Large-scale Fracture Network Research Articles

Modeling of transport processes through large-scale discrete fracture networks using conforming meshes and open-source software

Most industrial and field studies of transport processes in Discrete Fracture Networks (DFNs) involve strong simplifying assumptions, especially at the meshing stage. High-accuracy simulations are therefore required for validating these simplified models and their domain of validity. The present paper proposes an efficient workflow based on open-source software to obtain transport simulations. High-quality computational meshes for DFNs are first generated using the conforming meshing approach FraC. Then, a tracer transport model implemented in the open-source code DuMux is used for simulating tracer transport driven by the advection-dispersion equation. We adopt the box method, a vertex-centered finite volume scheme for spatial discretization, which ensures concentration continuity and mass conservation at intersections between fractures. Numerical results on simple networks for validation purposes and on complex realistic DFNs are presented. An a-posteriori convergence study of the discretization method shows an order of convergence O(h) for tracer concentration with h the mesh size.

Evaluation on the effectiveness of natural fractures in Changxing Fm reef-flat facies reservoirs, Yuanba area, Sichuan Basin

Study on the effectiveness of fractures is of great significance for understanding reservoir types and properties, identifying reservoir seepage mechanisms and delineating the reasonable development technologies and policies. In this paper, the Changxing reef-flat facies reservoirs in the Yuanba area, Sichuan Basin, was taken as an example. After the characteristics of natural fractures were evaluated, the effectiveness of different types of fractures was investigated by using core, thin section, imaging logging and production performance data. Then, the main geological factors that influence fracture effectiveness were analyzed, and the development significance of effective fractures was illustrated. The following results are obtained. (1) Structural fractures and diagenetic fractures are mainly developed in Changxing Fm carbonate reservoirs in Yuanba area. Structural fractures include shear fractures and extensional fractures, and diagenetic fractures include dissolution fractures, structural-dissolution fractures and pressure-solution fractures. (2) High-angle structural fractures are the most effective, followed by horizontal fractures and then oblique fractures, and pressure-solution fractures are the least effective. (3) Among structural fractures, those of NW–SE and nearly E–W oriented are more effective than those of the NE–SW oriented. (4) The earlier the fractures are formed, the more likely they are to be filled with calcite or dolomite and become invalid. (5) The fractures which are formed before or during the oil and gas charging tend to be filled with organic matters and become invalid. The late fractures which are formed after oil and gas charging are mostly effective and their contribution to the reservoir is the greatest. (6) The fractures nearly parallel to the maximum principal stress direction of current ground stress present good effectiveness with large opening. It is concluded that the opening and filling features of natural fractures help determine if fractures are effective or not, and the development degree, distribution and combination features of effective fractures and the matching relationship between fractures and pores further dominate the development significance of effective fractures; that when the effective fractures are more developed and are connected with each other to form a large-scale fracture network, separated and isolated pores and dissolved fractures and cavities can be connected, as a result, the physical properties of reservoirs are improved and high production rates of gas wells are realized.

Experimental investigation on fracture surface strength softening induced by fracturing fluid imbibition and its impacts on flow conductivity in shale reservoirs

