Modelling fluid flow through a single fracture with different contacts using cellular automata

Abstract

The representation of the surface of a rock fracture and a numerical method to simulate fluid flow in single fractures are the keys to understanding the hydraulic behaviour of rock fractures. In this paper, a cellular automaton (CA) approach is used to generate the single fracture structure, which is assumed to be composed of contacts and voids. We develop a CA evolution rule to produce a contact area, and randomly model a single rock fracture with different contact ratios to reflect natural fracture properties such as dead voids, islands and tortuous flow path. Then, based on the localisation theory of a CA, a numerical method to simulate fluid flow in single fractures with contacts is developed. In this method, the fracture is discretised into a system composed of cell elements. Different apertures, i.e., zero for contacts and non-zero for voids, are assigned to each cell element. Therefore, the contribution of the cell elements in a contact on a cell’s transmissivity can be ignored completely. The local transmissivity is assumed to conform to the cubic law. The fluid flow in a fracture with different contact situations is then modelled using the method established in this paper. The fluid flow path, flow velocity and fluid head distributions as well as the channel flow in the fracture are well-modelled. The flow behaviour of the fracture strongly depends on the effective fluid flow path.