A Mathematical Model to Predict Hydraulic Fracture Geometry in Shale Gas Formation

Abstract

Shale gas represents a new abundance for natural gas, which could aid keeping up with increasing world demand for energy. Enormous quantities of shale gas reserves are in Africa and China; however the technology to extract natural gas from shale formations is not yet developed in these regions. Hydraulic fracturing is the most viable technique to recover shale gas in economical quantities. Designing and controlling fracture geometry are crucial to achieve economical production rates from shale gas formations. Currently there is no universal model that can be applied to predict the fracture height and half-length in shale gas formation. Earlier models have addressed the issue of fracture geometry that is induced by hydraulic fracturing operation in conventional formations. Models such as KGD (Khristianovich- Geertsma-DeKlerk) and PKN (Perkins-Kern-Nordgren) solving the problem by assuming fixed fracture height, while complicated 3D models (planar and pseudo) are used to describe fracture geometry. Pseudo-3D model suffers from unrealistic fracture height outputs when the assumptions are violated. In this paper new equations for both fracture’s height and half-length are developed using Bingham theory in combination with a statistical approach (Monte Carlo simulation). The equations can be applied for wide ranges of rock properties and operational conditions of hydraulic fracturing.Model’s outcomes validation was verified using available data in the literature. Moreover, a parametric study showed that fluids viscosity and Poisson’s ratio were the major parameters that control fracture half-length. On the other hand, fracture height has been found to predominantly be controlled by formation thickness. These results are in line with the previous models outcomes.