HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPREM Vol. 30. pp. 107- 112 (2002) THE COMPUTER ASSISTED SYNTHESIS FOR OPTIMAL HEAT EXCHANGER NETWORK AT STYRENE POL YMERISATION R. DIACONESCU and R. Z. TUDOSE (Technical University "Gh. Asachi" I~i, Department of Chemical Engineering, B-dul D. Mangeron no. 71A, 6600 IA~I, ROMANIA) Received: November 07,2001 In this paper a synthesis of an optimal heat exchang~r network has b~e~ studi~d to re~lize the required thermal regime at styrene bulk polymerisation in a continuous operatwn. The synthesis IS realized usmg a method based o~ the balance calculations, and supposes: the thermal balance over each chemical reactor, the heat exc~anger calculatwn~ and the determination of the optimal heat exchanger network. The calculation of the heat exchangers mvolves the selectwn of the exchanger type, the choice of the thermal agents and the cost calculation. The optimal heat e_xchan?er_network can be obtained by selecting the heat exchanger for each reactor, which corresponds to the technological cntenons and has the minimum total cost. Key words: heat exchanger, network synthesis, styrene polymerisation, and thermal regime Introduction The heat exchanger network synthesis has two main objectives: the determination of the maximum heat amount which can be recovered from process, respectively, the obtaining of the heat exchanger network realizing the minimum cost. The synthesis of the heat exchanger networks is the well-tested problem from those of the synthesis of different subsystems, like separation sequence synthesis or reactor systems. Gundersen and N aess [ 1], in an ample detailed review, note more than 200 papers in this field. Further, Gundersen [2] is referring at 30 papers on the same topic. Jezowski [3, 4] presents and analyses 142 works for the synthesis of heat exchanger networks. Recently, some papers present synthesis methods for retrofitting flexible or multi-period heat exchanger networks [5] and, respectively, heat exchanger networks under uncertainty [6]. In order to systematize such a literature, the available synthesis methods of heat exchanger networks are classified in two groups: methods based on the balance calculation and methods using the optimising techniques. The methods using the optimising techniques solve the heat exchanger network synthesis problem like a formal optimising problem, by mathematical instruments, while the methods based on the balance calculation avoid the mathematical techniques and involve the knowledge of the problem. the thermodynamics laws and the logical judgments. In this work, a method based on balance calculation for synthesizing optimal heat exchanger networks is presented. The method is applied to the optimal heat exchanger network synthesis which realizes the required thermal regime at the styrene bulk polymerisation in a continuous operation. The optimal heat exchanger network, by its capacity and thermal regime, belongs to a system containing an optimal industrial reactor network. The realization of the pre-established thermal regime, during the styrene bulk polymerisation, is a very difficult problem, which is unsolved yet. The difficulty is due to a very complicated reaction system having a large number of reaction components and reactors. To those, the special behaviour of the polymer during polymerisation must be added, when the conversion and temperature is changing. The temperature increase complicates the problem because of strong exothermal reaction and its influence upon the polymer properties. From the above considerations, it results the necessity of an optimal system synthesis of heat exchangers to realize the required thermal regime for the polystyrene production. The synthesis algorithm supposes the thermal balance over each reactor, the calculation of the heat exchangers and the determination of the optimal h~t exchanger network. This algorithm was impl:mented ~n MathCAD 2000 ProfessionaL In the modelhng and m the optimisation of the heat exchangers, all required parameters have been established. The optimal heat 108 Mv" PFR / Fig.] Reactor network for polystyrene production by bulk polymerisation exchanger network for the styrene polymerisation has been obtained