| Using current technology an engineer can accurately evaluate the various layers within a petroleum reservoir and can compute the mechanical and fluid properties of the layers. To use these parameters, three-dimensional hydraulic fracture models must be applied to design and analyze fracture treatments. The classic two-dimensional fracture models assume a constant fracture height and do not use the layer data in a meaningful way. A fully three-dimensional finite-element model can use available layer data rigorously, however, take too much time and require super computers to run efficiently. For the design engineer, these models are difficult to run because of their complexity. Pseudo-three-dimensional models usually run rapidly on personal computers. However, pseudo three-dimensional models are mainly applicable to fractures where the total fracture length is several times greater than the fracture height.; In this research work, I describe a fully three-dimensional, semi-analytical fracture propagation model that enables us to predict accurate fluid pressures and fracture dimensions in a multilayer medium with asymmetric reservoir characteristics. This model assumes two-dimensional fluid flow inside the fracture and computes a pressure drop in both the direction of the fracture height and fracture length. A cubic polynomial equation to represent fluid pressure and a non-symmetric in-situ stress distribution is assumed in order to apply analytical methods to determine fracture displacements. Using the first variational technique to approximate the partial differential equations, and introducing a new domain in the solution procedure, asymmetric fracture growth can be solved for a multilayer system, where each layer has unique mechanical properties. This model is validated against several published examples with wide ranges of rock and fluid properties for both symmetric and asymmetric fracture growth in multilayer media. The model is fast and can be run efficiently on a personal computer. |
