Optimization of CO2 Capture Process with Aqueous Amines—A

Article pubs.acs.org/IECR

Optimization of CO2 Capture Process with Aqueous AminesA Comparison of Two Simulation−Optimization Approaches Aroonsri Nuchitprasittichai and Selen Cremaschi* Department of Chemical Engineering, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, United States S Supporting Information *

ABSTRACT: Aqueous amine is a solvent considered for carbon dioxide (CO2) recovery from the flue gas of a refinery gas turbine by chemical absorption/desorption process. The performance and the economics of this process depend on the choice of the amine absorbent, the concentration of the amine absorbent, the number of stages in the absorber and stripper columns, and the operating conditions. We used response surface methodology (RSM)a simulation−optimization technique, which uses local searches to estimate an appropriate direction to reduce the objective functionto optimize the amine-based CO2 capture process in a previous work [Nuchitprasittichai and Cremaschi Comput. Chem. Eng. 2011, 35, 1521−1531]. However, RSM does not provide any information about the quality of the obtained solution. In this paper, the RSM results are compared to those obtained by optimizing a global surrogate model of the system over the whole decision space with a global solver. We used an artificial neural network (ANN) as the global surrogate model. Depending on the accuracy of the global surrogate models, the solutions obtained using them can be shown to be global within the bounds of the data used to generate them. The comparison is used to assess the quality of the RSM results and their relative computational costs. Monoethanolamine (MEA), diglycolamine (DGA), diethanolamine (DEA), methyl diethanolamine (MDEA), triethanolamine (TEA), and blended aqueous solutions of these amines are considered in our analyses. The results reveal that the RSM algorithm yielded optimum solutions close to those obtained by the ANN approach for all solvents. the overall cost of a CO2 capture process12 were performed using a parametric study. The total operating cost was minimized by comparing different schemes of the CO2 capture process. Each scheme was optimized using a logical search plan method.13 The CO2 capture efficiency was maximized, and the operating cost was minimized using a jumping gene based multiobjective simulated annealing technique.14 A proposed mathematical model of both absorber and stripper columns were solved using the General Algebraic Modeling System (GAMS) and CONOPT to maximize the CO2 removal efficiency.15 The total annual cost of the CO2 capture process was minimized for different CO2 emission targets using the mixed optimization option in HYSYS version 3.2. Both operating and investment costs were considered for the study.16 Recently, response surface methodology (RSM) and artificial neural networks (ANNs) have been used to optimize the amine-based CO2 capture process. The RSM minimizes an unknown function by fitting first- or second-order models to small regions to guide the optimization search. The design variables and the operating conditions of the process move along the search direction to find an improved or optimal objective function value. In a previous study, the authors applied RSM to find the optimal operating conditions and design parameters for minimizing the CO2 capture cost.1 However, main disadvantage of the RSM is its inability to return any information regarding the quality of the obtained

1. INTRODUCTION Greenhouse gas emissions, mainly carbon dioxide (CO2), have an impact on global climate change. Power generation from fossil-fuel-fired power plants is known as the largest source of CO2 emissions.2 There are three main technologies used to capture CO2 from the combustion of fossil fuels: precombustion, postcombustion, and oxy-combustion.3−5 In the postcombustion capture, CO2 is recovered from the flue gas, whereas in precombustion capture, carbon is removed from the fuel prior to combustion. In oxy-combustion capture, the fuel is burned using an almost pure oxygen stream resulting in an almost pure CO2 stream. Postcombustion capture offers an advantage over the other two technologies in that it can retrofit existing power plants without requiring significant changes to equipment configurations.2 In the postcombustion capture, chemical absorption is the preferred method to capture CO2 from flue gas with low CO2 concentrations.6 In this process, CO2 reacts with the solvent and forms a weak compound. Then, the absorbent is stripped off of its CO2 by the application of heat.3 Alkanolamines are commonly used as the solvents in chemical absorption.7 However, the high operating and capital costs of a large-scale process of the amine-based CO2 capture prohibits its widespread adaption.8 There have been several studies to optimize the design and operation of the amine-based CO2 capture process.9,10 For example, the stripper reboiler duty was minimized by decomposing the flow sheet into a stand-alone absorber and a stand-alone stripper. This method provided a good initial point for building a combined flow sheet of the CO2 capture process using the aqueous MEA solvent.10 The minimization of the thermal energy requirement for solvent regeneration,11 and © 2013 American Chemical Society

Received: Revised: Accepted: Published: 10236

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Figure 1. Process flow diagram of a conventional amine-based CO2 capture process.

