Ind. Eng. Chem. Res. 2008, 47, 4937–4943
4937
Regression Analysis Study on the Carbon Dioxide Capture Process Q. Zhou, Christine W. Chan,* and P. Tontiwachiwuthikul Faculty of Engineering, UniVersity of Regina, Regina, Saskatchewan, Canada S4S 0A2
Research on amine-based carbon dioxide (CO2) capture has mainly focused on improving the effectiveness and efficiency of the CO2 capture process. The objective of our work is to explore relationships among key parameters that affect the CO2 production rate. From a survey of relevant literature, we observed that the significant parameters influencing the CO2 production rate include the reboiler heat duty, solvent concentration, solvent circulation rate, and CO2 lean loading. While it is widely recognized that these parameters are related, the exact nature of the relationships are unknown. This paper presents a regression study conducted with data collected at the International Test Center for CO2 capture (ITC) located at University of Regina, Saskatchewan, Canada. The regression technique was applied to a data set consisting of data on 113 days of operation of the CO2 capture plant, and four mathematical models of the key parameters have been developed. The models can be used for predicting the performance of the plant when changes occur in the process. By manipulation of the parameter values, the efficiency of the CO2 capture process can be improved. 1. Introduction Carbon dioxide (CO2) is an important component of the greenhouse gas (GHG) responsible for global warming. CO2 capture has become an important method for mitigation of the risks posed by CO2 pollution. The current CO2 capture technologies include chemical absorption, physical absorption, membrane separation, cryogenic fractionation, and physical adsorption.1 Amine-based chemical absorption is now the most dominant technique widely adopted in the natural gas processing and chemical processing industries. The goal of CO2 capture is to capture and remove CO2 from industrial gas streams before they are released into the atmosphere. The process of amine-based CO2 capture at the International Test Centre for CO2 capture (ITC) can be briefly described as follows: prior to CO2 removal, the flue gas is cooled down, and particulates and other impurities such as SOx and NOx are removed as much as possible. The pretreated flue gas contacts the lean amine solution countercurrently in the absorber column, and the amine selectively absorbs CO2 from the flue gas. The amine solution carrying CO2, which is called CO2rich amine, enters the stripper column, where CO2 is extracted from the amine solvent and the original amine solvent is regenerated. The amine solvent is returned to the absorber column and used in the CO2 removal process again. The CO2 stream produced is essentially pure and can be either developed to a food grade quality or pressurized and transported to a suitable site for geological storage. The CO2 capture process is depicted in Figure 1. Research that focused on improving the effectiveness and efficiency of the amine-based CO2 capture has been ongoing for the past decade. From a survey of the relevant literature, we observed that the most significant parameters influencing the CO2 production rate include the heat duty, circulation rate of the solvent, CO2 lean loading, and solvent concentration. The survey also showed that studies on process simulation and analysis of fundamentals were applied to discover the correlation among these parameters. However, because no models were developed in the studies, the relations among the parameters were not explicit, and it remained unknown how much one * To whom correspondence should be addressed. Tel.: +1 306 585 5225. Fax: +1 306 585 4855. E-mail:
[email protected].
