Fractured Reservoir Simulation Research Articles

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.

Numerical Simulation of Fractured Reservoir with Full Coupling Matrix Finite Element Method

Fractured reservoir is an important part of China’s oil and gas resources, which is a phenomenon that will be encountered in the exploitation of most oil and gas resources. However, there are many difficulties in the exploitation of fractured reservoirs, such as internal complexity, basic assumptions of models, fracture identification technology, computer hardware and so on. Therefore, we must consider the full coupling matrix finite element analysis, which will overcome the limitations of the traditional dual medium model and the discrete fracture network model. Through the full coupled matrix finite element analysis, we can establish a new numerical simulation of fractured reservoir. First, this paper analyzes the basic types of fractured reservoirs. Then, this paper analyzes the full coupling matrix finite element method.

Numerical simulation model adaptability research for fractured reservoir

Characterization and forecasting in fractured reservoirs is one of the most challenging topics in oil and gas industry. Due to significant difference of fluid flow mechanism in fracture and in matrix, managing such reservoirs requires construction of representative reservoir models. Dual porosity & dual permeability model (DPDP) is the first choice of fractured reservoirs, but history matching and plan prediction of this model facing poor convergence and long running time. Other models like dual porosity & single permeability model (DPSP), single porosity & single permeability model (SPSP) sometimes can replace DPDP and can be able to improve convergence and save calculation time, but lack of model equivalence criterion. In this study, 84 cases of 4 reservoir models has been built and simulated to study the equivalence criterion. Permeability difference and oil viscosity are considered to be the main influencing factors affecting model equivalence. With the application of the equivalence criterion, weak convergence and time consuming of fractured reservoir simulation can be improved.

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.

An Efficient Hybrid Model for 3D Complex Fractured Vuggy Reservoir Simulation

Summary Fractured vuggy reservoir is a typical type of carbonate reservoir. The 3D complex fracture networks and Stokes flow inside vugs make fractured vuggy reservoir simulation remain a challenging problem. Most of the proposed models in previous studies are computation consuming, which cannot meet with the demand of field application. In this paper, a novel and efficient hybrid model, consisting of a modified embedded discrete fracture model (EDFM) and a vug model, is proposed to simulate multiphase flow in 3D complex fractured vuggy reservoirs. The modified EDFM improves the fracture-discretization process by using two sets of independent grids for matrix and fracture systems, which promotes the modeling of 3D complex fractures in real geological structures. Meanwhile, the vug model simplifies the coupled porous-free flow with the assumption of multiphase instantaneous gravity differentiation. The accuracy of the modified EDFM and the vug model is demonstrated by comparing the results with those of the conventional EDFM and volume of fluid (VOF) method. After that, a series of case studies, including three conceptual fracture-vug unit models and a real field model, have been conducted to test the proposed hybrid model. The results of the three fracture-vug unit models indicate the significant effect of a local fracture-vug structure on the flow characteristics and production performance. Finally, the application with a real field model with 3D complex fracture and vug geometries further verifies the practicability of our proposed model in real fractured vuggy reservoirs.

A modified projection-based embedded discrete fracture model (pEDFM) for practical and accurate numerical simulation of fractured reservoir

pEDFM is a new numerical model which is proposed in the last three years to handle the flow simulation with complex fracture networks. Previous works show that classical EDFM has a good performance only for production or injection simulation of multistage fractured well, but pEDFM can effectively handle more general cases than EDFM. Although pEDFM has been validated by by some works, this paper points out that there are still some limitations in previous pEDFM need to be resolved, lying on lack of a practical method to select projected faces, the proficiency in the transmissibility formula of f-m connections, and poor performances in some cases. Then, corresponding modifications are presented to resolve these limitations, and these modifications include A practical algorithm called “micro-translation method” to select projected-faces combinations, the physical transmissibility formula of additional fracture-matrix (f-m) connections and an extended pEDFM framework by considering additional fracture-fracture (f-f) connections. Some test cases are implemented to illustrate the necessity and validity of these modifications. Besides, two examples are implemented to illustrate the robustness of the modified pEDFM workflow for practical application of a fractured reservoir.

