Multiobjective optimization scheme for industrial synthesis gas sweetening plant in GTL process

Journal of Natural Gas Chemistry 20(2011)99–109

Multiobjective optimization scheme for industrial synthesis gas sweetening plant in GTL process Alireza Behroozsarand1∗ , Akbar Zamaniyan2 1. Department of Chemical Engineering, Islamic Azad University, Ilkhchi Branch, P.O.Box: 651335-1996, Tabriz, Iran; 2. Department of Natural Gas Conversion, Gas Research Division, Research Institute of Petroleum Industry (RIPI), Tehran 14665-1998, Iran [ Manuscript received April 9, 2010; revised October 6, 2010 ]

Abstract In industrial amine plants the optimized operating conditions are obtained from the conclusion of occurred events and challenges that are normal in the working units. For the sake of reducing the costs, time consuming, and preventing unsuitable accidents, the optimization could be performed by a computer program. In this paper, simulation and parameter analysis of amine plant is performed at first. The optimization of this unit is studied using Non-Dominated Sorting Genetic Algorithm-II in order to produce sweet gas with CO2 mole percentage less than 2.0% and H2 S concentration less than 10 ppm for application in Fischer-Tropsch synthesis. The simulation of the plant in HYSYS v.3.1 software has been linked with MATLAB code for real-parameter NSGA-II to simulate and optimize the amine process. Three scenarios are selected to cover the effect of (DEA/MDEA) mass composition percent ratio at amine solution on objective functions. Results show that sour gas temperature and pressure of 33.98 ◦ C and 14.96 bar, DEA/CO2 molar flow ratio of 12.58, regeneration gas temperature and pressure of 94.92 ◦ C and 3.0 bar, regenerator pressure of 1.53 bar, and ratio of DEA/MDEA = 20%/10% are the best values for minimizing plant energy consumption, amine circulation rate, and carbon dioxide recovery. Key words amine plant; multiobjective optimization; Non-Dominated Sorting Genetic Algorithm; amine circulation rate

1. Introduction Natural and refinery gases contain typically acid gases in concentrations ranging from a few parts per million to tens of volume percentage [1]. The major acid gases are hydrogen sulfide (H2 S) and carbon dioxide (CO2 ). The typical product is a CH4 -enriched residue stream containing less than 2% CO2 , which is sold as a pipeline fuel [2,3]. Carbon dioxide, which falls into the category of acid gases, is highly corrosive and rapidly destroys pipelines and equipment; it also reduces the heating value of a natural gas stream and wastes pipeline capacity [2,4]. Acid gas removal and dehydration are the most commonly employed processes and various technologies are available to design engineer for these processes [5]. Acid gas removal technologies include absorption with an aqueous alkanolamine solution, cryogenic adsorption and membrane processes [4,6]. The chemical solvents and physical solvents or combination of these two have been used extensively in existing base load LNG facilities. In the past few years, mixed amine solvents for the removal of acid gases have received increased attention. In most cases, the mixtures contain MDEA ∗

as the base amine with the addition of one or two more reactive amines such as MEA or DEA. The major advantage of the amine treatment is that it is a widely commercialized technology in which the hydrocarbon loss is almost negligible. However, the operating and capital costs shoot up very rapidly as the concentration of carbon dioxide in the feed gas increases [2]. Technology using alkanolamine solutions, or simple amine solutions, for the removal of hydrogen sulfide and carbon dioxide from natural gas has been around for decades. Since the 1960s and 1970s, several amines have come into general use, but there is little information available on which amine is best suited to a particular service. Many inefficient amine gas sweetening units can be optimized by simply changing their amine solutions [7]. Aqueous alkanolamine solutions are widely used for the removal of acid gases such as CO2 and H2 S from gas streams. Examples of such streams include natural gases, synthesis gases from the gasification of coal and heavy oils, and tail gases from sulfur plants and petroleum chemical plants. Aqueous solutions of alkanolamines react reversibly with acid gases and therefore

Corresponding author. Tel: +98(412)3459142; Fax: +98(412)3444355; E-mail: [email protected] (A.Behroozsarand)

Copyright©2011, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. All rights reserved. doi:10.1016/S1003-9953(10)60153-3

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are widely used to remove them. The alkanolamines solution groups include monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), di-propanolamine (DIPA), and diglycolamine (DGA). Although the acid gasamine reactions are reversible, irreversible reactions may also occur, resulting in the products from which the amines are not easily recovered. The Fischer-Tropsch process (or Fischer-Tropsch Synthesis) is a catalyzed chemical reaction in which synthesis gas (syngas), a mixture of carbon monoxide and hydrogen, is converted into liquid hydrocarbons in various forms. The most common catalysts are based on iron and cobalt, although nickel and ruthenium have also been used. The principal purpose of this process is to produce synthetic petroleum, typically from coal, natural gas or biomass. In the FT process, produced synthesis gas enters gas sweetening plant to capture carbon dioxide and hydrogen sulfide. According to experimental data, in iron based FT process, carbon dioxide and hydrogen sulfide concentrations in synthesis gas stream must be lower than 2% (mol%) and 10 ppm, respectively. Because higher carbon dioxide and hydrogen sulfide contents cause side reactions and deactivate iron catalysts. In this paper, an industrial amine plant is simulated us-

