MODELING AND VALIDATION OF THE CONTINUOUS HTST THERMAL PROCESSING OF LIQUID FOODS WITH PLATE HEAT EXCHANGERS. Abstract

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1 MODELING AND VALIDATION OF THE CONTINUOUS HTST THERMAL PROCESSING OF LIQUID FOODS WITH PLATE HEAT EXCHANGERS Rafael V. Benze, Jorge A. W. Gut University of Sao Paulo, BRAZIL NAPAN: Food and Nutrition Research Center, USP, BRAZIL Abstract The continuous HTST thermal processing of a liquid food using a three-section plate heat exchanger (heating, cooling, heat regeneration) was modeled to obtain the product temperature history and the distributed lethality. The model consists of differential equations and boundary conditions for heat transfer and thermal inactivation along the exchanger channels and tubular sections. For the residence time of each step, the space time, the experimental mean residence time or the minimum residence time can be used depending on the analysis (evaluation or design). The model was tested and validated using a laboratory-scale equipment processing an enzymatic time-temperature integrator (TTI) at four different conditions (7, 75, 8 and 85 ºC). Previous studies on heat transfer and residence time distribution provided parameters for the model simulation. The results for temperature distribution were in excellent agreement with the experimental values (mean absolute error of 1.1 ºC). The predicted residual activity of the TTI was close to the experimental values assessed at after the heating section and at the end of the process. A case study showed that the inlet and outlet connections of the holding tube have a significant contribution to the lethality. The proposed model can be useful for process evaluation or equipment design, taking into account the heat integration of the process. Introduction Thermal processing of liquid foods aims the inactivation of micro-organisms and enzymes that compromise the safety or the shelf life of the product. The design of continuous processes using heat exchangers usually rely on simplifying assumptions that provide a wide safety margin and facilitate calculations, such as isothermal processing only at the holding tube at the minimum residence time. These assumptions can impair sensory or nutritional attributes of the product because of unnecessary over-processing [1, 2]. The aim of this work was to develop and validate a phenomenological model to simulate the continuous HTST pasteurization with plate heat exchangers in order to determine the distribution of the temperature of the fluids and of the concentration of the target micro-organism or activity of the target enzyme throughout the process. This physical model should be based on conservation and transport equations and take into account the heat integration of the process. Mathematical Modeling The considered pasteurization process comprises an inlet tank, a plate heat exchanger (PHE) with three sections (heating, cooling and heat regeneration), a holding tube, two tubular connections between the PHE and the holding tube, a hot water circuit and a cold water circuit, as shown in Figure 1

2 1. The model includes equations for flow, heat exchange and lethality. Main assumptions were: steadystate operation, plug-flow in the channels of the PHE and tubes, uniform flow distribution among PHE channels, heat exchange with environment in the tubular sections, no axial diffusion and uniform thermo-physical properties in each section. Figure 1. Representation of the HTST thermal process unit The heat transfer in a PHE section was modeled according to Gut and Pinto [3]. Each channel i of the PHE provides one differential equation for the axial channel temperature distribution T i (), as in Eq.(1), where is the dimensionless length and i is the dimensionless overall heat transfer coefficient that corresponds to channel i. The required boundary condition for this equation is the inlet temperature of the channel, which depends on the pass arrangement and flow configuration of the PHE. The overall heat transfer coefficient was calculated based on the thermal resistances to heat transfer [3]. Ti i T i1 2Ti Ti 1 (1) The axial temperature distribution T t () in a tubular section can be obtained from Eq.(2), where t is the dimensionless overall heat transfer coefficient between the food product and the environment and T is the room air temperature. Tt t T t T (2) The concentration of the target micro-organism or activity of the target enzyme was represented by the distributed variable C A (). In principle it was assumed that the thermal inactivation 2

