Experimental Design to Optimize Operating Conditions for SAGD ...

SPE 145917 Experimental Design to Optimize Operating Conditions for SAGD Process, Peace River Oilsands, Alberta.

Huy X.Nguyen1,SPE, Wisup Bae1,SPE, Xuan V.Tran2, Taemoon Chung1,SPE; 1Sejong University. 2Ho Chi Minh City University of Technology

Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Asia Pacific Oil and Gas Conference and Exhibition held in Jakarta, Indonesia, 20–22 September 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract The SAGD process is a promising recovery method for producing heavy oils and bitumen resources. However, SAGD process has several economic risks including the high capital cost of initial investment for building ground facilities and uncertainties related to oil and gas prices. These risks may be critical in SAGD operation if the design for initial operating conditions is unsuitable. In order to ensure maximize profitability, optimal operation conditions should be evaluated by reservoir simulations. In this study, central composite design and response surface methodology (RSM) were applied to determining optimal conditions for SAGD process. It was aimed to mitigate the risk of incomprehensive economic assessment on the process operation. The study started with the central composite face-centered (CCF) design to screen variables, and then insignificant variables were excluded from the study before developing the optimal design by response surface method. A two-stage approach was employed based on the efficient local optimization. At first, an initial sample of design was obtained using design of experiment technique. Simulation runs for design points were used to estimate oil recovery as well as NPV for each case. Based on the standard of CCF design, total 28 cases was run to optimize the parameters of operating conditions and the NPV responses during 10 years of simulation period. Second, RSM was used to search for promising designs in contour plots and response surface map. The best choice of operating conditions for maximizing the NPV correspond to well pattern spacing of 78m, steam rate of 640 m3/d, injector producer spacing of 14m, injection pressure of 6330 kPa, subcool 80C, respectively. Simulation results showed that cumulative oil for Fast-SAGD process does not significantly increase and even NPV is the lowest among the mentioned SAGD cases. In addition, cumulative oil recovery of SAGD1 base case is higher than those of SAGD2 and Fast-SAGD cases, as well as the lowest CSOR. However, in the economic point of view recognized that the case SAGD2 achieves the highest NPV, with the predicted values matched the experimental values reasonably well with R2 of 0.99 and Q2 of 0.88 for NPV response, while the NPV of Fast-SAGD process is the lowest because of the increasing capital cost for additional offset wells. Actually, the difference of 10kPa between steam injection pressure and reservoir pressure is not sufficient to increase the NPV for both Fast-SAGD and SAGD1 base case operations. The high cumulative oil is favorable conditions for accelerating profit, but oil and gas prices at that time is crucial to decide for operation conditions in heavy oil projects. Introduction Many countries in the world have large deposits of oil sands, including the United States, Russia, and various countries in the Middle East. However, the world's largest deposits concentrate in two countries Canada and Venezuela, each of which has oil sand reserves approximately equal to the world's total reserves of conventional crude oil (Wikipedia). As a result of the development of Canadian oil sands reserves, 44% of Canadian oil production was from oil sands, with an additional 18% being heavy crude oil, while light oil and condensate had declined to 38% of the total. Oil sands represent as much as twothirds of the world's total liquid hydrocarbon resource, with at least 1.7 trillion barrels in the Canadian Oil Sands (assuming a 10% recovery). However, extremely high viscosity of bitumen at normal reservoir temperature is one of the biggest challenges for recovery process. The steam-assisted gravity drainage (SAGD) process is an effective method for heavy oil and bitumen production utilizing two parallel horizontal wells, one above the other. The top well is steam injector and the bottom one is the