The economic development of shale gas reservoir requires not only the large-scale complex fracture network, but also the sufficient fracture conductivity. Field operations have demonstrated that large amounts of fracturing fluids are retained in shale formations due to low flow-back efficiency. The fluids can enter into the surrounding reservoir matrix through hydraulic fractures. A series of microcosmic physical and chemical reaction can lead to fracture surface softening. In this paper, comparative imbibition experiments are conducted on 9 core samples from different shale formations. Nuclear magnetic resonance technique is used to evaluate the water-rock interaction range. Then, a large number of gird indentation tests for surface hardness with spontaneous imbibition time are designed to investigate change rules of fracture surface mechanical properties in the interaction between fluid and shale. Furthermore, the long-term fracture conductivity experiments, which are performed by gas and water alternately, are carried out to analyze the influence of water-rock interaction and fracture surface softening on fracture conductivity. The results show that the main affected area of water-rock interaction (water saturation>50%) during the seven-day water imbibition in the tight shales is located several millimeters inward near the imbibition surface. The first 1 h of the imbibition in the fracture surface is the beginning stage when mesoscopic damages to rock surface hardness occur, which results in gentle hardness decline. In the following 24 h, damages intensify, leading to considerable hardness decline, which accounts for 50%–75% of the total. After that, damages continue to increase slowly. The fracture surface strength softening has no direct relation with the water imbibition rate and the imbibed volume per unit volume of rocks. The intensity of such kind of physical and chemical reaction can be reflected by the pore volume multiple of imbibed water and the effective driving force coefficient, whose higher values indicates stronger water-rock effects and more serious fracture conductivity damages. This study preliminarily explores the interior relation between the spontaneous imbibition capacity and the fracture surface softening. It can also provide new methods for the evaluation and analysis of proppant embedment and fracture conductivity damages.

Simulation of micro-seismicity in response to injection/production in large-scale fracture networks using the fast multipole displacement discontinuity method (FMDDM)

Analysis of fluid flow, permeability, and micro-seismicity in large fracture networks are essential for economical production from engineered geothermal and petroleum reservoirs. In this work, the fluid pressure change, as a result of injection and production inside a stochastic, deformable, non-propagating fracture network is modeled using the fast multipole displacement discontinuity method combined with the finite difference method. The former is employed to simulate the response of the fracture network to changes in the pressure due to fluid injection. In addition to pressure changes inside the fracture network, changes in fracture status with respect to normal (“joint” versus hydraulic fracture) and shear (stick versus slip) deformation, dilation, and friction coefficient are considered. Rate-and-state friction model and the Mohr-Coulomb criterion are used to model slip and potential micro-earthquakes and their seismic moments. Simulation results show that increase in pressure inside a fracture network leads to permanent slip and nucleation of micro-earthquakes which are mostly influenced by the orientation of the fractures and the magnitude of fluid pressure and the injection rate. Injecting the same volume of water over a longer time period decreases the number and magnitude of seismic events.

Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks

The apertures of natural fractures in fractured rock are highly heterogeneous. However, in-fracture aperture variability is often neglected in flow and transport modeling and individual fractures are assumed to have uniform aperture distribution. The relative importance of in-fracture variability in flow and transport modeling within kilometer-scale field–scale fracture networks has been under a matter of debate for a long time because the flow in each single fracture is controlled not only by in-fracture variability but also by boundary conditions. Computational limitations have previously prohibited researchers from investigating the relative importance of in-fracture variability in flow and transport modeling within large-scale fracture networks. We address this question by incorporating internal heterogeneity of individual fractures into flow simulations within kilometer scale three-dimensional fracture networks, where fracture intensity, P32 (ratio between total fracture area and domain volume) is between 0.027 and 0.031 [1/m]. A recently developed discrete fracture network (DFN) simulation capability, dfnWorks, is used to generate DFNs that include in-fracture aperture variability represented by a stationary log-normal stochastic field with various correlation lengths and variances. The Lagrangian transport parameters, non-reacting travel time and cumulative retention, are calculated along particles streamlines. It is observed that due to local flow channeling early particle travel times are more sensitive to in-fracture variability than the tails of travel time distributions, where no significant effect of the in-fracture transmissivity variations and spatial correlation length is observed.

