ON-LINE CONTROL CONDUCTION.pdf

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Journal

of Food Engineer ing 0 (1993) 283-295

Short Communication

Mathematical Models and Logic for the Computer

Control of Batch Retorts: Conduction-Heated Foods

Ricardo Simpson, Sergio F. Almonacid-Merino

J. Antonio Torres*

Food Engineering Group, Department of Food Science and Technology,

Oregon State University, Corvallis, OR 97331, USA

Received 29 August 1990; revised version received 4 June 1992;

accepted 15 July 1992)

ABSTRACT

A computer pr ogram was developed to implement a mathemati cal model

to control on-l ine batch retort operations for conduction-heated foods.

The model is based on a numer ic solu tion f or heat transfer n cylindri cal

cans. The heat transfer equation was solved using a numeric method with

a variable gri d. I ntegrated lethal i ty values are calculated assumi ng f irst-

order kinetics or mi crobial inactivation, taking into account the cumula-

tive lethal ity of the heating and cooling per iod. The program adjusts

process time automatically to compensate for any unexpected variation in

retor t temperatur e, and was vali dated using processes reported in the

l iterature. The computational speed of the numeric method descri bed

could be applied to other calculation-intensive simul ations,

NOTATION

a

G

CO

Radius of the can (m)

Correction factor for deviant thermal processes for conduc-

tion-heated foods

Concentration of spores at time zero (counts/m3)

*To whom correspondence should be addressed.

283

Journal of

Food Engineering 0260-8774/93/ 06.00 - 0 1993 Elsevier Science

Publishers Ltd, England. Printed in Great Britain


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284

R. Simpson, S. F. A lmonacid-M eri no, J. A . Tor res

Cbx,t)

D

D,

F

F, t)

;;

k

L

Ik i)

RTd

RT t)

t

tc

;

T

T,

T i,j)

Spore concentration

(

counts/m3)

Decimal reduction time at temperature T min)

Decimal reduction time at temperature T = T, (mm)

Process lethality at

T, =

121.1C (min)

Accumulated lethality at time t (min)

Desired process lethality (min)

Integrated lethality achieved during heating with no tempera-

ture deviations (min)

First-order reaction constant (s - )

Half-height of the can (m)

Radial distance (m)

Location of grid increment

(

i) in the radial direction (m)

Desired retort temperature C)

Retort temperature at time t C)

Time (s)

Cooling time

(s)

Heating time (s)

Heating time to accomplish 80% of Fk s)

Temperature

Reference temperature ( = 12 l*lC)

Temperature in volume element

(

i, j) C)

T r,Z, t) Temperature at location r, Z) at time t C)

TW t) Cold water temperature at time t C)

Z

Inverse slope of thermal death-time curve (C)

Z Vertical distance (m)

i R i)

Thermal diffusivity (m'/s )

Variable grid increment in the radial direction (m)

At

Time increment (s)

A Z(i)

Variable grid increment in the vertical direction (m)

INTRODUCTION

The advent of low-cost microcomputers has facilitated the imple-

mentation of strategies for the on-line control of processes. Computer

control systems deliver uniform product quality and minimize worker

supervision, human error and energy consumption. In the specific case

of canned foods, computer control addresses production problems with-

out compromising product quality and safety. Computer control allows

on-line corrections for temperature deviations from the pre-established

process and the implementation of optimum processes (Saguy & Karel,


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Computer control of batch retor ts 285

1979; Ohlsson, 19804 6; Van Boxtel

&

De Fielliettaz Goethart, 1982)

identified by mathematical modelling (e.g. Texeira et al., 1975; Ohlsson,

1980

b .

Other potential benefits include automatic documentation of the

process (Holdsworth, 1983) and on-line measurement of heat penetra-

tion data.

Design factors to be considered in automatic sterilization systems

include the capital cost of the system, interaction between operators and

instruments, maintenance of hardware and software, reliability, instru-

mentation accuracy, and the interaction between management and the

system. Lappo & Povey

(

1986) described the development and perform-

ance of a facility, comprising a steam sterilizing retort, a microprocessor

development system and all associated instrumentation and control

equipment. The influence of instrument accuracy on the control of

sterilization was also explored. A sterilization monitor capable of

scanning 10 thermocouples and computing individual sterilization or

cook values for each channel was also described.