taking into consideration the technical and economical criterions, the technical criterions are the most important. For given initial conditions and specified thermal regime, the optimal network contains five coil heat exchangers. The results of the system synthesis of heat exchangers attest the viability of the optimal reactor network obtained preliminarily for polystyrene production, in which the thermal regime problem was solved. Problem formulation The optimal heat exchanger network has been synthesized on an optimal reactor network, obtained also by computer assisted synthesis [7]. This network is presented in Fig.l. The considered reactor network represents an industrial system, it produces· 2000 polystyrene tones /year. The thermal regime is in the 80 oc - 200 °C range, according to the production scale technologies [8, 9]. The reactor network for the styrene bulk polymerisation, in a continuous system, contains eight reactors, working in isothermal conditions, as follows: Two continuous stirred tank reactors, CSTRl and CSTR2, with parallel connection, operate at 80°C. These provide the required capacity of the polymerisation system. Other six plug flow reactors (PFR) provide the required conversion, of 97%, and 641 numerical average polymerisation degrees. These operate in isothermal conditions for temperatures of l 00°C for PFRI and PFR2. 150°C for PFR3, 180°C for PFR4 and PFRS. and 200°C for PFR6. In the specified conditions.. the problem solved in this paper is formulated as follows: one gives the reaction mixture containing styrene, polystyrene and initiating agent~ each one having a specified initial temperature, the required exit temperature. the specific heat and the flow rate and. also, a set of thermal agents for beating and cooling and their properties ( entbalpies, working temperature). The heat exchanger network bringing the reaction mixture at desired temperature is synthesizing and the annual cost for operating and investment charge is minimizing. Since the reaction mass follows a pre-established way by the reactor network, the heating or cooling is realized only with thermal agents who can be associated between them. Synthesis algorithm The synthesis problem is decomposed in sub-problems treating each reactor with a distinct thermal regime. As long as, both of the continuous stirred tank reactors for pre-polymerisation (Fig.J) work in the same condition regarding feed and temperature, it is enough a single calculation. Also, the plug flow reactors working in the same conditions, in a series arrangement, it can be considered as a single reactor. Thus, one treats together the plug flow reactors, PFRl and PFR2, working at 1 00°C, and PFR4 and PFRS working at 180°C. For each considered reactor, the design calculation of the heat exchangers realizes the required heat transfer using the available thermal agents. The agent can be at its first use or can be a thermal agent which was heated /cooled in other heat exchanger, by taking-up or transfer of the excess heat of the reaction mass from other reactor. From the above considerations, it results that the algorithm of the optimal heat exchanger network synthesis has the following steps; The effectuation of the thermal balance over each reactor in order to determine the needed heat to be transferred and the sense of the heat transfer leading to heating or cooling of the reaction mass. The calculation of the heat exchangers involving1:he selection of the heat exchanger and of the thermal agents, taking into account the technological characteristics of the polymerisation and the heat amount to be transferred. For the selected heat exchangers, one calculates the flow rate, the overall heat transfer coefficient, the heat transfer surface area and the coil length. ·Finally, for one year operation (8000 hours), the cost of the heat exchangers and of the thermal agents is calculated. The determination of the optimal heat exchanger network consisting in the selection, for each reactor, of the heat exchanger which respects the technological criterions and has the minimum total cost (operating cost and investment charge). The obtained network by the interconnection of the selected heat exchangers is the network realizing the