ing HYSYS v.3.1 software. The plant is used for carbon dioxide and hydrogen sulfide capture from synthesis gas in the FT process (iron catalyst based). After that, three optimization scenarios of plant using Non-Dominated Sorting Genetic Algorithm-II is performed by considering minimizing the plant energy consumption, amine circulation rate, and maximizing carbon dioxide recovery. 2. Amine treating facility Figure 1 represents a simple amine treating facility. Sour gas is introduced in the absorber where it contacts lean amine solution traveling down the column. The acid gas component, CO2 and H2 S, is absorbed by the amine solution and the sweet gas leaves the absorber for further processing. The rich amine solution is sent to a flash tank and absorbed hydrocarbons exit as the flash-tank vapor. The rich amine flows through the lean/rich exchanger to increase the temperature to about 90−110 ◦ C. The hot rich amine is stripped at low pressure to remove the absorbed acid gases, dissolve hydrocarbons and some water. The energy required to strip the amine is the sum of the sensible heat required to raise the solution temperature, the energy of absorption, and latent heats [8].

Figure 1. Schematic of simple amine sweetening plant [8]

The pressure of stripping column should be operated at as high as possible to increase the reboiler temperature for optimum stripping [9]. However, the amine degradation temperature should not be exceeded. The stripped or lean amine is sent back through the lean/rich exchanger to decrease its temperature. A pump boosts the pressure such that it is greater than the absorber column. Finally, a heat exchanger or air cooler cools the lean solution before the loop is back to the absorber completely. In this study, the response factors are the plant energy consumption (tower energy), amine circulation rate, and carbon dioxide recovery: E Net = (QCondunsor + QCooler) + (QPump − QReboiler)

(1)

RCirculation = Amine circulation molar flow (kgmole/h) (2) CO2 recovery (ReCO2 )(%) =

F(CO2 )in − F(CO2 )out × 100 F(CO2 )in (3)

3. Genetic algorithm for multiobjective optimization 3.1. Genetic algorithm As the new methods, genetic algorithms have been suc-

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cessfully applied to nonlinear optimization problems in many dimensions, where traditional methods are often found to fail [10]. Moreover, more traditional ones such as deterministic and gradient-based optimization methods do not search the parameter space and can tend to converge towards local extreme of the fitness function. It is clearly unsatisfactory for problems where the fitness varies non-monotonously with parameters. On the other hand, genetic algorithms are able to depart from local optima due to the variability of the parameters within the ”gene pool” and the element of randomness inherent within the methods. Furthermore, genetic algorithms do not require knowledge of the gradient of the fitness functions, which makes them particularly suited to optimization problems for which an analytical expression is not known for the fitness functions.

provide a true picture of trade-offs for the decision-maker. (3) The best-known Pareto front should capture the whole spectrum of the Pareto front. This requires investigating solutions at the extreme ends of the objective function space [11].

3.2. Multiobjective optimization

3.4. Model equations for process parameter optimization

There are two general approaches to multiple-objective optimization. One is to combine the individual objective functions into a single composite function or move all but one objective to the constraint set. In the former case, determination of a single objective is possible with methods such as utility theory, weighted sum method. But the problem lies in the proper selection of the weights or utility functions to characterize the decision-maker’s preferences [11]. The second general approach is to determine an entire Pareto optimal solution set or a representative subset. A Pareto optimal set is a set of solutions that are non-dominated with respect to each other. While moving from one Pareto solution to another, there is always a certain amount of sacrifice in one objective(s) to achieve a certain amount of gain in the other(s). Pareto optimal solution sets are often preferred to single solutions because they can be practical when considering real-life problems since the final solution of the decision-maker is always a trade-off. Pareto optimal sets can be of varied sizes, but the size of the Pareto set usually increases with the increase in the number of objectives. The ultimate goal of a multiobjective optimization algorithm is to identify solutions in the Pareto optimal set. However, identifying the entire Pareto optimal set, for many multiobjective problems, is practically impossible due to its size. In addition, for many problems, especially for combinatorial optimization problems, proof of solution optimality is computationally infeasible. Therefore, a practical approach to multiobjective optimization is to investigate a set of solutions (the best-known Pareto set) that represent the Pareto optimal set as well as possible. With these concerns in mind, a multiobjective optimization approach should achieve the following three conflicting goals [12]: (1) The best-known Pareto front should be as close as possible to the true Pareto front. Ideally, the best-known Pareto set should be a subset of the Pareto optimal set. (2) Solutions in the best-known Pareto set should be uniformly distributed and diverse over the Pareto front in order to

The optimization problem is considered for an industrial retrofit amine plant. In this optimization, sour gas flow rate is constant. By study of sensitivity analysis of effective parameters on objective functions (Section 4.1), the trend of three main objective functions, amine circulation rate, plant energy consumption, and carbon dioxide recovery, were investigated in wide ranges of operation conditions. It can logically search for operating scenarios that will minimize plant energy consumption, amine circulation rate and maximize carbon dioxide recovery simultaneously. Performing a constrained optimization with both of them as objectives can identify such scenarios. The optimization problem can be expressed mathematically as following: Minimize

3.3. Multiobjective GA Being a population-based approach, GA is well suited to solve multiobjective optimization problems. A generic singleobjective GA can be modified to find a set of multiple nondominated solutions in a single run. The ability that GA simultaneously searches different regions of a solution space makes it possible to find a diverse set of solutions for difficult problems with non-convex, discontinuous, and multi-modal solutions spaces.

