Iraqi Journal of Chemical and Petroleum Engineering Vol.16 No.3 (September 2015) 35- 44 ISSN: 1997-4884 Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data Hassan Abdul Hadi University of Baghdad, College of Engineering, Petroleum Dept. Abstract This paper provides an attempt for modeling rate of penetration (ROP) for an Iraqi oil field with aid of mud logging data. Data of Umm Radhuma formation was selected for this modeling. These data include weight on bit, rotary speed, flow rate and mud density. A statistical approach was applied on these data for improving rate of penetration modeling. As result, an empirical linear ROP model has been developed with good fitness when compared with actual data. Also, a nonlinear regression analysis of different forms was attempted, and the results showed that the power model has good predicting capability with respect to other forms. Key Words: operation, Rate of Penetration (ROP),Modeling Introduction During the last decades, the drilling engineers have been concerned extensively on prediction of drilling rate. This step is necessary since it help in the process of selection of drilling parameters (drilling optimization), which is important to decrease drilling cost per foot [1, 2]. It is well known that penetration rate is affected by controllable and uncontrollable factors. The controllable factors included weight on bit, rotary speed, bit type, mud properties, and hydraulics. While the formation characteristics is one of the uncontrollable factors that had significant effect on penetration rate [3]. Unfortunately, there is no comprehensive mathematical drilling model that related the drilling rate and different drilling parameters. The primary reason for that is the large number of factors influencing the drilling rate, and due complexity and nonlinearity of relationship of these factors to each other and to drilling rate[4]. However, experts have put forward some suggestions to address this issue. They have succeeded to model the effects of different drilling parameters involving drilling rate as mathematical functions. Bourgoyne and Young is one of these model that is widely in practice [5]. Rate of penetration modeling is recognized as a tool which can be used to reduce drilling costs by assisting bit selection and drilling optimization. There are many rates of penetration models available in drilling operations. But these models have two major problems. Firstly, these models are derived under specific conditions, particularly from laboratory controlled experiments which are limited by the differences between the experimental and field data conditions. Secondly, the Iraqi Journal of Chemical and Petroleum Engineering University of Baghdad College of Engineering Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data 36 IJCPE Vol.16 No.3 (Sept. 2015) -Available online at: www.iasj.net models derived from field data have lacked a detailed and systematic analysis of bit run data tacking into account the particular conditions of the bit run. The lack of the availability of a comprehensive computerized data base has also slowed down progress in ROP modeling [6]. Today, a mud log provides foot-by- foot data base which assists in modeling of ROP accurately. These data includes, WOB, RPM, HIS etc., and electric wireline logs, such as Δt, Gamma ray, Resistivity and caliper logs. This data base provides an opportunity for ROP modeling taking into different parameters which permits the modeling process more accuracy [7]. Raw Logging Data The raw mud logging data were recorded for Al Zubair oil field. This field is located in south Iraq, Basrah city. The sequence of formations in this field are Upper Faris,Tenoma, Sheransh, Umm Radhuma respectively. Umm Radhuma