The best operating conditions of the Fast-SAGD1 process were an injector–producer spacing of 9 m, injection pressure of 6409 kPa, steam injection rate of 610 m3/d, subcool 61C for the SA
Trang 1Using response surface design for optimizing operating conditions
in recovering heavy oil process, Peace River oil sands
X.H Nguyena,c, Wisup Baea,n, Trianto Gunadia, Yunsun Parkb
a
Sejong University, 98 Gunja-dong, Gwangjin-ku, Seoul, South Korea
b Myungji University, Seoul, South Korea
c
Ho Chi Minh City University of Technology, Vietnam
a r t i c l e i n f o
Article history:
Received 15 March 2013
Accepted 8 February 2014
Available online 16 March 2014
Keywords:
SAGD
fast-SAGD
operating condition
NPV
response surface method
a b s t r a c t
In order to maximize oil recovery with minimal environmental damages and lower production costs for producing heavy oil and bitumen resources in Peace River oil sands, optimal operating conditions were conducted by using design of experiment and response surface methodology This study was aimed to mitigate the risks of incomprehensive economic assessment and engineering in the process operation Simulation responses for 26 design points were estimated based on amount of oil recovery and net present value for each case Response surface methodology was applied to search for promising designs
in contour plots and the response surface map The best operating conditions of the Fast-SAGD1 process were an injector–producer spacing of 9 m, injection pressure of 6409 kPa, steam injection rate of
610 m3/d, subcool 61C for the SAGD system; while for the CSS well, injection pressure of 8333 kPa and a steam injection rate of 1007 m3/d In this study, the amount of oil recovery produced through the Fast-SAGD1 process increased significantly and appeared to be more effective than the conventional SAGD process In addition, it was observed that using lower injection pressures will not yield economical results in either SAGD or FastSAGD processes due to insufficient heat transfer from the steam into the solid bitumen
in the reservoir, consequentially causing low NPV and oil recovery The results presented can be widely applied and are practical for the effective recovery of unconventional resources in Alberta's oil sands
& 2014 Elsevier B.V All rights reserved
1 Introduction
Heavy oil production from unconventional resources has been
accelerating dramatically due to rising energy consumption needs
Many heavy oil deposits are spread out over the United States,
Russia, and various countries in the Middle East However, most of
the world's heavy oil deposits are concentrated in two countries,
Canada and Venezuela, where estimated heavy oil reserves
approxi-mately equal the world's total reserves of conventional crude oil
From studies contributing to the development of Canadian oil sands
reserves, it was shown that 44% of Canadian oil production was
recovered 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 two-thirds of the world's total liquid
hydrocarbon resources, with at least 1.7 trillion barrels in the
Canadian oil sands (assuming 10% recovery with current technology)
However, the extremely high viscosity of bitumen at normal
reser-voir temperature is one of the greatest challenges for its recovery
process
The steam-assisted gravity drainage process (SAGD) is an effective method for heavy oil and bitumen production utilizing two parallel horizontal wells, one above the other The top well functions as a steam injector, while the bottom well functions as the oil collector
As steam is continuously injected in the upper well, a steam chamber forms in the reservoir and grows upwards to its surroundings, displacing heated oil following a gravity-mechanism drain into the producer (Butler, 2001) Studies in economics highlight the chal-lenges and risks due to the high capital cost of initial investment for surface facilities, operating costs, and uncertainties related to oil and gas prices in the market The risk may be critical in SAGD operations when the operating design is unsuitable In order to predict reservoir performance and profitability, various scenarios using SAGD and Fast-SAGD processes were investigated and simulated The target is
to maximize economics in operation, which will significantly affect the operating design of injector–producer spacing, injection pressure, steam injection rate, and subcool temperature
Nestor et al (2002) developed a surrogate modeling-based optimization of the SAGD process to maximize oil recovery and net present value Gates and Chakrabarty (2005)used a genetic algorithm to define the optimal operating pressure Their results proposed that higher injection pressure should be applied in SAGD start-up until the growth of steam chamber contacts to the top
Contents lists available atScienceDirect
journal homepage:www.elsevier.com/locate/petrol
Journal of Petroleum Science and Engineering
http://dx.doi.org/10.1016/j.petrol.2014.02.012
0920-4105/& 2014 Elsevier B.V All rights reserved.
n Corresponding author.