Object (1) = ENet

(4)

Object (2) = RCirculation

(5)

Object (3) = ReCO2

(6)

Maximize Subject to six decision variables: 12.5 ≤ FDEA /FCO2 ≤ 14.5

(7)

27 ≤ T Sourgas(◦ C) ≤ 35

(8)

10 ≤ P Sourgas (bar) ≤ 15

(9)

90 < TReg.gas (◦ C) < 95

(10)

3.0 < PReg.gas (bar) < 7.0

(11)

1.5 < PRegenerator (bar) < 2.0

(12)

(MDEA/DEA) Mass(%) = 0%/30%− 10%/20% − 20%/10%

(13)

CO2 (Mole%)@Sweet gas < 2.0%

(14)

H2 S(Mole%)@Sweet gas < 10 ppm

(15)

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The range of the feed temperature, feed pressure, pressure of regeneration gas, regenerator pressure, and DEA/CO2 molar flow ratio constraints have been selected based on the general industrial amine plants data and sensitivity analysis of simulation results. The ratio of (DEA/MDEA) mass composition percentage at amine recycling stream is the special decision variable. Because of changing value of this variable among simulation running is impossible, three scenarios have been predicted for studying effect of ratio of (DEA/MDEA) mass composition percentage on optimization problem. Three scenarios are: (1) DEAmine and MDEAmine mass composition percentages in recycling amine stream are equal to 30% and 0%, respectively. (2) DEAmine and MDEAmine mass composition percentages in recycling amine stream are equal to 20% and10%, respectively. (3) DEAmine and MDEAmine mass composition percentages in recycling amine stream are equal to 10% and 20%, respectively.

Table 2. Gas sweetening plant operation conditions Parameter Amine circulation rate (kgmol/h) Absorber column top/bottom pressure (bar) Absorber column top/bottom temperature (◦ C) Stripper column top/bottom pressure (bar) Stripper column top/bottom temperature (◦ C) Number of actual tray (absorber) Number of actual tray (stripper)

Value 39440 14.4/14.9 24/48 1.18/2.5 48/124 18 22

Table 3 presents results of the model output and industrial data. It shows that the model is able to predict the plant performance with high accuracy. Table 3. Comparison between simulation and plant data Parameters Rich amine loading Lean amine loading CO2 of sweet gas (mol%) Absorber column top (◦ C) Bottom temperature (◦ C) Stripper column top (◦ C) Bottom temperature (◦ C)

Operating data 0.45 0.08 <0.4 24 48 55 124

Simulation data 0.43 0.07 0.3 25.5 44.66 50 126

R.E. (%) 4.44 12.50 − 6.25 6.96 9.09 1.61

Relative error (R.E.) (%) = Absolute ((Operating data–Simulation data)/Operating data)×100

4. Results and discussion 4.1. Simulation and sensitivity analysis A typical Iranian gas plant (Kangan gas refinery) is selected for this study. The gas sweetening facility has multiple amine trains for CO2 and H2 S removal. Each train is composed of one absorber and one stripper column. The HYSYS v.3.1 plant simulator was used to simulate the process. The Amine Package thermodynamic model was used. The absorber feed gas composition is shown in Table 1. It shows that the feed contains mainly H2 , CO, CO2 , H2 S, and CH4 that the CO2 and H2 S should be removed. Operating conditions are summarized in Table 2.

In the following section effects of process variables on objective functions are considered. 4.1.1. Sour gas temperature Figure 2 presents effect of sour gas temperature on tail gas methane flow (FCH4 ), plant energy consumption (ENet ),

Table 1. Sour gas stream composition data Parameter Mass flow (kg/h) STD gas flow (STD·m3 /h) Component name Hydrogen CO CO2 H2 S Methane H2 O Oxygen Nitrogen Ethane Propane i-Butane n-Butane n-Pentane i-Pentane DEAmine MDEAmine

Value 108448.8 118222.2 Composition (mol%) 29.83 29.25 19.38 0.68 15.95 2.41e-01 0 0 3.42 1.01 1.62e-04 1.93e-01 1.49e-02 2.16e-02 0 0

DEAmine: ρ = 1095 kg/m3 , MW = 105.14; MDEAmine: ρ = 1040 kg/m3 , MW = 119.17

Figure 2. Effect of sour gas temperature on objective functions and tail gas molar flow

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amine circulation rate (RCirculation ) and carbon dioxide mole percentage of sweet gas (CO2 (%)). The carbon dioxide mole percentage of sweet gas represents the carbon dioxide recovery behavior. It is obvious that both tail gas methane flow and plant energy consumption are increased and amine circulation rate is decreased with the increase of the sour gas temperature as an adjustable input variable. From 22 ◦ C to 32 ◦ C of sour gas temperature, the CO2 mole percentage is decreased, but at higher temperature, this parameter is increased. It is clear that the increase of plant energy consumption and tail gas flow is undesirable because of economic and environmental aspects. According to trend of parameters in Figure 2 and optimization purpose, temperature between 25 ◦ C to 35 ◦ C is the best choice for sour gas temperature constraint. In this simulation, amine circulation rate has been adjusted by ratio of DEAmine to CO2 molar flow.

