Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management (2026) — Harun Ur Rashid, Aleksandra Pachalieva, Daniel O’Malley — Scientific ReportsAbstract
Abstract 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.
Physics‐Informed Reservoir Characterization From Bulk and Extreme Pressure Events With a Differentiable Simulator (2026) — Harun Ur Rashid et al. — Journal of Geophysical Research: Machine Learning and ComputationAbstract
Abstract Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and , , and wastewater injection operations. This challenge becomes especially acute in extreme pressure events, which are rarely observed but can strongly affect operational risk. Traditional history matching and inversion techniques rely on expensive full‐physics simulations, making it infeasible to handle uncertainty and extreme events at scale. Purely data‐driven models often struggle to maintain physics consistency when dealing with sparse observations, complex geology, and extreme events. To overcome these limitations, we introduce a physics‐informed machine learning method that embeds a differentiable subsurface flow simulator directly into neural network training. The network infers heterogeneous permeability fields from limited pressure observations, while training minimizes both permeability and pressure losses through the simulator, enforcing physical consistency. Because the simulator is used only during training, inference remains fast once the model is learned. In an initial test, the proposed method reduces the pressure inference error by half compared with a purely data‐driven approach. We then extend the test over eight distinct data scenarios, and in every case, our method produces significantly lower pressure inference errors than the purely data‐driven model. We also evaluate our method on extreme events, which represent high‐consequence data in the tail of the sample distribution. Similar to the bulk distribution, the physics‐informed model maintains higher pressure inference accuracy in the extreme event regimes. Overall, the proposed method enables rapid, physics‐consistent subsurface inversion for real‐time reservoir characterization and risk‐aware decision‐making.
A Continuous Projection-Based EDFM Model for Flow in Fractured Reservoirs (2024) — Harun U. Rashid, Olufemi Olorode — SPE JournalAbstract
Summary Various researchers have evaluated different methods of modeling fractured reservoirs accurately and efficiently. Of these methods, the embedded discrete fracture model (EDFM) is one of the most popular because it does not require the mesh for the simulation domain to conform to the orientation of the natural fractures. However, it is limited because it cannot accurately model low-conductivity fractures. Although the projection-based EDFM (pEDFM) was developed to address this limitation of the EDFM, recent studies show that pEDFM still cannot accurately model low-conductivity fractures that are neither parallel to the simulation grid nor cutting through the matrix cell diagonals. In these cases, it has been observed that reservoir fluids can flow around low- or even zero-conductivity fractures. This paper presents a rigorous analysis, which reveals that the error when modeling inclined low-conductivity fractures with pEDFM is because the projections of the fracture on the gridblock faces are discontinuous. This discontinuity implies that the matrix cell interfaces along the path of the fractures only project a fraction of the fracture area on these interfaces in each direction. So, none of these faces captures the sealing potential of these interfaces, and the pore fluid can flow around even zero-conductivity fractures. We present a robust algorithm that ensures that the projections of inclined fractures on cell faces are continuous in 3D. We refer to the model based on this algorithm as the continuous projection-based EDFM (CPEDFM) and show that it directly solves the pEDFM limitation. We present the simulation of several cases and their selected projection faces to demonstrate why CPEDFM works. We also verify the CPEDFM method by comparing the CPEDFM and pEDFM model results to high-resolution simulation results. To demonstrate the feasibility of modeling complex, realistic systems using CPEDFM, we simulate a 3D compositional Eagle Ford shale reservoir with 75 low-conductivity and 75 high-conductivity fractures. The results show that pEDFM overestimates production because it does not fully account for the sealing effects of inclined low-conductivity fractures. In conclusion, this paper presents a novel numerical model for accurately and efficiently simulating reservoirs containing fractures of arbitrary conductivity, size, and orientation in 3D.
