Engineers use boundary-dominated productivity equations for fracture designs in medium permeability formations. These equations are critical to optimize fracture designs and are different for primary depletion and formations under waterflooding processes.

This paper presents two new models to calculate the dimensionless productivity index, JD, of finite-conductivity fractured wells producing either at pseudo-steady or steady state conditions. These models use a new "definition" of the equivalent wellbore radius to incorporate the finite conductivity and fracture penetration dependency of the solution. New easy-to-use correlations (from 1500 numerical simulation runs) to calculate consistent shape factors and f-functions for fractured wells are also presented in the paper. The f-functions are an extension to PSS and SS conditions from the Cinco-Ley’s original work. These equations are used to regenerate JD type curves of a finite-conductivity fractured well under pseudo-steady or steady state conditions. A comparison of the JD type curves of SS versus PSS is also presented. The maximum JD value, for fully penetrated infinite conductivity fractured well was 4/PI for SS versus 6/PI for the same case under PSS.

These productivity equations are also used to understand more post-fracturing production performance and to push the limits in hydraulic fracturing by injecting very large volumes of proppant of very large retained permeability. The paper will present the production results of the evolution of this hydraulic fracturing technique in these turbidite formations in Russia. It will be shown how the dimensionless productivity indices have been improving as the proppant volume per foot and proppant size has been increased. Statistics has shown how productivity index JD has increased from 0.3 to 0.55 when proppant concentration is increased from 4 tons/meter to 8 tons/meter. Definitely, pushing the fracturing limits in Russia has had a great impact on the production increase on these turbidite formations.

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