Experimental and theoretical study on the effect of unsteady flow on the fracturing pressure in hydraulic fracturing test

Reasonable determination of formation fracturing pressure concerns the stable operation of underground fluid injection projects. In this work, we studied the effect of unsteady flow on fracturing pressure. Hydraulic fracturing tests on low permeable sandstone were conducted with the injection rate between 0.1 and 2.0 ml/min. Then, the fracturing pressure prediction models for hollow cylinder under both unsteady flow and steady flow conditions were deduced. Finally, the effect of unsteady flow on the fracturing pressure was studied based on the experimental result and several influence factors. It was shown that fracturing pressure increased with the elevated pressurization rate in the tests, while the slope of the variation curve decreases. The model considering unsteady flow can reflect the variation tendency of fracturing pressures in experiments, while fracturing pressures from the model considering steady flow are invariant with different pressurization rates. Fracturing pressure decreases with the elevated rock permeability and increases with the elevated fluid viscosity, and these two effects are actually generated by the unsteady flow. Whether to consider the unsteady flow has no significant influence on the effect of rock tensile strength on fracturing pressure when the tensile strength is very low. However, when the tensile strength is high, the effect of unsteady flow cannot be neglected.