DSpace at VNU: An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by Response Surface Methodology

DSpace at VNU: An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by R...

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Energy Sources, Part A: Recovery, Utilization, and Environmental Effects

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An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by Response Surface Methodology

H X Nguyenab, T B N Nguyena, W Baea, T Q C Dangac & T Chunga

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

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Downloaded by [University of Calgary] at 23:33 03 September 2014

Energy Sources, Part A, 36:1103–1114, 2014

Copyright © Taylor & Francis Group, LLC

ISSN: 1556-7036 print/1556-7230 online

DOI: 10.1080/15567036.2010.545796

An Approach for the Prediction of Optimum Conditions for the Steam Assisted Gravity Drainage Process by

Response Surface Methodology

H X Nguyen,1;2T B N Nguyen,1 W Bae,1 T Q C Dang,1;3 and T Chung1

1Sejong University, Seoul, Korea

2Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnam

3Department 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 5 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

1 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

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

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 ˇ0C

k X

i D1

ˇiXiC

k X

i D1

ˇi iXi2CX

i <j

where Y is the predicted response, ˇ0the intercept coefficient, ˇi the linear terms, ˇi ithe squared terms, ˇij the interaction terms, and xi and xj represent the coded independent variables In this study, a second-order polynomial equation was obtained using the uncoded independent variables

as such:

Y D ˇ0Cˇ1X1Cˇ2X2Cˇ3X3Cˇ4X4Cˇ11X12Cˇ22X22Cˇ33X32Cˇ44X42

Cˇ12X1X2Cˇ13X1X3Cˇ14X1X4Cˇ23X2X3Cˇ24X2X4Cˇ34X3X4:

(2)

The coefficient of the model for the response was estimated using a multiple regression analysis technique included in the RSM Fit quality of the models was judged from their coefficients of correlation and determination

3 DESIGN OF EXPERIMENT USING CENTRAL COMPOSITE DESIGN 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 design (CCD), originally developed by Box and Wilson and improved upon by Box and Hunter in 1957 The CCD gives almost as much information as

OPTIMUM CONDITIONS FOR SAGD 1105

a three-level factorial, requires much fewer tests than the full factorial, and has been known to be sufficient to describe the majority of steady-state process responses

Currently, CCD is the most popular class of designs used for fitting second-order models The total number of tests required for CCD is 2kC2k C n0, including the standard 2kfactorial points with its origin at the center, 2k points fixed axially at a distance, say ˇ.ˇ D 2k=4/, from the center

to generate the quadratic terms, and replicate tests at the center n0/, where k is the number of independent variables

3.1 Experiment Design for SAGD Operating Conditions

Two-dimensional numerical simulations were performed with a grid cell (101  1 m in the lateral direction and 25 m thickness in the vertical direction) with CMG’s STARS using the petrophysical parameters of the Athabasca reservoirs as described in the previous literatures (Shin and Polikar, 2005) The SAGD simulation model in the present application considered two well pairs parallel, horizontal wells of 900 m length, oriented in the j direction, within a reservoir of McMurray formation is located in shallow depth regions from 200 to 210 m, with no dip and 1,500 kPa

of initial pressure The dimensions of each block were 1 m in i and k directions and 900 m in the j direction Constant values of porosity (35%) and directional permeability (Kv D 5d and

Kh D 2:5d) were considered through the entire reservoir The initial temperature was 18ıC and all thermal properties of rock and fluids were the same for all runs, except the rock thermal conductivity All surfaces of the model have a no-flow boundary, but heat loss is assumed at the overburden No aquifer or gas cap zones were considered A three-phase fluid model was assumed

to account for the methane content in the oil Steam at 95% quality was injected at 265ıC The net present value over a period of 10 years of production was selected as the variable to measure the SAGD production performance, and therefore, the dependent variable in the proposed surface response correlation This selection was done based on the comparison of the NPV with the cumulative (CSOR) and instantaneous steam-to-oil ratio (ISOR), two common measurements

of SAGD performance It can be seen that the maximum value of NPV coincides with the value

of SOR equal to four, considered as the limit value of maximum profitability Above this limit, the project is assumed not to be cost-effective (Shin and Polikar, 2005)

The design of the economic model was based on the one discussed in the Canadian National Energy Board reports (2006, 2008) The economic model was a simplified cash flow model in an Excel spreadsheet that included depreciation and a typical Alberta’s fiscal regime All simulation cases were run over a period of 10 years, and the result of the yearly cumulative oil production and steam injection was the base to calculate the yearly income The NPV was calculated considering only the average price of bitumen ($60/bbl) and gas price 4.71$/GJ at an interest rate of 10%

a year Drilling and completion costs of a well pair (2.5 $mm) were also considered as capital investments The production estimate is matched with investment and operating costs and rates of return on capital to calculate the NPV

The experimental design selected in this application is the central composite design (CCD) to determine the relationship between four operating variables of the SAGD process, namely, spacing between injector/producer (IPS), injection pressure (IP), maximum steam injection rate (MSIR), and SAGD well pattern spacing (WPS) The number of tests at the center points was three, making the total number of tests required for the four independent variables: 24C.2
4/ C 3 D 27 The injector/producer spacing X1/, injection pressure X2/, maximum steam injection rate X3/, and well pairs pattern spacing X4/ were independent variables studied to predict Y responses (net present value) The four independent variables and their levels for the CCD used

in this study are shown in Table 1 Using the relationships in Table 1, coded and actual levels

of the variables for each of the experiments in the design matrix were calculated as given in Table 2 Based on this table, the experiments were conducted for obtaining the response, i.e.,