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DEAmine liquid phase in absorption tower. According to Figure 3 the above pressure (10−15 bar) is acceptable value for sour gas pressure. According to the literatures [13,14–17], FT reactions occur at 15−30 bar. But high manufacturing and facility cost of amine plant in the high pressure urges us to choose the lowest possible pressure of 15 bar. 4.1.3. DEA/CO2 molar f low ratio Figure 4 presents effect of ratio of DEAmine to feed CO2 molar flow on FCH4 , ENet , RCirculation and carbon dioxide mole percentage of sweet gas. It is clear that increasing DEA/CO2 molar flow causes all parameters, except carbon dioxide mole percentage of sweet gas increased.

4.1.2. Sour gas pressure Figure 3 shows effect of sour gas pressure on FCH4 , ENet , RCirculation and carbon dioxide mole percentage of sweet gas. By increasing sour gas pressure, all parameters, except FCH4 are increased. Therefore increasing sour gas pressure has unfavorable effect on optimization objects. It must be noted that regularly inputting sour gas to amine plant has pressure about 10 to 15 bar. High pressure is needed for solving gas phase in

Figure 4. Effect of DEA/CO2 molar flow ratio on objective functions and tail gas molar flow

In industrial cases, such as hydrogen plant, the carbon dioxide mole percentage in feed gas is limited to prevent the catalyst deactivation in the reactors. So in some cases we must use high amine circulation rate for this purpose. Using the wide range of DEA/CO2 molar flow ratio in optimization problem for observing plant treatment is proposed. 4.1.4. Regeneration gas temperature Figure 3. Effect of sour gas pressure on objective functions and tail gas molar flow

Figure 5 presents effect of regeneration gas temperature on FCH4 , ENet , RCirculation and carbon dioxide mole percent-

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age of sweet gas. Increasing regeneration gas temperature decreases the four parameters. According to Figure 5 carbon dioxide mole percentage of sweet gas is almost constant after temperature above 93 ◦ C. It is noted that increasing regeneration gas temperature causes that duty of heat exchanger before regeneration tower is increased and mechanical design of stripper should be performed in higher temperature. So the best temperature range could be gained by considering all parameters (90–95 ◦ C).

pressure and high temperature has high yield. Therefore high pressure in stripper is suitable for stripping of CO2 and other light soluble gases from DEAmine liquid phase.

Figure 6. Effect regeneration gas pressure on objective functions and tail gas molar flow

Figure 5. Effect of regenerated gas temperature on objective functions and tail gas molar flow

4.1.5. Regeneration gas pressure Figure 6 presents effect of regeneration gas pressure on FCH4 , ENet , RCirculation and carbon dioxide mole percentage of sweet gas. According to Figure 6 minimum ENet , RCirculation and carbon dioxide mole percentage of sweet gas are obtained at low pressure of regeneration gas. But at low pressure, methane molar flow of tail gas is increased. 4.1.6. Regeneration tower pressure Figure 7 presents effect of regeneration tower pressure on RCO2 , ENet , RCirculation , and carbon dioxide mole percentage of sweet gas. As an industrial experience, stripping at low

Figure 7. Effect of regeneration tower pressure on objective functions and tail gas molar flow

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4.1.7. DEA/MDEA mass f low ratio

Table 4. Effect of an increase in the decision variable on the objective functions

After running optimization problem code without DEA/MDEA mass composition ratio as decision variable, the effect of this parameter is investigated on final Pareto optimal solution sets of optimization problems. All results of three scenarios are shown in Figure 8.

Objective Effect of increase in function TSourgas PSourgas TReg.gas PRegenerator PReg.gas F DEA /F CO2 Net plant energy ↑ ↓ ↓ ↑ ↑ ↑ consumption (MJ/h) Amine circulation ↓ ↑ ↓ ↑ ↑ ↑ rate (kgmole/h) RCO2 ↑ ↑ ↑ ↓ ↑↓ ↓ (kgmole/h)

The objective functions were optimized to fulfil the constraints given in Eqs. (7)–(15). As stated earlier the NSGAII algorithm was used to obtain the Pareto optimal solutions. A MATLAB code for real-parameter NSGA-II described in previous section has been used to optimize the parameters. A population size 50 was chosen with cross over 0.9 and mutation probability of 0.1. All governing parameters of NSGA-II are presented in Table 5. The different operations were performed for 100 generations to obtain the nondominated Pareto optimal solutions. The Pareto optimal solution sets after 100 generations for three scenarios are shown in Tables 6–8. Table 5. Governing parameters of NSGA-II Figure 8. Effect of DEA/MDEA ratio on Pareto optimal solution sets

4.2. Optimization results The optimization problem involves three objective functions: RCO2 , ENet , and RCirculation . Table 4 shows the effect of variation in the decision variables on the objective functions. It has been generated based on a parametric sensitivity analysis of the simulated mathematical model of the system.

