A modeling approach for evaluating process uniformity during batch high hydrostatic pressure processing: combination of a numerical heat transfer model and enzyme inactivation kinetics

Innovative Food Science & Emerging Technologies 1 Ž2000. 5]19

A modeling approach for evaluating process uniformity during batch high hydrostatic pressure processing: combination of a numerical heat transfer model and enzyme inactivation kinetics Siegfried Denys, Ann M. Van Loey, Marc E. Hendrickx U Department of Food and Microbial Technology, Laboratory of Food Technology, Faculty of Agricultural and Applied Biological Sciences, Katholieke Uni¨ ersiteit Leu¨ en, Kardinaal Mercierlaan, 92, B-3001 He¨ erlee, Belgium Received 6 August 1999; accepted 10 November 1999

Abstract A numerical conductive heat transfer model for calculating the temperature evolution during batch high hydrostatic pressure ŽHHP. processing of foods was tested for two food systems: apple sauce and tomato paste. Hereto, relevant thermal and physical properties of the products were determined. For a comprehensive evaluation, both ‘conventional’ HHP processes with gradual, step by step pressure build-up and pressure release were simulated. In all cases, satisfactory agreement between experimental and predicted temperature profiles was obtained. The model provides a very useful tool to evaluate batch HHP processes in terms of uniformity of any heat- andror pressure-related effect. Uniformity of inactivation of Bacillus subtilis a-amylase and soybean lipoxygenase during batch HHP processing was evaluated. Hereto, a theoretical as well as an experimental approach was used. The residual enzyme activity distribution appeared to be dependent on the inactivation kinetics of the enzyme under consideration and the pressure]temperature combinations considered. Good agreement between the theoretical considerations and experimentally obtained activity retentions was found for Bacillus subtilis a-amylase. In case of soybean lipoxygenase, less agreement was found. This work presents a first step in the development of indicators to assess process uniformity in HHP processing of foods. Q 2000 Elsevier Science Ltd. All rights reserved. Keywords: High pressure processing; Modeling; Heat transfer; Process uniformity Industrial rele¨ ance: The fundamental and systematic approach pursued by the authors to identify high pressure processing uniformity is of high relevance for the optimization and regulation of high pressure processing of foods, because process inhomogeneity may lead to insufficient inactivation of microorganisms and enzymes, especially in large scale batch type high pressure units.

1. Introduction Consumer demand for fresh-like food products with minimal degradation of nutritional and organoleptic properties has stimulated research on new non-thermal treatments or combined Ž‘hurdle’. processes in food industry ŽHoover, Metrick, Papineau, Farkas, & Knorr, U

Corresponding author. Tel.: q32-16-321585; fax: q32-16-321960. E-mail address: [email protected] ŽM.E. Hendrickx.

1989; Mertens, 1995.. High hydrostatic pressure ŽHHP. is an emerging technology in the area of food processing and preservation and has been applied for preservation purposes and as a method to change the physical and functional properties of food systems ŽHayashi, 1989; Cheftel, 1991; Knorr, 1995; Messens, Van Camp, & Huyghebaert, 1997; Hendrickx, Ludikhuyze, Van den Broeck, & Weemaes, 1998.. It is generally known that high pressure is set immediately and uniformly throughout the pressure vessel Žthe Pascal principle.. Consequently, it is often stated that the processing

1466-8564r00r$ - see front matter Q 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 4 6 6 - 8 5 6 4 Ž 9 9 . 0 0 0 0 3 - X

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S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

time is independent of product size and geometry ŽFarr, 1990; Cheftel, 1991; Knorr, 1993.. However, care should be taken with this statement, since temperature gradients may prevail in the processed product ŽDenys, Van Loey & Hendrickx, 2000.. Batch HHP processes require compression of the workload, resulting in a proportional temperature increase, the extent of which depends on the thermal and physical properties of the compressed product. After compression, heat loss through the metal wall of the high pressure vessel causes temperature gradients in the processed product. The different pressure]temperature]time profiles perceived during a process at different locations in the high pressure vessel may result in a pronounced nonuniform distribution of enzyme andror microbial inactivation, nutritional andror sensorial quality degradation, etc ., within the processed product. Depending on the pressure]temperature degradation kinetics of the component that is focussed on, the effect will be more or less pronounced. In previous work, the authors presented a numerical conductive heat transfer model, capable of predicting the temperature evolution within a workload during batch HHP processes ŽDenys, Van Loey & Hendrickx, 2000.. The model was tested for a food simulator Žagar gel 1.5%. and provides a useful basis for evaluating the uniformity of HHP processes. In the present paper, the validity of the model was further tested for two real food systems: apple sauce and tomato paste. This implies incorporating the correct thermal and physical properties needed in the model. A line heat source probe method was used in previous work for measuring the thermal conductivity of products in a high-pressure apparatus. Thermal conductivity measurements of apple sauce and tomato paste were determined ŽDenys & Hendrickx, 1999.. The method proved to be a fast and accurate way for obtaining the thermal conductivity of materials at high-pressure and the obtained values will serve for evaluating the heat transfer model in the present work. Other properties need to be determined. These include density, specific heat and thermal expansivity wi.e. the thermodynamic coefficient determining the relative volume change per unit temperature change a s 1rV? Ž­Vr­T .P x. Furthermore, the model was used to evaluate HHP processes in terms of process uniformity by incorporating pressure]temperature inactivation kinetics in the numerical scheme. Inactivation of Bacillus subtilis aamylase ŽBSAA. and soybean lipoxygenase ŽLOX. were examined as case studies. These enzymes were selected because their combined pressure]temperature inactivation have been thoroughly studied by Ludikhuyze Ž1998., who formulated a mathematical model describing the Žfirst order. inactivation of these enzymes as a function of pressure, temperature and time. Parame-

ters describing the reaction kinetics for destruction of microorganisms, enzymes, etc., should insure that the objective of the process has been accomplished everywhere within the food product. In this work, uniformity tests were conducted to validate the approach.

