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Multiobjective Optimization of the Industrial Naphtha Catalytic Re- forming Process* HOU Weifeng(@E@), SU Hongye( 5 2 &)**, MU Shengjing(+ ! & $$) and CHU Jian(&@)

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Multiobjective Optimization of the Industrial Naphtha Catalytic Re- forming Process* HOU Weifeng(@E@), SU Hongye( 5 2 &)**, MU Shengjing(+ ! & $$) and CHU Jian(&@)
  Chin. J Chem. Eng., 15( 1) 75-80 (2007) Multiobjective Optimization of the Industrial Naphtha Catalytic Re- forming Process* HOU Weifeng(@E@), SU Hongye( 5 &)**, MU Shengjing(+ & $$) and CHU Jian( @) National Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou 310027, China Abstract In this article, a multiobjective optimization strategy for an industrial naphtha continuous catalytic reform- ing process that aims to obtain aromatic products is proposed. The process model is based on a 20-lumped kinetics re- action network and has been proved to be quite effective in terms of industrial application. The primary objectives in- clude maximization of yield of the aromatics and minimization of the yield of heavy aromatics. Four reactor inlet tem- peratures, reaction pressure, and hydrogen-to-oil molar ratio are selected as the decision variables. A genetic algorithm, which is proposed by the authors and named as the neighborhood and archived genetic algorithm (NAGA), is applied to solve this multiobjective optimization problem. The relations between each decision variable and the two objectives are also proposed and used for choosing a suitable solution from the obtained Pareto set. Keywords multiobjective optimization, catalytic reforming, lumped kinetics model, neighborhood and archived genetic algorithm (NAGA) 1 INTRODUCTION Petroleum refining and petrochemical industries aim at maximizing one prime product while simulta- neously minimizing another accessory product to im- prove the quality of the prime product. Unfortunately, the two requirements are often conflicting or incon- sistent. It is necessary to determine the trade-off com- promises to balance the two objectives[ 1,2]. As the core of aromatics complex unit, catalytic reforming is a very important process for transforming naphtha into aromatics feedstock[3]. In this process, the yield of aromatics, including benzene, toluene, para-xylene, meta-xylene, ortho-xylene, ethyl-benzene, and heavy aromatics (i.e. 9 and more carbon aromat- ics), are regarded as the main index that determines the quality. However, heavier aromatics are not re- quired and will increase the load on the downstream units of the aromatics complex process, especially on the disproportionation and xylene fractionation units. Thus, the design and operation of the catalytic re- forming process require multiobjective optimization to balance the various objective functions. Multiobjective optimization, involving more than one objective function, was typically modeled and solved by transforming it into a single objective prob- lem using different methods, such as the restriction method, the ideal point method, and the linear weighted sum method. These methods largely depend on the values assigned to the weighted factors or the penalties used, which are done quite arbitrarily. An- other disadvantage of the above methods is that these algorithms obtain only one optimal solution at a time and may miss some useful information[4]. Recently, multiobjective evolutionary algori-thms are used more popularly in industrial process model- ing, optimal design, and operation[4]. These may pro- duce a solution set, which is named as a Pareto set, in a single run of the algorithms. The Pareto solutions are extremely useful in industrial operations as these nar- row down the choices and help to guide a deci- sion-maker in selecting a desired operating point (called the preferred solution) among the (restricted) set of Pareto optimal points, rather than from consid- erably large number of possibilities[5]. Coello[6] pre- sented comprehensive reviews on the development of the evolutionary (especially genetic) multiobjective optimization. When compared with the previous methods, such as the nondominated sorting genetic algorithm (NSGA) [7], the niched