required thermal regime for a total minimum cost and, consequently, this is the optimal network. Thermal balance over reactors The thermal balance has been realized over each reactor having a distinct thermal regime in the polymerisation system. One considers the steady state. The energy conservation law is: the amount of inlet heat plus the generated heat are equal to the outlet heat. 109 Table 1 Reactor network characteristics for polystyrene production by bulk polymerisation Reactor Inlet Outlet Conversion Final position flow flow Average concentration on rec.:ctor degree in conversion in the for for network reactor reactor M~i Mvi Cj,t Cj,2 Cp,o Cp,l (Vs) (Vs) (moVl) (moVl) (moVl) (moVl) 3.9xl0·2 0.110 7.187 5.285xl0·3 9.69x1o-9 1.96xl0·5 2 3.9xl0·2 0.110 7.187 5.285xl0·3 9.69xl0·9 1.96xto·5 3 0.110 0.126 5.19 8.638xl04 6.875xl0·9 1.79xl0"5 4 0.126 0.141 4.25 3.99xto·5 5.515xto·9 1.655xl0·5 5 0.141 0.152 3.31 1.05x10-6 7.035x10·9 1.65xto·5 6 0.152 0.167 2.205 3.735xi0-10 7.12x1o·9 1.38x10·5 7 0.167 0.255 1.112 1.195xl0-9 7.07x10·9 1.375xl0·5 8 0.255 0.465 0.458 2.39x10·9 7.00xl0·9 1.365xl0·5 For a j reactor, the inlet heat is the sum of the reaction mixture heat and polymerisation reaction heat (strong exothermal, ~H=671,238 J/kg [10]). Inlet heat inj reactor: Qi . =Mw ·c . -l st,1 st p st,1 1 (1) (2) Q i -M i . - w ·cp . ·t. pob,1 pob pob,1 1 (3) Qr. =Mw -(x. -X. )·AH 1 st 1 1-1 (4) Outlet heat from j reactor: Qe . =Mw -(i-x ·)·t~ st,1 st 1 1 (5) Qe =Mw ·c . ·te pob,j pob p pob,j j (6) Qe t . = Mw t ·X . · cp . · t~ ps ,1 s 1 pst,] 1 (7) The transferred heat is: (8) Obviously, for Q~ > Q; it is necessary the cooling, and for Q~ < Q; the heating of the reaction mass. The thermal balance over the reactors of the optimal synthesis network for the polystyrene production by bulk polymerisation has been realized by the Eqs.( 1 )- (8). For the first reactor, the heat losses have not been considered because these favour the cooling. For the other reactors, the heat losses have been 1% of the inlet heat. The flow of the reaction mass components and the conversion of each reactor are presented in Table I. The specific heats for the inlet and outlet streams were taken from the available literature [10~ 11]. The results of the thermal balance over the optimal reactor network for the styrene bulk polymerisation are presented in Table 2. the j reactor degree Cp,2 Cj,4,0 Cj,4,1 Cj,4,2 XJ Xr (mol/1) (moVl) (mol/1) (moVl) 7.91xto·2 4.72xl0·3 0.522 3.01xl03 0.350 0.350 7.91xto·2 4.72xl0·3 0.522 3.01X103 0.350 0.350 0.104 5.lxl0·3 0.588 3.88xl03 0.166 0.458 0.106 5.265xto·3 0.558 6.05xl03 0.199 0.566 0.078 4.765x1o·3 1.335 8.825x103 0.248 0.674 0.055 4.84xl0·3 2.065 1.18xl04 0.449 0.820 0.055 4.08xl0·3 2.265 1.185x104 0.583 0.925 0.055 2.595x1o-3 1.61 8.225xl03 0.600 0.970 Table 2 Thermal balance results over each reactor of the network for polystyrene manufacturing by bulk polymerisation Reactor Inlet heat (W) Outlet Transferred Sens of heat heat the heat (W) (W) transfer CS1R working at 80°C 9.45·103 4.97-103 4.48-103 Cooling CS1R working at 80°C 9.45-103 4.97·103 4.48-103 Cooling PFR working at 1 00°C 2.03·104 1.25·10 4 7.76·103 Cooling PFR working at 150°C 1.78-104 2.05-10 4 2.77·103 Heating PFR working at 180°C 3.27-104 2.95·10 4 3.18·103 Cooling PFR working at 200°C 3.19-104 3.39·10 4 1.98-103 Heating Heat exchangers calculation The selection of the heat exchangers and of the thermal agents is based on the thermal balance results. Due to the difficulty of the heat transfer between the reaction mass and the thermal agent, the coil heat exchangers have been considered. Because the heat amount transferred into the reactor network is small, a jacket heat exchanger is not necessary. Since the reaction mass has a very high viscosity in the last reactor (PFR6), the Reynolds number is small and the heat transfer rate is reduced, therefore electrical heating has been chosen. In the continuous stirred tank reactors, being connected in parallel, the temperature is 80 °C, one can use water of different temperatures as cooling agent. For the variants with high outlet water temperatures from reactors, for instance, 50°C for inlet temperature and 60°C for outlet temperature, even if the water consumption