A BEM solution of steady-state flow problems in discrete fracture networks with minimization of core storage
A boundary element method (BEM) solution for the problem of the fluid flow in a three-dimensional discrete fracture network (DFN) is proposed. A DFN is an assembling of polygons which resemble the fractures in a rock mass. The position, extension, orientation and transmissivity of each fracture of the network are excluded by specific statistical distributions. For a single problem, a significant number of DFNs has to be generated and the fluid flow has to be assessed in each of them in the context of a Monte-Carlo procedure. Even for relatively small domains, a DFN may include a large number of fractures. As a consequence, in order to solve the whole problem with standard finite-element method (FEM) codes, a big amount of core memory and large input data files are required. The main advantage of the proposed solution is mainly the minimization of the core memory. This is attained by handling the flow quantities in such a way the equation system of the overall network is never assembled. Only a relation per each fracture among nodal fluxes and heads of the traces (i.e., intersections among fractures) is defined and stored in a random access file. This relation is obtained by means of the application of the BEM to each single fracture of the network. Both constant and quadratic element representations are used in order to define the relevant nodal quantities. The use of constant elements allows to avoid the direct treatment of the points of flux discontinuity. No special care is applied to the discretization of the boundary of each fracture. The overall problem is solved by means of an iterative procedure, by retrieving the necessary coefficients from the random access file. The results are in acceptable agreement with the ones provided by a commercial FEM code. We remark that saving core memory without special care in the discretization of the DFN makes the solution competitive, especially when dealing with networks with a high number of fractures. (C) 2003 Elsevier Ltd. All rights reserved.
discrete fracture network boundary element method fractured media relaxation procedure steady-state fluid flow