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Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.
Optimizing conformance control for gas injection EOR in unconventional reservoirs
Field observations have shown that interference between wells caused by connected fractures commonly exists in unconventional reservoirs. The well interference effect and conformance issues could lead to minimal enhanced oil recovery response (EOR) in actual operations if they are not properly controlled. A series of data analysis, modeling, and experimental activities were performed in this study to investigate the gas EOR strategies in the Bakken Formation. Employing the embedded discrete fracture modeling technology, a multiple-well, multiple-fracture model was developed to capture the well interference and conformance issues in the Bakken. The model made it possible to investigate the complex flow behavior between wells in the EOR (huff ‘n’ puff) processes. Alternative EOR and conformance control strategies using water and surfactant injections were studied to improve oil production performance based on experimental observations. Results showed that water injection could be used for conformance control in the Bakken because of its relatively low mobility compared to gas; however, water could also block oil flow around the conformance control wells because of the high interfacial tension between oil and water. Adding surfactant to the injection water is more effective for improving gas EOR performance since surfactant reduces the oil–water interfacial tension and contact angle effectively. Up to 9.4% more oil could be produced from the huff ‘n’ puff wells in 2 years of EOR operations when rich gas was injected at only 3 MMscf/d with 6000 psi of surfactant injection in the offset wells for conformance control.
Modeling CO 2 flow through faulted/fractured reservoirs using tEDFM in corner-point grids
The interest in underground CO 2 storage has increased significantly over the last decade because of the rising concern about global warming due to the growing levels of greenhouse gases in the atmosphere. Considering that CO 2 accounts for 80% of these greenhouse gases, carbon capture, utilization, and storage (CCUS) is regarded as one of the most direct approaches to achieving the net zero carbon target. Although CO 2 storage in deep saline aquifers and depleted gas reservoirs has been studied extensively, most studies use commercial simulators that model faults/fractures by simply modifying the transmissibility in the direction perpendicular to the fault surfaces. Here, this work shows that this simplistic approach ignores the accelerated flow in the directions parallel to the fault plane, leading to significantly higher leakage along the fault surface. To accurately model the flow of CO 2 in faulted reservoirs, we present the first transient embedded discrete fracture model for corner-point grids (tEDFM-CPG). By comparing the results of the tEDFM-CPG to high-resolution reference solutions, we show that this approach is accurate and efficient at predicting CO 2 flow in faulted/fractured reservoirs. Finally, this work presents the use of mixed reality (MR) to efficiently observe CO 2 gas migration in the interior of these corner-point grid systems.
Modeling Co2 Flow Through Faulted/Fractured Reservoirs Using Tedfm in Corner-Point Grids
Interest in underground CO2 storage has increased significantly over the last decade, driven by growing concern about global warming and rising levels of greenhouse gases in the atmosphere. Given that CO2 accounts for 80% of these greenhouse gases, carbon capture, utilization, and storage (CCUS) is considered one of the most direct approaches to achieving the net-zero carbon target. Although CO2 storage in deep saline aquifers and depleted gas reservoirs has been studied extensively, most studies use commercial simulators that model faults/fractures by simply modifying the transmissibility in the direction perpendicular to the fault surfaces. This work shows that this simplistic approach ignores the accelerated flow in the directions parallel to the fault plane, leading to significantly higher leakage along the fault surface. To accurately model CO2 flow in faulted reservoirs, we present the first transient embedded discrete-fracture model for corner-point grids (tEDFM-CPG). By comparing the tEDFM-CPG results with high-resolution reference solutions, we show that this approach is accurate and efficient at predicting CO2 flow in faulted/fractured reservoirs. In conclusion, this work presents the use of mixed reality (MR) to efficiently observe CO2 gas migration in the interior of these corner-point grid systems.
An embedded 3D fracture modeling approach for simulating fracture-dominated fluid flow and heat transfer in geothermal reservoirs
In this paper, we describe an efficient modeling approach, named embedded discrete fracture method (EDFM), for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology. This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while maintaining enough accuracy. Several numeral simulations are presented to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to the simulation of fractured geothermal reservoirs with both artificial and natural fractures.
