Reservoir Management of Enhanced Geothermal Systems

    Yan, Bicheng; Xu, Zhen; Gudala, Manojkumar; Tariq, Zeeshan; Sun, Shuyu; Finkbeiner, Thomas (Elsevier BV, 2022-12-20) [Preprint]
    With the energy demand arising globally, geothermal recovery by Enhanced Geothermal Systems (EGS) becomes a promising option to bring sustainable energy supply along with mitigating CO2 emission. However, reservoir management of EGS primarily relies on reservoir simulation, which is quite expensive due to the reservoir heterogeneity, the interaction of matrix and fractures, and the intrinsic multi-physics coupled nature. Therefore, a robust optimization framework is critical for the management of EGS.We develop a general Physics-Informed Machine Learning (PIML) framework for reservoir management with multiple optimization options. A robust forward surrogate model fl is developed based on a convolutional neural network, and it successfully learns the nonlinear relationship between input reservoir model parameters (e.g., fracture permeability field) and interested state variables (e.g., temperature field and produced fluid temperature). fl is trained using simulation data from the EGS coupled thermal-hydro simulation model by sampling reservoir model parameters. As fl is accurate, efficient and fully differentiable, EGS thermal efficiency can be optimized following two schemes: (1) training a control network fc to map reservoir geological parameters to reservoir decision parameters by coupling it with fl; (2) directly optimizing the reservoir decision parameters based on coupling the existing optimizers with fl.We evaluate the impact of reservoir model parameters on the thermal recovery based on simulation datasets through sensitivity analyses, and demonstrated that injection mass rate dominates thermal recovery. Further, the forward model fl performs accurate and stable predictions of evolving temperature fields (relative error 1.27+-0.89%) in EGS and the time series of produced fluid temperature (relative error 0.26+-0.46%), and its speedup to the counterpart high-fidelity simulator is 4564 times. When optimizing with fc, we achieve thermal recovery with a reasonable accuracy but significantly low CPU time during inference, 0.11 seconds/task. When optimizing with Adam optimizer, we achieve the objective perfectly with relatively high CPU time, 4.58 seconds/task. This is because the former optimization scheme requires a training stage for fc but its inference is non-iterative, while the latter scheme requires an iterative inference without training. We also investigate the option to use fc inference as an initial guess for Adam optimizer, which decreases Adam’s CPU time but achieves excellent convergence in the objective function. This is the highest recommended option among the three evaluated. The efficiency, scalability and accuracy observed in our reservoir management framework makes it highly applicable to near real-time reservoir management in EGS as well as other similar system management processes.
  • Interfacial behaviors of the H2O+CO2+CH4+C10H22 system in three phase equilibrium: A combined molecular dynamics simulation and density gradient theory investigation

    Yang, Yafan; Ruslan, Mohd Fuad Anwari Che; Zhu, Weiwei; Zhao, Guangsi; Sun, Shuyu (JOURNAL OF MOLECULAR LIQUIDS, Elsevier BV, 2022-12-16) [Article]
    The interfacial behaviors in H2O+gas+oil 3-phase systems are critical for CO2 near-miscible/immiscible flooding and sequestration processes but require further investigation. In this article, molecular dynamics (MD) simulation and density gradient theory (DGT) with PC-SAFT equation of state were simultaneously conducted to study the interfacial behaviors in the H2O+CO2+C10H22 3-phase system and the effect of impurity gas CH4 on the interfacial properties at different temperatures (323–423 K) and pressures (up to around 16 MPa). We found reasonable agreement between the estimations from MD and DGT. When the H2O+CO2+C10H22 3-phase system is in contact with CH4, the interfacial tensions (IFTs) of all three interfaces increase. The increment of IFT is pronounced at low temperatures and high pressures. Remarkably, CH4 molecules accumulate in all three interfaces. However, the positive surface excesses of CH4 are smaller than those of CO2, which may explain the increment of IFT. Moreover, the spreading coefficients S in the H2O+CO2+C10H22 3-phase system are negative indicating the existence of 3-phase contact. The behaviors of S in the H2O+CO2+CH4+C10H22 3-phase system are similar to those in the system without CH4. Nevertheless, the effect of temperature on S is little due to the changes of IFT caused by CH4. These insights could help to enhance the understanding of the effects of impurities on CO2 enhanced oil recovery methods under geological conditions.
  • Fully Connected Neural Network Model for Fractured Geothermal Reservoir using Supercritical-CO2 as Geofluid with THM Model

    Gudala, Manojkumar; Tariq, Zeeshan; Govindarajan, Suresh Kumar; Xu, Zhen; Yan, Bicheng; Sun, Shuyu (Elsevier BV, 2022-12-15) [Preprint]
    In the present work, a thermo-hydro-mechanical (THM) model was utilized to examine the behaviour of fractured geothermal reservoir with supercritical-CO2 (SCCO2) as geofluid. The impact of natural fractures, orientation, and their interaction with hydraulic fractures on the extraction of heat and extension of injection fluid is examined. The development of thermal strain occupied regions were recognized significantly in the vicinity of fracture and injection well. The comparison between water-enhanced geothermal system (EGS) and SCCO2-EGS on the production temperature, thermal strain, and mechanical strain are performed. Injection temperature, injection/production (inj/prod) velocity, aperture of hydraulic fracture (HF), and HF length in a fractured geothermal reservoir are considered as primary control parameters and used as the inputs for the hybrid neural networks and time series models to predict the temperature at the production well. The fully connected neural network (FCN) model shows better predictions based on the loss functions. A mathematical equation is developed using the FCN model to predict the production temperature. Thus, the proposed system of numerical investigations with integrated FCN model could be a benefit in studying the temporal behavior of production temperature.

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