On the problem of fluid leakoff during hydraulic fracturing

Abstract

While a hydraulic fracture is propagating, fluid flow and associated pressure drops must be accounted for both along the fracture path and perpendicularly, into the formation that is fractured, because of fluid leakoff. The accounting for the leakoff shows that it is the main factor that determines the crack length. The solved problem is useful for the technology of hydraulic fracturing and a good example of mass transport in a porous medium. To find an effective approach for the solution, the thin crack is represented here as the boundary condition for pore pressure spreading in the formation. Earlier such model was used for heat conduction into a rock massif from a seam under injection of hot water. Of course, the equations have other physical sense and mathematically they are somewhat different. The new plane solution is developed for a linearized form that permits the application of the integral transform. The linearization itself is analogous to the linearization of the natural gas equation using the real gas pseudo-pressure function and where the flux rates are held constant and approximations are introduced only into the time derivatives. The resulting analytical solution includes some integrals that can be calculated numerically. This provides rigorous tracking of the created fracture volume, leakoff volume and increasing fracture width. The solutions are an advance over existing discreet formulations and allow ready calculations of the resulting fracture dimensions during the injection of the fracturing fluid.

The influence of pumping parameters in fluid‐driven fractures in weak porous formations

“…The problem of the influence of the injection rate on the leak‐off process and the transition to important poroelastic effects was recently addressed by Kovalyshen, Kovalyshen and Detournay, and Economides et al . , whereas the cake building mechanisms on the fracture walls was studied by Entov et al . .…”

A Reexamination of the Classical PKN Model of Hydraulic Fracture

“…Construction of self-similar solutions for the PKN model when the leak-off is not restricted by Carter's law is presented by Gordeyev and Zazovsky (1992), who derived solutions for a constant pressure at the fracture inlet, by neglecting the pore pressure gradient along the crack. Approximated solutions for the case where the injection rate is prescribed at the inlet are proposed by Economides et al (2007).…”

Creating the link between micro-seismic observations and hydro-mechanical changes in the reservoir

“…The precipitation and dissolution of material is often considered to occur at rates where permeability alteration effects are noted after no less than a day, suggesting that geochemical effects can be neglected when considering the initial fracture network stimulation. A somewhat separate issue, however, is the formation of a "filter cake" on the fracture surfaces, which causes the well--known reduction of permeability between a fracture and the matrix rock that it interfaces as a function of time [53][54][55]. The flow of fluid from the fracture conduits into the surrounding matrix rock is often referred to as "leak--off".…”