is larger and the coil length is also larger, there is the advantage of a small temperature variation into the reaction mass and its properties are unchanged. In the plug flow reactors PFRl and PFR2. the inlet temperature of the reaction mass is 80°C and outlet temperature is l00°C. Consequently, the cooling agent for reaction mass is the water with different temperatures. The plug flow reactor working at 150°C (PFR3 ), according to the thermal balance, needs the beating. As 110 Table 3 The calculation results for the heat exchanger design realizing the needed thermal regime in a CSTR e e '(;$ § ~~ +"' i ~ ~ C1) ~·"""' .s~ .. ~s g ~ ,d ~ ~ Q ~- u C1:l '"" "0 ,d"'"' g§ "' C1:l ..9 §~ Q),....,_ f3"G ~ ~ ~ g"~ a Q,) 1 i3".£-J !:I; bl} <1)0 .g! d a.e .s- .... '-' ~'-'~M~ ..... <1) ~ C1:l u 0 d >~ ~ § <1)~ ·s ~ ~ ~ a C1:l 0"''-...s 0 f:: g ::=a,s ::z:: fi1 c.; 15 30 638.1 0.0713 0.359 7.15 4.11·108 gp .. 15 40 8 536.1 0.0428 0.497 9.86 2.47·108 ~j 25 40 oO 676.0 0.0713 0.395 7.85 4.11·108 ~ ..,f 25 50 565.7 0.0428 0.568 11.3 2.47·108 heating agent steam of different pressures or Dowtherm A is used. The plug flow reactors (PFR4 and PFR5) working at 180 °C, needs cooling. Due to the high temperatures, one proposed boiling water under pressure of 1 bar or 2 bar, as cooling agent. · Conclusively, for each reactor from the synthesis network, the amount of heat to be transferred, the heat exchanger type and the available thermal agents have been established. Hereinafter, for each reactor, the needed thermal agent flow rate, the overall heat transfer coefficient, the heat transfer surface area, the coil length and the total cost have been calculated. Investment charge can be calculated with the relation: (9) where A is the heat transfer surface area, a and f3 are specific constants for the heat exchanger type: a =145 and f3=0,65-0,95 [12, 13]. The operating cost is CO i = Mw · cu · nh , where cu represents the unit cost for the thermal agent and nh=SOOO the hours number of operating a year. Therefore. the total cost for thermal transfer to realize the needed isothermal regime into reactor is: crj; ci + coj (10) Table 3 presents the calculation results for the heat exchanger design using water of different temperatures~ in order to realize and maintain the constant temperature of 80 °C, of the stirred tank reactor. The plug flow reactors working at 100 °C (PFR1 and PFR2)~ based on the thermal balance result~ both need the cooling of the reactton mass (Table 2). To this gt 11. the water with different inlet/outlet temperatures has been chosen. Being that. from stirred tank reactors results water of 40 °C and 50 °C (Table }). This can be used for the reaction mass cooling from the plug flow reactors working at I 00 °C. The overall heat transfer coefficient KPFR 12 has been calculated as function of individual heat transfer coefficient and thermal resistance of the wall. The calculation of the individual heat transfer coefficient was made using the relations obtained from literature [H-J•H. Table 4 The needed characteristics for the heat exchanger design realizing the needed thermal regime in the PFR 1 and PFR2 15 30 15 40 20 20 25 25 30 40 40 50 40 60 50 70 139.1 0.125 0.835 8.86 7.20-108 131.0 0.075 0.994 10.54 4.32·108 143.5 0.189 0.851 9.03 1.09·109 8 136.1 0.094 0.961 10.19 5.41-108 ~ 140.9 0.126 0.975 10.34 7.26·108 r..: 134.8 0.075 1.108 11.76 4.32·108 140.4 0.095 1.382 14.97 5.47·108 140.3 0.095 1.892 20.08 241.49 The needed characteristics for the heat exchangers design are presented in Table 4, for different cooling water types. The thermal balance over PFR3 working at 150 °C, showed that, for a good polymerisation, it is needed to supply a heat amount of 2,77·103 W. To this aim, the proposed thermal agent is either steam with different temperatures or liquid Dowtherm A. The steam flow for the heating of the reaction mass has been obtained as function of needed heat amount for the heating and steam characteristics. In the following, the individual heat transfer coefficient for the reaction mass was calculated. The reaction mass properties were taken from literature [10], at average temperature in the reactor working at 90 °C, for a conversion degree of 67, 4%. In these conditions, the