(local) optimum solution. ANNs are currently used as predictive models and for pattern recognition.17 The main advantage of ANNs is that they learn from example, so a prior knowledge of the relationships between the variables is not required. An ANN has been developed to model the solvent regeneration column in the amine-based CO2 capture unit.18 Some of the literature has combined ANNs with sensitivity analysis for studying the amine-based CO2 capture process.19−23 The ANNs were developed for modeling the relationship between independent (input) variables and dependent (output) variables, and the sensitivity analysis was conducted to determinate the influence of each input variable on the predicted output variables.19−23 The quality of the optimization problem solution with ANNs depends on the accuracy of the ANN.24 It has been shown that an ANN with high accuracy coupled with a global optimization technique is able to yield the global optimum within the bounds of the data used to generate the network.24,25 This paper compares the optimum design variables and operating conditions, and the resulting CO2 capture cost obtained by the RSM algorithm1 to the ones obtained by performing the optimization using the ANN approach26 for the amine-based CO2 capture process. The ANN approach uses an artificial neural network as the objective function coupled with the global optimization solver to minimize the total CO2 capture cost of the amine-based process. This comparison provides an assessment about the accuracy and the validity of the RSM results for this process. The results are compared in terms of the number of simulation runs, which is the main computational cost for both simulation−optimization approaches and the quality of the solutions. The aqueous amine solvents in our analysis were both single and blended amines. The single amines are the primary amines monoethanolamine (MEA) and diglycolamine (DGA), the secondary amine diethanolamine (DEA), and the tertiary amines methyldiethanolamine (MDEA) and triethanolamine (TEA). The blended amines are the mixtures of MEA and MDEA, MEA and TEA, DEA and MDEA, and DEA and TEA. A problem statement is given in section 2. The CO2 capture process simulation and economic evaluation are introduced in section 3. A short review of simulation-based optimization and a brief overview of both simulation−optimization approaches1,26 are described in section 4. Section 5 summarizes the required numbers of sample points and simulation runs, and the solutions (which corresponds to the minimum CO2

capture cost) obtained by both approaches, and discusses the results. Finally, section 6 presents the conclusions.

2. PROBLEM STATEMENT Given the feed specifications, the amine solvent, and the required CO2 purity of the product, the goal is to determine the operating conditions and design variables of the amine-based CO2 capture plant which yields the minimum CO2 capture cost. The decision variables are the number of stages for the absorber and stripper columns, the solvent concentration(s), the solvent circulation rate, the reboiler duty, and the regenerator-inlet temperature. Two different simulation− optimization approaches are used for solving this optimization problem: response surface methodology and ANN-based optimization. The RSM results are compared to ones of the ANN approach. 3. PROCESS SIMULATION AND ECONOMIC EVALUATION A conventional amine-based absorption/desorption plant was developed using Aspen HYSYS version 7.1 to process 1365 kg mol/h of gas turbine flue gas. The information about the gas turbine flue gas can be found in our previous work.1 The thermodynamic properties were calculated with the amines property package using the Li−Mather electrolyte model. Figure 1 is a schematic diagram of the amine-based CO2 absorption plant. The inlet flue gas flows in the countercurrent direction with respect to the lean amine solvent inside the absorber column. The solvent reacts chemically with the CO2 in the gas and then leaves at the bottom of the column as rich amine. The washed gas is released to the atmosphere as sweet gas. The rich amine with high CO2 content is heated through the lean/rich amine heat exchanger and sent to the stripper for solvent regeneration. The CO2 and some water vapor leave the stripper through an overhead condenser as the CO2 product. In this work, the product stream is specified to be 96 mol % CO2 purity. The lean amine solvent with less CO2 content leaves the reboiler and then passes through the lean/rich amine heat exchanger where it is cooled. The solvent is then mixed with the makeup water, cooled by the cooling water, and recycled back to the absorber. A purge stream is used when excess water, which is condensed from the flue gas, is present in the system. In Figure 1, the “Make-up Amines 1” stream is used for the process simulations with single amines. Both “Make-up Amines 1” and “Make-up Amines 2” streams are used for the process 10237

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Figure 2. Developed algorithm for the simulation−optimization with ANNs.