parameter is influenced by changes in other parameters. Hence, we adopt a different approach. In this paper, we present a regression study conducted with the objective of unraveling the relationships among these critical parameters of the amine-based CO2 capture process. A multiple-regression technique has been applied for analyses of data collected at the CO2 capture pilot plant at the ITC. Before the regression analysis was conducted, the data were examined and filtered so that only the stable data were used for modeling. This was done to enhance the accuracy and reliability of the model. The Statistical Package of Social Sciences (SPSS, trademark of SPSS Inc., Chicago, IL) was adopted for developing four regression models, and correlation and regression analysis were performed. Then, the acceptability and reliability of the models were assessed. This paper describes the procedures of model development and assessment. The paper is organized as follows: Section 2 presents the background literature relevant to the area of CO2 capture and the regression technique. Section 3 describes the process of parameter analysis and data filtering. Section 4 presents the development of models with the SPSS software. Section 5 describes the procedure of model assessment with SPSS and gives a summary of the models. Section 6 includes some discussion and gives a conclusion. 2. Background Literature 2.1. CO2 Absorption Performance. Some existing research on the relationships among the parameters of the CO2 capture process and their effects on the efficiency and absorption performance are discussed as follows. Rao and Rubin (2002) conducted technical, economic, and environmental assessment of amine-based CO2 capture technology and studied the key parameters that affect the performance, costs, and environmental acceptability of different technology options.2 Rao et al. (2006) again identified the key process parameters that have the greatest influence on the performance and cost of the system based on quantitative expert judgment; he also estimated the potential for future performance improvements and cost reductions.3 Yokoyama (2006) suggested that, for the amine-based absorption technology, key parameters that affect cost-effectiveness included the heat duty of the reboiler, the circulation rate of the
10.1021/ie701747f CCC: $40.75 2008 American Chemical Society Published on Web 06/18/2008
4938 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008
solvent, and the concentration of solvents. The reboiler heat duty is the amount of steam for stripping CO2 and regenerating the lean amine solvent, and it represents the energy consumption in the CO2 capture process.4 Sakwattanapong et al. (2005) proposed that the level of heat duty directly related to the quantity of CO2 stripped from the stripper column and the quality of lean solvent fed back to the absorber column.5 Aroonwilas and Veawab (2004) concluded that the absorption performance of the plant could be enhanced by decreasing CO2 loading of the solvent or increasing the solvent circulation rate.6 In 2007, Aroonwilas and Veawab concluded that the lower steam pressure supplied to the CO2 capture plant for solvent regeneration results in greater CO2 capture efficiency and lower heat duty.7 2.2. Statistical Regression Technique. The purpose of multiple regression is to develop a linear equation in which each predictor variable has its own coefficient and the outcome variable is predicted from a combination of all of the variables multiplied by their respective coefficients. The equation can be expressed as follows:8 Y ) β0 + β1X1 + β2X2 + ... + βnXn + i Y is the outcome variable, β1 is the coefficient of the first predictor X1, β2 is the coefficient of the second predictor X2, βn is the coefficient of the predictor Xn, and i is the difference between the predicted and observed value of Y. SPSS was widely adopted for performing regression analysis in industrial applications. SPSS has been selected for a number of reasons. It supports both linear and nonlinear function modeling, it can implement multivariate statistical procedures, and it can perform multiple-regression analysis for linear modeling. Moreover, it provides 10 curve functions for nonlinear function modeling. 3. Parameter Analysis and Data Filtering 3.1. Parameter Analysis. The expert operator identified four parameters of the CO2 capture process to be consequent variables in the regression analysis: (1) heat duty of reboiler, (2) absorption efficiency, (3) CO2 lean loading, and (4) CO2 production rate (the tag identifier in the ITC process is FT700). As well, seven parameters were chosen as candidate conditional or predictor variables in the regression analysis: (1) amine circulation rate (FT-600), (2) pressure of the inlet steam of the reboiler (PT-103A), (3) flow rate of the outlet steam of the reboiler (FT-103C), (4) reboiler pressure (PT-660), (5) amine concentration, (6) heat duty, and (7) CO2 lean loading. It is noted that heat duty and lean loading are both consequent and predictor variables. While being regressed by other predictor variables, they were also used as predictors to regress against the CO2 production rate and absorption efficiency because they have significant effect on them. The process of model development for the CO2 production rate is discussed in detail in sections 4 and 5. The models for heat duty and lean loading are developed and assessed with the same procedures, and the model for the absorption efficiency is developed with the curve estimation because the relationship between the absorption efficiency and its predictor variable is unlikely to be linear. 3.2. Data Filtering. The sources of data for the regression analysis study are the property of ITC; the data were taken from annual reports and were collected from the ITC plant during the years from 2003 to 2006. The data on the plant process were collected from the sensors every 5 min of each day. The ranges of values of the process parameters are summarized as follows: the amine concentration applied is between 4 and 6.5
