An efficient computation of leak-off induced poroelastic stress for a hydraulic fracture

This study investigates the problem of a hydraulic fracture propagating in a permeable formation with an emphasis on the computation of the poroelastic stresses caused by fluid leak-off into the formation. By using the assumption of smallness of the diffusion length scale relative to the fracture size, the three-dimensional poroelastic problem around the fracture splits into two simpler problems, one involving the undrained response due to fracture opening, and another one involving one-dimensional fluid flow in the direction perpendicular to the fracture and poroelastic stresses caused by an elevated pore pressure around the fracture. The latter leak-off induced stresses are often ignored due to difficulties associated with the complexity and/or computational demands needed to solve the problem. This study addresses this issue and presents an efficient solution for the problem that also makes it possible to better understand the influence of the leak-off induced stresses on hydraulic fracture propagation for large scale problems. It is shown that for the case of a planar fracture, the leak-off induced stress can be represented via an additional effective width, whose value is proportional to the total fluid loss. However, this does not apply for the general case of multiple hydraulic fractures since the off-plane spatial stress variation due to the pore pressure change and fracture opening are different (even though coincide on the fracture plane). To illustrate the developed concept, several numerical examples for various fracture configurations are presented.