Numerical Investigation into the Influence of Bedding Plane on Hydraulic Fracture Network Propagation in Shale Formations

Shale formations are often characterized by low matrix permeability and contain numerous bedding planes (BPs) and natural fractures (NFs). Massive hydraulic fracturing is an important technology for the economic development of shale formations in which a large-scale hydraulic fracture network (HFN) is generated for hydrocarbon flow. In this study, HFN propagation is numerically investigated in a horizontally layered and naturally fractured shale formation by using a newly developed complex fracturing model based on the 3D discrete element method. In this model, a succession of continuous horizontal BP interfaces and vertical NFs is explicitly represented and a shale matrix block is considered impermeable, transversely isotropic, and linearly elastic. A series of simulations is performed to illustrate the influence of anisotropy, associated with the presence of BPs, on the HFN propagation geometry in shale formations. Modeling results reveal that the presence of BP interfaces increases the injection pressure during fracturing. HF deflection into a BP interface tends to occur under high strength and elastic anisotropy as well as in low vertical stress anisotropy conditions, which generate a T-shaped or horizontal fracture. Opened BP interfaces may limit the growth of the fracture upward and downward, resulting in a very low stimulated thickness. However, the opened BP interfaces favor fracture complexity because of the improved connection between HFs and NFs horizontally under moderate vertical stress anisotropy. This study may help predict the HF growth geometry and optimize the fracturing treatment designs in shale formations with complex depositional heterogeneity.

A semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks

Summary This paper presents a semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete fracture model. The small-scale fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the fracture network characteristics while keeping the computational work manageable. For example, the large-scale fracture network may have complex geometry and varying conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in fractured reservoir with multi-scale fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale fracture network linear flow, bilinear flow, small-scale fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale fracture network behaves as if it only drains in the small-scale fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale fracture network linear flow are predominantly determined by the dimensionless large-scale fracture conductivity. And low dimensionless fracture conductivity will generate large pressure drops in the large-scale fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

Large-scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

Summary An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time-marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large-scale problems have accounted only for elastic rocks, neglecting the fluid leak-off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large-scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field-scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling injection/extraction in a fracture network with mechanically interacting fractures using an efficient displacement discontinuity method

The displacement discontinuity method (DDM) is frequently used for modeling the behavior of fractures in reservoir modeling. However, the DDM is not computational efficient for large systems of cracks, limiting its application to small-scale situations. Recent fast summation techniques such as the Fast Multipole (FM) Method accelerate the solution of large fracture problems, demanding linear complexity O(N) in memory and execution time with very modest computational resources. In this work we use the FM-DDM method to simulate fracture response while considering fluid flow through the fracture network. This is a novel and efficient approach for solution of large scale coupled fluid flow-geomechanical problem in naturally fractured reservoirs. Several case studies involving fracture networks with several hundred thousands of boundary elements are presented. The results show a good level of accuracy and computational efficiency compared to the conventional DDM. In addition, the approach is shown to be very useful for the design of exploitation strategies in large-scale fracture network situations. The relative positions between injectors and producers and the fracture permeability variation with injection/extraction play an important role on the distribution of stresses in the fracture network, which in-turn, influence the conditions for the fluid-flow such as fluid pressure and fracture permeability.

Experimental Investigation into Hydraulic Fracture Network Propagation in Gas Shales Using CT Scanning Technology

Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ v ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ h ≤ 6 MPa and simple transverse fracture for Δσ h ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ h from 6 MPa to 12 MPa.

Fractional dynamics of tracer transport in fractured media from local to regional scales

AbstractTracer transport through fractured media exhibits concurrent direction-dependent super-diffusive spreading along high-permeability fractures and sub-diffusion caused by mass transfer between fractures and the rock matrix. The resultant complex dynamics challenge the applicability of conventional physical models based on Fick’s law. This study proposes a multi-scaling tempered fractional-derivative (TFD) model to explore fractional dynamics for tracer transport in fractured media. Applications show that the TFD model can capture anomalous transport observed in small-scale single fractures, intermediate-scale fractured aquifers, and two-dimensional large-scale discrete fracture networks. Tracer transport in fractured media from local (0.255-meter long) to regional (400-meter long) scales therefore can be quantified by a general fractional-derivative model. Fractional dynamics in fractured media can be scale dependent, owning to 1) the finite length of fractures that constrains the large displacement of tracers, and 2) the increasing mass exchange capacity along the travel path that enhances sub-diffusion.