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oil collector. When steam is continually injected in the top well, a steam chamber forms in reservoir and grows upward to the surroundings displacing heated oil following gravity mechanism drain into producer (Butler, 2001). However, SAGD process has economic risk including the high capital cost of initial investment for building ground facilities and uncertainties related to oil and gas prices in the market. The risk may be critical in SAGD operation if the design for initial operating conditions is unsuitable. In order to ensure profitability of SAGD process, optimal operation conditions should be determined by reservoir simulations. The target of the production strategy is how to maximize net present value (NPV) of recoverable oil as SAGD performance, which is significantly affected by operating conditions of injector/producer spacing, injection pressure, steam injection rate, subcool temperature and distance between two well pairs. Polikar (2000), Gong (2002) and Shin (2007) have conducted optimization of SAGD process by classical methods based on their numerical simulations and experiments. However, there is a lack of confidence level in the optimized conditions because they didn’t determine the significance level of operational parameters and ignored interactions effects between considered parameters, which may lead to low efficiency issues in a field operation. These limitations of the classical method can be avoided by applying central composite design (CCD) and response surface methodology (RSM) that involves statistical design of experiments in which all factors are varied together over a set of experimental runs. In addition, the economic models in previous studies were not comprehensive enough with limited consideration on only three factors, steam cost, bitumen price and discount rate. That approach could significantly reduce the accuracy of economic evaluations and make it very difficult to predict the best choice of process operation. In this study, central composite design and response surface methodology were applied to indicate optimal conditions for SAGD process. It was aimed to mitigate the risk of incomprehensive economic assessment on the process operation. The study started with the central composite face-centered (CCF) design to screen variables, and then insignificant variables were excluded from model before developing the optimal design by response surface method. A two-stage approach was employed based on the efficient local optimization. First, an initial sample of design was obtained using design of experiment technique, such as CCF. Simulation runs for design points was used to estimate oil recovery as well as NPV for each case. Second, response surface methodology was used to search for promising designs. The uncertainties of NPV were evaluated, and the optimization of operating conditions was identified by building a surface response map. Reservoir model The SAGD and Fast-SAGD processes are modeled an oil reservoir of 151mx850mx20m with no aquifer belonged to Bluesky formation, Peace River region. The SAGD model employed two well pairs, and each well pairs has two horizontal wells, one injector located above the other which the oil producer. Steam is injected continually while heated oil drains into the producer well. Reservoir fluids were modeled as three phases (oleic, gaseous, and aqueous), and there are three components: heavy hydrocarbon, water and gas. Oleic phase composed of gas and oil. Aqueous phase consists of only water. Gaseous phase can contain steam and gas. Grid, rocks, and fluid properties used in the simulation model are listed in Table 1. The NPV over simulation period of 10 years was selected as the response variable to measure the production performance, and therefore the dependent variable in the proposed surface response correlation. Economic model The economic model was designed based on the previous discussion in the Canadian National Energy Board reports (2006, 2008). The cash flow method in Microsoft Excel spreadsheet is applied to calculate NPV reflecting property depreciation and 10% yearly interest rate during 10 years of production phase. The input parameters of economic model included cumulative oil production, steam injection rate and amount of water produced from CMG’ Start simulation result. The average prices of bitumen and gas are $70/bbl and 3.8 $/mcf, respectively. Drilling and completion costs of a SAGD well pair is 3.0 mm$ as capital investments, the cost of CSS single well is 1.5 mm$ in Fast-SAGD. Total operating costs is comprised of the electric cost 0.95$ per barrel of produced oil, water handling cost of 3$ per barrel, non-gas cost of 5$/bbl, and emission cost of 1$/bbl. The production estimate is combined with initial capital, operating costs, and the rates of return on capital to calculate the NPV. The result showed that the operating costs depended on gas price of steam injection volume and water handling cost, which significantly affected the NPV. Response surface methodology and central composite design Response surface methodology is statistical methods based on the multivariate non-linear model that has been widely used for optimization of process variables of operating conditions (Box, 1951). Further, RSM consists of designing experiments to provide adequate and reliable measurements of the response, developing mathematical model having the best fit to the data obtained from the experimental design, and determining the optimal value of the independent variables that generates a maximum or minimum response (Myers, 2008). It is also useful in studying the interactions of the various parameters affecting process. In recent years, RSM has played an important role in oil field, especially applications in enhanced oil recovery (Vanegas, 2008). The experimental design techniques commonly used for process analysis and modeling are the full factorial, partial factorial and central composite rotatable designs. An effective alternative to the factorial design is the central composite

