Ian David Lockhart Bogle and Michael Fairweather (Editors), Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, 17 - 20 June 2012, London. © 2012 Elsevier B.V. All rights reserved.
Pilot-plant Simulation, Experimental Campaign and Rigorous Modeling of a Batch MMA Polymerization Reactor for the Fabrication of Bone Tissue Lamia Zuniga Linan*a, Nádson M. N. Limaa, Laura Plazas Tovara, Flavio Manentib, Rubens Maciel Filhoa, Maria R. Wolf Maciela, Marcelo Embiruçuc a
University of Campinas (UNICAMP), Department of Chemical Processes, P.O. Box 6066, 13083-970 Campinas-SP, Brazil b Politecnico di Milano, CMIC Dept. “Giulio Natta” , Piazza Leonardo da Vinci 32, 20133 Milano, Italy c Federal University of Bahia (UFBA), Polytechnic Institute, 40210-630 Salvador-BA, Brazil * Corresponding Author. Phone: +55 19 3521 3971; Email:
[email protected]
Abstract As a first crucial stage for production of PMMA scaffolds, this work provides the kinetic and dynamic characterization of the MMA/Ethyl Acetate/AIBN polymerization process. Kinetic parameters are estimated by means of experimental campaigns performed on a dedicated pilot plant (batch reactor). A novel, rigorous mathematical model is developed and implemented in Fortran 90 so as to consider the peculiar characteristics and the new structure of the pilot plant and the batch reactor: actually, the new plant configuration is designed to produce the appropriated PMMA scaffolds for medical application (with very stringent specifications for low toxicity and high biocompatibility). The good agreement between model previsions and experimental results validates the kinetic parameters and the dynamic modeling. Keywords: Poly(methyl methacrylate), batch free-radical polymerization, mathematical modeling, bone tissue engineering.
1. Introduction Bone Tissue Engineering (BTE) is one of the most important research policies in the tissue engineering area. This provides alternative solutions to improve the mechanical properties of the commonly used bone tissue, to reduce the vascular impact of the bone implant, to prevent the stress shielding and to reduce the incidence of osteopenia associated to the implant (Yunfeng et al., 2009). A major challenge for the BTE science is to create prostheses that could be a reproduction of natural bone. Bone tissues are traditionally built as scaffolds using synthetic polymers and its compounds as raw material. Poly(methyl methacrylate) (PMMA) is a Food and Drug Administration (FDA) approved synthetic biomaterial widely used to fabricate reconstructive structures, including dental implant, implants for craniofacial defects or as bone cement to remodel lost bone and affix implants (Espalin et al., 2010). Commercial PMMA powder used to construct scaffolds must have appropriate properties to achieve good mechanical and handling properties and high bioactivity. These properties mainly include the weight and number average molecular weights (Mw and Mn, respectively) and the
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polydispersity, beyond the pore diameter and the pore volume, which they are difficult to measure in real time. Therefore, the control of these variables is often carried out by manipulating the reaction temperature which influences them and the monomer conversion significantly. The batch polymerization is widely used in industries for PMMA production by its availability and flexibility in operation (Chang and Liao, 1999). Nevertheless, high exothermic reactions in the process require considerable effort in controller tuning to achieve the proposed objectives (Lima et al., 2010). In this work, a more complex mathematical model that describes the dynamic of the batch solution polymerization of methyl methacrylate (MMA) is presented. The model includes: chain transfers to the monomer and solvent and termination by both combination and disproportionation, the volume change of the reactor contents and the gel effects. Besides, by considering the medical application of the polymer, a different combination of the mixture monomer-solvent-initiator was chosen, MMA/Ethyl acetate/AIBN (instead of the traditional Benzene and Toluene as solvent and Benzoyl peroxide as initiator). Thus, the risk of rejection by harmfulness and toxicity of the implant in contact with the human tissue are decreased. The thermodynamic variables are computed from literature data banks and the kinetic parameters are estimated through of the experimental data fitting using the most recent optimization techniques (Manenti and Buzzi-Ferraris, 2009). A PID controller is applied to track the reaction temperature through the manipulation of the electrical power supply to heat the jacket fluid. The model was validated by means of isothermal experiment.
