A Hybrid-Dimensional Iterative Coupled Modeling of Lubrication Flow in Deformable Geological Media with Discrete Fracture Networks.

Discrete fracture network (DFN) and stochastic continuum (SC) are two common modeling approaches used for simulating fluid flow and solute transport in fractured media. Fracture continuum approaches combine the merits of each approach; details of the fracture network are preserved, and a computationally efficient grid is utilized for the solution of fluid flow by assigning a conductivity contrast between the grid cells representing the rock matrix and those representing fractures. In this paper, we propose a fracture continuum approach for mapping individual fractures onto a finite‐difference grid as conductivity fields. We focus on several issues that are associated with this approach, such as enhanced connectivity between fractures that would otherwise not be in connection in a DFN simulation and the influence of grid cell size. To addresses these issues, both DFN and the proposed approach are used to solve for fluid flow through two‐dimensional, randomly generated fracture networks in a steady‐state, single‐phase flow system. The DFN flow solution is used as a metric to evaluate the robustness of the method in translating discrete fractures onto grid cell conductivities on four different regularly spaced grids: 1 × 1 m, 2 × 2 m, 5 × 5 m, and 10 × 10 m. Two correction factors are introduced to ensure equivalence between the total flow of the grid and the original fracture network. The first is dependent on the fracture alignment with the grid and is set to account for the difference between the length of the flow path on the grid and that of the fracture. The other correction is applied for areas in the grid with high fracture density and accounts for the artificial degree of connectivity that exists on the grid but not in the DFN. Fifteen different cases are studied to evaluate the effect of fracture statistics on the results of the proposed approach and by taking average results of 100 realizations in each case in a stochastic Monte Carlo framework. The flow equation is solved for the DFN, and total flow is obtained. The flow is also solved separately for the four‐grid resolution levels, and comparisons between the DFN and the grid total flows are made for the different cases and the different grid resolution levels. The approach performed relatively well in all cases for the fine‐grid resolution, but an overestimation of grid flow is observed in the coarse‐grid resolution, especially for cases wherein the network connectivity is controlled by small fractures. This overestimation shows minor variation from one realization to another within the same case. This allowed us to develop an approach that depends on solving limited number of DFN simulations to obtain this overestimation factor. Results indicate that the proposed approach provides improvements over existing approaches and has a potential to provide a link between DFN and SC models.

Two of the commonly used approaches in modelling flow and transport in fractured geological media are the discrete fracture network (DFN) approach and the stochastic continuum (SC) approach. The former approach is computationally demanding and requires large input parameters, whereas the latter approach is computationally efficient and requires fewer parameters but at the expense of not preserving fracture network details and properties. The fracture continuum (FC) approach combines the advantages of both the DFN and SC approaches. The main objective of this research is to develop a mapping technique utilizing the FC approach to preserve transport characteristics between DFN and the mapped continuum. A two-dimensional particle tracking model is developed to simulate conservative contaminant transport through DFN. The fracture network is randomly generated in a stochastic Monte Carlo framework, and the flow problem is solved using mass conservation at the fracture junctions. The transport problem is then solved via the developed particle tracking model on the DFN. The obtained transport solution is used as a reference solution. The fracture network is mapped onto a finite difference grid at four different grid cell sizes: 1 m × 1 m, 2 m × 2 m, 5 m × 5 m, and 10 m × 10 m, and the flow problem is solved via MODFLOW. The transport problem is solved on the grid using a particle tracking method. Comparisons between the transport characteristics for both approaches (DFN and FC) are performed, and the percentage error in each case is quantified. It is found that a new correction factor is needed to preserve conservative transport characteristics on the grid. The developed correction factor improves the ability of the FC technique to preserve transport on the grid for the case of conservative contaminant transport.

Advancements towards DFKN modelling: Incorporating fracture enlargement resulting from karstic dissolution in discrete fracture networks