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design, originally developed by Box and Wilson and improved upon by Box and Hunter in 1957. The CCD gives almost much information as a three-level factorial, requires much fewer tests than the full factorial and has been own to be sufficient to describe the majority of steady-state process responses. Nowadays CCD is the most popular class of designs used for fitting second-order models. The total number of tests required for CCD is 2k-p +2k + n0, including k is the number of studied variables, 2k points fixed axially at a distance, p the fractionalisation element (full design, p = 0), from the center to generate the quadratic terms, and replicate tests at the center (n0). Central composite face-centred design (CCF) was used to maximize NPV from spacing between injector and producer (IPS, X1), steam injection pressure (IP, X2), steam injection rate (MSIR, X3), SAGD well pattern spacing (WPS, X4) and subcool temperature (Strap, X5). For each of the five variables studied, high (coded value: +1) and low (coded value:-1) set points were selected according to the results obtained in Table 2. The numbers of tests required for the five independent variables are 28 cases correspond to each NPV response. The five independent variables and their coded levels for the CCF design used in this study are listed in Table 3. A full second-order polynomial model obtained by multiple regression technique for five factors and the effects of the interactions between two-factor as well as main factors included, objective function can be rewritten: Y= β0 + β1X1 + β2X2 + β3X3 + β4X4+ β5X5 + β11X12 +β22X12 + β33X32 + β44X42 + β55X52 +β12X1X2+β13X1X3 + β14X1X4 + β15X1X5+β23X2X3 + β24X2X4 + β25X2X5+ β34X3X4 + β35X3X5 + β45X4X5 (1) The coefficients of the main effects βi - and two-factor interactions (βij) were estimated from the experimental data obtained by computer simulation programming utilizing least squares method of @R 12.2.1 software. Results and discussions In this study, CCF design for five variables was used as the experimental design model. The model has the advantage that it permits the use of relatively few combinations of variables for determining the complex response function. A total of 28 experiments were required to be performed to calculate 21 coefficients of the second order polynomial equation. In Table 3 showed that cumulative oil of case 25 is the highest, its NPV is lower than other cases due to the change of well pattern spacing and IP spacing, while the highest NPV of case 18 was obtained under the experimental conditions of IPS 16m, IP 6000 kPa, MSIR 600 m3/d, WPS 99m, and subcool temperature 80C. The coefficient of the model for the response was estimated using multiple regression analysis technique included in the RSM. The quadratic model thus obtained was given as follows: NPV = 74.55+ 5.65X1 + 2.71X2 + 3.5X3 – 15.92X4 –1.86X5 – 4.78X12 – 6.37X22 – 4.33X32 –18.52X42 –2.6X52 + 1.66X1X2 + 2.28X1X3 – 1.85X1X4 + 2.85X1X5 + 0.86X2X3 + 1.91X2X4 + 1.46X2X5 + 4.49X3X4 – 0.65X3X5 + 1.26 X4X5 (2) Statistical analysis of the model was performed to evaluate the analysis of variance (ANOVA) in Table 4. The R2 value closer to 1 denotes better correlation between the observed and predicted values. The higher values of R2 (0.999) and adjusted R2 (0.994) also indicated the efficiency of the model suggesting that 99.99% and 99.4% variation could be accounted for by the model equation respectively. At the same time, a very low value of coefficient of residual standard deviation (RSD=1.7) clearly indicated a high degree of precision and reliability of the experimental values and in relation to the power of prediction, Q2 = 0.88. Student’s t-test was performed in order to evaluate quantitative effects of the main factors. The regression coefficient values of Eq. (2) are listed in Table 5 with standard errors and P-values. The P-values were used as a tool to check the significance of each coefficient, which in turn may indicate the pattern of interactions between variables. It can be seen from Table 5 that the most variables were significant, with very small P-values (P < 0.05), except X52, X2X3, X3X5 were insignificant (P > 0.05). It is note worthy a positive sign indicates a synergistic effect, while a negative sign represents an antagonistic effect of a factor on the selected response. Effect of operating factors on NPV In figure 1 presented the Pareto chart of standardized effects at p=0.05 for NPV. All the standardized effects were in absolute values to verify which were positives and negatives. It helps identify important factors that significantly affect overall outcome of NPV. This graph can be divided into two regions. The region below zero, where factors have negative coefficients (WPS.WPS, WPS, IP.IP, IPS.IPS, MSIR.MSIR, strap, strap.strap, MSIR.strap, IPS.WPS), indicated that NPV decreased with an increased in the factors. In the region above zero, factors have positive coefficients (IPS, MSIR.WPS, MSIR, IPS.strap, IP, IPS.MSIR, IP.WPS, IPS.IP…) and the NPV increased with an increased in the factors. From the graph of Fig.1 and the values listed in Table 5, it can be inferred that the interaction factors of well pattern spacing and IP, the individual of WPS and IPS were the most important variables that significantly affected the NPV of SAGD performance. The reasonable design in well pattern spacing is about 78-80m to reach a peak NPV in SAGD operation (Fig.2). The subcool temperature in range of 6-8 0C obtained the peak NPV also played an important role in affecting on the NPV. The IP spacing in range of 13-15m was the best SAGD performance with maximum NPV. When the IP spacing is lower than 14m, the NPV will reduce because steam chamber is much larger and could not come the top of reservoir. Similarily, injection