Compositional simulation of fractured shale reservoir with distribution of nanopores using coupled multi-porosity and EDFM method

Shale reservoir contains highly heterogenous pore systems due to the wide-range distributions of nanopores in shale matrix and hydraulic/natural fractures. To explicitly include pore size distribution in simulation of shale reservoir, a multi-porosity model is applied to subdivide the matrix into multiple continua based on experimental pore size data. Each continuum has its own pore size, porosity and permeability, as well as other petrophysical properties. Besides, the embedded discrete fracture model (EDFM) is coupled with multi-porosity model to describe the complex fractures networks with any angles and intersections. To evaluate effects of pore size distribution on production, compositional simulation is conducted in a fractured shale reservoir using different number of continua in shale matrix. Simulation results show that the use of multiple continua results in lower oil and gas production. Different pressures, oil and gas saturations and compositions are observed in different continua. To further investigate the effects of distribution of nanopores, oil-gas capillary pressure is rigorously calculated in every continuum. The existence of large capillary pressure leads to different fluid properties in different size of nanopores. Moreover, capillary pressure reduces oil and gas recovery and alters compositions of residuals. The effects of capillary pressure are more significant in the low permeable continua due to smaller pore sizes.

An integrated workflow for fracture propagation and reservoir simulation in tight oil

Various fracture-propagation models have been used to capture complex hydraulic fracture (HF) geometry. However, they cannot obtain the production performance. Besides, many researchers developed reservoir simulators to obtain production performance with given fracture geometry. However, these geometries are easy to deviate from the reality of a certain reservoir. To fill this gap, there is an urgent demand to integrate the simulation of fracturing and production processes. In this work, we present an integrated workflow for fracture-propagation and reservoir simulation for tight oil. First, we employ cohesive zone model (CZM) to simulate fracture propagation. In comparison with previous studies, our CZM can simulate complex fractures. Then, we apply the complex fracture geometry to embedded discrete fracture model (EDFM). In this reservoir simulator, nonlinear flow in the tight matrix, complex HF geometry, and pressure-dependent fracture permeability (stress sensitivity effect) are considered simultaneously. Finally, we obtain production performance of this fractured well. To verify the reliability of our models, we compare the results of laboratory experiment and commercial simulator with CZM and EDFM, respectively. Using this workflow, we studied the effect of geological factor (i.e. natural fracture distribution) and fracturing schedule (i.e. injection rate) on production performance. Results reveal that the cumulative oil production in the case with regular natural fracture (NF) is 1.67% higher than that with staggered NF, and 14.6% higher than that without NF. There is an optimal injection rate to maximum production performance. In this case, medium injection rate increases cumulative oil production by 2.42% than higher injection rate, and 1.1% than lower injection. Most importantly, the continuous simulation of fracturing and production processes is implemented in our proposed simulation workflow. In this way, this workflow can be used to optimize both fracturing and production schedule to maximize production performance and/or economic benefit for tight oil in our future work. Furthermore, our method can be further extended to the simulation of multi-stage fractured horizontal well (MFHW) in tight oil or other unconventional oil and gas resources.

Numerical Simulation of the Impact of Natural Fracture on Fluid Composition Variation Through a Porous Medium

In order to lessen the computational time in fractured oil reservoir simulations, all fractures are usually assumed to be as one equivalent fracture at the center or around the model. This, specially, has applications in industrial engineering software, where this assumption applies. In this study, using two general contradictory examples, it is shown that ignoring a fracture network and assuming an equivalent single-fracture has no logical justification and results in a considerable error. The effect of fracture aperture on composition distribution of a binary and a ternary mixture was also investigated. These mixtures were C1 (methane)/n-C4 (normal-butane) and C1 (methane)/C2 (ethane)/n-C4 (normal-butane), which were under diffusion and natural convection. Governing equations were numerically solved using matlab. One of the main relevant applications of this study is where permeability and temperature gradient are the key difference between reservoirs. Compositional distribution from this study could be used to estimate initial oil in place. Using this study, one can find the optimum permeability, namely the permeability at which the maximum species separation happens, and the threshold permeability (or fracture aperture), after which the convection imposes its effect on composition distribution. It is found that the threshold permeability is not constant from reservoir to reservoir. Also, one can find that full mixing happens in the model, namely heavy and light densities of top and bottom mix up together in the model. Furthermore, after maximum separation point, convection causes unification of components.

