III-39H

memes

’I’tiIII-IIIIIzsII-I

-‘ did {U

,~

'\\~\‘ <

5..-

-~ aw. «‘4 - ‘Oct- . .

Qt;

 

THERMAL INACTIVATION 0F .POLYALACTURONASE
IN A HELICALLY COILED HEAT EXCHANGER
Thesis for the Degree of M. S.
‘ MICHIGAN ST ATE UNIVERSITY .
PEI ER MINTZIAS ‘
1977 .

Q
.
- ..
I
. 0'.
r-.—.
-. t
‘I
-.. ,.
..
a ' '
'
0v "
. -
. -

 

Univcrsity 6‘
mm.u.:c~A

 

 

 

 

ABSTRACT

THEEMAL INACTIVATIG‘I OF RDLYGALACI‘UFONASE IN
A HELICALIX (DILED HEAT EXOiANIER

By
Peter Mintzias

The softening of brined cherries was first noticed about 1947. A
pectin degrading polygalacturonase has proven to be responsible for this
danage. Since spent cherry brine is a strong pollutant, its disposal
into rivers and estuaries or into Inmicipal sewage systens my cause
serious pollution problems depending upon the size of the systan and the
amount of the disposed brine. Recycling of the spent brine seems to be
a satisfactory answer to the disposal question. Such a brine must be
heated before reusing to prevent softening of the cherries due to
polygalacturonase activity.

'Ihe basic objective of this study was to detennine the mount of
inactivation of polygalacturonase while it was receiving a certain and
carefully controlled heat treatment in a helically coiled heat exchanger.
The degree of inactivation was determined by the "cup-plate" procedure
as described by Dingle _e_t_a_1_ . (1953) and Athanasopoulos (1976). Predic-
tin: of the expected inactivation under pre-establ ished conditions was
done by both the general and the analytical methods. Predicted and
measured values were found to vary insignificantly, sanetimes less than
-1.0%.

Peter Mintzias

Hot and cold water was used as the heating and the cooling medium,
respectively. Side wall friction factors and heat transfer coefficients
of a helical tube were found to be higher than those in a straight tube.
'lhe nagnitude of the coil diameter has a significant effect on the pressure
drop and heat transfer through the coils. 'Ihe over-all heat transfer
coefficient was predicted by an exponential relationship of temperature
and time in the helix. 'lhe predicted values and those calculated by
taking into account the resistance to heat flow fran one fluid to the
other were fomd to vary from -0.9% to +9.0%. Viscosity, density,
thermal conductivity, and specific heat of the treated brine were
assumed to be identical to those of water.

Based on heat transfer informtion and the heat stability of
polygalactumnase measured by Athanasopoulos (1976) a tenperature of
80°C throughout the holding coil for 9 sec resulted in 99.985%

inact ivat ion .

'I‘HERMAL INACI‘IVAT ION OF FOLYXiAcrURONASE
IN A HELICAILY (DILED HEAT EXCHANGER

By

Peter Mintzias

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF $1M

Department of Ibod Science and Human Nutrition

1977

To nw wife, Katherine

The author wishes to express his deep sense of gratitude to
Professor Alvin L. Rippen, Department of Food Science and Hum
Nutrition, for his guidance, support and.patient tutelage throughout
the course of this study.

Dr. Pericles N. markakis and Dr. Richard.C. Nicholas, Professors
of Food Science and Human Nutrition, are also acknowledged for their
suggestions.

Special appreciation is also due to Lloyd E. Lerew, whose
recomnendations were seriously considered during the course of this
amukn

Finally, the author is particularly indebted.to Dr..Dennis R.
Heldman, mailman of the Agricultural Engineering Departnent, for his

perceptible assistance and brilliant counsel .

iii

TABLEOFCINI‘EN’I‘S

LIST OF TABLES .
LIST OF FIGURES
SYLBCIS
INI‘WJCI‘ICN
LITERATURE REVIEW
A. HEATTRANSFERAI‘DPRESSUREDKPINODILS .