Parameter name Number of decision variables Number of objectives Population size Maximum generations Replace proportion Tournament pool size Crossover method Crossover probability Mutation method Mutation probability

Method & value 6 3 50 100 0.9 2 two point 0.9 selective 0.1

Table 6. Non-dominated Pareto optimal solutions after 50 generations for scenario (1) Pop. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Ratio of F DEA /F CO2 14.41 13.68 12.52 15.44 12.54 15.49 15.44 15.50 12.54 12.88 15.44 13.90 15.44 15.49 13.63 14.70 15.50 15.21 15.44 13.74 13.89 12.54

TFeed 25.63 34.65 33.24 34.61 33.55 34.96 34.57 33.39 33.24 34.65 34.57 34.69 34.41 34.65 34.65 34.61 33.39 34.69 34.57 34.65 34.69 33.27

PFeed 12.24 11.53 12.96 14.92 14.65 14.75 14.92 14.65 12.96 14.65 14.98 14.71 14.92 14.65 14.65 14.82 14.65 14.71 14.92 13.78 14.78 12.96

TReg.Feed 92.88 92.29 94.76 88.84 93.67 89.75 87.31 94.06 94.76 94.14 89.16 93.86 88.84 91.39 94.14 94.06 94.69 94.49 86.92 94.06 93.86 94.76

PReg.Feed 5.76 3.00 3.00 6.72 3.03 3.53 6.56 6.59 3.00 3.05 4.96 6.59 6.53 6.84 3.05 6.59 5.59 6.84 6.72 5.53 5.59 3.06

PTower 1.57 1.95 1.55 2.00 1.55 2.00 2.00 2.00 1.55 1.85 2.00 2.00 1.97 2.00 1.83 1.81 1.56 1.87 2.00 1.96 2.00 1.53

FCirculation 32021.90 29799.19 24826.77 40015.87 25608.94 37439.61 40516.63 36267.71 25250.35 26712.16 39034.89 32183.63 39692.15 37705.57 28394.99 33358.37 33769.58 35015.05 40973.45 30938.41 31609.73 25110.44

ENet 4.32 4.05 4.07 4.52 4.24 4.03 4.50 2.98 4.55 3.76 4.52 3.43 4.57 3.93 3.75 4.36 4.87 3.96 4.56 3.21 3.58 4.22

ReCO2 96.68 97.37 93.69 99.96 95.51 99.43 99.93 98.11 94.90 96.39 99.94 98.09 99.99 99.28 97.75 99.28 99.40 99.13 100.02 97.32 98.25 94.33

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Pop. No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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Ratio of F DEA /F CO2 12.52 12.90 12.82 15.45 15.44 15.05 15.44 15.50 12.82 13.63 15.49 13.63 14.45 12.52 15.39 15.45 14.03 15.49 13.68 13.98 12.62 15.10 14.68 12.71 13.90 15.44 12.54 15.49

TFeed 33.24 32.61 33.47 34.57 33.24 33.16 34.61 33.31 33.47 33.86 34.96 34.65 34.65 33.24 34.69 34.61 32.53 34.65 34.69 34.76 33.24 33.16 32.10 32.69 34.69 34.57 33.55 34.80

PFeed 13.75 13.27 14.22 14.92 14.22 14.22 14.96 14.65 14.22 14.65 14.75 14.65 14.02 13.75 14.82 14.71 14.92 14.65 14.78 14.69 14.39 14.18 14.82 14.92 14.71 14.92 14.63 14.69

Table 6 (Continue) TReg.Feed PReg.Feed 94.45 3.03 93.55 3.00 94.14 3.55 87.86 5.76 94.73 3.00 93.82 3.55 93.86 5.59 94.22 3.55 94.06 6.53 92.29 3.00 89.75 3.53 94.69 3.58 93.51 3.13 94.45 5.04 87.90 4.90 93.86 6.59 93.86 6.47 91.67 4.96 93.86 5.59 94.06 4.58 91.51 5.53 94.45 3.28 94.02 5.02 93.90 6.80 94.14 5.76 94.49 6.84 93.67 4.25 94.69 4.58

PTower 2.00 1.95 1.97 1.57 1.55 1.94 2.00 1.98 1.97 1.95 1.97 1.54 1.55 1.98 1.87 1.99 2.00 2.00 2.00 1.81 1.96 1.94 1.99 1.55 1.57 1.87 1.57 1.81

FCirculation 25987.16 27067.23 27308.13 38226.82 31672.37 33037.09 35906.52 34431.86 28967.07 29328.06 37295.07 28089.13 29974.68 27444.43 38570.81 36797.02 32320.15 37014.48 31292.39 30860.94 29122.81 32638.78 33545.55 27790.74 30509.02 35499.88 26320.64 34367.41

ENet 3.72 3.58 3.69 5.31 4.86 3.99 3.74 4.00 3.59 3.75 4.32 4.12 4.73 3.36 3.72 4.32 4.03 3.88 3.40 3.72 3.36 4.01 3.45 4.42 4.42 3.75 3.92 4.45

ReCO2 95.00 95.98 96.39 100.00 99.25 98.98 99.06 99.24 96.60 97.85 99.72 97.63 98.76 95.19 98.73 99.76 98.78 99.22 97.91 98.15 95.90 98.98 98.30 96.81 98.42 98.86 95.32 99.63

ENet 2.87 3.77 4.99 3.99 4.06 4.38 3.78 3.66 3.69 4.24 3.97 3.41 4.26 3.51 4.56 4.52 4.47 4.51 3.43 4.05 3.55 3.62 3.56 3.49 4.17 3.66 4.26 4.79 3.31 3.83 3.86

ReCO2 97.43 99.28 99.61 99.55 97.29 97.87 99.02 99.10 99.19 98.15 99.47 98.45 98.84 98.78 98.85 99.13 99.41 99.85 97.68 98.85 98.28 98.73 98.70 98.69 99.72 97.47 97.74 99.40 98.23 99.37 99.36

