Fractured Reservoir Simulation Research Articles

Multiphase flow simulation of fractured karst oil reservoirs applying three-dimensional network models

The characteristics of karst reservoirs are extremely varied and anisotropic, exhibiting notable differences in porosity, permeability, and corresponding fluid flow pathways. Fractured karst petroleum reservoirs, such as distinct caverns and fractures, are an example of a typical discrete media type. The traditional reservoir modeling approach and discrete fracture-like local refinement models are unsuitable for field application of fractured karst oil reservoirs due to the needs of high fidelity geological description and huge computing efforts. Based directly on the spatial characteristics of seismic surveys, a numerical simulation model in three dimensions, akin to a node-like network, is presented here for cracked karst oil reserves. First, the watershed image processing technique and the automatic connection identification procedure are used to extract the three-dimensional node-network model. After that, automatic differentiation is used to build the numerical finite volume scheme, and the proper gradient-based adjoint approach is used to conduct the related historical matching rapidly. After validation by a synthetic model in a commercial simulator, this proposed three-dimensional network numerical model is used for a field reservoir block of deep formation in the Tarim basin to demonstrate its computational efficiency and viability for enormously comparable karst oil reservoirs.

Nonlinearly Constrained Pressure Residual (NCPR) Algorithms for Fractured Reservoir Simulation

Nonlinearly Constrained Pressure Residual (NCPR) Algorithms for Fractured Reservoir Simulation

Fracture Conductivity Work Flow Models Well Spacing, Completions Design

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 2023-3864710, “A Comprehensive Simulation Study of Hydraulic Fracturing Test Site 2 (HFTS-2): Part I—Modeling Pressure-Dependent and Time-Dependent Fracture Conductivity in Fully Calibrated Fracture and Reservoir Models,” by Han Li, Jichao Han, SPE, and Jiasen Tan, SPE, Occidental Petroleum, et al. The paper has not been peer reviewed. _ Combining fracture and reservoir diagnostic analysis with integrated geomechanics and reservoir simulation is an efficient and cost-effective approach to generate realistic fracture geometry, understand fluid flow behavior, and define fracture-conductivity distribution in unconventional reservoirs. The complete paper presents a case study of integrated geomechanical and reservoir simulation with a developed fracture-conductivity-calculation work flow that was validated with diagnostic results to evaluate well spacing and completions design. Introduction This study extends that of previous authors by matching field fracture diagnostics and reservoir simulation using variable fracture conductivity. In the example used by the authors from the Hydraulic Fracturing Test Site 2 (HFTS-2) development, multiple fracture diagnostic methods were used to calibrate hydraulic fracture models. Once the model was calibrated, a new proppant-conductivity algorithm assigned conductivity values along the hydraulic fractures based on a physics-based model calculation of proppant concentration. Multiple mechanisms, such as stress- and pressure-dependent effects, time-dependent conductivity degradation, unpropped fractures, and proppant embedment, can all be considered in the novel fracture-conductivity-calculation methodology. Fracture-Conductivity-Calculation Work Flow The conductivity work flow developed by the authors uses simulated proppant concentration from a fracture model and experimental conductivity measurements of propped and unpropped fractures to define variable conductivity along hydraulic fractures. Conductivity measurements included sets of long-term (50-hour) experimental fracture-conductivity tests with various mesh sizes, proppant types, and closure stresses. The conductivity-calculation work flow developed by the authors was applied to the integrated simulation project of multifractured horizontal wells in the HFTS-2 project. Fig. 1 shows a flow chart of the work flow from fracture propagation modeling through integrated reservoir simulations. In general, the work flow consists of developing a 3D geological model, creating and calibrating parent wells’ hydraulic fracture models, calculating the fracture conductivity based on proppant concentration, history-matching the parent wells’ production and constraints with reservoir simulation, performing fracture-propagation modeling for child wells, and history matching and predicting the estimated ultimate recovery (EUR) for the entire pad. HFTS-2 Project Overview The HFTS-2 is in the Delaware Basin and is a cost-shared, field-based project designed to study hydraulic fracturing processes and production using state-of-the-art diagnostics, including fiber optic (FO) distributed temperature sensing and distributed acoustic sensing (DAS) pressure monitoring, image logs, cores through the fractures, and microseismic monitoring. Many studies have detailed the project overview of the HFTS-2, and this paper’s authors only include the overview of completions in the HFTS-2 project.