The process is repeated until a termination criterion is satisfied.29 In meta-model-based methods, the simulation model is replaced by a surrogate model which is a mathematic function used to represent the relationship between the inputs and the outputs of the system. The common approaches used to construct the surrogate model are statistics-based and machinelearning.32 In the statistics-based approach, the surrogate model is constructed by regression analysis of the decisions variables, values of which are obtained using a preselected design of experiments, and the corresponding outputs. In the machinelearning approach, the data obtained from the simulations are used to train the surrogate model. The artificial neural network is an example of surrogate models obtained using machinelearning approaches. In this study, we focus on simulation-optimization of the amine-based CO2 capture process using meta-model-based approaches. Meta-model-based approaches were chosen because they are the most commonly used simulation− optimization technique,32 and they provide solutions for otherwise intractable problems by using surrogate models to represent the relationship between the inputs and the outputs. The optimum operating conditions and design variables for the amine-based CO2 capture process were obtained using two different approaches: (1) local surrogate models of the objective function were constructed using regression analysis, and the optimization was performed using RSM, and (2) the surrogate model of the objective function was represented with an artificial neural network (ANN) over the whole decision domain and optimization was performed using a global solver. The quality of the solutions obtained from the RSM was tested by comparing them to the results obtained using the ANN with a global optimizer. In what follows, we give brief explanations of both approaches. 4.1. Response Surface Methodology (RSM). RSMs utilize local first- and second-order regression models of objective function to guide the search toward the optimum solution.33 Our previous work1 presented an RSM algorithm to optimize the amine-based CO2 capture process for the minimization of the CO2 capture cost. The developed algorithm includes two main steps. In the first step, the process simulation is run at the input data set (that corresponds to the operating conditions and design variables) generated by a full factorial experimental design and Box-Behnken design (BBD). The combination of the decision variables as the inputs and the CO2 capture cost as the outputs is then used to obtain the first-

simulations with blended amines. Details of the simulation are given in Supporting Information A. Our cost calculations considered both capital and operating costs. The equipment sizing and capital cost was estimated using the equations and the data from the capital equipmentcosting program (CAPCOST).27 The assumptions used in the process simulation and the economic analysis are given in our previous work.1

4. SIMULATION−OPTIMIZATION APPROACHES Simulation−optimization approaches are one of the powerful ways that can be used to solve the cost minimization problem of the CO2 capture process. In these approaches, an optimization module, which searches the decision space systematically, is coupled with a simulation module that evaluates the objective function at decision variable values passed by the optimization module.28 In general, we can group simulation−optimization approaches into four main categories: gradient-based methods, statistical-based methods, meta-heuristic methods, and metamodel-based methods.29 In gradient-based approaches, the derivatives of objective function are estimated from simulation data to guide the search toward the optimum solution. Statistical-based methods are commonly used in problems with discrete decision variables to compare alternatives and to select one of the system configurations for optimum system performance.29 The meta-heuristic method is an iterative search strategy that guides the search process from the current solution to a potentially better solution. The most widely used techniques are Simulated Annealing (SA), which is analogous to the physical annealing process, and Genetic algorithms (GA), which are analogous to biological evoluation.30 In SA, the initial solution is randomly chosen. The neighborhood of the current solution is searched for improved solutions, e.g., in K neighborhood strategy, k neighbor solutions of the current solution are examined. If the objective function improves, the current solution is then replaced by the best neighbor. Otherwise, the current solution is accepted with some probability.29 In GA, a set of initial solutions is generated and, then, evaluated using the simulation model. New solutions are then produced through the selection of the parents (the design solutions) and production of offspring (the new solutions) via genetic operators, i.e., crossover and mutation.31 The new solutions are then evaluated by the simulation model. 10238