Fractured media are very heterogeneous systems where occur complex physical and chemical processes to model. One of the possible approaches to conceptualize this type of massifs is the Discrete Fracture Network (DFN). Donado et al. (2005) modeled flow and transport in a granitic batholith based on this approach and found good fitting with hydraulic and tracer tests, but the computational cost was excessive due to a gigantic amount of elements to model. We present in this work a methodology based on percolation theory (Berkowitz, 2002) for reducing the number of elements and in consequence, to reduce the bandwidth of the conductance matrix and the execution time of each network. DFN poses as an excellent representation of all the set of fractures of the media, but not all the fractures of the media are part of the conductive network. Percolation theory is used to identify which nodes or fractures are not conductive, based on the occupation probability or percolation threshold. In a fractured system, connectivity determines the flow pattern in the fractured rock mass. This volume of fluid is driven through connection paths formed by the fractures, when the permeability of the rock is negligible compared to the fractures. In a population of distributed fractures, each of this that has no intersection with any connected fracture does not contribute to generate a flow field. This algorithm also permits us to erase these elements however they are water conducting and hence, refine even more the backbone of the network. This percolation theory seeks to find a network of conductive fracture smaller than the original, but without departing from the actual behavior of the fluid in a fractured medium and thus improve the calibration of the flow inverse modeling done with TRANSINIV. Donado (2000) used 100 Different generations Fracture Network (DFN) that were optimized in this study using percolation theory. In each of the networks calibrate hydrodynamic parameters as hydraulic conductivity Κ and specific storage coefficient Ss, for each of the five families of fractures (tectonic defined criteria), yielding a total of 10 parameters to estimate, at each generations. The 100 DFNs used have the following characteristics: (i) they are not a trellis system, this means that a 3D system fractures do not follow a path of any geometric shape known as a cube, diamond, or honeycomb; (ii) from any node can leave many items to other nodes (Fig. 1); (iii) the length of failure of these fracture networks are not standardized and is constant, this means that on average, the minimum length is 23 m and found the maximum length is 955 m; (iv) the fracture networks are contained in a real finite system known limits, with approximate dimensions of a rectangular 710 × 1040 × 576 m. With these features the fractal dimension of this large cluster (which determines the spatial distribution of network connectivity) and the fractal dimension of the backbone (which determines the flow path) are different from those predicted by the classical theory of percolation. Since the effect of the distribution of fault orientation changes the value of the percolation threshold, but not the universal laws of classical percolation theory, the latter is applicable to such networks. Under these conditions, percolation theory permits to reduce the number of elements (90% in average) that form clusters of the 100 DFNs, preserving the so-called backbone. In this way the calibration runs in these networks changed from several hours to just a second obtaining much better results (Fig. 2). Green line represents the previous results using all the fractures and purple line shows new results with optimized fractures.

The discrete fracture network (DFN) model simulation, in which the fracture network can have a natural heterogeneity, is one of the most effective approaches in fluid flow analyses for a fractured reservoir. In the DFN model simulation, the fracture is modeled by a pair of parallel smooth plates although real fractures have rough surfaces. However, numerous field and laboratory observations have suggested that fluid flow through a fracture occurred in specific preferential flow paths (channeling flow) due to a heterogeneous aperture distribution formed by the rough surfaces. The conventional DFN model simulation therefore gives us a serious concern about the reality. To address this concern, we have developed a new concept DFN model simulator, GeoFlow, in which the fracture can have the heterogeneous aperture distribution. Three dimensional fluid flow simulation was performed for a simple fracture network by both the conventional and the new concept DFN models. In the conventional DFN model simulation, the fracture had no aperture distribution, and fluid flow in the fracture plane was quite uniform. On the other hand, the GeoFlow simulation showed formation of three dimensional preferential flow paths in the fracture network. In addition, another GeoFlow simulation showed that productivities of the wells highly depended on their locations even when the wells intersected the same fracture. The productivities were considerably smaller when the wells intersected the regions with smaller aperture conductivities, where the preferential flow paths were difficult to form at the natural condition (no well condition). The results demonstrated occurrence of three dimensional channeling flow in fractured reservoirs, which should be addressed for effective developments of the reservoirs. Introduction Fluid flows through rock fractures in the Earth's crust have been a subject of interest for some time because rock fractures usually have much greater permeability than the rock matrix. Rock fractures are therefore recognized as the predominant pathways of resources and hazardous materials such as groundwater, oil/gas, geothermal fluids, and the high-level nuclear wastes. The fluid flow properties of rock fractures have been investigated with respect to the geological disposal of the high-level nuclear wastes. As a result, our understanding of the subsurface flow system has been greatly improved and has been applied to the development of geothermal and oil/gas fractured reservoirs. Recently, the prediction of flow and transport phenomena through rock fractures based on a precise modeling of the flow system in a fractured rock mass with natural heterogeneities has become increasingly important because recent environmental and energy problems require urgent solutions using underground space based on the safe and effective development of reservoirs. A modeling with a natural heterogeneity of a fracture network has been established by the Discrete Fracture Network (DFN) modeling technique [1–5]. In the DFN modeling, rock fractures have been described by parallel smooth plates. However, field and laboratory studies have suggested that fluid flow through a rock fracture is far from the fluid flow through parallel smooth plates, due to channeling flow in a heterogeneous aperture distribution by rough surfaces [6–14]. When channeling flow occurs in a single fracture of granite, the area where flowing fluid exists is expected only 5–20% at confining pressures of up to 100 MPa, with various features in the preferential flow paths [14].

