Modified leak-off equation for hydraulic fracture modelling

Abstract Carter’s equation is routinely used to describe the leak-off rate and the cumulative fluid loss during deposition of solids on porous media from a suspension. According to this equation, the leak-off rate is inversely proportional to the square root of time. This creates an unphysical singularity at time equal to zero. To remove this singularity, a modification is made to Carter’s law in this contribution. Another modification to Carter’s law made herein accounts for dynamic loss conditions where cross-flow filtration leads to only partial deposition. The modified leak-off law provides a satisfactory fit to the experimental data as long as cross flow is not turbulent. The modified leak-off law is calibrated against experimental data of an earlier study, in both static and dynamic fluid loss tests. A static fluid loss test is used to calibrate the model for the filter cake porosity and permeability as well as spurt loss. Dynamic fluid loss tests are then used to calibrate the model for the particle adhesion probability for each shear rate value.