Post-frac evaluation of deep shale gas wells based on a new geology-engineering integrated workflow

The development of shale gas reservoir is now shifting focus from mid-shallow reservoirs to deep reservoirs in the southern Sichuan Basin. For such reservoirs with high temperature, pressure, and stress difference, along with multiple folds, faults, and complex fracture networks, improving the stimulation performance of shale gas wells is the ultimate challenge. This study presents a new geology-engineering integrated workflow coupling hydraulic fracture simulation and reservoir simulation together with artificial intelligence to perform post-frac evaluations. A two-step calibration workflow of fracturing and reservoir simulations generated an ensemble of representative models, and a confidence interval of estimated ultimate recovery forecast were obtained. Four deep shale gas wells with two different completion versions (version 1.0 and version 2.0) in Y101 study area were evaluated. Some of the key learnings include: (1) the ratio of stimulated rock volume and drained rock volume is quantified to 8%–25% for the four characterized deep shale gas wells; (2) the version 2.0 completion design is able to stimulate the near-well region more effectively than version 1.0; (3) this novel geology-engineering integrated workflow performed the first reliable, robust and quantifiable post-frac evaluation in the southern Sichuan Basin deep shale reservoir.

Numerical Modeling of Natural Fracture Distributions in Shale

AbstractThe production efficiency of shale gas is affected by the interaction between hydraulic and natural fractures. This study presents a simulation of natural fractures in shale reservoirs, based on a discrete fracture network (DFN) method for hydraulic fracturing engineering. Fracture properties of the model are calculated from core fracture data, according to statistical mathematical analysis. The calculation results make full use of the quantitative information of core fracture orientation, density, opening and length, which constitute the direct and extensive data of mining engineering. The reliability and applicability of the model are analyzed with regard to model size and density, a calculation method for dominant size and density being proposed. Then, finite element analysis is applied to a hydraulic fracturing numerical simulation of a shale fractured reservoir in southeastern Chongqing. The hydraulic pressure distribution, fracture propagation, acoustic emission information and in situ stress changes during fracturing are analyzed. The results show the application of fracture statistics in fracture modeling and the influence of fracture distribution on hydraulic fracturing engineering. The present analysis may provide a reference for shale gas exploitation.

Impact of fractures with multi-scale aperture variability on production observations of geothermal reservoir units

We incorporated aperture variability considering contact obstacles into an ensemble of fractured geothermal reservoir simulations to quantify how variations in this multi-scale aperture feature could impact flow field organization and heat transport behavior at the fracture scale. This work considered the variability of the correlation length and successfully developed two observational parameters for production prediction. Our calculations demonstrated that the degree of flow tortuosity was increased by the correlation length, which in turn affected heat transport. The results showed that using the traditional parallel plate model could overestimate the production temperature and could underestimate the cumulative heat production, and these two observation parameters exhibited scale dependence on the correlation length. However, the plate model with the effective hydraulic aperture inferred from flow could capture the production trend of fractured geothermal reservoirs, which indicates that considering a correction coefficient related to the correlation length could effectively improve the prediction accuracy. We also found that the cumulative heat production attained a positive logarithmic correlation with the channelized flow area and a linear negative correlation with the flow tortuosity. This study contributes to a greater understanding of the uncertainty in production observations of fractured geothermal fields with heterogeneous aperture characteristics.

Technology Focus: Field Development (September 2022)

In this month’s Field Development feature, SPE conference authors place an emphasis not only on original research and findings but also on validation and refinement of existing techniques that may not have received thorough attention in the literature. As operators strive to achieve the greatest returns possible from technically, environmentally, and economically challenging plays, they are driven to innovate new approaches and to fine-tune existing ones. In paper SPE 206267, the authors investigate the performance of a distributed quasi-Newton (DQN) derivative-free optimization (DFO) method, which, they write, had not yet been validated by realistic applications or compared with other DFO methods. They integrate DQN into a versatile field-development optimization platform designed for iterative work flows enabled through distributed parallel flow simulations. The method was field-tested on two realistic applications and identified the global optimum with the least number of simulations and the shortest run time on a synthetic problem with a known solution. The authors of paper SPE 207146 create and evaluate a development plan for an oil field discovered in a remote offshore environment in the Niger Delta. Because the oil in place was uncertain, a probabilistic approach was used to estimate the stock-tank oil originally in place using low, mid, and high cases. Keeping in mind governmental regulations to maintain the reservoir pressure above bubblepoint, the authors propose a development plan that is marginally base modeled and, despite the uncertainty of oil prices in the market, able to cover any unforeseen situations. Finally, the authors of paper SPE 208882, addressing the challenge posed by cumbersome integrated technical work flows for multiwell fracture modeling and reservoir simulation, use tools existing in the literature to quantify the effect of changing well spacing on well productivity for a given completion design using a simple, intuitive empirical equation. After describing and qualifying the use of their approach, they apply it to a case study from the Permian Basin. Recommended additional reading at OnePetro: www.onepetro.org. OTC 31151 - Autonomous Subsea Field Development—Value Proposition, Technology Needs, and Gaps for Future Advancement by Giorgio Arcangeletti, Saipem, et al. SPE 206533 - Field Development Optimization Using Machine-Learning Methods To Identify the Optimal Waterflooding Regime by Alexey Vasilievich Timonov, Consultant, et al. URTeC-2021-5301 - Unconventional Reservoir Development Performance Reviews—the Northern Midland Basin Case Study by Hongjie Xiong, University Lands, et al.