ABSTRACT: Genetic discrete fracture network (DFN) modeling is a dynamic modeling approach that simulates fracture growth processes in DFN generation. The modeling procedure incorporates growth-related input parameters, such as the growth time, step size, and coefficients of nucleation and growth, which are difficult to deduce directly from survey data. This study introduces a method for conditioning these growth parameters to trace length distribution using an optimization procedure, where the growth parameters are fine-tuned to produce genetic DFNs that align with the observed distribution. The optimization objective function is formulated to minimize the difference in trace length distributions and the number of traces between the observed trace map and that derived from a genetic DFN. In case studies involving synthetic and real trace maps, the conditioned genetic DFNs reproduced trace maps that exhibit a high level of fitness to the observed data. Considering the representation of complex growth processes and fracture interactions, these models can provide a robust foundation for DFN extrapolation beyond the surveyed areas. 1. INTRODUCTION Natural fracture networks can be modeled in the form of discrete fracture networks (DFNs) that capture the spatial characteristics of the observed network. In DFNs, fractures are simplified as discrete objects, commonly as disks, which replicate the geometric properties of fractures. The geometric properties of these fracture disks, including size and orientation, can be determined by analyzing the distributions of surveyed data and directly sampling values from these distributions to match the observed data. This modeling approach is termed as "stochastic" or "Poisson" DFN modeling, where fractures are randomly generated by corresponding statistical models (Lei et al., 2017). While stochastic DFNs follow the statistical models of geometric properties, such as size and orientation, they exhibit clear limitations in reproducing the organization or topology of fracture networks, especially the specific fracture terminations in the form of T-type intersections (Selroos et al., 2022). The stochastic DFN approach fundamentally lacks physical integrity as it is purely statistical and does not consider the physical process involved in fracture network generation.

Fluid flow and solute transport simulations in tight geologic formations: Discrete fracture network and continuous time random walk analyses

Fractured media are heterogeneous systems in which water flows primarily across rock fractures. Flow dynamics and transport of dissolved substances are controlled by the topological distribution and hydraulic properties of the fracture network (including aperture , hydraulic conductivity K and porosity). These topological and hydrodynamic properties are usually insufficiently characterized in field applications, generating uncertainty in the predictions of flow and solute transport. This paper explores a possible application of the concept of geological entropy, in particular the entrogram, as an approach to describe and potentially predict flow and transport in fractured media. In porous media, the entrogram was proven to be an effective approach to represent the spatial persistence and connectivity of high K patterns, enabling predictions for solute transport when proper correlations are established. Given the similarities between high K patterns in porous media and water-bearing fractures in fractured media, preliminary tests were realized to evaluate an idealized two-dimensional fractured system with regular distribution of two sets of fracture networks, one with a more persistent spatial distribution of fractures than the other. A multiphase flow model based on discrete fracture network is used to simulate a tracer test during which a conservative species displaces an immiscible one injected through a well. The analyses of the breakthrough curves (BTCs) of the relative saturation of each phase at another well allows evaluating the relationship between entrogram metrics and the shape of the BTCs. The initial results are promising and push for a more rigorous evaluation of the link among the metrics. This would require primarily the reproduction of more realistic fracture network including multidimensional systems.

Towards simulating solute transport in complex, regional-scale fracture networks: a rapid upscaled approach

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

Advanced characterization methodologies are now able to provide realistic pictures of fracture networks. We recently developed a software to simulate the transient and pseudo-steady-state flows of a slightly compressible fluid in Discrete Fracture Network (DFN) models. This simulator is used to validate the fracture network geometry and to calibrate the hydraulic properties of the fractures via dynamic data obtained from flow meters, interference and well tests. This paper is dedicated to the extension of the methodology to gas cases, taking into account the high fluid compressibility and the non-Darcian effects near the well bore. The main specific features of our simulator are described and illustrated through demonstrative examples. Our DFN simulation approach is based on an optimised explicit representation for both matrix and fracture media and a specific treatment for matrix-fracture and matrix-matrix exchanges. A pseudo-pressure function is included in the diffusivity equation to take into account highly compressible fluids. The hydrodynamic behaviour of gas fluid flow near the well bore is taken into account via a skin effect proportional to the flow-rate for both matrix-well and fracture-well transmissivities. This innovative numerical simulator is validated against existing analytical solutions and compared with finite-volume solutions computed with a suitable grid. Then, for application purposes, a complex realistic case involving a multi-scale natural fracture network with small-scale fractures and major objects such as seismic and sub-seismic faults is presented. An interference test is simulated on a representative DFN model and on the equivalent dual-porosity model built thanks to up-scaling procedures. This up-scaled reservoir model is shown to remain consistent with the geological DFN model in terms of gas flow. This example illustrates the practical use of DFN models in our fractured reservoir modelling workflow.

