Abstract
In this study, the propagation of a hydraulic fracture in a three-layer medium is investigated using a robust finite element method. The top and bottom layers have similar properties, while the soft middle layer has variable thickness and stiffness. Both two-dimensional plane-strain and three-dimensional models are used to evaluate the vertical and lateral growth of the fracture, initiated from the bottom layer. In 2D model, the competition between the gravity forces and the stress concentration at the layer boundary dictates whether the fracture grows upward or downward, while in the 3D model, the lateral growth of the fracture is also captured. Results from the 2D model show that in majority of cases (6 out of 9) the fracture reaches to the middle layer, and due to the lower minimum principal stress in this layer, an extensive propagation occurs in this layer. When the lateral growth is considered utilising the 3D model, depending on the stress concentration and the position of the fracture in the bottom layer, the downward or lateral growth may become dominant. Thus, the geometry of the fracture can vary between a long and narrow shape towards a round shape. The lateral growth of fractures in the 3D model undermines the suitability of 2D plane-strain model results.
Highlights
Hydraulic fracturing technique has been extensively used to improve reservoir performance in hydrocarbon [1] as well as geothermal reservoirs [2], and for preconditioning the rock masses in underground mines [3]
Results from the 2D model show that in majority of cases (6 out of 9) the fracture reaches to the middle layer, and due to the lower minimum principal stress in this layer, an extensive propagation occurs in this layer
For instance in the case with lowest stiffness of the middle layer (E = 5 GPa), the fracture hardly grow upward and it mainly advances downward, in the case with highest stiffness (E = 15 GPa, i.e., lowest stiffness contrast), under the gravity effects, the fracture reaches to the middle layer, but it stops growing in that layer as the stress increases towards the centre of the layer
Summary
Hydraulic fracturing technique has been extensively used to improve reservoir performance in hydrocarbon [1] as well as geothermal reservoirs [2], and for preconditioning the rock masses in underground mines [3]. Additional complexities can be envisaged by taking into account additional (but sometimes important) factors such as presence of layers with different properties, changes in in situ stresses, the leak-off of the injected fluid into the rock matrix, and the presence of a natural fracture or fracture network [4]. Simonson et al [5] studied the stress intensity factor as the fracture approached the interface of a layer with different Young's modulus. Zhang et al [26] developed a model using a finite element approach where they studied the effect of in situ stress contrast, modulus contrast, tensile strength contrast and viscosity of the fracturing fluid. Huang et al [30] investigated the height growth under the influence of stress barriers and natural fractures using the finite element method for the mechanical response and finite volume method for the fluid flow. Both 2D plane-strain and 3D fracture models are utilised for the simulations and the results are presented and discussed
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