Pareto genetic algo- rithm (NPGA)[8], the Pareto archive evolutionary strategy (PAES)[9], and the strength Pareto evolution- ary algorithm (SPEA) [ o], the method employed in this study, the neighborhood and archived genetic al- gorithm (NAGA)[l1,12], offers several advantages: (1) low computation complexity; (2) insensitivity of the efficiency to the method parameters; and (3) uniform distribution on the Pareto front. In this article, the multiobjective optimization strategy for an industrial naphtha continuous catalytic reforming process is built to improve the operation level. A 20-lumped kinetic model is employed for the industrial catalytic reforming reaction and the corre- sponding process model is validated by successful industrial applications[ 131. In the catalytic reforming unit, the objectives are to maximize the aromatics yield and minimize the yield of heavy aromatics. The multiple Pareto optimal solutions of the problem are obtained by applying the multiobjective genetic algo- rithm, NAGA. It presents an operating parameter set for operators for various operational targets. 2 DESCRIPTION OF THE PROCESS AND MODELING The simplified continuous catalytic reforming process flow diagram is shown in Fig.1. The naphtha, used as the catalytic reformer feedstock usually Received 2005-11-19, accepted 2006-07-03. * Supported by the National Natural Science Foundation of China (No.60421002). ** To whom correspondence should be addressed. E-mail:  76 Chin. J. Ch. E. Vol. 15, No.1) RIkR4: reformer to hydrogen-consuming unit cooler recycle gas naphtha feed R4 spent catalyst iromatics product Figure 1 Flowsheet of a continuous catalytic reforming process containing more than 300 chemical compounds of paraffins, naphthenes, and aromatics in the carbon number range of C4 to Clz, s combined with a recycle gas stream containing 60 to 90% (by mol) hydrogen. The total reactor charge is heated and passed through the catalytic reformers, which are designed with four adiabatically operated reactors and four heaters be- tween the reactors to maintain the reaction tempera- tures at design levels. The effluent from the last reac- tor is cooled, which then enters the product separator. The flashed vapor circulates to join the naphtha feed- stock as recycle gas. Excess hydrogen from the sepa- rator is sent to other hydrogen-consuming units. The separated liquid that chiefly comprised the desired aromatics together with light gases and heavy paraf- fins is sent to the separation system to obtain aromat- ics products. The aromatics products are obtained by the con- version of n-paraffins and naphthenes in naphtha to iosparaffins and aromatics over bifunctional catalysts such as Pt-SdA1203 in the four reactors. The domi- nant reaction types of catalytic reforming are dehy- drogenation of naphthenes, isomerization of paraffins and naphthenes, dehydrocyclization of paraffins, hy- drocracking of paraffins, and hydro-dealkylation of aromatics. Dehydrogenation is the fastest reaction followed by isomerization, which is moderately fast, whereas dehydrocyclization and hydrocrackmg are the slowest. As mentioned above, the naphtha feedstock is very complex and each of these undergoes various reactions. To reduce the complexity of the model to a manageable level, the large number of naphtha com- ponents are assigned to a smaller set of kinetics lumps, each of which is composed of chemical species that are grouped together according to some criteria[ 141. Accordingly, various lumped lunetics models with varying levels of sophistication that represent catalytic reforming reactions have been reported in the litera- ture[ 15-20]. In the previous study[l3], a simple lumped h netics model for catalytic reforming with 20 lumps involving 31 reactions was presented. The corre- sponding reaction network is shown in Fig.2. In this model, the total reactor charge is characterized as par- affins (P), naphthenes (N), and aromatics (A) lumps with the carbon number ranging from 6 to 9+(9+indicates a carbon number of 9 and above) and light paraffins (PI-P5), in which the 8-carbon aro- matics are subdivided into their four isomeric com- pounds, i.e. PX (para-xylene), MX (meta-xylene), OX (ortho-xylene), and EB (ethyl-benzene). The