Giannoni-Succar and Hayakawa ( 1982) developed a procedure to

estimate the values of a correction factor, C,, for deviant thermal pro-

cesses for conduction-heated foods. Sterilizing values at the thermal

center of the food were used as a criterion for the estimation. The proce-

dure was based on a regression equation obtained through the dimen-

sional and statistical analyses of theoretically determined C, values.

Datta

et al

(1986) developed a control logic algorithm for use with

computer-based control systems for batch retort operations capable of

automatically adjusting process time during the cook cycle to compen-

sate for any unexpected deviation in retort temperature. To evaluate F,,

the temperature was taken to be the temperature of the slowest heating

point in the product. A similar strategy was used by Gill et

al

(1989).

A review of the current literature found no control systems evaluating

F,, values as a mass average lethality. The slowest heating point is not

necessarily where the probability of bacterial survival is greater. Com-

puter-supported experiments by Texeira et al. ( 1969 a) have been used to

show that this location may vary, depending on the container geometry

and size, food product, and the processing conditions. Although we have

reproduced the values observed by these workers for constant retort

temperature (data not included), we should note that the center point

was only slightly more lethal than other can locations. Our rationale for

the use of average lethality calculations is based on the consideration that

process deviations causing unusual container lethality profiles may be

safely corrected using integrated lethality. Even using computer simula-

tions, it would be impractical to determine for all can dimensions and


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286

R. Simpson, S. F. Al monacid-M eri no, .I. A. Torr es

product types the location of least point lethalities for all forms of

process deviations that might occur during retort operations.

Teixeira et

al.

(

1969b) and, more recently, Simpson

et al.

(1989a, b)

have shown that the accuracy of the predicted integrated lethality using

numerical methods with uniform grid depends on a large number of

space and time intervals. However, a software program for the on-line

control strategy requires a program capable of completing all calcula-

tions before the next temperature reading. The method developed by

Teixeira et al. ( 1969 b) and used by Datta et a 1. 1986) does not fulfill this

requirement because of its large partitioning grid ( 10 X 10).

In this paper we present simulation results of a program for the on-

line control for the thermal processing of canned foods in cylindrical

containers using an integrated F0 as the safety criterion. An integrated

lethality criterion required a more efficient numeric calculation process

as compared with that used by Datta et al. (1986). The variable grid

method developed by Hayakawa (1967), which uses only 12 points to

calculate integrated lethality, was used to reduce computational time.

This calculation was executed assuming simulated arbitrary deviations in

retort temperature.

METHOD

Sterilization criteria

In controlling thermal processes, the objective is to meet the designed

level of sterilization (F,d) for the process, irrespective of any retort

temperature variation RT( t) occurring during processing time ( ), and

with a minimum of overprocessing. The lethal effect of thermal proces-

sing is achieved during the heating

( th)

and cooling period of the can

(t,),

respectively. If C = C( r, 2, t) is the concentration of spores at a location

(

,

2) and time t he sterilization process can be described as follows:

with k = ln 10/D and D = D,lO;- T)z. ntegration over time and using

T, = 250F leads to:

Chz,t)

co

=exp[

-(h lo/D,)

(2)


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Comput er control of batch et ort s 287

The integrated sterilization value for a cylindrical can was calculated as

follows. The time integral in eqn (2) was evaluated using the Simpson

integration method. The [ C( r,z, t)/Co] values thus obtained are integrated

over the entire can using the following expression evaluated by the Gauss

integration method (Abramowitz & Stegun, 1964):

-_=-

[C(r,z,t)/C,]

rdr dZ

The values obtained from eqn (3) can be converted into an integrated F,

on the basis of the II, value used in eqn (2).

The grid defined to evaluate the Gauss integration included three

nodes in the radial direction and eight in the vertical direction. As the

cylindrical container is symmetric on both axes, Gauss integration was

evaluated with 12 points as shown in Fig. 1, and analogous to the

variable 3 x 4 grid reported by Hayakawa ( 1967) to calculate integrated

lethalities. This procedure achieved computational speed, an essential

component of computer-supported process control strategies, while

retaining the flexibility of a numeric method.

