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At least 19 records

On the feasibility of using physics-informed machine learning for underground reservoir pressure management

In this work, we evaluate the feasibility of using physics-informed machine learning (PIML) for underground energy-related pressure management. To this end, we develop a PIML framework to manage underground reservoir pressures by training neural networks to determine fluid extraction rates for dedicated extraction wells during fluid injection operations given a range of reservoir conditions (e.g., transmissivity and storativity). We implement an automatically-differentiable analytical physics model of fluid flow in porous media within the PIML framework as a proxy for more complicated models. This allows us to execute a sufficient number of training scenarios to fully evaluate the feasibility of using PIML to support pressure management activities. We quantify the number of physics-model parameters required for automatic differentiation to become more efficient than finite-difference gradient calculations. We use a simple scenario with a single injector, extractor, and critical location for our feasibility analysis. We evaluate the effect of the size of the training dataset (i.e., the number of reservoir condition samples) on the accuracy and efficiency of the PIML framework. For an equivalent number of model evaluations, the larger training dataset took less time to train and produced a neural network that was able to more accurately manage reservoir pressures. We also evaluate the effect of the training dataset batch size (i.e., number of reservoir condition samples used to update the neural network coefficients during training; i.e., how the training dataset is partitioned). While training ran faster with larger batch sizes, they produced neural networks that managed pressures less accurately. We demonstrate the approach on a more complex scenario involving 10 injectors, 10 extractors, and 4 critical locations (a relatively high well density of 20 wells/km2). We provide the number of forward and adjoint model evaluations required in each case as an indication of the feasibility of using PIML for pressure management when more complicated physics models with longer execution times are used.

54 ENVIRONMENTAL SCIENCES↗

Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management

Abstract Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO $$_2$$ 2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO $$_2$$ 2 fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir simulators. To tackle this, we use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization at critical reservoir locations. We use DPFEHM framework, which has trustworthy physics based on the standard two-point flux finite volume discretization and is also automatically differentiable like machine learning models. Our physics-informed machine learning framework uses convolutional neural networks to learn an appropriate extraction rate based on the permeability field. We also perform a hyperparameter search to improve the model’s accuracy. Training and testing scenarios are executed to evaluate the feasibility of using physics-informed machine learning to manage reservoir pressures. We constructed and tested a sufficiently accurate simulator that is 400 000 times faster than the underlying physics-based simulator, allowing for near real-time analysis and robust uncertainty quantification.

54 ENVIRONMENTAL SCIENCES↗

Quantifying the effects of pressure management for the Williston basin Brine Extraction and Storage Test (BEST) site using machine learning

Active reservoir management (ARM) through brine extraction can reduce pressure buildup during large-scale implementation of carbon capture and storage (CCS) projects. This study used machine learning (ML)-assisted approaches to analyze bottomhole pressure (BHP) responses to various brine injection and extraction scenarios. Field monitoring data were collected over a 2-year operation period at two injection wells and one extraction well (about 400 meters away) as part of a Brine Extraction and Storage Test (BEST) in the North Dakota portion of the Williston Basin. Injection activities increased the BHPs at the injection wells by around 0.70 MPa (~100 psi) during the operation period. Extraction activities demonstrated the capability to decrease the BHPs at the injection wells by approximately 0.21–0.34 MPa (30–50 psi) depending on the ratio of the extraction and injection well flow rates (the “extraction ratio” – a normalization procedure used in the analysis). The pressure reduction provided by the extraction well equated to 30%–50% of the pressure buildup at the injection well. Furthermore, this work shows how ML analytics can play a key role in estimating reservoir pressure responses for complex injection and extraction activities during pressure management practices of CCS projects.

58 GEOSCIENCES↗

Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management

Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations – compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.