formation is predominantly limestone .Its considered the thickest formation in this sequence, about450 m, which made it a good selection for developing correlation. Figs. (1), (2), and (3) shows the measurements interval feet by feet for ROP, WOB, and RPM with depth for this formation. These figures illustrate the difficulties of evaluating the relationship between ROP and WOB, RPM due to high fluctuation in these dataset. Fig.1, Raw ROP versus Depth Data Hassan Abdul Hadi -Available online at: www.iasj.net IJCPE Vol.16 No.3 (Sept. 2015) 37 Fig.2, Raw WOB versus Depth Data Fig.3, Raw RPM versus Depth Data Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data 38 IJCPE Vol.16 No.3 (Sept. 2015) -Available online at: www.iasj.net Penetration Rate Modeling Statistical software called "SPSS" was used to perform various statistical analysis for modeling penetration rate with other drilling parameters. The raw data for Umm Radhuma formation was extracted from mud log data of well ZB-232.As first step, a linear regression model was attempted for the modeling. Table (1) shows the main drilling parameters that used in regression analysis and some statistical analysis for each parameter entered in the modeling. The ROP is dependent variable, while the WOB, RPM, MW, and Q are the independent variables. Table 1, Statistical Analysis of Drilling Parameters N Range Minimum Mean Std. Deviation Variance Statistic Statistic Statistic Statistic Std. Error Statistic Statistic ROP 2251 395.41 1.00 17.3373 .27307 12.95550 167.845 WOB 2251 27.03 .01 14.0190 .16803 7.97226 63.557 RPM 2251 79 73 119.33 .226 10.721 114.948 MW 2251 .05 1.10 1.1239 .00052 .02458 .001 Q 2251 1696 1508 3023.55 1.945 92.267 8513.115 Valid N (listwise) 2251 Table(2) provides the analysis of variance for the data of the model. Each items of this analysis can be defined by the following equations: SSR= … (1) SSE = … (2) MSR=SSR/K … (3) MSE=SSE/N-K-1 … (4) F=MSR/MSE … (5) Where: SSR=sum of square regression SSE=sum of square error(residual) MSE= mean of sum error MSR=mean of sum regression K=No.of parameters N= no. of points Yi=actual value Ῡ=mean value Ỹ=predictive value Df=degree of freedom Table 2, Analysis of Variance of the Liner Model Model Sum of Squares df Mean Square F Sig. 1 Regression 74872.621 4 18718.155 138.851 .000 b Residual 302778.652 2246 134.808 Total 377651.273 2250 Table 3, Values of Coefficients of Linear Model Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -105.346- 17.467 -6.031- .000 WOB -.799- .034 -.491- -23.471- .000 RPM .049 .025 .040 1.939 .053 MW 125.132 11.939 .237 10.481 .000 Q -.004- .003 -.030- -1.512- .131 Hassan Abdul Hadi -Available online at: www.iasj.net IJCPE Vol.16 No.3 (Sept. 2015) 39 Table 4, Model Summery Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 df2 Sig. F Change 1 .445 a .198 .197 11.61068 .198 138.851 4 2246 .000 Fig.4, Fitted and Actual ROP with Depth before Improving According to these statistical analysis of the interest data , the values of coefficients of this linear model are shown in the table(3).Table (4) shows a weak strength of this relationship between ROP and the other parameters since the value of square correlation coefficient is 0.197. Fig. (4) displays the actual and fitted rate of penetration values as functions of depth for this data set. Improving Data Quality In order to obtain more representative relationship between ROP and its related variables, the quality of logging data for ROP modeling must be improved by the following means: A. Exclusion of Outliers Outlier may defined as the value that are far from the middle of distribution. In statistics language, any points that are beyond the outer fences are considered as outliers. Thus, the statics software SPSS performs this exclusion process for logging data and detected the outliers for each parameter included in the modeling(ROP,WOB,RPM,Q ,MW) as shown in Figs.