A non-local model for fracture closure on rough fracture faces and asperities

Abstract

Natural fractures, hydraulic fractures, and acid etched fractures have some degree of surface roughness. These surface asperities are largely responsible for the hydraulic conductivity of these fractures. This paper presents a model to quantify the fracture closure process that is crucial to predicting the stress dependent conductivity of fractures and estimating the minimum in-situ stress using fracture injection tests. Past studies that have investigated the fracture closure process have assumed the fracture surfaces to be two parallel plates closing in uniformly on rough surfaces and asperities. In reality, hydraulically induced fractures are wider in the middle and narrower near the fracture tip. As a result, asperities on the rough fracture surfaces come into contact near the fracture tip well before they do near the middle of the fracture. This evolution of the entire fracture geometry and its impact on stress redistribution and contact behavior has not yet been investigated.In this paper, we present a method and general algorithms to model the dynamic closure behavior of a hydraulic fracture while accounting for the initial fracture shape, rough fracture surfaces and deformation of asperities in contact. Analytic solutions from linear elastic fracture mechanics for three fracture models (PKN, KGD and radial fracture geometry) are coupled with a general contact law to show that the fracture closure process is a gradual, non-local process, which occurs at the fracture edges initially and then moves progressively to the center of fracture, as the fluid pressure inside the fracture declines. Our study also reveals that the minimum in-situ stress should not be picked at the occurrence of mechanical closure from fracture injection tests as conventional practice suggests.