2. Working equations 2.1. Kinetic mechanism The free-radical polymerization mechanism that represents the reaction kinetics is given in Ahn et al. (1998). Each kinetic rate constants were computed by Arrhenius expression of the form: k i = ai e ( − E / RT ) . i
r
2.2. Mass balance Based on the kinetic mechanism, differential equations characterizing the concentrations of monomer, solvent and initiator in the polymer mixture are formulated together with the concentrations of the first three moments of the living and dead polymer, including the volume variation of the reaction mixture. Equations are detailed in Appendix I. 2.3. Energy balance From the energy balance by Congalidis et al. (1989) the equations of variation of the reactor temperature and jacket temperature were formulated by considering the volume variation of the reaction mixture and the particular heat transfer system on the pilot plant (see Appendix I). 2.4. Volume change of the reaction content Volume shrinkage in the polymer, monomer, solvent and initiator as a result of increase of the density were formulated (see Appendix I). 2.5. Gel effect The free-volume correlations proposed by Schmidt and Ray (1981) were taken into account to represent the gel effect; thus, the propagation and termination rate constants were corrected (see Appendix I). 2.6. Physicochemical properties The variation of the density and the heat capacity of the polymer mixture due to the increase of the conversion were calculated according to the mixing rules, while the
Pilot-plant Simulation, Experimental Campaign and Rigorous Modeling of a Batch MMA Polymerization Reactor for the Fabrication of Bone Tissue 3 variation of the mixture viscosity due to the polymer growth was calculated through of the free-volume theory (López-Arenas et al., 2006). On the other hand, the heat transfer coefficient changes during the polymerization process due to the viscosity variations of the polymer mixture. Chilton, Drew and Jebens’s equations were applied to model the pilot plant (see Appendix I). 2.7. Molecular weight The method of moments was adopted to determine the weight and average molecular weights. These properties are obtained from the moment equations of living and dead polymer concentrations (see Appendix I).
3. Experimental campaign Figure 1 provides the schematic diagram of the batch PMMA polymerization system used in this work. The jacketed stainless-steel reactor has a capacity of 15 L and it is equipped with a pitched-turbine stirrer for the mixture of the reactants. An inverter is adopted to maintain the stirring speed at 360 rpm. The reactor temperature is controlled by manipulating the electrical power of the thermal oil heater and by manipulating the electrical power supplied to the six resistances that act on the fluid in the jacket. The collar type resistances connected in parallel to the tube of the jacket inflow can vary in the range of 0.0 – 61.6 W to manage the reactor temperature by split-range and cascade PID control algorithm. A HP (s5520br) personal computer and PLC (P7C, HI Tecnologia) is employed for data acquisition and polymerization process control. The MMA is treated by using the Sigma-Aldrich prepacked column (306312) to remove the inhibitor, the ethyl acetate (99.5%, Labsynth) and the AIBN® 64 (Du-Pont) are used as they are supplied. A flow rate of 0.04 l/min of gaseous nitrogen (grade 5.0 White Martins) is bubbled through the reacting medium to keep oxygen out of the reactor. An adapted experimental procedure from Chang and Liao (1999) is followed in this study. Samples of polymeric mixture (40 mL) are taken each 40 min to determine the density, viscosity and the conversion by the gravimetric method. These samples are quenched with methanol to precipitate the produced PMMA, and, next, are dissolved into Tetrahydrofurane (THF) for molecular weight analysis by gel permeation chromatography (GPC). A Viscotek GPCmax; VE2001 GPC solvent/sample module equipped with RI detector and two Phenogel columms (5µ 50 Å and 5µ 100 Å) is used. The calibration curves are built by using two standards polystyrene with a narrow molecular weight distribution (PS99K and PS280K). (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
Figure 1. Experimental reactor system.
Monomer storage tank initiator and solvent storage tank BATCH polymerization reactor product storage tank thermal oil storage tank reflux condenser thermal oil heater monomer pump initiator and solvent pump thermal oil pump cooling bath monomer stirring motor initiator and solvent stirring motor reactor motor product outlet solenoid valve helical coil (serpentine) jacket
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4. Determination of kinetic parameters The kinetic parameters of the polymerization are estimated by minimizing the sum of squares deviations of the Mw, Mn and monomer conversion, X predicted by the model from the experimentally measured values: N
2
n
(1)
f = ∑∑ (Fij mod − Fij exp ) i =1 j =1
where F = analyzed property, N = number of properties and n = number of data point. Sequential quadratic programming (SQP) method is adopted.