A—l. Pressure Drop ,
A—2. Heat transfer in coils

B. SHELL-SHE HEAT TRANSFER AND PRESSURE DKP

B—l. Pressure drop .
B—2. alell—side heat transfer coefficients

C. MAME OF HEAT W
D. RECYCLING THE CHERRY BRINE.
E. THE POLYGALACI‘UKNASE ENZYME
E—l. Polygalacturonase in brined cherries
E-2. Polygalacturonase kinetics, rate constants

and stability

F . POLYGALACTUM‘JASE INACI‘IVATIG‘I LEASURFMEN'I‘S AND
CALCULATICN ,

F—l. Enzyme activity measurenents
F—2. Process calculation ,

WWW
A. INSIRIWI‘SANDMATERIAIS ,

B. 'I‘EMPERA’IUREMEASUREMENI‘S

iv

Page
vi
vii

ix

Loewe:

12

13
15
17
19

19
19

22

22
22

26

31

D.

E.

PRESSURE DRIP AND HEAT TRANSFER DETERMINATION

C-l. Pressure drop . . .
0—2. Heat transfer calculations .

PERFCRMANCE CALCULATICN .

DEGREE OF INACI‘IVATIQ‘I MEASURE/[EMT AND CALCULATION

RESULTS AND DISTUSSICN .

A. PRESSURE DRIP.
B. HEAT TRANSFER.
C. PERFORMANCE OF THE EDPERIMENI‘AL HEAT EXCHANGER
D. POLYGALACI‘UIDNASE HEAT TREATMENT . . .
E. OPERATIONAL (DST OF THE PASI‘EURIZATICN PIDCESS
(DNCLUSICNS .
BIBLIGERAPHY.
APPENDIX A
APPENDIX B

APPENDIX C

.33

.37
-38
«47
~47
~52
.59
.63
.73
.76

.78

.85

Table

LIST OF TABLES

Specifications of the experimental heat exchanger .
Calculation of cunnlative lethality.

Calculated and neasured total internal pressure drop
in the pasteurization unit, at several flow rates .

Comparison of calculated and predicted shell-side
heat transfer coefficients (W/m2.°C), under
different temperature conditions .

The over-all heat transfer coefficient (W/m2.°C),
calculated under several tenperature conditions

Effectivaiess and NTU of the experinental heat
exchanger for pasteurizing cherry brine at a flow rate
of 1 Kg/min at several process tenperatures

Percent inactivation determined by the three
nethods and percent deviation of the general and
the analytical methods from plating.

Polygalacturonase inactivation in each section of
the experimental heat exchanger, calculated by the
analytical method, using constant tenperature
along the holding coil . . . .

Rate constants for polygalacturonase at pH=3.0
and for pectinase from P. janthinellum at pH=3.7

 

Brine couposition for certain cherry varieties
in Michigan

Vi

Page
28

46

52

62

67

72

Figure

10.

11.

13.

LIST OF FIGURES

Cross section of a tube in a helix showing
secondary flow . . . . .

Schematic diagram of the heating and cooling
system for pasteurization of cherry brine

'I‘hemocouple locations for the wall, wall surface
and fluid stream tenperature neasurement.

Standard curve for polygalacturonase activity
measurement . .

Effect of the Be on the friction factor in straight
and coiled tubes for laminar and turbulent flow

Effect of curvature ratio on frictional factors
in coils

Effect of flow rate on the calculated total
pressure drop in the coils of the pasteurization
unit . .

Inside heat transfer coefficients in the coils for
different Re and differart curvature ratio

Effect of the temperature difference ratio of the
two fluids in the heater, on the over-all heat
transfer coefficient.

Effect of tenperature difference ratio of the two
fluids in the cooler on the over-all heat transfer
coefficient

Tenperature profiles in the heater of the
experimental heat exchanger

Temperature profiles in the cooler of the experi-
mental hat exchanger . . .

Effect of temperature on the degree of
inactivation . . . .

vii

Page

27

4O

48

51

53.

57

58

61

Figure
14 .

15.

16.

