The filtration of solids in the injection water in a frac-pack is the primary factor which controls the injectivity decline in frac-packed water injection well completions. The injectivity may decline rapidly or much more slowly depending on the degree of frac-pack filtration. the widening and lengthening of frac-packs and the associated loss of sand control are affected as well. However, there is no experimental data for the filtraiton coefficient in high velocity flows in frac-packs. In this research, the filtration coefficients were experimentally measured in high velocity flows encountered in frac-packs. The solid concentrations and pressure drops across proppant pack sections were measured to properly utilize filtration theory and permeability decline models. Teh filtration coefficients were measured at various flow rates and for different proppant sizes. Our experiments show that at high fluid velocities, the filtration coefficient is significantly lower than that estimated from prior correlations that are based on low velocity filtration.

Our experimental results were used to obtain new empirical correlations for filtration coefficients at high flow rates in frac-packs. The experimental coefficients were used as the primary input into a well injectivity model. The propper stimation on the filatration enabled us to analyze the impact of injection rates and proppant selection on injector performance, i.e., predict long-term injection well behavior. The effect of particle filtration in the frac-pack and its effect on injector performance was captured accurately for the first time.  The empirical correlations together with a model for frac-pack growth in the injection well allowed us to accurately estimate fracture dimensions and the long-term water injectivity of frac-packed injectors. These results can be used for frac-packed design, proppant selsction and specification of injection water quality.