E-mail address: wsbae@sejong.ac.kr (W Bae).
Trang 2reservoir, followed by lower injection pressures.Yang et al (2009)
presented economic optimization and uncertainty assessment
strategies of SAGD operations using CMG's designed exploration
and controlled evolution (DECE) optimization method The optimum
operating conditions were obtained when using a high initial steam
rate and high production rate to develop the steam chamber
Polikar et al (2000),Gong et al., (2002), andShin and Polikar
(2007) conducted optimal operating conditions of the 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 the significance level of
opera-tional parameters was not presented Also these studies ignored
interactions along with their effects between the considered
parameters Based on discrete simulation results and economic
indicators,Shin and Polikar (2007) suggested that the operating
conditions of the Peace River reservoir should have an injector–
producer spacing of 15 m and a steam injection rate of 600 m3/d at
a maximum injection pressure of 4510 kPa However, as stated
before, these results did not mention the confidence level of the
optimization process This might lead to low efficiency issues
in field operation Moreover, the economic models in previous
studies were not comprehensive enough, with limited
considera-tion on only three factors steam cost, bitumen price and discount
rate That approach could be accepted with low prices; however it
may not be when extrapolated to future conditions These
limita-tions of the classical method can be avoided by applying central
composite design (CCD) and response surface methodology (RSM)
that involve statistical design of experiments in which all factors
are varied together over a set of experimental runs Hence, the
optimal operating conditions should be reevaluated
In this study, integrating central composite design and response
surface methodology is necessary for indicating the optimal
condi-tions for SAGD and Fast-SAGD processes It was aimed to mitigate
the risk of incomprehensive economic assessment on the process
operation The study started with the central composite
face-centered design (CCFD) to screen variables, and thenfinding the
optimal design based on the response surface method The efficient
local optimization was employed by a two-stage approach First, an
initial sample of design was obtained using the design of
experi-ment technique (DOE) Simulation responses for 26 design points
were estimated by oil recovery and NPV for each case Second,
response surface methodology was used to determine the
reason-able operating design, represented as contour plots and a response
surface map Sensitivity analysis for variables influenced the net
present value (NPV) and oil recovery Afterwards, the best choice of
operating condition between SAGD and Fast-SAGD processes based
on the technical-economic assessment are discussed
1.1 Reservoir model
The SAGD and Fast-SAGD models are built on a bitumen reservoir
of 101 m 900 m 25 m with no aquifer belonging to Bluesky
formation, Peace River region The STARS module of Computer
Modeling Group (CMG) software was used to investigate the effects
of operating parameters The SAGD process employed two horizontal wells, one injector located above the other oil producer Steam is injected continuously into the heated bitumen reservoir causing oil
toflow into the producer Reservoir fluids were modeled as oleic, gaseous, and aqueous phases corresponding to three components of hydrocarbon, gas, and water, respectively The oleic phase is consti-tuted of gas and oil, while the aqueous phase is composed of only water The gaseous phase encompasses steam and gas Grid, rocks, and fluid properties of the reservoir model are listed inTable 1 NPV is considered the response variable to measure the degree of production
efficiency during the operating process, and therefore this dependent variable is proposed in surface response correlation
1.2 SAGD economic model The economic model was designed based on the previous literatures in the Canadian National Energy Board reports (2006,