Predicted time-tamerature profiles at several
constant tenperatures along the holding coil.

Themal resistance curves for pectinase from

Aspeiillus niggr at pH 3.0 and for pectinase
from Penicillium janthinellum at pH 3.3 .

Arrhenius plot for polygalacturonase at pH 3.0
and pectinase from P.janthinellum at pH 3.7.

 

viii

.65

7O

.71

SYLBOLS

A Area, m2

A Proportionality constant in Arrhenius equation, sec41

b Temperature ratio in equation 43

c Specific heat at constant pressure, KJ/Kg—°C

di Inside diameter of tube, m

Dh Diameter of the helix, m

D Decimal reduction time, sec

Ea Activation energy, cal / mole

f Fanning friction factor

g Acceleration of gravity, m/sec2

h Convective heat transfer coefficient, W/m2-°C

k Thermal conductivity, W/m— °C

k Velocity constant of enzyme activity, sec-1

K Time parameter in equation 43, sec'1

L Length, m

m Mass flow rate, Kg/sec

P Pressure, N/m2

J Temperature parameter in equation 43, °K
Heat transfer rate, KJ/hr

R Universal gas constant, cal/g-mol-°K

t Time, sec

T Temperature, °C or °K

U Over-all heat transfer coefficient, W/m2-°C
V Velocity, m/sec

Design criterion

 

W Mass of brine in contact with the area of the heat
exchanger, Kg

x Characteristic dimension in the dimensionless groups, m
Greek

a Thermal diffusivity, mZ/sec

B Coefficient of thermal expansion, l/°C

6 Effectiveness

11 Dynamic viscosity, Kg/m—sec

v Kinematic viscosity, mZ/sec

p Density, Kg/m3

Dimensionless Groups

 

 

 

 

Dn = Re(di/Dh)0'5 Dean number

Gr = gB('I\:2- T) x3 Grashof mmber
Gz = :1 :p Graetz number
Pr = Cpk“ Prantdl number
Re = 49—3—1 Reynolds number
Nu = 9—1-35 Nusselt number

INI‘RGIIZTIQ‘I

Spent cherry brine is difficult to handle in conventional waste
treatment systems since it contains several thousand ppm 802, color
and a considerable amount of solids. The brine has low pH also.

Recycling of the brine has been proposed as a solution to the
pollution problem and several researchers investigated the feasibility
of a reclamation process. Spent brine may be contaminated during
brining with polygalacturonase. A possible reuse of this material may
result in enzymatic softening of the fruit. Therefore, pasteurization
of the recycled brine is necessary.

Athanasopoulos and Heldman (1976) examined possible commercializa-
tion of a reclamation system based upon the work of other investigators
(Soderquist, 1971; Panasiuk 932.1, 1976). Their pasteurization unit
consisted of a helically coiled heat exchanger which was connected in
line with the brine reclamation system.

Pasteurization of polygalacturonase in a continuous process should
be examined for a commercial operation to be rapid and controlled.

Also such a unit will allow a predictable polygalacturonase inactivation.

The objectives of this study were:

1. To determine the amount of inactivation of polygalacturonase
present in spent cherry brine after heat treatment in a
helically coiled heat exchanger.

2. To review the literature in heat transfer and pressure drop
through coils and to modify several equations according to the

1

situation examined.
3. Tb calculate the performance of a helically coiled heat

exchanger .

LITERATURE REVIEW

A. Heat Transfer and Pressure DrOp in Coils

Coils have two major advantages over straight tubes, namely:
(a) heat transfer coefficients in coils are higher than in
straight tubes,
(c) coils allow a greater heat transfer area to be packed into
a given space more economically and more conveniently than
in straight tubes.
However, it is much easier to rerove scale from straight tubes than in
coils. Friction factors are also higher in coils.
The first theoretical analysis of the flow of nonconpressible fluids

through helices was done by Dean (1927), who predicted the flow in the
helix to be as illustrated in Figure 1, which shows a cross section of
the tube in the helix.

