Investigating the Effects of Permeability and Porosity Variations on Formation Breakdown Pressures Using a New Hybrid Analytical and Computational Approach
Authors: Almani Tameem , Khan Khaqan , Altwaijri Mohammad 
Published: February 2022

Abstract
In hydraulic fracturing, the borehole pressure at which fractures initiate is called the breakdown pressure. In-situ stress tests, such as injectivity tests, can be used to determine the formation breakdown pressure. Through these tests, borehole pressure versus time curves are generated, and the breakdown pressure is considered as the peak pressure at which the intact formation at the borehole wall is broken in tension (Ito and Hayashi 1991; Ito 2008). Estimating this value correctly is very crucial from an operational point of view, as the required horsepower on site and the pressure rating of well completions are all based on that. Operational failure can result from underestimating the breakdown pressure, and expenditure loss can result from overestimating it. Therefore, an accurate estimation of the breakdown pressure is a huge step toward achieving a successful hydraulic fracturing operation.
Several methods and approaches for estimating the breakdown pressure exist in literature. Most of these methods do not include all the underlying physical parameters involved such as poroelastic stresses, and formation permeability. In general, breakdown pressure prediction algorithms can be grouped in two main categories: experimental and analytical based methods, and computational based methods. Experimental and analytical based methods use experimental correlations together with simplified derived analytical solutions to estimate the formation breakdown pressure (Ito and Hayashi 1991; Ito 2008; Schmitt and Zoback, 1989; Haimson and Fairhurst, 1969). In contrast, computational based methods employ numerical simulations of coupled geomechanical and flow models to compute the underlying stress and pressure fields (Almani, 2016; Almani et al., 2017 (1,2), Borregales et al., 2018; Dana et al., 2018; Kim et al., 2009; Castelletto et al., 2015; Kim et al., 2011; and Jha and Juanes, 2014). The computed pressure and stress fields are then used to estimate formation breakdown pressures (Fatahi et al., 2016). In this work, we will combine these two approaches, and we will derive and implement a new hybrid analytical and computational algorithm to compute formation breakdown pressure as a function of all the underlying physical parameters involved, and in particular rock porosity and permeability. The developed algorithm can be used for several purposes including studying the effects of rock porosity and permeability on the breakdown pressure values.
As stated earlier, in this paper, a new hybrid algorithm for estimating formation breakdown pressure as a function of all the underlying physical parameters involved will be introduced (Almani et al., 2021). This algorithm differs from previously published approaches in the fact that it does not incorporate any empirical parameters, and instead computes the breakdown pressure as a function of in-situ stresses, pore pressure and poro-elastic stresses. The pore pressure and poroelastic stresses are computed by a novel hybrid analytical and numerical approach, incorporating the rock porosity and permeability, the Biot poroelastic parameter α, the Poisson's ratio, the fracturing fluid viscosity and compressibility, the initial wellbore pressure, and the wellbore radius. Combining in-situ stresses into the model results in a comprehensive and accurate framework for estimating the breakdown pressure, as a direct function of all the underlying physical parameters, including rock porosity and permeability.