Iraqi Journal of Chemical and Petroleum Engineering Vol.13 No.2 (June 2012) 37- 45 ISSN: 1997-4884 Thickening Time and Compressive Strength Correlations for Bentonitic- Class "G" Cement Slurries Riyadh Hazim Fawzi Baghdad University, College of Engineering, Department of Petroleum Engineering, Baghdad, Iraq Abstract Empirical equations for estimating thickening time and compressive strength of bentonitic - class "G" cement slurries were derived as a function of water to cement ratio and apparent viscosity (for any ratios). How the presence of such an equations easily extract the thickening time and compressive strength values of the oil field saves time without reference to the untreated control laboratory tests such as pressurized consistometer for thickening time test and Hydraulic Cement Mortars including water bath ( 24 hours ) for compressive strength test those may have more than one day. الخالصة لسمنت نوع "ج" المحضر بالبنتونايت والذ ي يمثل ةللتنبؤ بقيم زمن التثخن وقوه الصالب ةالمعادالت التجريبي )لمختلف النسب(. ان استعمال معادالت للتنبؤ بقيم زمن ةالظاهري ةالماء الى السمنت واللزوج ةلنسب ةكدال الحقل النفطي يوفر الوقت دون الرجوع الى الفحص المختبري واستعمال ة في التثخن وقوه الصالب ة( لقياس قوة صالبةساع 42) ةوالحمام المائي لمدة السمنت واعمدلقياس زمن التثخن ةالخاص ةاالجهز السمنت وكلها قد تحتاج الى اكثر من يوم. Keywords Correlations, Thickening time, Compressive strength, Drilling, Cementing materials. Introduction Physical and rheological properties of cement slurries with additives are important tools in cementing jobs. Many investigation were made by researchers, manufactures and service companies to evaluate each addition in both the laboratory and the field. Ibrahim [1] performed laboratory tests on class "G" cement slurries containing different bentonite to cement ratios (dry bentonite), his results were 28 different plots and two correlation equations for thickening time and free water content. Data All cement slurries data from Ibrahim [1] (experimental work) , the range of data and data used are shown in Tables (1) and (2) respectively and the (m) values were calculated from this study. Iraqi Journal of Chemical and Petroleum Engineering University of Baghdad College of Engineering Thickening Time and Compressive Strength Correlations for Bentonitic- Class "G" Cement Slurries 38 IJCPE Vol.13 No.2 (June 2012) -Available online at: www.iasj.net Correlations 1. Thickening Time Correlations 1.1. Thickening time correlation(this study) The following general relation of thickening time of cement slurries with its rheological properties was assumed. Thickening Time = f (ú, m ) …(1) Thickening Time  ( 1/ú,m ) …(2) Table (2) shows 30 experimental points that were used to develop the following correlation equation ( this study ) , non linear model was used to develop the following relation: T.T = a1 +exp ( a2 + a3/ú + a4*m + a5/ú 2 + a6*m 2 + a7/ú 3 + a8*m 3 + a9/ú 4 + a10*m 4 + a11/ú 5 + a12*m 5 ) …(3) where a1 = - 9150.24 a2 = 9.360349 a3 = 4.384563 a4 = -1.60827 a5 = - 239.746 a6 = 3.909896 a7 = 6054.842 a8 = - 4.61193 a9 = - 68215.6 a10 = 2.641999 a11 = 285946.6 a12 = - 0.588621 1.2. Thickening Time Correlation (Ibrahim[1]) Ibrahim [1] wrote the following equation using apparent viscosity range of 35 to 95 C.P . But in this study and for comparative purposes , the following equation was used for all data. T.T = 134.1 - 0.427 * ú …(4) He assumed Thickening Time = f (ú ) …(5) Thickening Time  (ú ) …(6) 2. Compressive Strength Correlation (This Study) Compressive strength = f (ú, m) …(7) Compressive strength (ú,1/m) …(8) Also Table (2) shows the 32 experimentally points that were used to write the following correlation equation(this study),also non linear model was used to write the following relation. C.S. = a1 + a2/m + a3*ú + a4/m2 + a5*ú 2 + a6/m3 + a7*ú 3 + a8/ m4 + a9*ú 4 …(9) where a1 =16934.070004 a2 = - 53758.83433 a3 = - 7.52898677 a4 = 62273.823273 a5 = - 0.1502096603 a6 =- 29671.46878 a7 = 0.0022956086 a8 = 5139.7132478 a9 = - 0.0000077643 Statistical Analysis The statistical parameter used for comparison equations for those parameters are given below: 1. Average Percent Relative Error It is the measure of the relative deviation in percent from the experimental data and defined by:    N i Ei N Er 1 1 …(10) where Ei is the relative deviation in percent of an estimated value from the experimental value ,,...2,1100 exp exp Ni X XXest Ei         ...(11) Riyadh Hazim Fawzi -Available online at: www.iasj.net IJCPE Vol.13 No.2 (June 2012) 39 where X est and X exp represent the estimated and experimental values, respectively. 2. Average Absolute Percent Relative Error It can be represented by the following formula    N i Ei N Ea 1 1 …(12) 3. Minimum and Maximum Absolute Percent Relative Error Calculation of both minimum and maximum values are scanned to know the range of error for each correlation. Ei N i E min 1min   …(13) Ei N i E max 1max   …(14) 4. Standard Deviation (Sx) Standard deviation, Sx , is the measures of the data dispersion around zero deviation.    N i iE N Sx 1 2 2 1 1 …(15) 5. Correlation Coefficient (r) The correlation coefficient, r , represents the degree of success in reducing the standard deviation by regression analysis.                      N i i N i i XX XestX r 1 2 1 2 2 )exp( exp )( 1 …(16) Where    N i i X N X 1 exp)( 1 …(17) Results and Analysis 1. Results and Discussion Tables (3, 4 and 5) show a the comparison between errors experimentally thickening time of 30 estimated data points and the experimentally compressive strength of 32 data points from two correlations of the thickening time and one correlation of the compressive strength. The correlation for thickening time of this study Eq.(3) achieved the lowest errors and standard deviation, with the highest correlation coefficient accuracy ( this study ) of 0.9957 comparison with the correlation coefficient accuracy ( Ibrahim[1] ) of 0.4335. The correlation for compressive strength Eq.(9) achieved the high correlation coefficient of 0.9904. 2. Cross Plots The cross plots of estimated vs. experimental values for thickening time correlations are shown in Figs. (1) and (2) Most of the plotted points of this study's Fig. (1) correlation fall very close to the perfect correlation of 45 o line ( 0.79 rad ). The correlation of Ibrahim[1] Fig.(2 ) reveal more overestimation than this study. Also the cross plot of estimated vs. experimental values compressive strength correlation are presented in Fig.(3) of the plotted data points of this study's. Thickening Time and Compressive Strength Correlations for Bentonitic- Class "G" Cement Slurries 40 IJCPE Vol.13 No.2 (June 2012) -Available online at: www.iasj.net Riyadh Hazim Fawzi -Available online at: www.iasj.net IJCPE Vol.13 No.2 (June 2012) 41 3. Error Distribution The statistical histograms with normal distribution curve for the thickening time correlation of this study and Ibrahim[1] are presented in Fig.