APPLICATION OF MATHEMATICAL DRILLING MODEL ON SOUTHERN IRAQI OIL FIELDS
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Abstract
Minimum-cost well drilling demands the best use of controllable drilling variables for each formation to be drilled. To reach this aim, this study was divided into two main parts: The first part deals with applying a mathematical drilling model to field data of forty wells
drilled at three major oil fields (RU, R, and Z). Bourgoyne & Young (1974) drilling model has been modified to take into consideration the combined effect of weight on bit, rotary speed, bit type, bit size, flow rate, drilling fluid density, drilling fluid viscosity, oil content, bit-nozzle size, formation drillability, formation abrasiveness, bit bearing constant, formation hardness, formation compressive strength, differential pressure between mud column pressure and formation pressure, and bit dullness on drilling rate at these fields. The measurements of formation compressive strength have been achieved using 34 core plugs. These plugs were cut and prepared for soft, medium, and hard formations under study. The drilling model was fitted to Field data by using multiple regression analysis technique. The results of analysis gave low standard deviation, high correlation coefficient, and good matching between measured and calculated drilling rate. The validity of modeling process has been verified by applying the proposed drilling model on other
wells that have not been included in the main analysis. The second part deals with using the drilling model together with non-linear optimization technique to determine the optimum values of the controllable drilling variables. These variables are: weight on bit, rotary speed, flow rate, drilling fluid density, drilling fluid viscosity, oil content, bit-nozzle size. Using the proposed mathematical drilling model together with the Constrained Rosenbrock optimization technique achieved a marked reduction in drilling cost about 60%, 75%, 80% in soft, medium, and hard formations respectively. The results of optimization were used to construct optimum bit record for the next wells to be drilled. For comparison purpose, this optimum bit record has been used to reduce the drilling cost for well RU263 and saved about 295000 $ in the total cost of this well which is equal to 394176 $.
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References
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