Modified variable grid MVG) method

The numeric method used to solve the partial differential equation for

heat transfer was the Alternating Direction Explicit Procedure (ADEP )

1.0 (

1

.

. .

.

h

go.6 -

.

%,a. - . .

-

f

Lo.4 -

Fi

.

. .

.

0.2

0.0

0.0 0.2

0.4 0.6

0.6

1.0

Fig. 1.

Variable grid to evaluate the volume integral by the Gauss method.


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288

R. Simpson, S. F. A lmonaci d-M eri no, J. A . Tor res

reported by Allada and Quon (1966) combined with a variable grid. The

expression for heat transfer in cylindrical coordinates is

aT

aT+laT ;a21

_---_-

a at a22 r ar a?

(4)

with the following boundary conditions:

T

surface (heating)

= R T ( ), i.e. the retort temperature at any time t

T

surface (cooling)

= TW t),

i.e. the cold water temperature at any time

t

The following expressions were used to evaluate the temperature

inside the can at any point and at any time:

AR i)[T i-l,j)-T i,j)

+

AR i

- l)[AR(i) +AR i - l)]

[

T i,j) - T i +

lj)]

AR i)[AR i)+AR i-l)]

[T i-l,j)-T i,j)

+AR i-l)[AR i)+AR i-l)]

(5)

(6)

? _ I,2

[

i,j +

1) -

T ij)]

azz

Az(/Y]Az(j) +Az(j - 1)]

[T i,j-l)-T i,j)

+AZ(j-l)[AZ(j)+AZ(i-l)]

(7)

1

aT [T i,j) - T i,j)]

-_---_

a

t

aht

Substituting eqns (5)-( 8) in eqn (4), and rearranging, it is possible to

obtain an expression for

T i,j)

t + l .

Although this expression is an implicit

equation, a suitable choice of the initial point conditions generates

explicit calculations (Allada & Quon, 1966).


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Comput er cont rol of batch et ort s 289

Control program strategy

The effect of the lethality accumulated during the cooling phase on the

evaluation of total mass average lethality was included to avoid over-

processing. The algorithm simulates the cooling cycle assuming constant

water temperature and evaluates the integrated average F,, before the

next temperature reading.

The first calculation step is to design a process to achieve the desired

sterilization process and use it to define the following variables:

F,(t) - accumulated lethality at time t;

- integrated lethality desired;

; j _*

mtegrated lethality achieved during heating with no tempera-

ture deviations;

th

- heating time;

t* - heating time to accomplish 80% of F,h.

For t < P, the program reads the temperature of the autoclave every

10 s. This information is used to calculate all temperatures inside the can

and also to predict an integrated average F,(t) value. When the accumu-

lated F,(t) is 2 0.8 F,h, .e. when t 2 t*, the program simulates the cooling

phase and predicts a final

F,

value. Given that now too many calculations

are needed to accomplish the cooling simulation, the time for each read-

ing of the autoclave temperature is increased to 20 s. Preliminary experi-

ments showed that the simulation time required to predict F,(t) after

each temperature reading takes only 0.16 s and that the simulation of the

cooling phase takes approximately 10 s. Other strategies used to reduce

the number of calculations for prediction of the cooling phase include

temperature predictions using a 20 s time increment and the calculation

of integrated average F, values only every 120 s.

Implementation of the control program

The control program was implemented on an IBM pS2 Model 55SX

using IBM Advanced Basic. The logic for the on-line control program is

based on the work reported by Datta et al. (1986). First, input data are

checked against specifications for the product. If they agree, steam is

turned on and the computer completes the venting cycle. The retort

temperature increases, and through a controller interface the computer

attempts to maintain the design retort temperature

(RF).

As the heat-

ing cycle continues, the retort temperature RT( t) is read at intervals of

time t. The temperature distribution within the can, T( r, Z, t), is then


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290

R. Simpson, S. F. A lmonacid -M eri no, J. A . Ton- es

calculated from RT(t) using the MVG method. The integrated average

lethality, F,(t), is then calculated.

