Interaction of Non-Darcy Flow Regimes Coupled and Pore Volume Compaction in Shale Gas Formations

Abstract

Abstract Shale resources have distinctive characteristics, such as micro-scale pore, ultra-low permeability, and complex fluid flow behavior. In order to predict productivity and deliverability in shale complex system, it is crucial to understand porosity and permeability relation. Since pore size distribution in shale formations is stretched down to nano-meters, the system response violates the predictions of Darcy's law. Depending on pore size and gas properties, non-Darcy flow mechanisms such as slip-flow, molecular diffusion, and Knudsen diffusion can affect the matrix deliverability. Although there are several models to predict permeability considering non-Darcy flow mechanisms, the impact of formation compaction has been neglected in calculations. However, correcting for pore volume shrinkage seems crucial for improved accuracy in evaluation of hydrocarbon reserve. In this work, we analyze different flow regimes coupled with effects of pore volume compressibility for Barnett and Haynesville shale plays. The pore compressibility values are calculated based on Mercury Injection Capillary Pressure (MICP) data. Using our mathematical formulation, we divide the shale matrix into accessible pores and inaccessible part of the rock (IRP) and characterize pore compressibility values as a function of pressure. As local pore pressure decreases, formation porosity, pore radius, Knudsen number and thus flow mechanisms are subjected to change with time. Hence, a new permeability model (total permeability) for shale matrix is developed which includes Darcy flow, slip flow, molecular diffusion, Knudsen diffusion, surface diffusion, and last but not the least pore compaction. The impact of pore shrinkage on total permeability reduction is analyzed. Our results indicate that substitution of accessible pore compressibility with total bulk compressibility can significantly change the production behavior. The results suggest that predicted compressibility values for accessible pores appear to be two to up three orders of magnitude greater than bulk compressibility for Barnett and Haynesville samples. Moreover, effects of pore compaction on permeability during pressure depletion seem significant for the samples studied here. Since Non-Darcy flow mechanisms are sensitive to pore radius, permeability values derived based on laboratory conditions are required to be adjusted before upscaling to reservoir condition.