rationale of selecting these lumps was based on both thermo- dynamic and lunetics considerations for the aromati- zation selectivity of paraffins and naphthenes. It is not necessary to split the paraffin or naphthene lumps into their individual isomers e.g.. isohexane and n-hexane) for achieving similar aromatization selectivity for the two lumps (except for methyl cyclopentane and hex- ane) and for faster isomerization reaction rates relative to dehydrocyclization and hydrocracking[ 15,161. In this reaction network, except for isomerization, all the dominant catalytic reforming reactions are included. Figure 2 Reaction scheme for naphtha reforming All the 31 rate equations are nonlinear pseudo-monomolecular in nature, with the rate coeffi- cients obeying the Arrhenius law, as shown in Eq.(l), kj =kOj.exp(-Ej/RT).Pf’ 4 O 4 <l, j=1-31 (1) February, 2007  Multiobjective Optimization of the Industrial Naphtha Catalytic Reforming Process 77 Under the normal reformer operating conditions, radial and axial dispersion effects were found to be negligible[ 131. For the radial flow reactor, the global material and the heat balance equations are given in Eqs.(2) and (3), respectively, where Y is the vector of the molar flow rates including 20 lumps and HZ. Eq.(2) is solved using a mixed nu- merical algorithm of fourth-order Runge-Kutta and Gear method, and Eq.(3) is solved using the modified Euler method. The thermochemical properties of each lump are computed by talung an arithmetic average of the properties of the corresponding pure chemical components constituting the lump. The product separator was modeled to perform in isothermal flash operation. A Peng-Robinson equation was used to compute the vaporAiquid equilibrium constants. The so-called sequential modular approach is implemented for the computation of this flowsheet. Except for the separation system, the reactors, the heaters, the product separator, and the heat exchangers are included in this computation. If the activation energies E), he pressure expo- nents (@, and the frequency factors ko) for all 31 re- actions are estimated, there will be 93 kinetics pa- rameters in total, and it is very difficult to determine these parameters synchronously. Generally, E and 0 values reported by different literatures for the specific catalyst are similar. To reduce the difficulty experi- enced in estimating parameters, the parameters E and 0 in this model are taken from Ref.[18] and only thirty-one ko, which considers the difference between the estimation of parameters E and 0 and the unmod- eled lunetics, are estimated. The procedure of parameter estimation is carried out by minimization of the sum of the squares of the deviations between the plant and the calculated values of the key variables such as the compositions of ef- fluent from the last reactor and the outlet temperatures of the four reactors. The operating and assaying data samples of several months for the industrial process, which are first reconciled by material balance, are used to estimate /Q by the BFGS optimization algorithm. 3 FORMULATION OF THE OPTIMIZATION PROBLEM The variables that affect the catalytic reforming process are the volume flow of naphtha charge to the volume of the catalyst (liquid hourly space velocity, LHSV), the latent aromatics content of naphtha charge (LA), the four reactor inlet temperatures (TI, T2, T3, T4), the reaction pressure Pr), the mole flow of hy- drogen in the recycle gas to the mole flow of naphtha charge (hydrogen-to-oil molar ratio, nH nHc , the product separator temperature (T,), etc.. Among the 9 process variables selected using mechanism analysis, the sensitivity analysis of each variable is performed using the process model presented in Section 2 to ob- tain its quantitative corrections with the aromatics yield and the yield of heavy aromatics. It is shown that the appropriate set point value of one variable for maximizing the aromatics yield may not be suitable for minimizing the yield of heavy aromatics. There- fore, the suitable trade-off solutions for the two opti- mal objectives should be considered. For the continuous catalytic reforming process in this study, the unit is in full load operation and the value of LHSV cannot be