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pressure and steam injection rate also exhibited the existence of optimal conditions that maximize NPV. The optimal conditions for injection pressure, steam injection rate, and well pattern spacing were proposed the vicinity values of 6330 kPa and 640 m3/d and 78m, respectively. Optimization of operating conditions by response surface methodology Response surface methodology plays a key role in efficiently identifying the optimum values of the independent variables, at which a dependent variable could arrive at the maximum response. The 3D response surface and 2D contour plots represented to predict the relationships between the dependent variable and a set of independent variables. The graphical representations of NPV contour plots and response surfaces are given in Fig.3, as IP spacing, injection pressure, steam injection rate, subcool temperature and well pattern spacing. The value of predicted maximum on the surface is confined in the smallest ellipse in the contour diagram. Elliptical contours are obtained in general when there is a perfect interaction between the independent variables. The values of independent variables in the smallest contour and the corresponding maximum are determined to be the optimal operating conditions and the response of the dependent variable. From the response surface plots, authors recognized that the best choice of operating conditions when maximizing the NPV was the red smallest region in Fig.3b, where the maximum NPV reached over 82 $mm. The optimal conditions of the favourable design are the well pattern spacing of 78m, steam rate of 640m3/d, IP spacing of 14m, imjection pressure of 6330 kPa, and subcool temperature 80C. The five main operation variables, most factors is significant affects the performance of SAGD process according to the regression coefficients significance of the quadratic polynomial model and gradient of slope in the 3-D response surface plot. Validation of model equation The validity of the objective function for predicting optimum response values was rechecked under an operating conditions with IPS 14m, IP 6330 kPa, MSIR 640 m3/d, WPS 78m and subcool temperature 80C (Fig.4c). This design for SAGD operation was determined by the RSM approach and was also used to validate the model by comparing the predicted values of the responses to the results of experimental simulation within the 95% confidence intervals. The total of cumulative oil produced from reservoir is about 554,408 m3 (Fig.5a) in the simulated operation of SAGD process. The oil production rate reaches a peak with 163,471 m3 in the first year, and then dramatically reduced until the end of 10th year of operation. These outcomes are taken into account to the economic model to yield a NPV of 78.41$mm as the highest NPV among experimental cases in Table 3. This result demonstrates the validity of the RSM model, which is reasonably adequate to predict the performance of SAGD operation. Optimization of operating conditions for Fast-SAGD process The Fast-SAGD models comprised two full SAGD well pairs and two CSS wells (Polikar, 2000), uses offset wells, which are placed horizontally about 50m away from the SAGD producer and each offset well. These offset wells are operated alternatively as injector and producer. When the steam chamber reaches the top of the reservoir after the SAGD operation has begun, the CSS operation is started at the first offset well. The CSS operation at other offset wells will be started later with a certain schedule after the CSS operation at the first offset well. SAGD well design: Operating conditions of SAGD wells in Fast-SAGD also conducted similar in SAGD system, with injection pressure of 4,510 kPa, IP spacing of 10m, steam injection rate of 400m3/d, subcool temperature of 50C, but SAGD wells pattern spacing of 150m (Shin, 2007). This result is the most suitable for Bluesky formation because of high cumulative oil in earlier of production period and relative low value of CSOR. Offset well design: proposed that the most favourable operating conditions for Peace River reservoir, which is thin and moderately permeable, give offset well spacing of 38 m, with a maximum injection pressure of 8,000 kPa, a maximum steam injection rate of 800 m3/d, and steam injection pressure of 8,000 kPa at the offset well, CSS startup time of 1.5 years. Reservoir simulation in figure 4a showed the performance of the growth steam chamber and capacity of oil recovery in FastSAGD process. Comparison economic efficiency between the performance of SAGD and Fast-SAGD processes The optimal point of response surface design was called SAGD2 case in figure 4c. For SAGD1 base case, Shin proposed that the most favourable SAGD operating conditions for Peace River-type reservoirs: I/P spacing of 10 m, steam rate of 600 m3/d at a maximum injection pressure of 4,500 kPa, subcool of 50C and well pattern spacing of 80 m (Fig.4b). Simulation results indicated that cumulative oil for Fast-SAGD process does not significantly increase and even NPV is the lowest among the mentioned SAGD cases. In addition, cumulative oil recovery of SAGD1 base case is higher than those of SAGD2 and Fast-SAGD cases, as well as the lowest CSOR (Fig.5b). However, in the economic point of view recognized that the SAGD2 (CCF design) achieved the highest NPV, with the predicted values matched the experimental values reasonably well with R2 closed to 1.0 and Q2 of 0.88 for NPV response, while the NPV of Fast-SAGD process was the lowest because of the increasing capital cost for additional offset wells (Tab.6). Actually, the difference of 10kPa between steam injection

