PORE CONNECTIVITY IN SHALE FORMATIONS

Shale formations demonstrate distinct characteristics, such as a wide spectrum of pore size from micro-scale to nano-scale, ultra-low permeability, and complex pore network system. Despite extensive research work over years to characterize details of shale and extremely tight formations, the interplay between pore connectivity and permeability still remains to be understood. In this research, analytic and numerical methods were used in tandem with experimental data to characterize and evaluate pore and hydraulic connectivity of shale formations. Impact of sample size, effective stress, pore structure and topology on the connectivity were evaluated. A new analytic model is proposed and developed using percolation theory and critical path analysis to explicitly express permeability as a function of pore connectivity. The definition of critical pore throat radius and electrical conductivity were revisited and reformulated from previously developed Katz & Thompson model. The new permeability model is expressed as a function of maximum pore radius, porosity, fractal dimension, and percolation threshold/average coordination number that makes it suitable for exploring the impact of pore connectivity on permeability. Next, accessible porosity and interconnected porosity is evaluated using mercury injection capillary pressure (MICP) data. Several samples from Barnett and Haynesville formations with different sizes are used to understand the effect of sample size on accessible and interconnected porosity. MICP data combined with percolation theory were used to explain the connectivity loss with increasing sample size. Additionally, a novel approach is presented to explain intrinsic permeability reduction of shale samples as a function of effective stress. Experimental results have shown orders of magnitude reduction in permeability as effective stress increases; this permeability reduction is usually explained through closure of micro-fracture while impact of pore connectivity loss is often neglected. Thus, an alternative approach is proposed here through which permeability reduction is described owing to combination of three main mechanisms: (1) micro crack closure (2) pore shrinkage and (3) connectivity loss due to bond breakage between interconnected pores. Next, a complementary study was conducted to model fluid flow through three-dimensional (3D) pore structure constructed using stacked focused ion beam scanning electron microscopy (FIB-SEM) images. Lattice Boltzmann Method (LBM) is used to simulate fluid flow to calculate permeability of the 3D pore volume. Finally, pore connectivity is quantified based on Euler-Poincare Characteristics as a function of sample size and impact of pore connectivity on permeability calculations is analyzed. Furthermore, accessible/fluid saturated porosity values calculated using mercury injection capillary pressure (MICP) data are evaluated for Barnett and Haynesville shale samples. A general approach is proposed consisting of three distinct corrections to accurately estimate the accessible porosity of shale sample using MICP data: (1) conformance, (2) grain compressibility, and (3) inaccessible pore compressibility. Accessible porosity calculated for both Barnett and Haynesville formations have been analyzed and compared to understand the impacts of pore structure and topology on the connectivity. Finally, a two-phase relative permeability model based on percolation theory is proposed and impact of the phase connectivity on relative permeability curves is investigated. Additionally, major factor dominating residual saturation is discussed. The result of this study suggests that in shale formations accessible porosity and permeability are strong function of pore/hydraulic connectivity. Moreover, unlike conventional formations, pore connectivity can significantly vary depending on pore structure, pore geometry, sample size, and the effective stress