25 ENERGY STORAGE↗

Managing Subsurface Pressure Buildup and Interference in Commercial-Scale CO 2 Storage Project with Proximal Injection Wells

Large-scale decarbonization using carbon capture and storage (CCS) is likely to involve many commercial-scale CO 2 storage projects located in close proximity to each other. This close proximity raises concerns over pressure interference among the storage projects. Pressure interference between injection and storage efforts can reduce the practicable CO 2 storage resource and force wells to inject CO 2 at a lower rate to avoid the fracture pressure thresholds per United States Environmental Protection Agency (EPA) Class VI well regulations to preserve injection and confining zone integrity and potentially mitigate against inducing seismic activity. These analyses employ numerical full-physics reservoir modeling to evaluate how pressure buildup fronts and CO 2 plumes evolve under commercial-scale injection volumes of CO 2 in which multiple storage sites located in close proximity occur in tandem. The simulation models mimic injection at pseudo basin-scale and assume homogeneous saline formation(s) as storage targets with a pair of upper and lower homogeneous seal layer/s. These analyses specifically investigate the efficacy of two basin-wide reservoir pressure management strategies in addressing the technical challenges associated with pressure buildup and CO 2 plume commingling. The strategies explored include: 1) enlarging the area of injection well spacing (WS) and 2) storing CO 2 in a stacked sequence (SSS) of saline formations compared to a single formation. The storage and confining zones properties assumed were held common across the scenarios, unless specified otherwise. Analyses results show that after injecting 4 million tons per year for 30 years using 4 separate wells (each injecting 1 million metric tons per year), the radius of CO 2 plume extends to a mere 3 km or less from injection wells. Meanwhile, the radius of pressure buildup ranges on the order of tens to a few hundreds of kilometers, depending on the magnitude of pressure buildup threshold that one would use to define the front. CO 2 plume commingling from different injection wells appears to occur 50 years post-injection, especially under scenarios with narrowly spaced (i.e., < 5 km apart) injection well locations. Findings from sensitivity cases on the well spacing suggest that storage formations modeled would require different well spacing to avoid fracture pressure thresholds. For instance, modeled storage formations with high fracture gradients (i.e., 0.8 psi/ft) would need less than 5–km well spacing, whereas those with lower fracture gradients (i.e., 0.7 psi/ft) would need approximately 20–km well spacing, based on assumed modeling parameters. Under stacked injection, the pressure challenges (described above) still exist but are more alleviated due to distributing the same injection volume across more available reservoir volume. These analyses demonstrate that stacked-sequence storage can effectively address the challenges, while still providing the same target CO 2 storage volumes and allowing a large number of storage projects to be deployed in the same basin by better utilizing the available storage resource across different reservoir depths. Among cases modeled, the resulting pressure buildup front is most suppressed when each storage project distributes injection volumes over several wells, each of which injects a portion of the total CO 2 across the stacked sequence. This strategy results in the smallest CO 2 aerial footprint amongst scenarios evaluated but also shows the largest reduction in the pressure buildup at the top of perforation at the injection wells (upwards of approximately 42 percent compared to the commercial-scale single-formation storage), the result of which is crucial to maintain caprock integrity. The findings presented by this research draw attention to the importance of greater coordination among storage operators and regulatory stakeholders to foster the upscaling and deployment of CCS. These analyses provide insights into required decision-making when considering multi-project deployment in a shared basin. Because these analyses evaluate a very specific geologic situation, they bear further investigations across other geologic situations.

42 ENGINEERING↗

Mechanistic Approach to Analyzing and Improving Unconventional Hydrocarbon Production [Slides]

DOE research is developing the physical basis and tools needed to manage pressure effectively to increase recovery efficiency. By coupling fast, accurate physics with machine learning, DOE is producing science-based platforms any operator can use. DOE’s research portfolio is targeting hydrocarbon transport at multiple scales, with the goal of increasing recovery efficiency. DOE’s research has led to new, fast & accurate platforms for predicting gas production from fractured shales. Using data from the MSEEL-I site to calibrate our physics-based model, we have early results on pressure management. We have shown that both mechanical and chemical processes in the matrix can negatively impact production.