5. Results and discussion The proposed model was validated under isothermal conditions at 70°C. Table 1 presents the kinetic parameters of polymerization reactions. Figure 2 compares the experimental results and model previsions obtained for the most relevant states (reactor temperature, Tr, jacket temperature, Tj, Mw, Mn, X and mixture density, ρmix). The continuous increase of the experimental density evidences that the gel effect is present during the polymerization. Model predictions are in good agreement with experiments. Table 1. Calculated kinetic parameters. kinetic rate constant kd kp kt ktm kts ktc/ktd
Ei (J.mol-1) -1.342x105 -7.222x104 -9.012x104 -3.843x104 -9.149x104 -6.005x104
ai 3.493x1015 (s-1) 1.308x1014 (L.mol-1.s-1) 1.936x1022 (L.mol-1.s-1) 6.299x102 (L.mol-1.s-1) 2.850x109 (L.mol-1.s-1) 1.085x1011 (L.mol-1.s-1) 1.0
100 90
0.8
80
0.6
60
X
T / °C
70
0.4
50 40
0.2
30 20
0
0.0
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
0
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
t/s
t/s
120
1500 1400 1300 1200
80
1100
ρ mix
60
-3
Mn x 10 , Mw x 10
-3
100
40
900 800 700
20 0
1000
600
0
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
t/s
500
0
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
t/s
Figure 2. Experimental results compared to the model predictions for the Tr, Tj, Mw, Mn, X and ρmix. and are predicted values, --- and --- and and and are experimental values.
6. Conclusions and future perspectives The novel reacting system to produce medical poly–methyl-methacrylate (PMMA) has been described, operated and modeled, taking in account the volume variation and the
Pilot-plant Simulation, Experimental Campaign and Rigorous Modeling of a Batch MMA Polymerization Reactor for the Fabrication of Bone Tissue 5 gel effects. Kinetic parameters of the reaction mechanism to produce PMMA for medical applications have been estimated. Model predictions and experimental results are in good agreement. The obtained results clarify the possibility to implement a optimal control theory looking forward the very stringent specifications in porosity, molecular weight and polidispersity required to construct the scaffolds.
References Schmidt, Ray, 1981, The dynamic behavior of continuous polymerization reactor – I Isothermal solution polymerization in a CSTR, Chemical Engineering Science, 36, 14011410. Espalin, Arcaute, Rodriguez, Medina, 2010, Fused, deposition modeling of patient-specific polymethylmethacrylate implants, Rapid Prototyping Journal, 16, 3, 164-173. Manenti, Buzzi-Ferraris, 2009. Criteria for Outliers Detection in Nonlinear Regression Problems, Computer-Aided Chemical Engineering, 26, 913-917. Chang, Liao, 1999, Molecular weight control of a batch polymerization reactor: Experimental study, Industrial and Engineering Chemistry Research, 38, 144-153. Congalidis, Richards, Ray, 1989, Feedforward and feedback control of a solution copolymerization reactor, AIChE Journal, 35, 6, 891-907. Yunfeng, Fudong, Huiyong, 2009, Review on techniques of design and manufacturing for bone tissue engineering scaffold, Biomedical Engineering and Informatics, 17-19 Oct., DOI 10.1109/BMEI.2009.5305696. Lima, Zuniga Linan, Maciel Filho, Wolf Maciel, Embiruçu, Gracio, 2010, Modeling and predictive control using fuzzy logic: Application for a polymerization system, AIChE J., 56, 965-978. Ahn, Chang, Rhee, 1998, Application of optimal temperature trajectory to batch PMMA polymerization reactor, Journal of Applied Polymer Science, 69, 59-68. López-Arenas, Sales-Cruz, Gani, 2006, Computer-aided model based analysis for design and operation of a copolymerization process, Chemical Engineering Research and Design, 84, A10, 911-931.