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pressure and reservoir pressure is not sufficient to increase the NPV for both Fast-SAGD and base case SAGD1 operations. The high cumulative oil can favorable conditions for accelerating profit, but oil and gas prices at that time is crucial to decide for operation conditions in heavy oil projects. In this case, the selection of Fast-SAGD process had non-economic because amount of oil recovery would not enough to compensate for the additional cost of CSS wells. Thus, the conventional SAGD process still applies common in field operation with its economic efficiency, especially the uses of response surface design to get the highest economic is extremely important in SAGD process. Conclusions - This research demonstrated that the CCF design and response surface methodology can be successfully employed for modeling operation parameters of SAGD process. The CCF design with RSM not only improves the economic feasibility of bitumen recovery process but provides economical way of obtaining the maximum profit in a short period of time with the fewest number of experiments. - Predicted values from the model equations were found to be in good agreement with observed values R2 of 1.00 and Q2 of 0.88 for NPV response. In order to gain a better understanding of the five variables for optimal operating conditions, the models were presented as 2-D and 3-D response surface graphs. The models allow confident performance prediction by interpolation over the range of data in the database; it was used to construct response surface graphs to describe the effect of the variables on the SAGD performance. The maximum NPV indicated that the best design for operating conditions are the injector producer spacing of 14m, injection pressure of 6330 kPa, steam injection rate of 640 m3/d, subcool temperature of 80C, and spacing between two well pairs of 78m in SAGD operation. - Results evidenced that the difference of 10kPa between steam injection pressure and reservoir pressure was not sufficient to increase the NPV for both Fast-SAGD and base case of SAGD1 operations. The production performance of SAGD1 base case and Fast-SAGD process are the same CSOR value, but cumulative oil production of SAGD1 base case is higher than 1.86% of SAGD2. However, the profit of the SAGD2 process obtained better than those of the Fast-SAGD and base case SAGD1 process. Compared to conventional SAGD, the Fast-SAGD process proved insignificantly incremental bitumen recovery as well as economic efficiency. Acknowledgements Financial support for this work is gratefully acknowledged from the MKE (Ministry of Knowledge Economy) and KETEP (Korea Institute of Energy Technology Evaluation and Planning: ETI Project). Moreover, the authors wish to thank Schlumberger K.K for the encouragement of writing paper. References 1. Box, G. E. P., & Wilson, K. B. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society. Series A (General), 13, 1–45. 2. Butler, R.M. 2001. Some Recent Development in SAGD. Journal of Canadian Petroleum Technology, Distinguished Author Series 40(1): 18-22. 3. Canada’s Oil sands: Opportunities and Challenges to 2015, ver.2006, 2008. Canadian National Energy Board. 4. Gong. J., Polikar. M., and Chalaturnyk. R.J. 2002. Fast SAGD and Geomechnical Mechanism. Paper CIPC 2002-163 presented at the Canadian International Petroleum Conference. Calgary, Canada, 11-13 June. 5. Myers, R.H., Montgomery, D.C., and Anderson-Cook, C. 2008. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Edition, John Wiley and Sons, New York, pp. 13-135. 6. Polikar M., Cyr. T.J. and Coates. R.M. 2000. Fast SAGD: Half the Wells and 30% less Steam. Paper SPE 65509 presented at the International Conference on Horizontal Well Technology. Calgary, Canada, 6-8 November 7. Shin. H. and Polikar. M. 2007. Review of Reservoir Parameters to Optimize SAGD and Fast-SAGD Operating Conditions. Journal of Canadian Petroleum Technology 46(1): 35- 41. 8. Vanegas J.W., Cunha L.B., 2008. Prediction of SAGD Performance Using Response Surface Correlations Developed by Experimental Design Techniques. Journal of Canadian Petroleum Technology, 2008. Petroleum Society of Canada.