08 HYDROGEN↗

Phase II Field Demonstration at Lansing Smith Generating Plant, Southport, Florida (Final Report)

The Final Technical Report: Field Test Design and Pressure Management Strategies for Phase II Field Demonstration of Optimal Pressure Control, Plume Management, and Produced Water Strategies presents the culmination of multi-year efforts under the U.S. Department of Energy’s Brine Extraction and Storage Test (BEST) program, led by EPRI in partnership with Gulf Power at the Plant Smith site near Panama City, Florida. The project was designed to evaluate and demonstrate the technical feasibility of managing subsurface pressures and fluid movement associated with large-scale CO₂ injection, using low-salinity water as a proxy fluid. Through a combination of field injection testing, reservoir modeling, and optimization studies, the research team developed and refined active and passive brine extraction strategies aimed at controlling injection-induced pressure buildup, mitigating risks of fault activation, and managing plume migration. The field demonstration incorporated a new injection well (TIW-2), a new monitoring/extraction well (TEMW-A), and an existing well (TIW-1) repurposed for passive pressure relief. Complementary geophysical monitoring was designed to track plume development and evaluate the effectiveness of pressure management strategies. The report details the integrated workflow encompassing wellfield development, regulatory permitting, model calibration, and survey design. It includes a comprehensive electromagnetic (EM) modeling and inversion study used to develop a cost-effective, time-lapse geophysical monitoring plan capable of imaging the evolving low-salinity plume within the highly saline Lower Tuscaloosa formation. Reservoir simulation results guided the design of the 17-month injection program and the timing of active extraction to maintain formation pressures below a hypothetical fault reactivation threshold. Supporting analyses evaluated potential injectivity risks related to clay fines migration and geochemical incompatibility, identifying practical mitigation measures such as salinity and pH control. The final design recommends a series of crosswell EM surveys—conducted before, during, and after injection—as the most effective and economical approach for plume imaging, supplemented by continuous downhole pressure and flow monitoring. Collectively, the study provides a field-ready framework for cost-effective pressure management and monitoring in support of future CO₂ storage projects.

01 COAL, LIGNITE, AND PEAT↗

Comparative Study of Commercial-Scale CO2 Storage Options in Single and Stacked Saline Formations in Managing Reservoir Pressure Buildup

Presentation at American Association of Petroleum Geologists (AAPG) Carbon, Capture, Utilization, and Storage (CCUS) held in Houston, Texas, April 25–27, 2023. The presentation emphasizes the importance of coordination among CO2 storage projects as CCUS deployment needs to be scaled up. The presentation focuses on findings from reservoir simulation studies in which different configurations of injection zones (a single saline formation and a stacked sequence of saline formations) are targeted for CO2 storage to accommodate the amplified storage volume needed while managing reservoir pressure buildup and interference induced by multi-well injection operations.

Wijaya, Nur↗

Challenges of designing, operating, and managing brine extraction at a carbon dioxide storage site

Developing and deploying commercial-scale carbon dioxide (CO 2 ) storage at a site requires operational strategies to manage pressure and CO 2 plume distribution. In the natural gas storage and oil and gas industries, fluid extraction has been successfully implemented as a strategy to manage pressure and control fluid distribution (i.e., hydrocarbon recovery and natural gas storage efficiency, respectively). The technical challenges of integrating brine extraction at CO 2 storage sites are expected to be similar, if not identical, to those in the natural gas storage and petroleum industries. Major technical challenges of using brine extraction to manage storage in a storage unit include (1) designing and completing the brine extraction wells, (2) locating the brine extraction well, (3) assessing the efficacy of brine extraction, and (4) handling the extracted brine. The design and completion of the brine extraction well include the well type (i.e., vertical or horizontal) and perforated interval. The location of the well is influenced by the timing of extraction operations (i.e., prior or after CO 2 injection starts) and project objectives (i.e., desired directional movement of the CO 2 plume and avoid or minimize CO 2 extraction). The efficacy of brine extraction requires a baseline projection of the pressure and CO 2 plume distribution. Options for handling extracted brine include subsurface disposal, surface disposal, and industrial use. Here this paper addresses means of overcoming technical challenges that may likely be encountered before or after CO 2 injection starts.

