Real Time Optimization for Freeze Drying Process

Transcription

1 Real Time Optimization for Freeze Drying Process Edinara Adelaide Boss *, Eduardo Coselli Vasco de Toledo and Rubens Maciel Filho Laboratory of Optimization, Design and Advanced Control, Chemical Process Department, Chemical Engineering Faculty State University of Campinas UNICAMP, C. P: 6066 Zip Code: Campinas, São Paulo, Brazil Abstract Freeze drying process has different applications including pharmaceutical products, foodstuffs (whose organoleptic properties are important and have to be maintained) and other industrial bioproducts (conservation of living microorganism, dehydration or concentration of heat labile). The interesting factors to be analyzed are the structural rigidity, which facilitates rapid and almost complete rehydration at a later time, little loss of flavor, and minimization of degradative reaction, which, normally, occurs in ordinary drying processes, such as protein denaturation, non enzymatic browning and enzymatic reactions. The process variable interactions are complex, and the experimental approach for examining the various operational policies is hard, expensive and time consuming. Multivariable process requires exhaustive simulation to understand the system behavior as well as to identify which are the most important process variables. This information are important for developing of optimization strategies. A theoretical model was developed and solved in order to describe quantitatively the dynamic behavior of the primary and secondary drying stages. The solution procedure involves the discretization of the equations by orthogonal collocation in the axial direction and the integration with respect to time by an algorithm based on the Runge- Kutta method. For the validation procedure the result of the solution model were compared with real values (pilot plant for skimmed milk and industrial plant for soluble coffee) to validity the proposal. The model allows carrying out numbers of simulation, so that it is possible to observe which are the design operationally variables that more significantly impact the system behavior. The objective of this work is, also, to obtain a mathematical model that can predict the experimental data to simulate the process to aim at high quality dried product with the minimum time process. The results show that the proposed model presents better prediction than the existing mathematical model since a more detailed description is provided. The next step was to definy the operational strategies and the implementation of optimization algorithms. For the freeze drying optimization process solution, the option was to use an algorithm based on the non linear programming routine developed by Schittkowsky (1985). This routine solves general problems of non linear programming and it was adapted quitelly well to the proposed mathematical model.the optimization of the freeze dryer process showed the real benefits by decreasing the process time and the amount of residual water. * Author to whom correspondence should be adressed : boss@lopca.feq.unicamp.br

2 Keywords: Freeze-drying, Dynamic Process, Mathematical Model, Optimization 1. Introduction Freeze drying is a process by which a solvent is removed from a frozen material or frozen solution by sublimation of the solvent and by desorption of the sorbed solvent, generally, under reduced pressure. This process involves the following three stages: freezing, primary drying and secondary drying stages. The performance of the overall freeze drying process depends significantly on the freezing stage. The material to be processed is cooled down to a temperature bellow the solidification. The shape of the pores, the pore size distribution, and the pore connectivity of the porous network of the dried layer formed by the sublimation of the frozen water during the primary drying stage depend on the ice crystals formed during the freezing stage. An excellent option is to obtain large dendritic ice crystals formed and a homogeneous dispersion due to the high mass transfer rate of the water vapor in the dried layer, so that the product could be dried more quickly. The solvent is removed by sublimation under a vacuum pressure and heat addition in the primary drying stage is carried out. A significant amount of the latent heat of sublimation is also kept when the water molecules sublime and enter the vapor phase. Because of this, the temperature of the frozen product is reduced. Then it is necessary to supply the heat to the product. The heat can be provided by conduction, convection and/or radiation. During the secondary drying stage the solvent is removed of the chamber and a small amount of sorbed water can be removed by desorption. The bound water is removed by heating the product under vacuum. In this paper a deterministic mathematical model is developed and validated through pilot plant experimental data for skimmed milk and industrial data for soluble coffee. Both processes are optimised by SQP method. 2. Mathematical Model A mathematical model based on fundamental mass and energy balance equations have been developed, based on an existent model (LIAPIS and SADIKOGLU, 1997), and used to know the amount of removed and residual water. The assumptions are the ones considered by Millman et. al. (1985) and Lichtfield and Liapis (1979). The energy balance of the developed dynamic model is shown in equation (1). The mass balance equations are described in equations (2) to (4). TI t ( N T ) H Cp vρ I Csw g t I C1. P =. ρ Ie. CpIe t ρ Ie. CpIe x ( C. ρ. L) Ie (1) The previous equation is valid for the primary an secondary dried periods, differing an application intervals and on the data to be used, which depend on the dried period that they refer to. For the first period, the interval is 0 x X and for the secondary period is 0 x L.

