Investigation on Nonlinear Flow Behavior through Rock Rough Fractures Based on Experiments and Proposed 3-Dimensional Numerical Simulation

Abstract

Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient $\nabla P$ and flow rate $Q$ , and the critical Reynolds number( ${\mathrm{Re}}_{\text{c}}$ ) and wall friction factor ( $f$ ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data $\nabla P$ ~ $Q$ decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of $f$ , $\mathrm{Re}$ , and relative roughness indicated that $f$ increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that $f$ could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient $B$ in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.