 

Figure 1. Cross section of a tube in a helix showing secondary flow.
3

The centrifugal force that exists in a curved pipe creates the
secondary flow. This type of flow causes a larger pressure drop and
heat transfer rate than that occurring in straight tubes. Dean introduced
a dimensionless group which characterizes the dynamic similarity of fluid
flow through a helix. This dimensionless group was named Dean's nurber

(111) and it is equal to:

Dn = Re(di/Dh)°‘5

where Re = Reynolds umber
di = inside diameter of the tube (cm)
Dh = diameter of the helix (cm)

A—l . Pressure drop.

 

Laminar Flow

 

The friction loss in a tube is given by the following equation:

AH = 2fLV2/gbdi (1)

where AH = Head loss (N/mz)

L = Length of the tube (111)
di = Inside diameter of the tube (m)
gC = Acceleration of gravity (m/secz)

f = Fanning friction factors, dimensionless

<1
ll

Velocity of the fluid (m/sec)

In straight tunes f = 16/Re. Therefore, frictional losses are highly
dependent on Re. The parameters on the left side in equation (1) are
all fixed for a certain process, except f. Thus, determination of f
is of great importance in pressure loss calculations.

Based on Dean's theoretical analysis, White (1929) proposed the

fol lowing equation:

f = C( l6/Re) (2)
for 11.6 < Dn < 2000
- O . 5

where-é-= l-[l—(ll.6£2%é2il )°°“5]1/M5
Since C is dependent on Re and Dh/di, high velocities and small helix
diameters will contribute to high pressure losses.

For both isothermal and non-isothermal flow, Seban _e_t__a_tl_. (1963),
taking into account the overall pressure drop , deduced the friction
factor on the basis of fluid properties at the mean film temperature.
They obtained results which were about 8 percent less than those
obtained by equation (2).

Flow of air within a curved tube was examined experimentally and
analytically by Mori gt_a_l_. (1965) . Using an approximation technique
for a series solution they derived the following equations for the

first and second approximation:

(fC/fS)I 0.1080Dn°’5 (3)

l-3.253
m0 ' 5

(fa/f5): (fC/fs)1/ (4)

where fc Fanning friction factor for coiled tube

f
3

Equation (4) gave results similar to those obtained with the following

Fanning friction factor for straight tube
equation:

fC/fs = 21.5 Dn / (1.56 + logm)5°73 (5)
Ito (1959) derived the above equation for

13.5 < D1 < 2000

The use of the ratio fc/fs for pressure drop determination has the

disadvantage that it cannot be used for Re greater than 2100 because
under such conditions, the flow in a straight tube ceases to be in the
laminar region while the flow in coiled tubes may be in the laminar

region at much higher Re (Srinivasan et a1. 1968).

The Critical Reynolds Number

 

The highest Re where the viscous forces still have an effect to
the dynamic forces streamline, is called critical feynolds umber.
While in straight tubes this value of Re is fixed, at approximately
Re 2100, in coiled tubes the curvature ratio determines the magnitude
of the critical Re.

Ito (1959) related the critical Re and the curvature ratio as
follows:

(R9) = 20000(di/Dh)°' 32 (6)

crit

According to Srinivasan et a1. (1968) the critical Re can be calculated

as follows:

(Re)crit = 2100(1 + 12(di/Dh))°‘5 (7)

Turbulent Flow

 

The work on pressure losses in smoth coiled tubes with isothermal
turbulent flow was summarized by Ito (1959), who proposed two equations

based on the results of several workers, namely
fc = 0.0076(Re)-°'25 + 0.00725(di/D)°'5 (8)

for 0.034 < Re(di/Dh)2 < 300
and

fC/fB = [Re<di/Dh>2]°'°5 (9)
for R9(di/Dh)2 > 6

where fB is the Blasious value for a straight tube

fB = 0.0791/Re

Fbr Re in the range of 6000 to 65600, Seban et a1. (1963) obtained
friction factors for isothermal and non-isothermal conditions. Their
experimental results and those of Ito were found to be in good agreement,
although they took the friction factor for a straight tube as

fs = 0.046/Re0'2.