2008) The cash flow method in Microsoft Excel spreadsheet is calculated by NPV reflecting property depreciation with a 10% discount rate during 10 years of production phase The production profiles from simulation result included an annual oil rate, a steam injection rate and the amount of water produced The average prices of bitumen and gas are $70/bbl and $4.0/GJ, respectively SAGD pair cost is $5.0 mm, and the cost of a cyclic steam stimulation (CSS) single well is $2.5 mm in the Fast-SAGD process
as capital investments Total operating costs covered the electric cost of $1.0 per barrel of produced oil, water handling cost of $3 per barrel, non-gas cost of $6/bbl, emission cost of $1/bbl andfield insurance of $0.5/bbl The production profiles are combined with initial capital, operating costs, and the rate of return on capital to calculate the NPV The feasible project economics analysis enforces that at least 36,500 bbl/year must be operated per well pair in order for it to be economic (NPVZ0) The results also presented that the fluctuation of gas prices substantially affects project
Abbreviations
ANOVA analysis of variance
CCD central composite design
CCFD central composite face-centred design
CSOR cumulative steam oil ratio
CSS cyclic steam stimulation
DOE design of experiment
Fast-SAGD fast-steam assisted gravity drainage IPS spacing between injector and producer
IP steam injection pressure MSIR maximum steam injection rate NPV net present value
RSM response surface methodology SAGD steam assisted gravity drainage Strap steam trap control/subcool temperature
Table 1 Reservoir properties.
Parameters Reservoir pressure, kPa 4500 Depth to top of reservoir, m 630 Reservoir thickness, m 25 Reservoir width, m 101 Reservoir temperature, 1C 18 Vertical permeability (K v ), D 1.95 Permeability ratio (K h /K v ) 0.334
Oil viscosity, cp 220,000 Rock thermal conductivity, kJ/m day 1C 660 Bitumen thermal conductivity, kJ/m day 1C 11.5 Gas thermal conductivity, kJ/m day1C 2.6 Rock heat capacity, kJ/m 3 1C 2400
Trang 3economics as well as production performance due to the related
operating costs
2 Response surface methodology and central
composite design
Response surface methodology is a statistical method based on
the multivariant non-linear model which has been widely used in
optimizing the process variables of operating conditions (Box and
Wilson, 1951) Furthermore, RSM of designing experiments
pro-vide adequate and reliable measurements of the response,
devel-oping a mathematical model that has 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 et al., 2008) It is also
useful in studying the interactions of the various processes
affecting parameters In recent years, RSM has played an important
role in oilfield operations, especially in applications improving the
oil recovery factor (Vanegas and Cunha, 2008)
The experimental design techniques commonly used process
analysis and modeling involve the full factorial, partial factorial
and central composite rotatable designs An effective alternative
to the factorial design is the central composite design, originally
developed byBox and Wilson (1951), and improved upon byBox
and Hunter (1957) The central composite design gives almost as
much information as a three-level factorial, requires much fewer
tests than the full factorial, and has been known to be sufficient in
describing the majority of steady-state process responses
Nowa-days, CCD is the most popular class of designs used for fitting
second-order models The total number of tests required for
the CCD formula is (2k–pþ2kþn0), including k as the number of
studied variables, 2k points fixed axially at a distance, p the
fractionalisation element (full design, p¼0) from the center to
generate the quadratic terms, and replicate tests at the center (n0)
Central composite face-centred design is performed to
max-imize the responses of NPV and the amount of oil recovery from