Appendix I - Working equations Mass balances dCI C = − kd CI − I dVti dt Vti
(I1)
dCM C = −2 fkd CI − k p CM CG0 − ktrM CM CG0 − M dVti dt Vti
(I2)
dCS C = −ktrS CS CG0 − S dVti dt Vti
(I3)
dCG0 dt dCG1 dt dCG2 dt dCF0 dt dC F1 dt dCF2 dt
= 2 fkd C I − kt CG0 2 −
CG0 Vti
(I4)
dVti
= 2 fkd CI + k p CM CG0 − kt CG0 CG1 + (ktrM CM + ktrS CS )(CG0 − CG1 ) −
CG0 Vti
= 2 fkd CI + k p CM (CG0 + 2CG1 ) − kt CG0 CG2 + (ktrM CM + ktrS CS )(CG0 − CG2 ) − = (0,5(kt + ktd )CG0 2 ) + (ktrM CM + ktrS CS )CG0 − = kt CG0 CG1 + (ktrM CM + ktrS CS )CG1 −
CF1 Vti
CF0 Vti
(I5)
dVti CG2 Vti
dVti
(I6) (I7)
dVti
(I8)
dVti
= ktc (CG0 CG2 + CG1 2 ) − ktd CG0 CG2 + (ktrM CM + ktrS CS )CG2 −
CF2 Vti
dVti
(I9)
Energy balances dTr (−∆H p )k p CM CG0 U j Aj (Tr − T j ) U serp Aserp (Tserp − Tr ) Tr = − + − dt ρ mis cmis Vti ρ mis cmis Vti ρ mis cmis Vti dVti dT j dt
=
Q j (T jent − T j ) Vj
+
U j Aj (Tr − T j )
ρ j c jV j
−
U ∞ A∞ (T j − T∞ )
ρ j c jV j
+
Pres
ρ j c jV j
(I10) (I11)
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where, dVti is the difference in volume between the current time and the before time dVti = (Vti – Vti-1). Pres is the total potency of the system of six electrical resistances that help the jacket temperature control. Volume change of the reaction content dV p dt
=−
1
dC
dC
dT
dC
I ( M M * C M ) + ( M S * C S ) + ( M I * C I ) dVti + ( M M * M ) + ( M S * S ) + ( M I * ) Vti + V p ( −1,0 ) r ρ p dt dt dt dt
M jC j M j Vti = dVti + ρ ρ dt j0 j0
dV j
dC j , with j = M , S , I dt
(I13)
Gel effect k p = g p k p 0 ; kt = g t kt 0 where,
(I14)
V f > V fpc 1.0 gp = −5 7.1 × 10 exp(171.53V f ) V f ≤ V fpc V fpc = 0.05
;
(I12)
0.10575exp(17.15V f − 0.01715 × (T − 273.15)) gt = −5 0.23 × 10 exp(75V f )
;
V ftc = 0.1856 − 0.2956 × 10−3 (T − 273.15)
;
V f > V ftpc V f ≤ V ftc
;
V f = 0.025 + α p (T − Tg p )ϕ p + α M (T − TgM )ϕ M + α S (T − TgS )ϕ S
Physicochemical properties ( ( xM / ρ M ) + ( xS / ρ S ) + ( xI / ρ I ) )−1 ; t = 0
ρ mis ( g.L−1 ) =
( ( xM / ρ M ) + ( xS / ρ S ) + ( xI / ρ I ) + ( xP / ρ P ) )
−1
; t > 0
(I15)
( xM * c p M ) + ( xS * c p S ); t = 0 c pmis ( J .g −1 .K −1 ) = ( x * c ) + ( x * c ) + ( x * c ); t > 0 pM S pS P pP M
−2,3ϕ M * A (Tr ) + B ϕ M
µmis (kg .m −1.s −1 ) = AV (Tr − 273,15)− B × exp V
(I16)
CV
(I17)
*
U j −ref U h h U j = U j0 ; U serp = U serp0 serp−ref ; U ∞ = j _ ∞ ∞ _ j U h U j ref 0 serp ref 0 j _ ∞ + h∞ _ j − −
(I18)
where, Uj, Userp and U∞ are the heat transfer coefficient between the reactor and the jacket, between the internal serpentine and the polymer mixture and between the jacket and the surroundings, respectively. T A* (Tr ) = AA + BA 1 − r T gP
T + C A 1 − r TgP
2
; ϕM
hr _ j h j _ r (VM 0 + VS 0 ) / Vt 0 ; t = 0 = ; U j −ref = hr _ j + h j _ r (VM + VS ) / Vti ; t > 0
Molecular weight and polidispersity G + F2 G + F1 Mw = 2 ; Mn = 1 ; G1 + F1
G0 + F0
P=
Mw Mn
; U serp−ref
=
hr _ serp hserp _ r hr _ serp + hserp _ r
(I19)
Nomenclature a : pre-exponential factor; E: activation energy; R: gas constant; A: area; AIBN: Azobisisibutyronitrile; C: molar concentration; c: heat capacity; f: initiator efficiency; g: gel effect correlation coefficient; H: enthalpy; k: kinetic rate constant; M: molecular weight; Q: volumetric flow rate; U: heat transfer coefficient; V: volume; x: molar fraction; AA, Av, A*, BA, Bv, CA, Cv: viscosity parameters; µ: dynamic viscosity; φ: volume fraction. Subscripts: c: combination; d: initiation, disproportionation; ent: entry; f: free; fc: critical free; Fk: k-th moment of polymer dead; Gk: k-th moment of polymer living; I: initiator; j: jacket; M: monomer; mis: mixture; P: polymer, propagation; r: reactor; ref: reference; res: resistance; S: solvent; serp: serpentine; t: tempo, termination; tr: chain transfer; ∞: ambient air.
Acknowledgements The authors acknowledge the financial support of FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo).