An efficient time-domain approach for simulating Pe-dependent transport through fracture intersections

In the subsurface, fractures commonly provide dominant pathways for fluid flow and solute transport. However, mechanisms responsible for dispersion in large-scale fracture networks are not completely understood. Scalable models of flow and transport in discrete fracture networks that accurately represent the small-scale physics controlling transport can provide a means for improving understanding of the large-scale dispersion mechanisms. Within fracture networks, mixing within fracture intersections can play an important role in mass transport. This mixing process results from a combination of advection and diffusion within fracture intersections. A number of high-resolution computational studies involving direct solution of the Stokes equations in fracture intersections show that mixing exhibits a strong dependence on Peclet number, Pe=V〈b〉Dm, where V is the mean fluid velocity, 〈b〉 is the mean fracture aperture and Dm is the molecular diffusion coefficient. However, such high-resolution techniques are not feasible in large-scale network simulations, so it is common to model mixing using either stream-tube routing (Pe→∞) or complete mixing (Pe→0). We present a novel probabilistic method that allows accurate and efficient calculation of the Pe-dependent solute transport through fracture intersections. Fundamental to our approach is a simplified approximation to the Stokes velocity field within fracture intersections based upon local application of the cubic law in each fracture entering and exiting the fracture intersection. In addition, we use a time domain approach to route particles across the fracture intersection in a single step; using this approach the influence of both advection and diffusion are represented explicitly. Results show that our new model accurately represents the trajectory and travel times of particles passing through a fracture intersection. Furthermore, the proposed algorithm is two to three orders-of-magnitude faster than comparable simulations relying upon detailed simulation of the Stokes velocity field.

History Matching of a Stochastic Model of Field-Scale Fractures: Methodology and Case Study

This paper focuses on the history matching of stochastic models of large-scale fractures under seismic resolution, namely sub-seismic faults and fracture swarms. First, we propose an object-based stochastic model for describing geological features of large-scale fractures. This model accounts for static constraints derived from seismic attributes, fault-related-strain-field, structural information (curvature), etc. Second, we review an upscaling procedure for performing fluid flow simulation in the presence of networks of large-scale fractures. Third, we present an algorithm for gradually moving and deforming stochastic fractures in the reservoir field while preserving their consistency with static constraints (location of seismic fractures, fracture density and orientation maps), whereby different realizations of the stochastic fracture network can be obtained. All these elements are integrated in an inverse procedure for calibrating stochastic models of large-scale fracture networks to hydrodynamic two-phase flow data. The above methodology is applied to an actual fractured reservoir. We build a field-scale fracture network constrained to the fracture density map and the orientations of the two fracture sets. Then we perform history matching of water-cut data in four zones of the field. Different calibration procedures are tested: global optimization that allows a general improvement of the model calibration to production data, and local calibration that further improves the match of each well. The results show the validity of the proposed methodology.

Flow Focusing in Unsaturated Fracture Networks: A Numerical Investigation

A numerical modeling study is presented to investigate flow–focusing phenomena in a large-scale fracture network, constructed using field data collected from the unsaturated zone of Yucca Mountain, Nevada, the proposed repository site for high-level nuclear waste. The two-dimensional fracture network for an area of 100 by 150 m contains more than 20000 fractures. Steady state unsaturated flow in the fracture network is investigated for different boundary conditions and rock properties. Simulation results indicate that flow paths are generally vertical, and that horizontal fractures mainly provide pathways between neighboring vertical paths. In addition to fracture properties, flow–focusing phenomena are also affected by rock–matrix permeability, with lower matrix permeability leading to a high degree of flow focusing. The simulation results further indicate that the average spacing between flow paths in a layered system tends to increase and flow tends to become more focused, with depth.