Multiple Regression Approach To Optimize Drilling Operations in the Arabian Gulf Area

Abstract

Summary. This paper reports a successful application of multiple regression analysis, supported by a detailed statistical study to verify the Bourgoyne and Young model. The model estimates the optimum penetration rate (ROP), weight on bit (WOB), and rotary speed under the effect of controllable and uncontrollable factors. Field data from three wells in the Arabian Gulf were used and emphasized the validity of this model. The model coefficients are sensitive to the number of points included. The correlation coefficients and multicollinearity sensitivity of each drilling parameter on the ROP are studied. Introduction The objective of this paper is to present a case study for optimizing drilling operations in the Arabian Gulf area. A drilling model that predicts the effects of various drilling parameters on ROP was used, and its reliability and limitations were demonstrated. Included in the model are the effects of formation strength, formation depth, formation compaction, pressure differential across the hole bottom, bit diameter and WOB, rotary speed, bit wear, and bit hydraulics. The modeling is accomplished through a multiple regression analysis of drilling data taken from wells in the Arabian Gulf area with the Statistical Analysis System (SAS) package. The important advantage of applying the regressed drilling model is the possibility of minimizing drilling cost through a proper selection of optimum WOB and rotary speed. In most of the Arabian Gulf areas, exploration strategies are currently being shifted toward exploring deep Paleozoic-Kuff and preKuff prospects because the Jurassic and younger prospects have preKuff prospects because the Jurassic and younger prospects have reached a relatively mature stage. Consequently, drilling costs will be shifted upward accordingly ($10 million to $15 million is a common amount to complete one deep well in the gulf area). Therefore, research and study directed toward reducing drilling costs through optimization of drilling operations should be encouraged and pursued by research institutions and operating companies. Such drilling parameters as WOB and rotary speed are based on normal field operation practices rather than calculated optimized values. If these weights and speeds vary substantially from the optimized values, significant drilling-cost reduction may be expected. Several drilling models were proposed to explain the effects of such drilling parameters as depth, WOB, rotary speed, mud properties, and type of formation drilled on the ROP. The most properties, and type of formation drilled on the ROP. The most comprehensive drilling model is the one proposed by Bourgoyne and Young, which considered the effects ofthe depth and the characteristics of the formation being drilled,the mechanical factors of the drilling process (e.g., WOB and rotary speed), andthe mud system properties. This paper tries to address the reliability of applying such a model and attaches statistical significance to the estimated parameters that were not included in Bourgoyne and Young's paper. The second objective of this paper is to identify, if possible, the correlations between the different drilling parameters that cause what is known in statistics as a "multicollinearity problem." One of the major assumptions in the proposed drilling model is that no linear dependence exists between the drilling parameters. Existence of multicollinearity in the regression results will violate such an assumption. Drilling Model The drilling model proposed by Bourgoyne and Young predicts the effect of the various drilling parameters, Xi, on the ROP, R, which is given by (1) The drilling behavior in a given formation type is modeled by selecting the constants a1 through a8 in Eq. 1, which can be rewritten (2) 2 Because Eq. 2 is linear, these constants can be determined from a multiple regression analysis of field data. Eight parameters (X1 through X8) were included in the model and were discussed thoroughly by Bourgoyne and Young. A quick review of these parameters might be helpful. Effect of Formation Strength. The constant a1 represents the effect of formation strength on ROP. It also includes the effects of drilling parameters that have not yet been mathematically modeled. Effect of Compaction. The terms a2X2 and a3X3 in the model account for the effect of compaction on ROP. X2 is defined by (3) and this assumes an exponential decrease in ROP with depth in a normally compacted formation. X3 is defined by (4) and this assumes an exponential increase in ROP with geopressure gradient. The effect of compaction on ROP, a2X2 +a3X3, has been normalized to equal 1.0 for a normally compacted formation (gp = 9 lbm/gal[1078 kg/m3]) at 10,000 ft [3048 m]. Effect of Differential Pressure. The term a4X4 accounts for the effect of pressure differential across the hole bottom on ROP. SPEDE P. 83