operating variables such as spacing between injector and producer (IPS, X1), steam injection pressure (IP, X2), maximum steam injection rate (MSIR, X3), and subcool temperature (Strap, X4) For each of the four variables studied, high (coded value: þ1), middle (coded value: 0) and low (coded value: 1) set points were selected according to the results in Table 2 The four independent variables and their coded levels for using CCFD are presented in Table 3 A number of tests required for the four independent variables are 26 cases to match each NPV response A full second-order polynomial model is accomplished by the multi-ple regression technique, and the effects of the interactions on the two-factors as well as the main factors included The objective function can be re-written as
Y¼β0þβ1X1þβ2X2þβ3X3þβ4X4þβ11X2
þβ22X2
þβ33X2
þβ44X2
þβ12X1X2þβ13X1X3þβ14X1X4þβ23X2X3þβ24X2X4þβ34X3X4
ð1Þ The coefficients of the main effectsβi– and two-factor inter-actions (βij) – were estimated from the experimental data by computer simulation programming utilizing the least squares method of @R 12.2.1 software
3 Results and discussion The results showed that amount of oil recovery of case 7 obtained the highest value with 2,318,793 bbls (Table 3), but NPV was lower than other cases due to an incompatible operating condition wherein a large number of steam was injected at high injection pressure While the highest NPV of case 22 was achieved
at $54.6 mm under the experimental conditions of IPS 10 m, IP
6000 kPa, MSIR 720 m3/d, and subcool temperature 91C The coefficients of the model are calculated by the multiple regression analysis technique, and the quadratic model was given as follows:
Y¼ 52:850:4IPSþ4:9IPþ6:47MSIR1:1Strap1:6IPS:IPS7:8IP:IP
7:2MSIR:MSIR1:8Strap:Strapþ2:6IPS:IP0:67IPS:MSIR þ0:93IPS:Strapþ0:12IP:MSIR þ0:94IP:Strap0:86MSIR:Strap ð2Þ The statistical result of the multiple regression function was evaluated by the analysis of variance (ANOVA) inTable 4 The R2
value closer to one represents a good correlation between the observed and predicted values The higher values of R2(0.98) and adjusted R2 (0.95) also indicated the efficiency of the model suggesting that 98% and 95% variation could be accounted for
by the model equation, respectively At the same time, a very low value of the coefficient of the residual standard deviation (RSD¼2.39) clearly informed a high degree of precision and
Table 2
Variables and experimental design levels in the SAGD process.
Variables Symbol Coded levels
Injector/producer spacing, m IPS 4 10 16
Injection pressure (IP), kPa IP 4500 6000 7500
Steam injection rate, m 3
/d MSIR 300 510 720 Subcool temperature, 1C Strap 0 9 18
Table 3
Central composite face-centered experimental design.
Case IPS IP MSIR Strap NPV Cum oil Case IPS IP MSIR Strap NPV Cumulative oil (m) (kPa) (m 3 ) (1C) (mm$) (bbl) (m) (kPa) (m 3 ) (1C) (mm$) (bbl)
1 1 1 1 1 26.5 1,431,325 14 1 1 1 1 30.4 1,608,844
2 1 1 1 1 21.3 1,240,048 15 1 1 1 1 42.9 1,991,283
3 1 1 1 1 30.6 1,547,243 16 1 1 1 1 48 2,119,005
4 1 1 1 1 35.4 1,646,577 17 1 0 0 0 50.1 2,189,048
5 1 1 1 1 45.9 2,081,735 18 1 0 0 0 52.2 2,190,790
6 1 1 1 1 33.3 1,738,825 19 0 1 0 0 38 1,867,387
7 1 1 1 1 45.1 2,318,793 20 0 1 0 0 51.9 2,206,455
8 1 1 1 1 45.6 2,312,011 21 0 0 1 0 36.6 1,690,708
9 1 1 1 1 26 1,424,022 22 0 0 1 0 54.6 2,253,399
10 1 1 1 1 21.3 1,240,048 23 0 0 0 1 52.6 2,263,499
11 1 1 1 1 30 1,513,647 24 0 0 0 1 49.4 2,075,359
12 1 1 1 1 35.4 1,646,577 25 0 0 0 0 53.3 2,205,948
13 1 1 1 1 33.8 1,581,006 26 0 0 0 0 53.3 2,205,948
Trang 4reliability of the experimental values and was in relation to the
power of prediction, Q2¼0.86
Student's t-test of statistics is designed to evaluate quantitative
effects of the main factors The regression coefficient values of
Eq.(2)are listed with standard errors and p-values inTable 5 The
p-value is used to check the significance of each coefficient, which
in turn may indicate the pattern of interactions between variables
It can be seen that the variables of IP and MSIR were significant,
with very small p-values (po0.05) It is noteworthy that a positive
sign designates a synergistic effect, while a negative sign
repre-sents an antagonistic effect of a factor on the selected response