Rogers and Mayhew (1964) experimentally obtained pressure drop
results for isothermal conditions through coils for Re in the range
of 3000 to 50000. They used coils with a different curvature ratio
and their results agreed within 1.5 percent of those of Ito's equations.

For non-isothermal conditions they suggested the following equation:

fc = fm, [<Pr)b/<Pr>w]“/3 (10)

Where fIto is given by equation (8) or (9), the subscripts b and w refer
to the properties estimated at the bulk and wall temperature respectively.
Fran the practical point of view, the best equation may be that published

by White (1932):
fC =0.08 Re-°'25 + 0.012(di/Dh)°‘5 (11)
for 1500 < Re < 100000

The simplicity of equation (11) is evident and since it can be applied
over a wide range of Re it can be used in various industrial helices
where high velocities are encountered.

In their investigation of air flowing in curved pipes, Lbri fl.
(1967 ) developed a model which gave satisfactory results in comparison
to equation (8) and to the experimental work of Seban _e_1_:_a_.]_._. (1963) and

Ibgers et a1. (1964). Their model can be simplified as

fc = 0.076 39‘0'25 + 0.00725(di/Dh)°°5 (12)

A—2. Heat transfer in coils.

Generally the heat transfer in tubes depends upon two parameters,
namely Reynolds and Prandtl number. In coiled tubes a third parameter
is introduced, that is the curvature ratio, di/Dh, which associates

the effect of the secondary flow in the mechanism of heat transfer.

Laminar Flow

 

For air, water, and Fssolube 30 oil in laminar flow within a coil,

Berg and Bonilla (1950) derived the following equation:

hidi

 

= [0.00002aa + 0.00063(di/D)] (1a)“29 (13)
GP pf f
where bi = inside heat transfer coefficient (W/m2.°C)
111. = dynamic viscosity at the film temperature (Kg/m.sec)
cp = specific heat of fluid (KJ/Kg.°C)

They found higher hi for oil and lower hi for air to the corresponding
values of hi in straight tubes, although it is evident that coils have
a higher hi.

The average hi is specified by Seban ELEL (1963) as

- —1/3
h; ‘11 (g) = A [f/8(Re)§]‘/3 <14)

 

for 12<Re<5600

100<Pr<675

10

where v = Kinematic viscosity (ma/sec)
a = Thermal diffusivity (mz/sec)
f = Friction factor for coiled tube

The disadvantage of equation (14) is that it was applied for two cases
of Dh/di (l7 and 104), therefore, a relatively applicable value of A
was not fixed. The effect of di/Dh in the mechanism of heat transfer
was also neglected.

Kubair and Kuloor (1966) related Nusselt and Graetz numbers in

heated water and glycerol as follows:

E

[1.98 + 1.8(di/Dh)] Gz°'7 (15)

for 10<Gz<1000
80<Re<6000

20<Pr<100

A modification of the Dittus—Boelter equation was applied by
Edney et a1. (1973) to determine hi in a coil within an agitated vessel.
Their results were in satisfactory agreement with previous works. The

equation can be simplified as
Nu = 0.0225 Fc (Re)°'°(Pr)°"' (16)
for 4.01XlO2 < Re < 9.2)(105

where Fc is a coil factor, ratio of hi in a coiled tube to that

in a straight pipe.

11

Fquat ion (16) may be valid within an agitated vessel but in the absence

of agitation the validity is questionable.
Turbulent Flow

A correlation for turbulent flow and heat transfer data as reported

by Seban et a1. (1963) resulted in the equation:
(Nu)f = 0.023(Re);'°5(pr);'“ (cu/uh)“l (17)

for 6000<Re<65600
15 <Nu<240

2.9 < Pr< 5.7

It is obvious that the equation is a modification of the Dittus—Boelter
equation.

Later experimental work of Rogers 3131. (1964) confirmed the
validity of equation (17) with a constant value equal to 0.021 instead
of 0.023.

