Propagation of natural hydraulic fractures

This paper is concerned with modeling the propagation of natural hydraulic fractures (NHF). Growth of a NHF is limited by the condition that change of the crack volume during propagation is equal to the volume of the fluid flowing from the rock into the crack. In this paper, we show that formulation of this problem can be reduced to a single integral equation on the crack length. It is shown that fracture growth is controlled by two dimensionless parameters: η = 2π/(E′S) which can be interpreted as a ratio of the amount of water required to propagate the fracture to the amount of water available in the rock; and μ = L_o/l, the ratio of the initial crack length to a characteristic length associated with initial pore pressure and maximum tensile stress. For μ ≤ 1 the crack is stable, i.e. it does not propagate. However, for μ = 1 + ε with ≠ 0, even small ε causes unstable crack growth. Decreasing ε leads to increasing time for which the fracture propagates very slowly.