Optimization methods of linear and non-linear programming have been used in the oil industry to study the scheduling of oil well production and drilling, and to determine the optimal investment policies.
There are few studies published in the area of optimization of well stimulation policies. This paper describes the application of non-linear mathematical programming methods to optimize the design and evaluation of oil and gas wells for stimulation.
The model presented is modular and it has three sub modules: SCREEN, DESIGN, and OPTIMIZE. The screening module combines pre-stimulation production performance data, geological and reservoir data to match a well to one of four stimulation operations, namely, hydraulic fracturing, matrix acidizing, acid fracturing and recompletion. In the second module, the design of the stimulation operation selected from the screening module is performed. The program uses widely - accepted equations and correlations to design hydraulic fracturing, matrix acidizing, acid-fracturing and recompletion. In the optimization module, analytical decline curve and economic discounting techniques are used to predict the production profile after the stimulation operation, and to determine the time value of money and production. The optimization model combines the reservoir and economic data to determine the optimal well stimulation strategy.
The constraints of the optimization model, include those imposed by the reservoir, the production facilities, operating costs, and operating budget of the field. Program development and validation procedures, and the application to field data are presented in the paper.