The Correlation Between Fluid Flow and Heat Transfer of Unsaturated Shale Reservoir Based on Fractal Geometry

Abstract

The dissimilar multi-scale structures of shale to conventional reservoirs make it a challenge to understand the fluid flow and heat transfer through unsaturated shale formations. In this paper, the pore structure and moisture content of shale samples are measured by low-field nuclear magnetic resonance technique and thermogravimetric differential scanning calorimetry test, respectively. A pore-scale model is accordingly developed for the immiscible two-phase fluid flow and heat conduction through unsaturated shale based on the statistically self-similar fractal scaling law of pore size distribution. The analytical expressions of effective and relative permeability, as well as effective thermal conductivity (ETC), are proposed, which indicate good agreement with experimental results. It has been shown that the capillary pressure and gas slippage play important role in multiphase flow through unsaturated shale. Both pore and tortuosity fractal dimensions show significant influence on the relative permeability for nonwetting phase (RPNW), while they indicate the marginal effect on the relative permeability for the wetting phase (RPW). The ETC decreases with the increase of pore and tortuosity fractal dimensions, and it is positively and negatively correlated with RPW and RPNW, respectively. The correlation between ETC and relative permeability is found to follow a logistic function. The present fractal model can characterize the multiscale structures of shale reservoirs and may help understand transport mechanisms of immiscible multiphase flow and heat transfer through unsaturated shale.