2. Materials and methods 2.1. Food products Apple sauce and tomato paste were purchased as canned products. These products were chosen for their homogeneous and uniform composition: this should insure repeatable measurements of the relevant thermal properties and of the temperature profiles recorded during HHP processes. 2.2. HHP equipment and processing A warm isostatic press ŽSO. 5-7422-0, Engineered Pressure Systems International, Belgium. with maximum operating pressure of 600 MPa and internal volume 590 ml Ždiameter 50 mm, height 300 mm. was used ŽFig. 1.. The pressure transfer medium was a mixture of 60% DowcalN ŽThe Dow Chemical Company, Switzerland. in distilled water. A fluid-flow tube jacket in thermal contact with the outer wall of the vessel and connected to a heating and cooling unit ŽHaake KT 50W, Haake GmbH, Germany., allowed heating and cooling of the system. The working temperature range of the equipment was y35 to 1008C. The equipment was provided with type K thermocouples for measuring temperatures at different positions inside the high-pressure vessel. Temperatures and pressure were monitored by a computerized data acquisition system ŽSCXI controlled by LabVIEW, National Instruments, Belgium.. Due to limitations of the equipment, an overshoot of pressure as compared as compared to the preset pressure was observed and consequently, it was difficult to control the exact pressure of a HHP process. As a result, the conditions of the HHP processes could slightly deviate from the desired conditions. After reaching the maximum pressure, a pressure drop is generally observed due to heat loss through the vessel wall and small leaks. The products were inserted in a cylindrical aluminum product container ŽFig. 1. Ž42 mm i.d., 3 mm wall thickness .. Only a thin layer Ž1 mm. of pressure transfer medium separated the product container from the inner wall of the vessel. Thus, the impact of Žconvective and conductive. heat transfer in this layer was minimized. The bottom of the product container consisted of a movable piston to transfer the applied pressure to the product ŽFig. 1.. The product container was covered with a lid connected to the stopper of the

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Fig. 1. Schematic representation of the isostatic press and the product container.

high-pressure vessel to position the container in the geometric center. For evaluating the heat transfer model, temperatures were recorded in the product: three hollow stainless steel tubes Ž2 mm o.d.. were soldered at the lid of the product container for positioning thermocouples in different positions of the product: one in the geometric center, one near the inner wall of the product container Ž20 mm from the geometric center. and a third in between the other two Ž10 mm from the geometric center.. In this way, thermocouples were positioned in the product while avoiding inflow of pressure transfer medium. The tips of the thermocouple tubes were also soldered to avoid mixing of pressure medium and product. After filling and centering the product container in the high pressure apparatus, a temperature equilibration period was exercised and a batch HHP process was simulated by compressing the system to a preset pressure. Both ‘conventional’ HHP processes and more complex HHP processes with gradual, step by step compression and decompression, were conducted to test the heat transfer model. Nine ‘conventional’ batch HHP processes were conducted for each product, each one characterized by a particular combination of initial

temperature Ž10.3" 0.18C, 20.2" 0.18C or 34.9" 0.18C. and applied pressure Ž167.8" 7 MPa, 313 " 13 MPa or 459 " 14 MPa.. In the case of gradual, step-by-step compression and decompression, pressure]time profiles as indicated by the dotted lines in Fig. 8 were applied. In all cases, the pressure and the temperature in the three positions were measured and recorded every 10 s. During compression and decompression steps, the time interval between two measures was reduced to 4 s. 2.3. Heat transfer model The model used for calculating heat transfer during batch HHP processes ŽDenys, Van Loey & Hendrickx, 2000., is based on a numerical solution of the Fourier ¨ equation for a conductive heating finite cylinder with finite surface heat transfer coefficient. A Delphi 3 computer program was applied for numerically solving the heat transfer differential equations in the cylindrical contents Žtwo-dimensional geometry. of the highpressure vessel, using an explicit finite difference scheme. Conductive heat transfer through the product and the pressure transfer medium was considered by

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constructing a spacial grid and associating the relevant properties to the apropriate nodes. To predict the temperature increase of the workload, corresponding to compression periods, Eq. Ž2. was incorporated in the Fourier ¨ balances as an internal heat generation term. This equation was derived from the second T dS equation for reversible adiabatic change of pressure ŽZemansky, 1957.: during a reversible compression or expansion of an adiabatic system, the entropy S remains constant and T dS s 0 s C p dT y T

ž ­V­T / d P p

Ž1.

or dT s d P?

T?V?a p Cp

Ž2.

In these equations, T represents temperature ŽK., P pressure ŽMPa. and V is the specific volume in cm3 gy1 . C p is the specific heat of the product ŽJ gy1 8Cy1 . and a p its thermal expansivity ŽKy1 .. dT represents the temperature change corresponding to a pressure change d P. A numerical approach to calculate the temperature evolution during compression Žor expansion. of food products has some important advantages: Ž1. temperature gradients caused by heat transfer through the wall of the high-pressure vessel are calculated Ži.e. the non-adiabatic nature of compression in a real system is accounted for.; and Ž2. non-linear thermal and physical properties can be handled. An overall heat transfer coefficient of 300 W my2 8Cy1 was used for all predictions. This value was obtained from the temperature gradient in a test product Žagar gel 1.5%., experimentally measured after compression to a particular pressure level in a certain time span. For a more detailed description of this model, the reader is referred to Denys, Van Loey, and Hendrickx Ž2000.. As for all heat transfer models, accurate thermal and physical properties of the products at the appropriate conditions are needed and thus, it was necessary to determine the pressure and temperature dependence of the relevant properties Žthermal conductivity, density, specific heat and thermal expansivity.. In previous work, the thermal conductivity of apple sauce and tomato paste was already measured using a line heat source probe method in the high-pressure apparatus ŽDenys & Hendrickx, 1999.. The theory behind this method is based on non-steady-state heat conduction in an infinite medium, caused by a step change line heat source. The temperature adjacent to the line source } heated at a constant rate } is monitored. A plot of the ln of time vs. temperature is linear, and the expression from which the thermal conductivity may be

obtained is ls

Q ln Ž t 2rt1 . ? 4 p T2 y T1

Ž3.

