IN1RODUCTION

Well stimulation procedures are designed to reduce the restrictions to flow from the reservoir into the wellbore and increase productivity.1  Hydraulic fracturing in low permeability reservoirs is an important and successful stimulation methodology widely used by the petroleum industry.

The design of the optimum fracture treatment has three basic steps. The first step involves calculating fracture dimensions and conductivity for various fracture fluid pumping schedules. The second step is determining the oil and gas production rates and recoveries using the values of propped fracture length obtained from the fracture treatment design. The third step requires one to determine the optimum fracture treatment design by maximizing the economic benefit of the treatment. Since a fracture treatment design involves selection of fracturing fluids, additives, proppant materials, injection rate, pump schedule, and fracture dimensions, the determination of the optimum combination of all variables can be quite complicated. In this research, we have developed two methods to investigate reasonable combinations of design and treatment parameters to determine the most profitable fracture treatment design. Depending upon the post-fracture treatment production rates, the related expenses, and the economic constraints, the optimum treatment can be easily determined.

The first optimization method is based on a mathematical technique called Mixed Integer Linear Programming (MILP).2  This method can be used to minimize or maximize a desired objective function subject to certain constraints. For this work, we have chosen the objective function to be the discounted net present value due to a fracture treatment. The constraints are related to the fracture dimensions and other items necessary to linearize the fracture design problem.3 

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