While the effect of the curvature ratio (di/D) in pressure drop and
heat transfer in coils is taken into account in every equation described
previously, the effect of pitch, which is the shortest distance between

the centers of two consecutive turns of the helix, has not been considered.

12

B. Shell-Side Heat Transfer and Pressure Drop

B—l. Pressure drop.

 

The flow in the shell-side is very similar to the flow normal to the
ttbe banks of parallel tubes. McAdams (1954) suggests the following

equation for flow over banks:

f = (”AP)N
zen/11f)2

(18)

For the same case Kreith (1961) proposed the following relationship:

0.08 AP

(RPLl)n] Re_o.15 (19)

f = [0.044 +

where AP = Pressure loss (N/mz)

N = Number of tubes transverse to flow

 

 

m = Mass flow rate (Kg/sec)
Af = Shell-side flow area (m2)
= . . _ axial separation + tube diameter
AP Ax 1a1 p ltCh tube diameter
= . . _ radial pitch + tube diameter
RP Radio separation tube diameter
f = Friction factor

n 0.43 + 1.13/AP
Messa et a1. (1970) formd that equation (18) predicts the pressure

data in the shell-side more accurately than equation (19).

13

B—2. Shell—side heat transfer coefficients.

The mechanism of flow and heat transfer on the outside of the coils
is very complicated and no analytical solution to the problem has been
found. Kern (1950) suggested that, in cases where the velocity of the
fluid that flows over banks of tubes is very small, the following
equation proposed by McAdams (1947) could be used:

Nu = 0.53 [Grf Prf] °°25 (20)

f
Since equation (20) was developed for pure natural convection, its
use in situations, as flow over banks, where natural and forced convec-
tion coexist, may lead to considerable error.
Messa 313331. (1970) successfully predicted the heat transfer coeffi—
cients in the shell-side of a helically coiled heat exchanger using the

following equation:
Nu = 0.0085 Re°'°“ Pr°'57 (21)

Their Re varied between 2000 and 10000. Equation (21) was not checked
using smaller Re values.

Fand and Keswani (1973) experimentally studied convective heat
transfer under conditions where natural and forced convection coexist .
They used an electrically heated cylinder with water flowing in the
vertically upward, vertically downward and horizontal directions' Their

data were related to four zones depending on the ratio Grf/Rez.

14

First Zone

 

Grf/Re2 < 0.5 (22)
The predominant heat transfer mechanism in this region is forced
convection. Application of published forced convect ion equations may be

applied with negligible error (i 5%).

Second Zone

 

0.5 < Grf/Re2 < 2
In this case the heat transfer is still due to forced convection.
lbwever, natural convection affects the over-all heat transfer coefficient
by as much as 10 percent. The heat transfer coefficient in this region
is given by,

Nu = [0.225 + 0.699Re°‘5° + C(Grf/Rez)m Grf°'25]Pr°'29 (23)

where m is a constant equal to 0.30, 0.15, and 1.0 for upward, downward,

and horizontal flow respectively.

Third Zone

 

2 < Grf/Re2 < 40

In the third zone natural and forced convection effects are of the

same order of magnitude. In this region it is very difficult to reach

15

steady state conditions because of the two extreme conditions (pre-
deminance of forced and predominance of natural convection). Heat

transfer coefficients are, therefore, difficult to predict.

Fourth Zone

 

Grf/Re2 > 40

This is the region where natural convection predominates. The Nu

in this region is given as,

Nu =0 [(KGrf)°'5 +Re§]°‘51>r°°25 (25)

f

where C, and K are constants having different values depending on the

geanetry and the tube arrangerent.
C. Performance of Heat Exchanger

In a conventional direct-type heat exchanger the parameters

relating to the heat transfer performance are as follows (Kays and Iondon,

1955):
U = The over—all heat transfer coefficient (W/m2.°C)
A = The surface area on which U is based (m2)
Thi = Inlet temperature of hot fluid (°C)
'IhO = Outlet terperature of hot fluid (°C)
TC 0 = Outlet temperature Of the cold fluid (°C)
Ch = (mop)h the hot fluid capacity rate (W/°C)
Cc =

(mcp)c the cold fluid capacity rate (W/°C)

16

Flow arrangement - i.e. counterflow, parallel flow, crossflow,
parallel-counterflow or combinations of these
basic arrangements.