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and second-order regression models of the objective function. If the first-order model is deemed accurate, the steepest descent is performed to move the system in the direction of maximum decrease in the objective function. We successfully utilized the R2 with a cutting value of 0.5 and adjusted-R2 statistics in our previous study to assess the fitness of the first- and secondorder response models. Otherwise, the second-order model is used as the objective function, and the optimum operating conditions and design variables of the CO2 capture process is determined using the Solver Add-in which is available in Microsoft Office Excel 2007. More details about the algorithm can be found in our previous study.1 4.2. Optimization Using an ANN as the Surrogate Model of the Objective Function. The optimization algorithm presented in our previous work26 was used in this study. The algorithm consists of two main steps: (1) determination of the appropriate sample size to construct the ANN, (2) optimization by using the constructed ANN with the sample size obtained from the first step as the objective function. The overall algorithm is shown in Figure 2. Table B1 in Supporting Information B gives the upper and lower bounds of decision variables for each amine solvent used in this paper. The upper and lower bounds are the maximum and the minimum values of all subregions explored by the RSM, respectively. In this work, we used a feed-forward ANN of single hidden layer with eight neurons26 to represent the objective function behaviorCO2 capture costin terms of the decision variablesthe number of stages for the absorber and stripper columns, the solvent concentration(s), the solvent circulation rate, the reboiler duty, and the regenerator-inlet temperature. The ANNs were constructed and trained via back-propagation learning algorithm using MATLAB version 7.8.0 (R2009a) and the Neural Network Fitting Tool (nftool). Tangent sigmoid and linear functions were used as the transfer function of the hidden and the output layers, respectively. In the first step, given the starting sample size, which is 10 times number of decision variables, a data set of operating conditions and design variables of the CO2 capture process is generated via the Latin hypercube sampling (LHS) technique. Process simulation and economic analysis is used to calculate the corresponding CO2 capture costs. An ANN is trained and validated using 10-fold cross-validation with the current number of sample points. For each tested sample point in 10-fold cross-validation, the surrogate−model deviation is calculated as the absolute difference between the observed data point (from HYSYS simulation) and the corresponding prediction of the surrogate model. The maximum value of all of the calculated surrogate−model deviations (σmax) is determined. A new sample size is generated using the incremental Latin hypercube sampling (iLHS)26 by increasing the number of sample points one-third of the current sample size and then rounding up to the nearest tenth. The slope value of σmax corresponding to the current iteration counter, i, is then calculated. This procedure is repeated until the slope ratio percentage of σmax stays below a preset value, α (set to 2% in this study), for two consecutive sample sizes. Figure 3 gives the plot of the maximum surrogate−model deviation, σmax, as a function of sample size for the CO2 capture process with aqueous TEA solvent. The percentage numbers shown in Figure 3 are the values of slope ratio percentage, α. The value of σmax changes and then stabilizes as the sample size increases. The slope of σmax at the sample size of 80 was the highest σmax

Figure 3. Maximum surrogate−model deviation, σmax, versus sample size for the CO2 capture process with aqueous TEA solvent.

slope (α = 100%). At the sample sizes of 110 and 150, where the value of σmax is not yet stabilized, the slope ratio percentages are higher than 2%. The two consecutive sample sizes, 200 and 270 samples, show the slope ratio percentage less than 2% (α = 0.93% and 1.24%). Therefore, the algorithm terminates at the sample size of 270 (shown by a solid vertical line in Figure 3), which is the appropriate sample size. In the second step, the data points of the sample size obtained at the termination of the first step are used to construct the ANN. The resulting ANN with its weights and biases and its transfer functions of the neurons are used as the objective function of the bounded optimization problem, which is formulated in GAMS version 23.5 and solved using the global optimization solver BARON version 9.0.6 with relative gap of 0.01. This formulation is given in Supporting Information C.