Where l s thermal conductivity of the sample ŽW my1 8Cy1 ., Qs heat generated by the line source ŽW my1 ., t 1 and t 2 s two arbitrary chosen times Žs., T1 and T2 s temperature at time t 1 and t 2 , respectively ŽK.. Application of the method in a high-pressure vessel was quite easy and proved to be a fast and accurate way for obtaining the thermal conductivity of materials at high-pressure. Thermal conductivity values of tomato paste and apple pulp were conducted at 308C and 658C, at pressures ranging from 0.1 to 400 MPa ŽDenys & Hendrickx, 1999.. Pressure]temperature relations were obtained from the results and were incorporated in the computer code. 2.3.1. Determination of density The density of a product is simply measured as the ratio of its mass and volume. Compressing a system increases its density and the pressure relation of volumetric properties Že.g. volumetric specific heat. can be calculated from the pressure relation of its density. Thus, density is a very important parameter in the context of the present work. Densities of apple sauce and tomato paste at atmospheric conditions were measured by immersion of plastic bags filled with product Ž300 g. in water and weighing the amount of displaced water. The pressure relation of the product’s density was determined after immersion of the bag in the pressure vessel and measuring the amount of pressure transfer medium to be pumped in the system for compressing it to a particular pressure. The product was not vacuum-treated before immersion in the pressure vessel. The necessary amount of pressure medium depends on the mass ratio of productrpressure transfer medium in the vessel, and the respective densities of both substances at the particular pressure. After compression and pressure stabilization, pressure was released from the vessel and the surplus pressure medium Žpumped in the vessel during the compression step. was collected and weighed. In this way, the pressure relation of the density of the product could be calculated from: P r product s

1 Mproduct

Ž4.

P Vproduct

Whereby P Vproduct s Vtot y

ž

1 P q D Mpressmed Mpressmed P r pressmed

/

Ž5.

S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

where r s density Žg my3 ., Ms mass Žg. and V s volume Žm3 .. Subscripts product and pressmed refer to the product and the pressure transfer medium, respectively, and superscripts represent the applied pressure. Vtot is the total volume of the pressure vessel and P D Mpressmed is the mass of the pressure medium collected upon decompression. Multiple measurements were conducted every 40 MPa within the range 0.1 to "540 MPa, at two temperatures: 208C and 608C. Obviously, the calculations require the pressure relation of P the density of pressure transfer medium r pressmed . Hereto, similar experiments Žsame conditions. were performed without product immersed in the apparatus. 2.3.2. Determination of specific heat The specific heat of apple sauce, tomato paste and pressure transfer medium was determined by differential scanning calorimetry ŽDSC. ŽDSC7, Perkin Elmer., from the energy required to establish a zero temperature difference between the substance and a reference material. This method is recommended for measuring specific heat ŽSweat, 1986.. Measurements were conducted within a temperature interval between 108C and 608C. Of course, the method does not provide values of the specific heat at high pressure. In fact, high pressure lowers the specific heat of pure water: at room temperature, compression to 500 MPa lowers the value to 90% of the value at atmospheric conditions Žaccording to the official international formulations for water properties, developed and maintained by the International Association for the Properties of Water and Steam IAPWS.. This effect was ignored in the heat transfer calculations. 2.3.3. Determination of thermal expansi¨ ity The thermal expansivity of apple sauce and tomato paste was determined at different combinations of pressure and temperature. Hereto, the product container was filled with product Žinitially at uniform temperature. and a pressure increase of "80 MPa was applied. The corresponding temperature increase in the center was measured and the thermal expansion coefficient a T P was derived from: aTP s

DT ? CP D P? T ? V

Ž6.

Where a T P ŽKy1 . represents the thermal expansivity of the product at temperature T ŽK. and pressure P ŽMPa., T and P respectively being the average temperature and pressures during the measured period of compression from initial pressure to final pressure. For the calculation of a T P , the specific volume V Žcm3 gy1 . at T and P, and the specific heat C p ŽJ gy1 Ky1 . at T, obtained by the above described procedures, were used in the equations. Measurements of a T P were con-

