Correct assessment of the proppant-fluid slurry hydraulic friction in the tubing is important to prevent premature shutdown of the hydraulic fracturing operation. Injection modeling in a hydraulic fracturing simulator always includes calculation of the friction of the fluid mixture with proppant in the tubing to calculate wellhead pressure. The effect of proppant on friction is calculated either using the Keck model or using the tabulated dependence of the friction multiplier on the proppant concentration. This tabulated function is part of the design input data and should be validated against field data. This paper presents a technique that allows one to restore this dependence without additional experiments using actual hydraulic fracturing data. The proposed method for restoring the proppant friction modifier needs actual data on flow rate, bottomhole and wellhead pressures and proppant concentration. It is assumed that friction maps of pure liquids are already up to date. The article discusses three ways of representing the friction modifier: linear, quadratic and piecewise linear function of concentration. The paper presents the formulation of the inverse problem of restoring the parameters of the selected dependence. Examples of testing the methodology are given. Some of the frac jobs analyzed are shown where a linear dependence has been successfully restored. Others require a quadratic dependence, and some others require the most complex, piecewise linear dependence. Approbation at 10 and 8 frac stages in two horizontal wells is presented. Approbation of the method shows that the dependence of hydraulic friction on proppant varies from well to well, but the method allows one to obtain reproducible results for successive stages of multi-stage hydraulic fracturing and neighboring wells and to refine the correction for proppant used as input data for design calculations in RN-GRID fracturing simulation software. The new technique allows one to restore the dependence of hydraulic proppant friction modifier and gives engineers a tool to maintain the relevance of friction correlations for the proppants used in the RN-GRID hydraulic fracturing simulator without additional lab research.
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