3.1 Effect of operating variables on NPV
A Pareto chart presented standardized effects at p¼0.05 on the
NPV responses (Fig 1) All the standardized effects were in absolute
values to verify which were positives and negatives This helps to
identify important variables that significantly affect the overall outcome of the NPV This graph was divided into two regions: the first region below zero is for negative coefficients of variables (IP.IP, MSIR.MSIR, Strap Strap, MSIR.Strap, IPS.IPS, Strap) that decrease the NPV due to an increase in combining of operating variables The second region above zero is the positive coefficients of individual and combining variables of the operating condition (MSIR,
IP, IPS.IP, IP Strap, IPS Strap…) The increase in these variables leads to
an increase to the NPV Based on this Pareto chart and the significant
of regression coefficients,Table 5inferred the double interaction of IP and MSIR, the individuals of MSIR and IP were the most important variables that considerably affected the NPV of production perfor-mance Based on the nonlinear results shown in the sensitivity chart result, the reasonable operating condition to obtain the maximum NPV should be designed on the IPS of 9–10 m, IP of 6200–6400 kPa, MSIR of 550–600 m3
/d, and subcool temperature in the range of
4–7 1C (Fig 2)
3.2 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 are represented for prediction between the dependent variable and
a set of independent variables The graphical representations of NPV contour plots and response surfaces are given inFig 3, as injector–producer spacing, injection pressure, steam injection rate, and subcool temperature The value of the predicted maximum on the surface plot is confined in the smallest ellipse in the contour diagram Elliptical contours are generally obtained when there is a perfect interaction between the independent variables The values
of independent variables in the smallest contour area and the corresponding maximum are determined to be the optimal oper-ating conditions for the response variable
From the response surface plots, the authors recognized that the best choice of operating conditions is located in the smallest region (red) in Fig 3, where the maximum NPV reached over
$55.2 mm According to the regression coefficients significance of the quadratic polynomial model and gradient of slope in the 3-D response surface plot, almost all factors significantly affected the SAGD performance Therefore, the best operating conditions were designed using the injector producer spacing of 9 m, steam injection rate of 610 m3/d, injection pressure of 6409 kPa, and subcool temperature 61C within the 95% confidence intervals 3.3 Validation of model equation
Sensitivity analysis denoted that the injection pressure and the amount of injected steam were important control parameters in the success of an SAGD operation Scenarios 1, 2, 5, 6, 9, 10, 13, 14, and 19 exhibited that the responses of oil recovery and calculated NPV were quite low because injection pressure operated near the reservoir pressure (Table 3) Low injection pressure operation was not strong enough to push the heat of the steam chamber into the bitumen pay Therefore, the amount of oil recovered may decrease considerably
The optimal operating condition was rechecked when the amount of oil recovered was obtained at 2,312,647 bbls in the simulated operation of the SAGD process The oil production rate peaked at 450,000 bbls in the second year, and then was drama-tically reduced until the end of the 10th year of operation time (Fig.4c) This production profile will yield a NPV of $55.47 mm, the highest NPV among experimental cases inTable 7 This result
Table 4
ANOVA for the response surface quadratic model.
Total 25 41909.6 1676.38
Constant 1 39219.8 39219.8
Total corrected 24 2689.75 112.073 10.5864
Regression 14 2632.59 188.042 32.8984 0 13.7128
Residual 10 57.1585 5.71585 2.39078
N¼27 Q 2 ¼0.857 R2
Adj ¼0.949 Conf lev.¼0.95 DF¼6 R 2
¼0.979 RSD ¼2.39
Table 5
Estimated regression coefficients for NPV by using coded units.