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ducted at T s 208C, 358C, 508C, and 658C for each temperature at Ps 40 MPa, 120 MPa, 200 MPa, 280 MPa, 360 MPa, 440 MPa and 520 MPa. 2.4. Enzymes 2.4.1. BSAA a-Amylase of Bacillus subtilis ŽBSAA, product no. 10069, production lot 42763, Fluka, Switzerland. was purchased as a dry powder containing 375 units mgy1 . One unit corresponds to an amount of enzyme that releases 1 mmol maltose from starch within 1 min at a pH of 6 and a temperature of 208C. The enzyme was dissolved in a 0.01 M Tris]HCl buffer of pH 8.6 in a concentration of 15 mg mly1 . 2.4.2. LOX Lipoxygenase ŽLOX. type IB from soybeans was purchased as a lyophilized powder, containing 60% protein and 1.8= 10 5 units mgy1 of protein ŽSigma, product L7395, St. Louis, MO, USA., and was used without further purification. One unit of enzyme causes an increase in A 234 of 0.001 miny1 at pH 9 and 258C, when linoleic acid is used as substrate in a volume of 3 ml of oxygenated buffer. One A 234 unit is equivalent to the oxidation of 0.12 mmol of linoleic acid. The enzyme was dissolved in Tris]HCl buffer Ž0.01 M; pH 9. at a concentration of 0.4 mg mly1 . 2.5. Acti¨ ity assays 2.5.1. BSAA BSAA activity was measured spectrophotometrically according to procedure no. 577 of Sigma Diagnostics ŽSt. Louis, MO, USA.. This procedure is based on the progressive hydrolysis of a-1,4-glucosidic bonds in pnitrophenyl-a-D-maltoheptaoside. p-Nitrophenol is released, absorbing maximally at 405 nm. Measurement were conducted at 308C. Activities were expressed as the change in optical density per minute, calculated by linear regression from a plot of the absorption as a function of time. In a preliminary test a standard curve was drawn, revealing up to which enzyme concentration there was a linear relationship with the measured activity. The samples were diluted with Tris]HCl to 1:50 before activity measurement. 2.5.2. LOX LOX activity was measured spectrophotometrically at 234 nm ŽUV-visible spectrophotometer, Biochrom 4060, Pharmacia LKB Biochrom Ltd, Cambridge, England. using sodium linoleate as substrate. The latter was prepared as follows: 280 mg of linoleic acid and 280 mg of the solubilizer Tween 20 were added to 4 ml of O 2-free water. After homogenization, 0.5 N NaOH was added to clear the solution. Finally, the solution

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was made up with distilled water to a total volume of 25 ml. The solution was flushed with N2 , divided into small portions of 1.5 ml, and stored in the freezer until used. The reaction was carried out at 258C in a quartz cuvette. The assay mixture contained 45 ml of enzyme solution, 25 ml of substrate solution, and 2.9 ml of 0.0125 M borate buffer at pH 9. The absorption at 234 nm was recorded as a function of reaction time Ž3 min., and the activity was determined from the slope of the linear portion of the curve.

1998.. The first order inactivation kinetics wEq. Ž9.x combined with the pressure and temperature relation of the inactivation rate constants wEqs. Ž7. and Ž8.x can easily be incorporated in the numerical calculations. In this way, the residual enzyme activity retention Ži.e. the proportion of enzyme activity retained. at any node could be calculated for any period in time by integrating the pressure]temperature]time profiles through the numerical scheme.

2.6. Pressure]temperature inacti¨ ation kinetics

2.7. Experimental e¨ aluation of HHP process uniformity

To evaluate batch HHP processes in terms of uniformity, the kinetic models for pressure]temperature inactivation of BSAA wEq. Ž7.x and LOX wEq. Ž8.x as derived by Ludikhuyze Ž1998. and Ludikhuyze, Indrawati, Van den Broeck, Weemaes, & Hendrickx Ž1998. for inactivation under isobaric]isothermal conditions, were incorporated in the numerical scheme. Both enzyme display first order activity loss in time wEq. Ž9.x: ln Ž k . s Ž a2 ? P 2 q b 2 ? Pq c 2 . y =

ž

1 1 y T Tref

ž

a1exp Ž yb1 ? P . R

/

/

Ž7.

ln Ž k . s Ž a4 ? u 2 q b4 ? u q c 4 . y

ž ddtA /

P ,T

ž

a3 ? uexp Ž yb 3 ? u . Ž Py Pref . RT

/

Ž8.

s yk? A

Ž9.

In these equations, P is the pressure ŽMPa., T is the absolute temperature ŽK., u is the temperature in 8C, A is the enzyme activity, k Žminy1 . is the inactivation rate constant at P and T, Tref is the absolute reference temperature Ž313 K., Pref is a reference pressure Ž500 MPa., R is the universal gas constant Ž8.314 J moly1 Ky1 . and a, b and c are constants representing values shown in Table 1 ŽLudikhuyze, 1998; Lukikhuyze et al.,

For experimentally evaluating the uniformity of a HHP process, 20 flexible tubes filled with 50 ml of enzyme solution were attached to a PVC tube holder, constructed as illustrated in Fig. 2 The PVC tube holder consists of four levels, positioned at equal distances Ž23 mm.. The highest level is designated as level 1, the lowest level as level 4. Level 3 of the PVC tube holder was located at the vertical center of the product container. At each level, five enzyme samples were positioned: one in the geometrical center and four samples at respectively 8, 11, 14 and 17 mm from the center. The enzyme sample in the geometrical center is designated as sample 1, the enzyme sample at the border as sample 5. The PVC tube holder was then positioned in the aluminum product container Ždescribed above. by attaching it to the lid. For spacesaving, no thermocouple tubes were connected to the lid of the product container Ži.e. no temperatures were recorded during processing.. The product container was filled with apple sauce for evaluation of process uniformity. Obviously, the presence of the PVC tube holder and plastic tubes filled with enzyme solution in the conductive heating medium Žapple sauce. affects heat transfer observed during a HHP process. This impact is minimized by the small size of the enzyme tubes and by appropriately positioning them on the PVC tube holder. ‘Conventional’ HHP processes, as described above, were conducted and the residual activities of the enzyme samples were measured and compared to the initial activity Žmeasured before processing..

