THE FLUID MECHANICS OF HYDRAULIC FRACTURING (OIL RECOVERY)

The hydraulic fracturing of thin two-dimensional cracks embedded in porous rock is analyzed. The primary application of the hydraulic fracture process is the stimulation of oil wells of relatively low permeability. This is accomplished by pumping high pressure fluid down the wellbore in an effort to fracture the surrounding rock, and thereby, increase the effective permeability of the well. The principal goal of the present study is to determine how the time to fracture of an individual crack emanating from the wellbore depends on the permeability and elastic constant of the rock, the viscosity of the fracture fluid, and the rate of injection.; Assuming a fixed crack shape, the problem is solved analytically for short time, T = {dollar}{lcub}rm T{rcub}sb0 < 1,{dollar} in order to provide a starting point for the numerical calculation. For incompressible Newtonian fluids, the pressure in the rock satisfies Laplace's equation, and therefore, a boundary element method can be used to obtain a solution at time {dollar}{lcub}rm T{rcub}sb0{dollar} for the crack shape assumed above. A new crack shape is computed from the pressure along the crack and the numerical calculation is repeated until the solution converges. The instantaneous stress intensity factor {dollar}{lcub}rm Ksb{lcub}I{rcub}(Tsb0{rcub}){dollar} can now be calculated by integrating the pressure along the crack. Next, the normal velocity of the propagating fluid front is computed so that the shape of the free surface can be determined at the subsequent time step. The analysis continues until {dollar}{lcub}rm Ksb{lcub}I{rcub}{rcub}{dollar} reaches the critical valve {dollar}{lcub}rm Ksb{lcub}Isb{lcub}c{rcub}{rcub}{rcub}{dollar} and fracture initiates according to Irwin's criterion.; The results show that the pressure along the crack, and hence also {dollar}{lcub}rm Ksb{lcub}I{rcub}{rcub}{dollar}, can be enhanced by increasing the viscosity of the fracture fluid. The same pressure enhancement is obtained at a proportionately earlier time by a similar increase in the injection rate. It is also shown that formations of low permeability develop the largest pressures and are therefore easier to fracture provided large enough pumps are available. Finally, it is demonstrated that for short times {dollar}{lcub}rm Ksb{lcub}I{rcub}{rcub}{dollar} is greater for stiffer rocks, but for later times it increases with the compliance of the formation.