laminar regime was obtained with very low RePFR3 = 5.55. This allows considering the free convection. Because the heat transfer coefficient for steam, used as heating agent. is much higher than that for the reaction mass, the thermal resistance for steam can be neglected. When Dowtherm A is used as thermal agent, the thermal resistance can be also neglected. For the required heat transfer realization, the overall transfer coefficient, the thermal transfer surface area~ the coil length and the total length have been calculated. The obtained results are presented in Table 5. The plug flow reactors PFR4 and PFRS work at 180°C. The thermal balance shows that the elimination of the heat from the inside reactors is necessary. for tr 3 • both. Q PFR45 = 3.18·10 W. The thermal agent was the water under pressure, so that by its evaporation, the water takes up a large amount of heat. The properties of the water under pressure were taken from [11]. For the overall heat transfer coefficient determinationt the individual heat transfe1 ~oefficient of the reaction mass was calculated, flmrwR•s= 147.14 W m"2K"1• The reaction mass properties are taken from [ 1 0] for 92.5 % conversion degree. Table 5 The calculation results for the heat exchanger design realizing the needed thermal regime in the PFR3 6 158.1 1.32 7 164.2 1.33 Steam 8 170 1.35 9 175 1.36 10 179 1.37 Dowtherm 1.2 190 8.78 A 1.5 225 9.19 138.818 0.57 6.04 3.04-107 138.818 0.51 5.39 3.06·107 138.818 0.44 4.70 3.11·107 138.818 0.40 4.27 3.13·107 138.818 0.37 3.92 3.16·107 133.268 0.32 3.39 1.01-109 133.268 0.21 2.20 1.06·109 Also, here the heat transfer coefficient for the water, boiling under pressure in the coil is much larger than that of the reaction mass and its value was admitted. The calculation results for PFR4 and PFRS, including the total costs of the required heat transfer, are presented in Table 6. One can assert that, for all considered reactors, the thermal resistance has the largest value for the reaction mass. Because the last reactor (PFR6) uses electrical heating, the heat calculation cannot be any more the objective for the heat transfer optimisation. Determination of the" optimal heat exchanger network The heat exchangers realizing the required thermal transfer for each considered reactor have been chosen from the lists presented in Tables 3, 4, 5 and 6. For selection, the technological criterions had the maximum importance. Hereby, the temperature variations, larger than 10°C for the reaction mass, have not been accepted. Consequently, for instance, the cooling water had a higher input temperature. Also, for heating, when the thermal agent can be the steam or Dowtherm A, the Dowtherm A was chosen because this can provide a higher temperature, and, finally the required quality of the reaction mass. In the same sense, a thermal agent has been recycled even if the heat transfer surface area has been larger and, thereafter, the investment charge (heat exchanger) has been higher, due to the driving force decrease. From technological point of view, the recycling was preferred because the operating expenses have to be reduced. The economical criterions, given by the total cost for the thermal transfer, have been used for the thermal agents' selection. The heat exchangers and the corresponding thermal agents have been selected on the above criterions and composed the optimal heat exchanger network, because this realizes the required thermal regime under adequate technological conditions with minimum cost. Ill Table 6 The calculation results for the heat exchanger design realizing the needed thermal regime in the PFR 4 and PFR 5 Water 99.1 0.00141 120.95 0.399 4.23 1.62·107 p~:S~:e 2 119.6 0.00144 3'179. 