Table 1 Estimated values for constants a, b and c in Eqs. Ž7. and Ž8. ŽLudikhuyze, 1998. Parameter a1 b1 a2 b2 c2

Estimated value wEq. Ž7.x 322.1" 16.8 Ž2.82" 0.08. = 10y3 Žy2.98" 0.20. = 10y5 Ž4.13" 0.22. = 10y2 y16.63" 0.64

y1

kJ mol MPay1 MPay2 MPay1

Parameter

Estimated value wEq. Ž8.x

a3 b3 a4 b4 c4

y15.6" 1.4 Ž7.1" 0.28. = 10y2 Ž2.66" 0.27. = 10y3 Žy1.39" 0.18. = 10y1 y3.12" 0.28

cm3 moly1 8Cy1 8Cy2 8Cy1

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transfer medium ŽDowcalN 60% in distilled water. are included. For comparison, the densities of pure water corresponding to the same conditions are also shown. These values were calculated with the NISTrASME Steam Properties Database, a software implementation of the official international formulations for water properties, developed and maintained by the International Association for the Properties of Water and Steam ŽIAPWS.. The pressure relations observed for all products were very similar to those of pure water, but the density of apple sauce seems to exhibit a stronger temperature dependency. Second degree polynomials were fitted to the obtained results Žsmallest R 2 s 0.9962.. A linear temperature relation of the density was assumed. The reverse of the density Ži.e. the specific volume V . was calculated and the pressure and temperature relations of this parameter for all products Žfood systems and pressure transfer medium. were incorporated in the numerical heat transfer model.

Fig. 2. Schematic representation of the PVC tube holder and its position in the product container.

3. Results and discussion

3.1.2. Specific heat Linear relations were fitted to the DSC specific heat data for the products. Results are given in Eqs. Ž10. ] Ž12. for pressure transfer medium, apple sauce and tomato paste, respectively Ž u represents temperature in 8C.. All equations resulted from average values of four DSC runs. C p s 3.3111q 0.0044)u J gy1 8Cy1

3.1. Determination of thermal and physical properties 3.1.1. Density Results of the density measurements are presented in Fig. 3. In the figure, the pressure relation of the density of apple sauce, tomato paste and pressure

Ž R 2 s 0.843.

Ž 10.

C p s 3.2354q 3.0766)10y3 )u J gy1 8Cy1 Ž R 2 s 0.861.

Fig. 3. Experimentally determined values of the density r of the products.

Ž 11.

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C p s 2.9717q 5.8819)10y3 )u J gy1 8Cy1 Ž R 2 s 0.806.

Ž 12 .

Pressure relations of the volumetric specific heat of food products and pressure medium were used in the model. These relations were simply calculated by multiplying the specific heat values obtained by DSC with the pressure related density of the respective products. 3.1.3. Thermal expansi¨ ity The thermal expansivity values for apple sauce and tomato paste, as obtained from the above-explained procedure, are presented in Fig. 4. Values were determined at four temperature levels, for every temperature at seven different pressures. For comparison, values for pure water at the same temperatures were calculated with the NISTrASME Steam Properties Database and are also included in the figure. The values of the thermal expansivity for the food products are lower when compared to the values for pure water. However, their pressure]temperature relation is very similar. The water content of both were similar: 74.4" 0.1% for apple sauce and 71.3" 2.1% for tomato paste Žaverage values of three measures.. The shift towards lower values likely depends on the water content of the product under investigation, but no conclusions could be drawn from the results. Furthermore, in the calculation of the thermal expansivity wEq. Ž6.x, specific heat values measured at atmospheric pressure wEqs. Ž11. and Ž12.x, were used. Neglecting the effect of pressure on the specific heat affects the value of the thermal expansivity, calculated from Eq. Ž6.. From the results, polynomial equations for the combined pressure]temperature dependence of the thermal expansion coefficient a TP of apple sauce and tomato paste were derived

through regression and were incorporated in the numerical heat transfer model as numerical parameters, thus accounting for a non-linear thermal expansion coefficient and, consequently, non-uniform temperature increase or decrease upon compression or decompression, respectively. The general form of these equations was: a TP s Ž a1 q b1 ? T . q Ž a2 q b 2 ? T . ? P q Ž a3 q b 3 ? T . ? P 2

Ž 13 .

Where a1 , a2 , a3 , b1 , b 2 and b 3 are coordinates obtained through linear regression. 3.2. E¨ aluation of the heat transfer model Typical temperature profiles recorded during a ‘conventional’ batch HHP process of tomato paste, are shown in Fig. 5. The processed product was initially at uniform temperature Ž20.2" 0.18C., and a compression to 342 MPa was applied. The temperature profiles in the center Žindicated by triangles., at the border Ždiamonds. and in a position between the latter two Ždots. are shown. Using the appropriate initial conditions ŽT s 20.28C; Ps 0.1 MPa. and the occurring boundary conditions Žactual compression time, applied pressure., temperature profiles at three positions corresponding to the locations of the thermocouples in the processed product were generated and are also shown in Fig. 5 Žfull lines.. For evaluation of the boundary conditions in terms of pressure, the compression time Ži.e. time required for pressure build-up., and the maximum pressure recorded after pressure build-up were used. The average pressure applied during the holding period was determined from the recorded pressure profile

Fig. 4. Experimentally determined values of the thermal expansivity a TP of the products.

S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

Fig. 5. Experimental and predicted temperature profiles for a ‘conventional’ batch HHP process of tomato paste Žinitial temperature 20.2" 0.18C; maximum pressure 342 MPa..

ŽFig. 5. and was used as boundary condition for calculating heat transfer during the holding time. Satisfactory agreement of experimental and predicted temperature profiles was obtained. Similar results were observed for the other processes Ži.e. other initial temperature and applied pressure; results not shown.. To illustrate the predictive capacity of the model, center temperature profiles observed when processing apple sauce are compared to the predicted profiles in Fig. 6, where nine

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HHP processes are included Žconditions are indicated in the legend of the figure.. The range of pressure values shown for each point reflected the drop in pressure during the subsequent holding period. This change in pressure was due to cooling and small leaks. There was no significant difference in predictive capacity of the model for apple sauce as compared to tomato paste. Obviously, the quality of a prediction largely depends on the calculation of the correct temperature increase associated with compression. In Fig. 7, the calculated adiabatic temperature increase corresponding to compressions up to 600 MPa at three different initial temperatures Ž108C, 308C and 508C., are presented for both food products and pure water. The adiabatic temperature increase corresponds to the temperature increase experienced in the center of the product. Very similar values are observed for the food products. The temperature increase of a product is likely determined by its water content. Fig. 8a,b show typical temperature profiles recorded for complex HHP processes Žgradual step-by-step pressure build-up and pressure release .. In these particular processes, the initial, uniform temperature of the product was 20.3" 0.18C. Process a was conducted with tomato paste whereas for process b, apple sauce was used. The experimental pressure]time profiles are also plotted in the figures Žsecondary ordinate.. Analogously as in the case of ‘conventional’ batch HHP processes, temperature profiles were generated with the model and are plotted in the figures Žfull lines..

