DSpace at VNU: An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by R...
This article was downloaded by: [University of Calgary] On: 03 September 2014, At: 23:33 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Energy Sources, Part A: Recovery, Utilization, and Environmental Effects Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ueso20 An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by Response Surface Methodology ab a a H X Nguyen , T B N Nguyen , W Bae , T Q C Dang Chung ac & T a a Sejong University, Seoul, Korea b Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnam c Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada Published online: 26 Mar 2014 To cite this article: H X Nguyen, T B N Nguyen, W Bae, T Q C Dang & T Chung (2014) An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by Response Surface Methodology, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 36:10, 1103-1114, DOI: 10.1080/15567036.2010.545796 To link to this article: http://dx.doi.org/10.1080/15567036.2010.545796 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information Taylor and Francis shall not be liable for any 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Methodology H X Nguyen,1;2 T B N Nguyen,1 W Bae,1 T Q C Dang,1;3 and T Chung1 Sejong University, Seoul, Korea Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnam Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada In this study, the application of response surface methodology and central composite design for modeling the influence of some operating variables on the performance of steam-assisted gravity drainage process for oil recovery was discussed The maximized net present value of 105.16 $mm was obtained when the optimum conditions of steam-assisted gravity drainage operation process was designed following as injector/producer spacing of m, injection pressure of 5,440 kPa, maximum steam injection rate of 725 m3 /d, and spacing between two well pairs of 40 m The predicted values match the experimental values reasonably well, with R2 of 0.967 and Q2 of 0.82 for net present value response Keywords: central composite design, net present value, response surface methodology, steam-assisted gravity drainage INTRODUCTION Global conventional oil and natural gas reserves are on the decline As a result, non-conventional resources reservoirs, such as Alberta’s oil sand, are experiencing heightened global interest Thus, bitumen and heavy oil production are expected to increase rapidly in the coming decade The Athabasca Oil Sands are the center of this focus as one of the largest and highest-quality oil sands resources in the world An estimated 174 billion barrels of oil in the Athabasca deposit are potentially recoverable with the present technology Steam-assisted gravity drainage (SAGD) was first developed by Roger Butler and his colleagues in Imperial Oil in the late 1970s (Butler, 2001) SAGD is an effective method of producing heavy oil and bitumen, which consists of pairs of two parallel horizontal wells drilled near the bottom of the pay However, the process is associated with high cost and high uncertainty if initial operating conditions design is unreasonable, it means that the amount of oil recoverable or profit will be lower than actual production and even field life can extend a long time To overcome this situation, process engineers need to determine the Address correspondence to Wisup Bae, Sejong University, 98 Gunja-dong, Gwangjin-ku, Seoul 143-747, Korea E-mail: wsbae@sejong.ac.kr Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ueso 1103 Downloaded by [University of Calgary] at 23:33 03 September 2014 1104 H X NGUYEN ET AL levels of the operation design parameters at which the response reaches its optimum The optimum could be either a maximum or a minimum of an objective function of the design parameters One of the methodologies for obtaining the optimum results is response surface methodology (RSM) (Myers and Montgomery, 1995) In this study, the experimental design and response surface methodology was applied to mitigate the risks and was aimed to obtain an optimal operating conditions design The study investigates the main four parameters for SAGD operation condition, including injector/producer spacing (IPS), injection pressure (IP), maximum steam injection rate (MSIR), and spacing between two well pairs (WPS), that affect the performance of SAGD operation as amount of oil recoverable and net present value (NPV) It is essential that an experimental design methodology is very economical for extracting the maximum amount of oil recoverable, a significant experimental time-saving factor RESPONSE SURFACE METHODOLOGY RSM is a statistical method based on the multivariate non-linear model that has been widely used for optimization of the process variables of the operation process Further, RSM consists of designing experiments to provide adequate and reliable measurements of the response, developing a mathematical model having the best fit to the data obtained from the experimental design, and determining the optimal value of the independent variables that produce a maximum or minimum response (Cornell, 1990; Montgomery, 2001; Myers and Montgomery, 2002; Myers et al., 2008) The single-response modeled using the RSM corresponded to independent variables By the RSM, a quadratic