25 ENERGY STORAGE↗

Dynamic modeling studies of basin-scale pressure interference and CO 2 plume evolution in multi-well geologic CO 2 storage

This research employs numerical modeling to analyze how CO 2 plumes and pressure fronts evolve when CO 2 is injected into a single storage formation from multiple projects located in proximity. Here, this analysis also evaluates the extent to which injection well spacing alleviates pressure buildup in the absence of active pressure management tactics. The simulation approach was based on a single, homogenous saline aquifer in which CO 2 injection occurs under a one-injector baseline case and several multi-well cases where well spacing varies. Analysis results show that the extent of pressure buildup is in the range of tens or a few hundreds of kilometers and contingent upon the defining pressure buildup demarcating the front edge. For the geological setting evaluated in this paper, our analysis suggests that without active basin pressure management strategies, commercial-scale projects would likely need to be sited far apart to avoid pressure interference from one another. Analysis results show the radius of CO 2 plume varies approximately from 2 to 3 km from injection wells (each injecting 1 Mt/year for 30 years) depending on cases and modeling parameters assumed. Given the pressure interference, this paper thus draws attention to the importance of greater coordination among storage operators and regulatory stakeholders. Because this analysis assumes a very specific geologic setting, this exploratory analysis bears further investigations across other geologic scenarios.

42 ENGINEERING↗

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗

Predictive valve control system

A pressure control system may include a plurality of inflatable objects, each of the inflatable objects having a respective pressure sensor and a respective inflation valve, wherein each of the inflation valves has a behavior profile predictive of an amount of current used by the valve when operated. A valve controller of the system may have a pressure management circuit that receives information from the pressure sensors and is configured to automatically maintain a respective selected pressure in each of the inflatable objects by issuing commands to operate the inflation valves. An electrical current management circuit of the valve controller may be configured to predict, based on the valve behavior profiles, what effect the command would have on a total current usage, when executed, and automatically prevent any command that would cause the total current usage to exceed a maximum allowable current.

Piraner, Alexander↗

Prediction and uncertainty quantification of shale well performance using multifidelity Monte Carlo

Uncertainty quantification is an integral component of reservoir management, especially considering the inherent uncertainty in subsurface systems. While a standard practice to estimate the uncertainty, Monte Carlo (MC) simulation is computationally intense when the sampling population comprises high-fidelity simulations. Alternatively, the Multi-fidelity Monte Carlo (MFMC) simulation overcomes this computational intensity by integrating low- and high-fidelity simulations. Our goal is to minimize the number of expensive high-fidelity simulations while maintaining accuracy and using numerous fast and cheap low-fidelity simulations to efficiently sample to input parameter space of interest. We selected gas production from unconventional wells to demonstrate the potential speedups and accuracy of the MFMC approach. The model fidelity usually determines the trade-off between accuracy and efficiency. While the high-fidelity model is more accurate, the low-fidelity model is more efficient. Our high-fidelity simulation includes reservoir simulations of a hydraulically fractured well. On the other hand, our low-fidelity model comprises the parallel-plate flow model. We used differential programming to efficiently solve the 1D flow model, where automatic differentiation is used to efficiently compute the gradients. We matched the production profile of high-fidelity simulations with our low-fidelity simulations. Then, we used a support vector regression to map the high- and low-fidelity input parameters. The mapping function is essential to tune the low-dimensional parameter space of the low-fidelity model to the high-dimensional parameter space of the high-fidelity model. We found that we can use a combination of 9 high fidelity and 10,000 low fidelity simulations to efficiently and accurately simulate pressure management. This method is at least two orders of magnitude faster than only using high-fidelity simulations. Finally, from a broader perspective, MFMC could efficiently estimate the uncertainty of various systems and models, integrating low- and high-fidelity models.

04 OIL SHALES AND TAR SANDS↗

Basin Management of Geologic CO2 Storage: Effect of Well Spacing on CO2 Plume and Pressure Interference

This is the conference paper accompanying an oral presentation made at the Society of Petroleum Engineers (SPE) Western Regional Meeting (WRM) held in Bakersfield, California, April 26–28, 2022. The paper provides the results of a basin-scale CO2 storage modeling project investigating subsurface pressure interference among CO2 injection wells located in proximity to each other.