3 T t II 2 TII = α II, X x L (2) 2 x 1 p R t T w I 1 N w = M wε x ρ I C M ε t w sw, 0 x X (3) 1 pin 1 N in R t = T, 0 x X (4) I M inε x C The term sw accounts for changes in the concentration of sorbed or bound t water with time. T I is the dried layer temperature (K), H v is the enthalpy of vaporization of sorbed water (J/kg ), ρ I is the dried layer density (kg/m 3 ), ρ Ie is the effective dried layer density (kg/m 3 ), Cp Ie is the effective dried layer heat capacity (J/(kg K)), Cp g is the gas heat capacity (J/(kg K)), N t is the total mass transfer flux (kg/(m 2 s)), T II is frozen layer temperature (K), α II is the frozen layer thermal diffusivity (m 2 /s), R is universal gas constant, p W is the partial pressure of the water pressure (N/m 2 ) and p in is the partial pressure of inert gas (N/m 2 ), M W is the molecular weight of the water pressure and M in is the molecular weight of inert gas, N W is the water vapor mass transfer flux (kg/(m 2 s)) and N in is the inert gas mass transfer flux (kg/(m 2 s)), ε is the voidage fraction. 3. Optimization The optimization is a tool through which can be solved problems referring project, construction, operation and analysis of plants. It is also one of the main quantitative tools in the mechanism of taking decisions. In this work it will be studied the process optimization of freeze drying process of the milk skimmed as for the process of the soluble coffee, using the mathematical model developed in the previous section. The method of Successive Quadratic Programming (SQP) will be used for resolution of the non linear equations that are included in the mathematical model developed. There are several subroutines for implementation that solve the problems of SQP non linear programming. For the freeze drying optimization process the option was a routine based on the routine NLPQL developed by Schittkowsky, in The routine NLPQL solves general problems of non linear programming and it adapted well to the used mathematical model. 3.1 Freeze drying optimization process of the skimmed milk In the freeze drying process the largest problem is the time of drying, as larger the time, larger the energy costs. Because of this it was chosen the objective function to minimize: the drying time. Based on the factorial design, 3 variables were manipulated: thickness of the layer on the tray of the freeze dryer (L), the temperature of the plates under the tray (Tplate) and the pressure in the freeze drying chamber (P).

4 As the freeze drying of the two drying stages is not possible to optimized at the same time, the optimization was focused in the first period that refers to the period in that happens the largest removal of water. After optimized the first period the results were analyzed for the second period. 3.1 Freeze drying optimization process of the skimmed milk The optimization of the freeze drying process for the soluble coffee was accomplished in the same way that the optimization of the freeze drying process of the skimmed milk. 4. Results and Discussion The results and discussion will be divided in the mathematical model results and the optimization results as the follow. 4.1 Mathematical results The predictions for the literature model (LIAPIS and SADIKOGLU, 1997) and the mathematical model developed are shown in Figures 1 and 2, together with the real data. It is observed that the developed mathematical model presents better prediction compared to the original model in relation to the real data. The Figures 3 and 4 show the amount removed and residual water compared to soluble coffee industrial data. A company that possesses a continuous plant in operation supplied the values of the parameters required to the calculation model. Figures 3 and 4 show that the developed mathematical model represents well the soluble coffee freeze drying process of a real plant in continuous operation. AMOUNT OF REMOVED WATER (KG) 0,6 0,5 0,4 0,3 0,2 0,1 CURVE1 CURVE2 0,15 0,05 CURVE1 CURVE2 0, Figure 1: Amount of water removed versus the time during the primary period of the process of "freeze drying" of the skimmed milk. CURVE1: existent model. : real data. CURVE2: developed model. Figure 2: temperature versus the time during the apprenticeship of primary period of the process of " freeze drying " of the skimmed milk. CURVE1: existent model. : real data. CURVE2: developed model.