polynomial equation was developed to predict the response as a function of independent variables involving their interactions (Box and Draper, 1987) In general, the response for the quadratic polynomial is described in Eq (1): Y D ˇ0 C k X i D1 ˇi Xi C k X i D1 ˇi i Xi2 C X ˇij Xi Xj C "; (1) i 0:05/ The full model filled Eq (3) made three-dimensional and contour plots to predict the relationships between the independent variables and the dependent variables TABLE Regression Coefficients of the Predicted Quadratic Polynomial Model Standard Error NPV Estimate Constant X1 X2 X3 X4 X1.X1 X2.X2 X3.X3 X4.X4 X1.X2 X1.X3 X1.X4 X2.X3 X2.X4 X3.X4 97.35 1.3877 6.87644 0.887579 3.99534 0.887579 2.83534 0.887579 9.54472 0.887578 1.10405 2.34831 8.55504 2.34831 2.11004 2.34831 5.40954 2.34831 6.16131 0.941419 0.51331 0.941419 2.01407 0.941419 0.33656 0.941419 1.10119 0.941419 0.561685 0.941419 Confidence level D 95% P 4.68E-17 5.21E-06 0.000725 0.007711 1.62E-07 0.64668 0.003369 0.386576 0.039937 2.75E-05 0.59557 0.050021 0.726923 0.264826 0.561837 OPTIMUM CONDITIONS FOR SAGD 1109 Downloaded by [University of Calgary] at 23:33 03 September 2014 5.1 Main and Interaction Effect Plots The main effect plot is appropriate for analyzing data in a designed experiment, with respect to important factors, where the factors are at two or more levels Figure shows the effect plots of variables on NPV, respectively This graph could be divided into two regions, the region with below to zero, where the factors and their interactions presented negative coefficients (WPS.WPS, WPS, IPS, IP.IP, IPS.IPS, MSIR.MSIR) indicating NPV decrease and the region with above zero, where the factors presented positive coefficients (MSIR, IPS.IP,IP, MSIR.WPS) indicating NPV increase By analyzing the graph of Figure and the values of Table 4, it can be inferred that the well pattern spacing (WPS) was the most important variable of operating condition effect strongest on NPV The increase in spacing between two well pairs led to a remarkable decrease of NPV because ultimate bitumen recovery decreases rapidly Narrower well pattern spacing will be more economical in SAGD operation The second important factor for overall optimization of an operating condition is injector producer spacing; an increase of IPS leads to decrease the NPV (Figures and 2a) The third important factor is injection pressure, when increase of IP leads to increase slightly the NPV (Figures and 2c) 5.2 Optimization of Operating Conditions for SAGD Process The full model filled Eq (3) was made three-dimensional and contour plots to predict the relationships between the independent variables and the dependent variables The graphical representations called the response surfaces, and the contour plots obtained the results of NPV affected by the injector/producer spacing, injection pressure, maximum steam injection rate, and well pairs pattern spacing (presented in Figures and 4) In the two figures, the maximum predicted value indicated by the surface was confined in the smallest ellipse in the contour diagram Elliptical contours are obtained when there is a perfect interaction between the independent variables The independent variables and maximum FIGURE The degree of factors effect on NPV Downloaded by [University of Calgary] at 23:33 03 September 2014 1110 H X NGUYEN ET AL FIGURE Main factors effect on NPV FIGURE Contour plot (2-D) showing the effects of variables on NPV Downloaded by [University of Calgary] at 23:33 03 September 2014 OPTIMUM CONDITIONS FOR SAGD FIGURE 1111 Response surface plots (3-D) showing the effects of variables on NPV predicted values from the figures corresponded with the optimum values of the dependent variables (responses) obtained by the equations The contour plot and the 3-D response surface plot of the NPV showed that the region of maximized NPV can increase over 104 $mm with operating conditions, which injector/producer spacing in the range of 5–8 m and the broad change of injection pressure from 2,500 to 7,800 kPa (Figures 3a, 3b, 3c, 4a, 4b, 4c) However, comparing three cases shows that the red smallest ellipse area is found as an optimization area (Figure 3a), where the maximize NPV reaches over 104 $mm while IPS range of 4–5 m, injection pressure change slight from 4,000 to 6,500 kPa, and the volume of steam injection at the lowest level 360 m3 /d, respectively At fixed well pattern spacing of 70 m in Figures 3d, 3e, 3f, 4d, 4e, and 4f indicated that the maximum NPV can be achieved over 104 mm$ with injection pressure of 4,000–6,000 kPa, but requires the use of larger quantities of steam injection at 840 m3 /d Therefore, this case will be uneconomical when compared with the case mentioned above If beyond this level, the NPV decreased with increasing injector/producer spacing When the well pattern spacing raises up 100 m, it indicates that the maximum NPV can only reach lower at the yellow region (88.6 mm$, Figure 3i), where IPS is about m and the injection pressure changes from 4,000 to 5,000 kPa, respectively It can be seen that the NPV in this case is lowest or infeasible This design should not be applied to optimize the operating condition for SAGD process As shown in Figures and and Table 5, it can be concluded that maximization NPV of operating condition design will be calculated by spacing between