Mathematical Modeling of Hydraulic Fracturing In Shale Gas Reservoirs

During the past few years, hydraulic fracturing and horizontal drilling have facilitated the production of gas from shale reserves that were uneconomic to produce in the past. Each shale formation has a specific nature, therefore every basin or well may need to be treated differently. Additionally, shales have characteristics such as extremely low permeability, sensitivity to contacting fluids, and existing micro fractures which cause complications while evaluating them. There is also an absence of a clear explanation for the application of 2D models and the effect of various parameters on the fracture in shale formations. Therefore, the objective of this study is to analyze different 2D hydraulic fracture geometry models while examining these models for their application in shale gas formations and to identify a 2D model that is most suitable to be used in the hydraulic fracture treatment design of shale gas reservoirs. It is also intended to investigate the effect of fracture height, fluid loss and rock stiffness on the fracture geometry and the well.
In this study the two most commonly used hydraulic fracture geometry models in the oil and gas industry, PKN and KGD, have been discussed and based on these models two mathematical computer codes were developed in order to calculate various parameters such as fracture length, average fracture width, wellbore net pressure, pumping time, and maximum fracture width at wellbore. The PKN-C model is identified as the most suitable 2D model to be used in shale gas reservoirs due to its more acceptable vertical plane strain assumption. Low permeability formations such as shale reservoirs require narrower and longer fractures for a higher productivity. Thus, using a model that would predict longer and narrower fractures, such as the PKN-C model, would be more suitable. The KGD-C model predicts a higher dimensionless fracture conductivity compared to the PKN-C model. However, the fracture geometry predicted by the PKN-C model results in higher post-fracture productivity. Additionally, it was observed that longer and narrower fractures are produced in rocks with a high Young’s modulus (such as shale). Additionally, increasing the leak off coefficient when fluid loss is small will result in slightly shorter fracture lengths, while increasing the leak off coefficients when fluid loss is high will result in significantly shorter fracture lengths.