NPV Estimate Standard error p value
Constant 52.85 1.03 1.96E13
Strap 1.06 0.56 8.91E02
IPSnIPS 1.62 1.50 3.04E01
IPnIP 7.82 1.50 3.89E04
MSIRnMSIR 7.17 1.50 7.38E04
StrapnStrap 1.77 1.50 2.64E01
IPSnIP 2.61 0.60 1.42E03
IPSnMSIR 0.67 0.60 2.89E01
IPSnStrap 0.93 0.60 1.50E01
IPnMSIR 0.12 0.60 8.46E01
IPnStrap 0.94 0.60 1.45E01
MSIRnStrap 0.86 0.60 1.82E01
Trang 5proved that the validity of the RSM model is reasonably adequate
to predict the production performance of the SAGD process
3.4 Optimization of operating conditions for Fast-SAGD process
The Fast-SAGD model comprises of two full SAGD well pairs
and two CSS wells (Polikar et al., 2000) It uses offset wells placed
horizontally about 50 m away from the SAGD producer and each
offset well These offset wells are operated alternatively as an
injector and producer First, the SAGD horizontal pair begins to
operate until the steam chamber grows to the top of the reservoir Then, CSS is carried out into the offset well until the steam chamber connects from the horizontal well pairs Afterwards it serves as an additional producer well This change occurs after
3 cycles of CSS
The operating conditions of SAGD wells in the Fast-SAGD process are designed using a similar approach to the SAGD system There are three essential cases in screening the operating condi-tions: 4510, 4600 and 6409 kPa injection pressures The responses
of scenarios are listed inTable 7
Fig.2 Effect of operating conditions on the NPV.
Trang 6Offset-well design: the usage of full-factorial design is to
choose a reasonable operating condition (Myers et al., 2008)
Two important parameters, injection pressure and maximum
steam injection rate, are investigated in the range of 7000–
10,000 kPa and 700–1100 m3/d, respectively The CSS wells will
start up after 250 days when the growth of the steam chamber
touches the top of the reservoir A total of nine cases were
generated by full-factorial design with the responses of cumulative
oil and NPV, respectively (Table 6) The optimal points of the
response surface methodology are determined in the vicinity of IP
8333 kPa and MSIR of 1007 m3/d (Table 7;Fig 4)
3.5 Technical-economic evaluation in the production performances
of SAGD and Fast-SAGD processes
For the SAGD system, different from the study by Shin and
Polikar (2007), operating at low injection pressure as in the SAGD2
case yields the lowest oil recovery The results imply that steam injection pressure should be operated at least at 4600 kPa for the operation to be efficient, and higher than 100 kPa compared
to reservoir pressure Using response surface design satisfies in adapting the best operating requirements for achieving the max-imum of both oil recovery and economic benefits
Simulation results demonstrated that the Fast-SAGD process was significantly more advantageous than the SAGD process Although it incorporates increasing capital costs for additional offset in the Fast-SAGD system, both oil recovery and economic profit increase more dramatically than within the SAGD process, illustrated especially by the highest oil recovery in the Fast-SAGD1 case (Fig 5) In practice, low injection pressure such as in the SAGD2 case is significantly less efficient than the Fast-SAGD2 case, and the responses were not as expected Additionally, the minor difference of 10 kPa between steam injection pressure and reser-voir pressure is insufficient to increase the amount of oil recovery
in both Fast-SAGD2 and SAGD2 operations
Fig 3 Optimal operating conditions in the SAGD process (a) Contour plot and
(b) response surface plot (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
Fig 4 Optimal operating conditions in Fast-SAGD process (a) Contour plot and (b) response surface plot.