The input data include a specified

F

which is the integrated average

F,

value normally achieved during heating when there are no tempera-

ture deviations. When F,,(t) exceeds the value 0%FE, the computer also

simulates the cooling cycle in addition to calculating T( r,Z, t) and F,(t)

during the elapsed heating period. If the F,(t) accumulated so far,

together with the simulated contribution from cooling, exceeds the

design total F. value for the process (F,d), .e. when the condition

F,( ~)heating,calculated + ( FO)cooling,simulated 2 F,d

(9)

is satisfied, the computer turns off the steam and lets in cooling water.

The computer continues to read the retort temperature RT(t) and

continues with the calculations of T(r,Z,t) and F,(t). When Tcenter, he

calculated temperature at the can center, is below a certain specified

value, cooling is ended by stopping the flow of cooling water and the

water is drained before unloading the retort. At the end of the process, a

complete documentation of measured retort temperature history RT( t)

and the accomplished

F,

is kept on file for process documentation

purposes.

RESULTS

Numeric procedure validation

The MVG method was verified against results obtained with the method

reported by Teixeira

et al.

(19696) and implemented by Ahnonacid-

Merino (1988). The data used to conduct these computer simulations

are described in the Appendix. No major accuracy differences were

observed between the MVG and Texeira et al. (19698) methods, as

shown by the constant-temperature examples presented in Table 1. The

MVG method was also validated using variable retort temperature.

Again, MVG calculations compared well with values obtained using the

method of Texeira et

al.

( 1969 b) (Table 1).

Control strategy implementation

There are three main differences between the control strategy reported

by Datta ef al. (1986) and the procedure here reported. First, F,(t) is

calculated using the integration method introduced by Hayakawa

(1969), which reduced the number of partitions needed to maintain


9/13

Computer control of batch retorts

291

TABLE 1

Validation Tests of the MVG Method

Process type Heating time (min)

Published methodb

MVG method

(a) At constant temperature

Experiment 1

Experiment 2

Experiment 3

(b) With emperature deviations

Experiment 1

O-50 min, 121.1C

50-72 min, 1294C

72-79 min, 121.1C

Experiment 2

O-20 min, 12 l.lC

20-40 min, 1294C

40-83 min, 121.1C

Experiment 3

O-60 min, 12O*oC

60-112 min, 115OC

80

80

100

100

140

142

79

80

83

82

112

112

Data used to conduct computer-supported experiments are summarized in the

Appendix.

bTeixeira

et al .

(19696).

calculation accuracy. However, it required the implementation of a finite

difference method with variable grid. Another difference from the

strategy used by Datta et al. (1986) is the criterion chosen to end the

cooling phase simulation, which was

F,(t)-Fo(t-120)~0~001 F,(t)

(10)

This criterion was derived from many computer simulations showing

that when two consecutive F, values (using 120 s intervals) vary by less

than O.l%, subsequent F, values do not change significantly. Figure 2

shows two examples of

F,

accumulated during the cooling period. The

dotted lines represent the end of the F. predictions and indicate that

after the computer interrupted the predictions no further significant

changes occurred in process lethality. A third difference is the time

intervals used to solve the differential heat transfer equation; there are

three time intervals - two for the heating phase (10 s and 20 s), and one

for the cooling phase (20 s).


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292

R. Simpson, S. F. A lmonacid-M eri no, J. A . Tor res

Fig 2 Simulation of F,, values during the cooling period. Experimental details are

given in the Appendix.

TEMPERATURE, C

78 min

\

TEMPERATURE C

-__L___

TEMPERATURE, C

_____

(b)

TEMPERATURE, C

82 min

\

Fig. 3. Examples of process corrections after various types of temperature deviation.

Heating time for the constant temperature process is 80 min. Further experimental

details are given in the Appendix.


11/13


12/13

294

R. Simpson, .F. Al monacid-M eri no, .I. A. Torres

Banga, J. R., Simpson, R., Almonacid-Merino, S. F. & Torres, J. A.

(

1991).

MOTI? multipurpose optimization of thermal processing. Presented at the

Annual Meeting of the Institute of Food Technologists, l-5 June, Dallas, TX.