The over-all heat transfer coefficient carbines the convective and

conductive mechanisms responsible for heat transfer from the hot to the
cold fluid into a relationship similar to (Jim's Law. This relationship

can be expressed as:

 

. . 1A.
1 1 A1X A1 1
—‘T' = ‘—.- + + + (25)
U1 hl Awkw tho hd AO

where Ui = is based on the inside area
A1 = Inside area (m2)
Aw = Average wall area
X = Wall thickness (m)
A o = External or outside area
kw = Thermal conductivity of the wall (W/m.°C)
1 /hd = Resistance due to scale on the ttbes

In situations where the wall is very thin and the resistance due to scale

deposit is negligible, equation (25) is reduced to,

(26)

C:‘.lr--l
51*“
p

5|”
81"

Exchange: Heat Transfer Effectiveness

 

According to Holman (1976)

actual heat transfer
maximum possible heat transfer

 

effectiveness = e =

17

01‘

Cher .- (20‘ T )

01(1)

.__._____= (27)
mania); ci : minETh T )

101

where Cmin is the staller of the Ch and Cc magnitudes.

In general it is possible to express
8 = F(NTU, Cmin/Cmax’ flow arrangement)

Where NI‘U (Nmber of Heat Transfer Units) is expressed as,

mu=—:‘}!=———1 fAUdA (28)

NI‘U and e are related asymptotically for a given capacity ratio.
Therefore, where NI‘U is small, the effectiveness is low and when NI‘U
is large the effectiveness approaches the value of unity asymptotically,
or the actual heat transfer approaches the value of the maximum possible

heat transfer.
D. Recycling the Cherry Brine

Sweet cherries to be processed into maraschino, cocktail, or glacé
fruit, are placed, directly after harvesting, into barrels that contain
a brine solution of sulfur dioxide and various calcium salts. The
brining process prevents quality deterioration of the fruit and further
bleaches the cherries to a bright light yellow color. The bleached
cherries also are stored in brine solution for later distribution in

the market. After use, the brine may be discharged to a mimicipal

18

sewage system or it may be stored in tanks, where the solids are reroved
by settling and the liquid is sprayed on land. The latter is adopted
by a number of plants in Michigan.

Spent brine contains a high content of solids, SOz. Ca++ and color
pigment. In addition, it is characterized by low pH (Table A-l). Such
a material is considered as a very strong pollutant. According to
Soderquist (1971) a plant discharging spent brine at a rate of 38m3/day
into the sewage system would be exerting a load (in terms of degradable
organics) equivalent to 40,000 people or more.

Brine recycling and reuse would solve a pollution problem and
further lower new brine preparation costs. In 1970 Beavers M.
introduced the idea of reclaiming the brine by passing it through
activated carbon. Soderquist (1971) and Panasiuk 53131; (1975) examined
the feasibility of a brine reclamation system and proved that treatment
of brine by passing it through activated carbon does not lower the
content of $02, CaH and soluble solids nor does it affect the pH,
while cherries stored in reclaimed brine were found to have superior
quality to those in a freshly prepared brine.

Athanasopoulos and Heldman (1976) developed a large scale brine
reclamation system based on the work of previous investigators. The
system consisted of the following units:

a. sand filter for suspended solids reroval,

b. six columns that contained activated carbon for anthocyanin

and polyphenol removal , and

c. pasteurization unit for the inactivation of PG enzyme.

19

E. The Polygalacturonase Enzyme

E—l. Polygalacturonase in brined cherries.

 

Softening of brined cherries was first noticed about 1947 (Wiegand,
1954). In 1954 McCready reported that soft brined cherries seem to be
attacked by a pectin degrading enzyme, since the stems fall off and part
of the outer skin begins to slough. Fresh cherries infected with "cats
claw" type of spoilage were found to contain an excessive amount of POly-
galacturonase that causes softening of the fruit when brined (Steele
fl. 1960).