(5),(6),(7),(8),and(9). As result of this process,32.5% of the variation in the data was obtained by the model(R 2 =0.325) as shown by the Fig.(10). 0 5 10 15 20 25 30 35 40 45 50 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157 163 Depth(ft) R O P (f t/ h r) Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data 40 IJCPE Vol.16 No.3 (Sept. 2015) -Available online at: www.iasj.net Fig.5, Outliers of ROP Data Fig.6, Outliers of WOB Data Fig.7, Outliers of RPM Data Fig.8, Outliers of Flow Rate Data Fig.9, Outliers of Mud Weight Data Fig.10, Predicted ROP after Removing Outliers Hassan Abdul Hadi -Available online at: www.iasj.net IJCPE Vol.16 No.3 (Sept. 2015) 41 Table 5, Groups of Modeling Data t data size depth ROP WOB RPM Density flow rate 1 8 1042.03 21.80 2.50 107.55 1.11 3015.21 2 42 1047.97 23.20 3.57 116.89 1.11 3015.05 3 17 1037.22 23.55 4.44 117.64 1.10 3015.01 4 28 1049.39 23.50 5.50 117.00 1.11 3015.18 5 29 1000.40 26.02 6.60 121.46 1.11 3015.34 6 33 1090.08 25.87 7.51 123.40 1.12 3015.29 7 23 1091.06 25.41 8.53 121.69 1.12 3015.39 8 48 1100.38 23.63 9.52 124.00 1.12 3015.68 9 42 1114.43 24.75 10.46 120.91 1.13 3015.25 10 45 1104.07 22.91 11.56 121.38 1.13 3015.40 11 49 1088.77 23.02 12.52 125.16 1.12 3015.68 12 66 1110.39 23.17 13.50 121.36 1.13 3015.45 13 47 1104.31 18.85 14.46 120.19 1.12 3015.26 14 117 1128.27 19.62 16.12 120.20 1.13 3015.26 15 73 1117.76 17.33 17.59 121.26 1.13 3015.30 16 76 1145.35 17.29 18.53 120.55 1.14 3015.20 17 45 1114.25 13.22 19.46 121.11 1.13 3015.30 18 53 1104.27 10.85 20.54 120.62 1.12 3015.40 19 57 1089.62 7.60 21.57 122.90 1.12 3015.50 20 64 1068.00 5.63 22.39 122.01 1.11 3015.69 21 17 1073.22 2.40 24.49 121.97 1.10 3015.37 22 9 1076.98 1.83 25.26 125.03 1.10 3015.91 23 4 1051.90 2.01 26.04 122.81 1.10 3015.00 Table 6, Descriptive Statistics for Grouped Data N Range Minimu m Maximu m Mean Std. Deviation Statistic Statistic Statistic Statistic Statistic Std. Error Statistic depth 23 144.95 1000.40 1145.35 1084.7885 7.15576 34.31784 ROP 23 24.19 1.83 26.02 17.5411 1.73989 8.34421 WOB 23 23.54 2.50 26.04 14.0278 1.53514 7.36229 RPM 23 17.61 107.55 125.16 120.7425 .74842 3.58928 MW 23 .04 1.10 1.14 1.1166 .00227 .01089 Q 23 .91 3015.00 3015.91 3015.3529 .04700 .22538 Valid N (listwise) 23 Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data 42 IJCPE Vol.16 No.3 (Sept. 2015) -Available online at: www.iasj.net B. Grouping the Data After removing the outliers, the logging data that were used for rate of penetration modeling will divided into number of groups. This approach for increasing the size of grouped data was proved statistically. With the aid of SPSS software, the Logging data were grouped into 23 groups for each variable as shown in table(5). Other statistics analysis of grouped data is shown in table (6). C. Regression of Grouping Data As a final step, a linear regression analysis of logging grouped data was conducted to establish general model that relating drilling rate with drilling variables. Table (7) summarizes the values of coefficients, while tables (8) and (9) provide other statistical analysis of this regression modeling. The final form of this model will be: ROP=20902.003-1.059WOB+ 1.11RPM+315.9MW+ 2.419Q… (6) Table 7, Coefficients values of Linear Model Model 95% Confidence Interval Upper Bound 1- Constant WOB RPM MW Q 20290.003 -1.059 1.11 315.902 2.419 As it was noticed from the above tables, a better relationship was obtained after processing logging data(R 2 =0.978) compared to the relationship before improving the interested log data. Figure(10) also shows clearly very