Abstract
Three-dimensional images of fractured rocks can be acquired by an X-ray micro-CT scanning technique, which allows researchers to investigate the ‘true’ inner void structure of a natural fracture without destroying the core. The 3D fractures in images can be characterised by measuring morphological properties on both fracture apertures and its trend surface, like the medial surface, that reveals the undulation of fracture planes. In a previous paper, we have proposed a novel method to generate fracture models stochastically. Based on a large number of such fracture models, in this work a modified factor was proposed for improving the performance of the cubic law by incorporating the flow-dominant characteristics, including two parameters (aperture roughness and spatial correlation length) for fracture apertures and two (surface undulation coefficient and spatial correlation length) for fracture trend-surface. We assess and validate the modified cubic law by applying it to natural fractures in images that have varying apertures and extremely bended trend-surfaces, with the permeabilities calculated by a Lattice Boltzmann Method as ‘ground truths’.
Highlights
Natural fractures are common features in many rocks, occurring at various length scales and at different intensities
Since intact rocks are often low in permeability, and the fracture network forms the main channels of flow, the effective permeability of a fractured rock is dictated by the permeability of the fracture network, which consists of numerous individual fractures
A 3D digitized rock, which reveals the pore structure in the rock matrix and fracture opening/void, is made up of a series of 2D images which are obtained by X-ray computed tomography (CT)
Summary
Natural fractures are common features in many rocks, occurring at various length scales and at different intensities. Understanding the fluid flow characteristics in natural fractured rock is of importance for petroleum reservoirs [1], geothermal energy development [2,3], nuclear waste disposal [4] and the geologic storage of carbon dioxide [5]. The fluid flow through a single fracture could form a basic building block for understanding the mechanical-hydraulic interactions of natural fractured rock, which has been extensively studied in recent years [6,7,8,9,10,11]. For steady laminar flow between smooth parallel plates, separated by a constant aperture, fracture transmissivity is proportional to the cubic power of fracture aperture, which is well known as the ‘cubic law’ [12]. The cubic law should, be tuned to incorporate more factors that influence fluid flow [7,13,14]
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