The method of Hooke and Jeeves using Fibonacci line search has been used to solve the non-linear, multi-variable, unconstrained, objective function. A comparison between the Hooke and Jeeves searching method and other optimization techniques, such as discrete Hooke and Jeeves and Rosenbrock methods is given. Also the effects of changing one decision variable on the drilling cost are studied for all the six variables.

It is concluded that the new developed drilling model gives better results than the Galle and Woods model. Therefore, the drilling companies could save thousands of dollars on one well and perhaps millions on one field. The optimum solution, using the accelerated Hooke and Jeeves search method, is more economical and realistic than solutions produced by other optimization techniques.

A new non-linear, unconstrained, mathematical model for the drilling process has been developed. The number of parameters to optimize are six, namely, the weight on bit, the rotary speed, the drilling fluid volumetric flow rate, the jet nozzle diameter, and the drilling fluid density and viscosity.