Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness.

High-Resolution Micro-Continuum Approach to Model Matrix-Fracture Interaction and Fluid Leakage

Understanding the fundamental mechanism of fracture-matrix fluid exchange is crucial for the modeling of fractured reservoirs. Traditionally, high-resolution simulations for flow in fractures often neglect the matrix-fracture leakage influence on the fracture hydraulic properties, i.e., assuming impermeable fracture walls. This work introduces a micro-continuum approach to capture the matrix-fracture leakage interaction and its effect on the rock fractures’ hydraulic properties. Because of the multiscale nature of fractured media, full physics Navier-Stokes (NS) representation everywhere in the whole domain is not feasible. We thus employ NS equations to describe the flow in the fracture, and Darcy’s law to model the flow in the surrounding porous rocks. Such hybrid modeling is achieved using the extended Darcy-Brinkman-Stokes (DBS) equation. With this approach, a unified conservation equation for flow in both media is applied by choosing appropriate parameters (e.g., porosity and permeability) for the corresponding domains. We apply an accurate Mixed Finite Element approach to solve the extended DBS equation. Various sensitivity analyses are conducted to explore the leakage effects on the fracture hydraulic properties by varying surrounding matrix permeability, fracture roughness, and Reynolds number (Re). Streamline profiles show the presence of back-flow phenomena, where in-flow and out-flow are possible between the matrix and the fractures. Further, zones of stagnant (eddy) flow are observed around locations with large asperities of sharp corners under high Re conditions. Numerical results show the significant effects of roughness and inertia on flow predictions in fractures for both impermeable and leaky wall cases. Besides, the side-leakage effect can create non-uniform flow behavior within the fracture that may differ significantly from the case with impermeable wall conditions. And this matrix-fracture leakage influence on hydraulic properties of rock fractures matters especially for cases with high matrix permeability, high fracture roughness, and low Re values. In summary, we present a high-resolution micro-continuum approach to explore the flow exchange behavior between the fracture and rock matrix, and further investigate the static and dynamic effects, including variable Reynold numbers, mimicking flow near and away from the wellbore. The approach and results provide significant insights into the flow of fluids through fractures within permeable rocks and can be readily applied in field-scale reservoir simulations.

Impacts of Fracture Roughness and Near-wellbore Tortuous on Proppant Transport Within Hydraulic Fractures

For unconventional reservoirs hydraulic fracturing design, a greater fracture length is a prime factor to optimize. However, core observation results from Hydraulic Fracturing Test Site (HFTS) show the propped fractures are far less or shorter than expected which suggests the roughness and tortuous of hydraulic fractures are crucial to sand transport. In this study a transport model of sands is first built based on experimental measurements on the height and transport velocity of sand bank in fractures with predetermined width and roughness. The fracture roughness is quantified by using surface height integral. Then, three-dimensional simulations are conducted with this modified model to further investigate the impact of fractures tortuous on sand transport, from which an analytical model is established to estimate the propped length of hydraulic fractures at a certain pumping condition. Experiments results show that height of sand bank in roughness fracture is 20-50% higher than that in smooth. The height of sand bank decreases with the reduction of slurry velocity and increases with the sand diameters increasing. Sand sizes do little effect on the transport velocity of sand bank but the increase in slurry velocity and sand volume fraction can dramatically enhance the migration velocity of sand bank. The appearance of tortuous decreases the horizontal velocity of suspended particles and results in a higher sand bank compared with that in straight fractures. When the sand bank gets equilibrium at the tortuous position, it is easy to produce vortices. So, there is a significant height of sand bank change at the tortuous position. Moreover, sand plugging can occur at the entrance of the fractures, making it difficult for the sand to transport deep in fractures. This study explains why the propped length of fractures in HFTS is short and provides an analytical model that can be easily embedded in the fracturing simulation to fast calculate dimensions of the propped fractures network to predict length and height of propped fractures during fracturing.

Digital Fracture Characterization at Hydraulic Fracturing Test Site HFTS-Midland: Fracture Clustering, Stress Effects and Lithologic Controls

In this case study, we apply a novel fracture imaging and interpretation workflow to take a systematic look at hydraulic fractures captured during thorugh fracture coring at the Hydraulic Fracturing Test Site (HFTS) in Midland Basin. Digital fracture maps rendered using high resolution 3D laser scans are analyzed for fracture morphology and roughness. Analysis of hydraulic fracture faces show that the roughness varies systematically in clusters with average cluster separation of approximately 20' along the core. While isolated smooth hydraulic fractures are observed in the dataset, very rough fractures are found to be accompanied by proximal smoother fractures. Roughness distribution also helps understand the effect of stresses on fracture distribution. Locally, fracture roughness seems to vary with fracture orientations indicating possible inter-fracture stress effects. At the scale of stage lengths however, we see evidence of inter-stage stress effects. We also observe fracture morphology being strongly driven by rock properties and changes in lithology. Identified proppant distribution along the cored interval is also correlated with roughness variations and we observe strong positive correlation between proppant concentrations and fracture roughness at the local scale. Finally, based on the observed distribution of hydraulic fracture properties, we propose a conceptual spatio-temporal model of fracture propagation which can help explain the hydraulic fracture roughness distribution and ties in other observations as well.