TABLE 1 Four Independent Variables and Their Levels for CCD

Coded Variable Level Low Center High

Injector/producer spacing (IPS), m X1 5 10 15 Injection pressure, kPa X2 2,500 5,500 8,500 Max steam injection rate (m 3

Well pairs pattern spacing (m) X4 40 70 100

TABLE 2 Independent Variables and Result for SAGD Operation Design by Central Composite Design Coded Level

of Variables

Actual Level

of Variable

Response (Simulation Observed) Run X1 X2 X3 X4 IPS, m IP, kPa MSIR, m 3 /d WPS, m NPV, $mm

OPTIMUM CONDITIONS FOR SAGD 1107

NPV is carried out at the corresponding independent variables addressed in the experimental design matrix These experimental data are used for validating the single-response model of the operation process The sequence of the experiment was randomized in order to minimize the effects of uncontrolled factors

4 RESPONSE SURFACE METHODOLOGY EVALUATION When fitting the model, various statistical analysis techniques were employed to judge the ex-perimental error, the suitability of the model, and the statistical significance of the terms in the model This is usually done with the help of a computer, using either a statistics package or a dedicated RSM program In the present work, the adequacy of the model was justified through analysis of variance (ANOVA)

The quality of the model is measured through statistics as R2, R2adj, and Q2 The coefficient

of multiple determination, R2, measures the percentage of variability observed on the response and explained by the regression It depends on the model and it will increase when adding more terms

to it For this reason, it is not a suitable statistic for comparing models An adjusted coefficient R2adj is defined as being able to compare the different possible models Any model with a value

of R2 and R2adj close to 1, indicates an excellent quality in fitting the observed data, but it does not give any information about its power of prediction between the available data points

In some cases, models that fit the experimental data properly are not good predictors In order to measure the power of prediction of a model, the statistic, Q2, is computed based on the prediction sum of squares (PRESS) PRESS is then computed as the squared differences between observed Y and predicted values Ypred The minimization of PRESS leads to an improvement on the power

of prediction of the model Once the model is constructed, it can be used to predict reservoir performance and to optimize controllable variables (Vanegas Prada and Cunha, 2008)

5 RESULTS AND DISCUSSION Response surface optimization is more advantageous than the traditional single parameter opti-mization in that it saves time, space, and injection raw material There were a total of 27 cases for optimizing the four individual parameters in the current CCD Table 2 shows the experimental conditions and the results of NPV according to the factorial design Maximum NPV (103.307

$mm) was recorded under the experimental conditions of the injector/producer spacing, 5 m; injection pressure, 2,500 psi; maximum steam injection rate, 840 m3/d; and well pairs pattern spacing, 40 m By applying multiple regression analysis on the experimental data, the response variable and the test variables were related by the following second-order polynomial equation:

Y D 97:35 6:88X1 C 3:995X2 C 2:83X3 9:54X4 1:1X1X1 6:16X1X2 0:51X1X3 C 2:01X1X4 8:55X2X2 0:34X2X3 1:1X2X4 2:11X3X3 C 0:56X3X4 5:41X4X4:

(3)

The results of the analysis of variance, goodness-of-fit, and the adequacy of the models are summarized in Table 3 The determination coefficient (R2 D 0.967) was showed by ANOVA

of the quadratic regression model, indicating that only 3.3% of the total variations were not explained by the model The value of the adjusted determination coefficient (Adjusted R2 D 0.93) also confirmed that the model was highly significant At the same time, a very low value

TABLE 3 ANOVA Analysis

Regression 14 5,022.48 358.748 25.299 0.000 18.9407

N D 27 Q2 D 0.82 Cond no D 6.6122

DF D 12 R2 D 0.967 Y-miss D 0

R2 Adj D 0.93 RSD D 3.766

(3.76) of residual standard deviation (RSD) clearly indicated a very high degree of precision and

a good deal of reliability of the experimental values The model was found to be adequate for prediction within the range of experimental variables and especially the one related to the power

of prediction, Q2 D 0.82

The regression coefficient values of Eq (3) are listed in Table 4 The P-values were used as

a tool to check the significance of each coefficient, which in turn may indicate the pattern of the interactions between the variables The smaller was the value of P, the more significant was the cor-responding coefficient It can be seen from this table that the linear coefficients X1; X2; X3; X4/,

a quadratic term coefficient X22; X42/, and cross product coefficients X1:X2; X1:X4/ were highly significant, with very small P-values P < 0:05/ The other term coefficients were not significant P > 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 4 Regression Coefficients of the Predicted Quadratic Polynomial Model

Standard

X3.X4 0.561685 0.941419 0.561837

Confidence level D 95%

OPTIMUM CONDITIONS FOR SAGD 1109

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 1 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 1 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 1 and 2a) The third important factor is injection pressure, when increase of IP leads to increase slightly the NPV (Figures 1 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 relation-ships 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 3 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 1 The degree of factors effect on NPV.

FIGURE 2 Main factors effect on NPV.

FIGURE 3 Contour plot (2-D) showing the effects of variables on NPV.