further increased. Similarly, the quality of naphtha feedstock e.g. LA) cannot be changed artificially for most domestic petro- leum-refining enterprises. The product separator tem- perature T, is not independent of other variables. Moreover, for further lowering of the temperature, coolers need to be included in the system, which in turn increase the operation costs. Hence, the remain- ing process variables are selected as the decision variables for optimization in this study. These are the four reactor inlet temperatures (TI, T2, T3, T4), he re- action pressure (PJ, and the hydrogen-to-oil molar ratio Thus, the two independent objectives, namely, the maximization of the aromatics yield (AY) and the minimization of the yield of heavy aromatics (HAY) are formulated mathematically as follows: ( ZH lnHC 1. maximize AY(T1, T2, T3, T4, Pr, nH nHc 1 minimize HAY(T1, Tz, T3, T4, pr H nHc subject to 520 G Ti, T2, T3, T4 G 530 0.8<pr<0.9 3.0< nH2 nHc G4.0 65 GAY <68 18GHAY <23 (4) The bounds of the decision variables and the ob- jectives have been chosen based on industrial practice. Because NAGA deals with only the minimization objective[ 1 I], the maximization of AY can be replaced by the minimization of a function f where fl=lIAY, without the replacement changing the location of the optima. To normalize the objective functions, the func- tion fi is transformed to fi=KflAY, and the function f2 may be simplified as f2=HAYlKc, where Kf=67 and Kc=20 are the reference operating values of the aromat- ics yield and the yield of heavy aromatics, respectively. 4 RESULTS AND DISCUSSION The solution for the multiobjective optimization problem described in Section 3 is obtained using NAGA. Table 1 provides the parameters of NAGA applied in ths study. Figure 3 shows the typical optimal solutions ob- tained by a single run of NAGA for the above formu- lated problem. The top of Fig.3 denotes the relationship Chin. J. Ch. E. 15 1) 75 (2007)  78 Chin. J. Ch. E. Vol. 15, No.1) 22 Table 1 Algorithm parameters used in this study Parameters Values volume of the archive 100 - maximum generation probability of crossover probability of mutation 500 0.8 0.01 population size 50 neighborhood size 0.05 between the two minimum objectives, fi vs fi whereas the bottom depicts the solutions of the two srcinal objectives. The conflict between the effects of the decision variables on the two objective functions, results in the optimum being a Pareto-optimal set rather than a unique solution. The Pareto set has the property that when one point on the set is moved to another, one objective function is improved eg. the aromatics yield increases), but the other function be- comes worse e.g. the yield of heavy aromatics in- creases accordingly). Hence, within the Pareto set, neither the solution dominates an over the other, and both indicate the optimal solation for the two objec- tive functions and the minimization of the yield of heavy aromatics with the given operating bound. The operators have to use the additional information, such as the market quotation, the operating cost, and the corresponding decision variable values to select an operating point (preferred solution) from the entire Pareto set for operation. Each point in Fig.3 represents a Pareto solution, which is associated with a set of the six decision vari- ables. Fig.4 is a plot of the decision variables corre- sponding to each of the points on the Pareto set. Ob- IS ic. 1 00 0.95 0.90 0.985 0.990 viously, the relations between each decision variable and the two objectives can also be observed. Among the six variables, T4 is unique in that all its points are close to its upper bound, which indicates that increas- ing T4 results in both an increase in the aromatics yield and a decrease in the yield of heavy aromatics. However, increasing the decision variables TI, T2, pr and nH2 nHc results in a decrease in the yield of heavy aromatics, but a decrease in the aromatics yield. In other words, the four variables have opposing ef- fects on the two minimum objectivesfi andfi. Besides the effects of the above variables, it is observed that the effects of T3 on the two objective functions are mild. All the above phenomena are confirmed by the process operators. These