Datta, A. K., Teixeira, A. A. & Manson, J. E. (1986). Computer-based retort

control logic for on-line correction of process deviation. 1.

Food Sci.,

51

480-3.

Giannoni-Succar, E. B. & Hayakawa, K. I. (1982). Correction factor of deviant

thermal processes applied to packaged heat conduction food. J.

Food Sci ., 47,

642-6.

Gill, T. A., Thompson, J. W., Leblanc, G. & Lawrence, R. (1989). Computerized

control strategies for a steam retort. 1.

Food Engng,

10 135-54.

Hayakawa, K. (1967). Mass average sterilizing value for thermal process. Part 2.

Development of a new method.

Food Technof ., 2

1 2 l-4.

Hayakawa, K. (1969). New parameters for calculating mass average sterilizing

values to estimate nutrient in thermally conductive food. J.

Can. Inst . Food

Technol ., 2,165-72.

Holdsworth, D. (1983). Developments in the control of sterilizing retorts. Pro-

cess

Bi ochem., 16( 5), 24-8.

Lappo, B. P. & Povey, M. J. W. ( 1986). A microprocessor control system for

thermal sterilization operations. J.

Food Engng, 5,31-53.

Ohlsson, T. (1980a). Optimal sterilization temperatures for flat containers. J.

Food Sci ., 45,848-52.

Ohlsson, T. (1980 b). Optimal sterilization temperatures for sensory quality in

cylindrical containers. J.

Food Sci ., 45, 15 17-2

1.

Saguy, I. & Karel, M. (1979). Optimal retort temperature profile in optimizing

thiamine retention in conduction type heating of canned food. J.

Food Sci.,

44,1485-90.

Simpson, R., Aris, I. & Torres, J. A. (1989 a). Retort processing operations: con-

duction-heated food in oval-shaped containers. OSU Sea Grant Technical

Report ORESU-T-89-002,2Opp.

Simpson, R., Axis, I. & Torres, J. A. (1989 b). Evaluation of the sterilization pro-

cess for conduction-heated foods in oval-shaped containers. J.

Food Sci ., 54,

1327-32,1363.

Teixeira, A. A., Dixon, J. R., Zahradnik, J. W. & Zinsmeister, G. E. (1969 a).

Computer determination of spore survival distributions in thermally-

processed conduction-heated foods.

Food Techno l ., 23,78-80.

Teixeira, A. A., Dixon, J. R., Zahradnik, J. W. & Zinsmeister, G. E.

(

19696).

Computer optimization of nutrient retention in the thermal processing of

conduction-heated foods.

Food Techno l ., 23,845-50.

Teixeira, A. A., Stumbo, C. R. & Zahradnik, J. W. (1975). Experimental evalua-

tion of mathematical and computer model for thermal process evaluation. J.

FoodSci ., 40,643-55.

Van Boxtel, L. B. J. & De Fielliettaz Goethart, R. L. (1982). Optimization of

sterilization process.

Voedingsmi ddl el el en ecnol ., 15

(Suppl. 24), 2-6.


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Comput er control of batch et ort s 295

APPENDIX: EXPERIMENTAL CONDITIONS FOR VALIDATION

TESTS

Constant temperature tests

Can type

307 x 409

Thermal diffusivity

l-6,??-7m2s-

Initialfood temperature

7 1.1 C

T,

121*1C

10C

Q

3min

TW coohg water)

26*6C

SimulationResults

Experiment 1

Experiment 2 Experiment 3

6 (h)

994

1 l-90

13.36

F;: (mui)

13.68

14.45

14.54

Retort temperature

("C ) 122.1

118.5

114.4

Variable temperature tests

Can type

307 X 409

Thermal diffusivity 1.538E - 7 m2 s-l

Initial ood temperature

7 1.1 C

T,

121C

10C

Q

4min

TW (cooling water)

26elC

SimulationResults

Experiment 1

Experiment 2 Experiment 3

Fobmid

Fadmm)

Retort temperature

11.12

10.94

13.8

16.96

15.0

15.0

See Table

1 See Table 1 See

Table 1

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