Derivation of equivalent pipe network analogues for three‐dimensional discrete fracture networks by the boundary element method

Abstract

Abstract. Discrete fracture network (DFN) models generally require solution of flow and transport equations in three-dimensional networks of either disc, polygonal, or pipe elements. Pipe network elements have significant advantages in computation for both flow and transport. However, there is a need to develop an efficient procedure for derivation of the properties of these pipes to ensure that they are hydraulically equivalent to the DFN network of polygonal elements. In this study a boundary element procedure for derivation of pipe properties is developed and demonstrated. The results show that the hydraulic behavior of pipe networks can be equivalent to that of polygonal-element DFN models. IntroductionThree-dimensional discrete fracture network (DFN) models are becoming accepted as a tool for modeling heterogeneously connected rock masses [Dershowitz and Einstein, 1988; Reeves et al., 1994]. DFN models provide a useful alternative to continuum approaches where discrete feature geometry and connectivity play a major role.Recent research has focused on ways to improve the efficiency of DFN models, which can be constituted by of the order of 105 or even 10 6 polygonal or disk-shaped fractures. In the proposed approach the conductance is estimated by means of the boundary element method (BEM) as an influence factor between each trace. This provides a better approximation than the qualitative relationship, because the BEM can be formulated to produce conductance values that are consistent with the flow pattern within each fracture.As a first approximation, conductances might be calculated 2685

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

“…Many factors can affect the magnitude of permeability of fractured rock masses, including fracture length [28][29][30][31], aperture [32][33][34], surface roughness [35,36], dead-end [37], number of intersections [38,39], hydraulic gradient [40], boundary stress [41,42], anisotropy [43][44][45][46], scale [47][48][49][50], stiffness [51], coupled thermo-hydro-mechanical-chemical (HTMC) processes [52][53][54][55], and precipitation-dissolution and biogeochemistry [56]. The discrete fracture network (DFN) model, which can consider most of the above parameters, has been increasingly utilized to simulate fluid flow in the complex 2 Geofluids fractured rock masses [57][58][59][60], although it cannot model the aperture heterogeneity of each fracture [61][62][63]. In the numerical simulations and/or analytical analysis, the linear governing equation such as the cubic law is solved to simulate fluid flow in fractures by applying constant hydraulic gradients ( ) on the two opposing boundaries, such as = 1 [57,[64][65][66][67][68]], = 0.1 …”

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

“…Bour and Davy (1998) studied the connectivity of 3-D fault networks, and found that faults larger than a critical length scale may form a well-connected fracture network, while smaller faults may be not connected on average. Dershowitz and Fidelibus (1999) established DFN models using the pipe network elements, and developed a boundary element procedure for derivation of pipe properties. Their results agreed well with those of polygonal-element models.…”

Impact of Induced Thermal Stresses During Circulation Tests in an Engineered Fractured Geothermal Reservoir: Example of the Soultz-Sous-Forêts European Hot Fractured Rock Geothermal Project, Rhine Graben, France

“…The 3D structure resulting of the superimposition of the connected portions of planes is thus treated as a 3D network of 1D pipes as in Cacas et al (1990). Equivalence of this channel flow approach with others solving true 2D flow in planes has been discussed (Dershowitz and Fidelibus, 1999).…”