3 follows first order kinetics; however, other models can be used as well. In the case where parameters D-value at reference temperature (D ref ) and z-value (z) are available, the equation for conservation of species C A () can be reduced to Eq.(3) for a single PHE channel or tubular section. Boundary condition for this differential equation is the inlet value of C A, which depends on the process flow configuration. The sign of the second term in Eqs.(1) and (3) is related to the flow direction. C A D ref ln T alog ref C T z A (3) In Eq.(3), is the space time (length velocity ratio) of the PHE channel or tube. In practice the mean residence time is smaller than the space time because of the presence of recirculation or stagnation areas that reduces the active volume of the vessel [4]. In the proposed model, the space time in Eq.(3) can be replaced by the experimental mean residence time or by the minimum residence time, depending on the desired study (evaluation, validation, design or optimization). For an evaluation study, the mean residence time would be more appropriate; however, for process design, the minimum residence time would be recommended in view of the process safety margin. The model consists of a system of differential equations with boundary conditions that can be solved by numerical methods. Model simulation provides axial distribution of product temperature and the associated lethality, allowing the assessment of the contribution of each process step on the lethal effect. Accordingly, the distributed sterilization value of a micro-organism can be calculated using Eq.(4), where C A is the process inlet value of C A. In the case of an enzyme, the distributed residual activity can be obtained through Eq.(5). C A SV log (4) CA RA C A (5) CA The degradation of nutrients or quality attributes can also be modeled using variable C A (), as long as the kinetic parameters for thermal degradation are available [1]. Materials and Methods In order to test and validate the model, it was applied for the evaluation of a laboratory scale plate pasteurizer processing an enzymatic time-temperature integrator (TTI). The equipment used was a FT-43A pasteurizer (Armfield, UK) that essentially consists of a plate heat exchanger with flat plates (.51 m²/plate), gaskets and connector plates, a peristaltic feed pump, a holding tube (75 ml), a feed tank (4 L), a hot water circuit with electric heating and temperature control and a chilled water circuit [5]. 3

4 The sections of the PHE were configured for series flow (one channel per pass) with 11 thermal plates in the heating section, 7 thermal plates in the cooling section and 19 thermal plates in the heat regeneration section. Product flow rate was 2 L/h and the flow rate of the service fluids was 1, L/min (hot water and cold water). Twelve thermocouples were inserted in the tubing and connected to a cdaq-9172 acquisition system with three NI-9211 modules (National Instruments, USA) and a computer running a data-logger software. Figure 2 presents the experimental equipment and indicates the temperature acquisition points in accordance to Figure 1. p5 p4 p3 p2 p1 c2 c1 h1 h2 p6 p7 p8 Figure 2. Experimental equipment showing temperature acquisition points in accordance to Figure 1. The tested product was phosphate buffer (ph = 6.6, ionic strength 5 mm) with alkaline phosphatase from bovine intestinal mucosa (EC ) acting as an enzymatic time temperature integrator (TTI), as proposed by Aguiar et al. [6]. Enzymatic activity was measured using a reflectometric method and the inactivation kinetic model used was first order with two isoenzymes. The adjusted kinetic parameters of the thermostable fraction were D S,ref = 478 s and z S = 7.57 ºC and the adjusted parameters of the thermolabile fraction were D L,ref = 3.53 s and z L = 6.57 ºC (T ref = 75 ºC). Parameter =.585 represents the fraction of the initial activity associated with the thermostable isoenzyme. Processing temperatures were 7, 75, 8 and 85 ºC and the controller manipulated the inlet temperature of the hot water in order to achieve the desired temperature at the end of the holding tube. Temperatures at twelve points along the process were continuously registered using the data acquisition system. Samples of the TTI were collected at the exit of the heating section of the PHE (point p3 in Figure 1) and after the cooling section (p8 in Figure 1). Collected samples were immersed in ice-water bath to stop the inactivation, prior to activity assessment. Samples of the unprocessed TTI were also reserved. Activity was measured in triplicates. The process was simulated using the proposed mathematical model in order to compare experimental and predicted results of temperature distribution and process lethality. Parameters provided for the model simulation were: geometrical parameters of plates and tubes, mean thermophysical properties, inlet temperatures and flow rates, inlet activity of TTI, kinetic parameters for thermal inactivation, heat exchange parameters of the PHE and mean residence times of each process 4

5 step. The model was solved using a finite difference method in software gproms 3.2 (Process System Enterprise). Discretized variables were the temperature of the fluids and enzymatic activity. The mean residence time in the channels of the PHE were obtained from the work of Gutierrez et al. [7] and the mean residence time in the holding tube were obtained from Gutierrez et al. [8]. Space time was calculated for the tubular connections because residence time distribution studies were not available for these parts. The Nusselt Reynolds correlation for the heat transfer in the PHE was obtained according to Gut et al. [5] for series pass arrangements with variable flow rate and number of plates. Mean overall heat transfer coefficients for tubular sections were acquired from experimental data. Results and Discussion The model simulation provided the temperature history of the product along the process and the distributed residual activity of the enzymatic TTI. Figure 3 presents the obtained experimental and simulation results for temperature and residual activity of the TTI for the four processing conditions (7, 75, 8 and 85 ºC). It can be seen that there was an excellent agreement between predicted and experimental temperatures at the registered points with a mean absolute error of ºC for all processing conditions. Taking into consideration that only the inlet temperature of the product was specified in order to predict the temperature at the other positions, the thermal simulation of the process can be considered successful ºC ºC ºC Figure 3. Obtained experimental and simulated results for temperature distribution and residual activity of the TTI for the four processing temperatures ºC