Numerical and Experimental Studies of Coupled THM Processes in Fractured Tight Rocks (2023) — A. Abdullah, H. U. Rashid, O. M. Olorode — 57th U.S. Rock Mechanics/Geomechanics SymposiumAbstract
ABSTRACT Several researchers address the question of the validity of coupled thermal, hydraulics, and mechanical (THM) simulation results by comparing them to published experimental data. However, the initial and boundary conditions of these experimental studies are typically not fully understood by the users of these results, leading to misleading assumptions in the simulation models. To address these gaps in the study of THM processes, we present an experimental and high-resolution, fully dimensional numerical study of THM processes in tight rocks with stochastic fractures in 3D. The idea is to provide experimental data and reference solutions for subsequent work on multiscale fracture modeling in tight rocks. The performance of these studies at high pressures, temperatures, and stresses makes the results representative of subsurface conditions in fractured tight rocks such as enhanced geothermal systems (EGS) and unconventional oil and gas (UOG) reservoirs. The quantification of the mechanical deformation of these rocks in response to pressure and temperature changes during production is essential for the safe development of these tight rocks. INTRODUCTION Crude oil and natural gas currently contribute approximately 68% of the total energy consumed in the United States. Of this oil and gas consumption, 65% comes from shale oil reservoirs while 79% comes from shale gas reservoirs (Nalley and LaRose, 2022). These rocks are typically tight and naturally fractured, requiring the combination of horizontal drilling and hydraulic fracturing to be produced commercially. The process of hydraulically fracturing rocks involves injecting cold fluids into subsur-face rocks at pressures sightly higher than the minimum (compressive) effective stress in the reservoir. To optimize such coupled THM processes in the subsurface, we need models that are accurate representations of the coupled processes in the subsurface. Despite the significant contribution of unconventional oil and gas (UOG) reservoirs to meeting the energy demands of the United States, there has been an increased concern about its environmental impact over the last decade. This includes the mechanical deformation and slip across faults because of the increased compressional stresses when oil and gas are produced, and the increased tensional and shear stresses when the wastewater from production and hydraulic fracturing are disposed of in basement complex rocks below the UOG reservoirs. These processes are related to the well-known problem of induced seismicity, which has increased significantly since the onset of UOG reservoir development (Murray, 2015). For instance, in 2015, North-Central Oklahoma saw a 900-fold increase in its rate of M3+ earthquakes (earthquakes with a magnitude of 3 and above) compared to what it was before 2009 (Langenbruch and Zoback, 2016). In 2014, Oklahoma surpassed California (historically the most seismically active region in the United States) in the number of M3+ earthquakes annually. To mitigate these environmental risks, it is essential to study the complex processes by which the earth moves or slips in response to anthropogenic activities such as wastewater injection (Hornbach et al., 2015), conventional oil and gas production (Van Wees et al., 2014), hydraulic fracturing (Meng and Wang, 2018), improved/enhanced oil recovery (Rubinstein and Mahani, 2015), development of geothermal resources (Majer et al., 2007; Rathnaweera et al., 2020), underground storage of carbon dioxide (Rutqvist et al., 2016; Vilarrasa et al., 2019), hydrogen and other gases (Burtonshaw et al., 2022), etc.
Analytical modification of EDFM for transient flow in tight rocks (2022) — Olufemi Olorode, Harun Rashid — Scientific ReportsAbstract
Abstract The commercial development of unconventional resources with multiply fractured horizontal wells has been in the spotlight over the last ten years because of the significant contribution of unconventional oil and gas (UOG) reservoirs to the total US oil and gas production. UOG reservoirs contain multiscale fractures with heterogeneous properties, so the focus has been on efficient and accurate models that can account for these fractures individually. One of such models is the embedded discrete fracture model (EDFM), which has been applied to various types of fractured reservoirs. This work shows that the application of EDFM in fractured tight rocks yields significant errors because it cannot account for the expected transient flow between the matrix and fractures. To address the limitation when EDFM is used in tight rocks with structured Cartesian grids, we modified the matrix/fracture non-neighboring connection (NNC) flux in EDFM by multiplying it with a transient factor. We obtained this factor as in the transient matrix/fracture transfer term for dual-continuum models and implemented it in in our open-source shale simulator. We simulated a single vertical fracture in the middle of a tight reservoir with and without this EDFM modification and show the importance of the proposed modification. We also simulated cyclic gas enhanced oil recovery (CGEOR) in a fractured Bakken shale oil well and analyzed the model results using standard rate-transient analysis plots to evaluate the significance of the proposed modification. The results show that the standard EDFM underestimates oil and gas production by up to 73% at early times. This work presents the first analytical modification of EDFM to account for the nonlinear pressure drop expected near fracture surfaces. Comparing the modified and standard EDFM model results to a reference solution shows that the modified EDFM matches it. In contrast, the standard EDFM cannot match the reference solution when we use structured Cartesian grids with linear spacing. Additionally, by timing the simulation of a representative Bakken shale oil reservoir with 256 fractures, we show that the analytical modification proposed is only 1.5% slower than the standard EDFM.
Three-Dimensional Projection-Based Embedded Discrete-Fracture Model for Compositional Simulation of Fractured Reservoirs (2020) — Olufemi Olorode, Bin Wang, Harun Ur Rashid — SPE JournalAbstract
Summary Most unconventional oil and gas reservoirs are known to have several natural fractures in different orientations, which are consistent with the prevailing stresses when they were created. The accurate and efficient modeling of natural and hydraulic fractures presents a significant computational challenge. In this work, we show the limitations of the embedded discrete-fracture model (EDFM) and present the first 3D projection-based EDFM (pEDFM) algorithm and compositional simulation studies with realistic fracture networks in a fully 3D space. The simulation results from this work indicate that the pEDFM presented can model realistic fractured unconventional reservoirs accurately and efficiently. To validate the model, we present some simplistic fracture cases that can be meshed and modeled easily using explicit-fracture modeling in commercial-reservoir simulators. From the cases studied, we observe that using progressively finer grids near the hydraulic-fracture surfaces helps to improve model accuracy because this allows us to capture the sharp pressure drops expected near these fracture surfaces. The simulation results show that, unlike EDFM, the robust pEDFM algorithm presented here is accurate even at the low fracture-conductivity values expected in many of these ubiquitous natural fractures. In this paper, we present the first full 3D compositional modeling with pEDFM. We demonstrate that our model can accurately and efficiently model multiply fractured horizontal wells in unconventional reservoirs, which have complex networks of thousands of fractures at various orientations.