Trang 7Fig 6 exhibits the cumulative steam oil ratio (CSOR)
perfor-mance change with production time As is known, the CSOR
parameter is closely related to steam cost, oil recovery, and NPV
A high CSOR means that a large amount of steam volume is
injected into the reservoir and this directly affects operating costs
This is similar to steam cost, which depends on the change of gas
prices of the following season If CSOR increases, oil recovery will
accelerate to a certain peak, but at the same time, the economic
benefit will be reduced because of an increase in steam cost It was evidenced that the highest CSOR value of Fast-SAGD1 case was 5.2 with high oil recovery (Table 7; Figs 5 and 6) However, the NPV of Fast-SAGD3 case was larger by a fraction than the NPV of Fast-SAGD1 case as a result of lower thermal efficiency In other cases, although low CSOR value is less than or equal to 4.0, both the amount of oil recovery and NPV reduces significantly Exam-ples are shown in the cases of SAGD2, SAGD3, and Fast-SAGD2
Table 6
Full-factorial design level of CSS well in the Fast-SAGD process.
Injection pressure (IP),
kPa
Steam injection rate, m 3
($mm)
Cum.oil (bbl)
Optimal operating condition
(m 3
)
Cum oil (bbl)
NPV ($mm)
Table 7
Optimization of operating conditions in the SAGD and Fast-SAGD processes.
Case SAGD1 (CCF) SAGD2 (low IP) SAGD3 (low IP) Fast-SAGD1 Fast-SAGD2 Fast-SAGD3
8333 (CSS)
4510 (SAGD)
8333 (CSS)
8333 (CSS) MSIR, m 3
Preheating, day 100 120 120
Cumulative oil, bbl 2,312,647 2,016,199 2,208,805 2,396,283 2,325,890 2,383,835 NPV (actual), $mm 55.47 43.00 53.47 62.33 53.95 62.89 NPV (predicted), $mm 55.30
Fig 5 Cumulative oil.
Fig 6 Cumulative steam oil ratio.
Trang 8Accordingly, reasonable control for injected steam mass and
injection pressure is an important requirement that determines
the success of an operation
Production performance with time is illustrated inFig 7 In the
first 3 years, the amount of oil recovery through the Fast-SAGD
process is much higher than the conventional SAGD process,
estimated to be equal to half of the Fast-SAGD process This is
quite a convenience because of payback and profit acquired in a
short period of time For this reason, the NPV of the Fast-SAGD
cases are greater than the SAGD cases However, thefluctuation of
oil and gas prices decides what kind of operation is the best
solution In economic aspects of cashflow with time, the minor
difference of NPV responses between Fast-SAGD1 and Fast-SAGD3
are considered as equivalent Consequently, the Fast-SAGD1 case is the best choice for an operating condition because of its high oil recovery
Fig 8 expressed the steam chamber performances in conven-tional SAGD and Fast-SAGD processes The steam temperature should achieve at least 2001C, which will heat up the bitumen and decrease oil viscosity enough to be efficiently produced by the producer well For SAGD models, the steam chamber growth contact to the top reservoir occurs after 250 days, 520 days, and
400 days corresponding to the cases of SAGD1, SAGD2, and SAGD3 respectively Afterwards, the CSS well will start to operate in accordance to the Fast-SAGD system The steam chambers of SAGD1 and SAGD3 cases grow in the vertical direction during
2 years, then expand towards the horizontal direction At that time, an increase of heat loss to the overburden and underburden occurs Meanwhile, steam chamber growth of SAGD2 case took a longer time (3 years) to touch the top of the reservoir due to the low injection pressures Therefore the lowest NPV was obtained using the SAGD2 case and this is mentioned inTable 7
The vertical growth of the steam chamber of the CSS well to the top of the reservoir in the Fast-SAGD1 case (520 days) is earlier than both the Fast-SAGD3 (620 days) and Fast-SAGD2 (750 days) cases The steam chambers contact between the SAGD well-pair and CSS well occurred after 600 days for Fast-SAGD1, 750 days for Fast-SAGD3, and 1050 days for Fast-SAGD3 After this time period, heat loss at overburden and underburden will cause higher CSOR and reduce oil recovery
The results showed that the operation selection of Fast-SAGD1 will yield the highest oil recovery and harbors an economical
efficiency much greater than other cases Nevertheless, this study showed that the application of DOE and RSM were useful and extremely efficient with a high confidence level for finding the
Fig 7 Oil rate.