5 AMOUNT OF REMOVED WATER (KG) 0,6 0,5 0,4 0,3 0,2 0,1 MODEL ,090 0,085 0,080 0,075 0,070 0,065 0,060 0,055 0,050 0,045 0,040 0,035 0,030 0,025 0,020 0,015 0,010 0,005 0,000-0,005 MODEL Figure 3: Amount of water removed versus time during the primary drying stage of freeze drying of soluble coffee. Figure 4: Amount of residual water versus time during the secondary drying stage of freeze drying of soluble coffee. 4.2 Optimization results Observing the Figures 5 and 6 is noticed that was obtained a significant improvement in the freeze drying process of the skimmed milk. For the same amount of removed water was used half of the time of the previous results. This also test that the freeze drying process is sensible to change values of some manipulated variables. The amount of residual water in the process optimized is much smaller than in the process without optimization, attesting larger efficiency after optimization In the Figures 5 and 6 were presented the real results compared with the optimized process of the skimmed milk. 0,65 0,12 AMOUNT OF REMOVED WATER (KG) 0,60 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0,20 OTM 0,15 WOTM ,08 0,06 0,04 0,02 0,00 OTM WOTM Figure 5: Amount of water removed versus time during the primary drying stage of freeze drying of skimmed milk. Comparison of the data without optimization (WOTM) and optimized data (OTM). Figure 6: Amount of residual water versus time during the secondary drying stage of freeze drying of skimmed milk. Comparison of the data without optimization (WOTM) and optimized data (OTM). The Figures 7 and 8 present the real results compared with the optimized for the freeze drying process of the soluble coffee. Observing the Figures 7 and 8 is noticed that it was obtained a significant improvement in the freeze drying process of soluble coffee. For the same amount of removed water

6 was used one hour and a half less of the time of the previous process. The amount of residual water in the optimized process is much smaller than in the process without optimization, attesting larger efficiency after optimization. 0,6 AMOUNT OF REMOVED WATER (KG) 0,5 0,4 0,3 0,2 0,1 OTMDATA 0,08 0,06 0,04 0,02 0,00 OTMDATA Figure 7: Amount of water removed versus time during the primary drying stage of freeze drying of soluble coffee. Comparison of the real data () and optimized data (OTMDATA). 5. Conclusions Figure 8: Amount of residual water versus time during the secondary dried stage of freeze drying of soluble coffee. Comparison of the real data () and optimized data (OTMDATA). The results show that the mathematical model represents well the processes. The optimization is an important tool to maximize the amount of removed water and the amount of residual water. Acknowledgement The authors acknowledge the financial support from FAPESP. Process: 99/ References Liapis, A. I. and Sadikoglu, H. (1997) Mathematical Modeling of the Primary and Secondary Drying Stages of Bulk Solution Freeze-Drying in Trays: Parameter Estimation and Model Discrimination by Comparison of the Theoretical Results with Experimental Data. Drying Technology. Missouri, v. 15, n 3-4, p , Lichtfield, R. J., Liapis, A I. (1979)An absorption-sublimation model for a freeze dryer. Chemical Engineering Science. Great Britain, v. 34, n. 9, p Millman, M. J., Liapis, A. I. and Marchello, J. M. (1985) An Analysis of the Lyophilization Process Using a Sorption-Sublimation Model and Various Operational Policies. AIChE Journal. Missouri, v.31, n. 10, p Schittkowski, K. (1985) NLPQL: A FORTRAN-subroutine for solving constrained nonlinear programming problems, Annals of Operations Research, v. 5, p