mol; the amine circulation rate is between 7 and 20 kg/min; the CO2 lean loading is between 0.08 and 0.4; the heat duty is between 60 000 and 120 000 BTU/lb · mol of CO2. To enhance the accuracy and reliability of the models, the data were examined and filtered so that only the stable data remained and were used for modeling before conducting the regression analysis. Three steps were used for filtering of the data, and each successive step would use only the data that remained from the previous step. Step 1. During some days, the data were collected during very short time frames, such as, half an hour. These data were considered insufficient to reflect the changing trend of the operations at the plant and, hence, were removed. Step 2. Typically, the plant does not perform in a stable manner in the morning and during the 1 h before shutdown, and the data collected during these periods of time were considered unreliable. Therefore, for all of the full-day data sets, the data before 12:30 pm and after 3:30 pm were removed. Step 3. After examining the data set, the first author found that some of the parameters behaved in an erratic manner; for example, the steam pressure increases 20 kPa in 10 min. These data exhibit abnormal performance and are deemed unreliable; hence, they are removed. The data that remained after these three filtering steps appeared to be stable and reflect noticeable trends on a daily basis. This indicates that the data describe normal and reliable plant performance. The data filtering that was performed did not include evaluation of the material and energy balance in the process because the purpose of the study was to develop statistical models on the operation ranges of data. For these data sets, the daily average of each parameter was calculated and grouped as a final data set to be used in the regression analysis. The averaging process was conducted so that the trends in data can be rendered more noticeable. The average values of the five parameters of the CO2 production rate (FT-700), amine circulation rate (FT-600), reboiler pressure (PT-600), heat duty, and amine concentration (molarity) were calculated and became one input for the regression analysis. Table 1displays some sample values of the five parameters collected on January 20, 2006. 4. Regression Model Development SPSS was used for implemention of the multiple-regression analysis. As mentioned earlier, the study targets the four consequent parameters of heat duty of reboiler, absorption efficiency, CO2 lean loading, and CO2 production rate (FT-700). For each consequent variable, the regression model was developed in the two steps of correlation analysis and regression analysis. The acceptability and reliability of the developed model was then assessed. Details of each step in the model development process will be discussed. 4.1. Correlation Analysis. A correlation is a measure of the linear relationship between two variables. Both the bivariate and partial correlation will be tested. The bivariate correlation is conducted to check the relationships between the consequent variable and each predictor variable. However, because all of the variables are correlated to some extent, the effects of the predictor variables on the consequent variable are confounding. That is, the correlation between the consequent variable with one predictor variable could not be unique and may be accounted for by another predictor variable.8 Hence, the partial correlation test was conducted to identify a unique relationship between the consequent variable and each predictor variable while controlling the effects of the other predictor variables. That is, the effects
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4939
Figure 1. Amine-based CO2 capture process flow diagram. Table 1. Daily Average of Data Sample
1/20/2006 13:35 1/20/2006 13.40 1/20/2006 13.45 1/20/2006 13:50 1/20/2006 13.55 1/20/2006 14:00 1/20/2006 14:05 1/20/2006 14:10 1/20/2006 14:15 1/20/2006 14:20 1/20/2006 14:25 1/20/2006 14:30 1/20/2006 14:35 1/20/2006 14:40 1/20/2006 14:45 1/20/2006 14:50 1/20/2006 14:55 1/20/2006 15:00 daily average
F1700
FT600
PT660
heat duty
molarity
0.70847 0.72167 0.72084 0.71331 0.72127 0.70986 0.71869 0.73518 0.74863 0.75190 0.75991 0.74364 0.73996 0.73828 0.72731 0.74089 0.74226 0.73752 0.73220
8.0421104 8.0361185 8.0362892 8.0209055 8.0094938 8.0270748 8.0286446 8.028182 8.0433311 8.02178 8.0284595 8.0211153 8.0373011 8.0425081 8.0282078 8.02143 8.0308027 8.018054 8.028989
24.385824 24.701452 24.905497 25.012833 25.13772 25.181517 25.243368 25.866854 26.237312 26.346712 26.595093 26.625092 26.532364 26.491171 26.495916 26.729198 26.990812 26.956528 15.91307
94.976 92.940 93.487 94.150 93.174 94.735 93.631 91.406 89.920 89.216 88.624 90.443 89.158 89.459 90.766 89.301 89.028 89.926 91.352
6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617 6.0617
Table 2. Correlation and Significance
Table 3. Output Table of Multiple-Regression Methods
predictor
partial correlation coefficienta
significance
heat duty reboiler pressure (PT-660) amine circulation rate (FT-600) amine concentration molarity
0.5185 0.1488 0.7436 0.2681
0.000 0.121 0.000 0.000
a
Consequent variable ) FT-700.
