| Hydraulic fracturing is the most critical well stimulation technique used to increase well productivity. A successful hydraulic stimulation requires a fracture that is more conductive than the surrounding formation. This conductivity is achieved by adding proppants to the fracturing fluids to keep the walls of the fracture propped open. Many resources have been allocated to improve hydraulic fracturing products, especially proppants since they play an integral role in the fracture's conductivity. One of these improvements is the ability to predict the expected conductivities over time of proppants of varying types and sizes. However, there are no publicly published conductivity equations that can produce such predictions considering multiple variables.;Actual proppant conductivity test results, which were conducted for fifty hours, provided by Stim-Lab, Inc. (Duncan, OK) were used to develop short-term (zero to fifty hours) and long-term (beyond fifty hours) baseline proppant conductivity equations for sand, ceramic, resin coated sand, and resin coated ceramic proppants of varying sizes. Multiple regression analysis was performed on all provided data to develop these equations taking into account the effects of proppant concentration, temperature, closure stress, time, proppant median diameter, and proppant grain density.;Statistically, the developed short-term equations were accurate with a multiple coefficient of determination (R2) in the 90% range, which indicated that the developed equations results strongly resemble actual conductivity values. These equations were also validated by performing a comparison between the predicted conductivity values produced by the short-term baseline conductivity equations and the available actual conductivity test results.;Since Stim-Lab, Inc. did not conduct any long-term conductivity tests (weeks, months, and years), the validity of the long-term equations was established using two methods: • Graphically, by comparing the shape of the curve of an actual nine-month test to a predicted long-term conductivity curve. •Mathematically, by comparing the conductivity decline rates using the Kozeny-Carman equation to the decline rates developed for the long-term equations.;These developed baseline conductivity equations will help identify the proppant type and size to use, based on the appropriate reservoir conditions, to attain optimum conductivity and therefore optimize the hydraulic fracture process and avoid investing in more expensive proppants with higher qualities that would add no value to a well's productivity. |
