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[1] A numerical model has been developed for fluid-driven opening mode fracture growth in a naturally fractured formation. The rock formation contains discrete deformable fractures, which are initially closed but conductive because of their preexisting apertures. Fluid flow that develops along fractures depends on fracture geometry defined by preexisting aperture distribution, offsets along a fracture path, and intersections of two or more fractures. The model couples fluid flow, elastic deformation, and frictional sliding to obtain the solution, which depends on the competition between fractures for permeability enhancement. The fractures can be opened by fluid pressure that exceeds the normal stress acting on them and by interactions with intersecting closed fractures experiencing Coulombtype frictional slip. The Newtonian fluid is assumed to flow through the conductive fractures according to a lubrication equation that relates the cube of an equivalent hydraulic aperture to fracture conductivity. The rock material is assumed to be impermeable and elastic. This paper provides the governing equations for the multiple fracture systems and the solution methods used. Flow distribution and fracture growth in conductive fracture sets are simulated for a range of geometric arrangements and hydraulic properties. Numerical results show that elastic interaction between fracture branches plays a controlling role in fluid migration, although initial apertures can give rise to a preferential fluid flow direction during the early stage. In the presence of offsets, fracture segments subject to strong compression are difficult to open hydraulically, and their resulting smaller permeability can increase overall upstream fracture pressure and opening. The patterns of fluid flow become more complicated if fractures intersect each other. A portion of injected fluid is lost into closed empty fractures that cut across the main hydraulic fracture, and this delays the pressure increases required for fracture growth past the crosscutting fracture. The nonlinear fluid loss rate depends on the geometric complexities of the fracture sets and on the fluid viscosity. Sometimes fracture growth can be accelerated by the fast fluid transport along an intersected, relatively conductive natural fracture.Citation: Zhang, X., R. G. Jeffrey, and M. Thiercelin (2009), Mechanics of fluid-driven fracture growth in naturally fractured reservoirs with simple network geometries,

SUMMARYThis paper analyses the plane strain problem of a fracture, driven by injection of an incompressible viscous Newtonian fluid, which propagates parallel to the free surface of an elastic half-plane. The problem is governed by a hyper-singular integral equation, which relates crack opening to net pressure according to elasticity, and by the lubrication equations which describe the laminar fluid flow inside the fracture. The challenge in solving this problem results from the changing nature of the elasticity operator with growth of the fracture, and from the existence of a lag zone of a priori unknown length between the crack tip and the fluid front. Scaling of the governing equations indicates that the evolution problem depends in general on two numbers, one which can be interpreted as a dimensionless toughness and the other as a dimensionless confining stress. The numerical method adopted to solve this non-linear evolution problem combines the displacement discontinuity method and a finite difference scheme on a fixed grid, together with a technique to track both crack and fluid fronts. It is shown that the solution evolves in time between two asymptotic similarity solutions. The small time asymptotic solution corresponding to the solution of a hydraulic fracture in an infinite medium under zero confining stress, and the large time to a solution where the aperture of the fracture is similar to the transverse deflection of a beam clamped at both ends and subjected to a uniformly distributed load. It is shown that the size of the lag decreases (to eventually vanish) with increasing toughness and compressive confining stress.