Experimental Verification of Dimensional Analysis for Hydraulic Fracturing

Abstract

Summary We have derived model laws that relate experimental parameters of a physical model of hydraulic fracture propagation to the prototype parameters. Correct representation of elastic deformation, fluid friction, crack propagation, and fluid leakoff forms the basis of the scaling laws. For tests at in-situ stress, high fluid viscosity and low fracture toughness are required. Tests on cement blocks agreed with the scale laws based on elastic behavior. Introduction In hydraulic fracture treatment design, numerical simulation is used to relate measured pressure to fracture geometry. As yet, there is no way to observe fracture geometry in field treatments, except in special tests with extensive monitoring (e.g., Ref. 1). Even then, much room is left for data interpretation. Laboratory tests should therefore serve as benchmarks for numerical simulations. Although there is an enormous difference in the scale of fractures in laboratory tests and in field applications, a numerical model should at least be capable of describing model tests with the appropriate boundary conditions. Many researchers have attempted to study fracture growth in physical model tests. Still, we must critically review previous experimental work in this paper because we think that such efforts can be greatly improved, at least in regard to two important (related) issues: correct scaling of the physical phenomena and stability of fracture propagation. Correct scaling implies that the physics of fluid-driven fracture propagation at field scale must be represented in the test. For instance, if tests are set up at in-situ stress and water is used for fracturing in the laboratory, the fracture pressures required to produce reasonable experimental times (and stable crack propagation) become so low that fracture toughness dominates the process, which is contrary to field observations (e.g., equal pressures during initial propagation and fracture reopening). In addition, the nonpenetrated zone at the fracture tip will disappear and the fracture will grow dynamically. Such experiments can bear no relation to the quasistatic process implied by field conditions nor to any credible numerical simulation of field fracturing.