Approach With Simple Tools Enables Well-Spacing Optimization for Unconventionals

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 208882, “No Reservoir Model? No Problem. Unconventional Well Spacing Optimization With Simple Tools,” by Patrick Miller, SPE, Darcy Redpath, SPE, and Keane Dauncey, SPE, Petronas. The paper has not been peer reviewed. _ Optimizing economics for unconventional resource development is a delicate balance. To search for the optimal pad design, operators often invest in integrated technical work flows with multiwell fracture modeling and reservoir simulation. Although useful, these work flows are not practical for every asset in a portfolio because they simply take too long. As an alternative approach, the complete paper builds on existing tools in the literature to quantify the effect of changing well spacing on well productivity for a given completion design, using a new, simple, intuitive empirical equation. Methodology: Understanding Well-Performance Changes With Well Spacing The four key drivers of pad economics for unconventional plays are commodity prices, reservoir deliverability, completion design, and well spacing. Completion design and well spacing must be considered together because the drainage area of an unconventional well is driven by the size of the fracture stimulation. Finding the global maximum of the optimization criteria with traditional technical work flows is intensive in terms of human resources and time. Furthermore, these traditional work flows are still only estimates of well performance under different conditions. This section of the complete paper provides a set of visual references for what is happening in the subsurface when well spacing is changed for a given fracture stimulation design and then discusses how this can be represented mathematically. The goal of the authors, in discussing currently used approaches, is to set the background for an alternative, easy-to-understand approach to define shared reservoir factor (SRQ) as a function of well density in a way that creates the expected concave down shape initially but which transitions to a linear relationship and trends toward a relative estimated ultimate recovery (EUR) of 0% at 0 well spacing. The methodology of this approach is provided mathematically in this section of the complete paper.

A new numerical simulation method of hydrogen and carbon compounds in shale reservoir

Hydrogen energy can be produced by the decomposition of hydrogen and carbon compounds. A numerical analysis method of accuracy and efficiency provides important reference value for optimizing development plans and predicting production performance of hydrogen and carbon compounds. In this work, embedded discrete fracture model (EDFM) is used to study the production performance of hydrogen and carbon compounds under non-liner seepage under the threshold pressure gradient and complex fracture systems consist of the hydraulic fractures, secondary fractures, natural fractures. A dual-permeability model of the same case is also constructed as a comparison study to analyze the development of hydrogen and carbon compounds. On this basis, the influence of threshold pressure gradient on production of hydrogen and carbon compounds is quantitatively evaluated in this paper to modify the numerical model and a novel method for the simulation of fractured hydrogen and carbon compounds reservoirs is provided. Through model comparison, the impact of fractures in the reservoir on production can reach 289.1%. A dual-permeability model of the same case is also constructed as a comparison study to analyze the development of the reservoir and the result shows a 7.9% distinction on the cumulative production. It is analyzed that when the threshold pressure gradient is increased from 0.1 MPa/m to 0.6 MPa/m, the output decline of different models ranges from 6% to 15% and a novel method improving model fidelity for the simulation of fracture reservoirs is provided.