of other predictor variables on the consequent variable are assumed to be constant. Table 2 lists the correlation between the CO2 production rate (FT-700) and each predictor and the significance of the correlation. Generally, social scientists accept any probability value below 0.05 to be statistically meaningful, so any probability value
variables entered/removeda model 1 2 a
variables entered heat duty (1000 BTU/lb · mol of CO2), FT-600b molarityb
variables removed
method enter enter
Dependent variable: FT-700. b All requested variables entered.
below 0.05 is regarded as indicative of a genuine effect.9 It can be seen from Table 2 that all predictor variables except PT-660 (which has a significant value of 0.121) were found to have a significant correlation coefficient. Thus, the conclusion can be drawn that PT-660 does not have a significant effect on FT700 and, therefore, is not included in the regression model.
4940 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 Table 4. SPSS Output of Regression Model Summary model 1 2
R
R a
0.841 0.847b
2
2
adjusted R
std error of the estimate
0.702 0.710
0.0274 721 6 0.027 082 73
0.707 0.718
a Predictors: (constant), heat duty (1000 BTU/lb · mol of CO2), FT-600. b Predictors: (constant), heat duty (1000 BTU/lb · mol of CO2), FT-600, molarity.
Table 5. ANOVAa for Prediction Model model 1 2
regression residual total regression residual total
sum of squares
df
mean square
F
sig.
0.201 0.83 0.284 0.204 0.080 0.284
2 110 112 3 109 112
0.100 0.001
132.956 0.000b
0.068 0.001
92.600 0.000 c
a Dependent variable: FT-700. b Predictors: (constant), heat duty (1000 BTU/lb · mol of CO2), FT-600. c Predictors: (constant), heat duty (1000 BTU/lb · mol of CO2), FT-600, molarity.
4.2. Method of Multiple Regression. During running of the multiple regression in SPSS, the way in which the predictor variables are entered into the model can have a great impact on the modeling results. As a general rule, the predictors should be entered into the model in order of their importance in predicting the outcome. Therefore, the three predictors were entered into the model in two steps based on their correlation coefficients because a larger correlation coefficient indicates its greater impact on the consequent variable. As shown in Table 3, heat duty and FT-600 were entered into the model in the first step because they have relatively high values of partial correlation coefficients (0.5185 and 0.7436 respectively). The model produced was named Model 1 and includes only two predictors. The amine concentration is associated with a relatively smaller correlation (0.2681), so it was entered in the second step. All three predictor variables were included in Model 2. SPSS provides the summary of both Model 1 and Model 2, which are described in the following sections. 4.3. Model Statistics. SPSS describes the overall model and generates output information on whether the model is successful in predicting the outcome variable. The output information consists of the model summary table and ANOVA. 4.3.1. Model Summary. The model summary is shown in Table 4. The values of the multiple correlation coefficients are shown in the column labeled R. It represents the correlation between the observed values of FT-700 and the values of FT700 predicted by the multiple-regression model. As Table 4 shows, the correlation coefficient of model 1 is 0.841 and the correlation coefficient of model 2 increases to 0.847. This indicates that there is a stronger correlation between the observed FT-700 and those predicted by model 2. R2 is called the coefficient of determination, which measures the “goodness of fit” of the model.8 It represents the amount of variation in the consequent variable of CO2 production rate (FT700) that is accounted for by the model and measures how well the regression model performs in predicting the consequent variable. R2 for model 2 is 0.718, which reveals that the three predictors of heat duty, amine circulation rate, and amine concentration can explain 71.8% of the variation in the CO2 production rate (FT-700). Cross-validation is for assessing the accuracy of a model across different samples. If a model can be generalized, then it is likely to be capable of accurate predictions in a different group of samples.8 In SPSS, the cross-validity of a model is indicated
