A new theoretical method to calculate shale fracture conductivity based on the population balance equation
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abstract
2015 Elsevier B.V. Shale fracture conductivity plays a critical role in determining the long term production of shale wells. High fracture conductivity is achieved by pumping more proppants and minimizing conductivity damage by fracturing fluid. Currently, fracture conductivity is either measured in laboratory following ISO 13503-5 or calculated using correlations derived from extensive laboratory tests by regression analysis. There is a need for a handy and practical tool to calculate shale fracture conductivity reflecting realistic fracturing designs. This paper presents a new correlation to calculate shale fracture conductivity that considers proppant properties, fracture design variables and formation mechanical properties. This correlation is based on the population balance equation for size reduction. It utilizes the population balance concept to predict the crushed proppant size distribution under increasing closure stress. Numerical solution of the integro-differential equation is validated by comparing the computed results with the measured data. The crushed grain size distribution determines the permeability of the sand pack. Fracture width is calculated separately by considering proppant embedment and proppant grain rearrangement. Fracture conductivity is then calculated and compared with laboratory measured conductivity. Finally, the effect of water damage to shale fracture conductivity is considered by bringing in a new modification term. Results show that the population balance equation can reasonably predict the crushed proppant size reduction by properly choosing the selection equation and breakage equation. The calculated shale fracture conductivity can match with the measured fracture conductivity using the Barnett Shale. An exponential expression can be used to account for the water damage effect in the Barnett Shale.