103 111.96 0.625 6.64 1.66·107 Cnm:.ofoptiwizatednetwork: 1.26 .10'u.c, Fig.2 Optimal heat exchanger network for polystyrene manufacturing by bulk polymerisation The described synthesis algorithm has been implemented in MathCAD 2000 Professional. The synthesized optimal heat exchangers network is presented in Fig.2. For the initial conditions and the specified thermal regime, the network contains five coil heat exchangers. as following: Two heat exchangers realize the required isothermal regime (80°C) in the continuous stirred tank reactor (CSTRI and CSTR2). These are using the cooling water as thermal agent having 25°C inlet temperature and 50°C outlet temperature. For the PFRl and PFR2 requiring an isothermal regime at 1 00°°C, a heat exchanger recycling the resulted water from CSTRI and CSTR2, having 50°C temperature has been used. The outlet water temperature is 60°C. PFR3 works at 150°C. The corresponding heat exchanger uses Dowtherm A at 190°C. The last heat exchanger, using cooling water at 2 bar pressure, realizes the isothermal regime, at 180°C, in PFR4 and PFRS. One asserts that the optimal heat exchanger network cannot use the heat of the reaction mass because this has a pre-established way which cannot be modified. Also, the single thermal agent enabling the recycling was the cooling water which results from CSTRI and CSTR2. Conclusions The optimal heat exchanger network realizing the required thermal regime for the reactor system at 112 styrene production, by bulk polymerisation in a continuous system has been determined by the computer assisted synthesis. The considered system has industrial capacity and operates at the thermal regime for commercial scale. Firstly, the synthesis method supposes the thermal balance effectuation over each reactor having a distinct thermal regime. Then, the heat exchangers have been calculated and the optimal heat exchanger network has been determined. The accurate analysis of the technological process and of the offered possibilities by system calculation allows solving the problem under optimal technological and economical conditions. The proposed heat exchanger network realizes the pre-established thermal regime under given conditions and for a minimum cost. This shows that the reactor network can be used in a practical application. We notice that the proposed synthesis method is efficient but depends on the designer experience in the field. The designer establishes the type exchangers, the thermal agents and the accepted temperature difference, based on the knowledge of the technological process. In the issue, the utilized synthesis method is recommended for the approached problem type of synthesis - the realizing of thermal regime for the manufacturing of the reaction mass in a known reactor network. The problem appears frequently in the industrial chemical processes and, especially, in the polymerisation process, which are strongly exothermic. j Q!t,j Q~st,j Q~.j Mw.st Mwpob CP.st,j CPpob.j t' J x F'x j-t AH QrJ Q~.j Q~t.j Q~.j tj SYMBOLS index for reactors inlet styrene heat in the j reactor, W outlet polystyrene heat in the j reactor, W inlet initiating agent in the j reactor, W styrene mass flow rate, kg/s initiating agent mass flow rate, kg/s styrene specific heat capacity at the inlet/outlet styrene temperature~ for j reactor, J/(kg·K) specific heat capacity of the initiating agent at the inlet/outlet temperature for j reactor. J/(kg·K) inlet reaction mass temperature for j reactor. oc monomer conversion degree in j/j-i reactor polymerisation heat. J/kg reaction heat in the j reactor. W outlet styrene heat for reactor j .. W outlet polystyrene heat for j reactor. W outlet initiating agent heat for j reactor. W outlet temperature for j reactor. °C ~ Qj Qjr A cj coj Mw uc nh CTj a,~ CSTR PFR inlet heat for j reactor, W outlet heat for j reactor, W transferred heat for j reactor, W thermal transfer surface area, m2 investment charge for j reactor, u. c. operating cost for j reactor, u.c. mass flow of thermal agent, kg/s unit cost of the thermal agent, u.c. hours number of operating a year total cost of the thermal transfer for j reactor, u.c. specific constants for the heat exchanger type Continuous Stirred Tank Reactor Plug Flow Reactor REFERENCES 1. GUNDERSEN T. and NAESS L.: Computers Chern. Eng., 1988, 12,505-530 2. GUNDERSEN T .: Retrofit Process Design Research and Applications of Systematic Methods, Proceed. Ofthe 3rd Conf On Foundations of Computer Aided Process Design, 213-240, Snowmass Village, Colorado, July 1990, Elsevier Public 3. JEZOWSKI J.: Hung. J. Ind. Chern., 1994, 22, 279- 294 4. JEZOWSKI J.: Hung. J. Ind. Chern., 1994, 22, 295- 308 5. BOCHENEK R. and JEZOWSKI J.: Hung. 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