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 fracture 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 fracture networks in unconventional reservoirs 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. The evolution of the entire fracture geometry and its impact on stress redistribution and dynamic fracture closure 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 as conventional practice suggests.

Estimating Unpropped-Fracture Conductivity and Fracture Compliance From Diagnostic Fracture-Injection Tests

“…Knowing the properties of surface roughness (represented by up-scaled contact width and contact reference stress ), and applying the non-local fracture closure model (Wang and Sharma 2017a;Wang et al 2017), the fracture width profile at any fluid pressure can be determined, regardless of whether the fracture is open, partially closed or completely closed (all asperities have come into contact with stress-dependent residual fracture width). Since the matrix permeability is low and there exists a linear relationship between the flow rate and differential pressure along the fracture during production, the fracture permeability can be calculated based on the cubic law (Watanabe et al, 2008): 4 The fracture conductivity is defined as the product of fracture permeability and fracture width:…”

“…(10) does not distinguish between before closure and after closure period, it is a global pressure transient model and the fracture closure process is implicitly reflected in . The relationship between and , such as the curves in Fig.1, can be obtained from non-local fracture closure modeling (Wang and Sharma 2017a;Wang et al 2017), where the pressure-dependent fracture stiffness is calculated by inputting rock property, fracture 6 geometry and surface roughness (represented by contact parameters and ).…”

“…However, when the fracture width is smaller than the contact width, the contact stress and fracture width follows a hyperbolic relationship, as reflected by Eq.(3). Fig.5 shows the corresponding fracture stiffness evolution based on the solutions of linear elasticity (Wang and Sharma 2017a;Wang et al 2017), for different with the given fracture geometry and rock properties (provided in Table 2). The results indicate that as the fracture width decreases, the rough fracture walls will come into contact sooner if the contact width is larger, so the noticeable changes of fracture stiffness occur earlier when the contact width is larger.…”

“…The fracture stiffness can be obtained from fracture closure modeling (Wang and Sharma 2017a;Wang et al 2018) using:…”

“…For open fractures at relative high pressure, can be determined analytically using Table-1. For more general circumstances, can be calculated numerically as the fracture closes progressively (Wang and Sharma 2017a;Wang et al 2018), and the numerical solution gives the same results as using the formulae in Table-1 Adjust the index so that , , then for :…”