Flow through fractures

Flow through fractures is often idealized as flow between two parallel plates (plane Poiseuille flow). The opening or aperture between parallel plates is unambiguous and its relation to flowrate is well known. However, fractures in rock have uneven walls and a variable aperture. A model for flow in a fracture is proposed wherein the fracture is represented by a set of parallel plate openings with different apertures. The model leads to a modified Poiseuille equation for flow which includes an aperture frequency distribution for the fracture. Any arbitrary aperture distribution can be used; in order to simplify computation and demonstrate the properties of the model a log normal form of distribution is assumed. Even when an analytical form of the distribution is assumed, two parameters, rather than a single value representing ‘aperture size’ are required to determine flowrate. Models of aperture change for a fracture undergoing compression (fracture walls deforming) and extension (fracture walls separating) are developed which constrain the additional parameter and allow calculation of flowrate as a function of mean aperture. The theoretical relationships developed between mean aperture and flowrate can be used to interpret published laboratory data for single fractures.