can also be rationally ex- plained by the reaction mechanism. In the first and second reactors, the inlet temperature of 520°C is adequate for the complete conversion of naphthenes to aromatics. A higher temperature is suitable for hydro- craclung of paraffins, which results in the decrease of aromatics. In the fourth reactors, dehydrocyclization and hydrocracking of paraffins are the major reactions and are both aided by hlgher temperatures. In this study, the competition is more favorable for dehydro- genation and results in an obvious increase in aromat- ics. In any reactor, exothermic hydrodealkylation of aromatics increases with an increase of temperature, which indicates a decrease of heavy aromatics. On the other hand, lower pressure favors dehydrocyclization and dehydrogenation, but not hydrocracking and hydrodealkylation, which result in increase of both gross aromatics and heavy aromatics. Less nH, / nHC indicates low partial pressure of hydrogen. Hence, nH2 nHc and pr have slmilar effects on the two objectives. :.. c.. z * * . XI ::. , . ., ~ : 5 . . 0.995 1.000 1.005 1.010 1.015 1.020 1.025 A .* .* .. 8 18 I I 1 65.0 65.5 66.0 66.5 67.0 67.5 6 AY, o Figure 3 Pareto-optimal set of solutions obtained from the simultaneous optimization nfi vs fi nd in the srcinal objectives of the aromatics yield and the yield of heavy aromatics February, 2007  Multiobjective Optimization of the Industrial Naphtha Catalytic Reforming Process 79 520 65 66 61 68 530 25 r T 520' I 65 66 67 68 0'90 TFJ 0.85 0.80 .-... 65 66 67 68 3.5 3.0 65 66 61 68 AY, Yo I 520 18 19 20 21 22 23 ow 520 18 19 20 21 22 23 525 520 18 19 20 21 22 23 52018 19 20 21 22 23 ..-. 0.85 19 20 21 22 23 . .om.. 3.5 3.0 18 19 20 21 22 23 HAY, Yo Figure 4 The decision variables corresponding to each of the Pareto-optimal solutions shown in Fig3 The above relations between each decision vari- able and the two objectives are useful for selecting a suitable solution from the entire Pareto set. For exam- ple, the decision variable values and the corresponding objectives of several typical solutions, points A, B, C, D, and E in Fig.3, are listed in detail in Table 2. The point N denotes the industrial normal operating point, which is above the Pareto solution front that is ob- tained. If the aim is to increase the aromatics yield, it may be feasible to increase T4 and (or) decrease pr and nH, /nHc as listed in point A or C. While aiming to decrease the yield of heavy aromatics, it may be feasi- ble to increase TI, Tz, T4 and (or) increase pr and nH2 nHc s listed in point B or E. In actual industrial operahons, pr and nH, /nHc are always maintained at higher values to protect the catalyst from rapid coking. As a solution to the above-mentioned problem, when other decision variables are approximately constant, only increasing T4 by about 5°C can lead to beneficial effects, an increase of 0.18 (by mass) in the aromat- ics yield and a decrease of 1.77 (by mass) in the yield of heavy aromatics, as listed in point D. The law that the increase of aromatics yield can only be ob- tained by slightly increasing T4 has been validated in the same industrial continuous catalytic reforming unit, as reported in the previous literature[21]. CONCLUSIONS The real-life challenge of promoting added value in the industrial naphtha continuous catalytic reform- ing process is described in this article. A 20-lumped kinetics model for catalytic reforming is used to solve the multiobjective optimization problem: maximiza- tion of the aromatics yield and simultaneous minimi- zation of the yield of heavy aromatics. By performing the optimization based on the neighborhood and Table 2 Comparison of the decision variables and objectives for normal operation and five possible cases of optimal operations Parameters Points TI, c T2, c T3, "C T4 "C pr, MPa n~~ ~HC mol.mol-' AY, % (by mass) HAY, (by mass) N 522.1 521.3 522.6 524.0 0.88 3.5 66.85 22.60 A 520.0 520.0 523.8 528.6 0.80 3 O 67.63 22.57 B 523.1 527.5 ,523.8 529.3 0.85 3.6 66.79 20.76 C 520.2 520.6 524.5 528.6 0.83 3.4 67.20 21.71 D 521.5 521.0 523.8 529.3 0.88 3.6 67.03 20.83 E 523.1 522.0 530.0 530.0 0.90 4.0 66.17 19.51 Chin. J. Ch. E. 15 1) 75 2007)
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