Impact of Well Placement in the Fractured Geothermal Reservoirs Based on Available Discrete Fractured System

Well placement in a given geological setting for a fractured geothermal reservoir is necessary for enhanced geothermal operations. High computational cost associated with the framework of fully coupled thermo-hydraulic-mechanical (THM) processes in a fractured reservoir simulation makes the well positioning a missing point in developing a field-scale investigation. To enhance the knowledge of well placement for different working fluids, we present the importance of this topic by examining different injection-production well (doublet) positions in a given fracture network using coupled THM numerical simulations. Results of this study are examined through the thermal breakthrough time, mass flux, and the energy extraction potential to assess the impact of well position in a two-dimensional reservoir framework. Almost ten times the difference between the final amount of heat extraction is observed for different well positions but with the same well spacing and geological characteristics. Furthermore, the stress field is a strong function of well position that is important concerning the possibility of high-stress development. The objective of this work is to exemplify the importance of fracture connectivity and density near the wellbores, and from the simulated cases, it is sufficient to understand this for both the working fluids. Based on the result, the production well position search in the future will be reduced to the high-density fracture area, and it will make the optimization process according to the THM mechanism computationally efficient and economical.

An implementation of mimetic finite difference method for fractured reservoirs using a fully implicit approach and discrete fracture models

In this paper, we present a fully implicit mimetic finite difference method (MFD) for general fractured reservoir simulation. The MFD is a novel numerical discretization scheme that has been successfully applied to many fields and it is characterized by local conservation properties and applicability to complex grids. In our work, we extend this method to the numerical simulation of fractured reservoirs using discrete fracture models. The MFD scheme supports general polyhedral meshes and full tensor properties which improves the modeling and simulation of subsurface reservoirs. Furthermore, we describe in detail the principle of our MFD approach and the corresponding numerical formulations of the discrete fracture model. In our tests, we use a fully implicit scheme that assures flux conservation and simulation efficiency. Several case studies are conducted to show the accuracy and the robustness of the proposed numerical scheme.

Similarity Criteria of Water Drive Physical Simulation of Pressure-Sensitive Fractured Reservoirs

A mathematical equation of water drive physical simulation of pressure-sensitive fractured reservoirs was established based on previous research results. In this study, the similarity criteria of water drive physical simulation of pressure-sensitive fractured reservoirs were derived according to the similarity theory. First of all, based on the three-dimensional differential equation of rock mechanics, a dimensionless analysis was conducted to determine the similarity relationship between the displacement of oil by water of pressure-sensitive fractured reservoirs, the similarity criterion was obtained, and the similarity criteria were formed. Secondly, according to the similarity criterion, the similar relationship between the stress-strain fields of the real object and the simulated object was worked out. Thirdly, the finite element software COMSOL Multiphysics was applied to model and calculate the multifield coupling process in the percolation of pressure-sensitive fractured reservoirs, verifying the correctness of the established similarity criteria and similarity relationship. The verifying results shows that the similarity between the physical model and the actual model can be realized by magnifying the geometric size N times in a certain direction and adjusting the load and boundary conditions according to the similarity principle, which can be used for the design of the pressure-sensitive fractured reservoir simulation model for a physical indoor test.

A novel hybrid model for multiphase flow in complex multi-scale fractured systems

We present a multi-level discrete fracture model (MLDFM) to guarantee a robust and efficient solution for naturally fractured reservoir simulation. In MLDFM, we apply a triple continuum model using structured grid for forward simulation where large-scale fractures are represented with numerical embedded discrete fracture model (EDFM) and the secondary fractures are upscaled as third continuum. What makes the triple continuum model different from the previous work is that both the numerical EDFM and the third continuum are treated in a dynamic approach by considering the effect of flow direction on the complex local-scale flow response. For that purpose, we construct a finer unstructured discrete fracture matrix (DFM) grid which represents all fractures explicitly and is conformal to the boundary of coarse structured grid. During a simulation run, we apply a basis function to generate the local boundary conditions at fine scale using the global solution. Benefit from that, we can use a more accurate flow-based approach in the extended local upscaling to re-compute the transmissibility in triple continuum model. Moreover, we apply a local-global upscaling formalism to guarantee dynamically updated local boundary conditions for upscaling. Besides, we present several cases using synthetic and realistic fractured networks to demonstrate the performance of MLDFM. The results prove that the proposed MLDFM approach more accurately captures the flow in complex fractured systems than EDFM solutions by comparing against fine-scale DFM. At the same time, MLDFM is more computationally efficient in comparison with fine scale DFM. • An advanced hybrid model for multiphase flow fractured systems is presented. • The model compared with state-of-the-art Discrete Fracture Model (DFM) and Embedded DFM. • The model provides a better accuracy than EDFM with Equivalent Continuum Model used for complex multi-scale fractures. • A set of benchmarks includes complex synthetic and realistic fractured networks.