Optimization of operational strategies for rich gas enhanced oil recovery based on a pilot test in the Bakken tight oil reservoir
Horizontal well drilling and multistage hydraulic fracturing have been demonstrated as effective approaches for stimulating oil production in the Bakken tight oil reservoir. However, after multiple years of production, primary oil recovery in the Bakken is generally less than 10% of the estimated original oil in place. Gas huff ‘n’ puff (HnP) has been tested in the Bakken Formation as an enhanced oil recovery (EOR) method; however, most field pilot test results showed no significant incremental oil production. One of the factors affecting HnP EOR performance is premature gas breakthrough, which is one of the most critical issues observed in the field because of the presence of interwell fractures. Consequently, injected gas rapidly reaches adjacent production wells without contacting reservoir rock and increasing oil recovery. Proper conformance control is therefore needed to avoid early gas breakthrough and improve EOR performance. In this study, a rich gas EOR pilot in the Bakken was carefully analyzed to collect the essential reservoir and operational data. A simulation model with 16 wells was then developed to reproduce the production history and predict the EOR performance with and without conformance control. EOR operational strategies, including single- and multiple-well HnP, with different gas injection constraints were investigated. The simulation results of single-well HnP without conformance control showed that a rich gas injection rate of at least 10 MMscfd was needed to yield meaningful incremental oil production. The strategy of conformance control via water injection could significantly improve oil production in the HnP well, but injecting an excessive amount of water also leads to water breakthrough and loss of oil production in the offset wells. By analyzing the production performance of the wells individually, the arrangement of wells was optimized for multiple-well HnP EOR. The multiwell results showed that rich gas EOR could improve oil production up to 7.4% by employing conformance control strategies. Furthermore, replacing rich gas with propane as the injection gas could result in 14% of incremental oil production.
DECOVALEX-2023: Task A Final Report
Task A, also known as HGFrac, examines the fracturing processes that may occur in the Callovo-Oxfordian claystone (COx) in the context of the high-level (HLW) and intermediate-level long-lived (ILW-LL) radioactive waste repository in France. Understanding these processes and improving numerical models to reproduce them will aid in the design, optimization, and safety of the repository. Heat and gas fracturing are studied in two independent subtasks following a stepwise approach: laboratory tests/benchmark exercises, in-situ experiment, and finally, an application case. The in-situ heater experiment aimed to thermally induce a hydraulic fracture; temperature and pore pressure were monitored to detect any evidence of fracturing. The in-situ gas injection experiment aimed to study the effect of the stress orientation and gas injection kinetics on the gas fracturing process. The occurrence of fracturing was monitored by gas pressure measured in the injection interval. In both experiments, the excavation-induced fracture network around the heater/injection boreholes played an important role in the reduction of the compressive stress state, leading to both a tensile and shear failure response of the COx. During the first two years of the project, the research teams working on each task developed and/or proposed numerical approaches for reproducing the occurrence of fracturing in the in-situ experiments. The failure criteria were defined by reproducing the measurements from laboratory extension tests for the heat fracturing subtask. In the gas fracturing subtask, their approaches were used for simulating several benchmark exercises, and an inter-comparison between models was carried out. In both tasks, the developed approaches were compared with a simplified approach considering poro-elasticity for the mechanical behaviour of the COx. Most of the developed approaches are based on a continuous medium that takes into account variations in hydraulic properties due to mechanical degradation, such as plastic deformation or damage. Other approaches implicitly modelled weak planes or embedded discontinuities to reproduce fracture propagation. The potential for fracture initiation was also studied through of a discrete approach. In the second half of the project, the research teams mainly focused on interpretative modelling of two in-situ experiments and a blind prediction exercise to test their respective approaches. The models developed by the research teams were also applied at the repository scale to evaluate fracture initiation in a case study under vi unfavourable conditions, particularly in terms of spacing between High-Level Waste cells. The results showed that the poro-elasticity approach could be an efficient tool for understanding the main processes occurring in the COx. One example is the explicit representation of the excavation-induced fracture network around the boreholes, which yielded acceptable results compared to the measurement data. However, advanced approaches were needed to evaluate the potential increase of the excavation-induced fracture network extend and better understand fracture initiation. The stress analyses carried out by the teams revealed that hydraulic boundary conditions had a strong impact on fracture initiation in the heater experiment. Furthermore, in most cases, the results required higher pore pressure increments to reach fracturing than those measured in the experiment. This implies that the measurements may have been biased by the packer’s capacity to fully isolate the piezometric chambers, leading to lower pressures. On the contrary, there was no agreement on the fracturing mode, as some reported either shear or tensile fracturing, while others reported a combination of the two modes. In the case of gas fracturing, the research teams were limited to the comparison of a single point, which complicated their task. Nonetheless, the numerical results were able to reproduce the measurements and capture processes such as longitudinal gas flow through the excavation-induced fracture network, as suggested by some evidence in the observation piezometric chambers. The numerical models also agreed with the measurements in the sense of higher probability of developing along the injection borehole than radially towards the sound rock. The approaches developed by the research teams showed that they are capable of analysing and reproducing fracture initiation in the COx. However, areas of future work should focus on the fracture propagation and fracture aperture, which were out of the scope of this task. To this end, additional data must be gathered for the parameter characterisation and validation of the numerical models. Nonetheless, various approaches showed promising results as they were able to reproduce fracture development under certain conditions.