6 Regarding the lethality, there was a good agreement between predicted and measured residual activities of the TTI at the end of the heating section since the simulated values were in the confidence interval of the experimental values. However, the simulated values of residual activity at the end of the process were consistently inferior to the measured values. This deviation can be explained by the use of the space time instead of the mean residence for the tubular connections. Since the experimental mean residence time is shorter than the calculated space time, the predicted residual activity was smaller for these high-temperature steps. Moreover, the adjusted kinetic model showed larger deviations for RA <.2, in which the calculated value was lower than the measured value. This could also explain the deviation of the process lethality at processing temperature of 85 ºC. In order to test the model, it was used to simulate the thermal processing of milk in the experimental equipment with respect to the inactivation of Coxiella burnetti. The results of distributed temperature and sterility value are presented in Figure 4. The temperature history and sterility value curve show that the inlet and outlet connections of the holding tube play an important role on the process lethality. On the other hand, the lethality associated with the heat exchangers was not significant in this case study. There was also an important contribution on the lethality from the nonisothermal holding tube that requires a higher temperature at its entrance. The predicted process lethality using the mean residence time of each process step was SV = 8.7. Instead, if the space time was used, an overestimated sterility value of 9.3 would be obtained. 8 7 SV Regeneration I Heating Conection I Holding Tube Conection II Regeneration II Cooling T Sterilization Value Mean Residence Time(s) Figure 4. Simulation results for the thermal processing of milk in the experimental equipment targeting the inactivation of Coxiella burnetti. 6

7 Conclusions The proposed simulation model allows the simulation of a continuous HTST thermal processing with plate heat exchangers in order to determine the temperature history and process lethality. With the experimental data used in this work it was possible to validate this model, which can be used for analysis, design or optimization problems. The main contribution would be in the sizing of the PHE sections, which is not trivial because of the heat integration of the process. Moreover, the model allows different parameters to be used as residence time of each process step (space time, experimental mean residence time or minimum residence time), depending on the desired analysis. References 1. Awuah, G.B.; Ramaswamy, H.S.; Economides, A. (27), Thermal processing and quality: Principles and overview, Chemical Engineering and Processing 46, pp Ávila, I.M.L.B.; Silva, C.L.M. (1999), Methodologies to optimize thermal processing conditions: an overview, in: Oliveira, F.A.R.; Oliveira, J.C. (Eds.), Processing Foods: Quality Optimization and Process Assessment, Boca Raton, CRC Press. 3. Gut, J.A.W.; Pinto, J.M. (23), Modeling of plate heat exchangers with generalized configurations, International Journal of Heat and Mass Transfer 46(14), pp Levenspiel, O. (1999), Chemical Reaction Engineering, 3rd ed., New York, John Wiley & Sons. 5. Gut, J.A.W.; Fernandes, R.; Pinto, J.M.; Tadini, C.C. (24), Thermal model validation of plate heat exchangers with generalized configurations, Chemical Engineering Science 59, pp Aguiar, H.F.; Yamashita, A.S.; Gut, J.A.W. (212), Development of enzymatic timetemperature integrators with rapid detection for evaluation of continuous HTST pasteurization processes, Lebensmittel-Wissenschaft + Technologie / Food Science + Technology 47(1), pp Gutierrez, C.G.C.C.; Dias, E.F.T.S.; Gut, J.A.W. (211) Investigation of the residence time distribution in a plate heat exchanger with series and parallel arrangements using a non-ideal tracer detection technique, Applied Thermal Engineering 31(), pp Gutierrez, C.G.C.C.; Dias, E.F.T.S.; Gut, J.A.W. (2), Residence time distribution in holding tubes using generalized convection model and numerical convolution for non-ideal tracer detection, Journal of Food Engineering 98(2), pp