by the adjusted R2. The ideal value of the adjusted R2 should be the same or very close to the value of R2. For model 2, the difference between R2 and adjusted R2 is about 0.8% (0.718–0.710 ) 0.008). The shrinkage in the value between R2 and adjusted R2 means that if model 2 was derived from the population rather than a sample, it would account for approximately 0.8% less variance in the consequent variable. Nonetheless, the approximating values between R2 and adjusted R2 indicate that the cross-validity of model 2 is very good. 4.3.2. ANOVA. ANOVA is an analysis of the variance, which tests whether the model is significantly better at predicting the consequent variable than using the mean, which is often calculated for prediction of a value because it is the simplest method available without using a regression model. Table 5 displays the important factors of the F ratio and the associated significance value of the F ratio. The F ratio is a measure of how much the model has improved the prediction of the outcome compared to the level of inaccuracy of the model.8 A good model can be identified when the improvement in prediction is large and the inaccuracy is small. That is, a good model should have a large F ratio, that is, at least greater than 1. The F ratio for model 1 is 132.96, which is highly significant (p < 0.001). For model 2, the F ratio is 92.60, which is also highly significant (p < 0.001). This comparison shows that, although model 2 can better explain the variance in the consequent variable of the CO2 production rate (FT-700), it has a lower inaccuracy of the prediction. However, considering that 92.60 is still a fairy high value that indicates a good accuracy of prediction, model 2 was selected because it has two advantages over model 1: (1) it can explain a greater variance in the CO2 production rate and (2) its F ratio is highly significant although its value is lower than that of model 1. 4.4. Coefficient Summary. Table 6 provides the details of the model parameters and the significance of these values. The estimated regression coefficients are given under the column heading “unstandardized coefficients B”, which represents the predicted change in the CO2 production rate (FT-700) when the predictor is changed by one unit. The regression model for the CO2 production rate (FT-700) is CO2 production rate ) 0.042 + 0.027(amine circulation rate) + 0.004(heat duty) + 0.025(amine concentration) The positive coefficients indicate positive relationships between the CO2 production rate (FT-700) and all of the predictor variables. Hence, the higher values for the amine circulation rate (FT-600), heat duty, or amine concentration would cause the CO2 production rate (FT-700) to increase. Also, the coefficients reveal the degree to which each predictor affects the CO2 production rate: (1) the amine circulation rate increases by 1 kg/min, causing the CO2 production rate to increase by 0.027 units, (2) the heat duty increases by 1000 BTU/lb · mol of CO2, causing the CO2 production rate to increase by 0.004 units, and (3) the amine concentration increases by 1 mol, causing the CO2 production rate to increase by 0.025 units. The t test is a measure of whether the predictor is making a significant contribution to the model.8 If the t test associated with a coefficient is significant, i.e., if the value in the column labeled “sig.” is less than 0.05, then the predictor is making a significant contribution to the model. The smaller the value of sig. and the larger the value of t, the greater is the contribution of that predictor variable. Table 6 displays the results of the t test of each predictor variable in the column labeled “t”. For
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4941 Table 6. Regression model parameters coefficientsa unstandardized coefficients
standardized coefficients
model 1
2
a
constant FT-600 heat duty (1000 BTU/lb · mol of CO2) constant FT-600 heat duty (1000 BTU/lb · mol of CO2) MOLARITY
95% confidence interval for B β
t
B
std error
0.193 2.531×10-2 3.601×10-3
0.63 0.002 0.001
3.051 1.247 14.095 0.591 6.675
0.003 0.000 0.000
0.068 0.022 0.003
0.319 0.029 0.005
0.340 0.340
2.944 2.944
4.233×10-2 2.667×10-2 3.726×10-3
0.097 0.002 0.001
0.438 14.107 0.611 6.960
0.662 0.000 0.000
-0.149 0.023 0.003
0.234 0.030 0.005
0.298 0.335
3.357 2.983
2.456×10-2
0.012
0.116
0.043
0.001
0.048
0.802
1.246
2.046
sig.
lower bound
collinearity statistics upper bound tolerance
VIF
Dependent variable: FT-700.