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Table1. Reservoir properties in Peace River Parameters Reservoir size 151m x 850m x 20m Reservoir pressure, kPa 4500 Depth to top of reservoir, m 602 Reservoir thickness, m 25 Reservoir width, m 151 Vertical permeability (Kv), Darcy 1.95 Permeability ratio (Kh/Kv) 0.65 Porosity 0.28 Oil saturation 0.8 Oil Viscosity, cp 220,000 Reservoir Temperature, oC 12 Steam quality 0.95

Table 2. Variables and experimental design levels for response surface Variables Symbol Coded levels -1 0 +1 Injector/producer spacing, m X1 4 10 16 Injection pressure, kPa X2 4500 6000 7500 Steam rate (m3/d) X3 360 600 840 Well pairs pattern spacing (m) X4 48 99 150 Subcool temperature (0C) X5 2 8 14

Table 3. Central composite face-centered experimental design with five independent variables NPV Cum. NPV Cum. Case X1 X2 X3 X4 X5 Case X1 X2 X3 X4 X5 (mm$) Oil (m3) (mm$) Oil (m3) 1

-1

-1

-1

-1

1

44.2293

435,724

15

-1

1

1

1

-1

30.7367

468,856

2

1

-1

-1

-1

-1

59.0468

517,426

16

1

1

1

1

1

46.5583

482,890

3

-1

1

-1

-1

-1

51.8425

520,020

17

-1

0

0

0

0

63.7801

530,251

4

1

1

-1

-1

1

63.5115

512,619

18

1

0

0

0

0

76.0516

534,940

5

-1

-1

1

-1

-1

51.249

489,274

19

0

-1

0

0

0

67.3687

519,987

6

1

-1

1

-1

1

56.9775

497,842

20

0

1

0

0

0

69.2579

534,738

7

-1

1

1

-1

1

38.5185

507,902

21

0

0

-1

0

0

68.5943

532,886

8

1

1

1

-1

-1

65.8457

542,148

22

0

0

1

0

0

72.1157

537,234

9

-1

-1

-1

1

-1

14.1268

309,083

23

0

0

0

-1

0

71.3237

532,144

10

1

-1

-1

1

1

10.918

294,537

24

0

0

0

1

0

41.0123

449,760

11

-1

1

-1

1

1

13.1933

304,040

25

0

0

0

0

-1

74.0864

546,653

12

1

1

-1

1

-1

16.3546

315,198

26

0

0

0

0

1

70.0262

514,628

13

-1

-1

1

1

1

14.5042

316,061

27

0

0

0

0

0

73.3968

536,196

14

1

-1

1

1

-1

28.5941

379,262

28

0

0

0

0

0

73.3968

536,196

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Table 4. ANOVA for response surface quadratic model DF SS MS F P Total 27 80399 2978 Constant 1 67822 67822 Total Corrected 26 12576 483.7 Regression 20 12559 627.9 216.6 0 Residual 6 17.4 2.9 N = 27 Q2 = 0.88 RSD = 1.70 DF = 6 R2 =1.000 R2 Adj. =0.994 NPV

SD

21.993 25.0586 1.70282

Table 5. Regression coefficients of the predicted quadratic polynomial model. NPV

Estimate

Standard Error

74.546

0.633

2.52E-11

X1

5.648

0.401

8.03E-06

X2

2.711

0.401

0.0005

X3

3.516

0.401

0.0001

X4

-15.912

0.401

1.72E-08

X5

Constant

P

-1.858

0.401

0.0035

2

-4.774

1.089

0.0046

2

-6.376

1.089

0.0011

2

-4.335

1.089

0.0073

4

-18.522

1.089

2.64E-06

2

-2.633

1.089

0.052

X1 X2 X3 X4 X5

X1X2

1.660

0.426

0.008

X1X3

2.283

0.426

0.0017

X1X4

-1.855

0.426

0.0047

X1X5

2.852

0.426

0.0005

X2X3

0.859

0.426

0.0899

X2X4

1.905

0.426

0.0042

X2X5

1.462

0.426

0.0139

X3X4

4.49

0.426

4.27E-05

X3X5

-0.646

0.426

0.1795

X4X5

1.257

0.426

0.0255

Table 6. Optimum conditions in SAGD and Fast-SAGD processes NPV ($mm) IPS MSIR WPS Subcool Cum.oil Cases

(m)

Fast-SAGD (extra steam 400m3/d after CSS ) SAGD 1 (base case) SAGD 2 (CCF design)

10

10 14

IP (kPa) (m3/d) 4510 (SAGD wells) 400 8000 (CSS well) 800 4500 600 6330

640

(m)

(0C)

150

5

(m3)

predicted actual

% difference

558,293 52.87

38 80

5

568,894

78

8

554,409

75.42 82

78.41

6%

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Figure 1. The order ranking of factors affecting on NPV

Figure 2. Effects of operating conditions on NPV

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Figure 3. Response surface plots showing the effects of operation variables on the NPV responses

800d

1085d

1460d

3650d

465d

1095d

1825d

3650d

100d

b. SAGD1 model (Base case) 913d 1460d

3650d

a. Fast-SAGD model

c. SAGD2 model (response surface design) Figure 4. The growth of steam chamber in SAGD and Fast-SAGD processes

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Figure 5. The Fast-SAGD and SAGD performances in Peace River region