5. RESULTS AND DISCUSSION A brief summary of the RSM results from our previous study is given in this paragraph for completeness; the details can be found in our previous work.1 The results show that the CO2 capture cost ($ per ton CO2 recovered) decreases as the number of absorber stages increases due to the increased amount of CO2 recovered. The concentrations of the primary and secondary amines have greater impacts on the CO2 capture cost than the concentrations of the tertiary amines. The CO2 capture cost decreases with a decrease in the solvent concentrations of primary amines and with an increase in the solvent concentrations of secondary amines. The reboiler duty affects the CO2 capture cost in terms of the operating cost. The operating cost decreases as the reboiler duty decreases. The number of stripper stages and the regenerator-inlet temperature slightly affect the CO2 capture cost compared to the number of absorber stages. The CO2 capture cost tends to decrease as the number of stripper stages and the regenerator-inlet temperature decrease. In what follows, we compare the results obtained from the RSM technique to the ones obtained by the ANN approach in terms of the number of sample points and simulation runs, and the optimum solutions. 5.1. Numbers of Sample Points and Simulation Runs. Table 1 summarizes the total number of sample points used for constructing the surrogate model used in the optimization problem (column 3) and the total number of simulation runs (column 4) for each amine solvent for both simulation− optimization approaches. Numbers in square brackets in column 4 represent the numbers of total explored regions (including the starting region) in the case of the RSM algorithm and the numbers of total iterations in the case of the ANN approach, respectively. The weights and biases of final ANNs, which give the relationship between the decision 10239

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descent. The following discusses how each set of sample points are generated: (1) Given the domain of each decision variable, full factorial design was used to generate sample points of operating conditions and design parameters of the CO2 capture process at each vertex of the domain. The data set and CO2 capture costs corresponding to these sample points was used to fit a first-order regression model to determine the significant variables. (2) The BBD was used to generate sample points at the middle point of each edge of the N-dimensional hypercube and the midpoint of the entire domain for the variables. The combination of the data sets and CO2 capture costs corresponding to the sample points obtained from the full factorial design and the BDD was used to build a first order regression model and to assess the fitness of the model. (3) The steepest descent was performed to move the system toward the direction of maximum decrease in the CO2 capture cost until an increase in the cost was noted. The number of simulation runs of the steepest descent is equal to the number of steps along the path of that steepest descent. 5.1.2. ANN Approach. In the first part of the optimization algorithm with the ANN approach, we determined the appropriate sample size that is used to build the objectivefunction surrogate model for each amine. The total number of sample points reported in Table 1 (column 3) gives these appropriate sample sizes. The number of simulation runs required for the ANN approach (column 4) is the sum of the number of starting sample points (the first iteration) and the additional sample points generated via iLHS26 for all iterations except the first iteration. It should be noted that the total

Table 1. Number of Sample Points for Each Amine Solvent solvent MEA DGA DEA MDEA TEA MEA− MDEA MEA− TEA DEA− MDEA DEA− TEA

approach

total number of sample points (the surrogate model)

RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN

77 480 77 640 89 480 69 200 77 270 141 350 153 350 141 840 141 630

total number of simulation runs 577 880 715 1216 479 891 232 328 405 484 1141 633 1401 646 513 1682 581 1232

[5] [8] [7] [9] [5] [8] [2] [5] [4] [6] [6] [6] [7] [6] [3] [9] [3] [8]

variables and the CO2 capture cost for all amine solvents, can be found in Supporting Information D. 5.1.1. Response Surface Methodology. The total number of sample points used to construct the surrogate model (column 3) for the RSM approach is the one that is used to build the last second-order regression model in the RSM iterations. The total number of simulation runs showed in column 4 consists of (1) the number of sample points generated by the full factorial design for all explored subregions, (2) the number of sample points generated by the BBD for all explored subregions, and (3) the number of simulation runs for all steps of the steepest

Table 2. Comparison of the Optimum Operating Conditions and Design Variables for the Amine-Based CO2 Capture Process between Both Approachesa CO2 capture costs ($/ton CO2 recovered)

operating conditions and design variables solvents MEA DGA DEA MDEA TEA blended A blended B blended C blended D

approaches

1 (m3/h)

2a (wt%)

RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN RSM ANN

62 58 26 23 33 32 57 57 65 74 59 59 62 55 48 43 47 55

14 13 48 48 39 39

8 10 12 10 32 32 33 33

2b (wt%)

3 (stages)

4 (stages)

5 (kW)

6 (°C)

predicted

actual

error

31 32 21 19 13 13 17 15 22 24 25 25

20 22 20 23 32 32 84 86 44 45 24 21 21 23 27 29 27 26

9 12 7 12 10 8 9 7 10 8 9 12 9 7 9 12 9 11

3848 3356 1903 1582 2087 2352 2687 2772 2543 3000 3678 3365 3681 3474 2687 2514 2668 3217

