Computer simulation of hydraulic fractures

Flow of viscoplastic suspensions in a hydraulic fracture: implications to overflush

“…Here, Cartesian coordinate system Oxy is introduced in the cell plane, so that y-axis (with the basis vector e y ) is vertical and origin O is located in the bottom left corner of the computational domain; C i are the fluid tracer concentrations (with i being the number of fluid, so that i = 0 corresponds to the yield-stress fluid filling the slot initially); w(x, y, t) is the width of the HeleShaw cell (currently it is a prescribed function of coordinates and time, while in the model describing the hydraulic fracture propagation, w is obtained via coupling the hydrodynamic equations describing the flow inside a hydraulic fracture with geomechanics equations describing the fracture growth [1]); v is the width-averaged fluid velocity; v l is the velocity of fluid leak-off through the porous walls; G is the correction to fluid mobility due to the yield-stress rheology (G = 1 for Newtonian fluid); differential operator '∇' acts in the (x, y) plane as we applied the averaging procedure along the cell width. The flow scales are as follows: L is the cell length, U is the scale of the injection velocity, d is the cell width scale, ρ 0 is the fracturing fluid density, µ 0 and τ 0 are the fracturing fluid plastic viscosity and yield stress, respectively; g is the gravity acceleration.…”

“…Proppant transport models incorporated into existing hydraulic fracturing simulators describe the flow of particle-laden suspension inside a hydraulic fracture in the framework of the lubrication approximation using the power-law rheological model (see [1]). Hydraulic fracturing suspensions with large concentration of solids or fibers show a yield-stress behavior in rheological experiments [2,3], which is not taken into account in the proppant transport models implemented into commercial simulators of hydraulic fracturing.…”

“…A state of the art in the modeling of injection of particle-laden suspensions into hydraulic fractures is the family of 2D width-averaged models based on the lubrication approximation to Navier-Stokes equations [1,4,5,6]. In the regime of non-inertial settling, the momentum conservation equation for particles is reduced to an algebraic relation for the particle velocity slip in the vertical direction given by the Stokes formula with a correction for hindered-settling effects due to a finite particle volume fraction.…”

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

“…Once the induced fractures have sufficient width, a proppant is added to the fluid. After the release of the pumping pressure, the induced fractures remain open under the highly confining stress due to the proppant and therefore greatly enhance the permeability of the reservoir [1]. Other applications of hydraulic fracturing include heat production from geothermal reservoirs [2] and measurements of in situ stresses [3].…”

“…A model to predict the hydraulic fracturing process can be used to optimize these processes. However, the correct modelling of the hydraulic fracturing process is complex since three different phenomena have to be taken into account: (i) the fluid exchange between the fracture and the rock formation (ii) the fluid flow in the fracture and (iii) the changing spatial configuration due to fracture propagation [1].…”