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

Abstract

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 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 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. Introduction Prediction of fracture geometry is one of the central Prediction of fracture geometry is one of the central issues in the engineering design of stimulation treatments as well as other oilfield processes involving fracturing of the reservoir rock. The complexity of the treatments has increased, but data-gathering techniques and the understanding of the basic phenomena have also advanced, so traditional design methods are now being replaced by more detailed simulations. In particular, a need exists for a more detailed and realistic modeling tool for prediction of 3D fracture growth. Such a model is needed for theoretical studies of containment and simulation of laboratory experiments as well as for optimization of fracturing-treatment design in the field. A model that describes fracture geometry more realistically allows much more information to be extracted from pressure data, such as those from minifracture tests and pressure measurements during actual treatments. On the other hand, a fracture-geometry design must be restricted to the essential features and dominant parameters because the completely general solution of the parameters because the completely general solution of the problem is still too complex and may be unnecessary from an problem is still too complex and may be unnecessary from an engineering viewpoint. This paper describes the development and testing of the P3DH designed for the range of conditions of interest in P3DH designed for the range of conditions of interest in fracturing operations. After an explanation and justification of the proposed concept, the paper treats the two types of conventional two-dimensional (2D) models that are used as components of P3DH. Results of these models, which are based on previous work (Refs. 1 and 2), are of great interest because they give correct, comprehensive solutions of the special 2D cases. Testing of the numerical techniques used to solve the components of P3DH is described in later sections. Some sample calculations demonstrate the role played by the principal containment mechanisms. The paper focuses on the prediction of fracture geometry. The details of the coupling of this problem with the fluid flow, heat transfer in the surrounding problem with the fluid flow, heat transfer in the surrounding reservoir, proppant transport, etc., are treated in a companion paper.