91 81 99 103 104 94 100 97 101 91 93 83 92 82 98 94 98 88

48.03 48.58 42.67 42.71 46.13 46.22 107.31 107.62 241.70 237.65 48.57 48.23 48.34 48.71 47.02 47.04 45.99 46.51

49.17 48.98 43.06 42.97 46.45 46.66 110.30 109.91 244.29 241.88 48.79 48.42 49.03 48.58 47.33 47.32 46.37 46.87

2.32% 0.82% 0.91% 0.61% 0.69% 0.94% 2.71% 2.08% 1.06% 1.75% 0.45% 0.39% 1.41% 0.27% 0.65% 0.59% 0.82% 0.77%

a

The numbers at the top of the table correspond to the operating conditions and design parameters: 1 represents the solvent circulation rate; 2a represents the solvent concentration of primary or secondary amine; 2b represents the solvent concentration of tertiary amines; 3 represents the number of stages for the absorber column; 4 represents the number of stages for the stripper column; 5 represents the reboiler duty; and 6 represents the regenerator inlet temperature. Blended A, B, C, and D correspond to MEA−MDEA, MEA−TEA, DEA−MDEA, and DEA−TEA, respectively. 10240

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models are within 3% of the original data for the tertiary amines. Hence, the ANN solution is within 1% + 1% (BARON relative optimality gap used to solve the problems) for primary, secondary, and blended amines, and 3% + 1% (BARON relative optimality gap used to solve the problems) for the tertiary amines of the global objective function value. Hence, we will assess the quality of the RSM solutions in comparison to the ANN-approach solutions. The RSM was able to locate the regions of minimum CO2 capture cost within the considered domain of the decision variables for all solvents. The minimum CO2 capture costs obtained from the RSM are slightly different from the ones obtained from the ANN approach for all solvents. Although the regenerator-inlet temperature and the number of stripper stages obtained by RSM are different from those obtained by the ANN approach in some cases, they have little impact on the CO2 capture cost.1 The percent error between the predicted cost and the actual cost obtained from the simulation for both approaches is similar for all solvents except for the MEA solvent. Although the RSM has a higher percent error than the ANN approach in the case of the MEA solvent, the model is able to predict the minimum CO2 capture cost close to the one obtained from the ANN approach. There may be several reasons why the RSM approach yielded minimum CO2 capture costs close to those obtained by the ANN approach in this study. First, the underlying models may be convex. Although the original problem formulation considered in this paper is not convex, the domain of the decision variables used in the ANN approach is defined by the boundaries associated with all explored subregions resulted from the RSM methodology, and the model may be convex within that domain. Second, the quality of the solution obtained by the RSM approach depends on where the search was initialized. It is possible that the RSM approach was initialized at the right starting point, and the local search directions yielded the correct region of minimum CO2 capture cost in case of nonconvex surface. It is also possible that the global optimum solution is robust (i.e., it sits on a flat region) and the change in several of the design variables within that region does not significantly change the CO2 capture cost. Nevertheless, the solutions obtained using the RSM for the CO2 capture process with the initial search space and for the solvents considered were similar to the ones obtained by the ANN approach.