Subsurface well spacing optimization in the Permian Basin

Optimum subsurface well spacing is key to developing unconventional reservoirs. From a field application perspective, this paper presents our systematic study on subsurface well spacing in the Permian Basin for unconventional reservoirs which consisted of four main components, i.e., numerical modeling, well interference quantification through simulation and regression, field pilot analogs, and economic evaluation. In this paper, field pilot wells are actual wells in the field to test different well spacing and completion designs.To capture upsized and downsized completions, a wide range of fracture designs in combination with different well spacing scenarios are conducted for both hydraulic fracture modeling and reservoir simulation. At the section level (1 mile by 1 mile, 640 acres), multiple wells are simulated to better capture well interactions and reservoir property variations. A complex fracture network is generated by considering interactions between natural fracture and hydraulic fracture. Well interference, which is determined by estimating ultimate recovery (EUR) difference between a single well and a middle well from multiple wells, is analyzed for general trend regressions and validated through field test results. At the section level, economics is done to evaluate capital efficiency of various scenarios. Resultsfrom both modeling work and pilots indicate that larger hydraulic fracture size without an increase in subsurface well spacing does not necessarily improve section EUR and there is a point of diminishing returns. Larger subsurface well spacing with bigger fracture size is thereby a preferable combination.

Study on the effects of fracture on permeability with pore-fracture network model

Reservoir quality and productivity of fractured gas reservoirs depend heavily on the degree of fracture development. The fracture evaluation of such reservoir media is the key to quantify reservoir characterization for the purposes such as well drilling and completion as well as development and simulation of fractured gas reservoirs. In this study, a pore-fracture network model was constructed to understand the effects of fracture on permeability in the reservoir media. The microstructure parameters of fractures including fracture length, fracture density, fracture number, and fracture radius were analyzed. Then two modes and effects of matrix and fracture network control were discussed. The results indicate that the network permeability in the fractured reservoir media will increase linearly with fracture length, fracture density, fracture number, and fracture radius. When the fracture radius exceeds 80 µm, the fracture radius has a little effect on network permeability. Within the fracture density less than 0.55, it belongs to the matrix control mode, while the fracture network control mode is dominant in the fracture density exceeding 0.55. The network permeability in the matrix and fracture network control modes is affected by fracture density and the ratio of fracture radius to pore radius. There is a great change in the critical density for the matrix network control compared with the fracture network control. This work can provide a better understanding of the relationship between matrix and fractures, and the effects of fracture on permeability so as to evaluate the fluid flow in the fractured reservoir media.

Time-dependent shape factors for fractured reservoir simulation: Effect of stress sensitivity in matrix system

Matrix-fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation in the modeling of fluid flow in fractured porous media. The chief feature within them is the accurate definition of shape factors. To date, there is no commonly accepted formulation of a matrix-fracture transfer function and shape factor. Many unsteady transfer formulations of shape factors for incompressible reservoirs have been presented and used. However, the assumption of incompressible reservoirs for these formulations is not consistent with the in-situ reservoir conditions, and a few have been reported on the application of time-dependent shape factor on dual-porosity numerical reservoir simulation. The focus of this study is, therefore, to find the time-dependent shape factor for the single-phase flow of stress-sensitive reservoirs. In this paper, the stress sensitive curves and corresponding fitting equations of a fractured reservoir are obtained based on the laboratory physical simulation; and, a model for the determination of the time-dependent shape factors that considers the stress sensitivity is presented; then the solution of nonlinear pressure diffusivity equation is used to derive the shape factor; finally, the shape factor obtained in this paper is segmented by time and applied to the dual-porosity numerical reservoir simulation. The Boltzmann transform, the separation variable method and the method of power series are used to solve the nonlinear governing equation by considering the stress sensitivity in matrix system. The approximate analytical model for the shape factor presented in this paper is verified using fine-grid, finite element numerical simulation. The dependency of the shape factor on the matrix stress sensitivity is also investigated. The theoretical analysis presented improved our understanding of transfer flow in fractured porous media, and provides a new method for dual-porosity numerical reservoir simulation of fractured reservoirs.

