Application of scaling laws to laboratory-scale hydraulic fractures

Design of hydraulic fracturing laboratory experiments that capture similar phenomena to those expected at the field scale requires consideration of the scaling laws intrinsic to the mathematical model. Analysis of the model for a radial, Newtonian-fluid-driven fracture in an infinite elastic homogeneous medium indicates that fractures evolve relative to three timescales associated with transitions between regimes characterized by large/small fluid lag, large/small effective fluid viscosity, and large/small fluid leak-off. The three invariants of the model are given by the ratio of the treatment time with these timescales, hence they provide the key for experimental design and interpretation that properly accounts for the difference between the field and laboratory scales. This paper presents a practical experimental design method based on these considerations. Experimental results are presented for which the invariant associated with fluid viscosity takes on different values. The results are in close agreement with a published solution that is based on modelling the crack tip using the classical Linear Elastic Fracture Mechanics when the viscosity invariant is small. However, when the viscosity invariant is O(1) the experimental results are in agreement with a published solution that utilizes a unique crack tip singularity associated with fluid-solid coupling in the tip region.