( 4) and ( 5) . The error ranges of (± 20 ) and (+60 to -80 ) are used for this study's and Ibrahim[1]. Correlations respectively. Fig. (6) shows the distribution for this study's correlation for compressive strength is (+30) and ( -40). 4. Conclusion 1. Thickening time and compressive strength correlations for bentonitic – class "G" cement slurries have been estimated using equations (3) and (9) respectively. 2. Equations (3) and (9) can be used for estimating all water/cement ratios and apparent viscosity without using any devices . 3. Deviations from experimentally data, indicated as average percent relative error , average absolute percent relative error, minimum and maximum absolute percent relative error and standard deviation were lower for this study than for estimation based on the correlation of Ibrahim[1]. 4. The correlation coefficients of the correlations of this study that are excellent and near one. Nomenclature. APRE = average percent relative error, (%) ,Eq. (10) C.S. = compressive strength,(PSI) Eq.(9) C.S.est = estimated compressive strength, (PSI) Ea = average absolute percent relative error, (%), Eq.(12) Ei = percent relative error, (%), Eq.(11) max E = maximum absolute percent relative error, (%), Eq.(14) min E = minimum absolute percent relative error, (%), Eq. (13) Er = average percent relative error, (%) , Eq.(10) f = function F.W = free water content, (%) m = water to cement ratio (by weight), dimensionless mo = bentonite to cement ratio (by weight), dimensionless ms = water to solid ratio (by weight), dimensionless N = number of variables r = correlation coefficient, Eq.(16) = Standard deviation, Eq. (15) T.T. = thickening time,(minutes),Eq.(3,4) T.T.est = estimated thickening time, (minutes) T.T.exp = experimental thickening time, (minutes) ú = apparent viscosity = Ø600/2 ,c.p [pa.s] X = average value of x exp, Eq.(17) X est = estimated value of X, X exp = experimental value of X ρ = slurry density, gm/cc Subscriptes est estimated from correlation exp experimental max maximum min minimum SI Metric Conversion Factors atm  1.013 250* E + 05 = Pa CP  1.0 * E 03 = Pa·s O F ( o F + 459.67)/1.8 = K Psi 6.894 757 E + 00 = kP References 1. Ibrahim , M.I. , (1989). Establishment of Graphical Relationships Between Ingredients of Bentonitic –Cement Slurry and its Main Physical and Sx Thickening Time and Compressive Strength Correlations for Bentonitic- Class "G" Cement Slurries 42 IJCPE Vol.13 No.2 (June 2012) -Available online at: www.iasj.net Rheological Properties. M.sc Thesis Baghdad University , College of Engineering , Department of Petroleum Engineering, Iraq. 2. London: W.H. Aleen and Co., Ltd. (1973). Hayslett , H.T.,Statistics Made Simple 3. Naji Tawfik. and Rashid Al – Salihi, (1989). Engineering Statistics. . Baghdad University , College of Engineering. Iraq : Higher Education Publication. Table 2 , Slurry and Set Class "G" Cement Properties at Variable Bentonite and Water Proportions (IBRAHIM[1]) Table 1, Range of Data Bentonite/Cement ratio, dimensionless 2/98 to 12/88 Water/Solid ratio, dimensionless 0.4 to 1.05 Water/Cement ratio, dimensionless 0.408 to 1.136 Apparent viscosity, C.P 9.5 to 138 Slurry density, gm/cc 