Advanced characterization methodologies are now able to provide realistic pictures of fracture networks. We recently developed a software to simulate the transient and pseudo-steady-state flows of a slightly compressible fluid in Discrete Fracture Network (DFN) models. This simulator is used to validate the fracture network geometry and to calibrate the hydraulic properties of the fractures via dynamic data obtained from flow meters, interference and well tests. This paper is dedicated to the extension of the methodology to gas cases, taking into account the high fluid compressibility and the non-Darcian effects near the well bore. The main specific features of our simulator are described and illustrated through demonstrative examples. Our DFN simulation approach is based on an optimised explicit representation for both matrix and fracture media and a specific treatment for matrix-fracture and matrix-matrix exchanges. A pseudo-pressure function is included in the diffusivity equation to take into account highly compressible fluids. The hydrodynamic behaviour of gas fluid flow near the well bore is taken into account via a skin effect proportional to the flow-rate for both matrix-well and fracture-well transmissivities. This innovative numerical simulator is validated against existing analytical solutions and compared with finite-volume solutions computed with a suitable grid. Then, for application purposes, a complex realistic case involving a multi-scale natural fracture network with small-scale fractures and major objects such as seismic and sub-seismic faults is presented. An interference test is simulated on a representative DFN model and on the equivalent dual-porosity model built thanks to up-scaling procedures. This up-scaled reservoir model is shown to remain consistent with the geological DFN model in terms of gas flow. This example illustrates the practical use of DFN models in our fractured reservoir modelling workflow.

Microseismicity is a physical phenomenon which allows us to estimate the production capability of the well after hydraulic fracturing (HF) in a naturally fractured (NF) reservoir. Some of the microseismic events are reactivations of NFs induced by a direct hit of HF, while others are induced by the fluid leak-off from the previous stages or by elastic waves emitted into the reservoir with hydraulic fracture plane propagation. The former NFs have a chance to be propped there as the latter will not significantly increase their contribution to the production. Identification of such microseismic events helps to reduce uncertainty in the description of fracture network geometry. Based on inferred data from core analysis NF densities and orientations, we generated multiple realizations of the semi-stochastic Discrete Fracture Network (DFN). In order to constrain them, we used time evolution of microseismic cloud in addition to results of core analysis. Fluid and proppant pumping schedule is used to identify such microseismic events because they should be located close to the pressure diffusion front generated by hydraulic fluid. Events outside of proposed region may be triggered by other factors, such as stress-strain relaxation from other stages and correspondent fractures. In most cases, they are not wide enough to take proppant from the main HF. This approach was used to reduce range of production for DFN realizations. This workflow is implanted to a 15-stage hydraulic fracture treatment on a horizontal well placed in a siltstone reservoir with intrinsic fractures. The spatio-temporal dynamics of microseismic events are classified into two groups by the front of nonlinear pressure diffusion caused by 3-dimensional hydraulic fracturing, considered as effective and ineffective events. DFNs with only effective microseismicity and with all the induced events are generated. Then, two types of DFN related uncertainties on production are performed to evaluate the impact of filtration. Results of aleatory uncertainty quantification caused by the randomness of DFN modeling indicate the filtered events can generate a production DFN with a more consistent connected fracture area. Moreover, sensitivity analysis caused by lack of accuracy in natural fracture characterization shows the production area of DFN with filtration process is more insensitive to the variation of fracture parameters. Finally, a history match with production data and pressure data indicates this DFN model properly represents the reservoir and completion. Our methodology characterizes well the conductive fracture network utilizing core data, microseismic data, and pumping schedule. It could restore the true productivity of each fractured stage from a massive microseismic cloud, which helps understand the contribution of fracturing job right after the treatment.

In the present work we consider the problem of performing underground flow simulations in fractured media, following the Discrete Fracture Network (DFN) model. We will focus on a quite recent approach to the problem, based on a PDE-constrained optimization formulation, which allows for the use of totally non-conforming meshes on the network. In this way arbitrarily complex DFNs can be effectively tackled, without requiring any modification of the geometry of the network. Extended numerical simulations are reported demonstrating the performances of the proposed method, and highlighting its robustness in handling networks with hard-to-mesh configurations, such as extremely narrow angles between intersecting fractures. The problem of advection-diffusion of pollutant species in networks of fractures is also addressed in a time-dependent framework, using the optimization-based approach both to derive the Darcy velocity and to solve the transport problem at each time frame.

Non-stationary transport phenomena in networks of fractures: Effective simulations and stochastic analysis