Figure 2. Residual plot.
Figure 4. Partial regression plot between FT-700 and FT-600.
Figure 3. Normal plot for residual distribution.
Figure 5. Partial regression plot between FT-700 and the heat duty.
model 2, it can be seen that, based on the t value, the amine circulation rate [t(113) ) 14.107, p < 0.001], the heat duty [t(113) ) 6.960, p < 0.001], and the amine concentration [t(113) ) 2.046, p < 0.05] are all significant predictors of the production rate of CO2. Moreover, the amine circulation rate (FT-600) has the largest impact and the amine concentration has the smallest impact on the CO2 production rate.
5. Regression Model Assessment After development of the multiple-regression model, the next step is to assess its acceptability and reliability. The modeling process has been conducted based on four assumptions, which include the following:8,9 1. There is no multicollinearity between the predictor variables. 2. The residuals are randomly distributed.
4942 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008
Figure 6. Partial regression plot between FT-700 and the amine concentration.
3. The residuals arise from a normal distribution. 4. The relation between each predictor variable and the outcome variable is linear. Therefore, only when these assumptions are satisfied can we conclude that the regression model is adequate and reliable. 5.1. Collinearity Diagnostic. The collinearity diagnostic assesses the assumption of no multicollinearity. Multicollinearity exists when there is a strong correlation between two or more predictor variables in a regression model. Multicollinearity introduces problems in multiple regression because its existence indicates that the predictor variables are intercorrelated; therefore, the effects of the predictor variables are confounded, and determining the importance of a given predictor variable becomes difficult. Hence, the existence of multicollinearity increases the variance of the regression coefficients, resulting in an unstable predictor model. The two parameters that indicate multicollinearity are variance inflation factor (VIF) and tolerance, shown in Table 6. VIF indicates whether a predictor has a strong linear relationship with the other predictors. It has been suggested that any VIF value greater than 10 would be a concern. On the other hand, tolerance is the reciprocal of VIF, and a value of tolerance below 0.2 causes concern, while values below 0.1 indicate serious problems. In the collinearity statistics displayed in Table 6, there is no tolerance value lower than 0.2, and no VIF value higher than 10. These results indicate that no multicollinearity existed between any two predictor variables in model 2; hence, the assumption of no multicollinearity is satisfied. 5.2. Random Residual Distribution. Residuals are the difference between the values of the consequent variable predicted by the model and the values of the consequent variable observed in the sample. The residuals effectively represent the errors present in the model. The SPSS provides a residual plot to test the assumption of random errors. It is a scatter plot of standardized residuals against predicted values. For a normally distributed sample, 95% of the standardized residuals should lie between -2 and +2 on the y axis. If more than 5% of the cases have standardized residuals with an absolute value greater than 2, then there is evidence that the level of error within our model is unacceptable. Figure 2 is the output of the residual plot generated by SPSS. Three horizontal reference lines were inserted at the y levels of +2, 0, and –2. It can be observed that 5 out of 113 cases (4.4%) have residuals with an absolute value greater than 2. This
satisfies the assumption that 95% of the standardized residuals lie within the range from –2 to +2. Moreover, it can be seen from Figure 1 that the residuals lie around zero without a large variance in the degree of scatter. Therefore, the results indicate that the assumption of random errors is satisfied. 5.3. Normality Distribution Diagnostic. It is assumed that the residuals in the model are normally distributed. The normality probability plot generated by SPSS is used for assessing whether the residuals are approximately normally distributed. It plots the standardized residuals expected from a standard normal distribution against the observed residuals. As shown in Figure 3, the straight line represents the expected normally distributed residuals, and the points represent the observed residuals. Departures from the straight line indicate deviations from normality. In a perfectly normally distributed data set, all points will lie on the line. From the normality probability plot of model 2 shown in Figure 3, most of the points lie on the line. It can be seen that the points that do not lie on the line are very close to the line. Therefore, the plot shows that the deviation from normality for model 2 is very small and, hence, acceptable. 