Abstract
A fully coupled three-dimensional finite-element model for hydraulic fractures in permeable rocks is presented, and used to investigate the ranges of applicability of the classical analytical solutions that are known to be valid in limiting cases. This model simultaneously accounts for fluid flow within the fracture and rock matrix, poroelastic deformation, propagation of the fractures, and fluid leakage into the rock formation. The model is validated against available asymptotic analytical solutions for penny-shaped fractures, in the viscosity-dominated, toughness-dominated, storage-dominated, and leakoff-dominated regimes. However, for intermediate regimes, these analytical solutions cannot be used to predict the key hydraulic fracturing variables, i.e. injection pressure, fracture aperture, and length. For leakoff-dominated cases in permeable rocks, the asymptotic solutions fail to accurately predict the lower-bound for fracture radius and apertures, and the upper-bound for fracture pressure. This is due to the poroelastic effects in the dilated rock matrix, as well as due to the multi-dimensional flow within matrix, which in many simulation codes is idealised as being one-dimensional, normal to the fracture plane.
Highlights
Hydraulic fracturing is the process by which one or more fractures are propagated into a rock formation, driven by the internal flow of a pressurised fluid
Fluid flow through the fracture is commonly modelled using lubrication theory, which is derived from the general Navier– Stokes equation for flow of a fluid between two parallel plates (Batchelor, 1967; Zimmerman and Bodvarsson, 1996), whereas the fracture aperture is calculated using linear elasticity in conjunction with Linear Elastic Fracture Mechanics (LEFM) to compute the mode I stress intensity factor at the fracture tip (Geertsma and de Klerk, 1969; Spence and Sharp, 1985)
A fully coupled three-dimensional finite element model has been presented for the simulation of hydraulically driven fractures in poroelastic rocks
Summary
Hydraulic fracturing is the process by which one or more fractures are propagated into a rock formation, driven by the internal flow of a pressurised fluid. The leakoff rate predicted by Carter’s model, at each position along the fracture, decreases proportionally to square-root of time; a scenario of fracture arrest is not possible (Mathias and van Reeuwijk, 2009) This model does not account for the fact that seepage of the fracturing fluid into the rock formation increases the fluid pressure in the matrix, causing dilation of the rock matrix. A dilated matrix applies stresses back onto the fracture, referred to as ‘back-stresses’ in the hydraulic fracturing literature, which tend to close the fracture (Kovalyshen, 2010) These factors affect the available semi-analytical solutions for leakoff-dominated regimes that use a simplified onedimensional leakoff model in their formulation. Fracture growth and the direction of growth are estimated using an energy-based criterion that is based on the modal stress intensity factors along the fracture tip (Paluszny and Zimmerman, 2013) This model is validated against available asymptotic solutions for penny-shaped hydraulic fractures. Numerical simulations conducted over a range of parameter values delineate the limits of validity of the various available asymptotic solutions
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