Experimental and numerical investigation of Non-Darcy flow in propped hydraulic fractures: Identification and characterization

Abstract

Non-Darcy flow occurs in all porous media. The phenomenon of non-Darcy flow is particularly evident in propped fractures. It is crucial to understand the causes of non-Darcy flow, identify its onset, and characterize it quantitatively. We first observed the phenomenon of non-Darcy flow in propped fractures through laboratory experiments. Subsequently, 75 pore-scale propped fracture models with different porosities, apertures, and proppant particle sizes were established, and 2850 simulations at different pressure gradients were performed to identify and quantitatively characterize the non-Darcy flow in propped fractures. Calculation of the non-Darcy coefficients of various regions in the numerical model revealed that non-Darcy flow arises due to flow resistance. A model for predicting the crucial Reynolds number based on the apparent permeability (Rec=ehkD−1β−1/99) was proposed to enable more accurate identification of the onset of non-Darcy flow, and the predicted results were in strong accord with the observed data. A more constitutive non-Darcy coefficient prediction model was developed to quantify the non-Darcy effect, which is expressed as β=408af−0.34s−0.76φ−4.44. This study explains the root cause of non-Darcy flow in propped fractures, identifies the occurrence of non-Darcy flow more efficiently, and accurately characterizes non-Darcy flow.