This paper develops a discrete fracture approach to flow analysis of dual-porosity systems. The well-established methods of analyzing dual-porosity flow in fractures deal primarily with matrix blocks having idealized shapes, such as slabs, blocks, and spheres. While these geometric simplifications allow analytical solution of difficult now problems, they also neglect the geometric complexities of real fracture systems. The discrete-fracture, dual-porosity approach presented here is an enhancement of discrete fracture network model which associates a volume of storative material with each fracture surface. The flow interactions between the storative volume and the fracture may be either steady-state or transient. Two applications are presented. The first uses a single horizontal fracture as a test case. The second employs a small number of vertical fractures to investigate local effects on drawdown behavior.
The analysis of flow in fractures has followed two broad approaches over the past several years. On one hand, there has been the discrete fracture approach which has attempted to study the flow in individually-identified fracture conduits. Among these have been the approaches of Long, et al: (1982), and Dershowitz (1984) which model flow in discrete fracture networks generated by stochastic simulators. On the other hand, there have been numerous methods which idealize the fracture systems as porous continua with special attributes such as being an anisotropic continuum (Hsieh, 1983) or heterogeneous (stochastic) continuum (e.g., Smith and Freeze, 1979). In these methods it is assumed that the fracture system behaves as a continuum at scales larger than a representative elementary volume.
As Moench (1984) points out, the theory of dual-porosity flow is a continuum approach in which there are two representative elementary volumes (REV's). One REV represents the fracture system, the other the matrix. As in all continuum approaches, the details of the fracture-system geometry are lumped into the properties of the continuum. Potentially important details on interconnection among fractures and between boundaries are lost.
This paper presents the extension of dual porosity concepts from continuum-flow analysis to discrete-fracture flow analysis. The paper begins with a discussion of dual-porosity continuum methods, concentrating on the description of flow between the matrix blocks and the fracture continuum. A dual-porosity model of discrete fracture flow is developed by associating a generic matrix block with each fracture segment in the discrete-fracture network. The paper concludes with presentation of two discrete-fracture, dual-porosity simulations. The first simulation uses a single horizontal fracture as a test of the model against a analytical solutions. The second uses a single horizontal fracture and several vertical fractures.
Among the continuum methods, the dual porosity approach has received considerable attention for applications in rock which contains both fractures and intergranular permeability (Warren and Root, 1963, Moench, 1984; Barker, 1985; Streltsova, 1988). The dual porosity approach idealizes the fracture-flow system as a porous reservoir with homogeneous properties. The rock matrix appears as blocks embedded within this porous aquifer. The blocks have a lower conductively and a higher storage than the fracture continuum.