Fig. 6. Experimental and predicted center temperature profiles for nine ‘conventional’ batch HHP processes of apple sauce Žinitial temperature 10.3" 0.1 8C, 20.2" 0.1 8C or 34.9" 0.18C.. The maximum pressure reached after compression, and the average pressure applied during the holding time, are indicated in the legend.

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temperature., resulting in an average BSAA or LOX activity retention of 50% after a certain processing time were determined with the model. The ‘average activity retention’ after each time step was calculated from:

Ý Ž A i , j ? Vi , j . A av s

i, j

Ý Vi , j

Ž 14 .

i, j

Fig. 7. Calculated adiabatic temperature increase corresponding to compressions up to 600 MPa for apple sauce, tomato paste and pure water. Temperatures indicated in the figure are initial temperatures Žbefore compression..

Considering the complexity of the pressure profiles, good agreement of experimental and predicted time]temperature profiles was obtained. Seemingly, the model is capable of predicting temperature changes caused by pressure build-up or pressure release, even in cases were a non-uniform temperature distribution precedes the compression or decompression. 3.3. Analysis of unformity during HHP processes using the proposed model From the above obtained results, it can be expected that the heat transfer model provides a very useful tool for evaluating the uniformity of any HHP process, supposing that the combined pressure and temperature degradation kinetics of the attribute under consideration Ženzyme inactivation, destruction of microorganisms, etc.. are known. Uniformity of HHP processes depends on extrinsic as well as intrinsic parameters, such as process conditions Žpressure, temperature, holding time., product properties, dimensions of the pressure vessel, but also on the pressure]temperature inactivation kinetics of the attribute under consideration. The influence of inactivation kinetics will be considered in this paper wEqs. Ž7. ] Ž9.x. To compare the uniformity of pressure processes, trials with the same processing time should be selected. Indeed, processes with longer holding times result in a more uniform inactivationrdegradation of the attribute under consideration throughout the pressure vessel. Therefore, process conditions Ži.e. applied pressure and initial

Where A av s average activity retention throughout the vessel; A i , j s activity retention in node Ž i,j . calculated by the model and Vi , j s volume associated with node Ž i,j .. Pressure ]initial temperature combinations, resulting in an average residual activity of 50% after 1500 s total process time are summarized in Tables 2 and 3 for BSAA and LOX, respectively. Box plots of the activity retention, representing the Žnon-.uniformity of these processes are shown in Fig. 9. Since the difference between the minimal and maximal residual enzyme activity can be seen as a measure for process uniformity, it can be stated that all processes considered for BSAA inactivation are characterized by a pronounced non-uniformity, and that there is not much difference between the selected processes. In case of LOX inactivation, a clear variation in process uniformity can be observed, with processes LOX5 and LOX6 resulting in a very uniform distribution. By means of interpolation, the process conditions resulting in the highest uniformity could be determined as 278C and 560 MPa. The effect of pressure]temperature inactivation kinetics of the target attribute on the uniformity of a HHP process can be explained by means of the iso-rate contour plots for inactivation of BSAA and LOX, represented in Fig. 10. The curved lines in these figures represent combinations of pressure and temperature that are characterized by the same inactivation rate constant. Rate constants experienced during a conventional HHP process vary in time and space, as indicated by the pathways of a virtual process ab Žpressure buildup., bc Žholding time., and cd Žpressure release . ŽFig. 10.. Since in most cases, the holding time Žconstant pressure. constitutes the major part of the total process time, rate constant values experienced during the holding time mainly affect the uniformity of the process. The enzyme inactivation rate at different positions in the apparatus may deviate. In the case of LOX, there seems to exist an antagonistic effect of pressure and temperature in the high pressure]low temperature range Ž‘antagonistic domain’.. This feature is clearly illustrated in Fig. 10 by the quasi horizontal iso-k-lines in the temperature range 10]458C. It is clear that in this temperature interval the inactivation rate constant

S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

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Fig. 8. Experimental and predicted temperature profiles for complex HHP processes. Process a was conducted with tomato paste whereas for process b, apple sauce was used. Table 2 Process conditions resulting in an average residual BSAA activity of 50% after 1500 s process time Process

Initial temperature Ž8C.

Pressure ŽMPa.

Process time Žs.

BSAA1 BSAA2 BSAA3 BSAA4 BSAA5 BSAA6 BSAA7 BSAA8 BSAA9 BSAA10

25 30 35 40 45 50 55 60 65 70

568.8 526.2 485.0 444.0 402.3 358.5 311.5 259.8 200.1 126.9

1500.6 1500.1 1498.9 1500.6 1498.2 1499.7 1499.0 1499.8 1497.1 1499.2

is almost independent of temperature. Processes with holding temperatures and pressures in this domain Že.g. processes LOX5 and LOX6 . will consequently be much more uniform with regard to LOX inactivation than processes characterized by higher holding temperatures Ž‘non-antagonistic domain; e.g. LOX10 .. The spacial distribution of the LOX activity retention for LOX3

and LOX10 are represented in Fig. 11. This figure shows that when pressure and temperature act synergistically Ž LOX10 ., the activity retention increases from the center to the border of the vessel. In the case of LOX3, an opposite effect is observed. During this Table 3 Process conditions resulting in an average residual LOX activity of 50% after 1500 s process time Process

Initial temperature Ž8C.