Characterization of mechanical discontinuities based on data-driven classification of compressional-wave travel times
Wave propagation and diffusive transport phenomena are influenced by the mechanical discontinuities in material. Here this study shows that certain bulk properties of the network of low-velocity mechanical discontinuities (e.g. air-filled cracks) in a material can be characterized by processing compressional-wave travel times using traditional data-driven classification techniques. To that end, we perform three tasks in chronological order: (1) use the discrete fracture network (DFN) method to create two-dimensional (2D) numerical models of crack-bearing material embedded with various types of low-velocity mechanical discontinuities, (2) use the fast marching method (FMM) to simulate the propagation of the wave/diffusion front from a single source through the 2D crack-bearing material to multiple receivers placed on the boundary of the material, and (3) train 9 data-driven classifiers to characterize the crack-bearing materials (i.e. bulk properties of the network of mechanical discontinuities in the crack-bearing material) by learning from the simulations of travel times detected by multiple receivers placed around the crack-bearing material. The classifiers identified the orientation, spatial distribution, and dispersion of the low-velocity mechanical discontinuities. Voting classifier performs the best among the 9 classifiers. For the characterization of bulk dispersion and distribution of discontinuities, the sensors located on the adjacent boundaries are more important; whereas for the characterization of bulk orientation of discontinuities, the sensors located on the opposite side are more important.
The influence of preexisting host rock damage on fault network localization
The transition from stable to unstable fracture propagation occurs when fractures begin to interact and link. Thus, fracture network coalescence controls how rocks and engineered structures fail. Here, to constrain the factors that influence localization in shear zones under brittle conditions, we build discrete element method models with a rough fault embedded in a shear zone. We add varying numbers of diffuse, randomly-placed weaknesses to examine the influence of diffuse damage on fracture network localization. The number of weaknesses controls the localization behavior of the fault network and the final fault geometry. We quantify localization using the Gini coefficient of the fracture volume, which measures the nonuniformity in a population. Each model generally increases in localization toward failure. However, models with more diffuse damage experience delocalization phases that are superimposed on the overall trend of increasing localization. The observed link between delocalization and host rock damage may help explain the varying localization of low magnitude seismicity in southern California. Models with more diffuse damage produce more complex fault geometries comprised of several parallel strands of wing cracks. The propagation of these wing cracks reduces the shear stress acting on the model boundaries, indicating that this fracture development increases the mechanical efficiency of the system.
Approaches for the Simulation of Coupled Processes in Evolving Fractured Porous Media Enabled by Exascale Computing
Models have historically represented fractured porous media with continuum descriptions that characterize the media using bulk parameters. The impact of small-scale features is not captured in these models, although they may be controlling the performance of subsurface applications. Pore-scale models can simulate processes in small-scale features by representing the pore space geometry explicitly but are computationally expensive for large domains. The alternative multiscale approach entails the combination of pore-scale and continuum-scale descriptions in a single framework. We use Chombo-Crunch, a computational capability that discretizes complex geometries with an adaptive, embedded boundary method to contrast these two approaches. Chombo-Crunch takes advantage of recent computational performance and memory bandwidth improvements resulting from the emergence of exascale computing resources. These combined improvements enable the efficient simulation of reactive transport in fractured media with a high degree of fidelity and the ability to capture the control small-scale processes exert on the overall medium evolution.
Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime
This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.
An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes
Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.
Implementation of extrinsic cohesive zone model (ECZM) in 2D finite-discrete element method (FDEM) using node binding scheme
The combined finite-discrete element method (FDEM) has been widely used for rock fracturing simulations. Conventionally, FDEM is realized using the intrinsic cohesive zone model (ICZM); however, it has the drawback of artificial compliance and high computational expense. As a complement, the extrinsic cohesive zone model (ECZM) is seen to be realized in FDEM recently, whereas the node splitting scheme utilized is cumbersome. Here, within the framework of ICZM-based FDEM, we propose a node binding scheme to efficiently bind the pre-discretized finite elements and thus guarantee the continuum behavior of materials in the elastic stage. The yield surfaces, controlled by ECZM, are dynamically embedded by invoking the pre-inserted cohesive elements. The effectiveness and efficiency of the proposed approach are validated and tested by performing a suite of numerical experiments. Compared with ICZM-based FDEM, the proposed approach can correctly capture material deformation and reduce the computation cost. In contrast to the existing ECZM-based FDEM, the proposed approach can overcome the frequent and complex element topology updating. Finally, this work provides a novel perspective that fully inherits the advantages of both ICZM and ECZM, but circumvents their shortcomings, which guarantees a more efficient and effective simulation of brittle material evolution from continuum to discontinuum.
Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems
Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.
Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system
The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.
Nonlinear Spring Finite Elements for Predicting Mode I-Dominated Delamination Growth in Laminated Structure with Through-Thickness reinforcement
One particular concern of polymer matrix composite laminates is the relatively low resistance to delamination cracking, in particular when the dominant type of failure is mode I opening. One method proposed for alleviating this problem involves the insertion pultruded carbon pins through the laminate thickness. The pins, known as z-pins, are inserted into the prepreg laminate using an ultrasonic hammer prior to the curing process, resulting in a field of pins embedded normal to the laminate plane as illustrated in Figure. 1. Pin diameters range between 0.28-mm to 0.5-mm and standard areal densities range from 0.5% to 4%. The z-pins are provided by the manufacturer, Aztex(Registered TradeMark) , in a low-density foam preform, which acts to stabilize orientation of the pins during the insertion process [1-3]. Typical pin materials include boron and carbon fibers embedded in a polymer matrix. A number of methods have been developed for predicting delamination growth in laminates reinforced with z-pins. During a study on the effect of z-pin reinforcement on mode I delamination resistance, finite element analyses of z-pin reinforced double cantilever beam (DCB) specimens were performed by Cartie and Partridge [4]. The z-pin bridging stresses were modeled by applying equivalent forces at the pin locations. Single z-pin pull-out tests were performed to characterize the traction law of the pins under mode I loading conditions. Analytical solutions for delamination growth in z-pin reinforced DCB specimens were independently derived by Robinson and Das [5] and Ratcliffe and O'Brien [6]. In the former case, pin bridging stresses were modeled using a distributed load and in the latter example the bridging stresses were discretely modeled by way of grounded springs. Additionally, Robinson and Das developed a data reduction strategy for calculating mode I fracture toughness, G(sub Ic), from a z-pin reinforced DCB specimen test [5]. In both cases a traction law similar to that adopted by Cartie and Partridge was used to represent z-pin failure under mode I loading conditions. In the current work spring elements available in most commercial finite element codes were used to model z-pins. The traction law used in previous analyses [4-6] was employed to represent z-pin damage. This method is intended for and is limited to simulating z-pins in composite laminate structure containing mode I-dominated delamination cracking. The current technique differs from previous analyses in that spring finite elements (available in commercial codes) are employed for simulating zpins, reducing the complexity of the analysis construction process. Furthermore, the analysis method can be applied to general structure that experiences mode I-dominated delamination cracking, in contrast to existing analytical solutions that are only applicable to coupon DCB specimens.