Table 7. Non-dominated Pareto optimal solutions after 50 generations for scenario (2) Pop. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Ratio of F DEA /F CO2 13.70 15.21 15.42 15.42 12.58 12.58 14.82 14.71 14.72 12.72 15.42 13.54 13.81 15.42 13.68 15.22 15.42 15.35 12.58 15.46 13.54 13.79 15.42 13.91 15.02 12.57 12.63 15.04 14.71 15.22 15.49

TFeed 34.10 34.14 34.80 34.96 33.98 33.98 33.98 34.80 34.96 33.94 34.57 34.84 33.59 32.14 34.14 34.06 34.96 32.96 34.14 32.14 34.14 33.59 32.14 34.96 29.94 29.12 34.14 34.80 34.80 34.06 34.76

PFeed 14.96 14.96 14.75 14.90 14.96 14.96 14.96 14.71 14.90 14.86 14.75 15.00 14.92 14.92 14.92 14.96 14.90 14.86 15.00 14.92 14.96 15.00 14.92 14.86 14.90 14.96 14.80 14.75 14.73 14.96 14.96

TReg.Feed 94.96 94.96 94.92 93.78 94.92 94.92 94.96 93.71 95.00 94.73 92.53 94.96 94.92 94.92 94.92 94.92 93.98 94.96 94.14 94.92 94.96 94.92 94.92 93.47 93.86 94.14 94.92 94.92 93.71 92.45 94.96

PReg.Feed 6.72 6.97 3.00 6.45 3.00 3.00 6.72 4.96 6.65 3.03 6.97 5.42 3.00 3.00 3.00 3.00 3.02 6.47 3.00 3.02 4.96 4.02 3.00 4.96 6.45 3.05 3.00 3.03 4.96 6.75 6.72

PTower 2.00 1.97 1.53 2.00 1.53 1.53 2.00 2.00 2.00 1.53 1.97 2.00 1.53 1.97 1.53 1.53 1.55 1.75 1.97 1.75 2.00 2.00 1.97 2.00 2.00 1.72 1.53 1.50 2.00 2.00 2.00

FCirculation 28131.68 31948.39 26947.94 31685.64 23390.28 23727.08 29775.30 32160.48 31487.72 24208.43 32417.23 28886.48 26123.49 29559.55 25929.24 26483.11 29400.41 32583.21 25051.41 27701.40 27187.81 28545.53 28307.85 30434.37 33590.10 24742.20 23843.07 27820.35 28974.81 32785.39 31181.13

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Table 7 (Continue) Pop. No. 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Ratio of F DEA /F CO2 12.58 15.42 13.65 14.71 15.42 12.81 15.49 15.30 15.45 13.79 15.37 15.42 12.81 13.37 12.58 12.78 13.68 15.44 12.58

Pop. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Ratio of F DEA /F CO2 14.58 14.31 12.71 15.50 12.51 12.71 15.50 13.34 15.41 13.62 15.50 14.84 12.51 13.62 15.06 15.45 15.50 12.86 15.50 12.71 14.18 15.50 14.82 15.50 13.34 12.86 13.62 12.92 14.78 12.71 15.08 14.02 15.48 15.41 13.32 12.71 13.62 12.86 15.50 12.57

TFeed 33.82 34.96 34.14 34.80 34.33 32.33 34.92 34.76 34.06 33.71 34.18 32.14 32.33 34.14 31.63 34.76 32.92 34.92 34.14

PFeed 14.96 14.92 15.00 14.86 14.76 14.92 14.88 14.96 14.96 14.90 14.75 14.92 14.92 14.96 11.24 14.71 14.82 14.88 14.96

TReg.Feed 91.98 94.69 94.14 94.18 93.63 94.92 89.94 93.67 94.92 93.86 94.92 94.92 93.67 94.96 94.29 94.92 94.92 94.92 94.61

PReg.Feed 4.95 3.13 3.00 6.47 4.68 6.22 6.22 3.08 3.00 6.33 3.00 6.22 3.00 4.96 3.02 3.00 3.00 6.47 4.02

PTower 1.85 1.97 1.97 2.00 2.00 1.94 2.00 1.62 1.54 2.00 1.53 1.94 1.97 1.97 1.75 1.54 1.53 2.00 2.00

FCirculation 26875.38 28652.07 27410.65 29985.71 30566.57 27568.34 33210.74 28382.12 26693.94 30153.22 28754.86 30981.70 25755.67 28067.32 24481.82 23964.91 25595.16 31313.45 26320.91

ENet 3.23 3.65 3.55 3.47 3.57 3.53 3.92 4.41 4.60 2.89 4.49 4.03 3.48 3.39 3.82 4.07 4.22 3.57 3.35

ReCO2 97.17 98.96 98.59 98.56 98.86 98.02 99.40 99.17 99.30 97.73 99.17 99.33 97.90 98.22 96.15 97.53 98.27 98.97 97.81

ENet 3.00 4.24 3.89 3.63 3.96 4.35 4.12 3.54 4.15 3.52 3.73 4.76 3.79 3.50 3.76 3.90 3.74 3.58 3.67 4.41 3.62 3.70 3.94 3.72 4.10 3.35 4.56 3.57 3.55 4.43 4.29 3.59 3.87 3.59 3.55 3.50 4.28 3.73 4.49 3.61