Three-dimensional and two-phase numerical simulation of fractured dry gas reservoirs

A significant percentage of hydrocarbon reservoirs around the world is fractured. Moreover, the major part of gas reservoirs in Iran is also fractured type, so the existence of an in-house software is necessary. In this study, an efficient, user-friendly, and indigenous simulation of a three-dimensional black oil fractured dry gas reservoir has been developed through IMPES method with the two-phase flow of gas and water. The presented simulator, which was written by C++ language and was known as fracture dry gas reservoir simulator, uses the implicit pressure and explicit saturation method for solving the equations. Also, effect of gravity pressure is neglected and effect of the capillary is considered in equations. By this simulator, we can investigate the dry gas reservoirs behavior with fractures. Darcy or non-Darcy fracture and matrix flow, Cartesian, cylindrical, and combination of Cartesian–cylindrical reservoir gridding, single porosity, dual porosity–single permeability, and dual porosity–dual permeability modeling are abilities of this simulator too. Additionally, this simulator is able to make outputs (such as pressure) at any given specific radius and time interval as numerical and/or graphical output in so little run time. Also, this simulator has PVT box and gridding box for doing the calculation of PVT and gridding. PVT box contains new correlations and EOS in comparison with another reservoir simulator. Gridding box makes us be able to simulate fractured dry gas reservoirs and hydraulically fractured well reservoirs too. Finally, the validity of this simulator was verified by comparing the simulation results with the other reservoir simulator (Eclipse) and showed a good compatibility between the developed software and Eclipse results in each time with different conditions such as various gridding conditions, various fluid data conditions and also various well configuration conditions.

Anisotropic Mesh Adaptation for 3D Anisotropic Diffusion Problems with Application to Fractured Reservoir Simulation

AbstractAnisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The 𝕄-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. In addition to mesh adaptation, preservation of the maximum principle is also studied. Some new sufficient conditions for maximum principle preservation are developed, and a mesh quality measure is defined to server as a good indicator. Four different metric tensors are investigated: one is the identity matrix, one focuses on minimizing an error bound, another one on preservation of the maximum principle, while the fourth combines both. Numerical examples show that these metric tensors serve their purposes. Particularly, the fourth leads to meshes that improve the satisfaction of the maximum principle by the finite element solution while concentrating elements in regions where the error is large. Application of the anisotropic mesh adaptation to fractured reservoir simulation in petroleum engineering is also investigated, where unphysical solutions can occur and mesh adaptation can help improving the satisfaction of the maximum principle.

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators. General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models. These methods suffer from drawbacks such as lack of flexibility and of ease of updating. In this study, I combined fracture modeling by elastic gridding which improves flexibility, especially in complex reservoirs. The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production. This is a dubious assumption, especially in reservoirs with a high production rate in the beginning. The proposed elastic fracture modeling considers changes in fracture properties, shape and aperture through the simulation. This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections. Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes, which consequently results in lower production compared with what was previously assumed. It is concluded that an elastic gridded model could better simulate reservoir performance.

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.

Two-phase numerical simulation of discrete fracture model based on multiscale mixed finite element method

