Propagation of a Plane Strain Hydraulic Fracture With a Fluid Lag in Permeable Rock

Based on the KGD scheme, this paper investigates, with both analytical and numerical approaches, the propagation of a hydraulic fracture with a fluid lag in permeable rock. On the analytical aspect, the general form of normalized governing equations is first formulated to take into account both fluid lag and leak-off during the process of hydraulic fracturing. Then a new self-similar solution corresponding to the limiting case of zero dimensionless confining stress (T = 0) and infinite dimensionless leak-off coefficient (L = infinity) is obtained. A dimensionless parameter R is proposed to indicate the propagation regimes of hydraulic fracture in more general cases, where R is defined as the ratio of the two time-scales related to the dimensionless confining stress T and the dimensionless leak-off coefficient L. In addition, a robust finite element-based KGD model has been developed to simulate the transient process from L = 0 to L = infinity under T = 0, and the numerical solutions converge and agree well with the self-similar solution at T = 0 and L = infinity. More general processes from T = 0 and L = 0 toT = infinity and L = infinity for three different values of R are also simulated, which proves the effectiveness of the proposed dimensionless parameter R for indicating fracture regimes.