number of required simulation runs in the ANN approach are higher than the sum of sample sizes for all iterations because of the iLHS algorithm.26 Increasing the sample size by any number of additional sample points using the iLHS algorithm does not guarantee that all existing sample points are reused. The number of required simulation runs is lower than the new sample size but greater than the additional sample points. 5.1.3. Comparison of Two Simulation−Optimization Approaches. Table 1 shows that the RSM approach required fewer sample points in constructing the surrogate model used in the optimization than the ones for the ANN approach. This is because the surrogate model in the RSM approach is used to represent a second-order polynomial regression model of the local subregion while the one in the ANN approach is used to represent the highly nonlinear model of the entire domain. In the case of the number of simulation runs, the optimization using ANN as the objective function required a larger number of simulation runs than the RSM algorithm for all aqueous amine solvents except the MEA−MDEA and MEA−TEA mixtures. This is partly due to the geometric increase in the number of sample points between iterations (ni+1 − ni). Furthermore, the iLHS algorithm cannot reuse all existing sample points from the previous data set, i.e., the number of required simulation runs is greater than the number of additional sample points. In case of the MEA−MDEA and MEA−TEA solvents, the RSM algorithm required a larger number of simulations than the ANN approach because it explores several regions (six regions in the case of the MEA−MDEA mixture and seven regions in the case of the MEA−TEA mixture) before finding the region of minimum CO2 capture cost. At each region, the numbers of simulation runs required for a full factorial experimental design for the mixture of amines are considerably high (27 = 128 simulation runs). The DEA−MDEA solvent required a large number of sample points for constructing an accurate ANN (840 sample points). We speculate that the underlying model of the CO2 capture process with the DEA− MDEA mixture is highly nonlinear which results in high fluctuation of the σmax value. 5.2. Optimum Solution. For both simulation−optimization approaches, the optimization was performed once the appropriate surrogate model representing the relationship between the CO2 capture process decision variables and the CO2 capture cost is obtained. The CO2 capture cost obtained from the optimization problem was compared to the one obtained from the process simulation coupled with the economic analysis to test the performance of the surrogate model. Table 2 compares the optimum operating conditions and design variables, and the minimum CO2 capture cost obtained using the RSM algorithm to the ANN approach. The predicted CO2 capture cost (column 10) is the one obtained from the optimization using the surrogate models as the objective functions. The actual cost (column 11) is the one obtained from the process simulation coupled with the economic analysis at the optimum operating conditions and design variables suggested by each approach. 5.2.1. Comparison of the RSM Results to the ANN Results. In this study, the results obtained from the ANN approach is considered to be the gold standard. The ANN approach solution quality depends on the accuracy of the neural network. In this work, the ANN predictions are within 1% of the original data (i.e., CO2 capture cost calculated using HYSYS simulation results) for primary, secondary, and blended amines and the

6. CONCLUSIONS In this work, we optimized a conventional amine-based CO2 capture process to minimize the capture cost using two simulation−optimization approaches: RSM and ANN. RSM uses local searches to estimate an appropriate direction to reduce the objective function while ANN uses simulation to build a global surrogate model of the objective function over the entire decision space and solves the optimization problem using a global solver. The solutions obtained by RSM are compared to the solutions obtained by ANN combined with the global optimization solver to assess the quality of the RSM results. From the results of the number of simulation runs, the minimum CO2 capture cost, and the percent error, it can be concluded that the RSM algorithm performed comparably to the ANN approach and was able to yield solutions close to those obtained by the ANN approach in this study. 10241

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ASSOCIATED CONTENT

S Supporting Information *

A.1: Detailed simulation of the single amine solvents. A.2: Detailed simulation of the blended aqueous amine solvents. B.1: Upper and lower bounds of the operating conditions and design variables. C.1: Optimization formulation of the ANN approach. D.1: ANN constructed with a sample size of 480 for the CO2 capture process with the aqueous MEA absorbent. D.2: ANN constructed with a sample size of 640 for the CO2 capture process with the aqueous DGA absorbent. D.3: ANN constructed with a sample size of 480 for the CO2 capture process with the aqueous DEA absorbent. D.4: ANN constructed with a sample size of 200 for the CO2 capture process with the aqueous MDEA absorbent. D.5: ANN constructed with a sample size of 270 for the CO2 capture process with the aqueous TEA absorbent. D.6: ANN constructed with a sample size of 350 for the CO2 capture process with the aqueous MEA−MDEA absorbent. D.7: ANN constructed with a sample size of 350 for the CO2 capture process with the aqueous MEA−TEA absorbent. D.8: ANN constructed with a sample size of 840 for the CO2 capture process with the aqueous DEA−MDEA absorbent. D.9: ANN constructed with a sample size of 630 for the CO2 capture process with the aqueous DEA−TEA absorbent. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +1-918-631-3422. Fax: +1-918-631-3268. E-mail address: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the University of Tulsa is greatly acknowledged. NOMENCLATURE ni = total number of sample points n at the iteration counter i σmax = maximum surrogate−model deviation α = present value of the slope ratio percentage of the current σmax slope to the highest σmax slope

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