Transient shape factors for dual-porosity simulation of tight rocks

The shape-factor concept provides an elegant and powerful upscaling method for fractured reservoir simulation. Many different shape-factors, among which the well-known Warren and Root, and Kazemi shape-factors have been proposed in the past. Since different shape-factors can lead to totally different reservoir behavior, selection of the appropriate shape-factor value is critical for accurate fractured reservoir modeling. Constant shape factor is commonly used for simulation of fractured reservoirs by assuming that pressure transient reaches to center of the matrix block within very small time. On the contrary, tight rocks exhibit longer duration of unsteady-state flow such that matrix – fracture transfer is not constant, but rather varies with time until reaching to a constant value. In this regard, dual-porosity simulation of tight rocks using constant shape factor does not capture actual physics of matrix to fracture flow and yields inaccurate performance prediction. In this study, analytical solutions of pressure diffusion and corresponding shape factors are presented for various matrix shapes. The results are compared to those obtained with simple empirical functions. Proposed functions significantly improve accuracy over existing approaches in the prediction of both mean matrix pressure and transfer function. Results of fine grid single-porosity model are compared with two different dual porosity models, one with constant shape factor and one with time dependent shape factor, to verify proposed approach.

Improved modelling of pressure-dependent permeability behaviour in coal based on a new workflow of petrophysics, hydraulic fracturing and reservoir simulation

Many coal seam gas (CSG) reservoirs (also known as coalbed methane) can have low permeability, require stimulation to produce economic rates and often exhibit pressure-dependent permeability (PDP) behaviour. Defining PDP behaviour in coal using reservoir simulation is a non-unique problem based on the uncertainty in coal properties and input parameters. Recent research demonstrated that an integrated analysis coupling of a diagnostic fracture injection test analysis, hydraulic fracture modelling and reservoir simulation can better characterise PDP behaviour in order to evaluate stimulation effectiveness in coals (Johnson et al. 2020). The present work aims to improve the recently developed model by including multilayer and permeability anisotropy effects. A reservoir model with multiple coal layers is established in a pressure-dependent reservoir simulator, based on the image log interpretations. Permeability anisotropy in the formation is realised by introducing heterogeneous distribution of permeability in different directions. Modelling results indicate effects of aspect ratio between multilayers on the pressure distribution and production history. A lower permeability anisotropy ratio yields better well productivity, and higher stimulation is required to increase the stimulated reservoir volume to maximise gas recovery. The improved model and workflow are applicable to other CSG fields for defining key variables where hydraulic fracturing performance has been unable to overcome limitations based on pressure dependency, often accompanied by low-permeability behaviour. This workflow has applications in Australia and many areas (e.g. China and India) exhibiting low-permeability and PDP behaviour and where only typically collected field data is available.

An efficient embedded discrete fracture model based on the unstructured quadrangular grid

It is important yet challenging to effectively and accurately predict the recovery of fractured reservoirs. Among numerous fractured reservoir simulation models, the embedded discrete fracture model (EDFM) is the most outstanding one for it incorporates the discrete fractures into structured grids of the matrix, which precisely describes the arbitrarily distributed fractures while not increasing the gridding and calculation complexity. However, the current EDFM still possesses drawbacks for its structured grid shows poor adaptivity to irregularly shaped reservoirs, and also causes a sharp pressure gradient between the matrix and fractures and weakens the simulation accuracy. To conquer the drawbacks of the current EDFM, an unstructured quadrangular grid-based EDFM (UnQ-EDFM) is proposed in this paper. In this model, a frontal Delaunay quadrangular grid is adopted that could perfectly adapt to irregular reservoir boundaries without increasing the grid number and gridding complexity; besides, local grid refinement could be achieved flexibly in anywhere of the reservoir, which effectively alleviates the simulation error while not adding too much calculation. Based on the UnQ-EDFM, the production of a multi-stage hydraulic fractured well in irregular shaped naturally fractured shale gas reservoir is simulated, the simulation results under different types of grids are compared. Furthermore, an optimization framework that applies WOA as the optimization algorithm and NPV as the objective function is constructed, the hydraulic fractured well in the above-mentioned reservoir is optimized and the reliability of the UnQ-EDFM is testified through thousands of times of simulation. The results of simulation and optimization demonstrate the reliability and superiority of the UnQ-EDFM over the traditional structured grid-based EDFM, for it adapts to complex-shaped reservoirs, maintains high simulation accuracy, and reduces simulation time, simultaneously. The UnQ-EDFM proposed in this paper severs as an efficient tool and contributes to the precise and efficient simulation for the fractured reservoirs’ development.