5.4. Partial Regression. It is assumed that the relationship between each predictor variable and the consequent variable is linear and the effects of several predictor variables are additive. SPSS provides the scatter plots of the residuals of the outcome variable and each of the predictors when both variables are regressed separately on the remaining predictors. From the partial plots, the relationship between the consequent parameter of the CO2 production rate (FT-700) and each predictor should appear approximately linear. Also, the gradient of the regression line in each plot is equal to the coefficient of the respective predictor variable in the regression equation. As observed from Figures 46, all three plots of the residuals show an approximately linear relationship. Therefore, it is concluded that the relationships between (1) the CO2 production rate and the amine circulation rate, (2) the CO2 production rate and the heat duty, and (3) the CO2 production rate and the amine concentration have been modeled reasonably well by the multiple-regression equation presented in section 4.4. 5.5. Model Summary. When the same procedures of correlation analysis, regression analysis, and model assessment are conducted, the models of heat duty and lean loading are developed. The models and their individual R2 values are listed in Table 7. During development of the model between absorption efficiency and lean loading, it was observed that R2 of the linear model between these two parameters had a very low value. Therefore, the relationship between the absorption efficiency and lean loading is likely to be nonlinear. Based on this observation, a curve estimation analysis of the data was conducted to determine which of the 10 different nonlinear functions provided by SPSS best describes the data plot. It was found that the cubic function had the highest fit with a value for R2 of 0.882. On the basis of the formula of the cubic function in SPSS, the model of absorption efficiency and lean loading was developed. For heat duty, the predictor variables included the flow rate of the outlet steam of the reboiler (FT-103C) and the pressure of the inlet steam of the reboiler (PT-103A). For lean loading, the predictor variables included the heat duty and amine concentration. The four models developed for describing relationships among the key parameters of CO2 production rate, heat duty, lean loading, absorption efficiency, amine concentration, amine circulation rate, flow rate of the outlet steam of the reboiler,
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4943 Table 7. Prediction Models
model 1 model 2 model 3 model 4
model
R2
CO2 production rate ) 0.042 + 0.027(FT-600) + 0.004(heat duty) + 0.025(amine concentration) heat duty ) 971(FT-103C) + 54.83(PT-103A) + 6495 lean loading ) –5.06 × 10-6(heat duty) – 5.69 × 10-2(amine concentration) + 0.903 absorption efficiency ) 104.575 - 308.37(lean loading) + 2165.95(lean loading)2 - 4744.5(lean loading)3
0.718 0.824 0.771 0.882
and pressure of the inlet steam of the reboiler in the CO2 capture process are presented in Table 7.
contributions during the processes of parameter analysis and verification of the model results.
6. Conclusion
Literature Cited
The multiple-regression technique was applied to analyze the relationships among critical parameters in the CO2 capture process based on the data collected from the CO2 capture plant at ITC. Before the regression analysis was conducted, the data were examined and filtered so that only the stable data were used for modeling. This was done to enhance the accuracy and reliability of the developed models. This paper has discussed the development of four regression models, as well as the assessment of acceptability and reliability of the models. These models serve to describe part of the CO2 capture process and can help to predict the performance of the CO2 capture process at ITC. They can be used for assisting plant operations and for enhancing the efficiency of the CO2 capture process. The models have been implemented as modules and incorporated as components of an expert decision support system that monitors and controls the CO2 capture process. Although the reliability of the models has been assessed and found to be satisfactory, their accuracy needs to be improved. Therefore, for future work, more new operational data will be employed and multiple technologies will be applied in an effort to improve the accuracy of the models. Also, the models can be further tested and verified with new data collected from the CO2 capture plant at ITC.
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Acknowledgment The authors are grateful for the generous support of a NSERC Research Grant and also thank Don Gelowitz for his invaluable
ReceiVed for reView December 21, 2007 ReVised manuscript receiVed March 4, 2008 Accepted March 6, 2008 IE701747F