Wijaya, Nur↗

The relationship between stress, anxiety and eating behavior among Chinese students: a cross-sectional study

Background The expansion of higher education and the growing number of college students have led to increased awareness of mental health issues such as stress, anxiety, and eating disorders. In China, the educational system and cultural expectations contribute to the stress experienced by college students. This study aims to clarify the role of anxiety as a mediator in the relationship between stress and eating behaviors among Chinese college students. Methods This study utilized data from the 2021 Psychology and Behavior Investigation of Chinese Residents, which included 1,672 college students under the age of 25. The analysis methods comprised descriptive statistics, t -tests, Pearson correlation analyses, and mediation effect analysis. Results The findings indicate that Chinese college students experience high levels of stress, with long-term stress slightly exceeding short-term stress. Both types of stress were positively correlated with increased anxiety and the adoption of unhealthy eating behaviors. Anxiety was identified as a significant mediator, accounting for 28.3% of the relationship between long-term stress and eating behavior (95% CI = 0.058–0.183). The mediation effect of short-term stress on eating behavior through anxiety was also significant, explaining 61.4% of the total effect (95% CI = 0.185–0.327). Conclusion The study underscores the importance of stress management and mental health services for college students. It recommends a comprehensive approach to reducing external pressures, managing anxiety, and promoting healthy eating behaviors among college students. Suggestions include expanding employment opportunities, providing career guidance, enhancing campus and societal support for holistic development, strengthening mental health services, leveraging artificial intelligence technologies, educating on healthy lifestyles, and implementing targeted health promotion programs.

Chai, Yulin↗

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗

Cyclic Injection Leads to Larger and More Frequent Induced Earthquakes under Volume-Controlled Conditions

As carbon storage technologies advance globally, methods to understand and mitigate induced earthquakes become increasingly important. Although the physical processes that relate increased subsurface pore pressure changes to induced earthquakes have long been known, reliable methods to forecast and control induced seismic sequences remain elusive. Suggested reservoir engineering scenarios for mitigating induced earthquakes typically involve modulation of the injection rate. Some operators have implemented periodic shutdowns (i.e., effective cycling of injection rates) to allow reservoir pressures to equilibrate (e.g., Paradox Valley) or shut-in wells after the occurrence of an event of concern (e.g., Basel, Switzerland). Other proposed scenarios include altering injection rates, actively managing pressures through coproduction of fluids, and preinjection brine extraction. Here, in this work, we use 3D physics-based earthquake simulations to understand the effects of different injection scenarios on induced earthquake rates, maximum event magnitudes, and postinjection seismicity. For comparability, the modeled injection considers the same cumulative volume over the project’s operational life but varies the schedule and rates of fluid injected. Simulation results show that cyclic injection leads to more frequent and larger events than constant injection. Furthermore, with intermittent injection scenario, a significant number of events are shown to occur during pauses in injection, and the seismicity rate remains elevated for longer into the postinjection phase compared to the constant injection scenario.

58 GEOSCIENCES↗

Supplementary Data for "Evaluation of the Economic Implications of Varied Pressure Drawdown Strategies Generated Using a Real-time, Rapid Predictive, Multi-fidelity Model for Unconventional Oil and Gas Wells" by Bello, K., Vikara, D., Sheriff, A., Viswanathan, H., Carr, T., Sweeney, M., O'Malley, D., Marquis, M., Vactor, R.T., and Cunha, L.

The Bello et al. study evaluates the impact of contrasting pressure drawdown on gas productivity and the resulting economics of a well in the Marcellus Shale of the Appalachian Basin. This research applies a techno-economic analysis approach to help identify potential ways pressure management strategies can be used to improve cumulative recovery of hydraulically fractured horizontal wells while maintaining project profitability. Gas production forecast outlook scenarios of the Marcellus Shale Energy and Environment Laboratory Laboratory's MIP-3H well were generated under varying pressure drawdowns using two approaches: 1) a novel physics-informed machine learning (PIML) workflow and 2) via traditional reservoir simulation in Computer Modeling Group’s (CMG) GEM Compositional & Unconventional Simulator. Cash flow and other economic metrics of interest were compiled on the production outlook using the U.S. Department of Energy's (DOE) National Energy Technology Laboratory (NETL) Unconventional Shale Well Economic Model (UShWEM).The sheets within this Microsoft ExcelTM workbook provide the economic metric outputs for the baseline condition and the one-at-a-time (OAT) sensitivity analysis of UShWEM's input parameters for each of the production scenarios evaluated.

Fracture Network Model↗