Pressure ŽMPa.

Process time Žs.

LOX1 LOX2 LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12

5 10 15 20 25 30 35 40 45 50 55 60

518.4 528.8 539.0 549.2 557.9 561.7 553.3 521.3 455.3 354.9 227.2 76.3

1498.5 1498.4 1500.0 1499.0 1501.0 1500.0 1499.0 1498.8 1500.0 1499.0 1500.0 1503.0

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S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

Fig. 9. Box plots of the BSAA and LOX activity retention, corresponding to process conditions outlined in Tables 2 and 3.

process, the higher temperature prevailing in the center results in less pronounced inactivation, since the effect of pressure is slightly counteracted by temperature Žantagonistic effect.. In case of BSAA inactivation, no antagonistic effects of pressure and temperature were observed ŽFig. 10.. The pressure]temperature conditions prevailing at distinct radial positions are consequently quite similar to the ones in the ‘nonantagonistic’ domain of LOX. 3.4. E¨ aluation of process uniformity: experimental ¨ alidation The setup of the experimental validation was based

on the theoretical considerations. For each enzyme considered, three HHP processes were experimentally conducted with 20 enzyme sample tubes positioned in apple sauce. In the case of BSAA, processes BSAA1, BSAA4 and BSAA7 ŽTable 2. were selected. In case of LOX, processes LOX3, LOX8 and the most uniform process Ž278C]560.3 MPa, designated as LOXu. were selected. In fact, LOX10 would be a more interesting combination to investigate than LOX8 but the long temperature equilibration time necessary in the setup would result in a partial inactivation of the } more temperature sensitive } LOX. Duplicate tests were conducted for every process Žmarked as a and b .. It should be noted here that for the ‘virtual’ HHP

Fig. 10. Iso-rate contour plots for inactivation of BSAA in Tris]HCl buffer Ž0.01 M; pH 8.6. and LOX in Tris]HCl buffer Ž0.01 M; pH 9., with indication of pathways passed trough during a virtual conventional HHP process.

S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

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seen that for the processes BSAA4a and BSAA4b Žconducted at 408C initial temperature., a consistent underestimation of the effect is obtained, whereas for processes at 258C and 558C, a better agreement results. The assessment of the accuracy of the predictions was made by comparing the predicted results with the experimental data, as calculated from: prediction error predicted activity retention ymeasured activity retention s 100 ? measured activity retention

Fig. 11. Spacial distribution of the LOX activity retention Ž%. for LOX3 and LOX10 Župper quarter of the pressure vessel..

processes, considered in the theoretical evaluation of process uniformity, the holding pressure was equal to the maximum pressure reached after compression. In reality, a pressure drop is observed due to heat loss through the vessel wall. Furthermore, as explained in Section 2.2, it was difficult to control the exact pressure of a HHP process and conditions of the actual HHP processes slightly deviated from the desired conditions. Therefore, for calculating the activity retention in each of the sample positions, process conditions Ži.e. compression rate, maximum pressure reached after compression, holding pressure and temperature of the pressure vessel. obtained through the data acquisition system were incorporated in the model. The average pressure applied during the holding period was determined from the experimental pressure profile. The actual conditions of all processes are shown in Table 4. The residual enzyme activities at the sample positions considered were calculated and compared to the values that were experimentally measured. Fig. 12 shows experimental and calculated residual BSAA activities for process BSAA1b. For all levels of the PVC sample holder, there is a reasonable agreement between the experimental and simulated values. The increase of the residual BSAA activity from the center to the border of the pressure vessel is in accordance with the above made theoretical considerations. An overview of the results obtained for all processes is given in Fig. 13. In this figure, experimental values are plotted against the predicted values for every sample position and all processes. From the figure, it can be

Ž 15 .

The prediction accuracy obtained was determined by the mean prediction error MPE Ždefined as the mean of the above described parameter associated to all data points. and its standard deviation. An MPE of ]8.0% with quite high standard deviation Ž22.5%. was obtained. Obviously, the predictive capacity of the model largely depends on the accuracy of the pressure]temperature denaturation kinetics of the enzyme under consideration. These kinetics were determined under isobaric]isothermal conditions ŽLudikhuyze, 1998., and could be less adequate to describe denaturation under dynamic conditions, as during a real HHP process. One explanation for the consistent underestimation of the effect in case of the processes at 408C could be a stronger curvature of the iso-k-lines when dynamic conditions are focussed. The limitations of the use of inactivation kinetics was clearly observed in the case of LOX inactivation ŽFig. 13.: the agreement between the experimentally determined residual activity and its calculated value was much lower. For LOX3a and LOX3b, the measured activity retention was almost negligible and results were not included in the figure. A partial explanation for the deviation between calculated and observed residual LOX activities is the occurrence of so-called cold-denaturation during decompression Žand Table 4 Actual process conditions of HHP processes conducted for evaluating the uniformity of BSAA and LOX Process

Initial temperature Ž8C.

Maximum pressure ŽMPa.

Average pressure ŽMPa.

Process time Žs.

BSAA1a BSAA1b BSAA4a BSAA4b BSAA7a BSAA7b LOX3a LOX3b LOXua LOXub LOX8a LOX8b

25.75 25.58 40.46 40.51 54.57 55.01 15.80 15.43 28.45 27.83 40.59 40.23

611 611 486 502 342 343 590 600 593 633 562 588

541 543 411 452 319 306 524 545 522 572 499 526

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500

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Fig. 12. Experimental and calculated residual BSAA activities for process BSAA1b ŽTable 4. at the four levels of the PVC tube holder.