ReCO2 93.69 94.83 93.72 96.23 92.78 93.83 97.06 94.27 96.71 95.19 97.21 96.06 93.45 93.13 96.97 96.02 96.00 94.07 96.21 93.59 96.06 96.03 96.60 96.94 95.06 93.52 95.78 94.05 96.30 94.02 95.69 94.74 96.14 96.91 94.66 93.78 95.39 93.22 96.61 93.40

Table 8. Non-dominated Pareto optimal solutions after 50 generations for scenario (3) TFeed 32.22 34.92 32.33 34.92 34.41 32.33 34.92 32.92 34.96 34.76 34.29 33.67 34.45 32.37 35.00 34.57 34.76 32.45 34.76 31.08 34.29 34.88 33.63 34.92 33.51 31.86 34.84 34.96 34.92 32.33 34.88 31.94 34.76 34.96 34.92 32.33 34.84 32.45 34.37 34.92

PFeed 14.61 14.76 14.88 14.92 14.82 14.88 14.75 14.75 14.98 14.76 14.76 14.88 14.82 14.82 14.88 14.59 14.75 14.82 14.90 14.88 14.86 14.59 14.88 14.92 14.82 14.82 14.76 14.75 14.76 14.86 14.75 14.82 14.75 14.98 14.84 14.90 14.76 14.98 14.76 14.82

TReg.Feed 94.06 94.73 94.69 94.96 94.76 94.10 94.41 95.00 94.88 94.73 94.73 93.78 94.76 94.73 94.73 94.88 94.96 94.88 95.00 94.10 94.76 94.88 94.61 94.96 94.76 94.88 94.10 95.00 94.73 94.10 94.76 95.00 94.65 94.88 94.96 94.92 94.73 93.63 94.73 94.49

PReg.Feed 3.88 3.22 3.03 3.13 3.22 3.16 3.16 3.16 3.03 3.05 3.24 3.16 3.16 3.03 3.22 3.13 3.16 3.03 3.03 3.03 3.03 3.00 3.03 3.25 3.16 3.66 3.09 3.03 3.09 3.16 3.13 3.03 3.16 3.03 3.25 3.16 3.72 3.03 3.24 3.05

PTower 1.97 1.61 1.63 2.00 1.61 1.52 1.69 2.00 1.73 1.98 1.61 1.52 1.60 1.98 1.61 1.73 1.93 1.98 1.98 1.52 1.99 1.98 1.71 1.98 1.60 2.00 1.57 1.86 1.98 1.52 1.62 1.95 1.90 1.69 1.98 1.98 1.61 1.73 1.61 1.95

FCirculation 26204.43 24412.11 23409.50 27654.04 22965.42 23542.73 28801.91 25101.52 26965.30 25994.32 28943.72 25667.45 23179.78 23858.89 27920.54 26670.43 27191.27 24699.30 27446.96 23345.66 27484.10 27260.29 27832.48 29507.30 24802.83 24930.76 25268.04 24220.51 28072.84 23714.71 25552.70 25581.56 27323.72 28002.22 25383.75 24560.45 25786.79 23643.33 26859.51 24057.30

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Table 8 (Continue) Pop. No. 41 42 43 44 45 46 47 48 49 50

Ratio of F DEA /F CO2 12.92 12.61 14.84 12.65 14.82 13.90 12.51 12.61 14.78 13.32

TFeed 34.96 33.82 34.92 31.86 33.35 34.92 34.53 34.06 34.92 34.76

PFeed 14.75 14.78 14.76 14.82 14.88 14.92 14.82 14.78 14.76 14.88

TReg.Feed 95.00 94.76 94.73 94.88 94.61 94.96 94.73 94.18 94.73 93.98

Figure 8 shows the Pareto set of optimal solutions obtained for the problem formulated above with considering DEA/MDEA ratio as decision variable. The values of ENet , RCirculation and RCO2 are plotted. The points in the Pareto set (Figure 8) indicate the minimum possible of ENet , RCirculation or maximum possible of RCO2 with the given operating constraints. The benefit of a multiobjective optimization is evident upon observing the wide choice of operating points available in the Pareto-optimal set. The CPU time taken to generate one set of Pareto-optimal solutions (such as those in Figure 8) is 100 min on the Pentium (R) 4 CPU 3.00GHz, 512 MB of RAM computer. The final optimal set results of NSGA-II algorithm (Tables 6−8) have been sorted smallest to largest of objective

PReg.Feed 5.04 3.16 3.22 3.66 3.03 3.25 3.36 3.09 3.16 3.03

PTower 1.87 1.60 1.98 1.90 1.69 1.95 1.98 1.86 1.57 1.71

FCirculation 23501.86 23269.08 26383.49 24566.47 27596.40 26627.28 24393.24 23070.03 25048.45 25162.35

ENet 3.66 3.76 3.58 3.43 4.10 3.56 3.51 3.68 4.38 4.06

ReCO2 91.47 93.54 95.33 93.34 96.60 95.63 93.41 92.08 95.33 95.01

functions value. Figure 9(a) shows the effect of DEA/MDEA mass composition percentage ratio on amine solution circulation rate. By increasing MDEA mole fraction of amine solution, circulation rate is decreased. Figure 9(b) represents the effect of DEA/MDEA mass composition percentage ratio on energy consumption. It is clear that by increasing ratio of DEA/MDEA in amine solution, the net energy consumption is decreased. This is because according to the previous figure, circulation rate is decreased when ratio of DEA/MDEA is increased. However, Figure 9(c) shows that increasing ratio of DEA/MDEA has unsuitable effect on CO2 recovery. It seems that DEA = 20% (MW%) and MDEA = 10% (MW%) are the desired compositions in amine solution but in special applications there may be some objective functions

