Stochastic-based liquid apparent permeability model of shale oil reservoir considering geological control

Abstract

Shale is a complex porous medium composed of organic matter (OM) and inorganic minerals (iOM). Because of its widespread nanopores, using Darcy’s law is challenging. In this work, a two-fluid system model is established to calculate the oil flow rate in a single nanopore. Then, a spatial distribution model of shale components is constructed with a modified quartet structure generation set algorithm. The stochastic apparent permeability (AP) model of shale oil is finally established by combining the two models. The proposed model can consider the effects of various geological controls: the content and grain size distribution of shale components, pore size distribution, pore types and nanoconfined effects (slip length and spatially varying viscosity). The results show that slip length in OM nanopores is far greater than that in iOM. However, when the total organic content is less than 0.3 ~ 0.4, the effect of the OM slip on AP increases first and then decreases with the decrease in mean pore size, resulting in that the flow enhancement in shale is much smaller than that in a single nanopore. The porosity distribution and grain size distribution are also key factors affecting AP. If we ignore the difference of porosity between shale components, the error of permeability estimation is more than 200%. Similarly, the relative error can reach 20% if the effect of grain size distribution is ignored. Our model can help understand oil transport in shale strata and provide parameter characterization for numerical simulation.