Accounting for dimensionless conductivity in express calculation of flow-rate in a well after multi-stage hydraulic fracturing

This paper presents an improved model of fluid inflow into hydraulic fractures. We also suggest here formulae for calculating flow rate in a horizontal well after multi-stage hydraulic fracturing job as dependent on the number of fractures, the angle of fracture deviation fr om the normal line to the horizontal section of the well and on the values of fractures’ dimensionless conductivity F_cd. In our previous papers we accounted for infinite conductivity, but only partially. In this paper we estimate the impact of fracture conductivity onto the total flow rate in a horizontal well after multi-stage hydraulic fracturing. The hydraulic fracture is viewed as a wedge-like channel with half-length of x_f, average width of w and constant height of h that is filled evenly with proppant and deviates at an angle ± from the normal line. Our assumption was that the pressure at fracture tip is higher than bottom-hole pressure p_тр> p_з, while the pressure at the beginning of the fracture (the point wh ere it enters the wellbore) is equal to bottom-hole pressure p_з. For F_cd>10 the previous and the current models render equal results. The new model is a powerful enabler for optimization of multi-stage fracturing it terms of identifying economically efficient number of ports as well as fracture half-length and the angle of fracture deviation from the normal line to the well.

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