Fractured reservoirs are characterized by complex fractures on multiple scales and are quite difficult to model. Numerical simulation of fractured media is usually done based on dual-porosity model and equivalent continuum model. Dual-porosity model treats matrix system and fracture system as two parallel continuous systems coupled by crossflow function. This model is only valid for reservoirs with highly developed fractures. Equivalent continuum model treats fractured media as a continuum media and equivalent absolute permeability tensors for each grid block are calculated to describe the heterogeneity of the reservoir. This model is efficient only when there exist representative element volume and the equivalent permeability are difficult to decide. Both models treat the fractured media as a simplified model and cannot describe the multiscale flows exactly, because they cannot precisely consider the diversion effect of the fractures. Although the discrete fracture network (DFN) model can provide a detailed representation of flow characteristic, traditional numerical method does not suitable for DFN. The major difficulty is the size of the computation. A tremendous amount of computer memory and CPU time are required, and this can exceed limit of today’s computer resources. Upscaling methods are generally used to reduce the computational cost. However, it is not possible to have a priori estimates of the errors that are present when complex flow processes are investigated using coarse models constructed via simplified settings. In this paper, multiscale mixed finite element method (MsMFEM) is proposed to simulate water/oil two phase flow in discrete fracture media. By combining MsMFEM with the discrete fracture model, we aim towards a numerical scheme that facilitates fractured reservoir simulation without upscaling. The MsMFEM uses a standard Darcy model to approximate pressure and fluxes on a coarse grid. The multiscale basis functions are constructed numerically by solving local differential equations on the fine-scale grid. The advantage of MsMFEM is that the basis functions capable of reflecting information about fractures within elements. Therefore, this method can capture the fine-scale effects on the coarse grid, that is, multiscale method can reduce the computational cost and keep high calculation accuracy at the same time. Traditional numerical methods generally difficult to deal with complex grid element, in this paper, mimetic finite difference (MFD) method is used to construct the multiscale basis functions due to its local conservativeness and applicability of complex grids. Compared with traditional multiscale mixed finite element methods, this method is suitable for arbitrary complex grid system. This paper introduced fundamental principles of the multiscale mixed finite element method and described the numerical scheme of discrete fracture model based on MsMFEM in detail. Then we deduced discrete fracture model computing formulate for the multiscale basis function by using mimetic finite difference method. Oversampling technique is applied to get more accurate small-scale details. IMPES scheme is used in the two-phase flow simulation. Physical experiment is used to prove the validity the multiscale method. The numerical results show that compared with traditional numerical method, the MsMFEM can represent the fine-scale flow in fracture networks exactly and meanwhile has a higher computational efficiency.

Numerical simulation of water flooding in natural fractured reservoirs based on control volume finite element method

A numerical method is employed to investigate the fluid flowing dynamics in fractured reservoirs in this paper. Owing to the multi-scales and strong heterogeneity, description of fracture network systems plays a significant role for a successful fractured reservoir simulation model. Comparing to previous works, this paper proposes a combination of dual continuum and discrete fracture network (DFN) model, which is used to simulate the flow in reservoirs with multi-scale fractures and proved feasible. In the first part of the paper, implicit flow equations of oil and water phase in fractured reservoirs are established to consider the nonlinearity properties. And then the control volume finite element method based on the unstructured grid system and N-R iteration are used to obtain the numerical solution. Moreover, the accuracy of this simulator is proved to be reasonable by field data; Sensitivity analysis shows that the existences of complex multi-scale fracture networks have great impacts on water flooding. Compared with the homogeneous reservoir, natural fracture (micro and large scale) networks can change the direction and velocity of the waterfront, which finally leads to the more serious water breakthrough, higher water cut and less recovery. The research and the numerical results obtained in this paper can provide theoretical guidance for efficient and scale development of natural fractured reservoirs.

Shape factor for dual-permeability fractured reservoir simulation: Effect of non-uniform flow in 2D fracture network

The flow properties of naturally fractured reservoirs are dominated by flow through the fractures. In a previous study we showed that even a well-connected fracture network behaves like a much sparser network when the aperture distribution is broad enough: i.e., most fractures can be eliminated while leaving a sub-network with virtually the same permeability as the original fracture network. In this study, we focus on the influence of eliminating unimportant fractures which carry little flow on the inferred characteristic matrix-block size. We model a two-dimensional fractured reservoir in which the fractures are well-connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, because information from the subsurface is limited, we test a number of cases: log-normal distributions (from narrow to broad), and power-law distributions (from narrow to broad). The matrix blocks in fractured reservoirs are of varying sizes and shapes; we adopt the characteristic radius and the characteristic length to represent the characteristic matrix-block size. We show how the characteristic matrix-block sizes increase from the original fracture network to the dominant sub-network. This suggests that the matrix-block size, or shape factor, used in dual-porosity/dual-permeability waterflood or enhanced oil recovery (EOR) simulations or in homogenization should be based not on the entire fracture population but on the sub-network that carries almost all of the injected fluid (water or EOR agent).