good correspondence between the measured and the calculated values of ROP from Eq. (6). Table 8, Linear Model Summery Model R R Square Adjusted R Square Std.Error of the Estimate 1 0.989 0.978 0.972 1.3592 Table 9, Analysis of Variance of the Linear Model Model Sum of Square df Mean Square F 1 Regression Residual Total 1173.423 25.866 1199.288 4 14 18 293.356 1.848 158.782 Hassan Abdul Hadi -Available online at: www.iasj.net IJCPE Vol.16 No.3 (Sept. 2015) 43 Fig.10, Actual and Fitted ROP Table 10, Nonlinear Parameters Estimation (Case1) Parameter Estimate Std. Error 95% Confidence Interval Lower Bound Upper Bound a 3.841 5.928 -8.795- 16.477 b .436 .543 -.722- 1.594 c .001 .000 .001 .001 d -3.694- .000 -3.694- -3.694- e .001 .000 .001 .001 f .892 .000 .892 .892 g .542 .000 .542 .542 h -2.668- 213062466.597 -454131900.271- 454131894.935 Table 11, Nonlinear Parameters Estimation (Case2) Parameter Estimate Std. Error 95% Confidence Interval Lower Bound Upper Bound a -10.792- 2.576 -16.183- -5.401- b 18.614 55.137 -96.789- 134.017 c 17.298 127.173 -248.879- 283.474 d -5.863- 32.434 -73.748- 62.021 D. Non Linear Regression A nonlinear regression analysis was also conducted on the logging grouping data for comparison purpose. In the first case a power model was attempted, and good fitness model was obtained (R 2 =0.91).Table (10) provided the values of coefficients of this power model which has the following equation. Correlation of Penetration Rate with Drilling Parameters For an Iraqi Field Using Mud Logging Data 44 IJCPE Vol.16 No.3 (Sept. 2015) -Available online at: www.iasj.net ROP=3.841WOB 0.436 +0.001RPM - 3.67 +0.001MW 0.892 +0.542Q -2.668 … (7) In the second case a natural log form was conducted on logging grouped data. The results of regression analysis showed moderate strength of the model (R 2 =0.597).Table (11) showed the values of coefficients for this model which has the following equation: LnROP=-10.8ln(WOB)+18.6 ln(RPM)+17.3ln(MW)-59ln(Q)… (8) Conclusions 1- An empirical linear model that relating rate of penetration with drilling parameters was developed for Umm Radhuma formation in ZUBAIR field , using mud logging data. 2- The accuracy of the linear developed model could be enhanced by statistical processing which including removing of outliers, and grouping the logging data. 3- A power modeling of logging data would also provide good estimation of rate of penetration, while the natural log model provided moderated estimation of rate of penetration. Nomenclature Df: degree of freedom K: No.of parameters MW: Mud Weight,ppg MSE: mean of sum error MSR: mean of sum residual N: No.of point data Q: flow rate,l/m R: Correletion coefficient. RPM: Bit revolution per minute ROP: Rate of Pentration,ft/hr SSR: sum of square regression SSE: sum of square error(residual) WOB: Weight on Bit,ton Yi: actual value Ῡ: mean value Ỹ: predictive value References 1- M.J.Kaiser,A survey of drilling cost and complexity estimation models,Int.J.Pet.Sci.Tech,vol.1,no.1 ,pp.1-22,2007. 2- T.Bourgoyne,K.K.Millheim and M.E.Chenvert,Applied Drilling Engineering,9 th Edition,SPE,Richardson,TX,2003. 3- F.Akgun,Drilling rate at Technical limit,Int.J.Pet.Sci.Tech.,Vol1.no.1,p p.99-118,2007 4- J.Ricardo,P.Mendes and T.C.Fonseca,Applying a genetic neuro-model reference adaptive controller in drilling Optimization,World Oil Mag.,Vol.288,no.10,pp29-36,2007. 5- T.Bourgoyne and F.S.Young,A multiple regression approach to optimal drilling and abnormal pressure detection ,Soc.Pet.J.,vol.14,no.4,pp.371- 384,1974. 6- Hong Xu.,W.Oliver and J,Jensen,How to organize Mud Logging Data for Modeling Rate of Penetration,SPE29252,1995. 7- H.M.Bahari,A.Bahari,and H.Moradi,Intelligent Rate predictor, Int.J.Inn.Com.Cnot.Vol.7,no.4,April l2011.