Fig. 13. Measured vs. predicted activity retentions Ž%. at sample position for all processes.

S. Denys et al. r Inno¨ ati¨ e Food Science & Emerging Technologies 1 (2000) 5]19

the concomitant temperature drop.. Indeed, colddenaturation of LOX has been frequently reported in literature ŽIndrawati, Van Loey, Denys, & Hendrickx, 1998.. However, cold-denaturation is not a likely explanation at the temperature levels experienced after decompression in case of processes LOX8a and LOX8b Žduring these processes, temperature does not fall below 208C.. Reasons for the disagreement should be further explored. When comparing the two model systems investigated in this work, it was concluded that the pressure]temperature inactivation kinetics of BSAA can serve as a system for assessing the uniformity of HHP processes of foodstuffs, whereas for LOX to be useful as an indicator, more research is demanded on effects of dynamic process conditions and possible cold denaturation.

4. Conclusions The numerical conductive heat transfer model was capable of predicting the temperature evolution during batch HHP processing of apple sauce and tomato paste. There was no significant difference in predictive capacity for tomato paste as compared to apple sauce. The quality of a prediction largely depends on the calculation of the correct temperature increase associated with compression. It would be very interesting to determine the necessary properties for food products with lower moisture content to test the method. Combination of the heat transfer model with inactivation kinetics appeared to be a useful basis to evaluate the uniformity of enzyme inactivation during batch high pressure processing of foods. In this way, it became clear that the uniformity of inactivation of BSAA and LOX during batch high pressure processing is dependent on the inactivation kinetics of the enzyme under consideration, and on the pressure]temperature]time conditions. For some selected pressure]temperature processes, the theoretical predictions were experimentally validated. Reasonable agreement between calculated and experimentally determined activity retentions was obtained in case of BSAA, whereas in case of LOX, no agreement between the simulated and experimentally determined values was obtained. Therefore, BSAA now represents a system for assessing the uniformity of HHP processes of foodstuffs. The determination of pressure]temperature denaturation kinetics valid under dynamic conditions and a broad range of pressures and temperatures is very important in this context. The method was applied for enzyme inactivation but could be used for evaluating the uniformity of any temperature]pressure related effect, provided that the pressure]temperature denaturation kinetics are known.

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Acknowledgements This research has been supported by the ‘Vlaams Instituut voor de bevordering van het Wetenschappelijk-Technologisch Onderzoek in de Industrie’ ŽIWT. and the European Commission as a part of the FAIRCT96-1175 project. References Cheftel, J.-C. Ž1991.. Applications des hautes pressions en technologie alimentaire Žhigh pressure application in food technology.. Industries Alimentaires et Agricoles, 108 Ž3., 141]153. Denys, S., & Hendrickx, M. E. Ž1999.. Measurement of the thermal conductivity of foods at high pressure. Journal of Food Science, 64 Ž4., 709]713. Denys, S., Van Loey, A. M., & Hendrickx, M. E. Ž2000.. Modeling conductive heat transfer and process uniformity during batch high-pressure processing of foods. Biotechnology Progress, in press. Farr, D. Ž1990.. High pressure technology in the food industry. Trends in Food Science and Technology, 1 Ž1., 14]16. Hayashi, R. Ž1989.. Application of high pressure to food processing and preservation: philosophy and development. In: W. E. L. Spiess, & H. Schubert, Engineering and food Žpp. 815]826.. London: Elsevier Applied Sci. Hendrickx, M., Ludikhuyze, L., Van den Broeck, I., & Weemaes, C. Ž1998.. Effects of high pressure on enzymes related to food quality. Trends in Food Science and Technology, 9 Ž5., 197]203. Hoover, D. G., Metrick, C., Papineau, A. M., Farkas, D. F. & Knorr, D. Ž1989.. Biological effects of high hydrostatic pressure on food microorganisms. Food Technology, 43 Ž3., 99]107. Indrawati, Van Loey, A., Denys, S. & Hendrickx, M. Ž1998.. Enzyme sensitivity towards high pressure at low temperature. Food Biotechnology, 12, 263]277. Knorr, D. Ž1993.. Effects of high-hydrostatic-pressure processes on food safety and quality. Food Technology, 47 Ž6., 156]161. Knorr, D. Ž1995.. Hydrostatic pressure treatment of food: microbiology. In: G. W. Gould, New methods of food preser¨ ation Žpp. 159]175.. Glasgow: Blackie Academic and Professional. Ludikhuyze, L. Ž1998.. High pressure technology in food processing and preservation: a kinetic case study on the combined effect of pressure and temperature on enzymes. Ph.D. Dissertation no. 362 at the Faculty of Agricultural and Applied Biological Sciences, Katholieke Universiteit Leuven, Belgium. Ludikhuyze, L., Indrawati, Van den Broeck, I., Weemaes, C., & Hendrickx, M. Ž1998.. Effect of combined pressure and temperature on soybean lipoxygenase. 2. Modeling inactivation kinetics under static and dynamic conditions. Journal of Agricultural Food and Chemistry, 46 Ž10., 4081]4086. Mertens, B. Ž1995.. Hydrostatic pressure treatment of food: equipment and processing. In: G. W. Gould, New methods of food preser¨ ation Žpp. 135]158.. Glasgow: Blackie Academic and Professional. Messens, W., Van Camp, J. & Huyghebaert, A. Ž1997.. The use of high pressure to modify the functionality of food proteins. Trends in Food Science and Technology, 8, 107]112. Sweat, V. E. Ž1986.. Thermal properties of foods. In: M. A. Rao, & S. S. H. Rizvi, Engineering properties of foods Žpp. 49]87.. New York: Marcel Dekker Inc. Zemansky, M. W. Ž1957.. Heat and thermodynamics. McGraw-Hill Book Company, New York, pp. 248]253.