Trang 9optimal operating conditions to maximize profit in a Fast-SAGD
process
4 Conclusions
This paper showed that the DOE and response surface
meth-odology was employed successfully for indicating operation
para-meters of SAGD and Fast-SAGD processes Predicted values from
the regression function are found to be in good agreement with
observed values of R2at 0.98 and Q2at 0.86 for the NPV response
In order to gain a better understanding the effect of the variables
on the SAGD performance and optimal operating conditions,
responses are presented on the 2-D and 3-D response surface map
For maximizing oil recovery, the best solutions were found on
the Fast-SAGD1 scenarios where operating conditions should be
designed with injector producer spacing of 9 m, injection pressure
of 6409 kPa, steam injection rate of 610 m3/d, subcool temperature
of 61C in SAGD operation, CSS is operated at an injection pressure
of 8333 kPa, and injection steam of 1007 m3/d with three cycles
Results showed that the minor difference of 10 kPa between
steam injection pressure and reservoir pressure was insufficient
to increase the NPV and oil recovery as Fast-SAGD2 and SAGD2
operations It is recommended that injection pressure should be
operated at least at 100 kPa higher than the initial reservoir
pressure for the process to be more efficient
This study not only supports a decision-making methodology
to choose the best technical solution, but also provides an
economical way of obtaining the maximum profit in a short period
with the fewest number of experiments
Acknowledgments
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 2012T100201728) Moreover, the authors wish to thank Schlumberger K.K for the encourage-ment of writing this paper
References
Box, G.E.P., Wilson, K.B., 1951 On the experimental attainment of optimum conditions J R Stat Soc.: Ser A (Gen.) 13, 1–45
Box, G.E.P., Hunter, J.S., 1957 Multi-factor experimental designs for exploring response surfaces Ann Math Stat 28 (1), 195–241
Butler, R.M., 2001 Some recent development in SAGD J Can Pet Technol., Disting Author Ser 40 (1), 18–22
Canada's Oil sands: Opportunities and Challenges to 2015, ver.2006, 2008 Canadian National Energy Board.
Gates, I.D., Chakrabarty, N., 2005 Optimization of Steam-Assisted Gravity Drainage (SAGD) in Ideal McMurray Reservoir Paper 2005193 Presented at the Canadian International Petroleum Conference, Calgary, June 7–9.
Gong J., Polikar M., 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.
Myers, R.H., Montgomery, D.C., Anderson-Cook, C., 2008 Response Surface Meth-odology: Process and Product Optimization Using Designed Experiments, 3rd
ed John Wiley and Sons, New York, pp 13–135 Nestor, V.Q., Javier, V.G., Salvador, P., 2002 Surrogate modeling-based optimization
of SAGD processes J Pet Sci Eng 35 (1–2), 83–93 Polikar, M., Cyr, T.J., 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.
Shin, H., Polikar, M., 2007 Review of reservoir parameters to optimize SAGD and Fast-SAGD operating conditions J Can Pet Technol 46 (1), 35–41
Vanegas, J.W., Cunha, L.B., 2008 Prediction of SAGD performance using response surface correlations developed by experimental design techniques J Can Pet Technol 47, 58–64, (Petroleum Society of Canada)
Yang, C., Card, C., Nghiem, L., 2009 Economic optimization and uncertainty assessment of commercial SAGD operations J Can Pet Technol 48 (9), 33–40