Development and Testing of a Pseudo-Three-Dimensional Model of Hydraulic Fracture Geometry

Summary A pseudo-three-dimensional (P3DH) model has been developed to describe realistically the evolution of geometry of a 3D hydraulic fracture produced by fluid injection into a reservoir. The present model bypasses the task of a fully 3D crack geometry calculation, which is at present prohibitively complex in the context of a complete practical fracturing simulator. The P3DH model presented formulates the problem in terms of equations for lateral fluid flow and crack opening for the main body of the fracture, coupled with a very efficient scheme for describing vertical fracture growth at each cross section. The equations for lateral flow are solved by finite differences, and the vertical propagation problem is solved by numerical implementation of a singular integral equation on a suitable set of Chebyshev points. The testing of P3DH components shows both an excellent agreement of the lateral propagation model with various analytical solutions (Ref. 1) and a strong sensitivity of vertical propagation to confining stress and stiffness contrast of adjacent strata and to fluid rheology. The sample simulations show that the model produces realistic fracture growth under a wide range of conditions, is extremely sensitive to the dominant containment parameters, and therefore can be used to study the effect of relevant design parameters on fracture shapes and pressures in stimulation treatments. The P3DH model is highly efficient and suitable for incorporation in a general 3D fracturing simulator. The computational effort for calculation of fracture geometry with P3DH is generally comparable to that required for the simulation of the fluid flow in the surrounding reservoir.