Numerical Investigation of the Effect of Partially Propped Fracture Closure on Gas Production in Fractured Shale Reservoirs

Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts.

A Dual-Grid, Implicit, and Sequentially Coupled Geomechanics-and-Composition Model for Fractured Reservoir Simulation

SummaryIn the development of fractured reservoirs, geomechanics is crucial because of the stress sensitivity of fractures. However, the complexities of both fracture geometry and fracture mechanics make it challenging to consider geomechanical effects thoroughly and efficiently in reservoir simulations. In this work, we present a coupled geomechanics and multiphase-multicomponent flow model for fractured reservoir simulations. It models the solid deformation using a poroelastic equation, and the solid deformation effects are incorporated into the flow model rigorously. The noticeable features of the proposed model are it uses a pseudocontinuum equivalence method to model the mechanical characteristics of fractures; the coupled geomechanics and flow equations are split and sequentially solved using the fixed-stress splitting strategy, which retains implicitness and exhibits good stability; and it simulates geomechanics and compositional flow, respectively, using a dual-grid system (i.e., the geomechanics grid and the reservoir-flow grid). Because of the separation of the geomechanics part and the flow part, the model is not difficult to implement based on an existing reservoir simulator. We validated the accuracy and stability of this model through several benchmark cases and highlighted the practicability with two large-scale cases. The case studies demonstrate that this model is capable of considering the key effects of geomechanics in fractured-reservoir simulation, including matrix compaction, fracture normal deformation, and shear dilation, as well as hydrocarbon phase behavior. The flexibility, efficiency, and comprehensiveness of this model enable a more realistic geocoupled reservoir simulation.

Adaptive dynamic multilevel simulation of fractured geothermal reservoirs

An algebraic dynamic multilevel (ADM) method for fully-coupled simulation of flow and heat transport in heterogeneous fractured geothermal reservoirs is presented. Fractures are modeled explicitly using the projection-based embedded discrete method (pEDFM), which accurately represents fractures with generic conductivity values, from barriers to highly-conductive manifolds. A fully implicit scheme is used to obtain the coupled discrete system including mass and energy balance equations with two main unknowns (i.e., pressure and temperature) at fine-scale level. The ADM method is then developed to map the fine-scale discrete system to a dynamic multilevel coarse grid, independently for matrix and fractures. To obtain the ADM map, multilevel multiscale coarse grids are constructed for matrix as well as for each fracture at all coarsening levels. On this hierarchical nested grids, multilevel multiscale basis functions (for flow and heat) are solved locally at the beginning of the simulation. They are used during the ADM simulation to allow for accurate multilevel systems in presence of parameter heterogeneity. The resolution of ADM simulations is defined dynamically based on the solution gradient (i.e. front tracking technique) using a user-defined threshold. The ADM mapping occurs algebraically using the so-called ADM prolongation and restriction operators, for all unknowns. A variety of 2D and 3D fractured test cases with homogeneous and heterogeneous permeability maps are studied. It is shown that ADM is able to model the coupled mass-heat transport accurately by employing only a fraction of fine-scale grid cells. Therefore, it promises an efficient approach for simulation of large and real-field scale fractured geothermal reservoirs. All software developments of this paper is publicly available at https://gitlab.com/DARSim2simulator.

Parallel implementation of coupled phase equilibrium-mass transfer model: Efficient and accurate simulation of fractured reservoirs

Molecular diffusion plays a vital role in production from fractured reservoirs in all stages of recovery, especially for fractured reservoirs with small matrix sizes and unfavorable wettability conditions. Molecular diffusion can only be simulated by compositional reservoir simulators, which have historically employed a decoupled phase equilibrium-mass transfer model. Regardless of having higher performance, such a model cannot properly simulate intra- and cross-phase molecular diffusion. In the current research, a compositional fractured reservoir simulator, called Osiris, has been developed in C++ using the coupled formulation. After presenting the primary equations and algorithms, the performance of Osiris has been evaluated through a series of case studies. Utilizing MPI, Osiris could keep its runtime reasonable, despite the high computational demand of coupled modeling. Additionally, the simulation results of Osiris clearly prove the precision of the coupled modeling; and considerable effects of diffusive mass transfer on fractured reservoir performance.