1.49 to 1.94 Thickening time, minutes 51 to 430 Compressive strength, PSI 420 to 2530 Free water content, % Nil to 19 mo=2/98 Sample NO. ms m ú (at 80 o F) C.P ρ gm/cc Thickening Time (at 125 o F, 5200psi) minutes Compressive Strength (at 140 o F and 24-hures) Psi F.W % A1 ! A2 * " A3*" A4 *" A5 *" A6 *" A7 " 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.408 0.510 0.612 0.714 0.816 0.918 1.02 120.5 80.0 56.0 36.0 21.5 12.0 9.50 1.94 1.83 1.74 1.67 1.61 1.56 1.51 ---- 94 109 123 184 430 ---- ---- 2530 2187 1600 1480 1093 812 Nil 0.6 1.8 2.3 5.4 12.0 19.0 mo=4/96 Sample NO. ms m ú (at 80 o F) C.P ρ gm/cc Thickening Time (at 125 o F , 5200 Psi) minutes Compressive Strength (at 140 o F and 24-hures) Psi F.W % B1*" B2*" B3*" B4*" B5*" B6*" 0.50 0.60 0.70 0.80 0.90 1.00 0.521 0.625 0.729 0.833 0.938 1.042 99.0 72.0 48.0 32.0 22.0 19.0 1.83 1.73 1.66 1.60 1.55 1.51 63 96 111 130 165 220 2380 1683 1553 1120 800 678 Nil 1.3 1.8 3.7 5.7 7.2 Riyadh Hazim Fawzi -Available online at: www.iasj.net IJCPE Vol.13 No.2 (June 2012) 43 (*) used in the thickening time correlation equation. (") used in the compressive strength correlation equation. (!) not used. The (m) values were calculated from this study. Table 2 , Slurry and Set Class "G" Cement Properties at Variable Bentonite and Water Proportions (IBRAHIM[1]) (continued) mo=6/94 Sample NO. ms m ú (at 80 o F) C.P ρ gm/cc Thickening Time (at 125 o F , 5200 Psi) minutes Compressive Strength (at 140 o F and 24-hures) Psi F.W % C1" C2*" C3*" C4*" C5*" C6*" C7 ! 0.50 0.60 0.70 0.80 0.90 1.00 1.05 0.532 0.638 0.745 0.851 0.957 1.064 1.117 138.0 97.0 71.0 48.0 28.5 19.5 17.0 1.83 1.73 1.66 1.60 1.55 1.51 1.49 ---- 79 97 111 135 211 ---- 2330 1650 1180 1000 650 533 ---- Nil Nil 0.95 1.70 3.80 5.40 7.40 mo=8/92 Sample NO. ms m ú CP at 80 o F ρ gm/cc Thickening Time (at 125 o F,5200 Psi) minutes Compressive Strength Psi (at 140 o F and 24-hures) F.W % D1 ! D2" D3*" D4*" D5*" D6*" D7*" 0.50 0.60 0.65 0.70 0.80 0.90 1.00 0.543 0.652 0.707 0.761 0.870 0.978 1.087 ---- 128.0 109.0 91.0 62.0 39.0 25.0 1.83 1.73 1.69 1.66 1.60 1.55 1.51 ---- ---- 51 95 104 116 151 2212 1620 1381 1150 543 533 450 Nil Nil Nil 0.20 0.60 1.45 4.00 mo=10/90 Sample NO. ms m ú (at 80 o F) C.P ρ gm/cc Thickening Time (at 125 o F, 5200 Psi) minutes Compressive Strength Psi (at 140 o F and 24-hures) F.W % E1 ! E2 ! E3*" E4*" E5*" E6*" E7*" 0.50 0.60 0.70 0.75 0.80 0.90 1.00 0.556 0.667 0.778 0.833 0.889 1.00 1.111 ---- ---- 111.5 94.5 75.5 46.0 26.5 1.83 1.73 1.66 1.63 1.60 1.55 1.51 ---- ---- 53 94 98 113 140 2190 1590 1140 622 530 515 428 Nil Nil Nil Nil 0.3 0.8 3.5 mo=12/88 Sample NO. ms m ú (at 80 o F) C.P ρ gm/cc Thickening Time (at 125 o F , 5200 Psi) minutes Compressive Strength Psi (at 140 o F and 24-hures) F.W % F1 ! F2 ! F3*" F4* F5*" F6*" 0.50 0.70 0.80 0.85 0.90 1.00 0.568 0.795 0.909 0.966 1.023 1.136 ---- ---- 101.5 78.0 60.0 33.0 1.83 1.66 1.60 1.57 1.55 1.51 ---- ---- 55 94 101 127 2175 1087 516 ---- 431 420 Nil Nil Nil 0.3 0.6 2.3 Thickening Time and Compressive Strength Correlations for Bentonitic- Class "G" Cement Slurries 44 IJCPE Vol.13 No.2 (June 2012) -Available online at: www.iasj.net Table 3, Comparision of Thickening Time Estimated by Correlations from This Study and IBRAHIM[1] T.T.est - TT.exp Ibrahim minutes T.T.est - TT.exp (this study) minutes Deviation in Percent of Estimated Thickening Time (APRE) Estimated Thickening Time (T.T.est) minutes Experimental Thickening Time (T.T.exp) minutes NO. Ibrahim This Study Ibrahim This study 2.340 -3.842 2.490 -4.088 96.340 90.158 94 1 -1.332 -0.116 -1.222 -0.106 107.668 108.884 109 2 -5.892 -1.921 -4.790 -1.562 117.108 121.079 123 3 -60.048 0.690 -32.635 0.375 123.952 184.690 184 4 -301.56 0.059 -70.131 0.014 128.436 430.059 430 5 24.37 5.360 38.686 8.508 87.372 68.360 63 6 4.116 0.317 4.288 0.330 100.116 96.317 96 7 0.444 6.914 0.400 6.229 111.444 117.914 111 8 -11.004 -5.178 -8.465 -3.983 118.996 124.822 130 9 -41.284 9.184 -25.021 5.566 123.716 174.184 165 10 -94.868 -3.013 -43.122 -1.370 125.132 216.987 220 11 9.316 -8.436 11.792 -10.679 88.316 70.564 79 12 3.588 5.247 3.700 5.409 100.588 102.247 97 13 0.444 5.522 0.400 4.975 111.444 116.522 111 14 -14.352 -6.189 -10.631 -4.584 120.648 128.811 135 15 -86.104 -1.208 -40.808 -0.572 124.896 209.792 211 16 31.652 10.343 62.063 20.279 82.652 61.343 51 17 -3.852 -13.598 -4.055 -14.314 91.148 81.402 95 18 0.836 3.817 0.804 3.670 104.836 107.817 104 19 -0.308 -1.383 -0.266 -1.192 115.692 114.617 116 20 -28.700 -1.397 -19.007 -0.925 122.300 149.603 151 21 28.472 6.849 53.721 12.923 81.472 59.849 53 22 -4.504 -17.541 -4.791 -18.660 89.496 76.459 94 23 0.464 -3.455 0.473 -3.525 98.464 94.545 98 24 -0.612 -0.116 -0.542 -0.103 112.388 112.884 113 25 -18.408 2.588 -13.149 1.848 121.592 142.588 140 26 31.192 11.048 56.713 20.087 86.192 66.048 55 27 3.284 -4.525 3.494 -4.813 97.284 89.475 94 28 4.780 5.202 4.733 5.150 105.780 106.202 101 29 -8.476 -0.418 -6.674 -0.329 118.524 126.582 127 30 Riyadh Hazim Fawzi -Available online at: www.iasj.net IJCPE Vol.13 No.2 (June 2012) 45 Table 4, Compressive Strength Estimated by Correlation from This Study C.S.est - C.S.exp (this study) Psi Deviation in Percent of Estimated Compressive Strength (APRE) Estimated Compressive Strength (C.S.est) Psi Experimental Compressive Strength C.S.exp) Psi NO. 2.983 0.118 2532.983 2530 1 -201.077 -9.194 1985.923 2187 2 84.385 5.274 1684.385 1600 3 -129.561 -8.754 1350.439 1480 4 -48.924 -4.476 1044.076 1093 5 -21.979 -2.707 790.021 812 6 0.695 0.029 2380.695 2380 7 134.612 7.998 1817.612 1683 8 -66.849 -4.305 1486.151 1553 9 36.986 3.302 1156.986 1120 10 71.182 8.898 871.182 800 11 -30.019 -4.428 647.981 678 12 2.903 0.125 2332.903 2330 13 61.682 3.738 1711.682 1650 14 53.688 4.550 1233.688 1180 15 -87.448 -8.745 912.552 1000 16 91.044 14.010 741.044 650 17 72.800 13.660 605.800 533 18 46.823 2.890 1666.823 1620 19 -18.372 -1.330 1362.628 1381 20 -59.576 -5.181 1090.424 1150 21 174.781 32.190 717.781 543 22 34.872 6.543 567.872 533 23 62.419 13.870 512.419 450 24 -125.727 -11.030 1014.273 1140 25 127.834 20.550 749.834 622 26 37.029 6.987 567.029 530 27 -73.193 -14.210 441.807 515 28 40.579 9.481 468.579 428 29 -67.969 -13.170 448.031 516 30 -161.247 - 37.412 269.753 431 31 -45.354 -10.800 374.646 420 32 Table 5, Statistical Accuracy ot Thickening Time and Compressive Strength Correlations Compressive strength Thickening time This study 0.5771 9.0610 0.0292 37.4122 12.2285 0.9904 Ibrahim[1] This study 0.8186 -1.3851 5.5389 17.6353 0.0136 0.2655 20.2794 70.1312 8.1341 27.3976 0.9957 0.4335 Average relative error , % Average absolute relative error , % Minimum absolute relative error , % Maximum absolute relative error, % Standard deviation , % Correlation coefficient