Figure 9. Comparison of three objective functions in three scenarios of DEA/MDEA ratio

Journal of Natural Gas Chemistry Vol. 20 No. 1 2011

that are more important than the others or some industrial constraints may exist. For example, CO2 recovery must be higher than 97%. In these cases user may select the practical optimal solution sets that satisfy the industrial constraints. Figure 9(d) represents the comparison of Pareto optimal sets of three scenarios. According to this figure, Scenarios (2) and (3) have lower circulation rate than the Scenario (1). On the other hand, Scenario (2) has the highest CO2 recovery. As mentioned above, it seems that DEA = 20% (MW%) and MDEA = 10% (MW%) are the better choice for operating condition of amine plant. Therefore, three sets of solutions are selected as optimal solutions from Table 7 (Related to DEA = 20% (MW%) and MDEA = 10% (MW%) scenario shown in Table 10). In the solution set Number 1, the plant energy consumption is minimized, in the solution set Number 2, the amine circulating rate is minimized, and in solution set Number 3, the carbon dioxide recovery is maximized. 5. Conclusions A gas sweetening plant was simulated and optimized by NSGA-II method. In amine plant some important parameters such as amine solution circulation rate, CO2 mole percent of sweet gas, and plant energy consumption affect the process economy. The simulation results have good agreement with experimental data. By analyzing process parameters, trend and constraint of adjustable variables have been obtained. The process has been optimized for obtaining CO2 mole fraction in the sweet gas below 2, and minimizing the energy load, amine circulation rate and released methane flow. Results show that sour gas temperature and pressure of 33.98 ◦ C and 14.96 bar, DEA/CO2 molar flow ratio of 12.58, regeneration gas temperature and pressure of 94.92 ◦ C and 3.0 bar, regenerator pressure of 1.53 bar, and ratio of DEA/MDEA = 20%/10% are the best values for minimizing plant energy consumption, amine circulation rate, and carbon dioxide recovery. Nomenclature Acronyms Abs Absolute DEA Diethanolamine DGA Diglycolamine DIPA Di-propanolamine FT Fischer-Tropsch GA Genetic algorithm GTL Gas to liquid MEA Monoethanolamine MDEA Methyldiethanolamine MW Molecular weight NSGA Non-sorting genetic algorithm PRSV Peng-robinson-stryjek-vera R.E Relative error STD Standard

Latin letters DAbsorber DRegenerator ENet Fi LAbsorber LRegenerator PSourgas PReg.gas PRegenerator QCondunser QPump QReboiler RCirculation ReCO2 TSourgas TReg.gas

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Absorber tower diameter (m) Regenerator tower diameter (m) Net plant heat load (kJ/h) Molar flow of streams (kgmole/h or lbmole/h), i = CH4 , CO2 , DEA· · · Absorber tower length (m) Regenerator tower length (m) Sour gas pressure (bar) Regeneration gas pressure (bar) Regeneration tower pressure (bar) Duty of condenser (kJ/h) Duty of pump (kJ/h) Duty of reboiler (kJ/h) Amine circulation rate (kg/h) Carbon dioxide recovery (%) Sour gas temperature (◦ C) Regeneration gas temperature (◦ C)

Greek letter ρ Density (kg/m3 )

References [1] Abdi M A, Meisen A. Ind Eng Chem Res, 1999, 38(8): 3096 [2] Datta A K, Sen P K. J Membr Sci, 2006, 283(1-2): 291 [3] Wauquier J P. Petroleum Refining: Separation Processes. Paris: Editions Technip, 2000 [4] Dortmundt D, Doshi K. In: Recent Development in CO2 Removal Membrane Technology, UOP LLC. Des Plaines: Illinois. 1999 [5] Geankoplis C J. Transport Processes and Unit Operations. New Jersey: Prentice Hall, 1993 [6] Bhide B D, Voskericyan A, Stern S A. J Membr Sci, 1998, 140(1): 27 [7] Khakdaman H, Zoghi A, Abedinzadegan M A. Petrol Tech Q, 2005, 10(5): 113 [8] Unsford M, Bullin A. In: Proceedings of the 1996 AIChE Spring National Meeting. New York [9] Kohl A L, Riesenfeld F C. Gas Purification. 4th Ed. Texas: Gulf Publishing Company, 1985 [10] Harris S D, Elliott L, Ingham D B, Pourkashanian M, Wilson C W. Comput Meth Appl Mech Eng, 2000, 190(8-10): 1065 [11] Konak A, Coit D W, Smith A E. Reliab Eng Syst Saf, 2006, 91(9): 992 [12] Zitzler E, Deb K, Thiele L. Evolutionary Computation, 2000, 8(2): 173 [13] Davis B H. Catal Today, 2003, 84(1-2): 83 [14] Donnelly T J, Satterfield C N. Appl Catal, 1989, 52(1): 93 [15] Eliason S A, Bartholomew C H. Appl Catal A, 1999, 186(1-2): 229 [16] Madon R J, Taylor W F. J Catal, 1981, 69(1): 32 [17] Raje A P, Davis B H. Catal Today, 1997, 36(3): 335