injector/producer spacing, m; injection pressure, 5,440 kPa; maximum steam injection rate, 725 m3 /d; and well pairs spacing, 40 m (Figure 5) Among the four parameters studied was the most significant factor to affect the NPV according to the regression coefficients significance of the quadratic polynomial model and gradient of slope in the 3-D response surface plot 1112 H X NGUYEN ET AL TABLE Predicted and Experimental Values of the Responses at Optimum Conditions IPS, m Downloaded by [University of Calgary] at 23:33 03 September 2014 Injection Pressure, kPa Max Steam, m3 /d Well Pattern Spacing, m NPV, $mm, Predicted NPV, $mm, Simulation Difference, % 5,440 725 40 110.166 105.164 4.54 FIGURE Design of optimal location and operating conditions of SAGD well pairs in reservoir 5.3 Verification of Predictive Model The suitability of the objective equation for predicting optimum response values was tested under the operating conditions for injector/producer spacing, m; injection pressure, 5,400 kPa; maximum steam injection rate, 725 m3 /d; and well pairs spacing, 40 m This set of conditions was determined to be optimum by the RSM optimization approach and was used to validate experimentally and predict the values of the responses using the model equation The total of cumulative oil produced from the reservoir is about 600,000 m3 However, in the second year, the oil production rate rapidly decreased until the steam oil rate increased over 4.0 at the third year (Figures and 7) These outcomes are sent to an economic model to account for a NPV of 105.164 $mm, demonstrating the validation of the RSM model, indicating that the model was adequate for the SAGD operation process (Table 5) CONCLUSIONS The factors of operating conditions have significant effects on the NPV Using the contour and surface plots in RSM was effective for estimating the effect of four independent variables The Downloaded by [University of Calgary] at 23:33 03 September 2014 OPTIMUM CONDITIONS FOR SAGD FIGURE FIGURE Oil recoverable at optimal condition Prediction production of SAGD performance at optimal condition 1113 1114 H X NGUYEN ET AL Downloaded by [University of Calgary] at 23:33 03 September 2014 optimal set of the independent variables was obtained graphically in order to get the desired levels of bitumen recovery The maximize NPV of 105.164 $mm was obtained when the optimum conditions of SAGD process were injector/producer spacing, m; injection pressure, 5,440 kPa; maximum steam injection rate, 725 m3 /d; and well pairs pattern spacing, 40 m Under these optimized conditions, the experimental purity of NPV agreed closely with the predicted yield of 4.54% (Table 5) This study demonstrates that the central composite design and response surface methodology can be successfully used for modeling some of the operating parameters of SAGD operation process for bitumen recovery; it is an economical way of obtaining the maximum profit in a short period of time and with the fewest number of experiments ACKNOWLEDGMENTS The authors wish to thank Schlumberger K.K for encouragement in writing this paper FUNDING This work was supported by the Energy Resources R&D program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No 20102020300090) REFERENCES Box, G., and Draper, N 1987 Empirical Model Building and Response Surfaces New York: John Wiley & Sons Box, G E P., and Hunter, J S 1957 Multi-factor experimental design for exploring response surfaces Ann Math Stat 28:195–241 Butler, R M 2001 Some recent development in SAGD J Can Pet Technol 40:18–22 Canadian National Energy Board 2006, 2008 Canada’s oil sands: Opportunities and challenges to 2015 Calgary, Alberta, Canada: Canadian National Energy Board Cornell, J A 1990 How to Apply Response Surface Methodology, 2nd Edition Milwaukee, WI: American Society for Quality Control Montgomery, D C 2001 Design and Analysis of Experiments, 5th Edition New York: John Wiley & Sons Myers, R H., and Montgomery, D C 1995 Response Surface Methodology: Process and Product Optimization Using Designed Experiments New York, NY: John Wiley & Sons, Ltd Myers, R H., and Montgomery, D C 2002 Response Surface: Process and Product Optimization Using Designed Experiments, 2nd Edition New York: John Wiley & Sons Myers, R H., Montgomery, D C., and Anderson-Cook, C 2008 Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Edition New York: John Wiley and Sons, pp 13–135 Shin, H., and Polikar, M 2005 New economic indicator to evaluate SAGD performance SPE Paper 94024 SPE Western Regional Meeting, Irvine, CA, March 30–April Vanegas Prada, J W., and Cunha, L B 2008 Prediction of SAGD performance using response surface correlations developed by experimental design techniques J Can Pet Technol 47:58–64 ... for a NPV of 105.164 $mm, demonstrating the validation of the RSM model, indicating that the model was adequate for the SAGD operation process (Table 5) CONCLUSIONS The factors of operating conditions. .. (3) The results of the analysis of variance, goodness -of- fit, and the adequacy of the models are summarized in Table The determination coefficient (R2 D 0.967) was showed by ANOVA of the quadratic... from the figures corresponded with the optimum values of the dependent variables (responses) obtained by the equations The contour plot and the 3-D response surface plot of the NPV showed that the