The polygalacturonase is a pectic enzyme capable of hydrolyzing
1,4—glycositic linkages of pectinic and pectic acids (Kertesz, 1951).
Possible sources of polygalacturonase in brined cherries may be from
microbial growth, certain cherry diseases, or the fruit itself might
synthesize the enzyme during ripening (Steele e311. 1960). The enzyme
sometimes retains active in the brine more than a year, and exposure to
this brine produces soft fruit (Brekke fl. 1966).

Several chemical methods have been proposed for polygalacturonase
inactivation but their commercialization is in doubt since the safety
of the chemicals involved may still be questioned. Inactivation by heat
might be the only approach because no chemicals are needed (Soderquist,

1971 ; Walters et a1. 1961).

E—2. Polygalacturonase kinetics, rate constants and stability,

 

The inactivation of an enzyme and the thermal destruction of an

organism can be described by first order kinetics,

dC/dt = -kC (29)
where dC/dt = activity change with time

C = activity at any time

k = velocity constant of the reaction (sec-1)

By integration equation (29) gives,
1n C/Co = ~kt or log C/Co = -kt/2.303 (30)

It is obvious that C in this relationship can never reach zero. By
introducing the factor D (=2.303/k), which stands for decimal reduction

time at a certain temperature, equation (30) gives,
C/Oo = 10_t/D (31)

Plotting temperature versus D on semi-log paper a straight line is ob-
tained, which is called the "thermal-death time" curve of a microorganism
or an enzyme. The reciprocal of the slope of the line is termed as the

Z value. The straight line can be expressed as,

T2 -T1

Z (32)

0T. = no X 10
If the Z value is large the texperature has a sraller effect on the TUI‘
tion if Z is small. Z and D values are fixed for a certain organism
or enzyme under specified conditions. Athanasopoulos (1976) emerimeltally
and theoretically determined the Z value of polygalacturonase to be
8.4°C and the D value to be 44.76 sec at 70°C.
The velocity constant k can be expressed by the Arrhenius

equation as follows:

21

k = A exp(—Ea/RT) (33)
where Ea = activation energy (cal/mole)
R = universal gas constant (cal/g.mole.°K)
T = absolute temperature (°K)

For a given environmelt, the velocity constant, k, for spores of a
particular species will be a function of terperature only. Equation (33)

can also be expressed as,
log k = log A - Ea/2.303RT (34)

which is the "Arrhenius Plot" of the reaction. The slope of the line
is -Ea/2.303R and the intercept log A. The activation energy of poly-
galacturonase is 64668.4 cal/mole (Athanas0poulos, 1976).

The inactivation rate constants are highly pH dependent. The pH
and decimal reduction time relationship is not linear because of the
enzyme being more resistant at pH 2.8 to 3.5 (Athanasopoulos, 1976).
Sugar concentration also affects the stability of the enzyme. The
decimal reduction time does not change significantly when the soluble
solids of the brine are in the range of 9 to 12%. However, when soluble
solids exceed 12% they affect the inactivation rate constants since
the strergth of the brine varies from one variety to another, influencing
the composition (302 content, pH, solids). Windsor brine has a higher
conceltration of 302, CaH, and pigrents, and exhibits lower rate

constants than Napoleon brine.

" 22

F. Polygalacturonase Inactivation Measurements and Calculation

F—l. Enzyme activity measurements.

 

The activity of an enzyme can be measured by determining the sub-
strate losses or by measuring certain changes in the physical properties
such as viscosity. RLmklyadeva and Korchagina (1975) introduced the
interferometric method for comrercial pectic enzyme preparation. The
method is rapid (less than two hours) and accurate (: 2%). Recently,
the solid media technique has been introduced in the quantitative
determination of enzyme activity. This procedure, developed for micro-
organism cultivation, has been used for detection of enzymes by
microorganism (Rankin and Anagnostakis, 1975).

The agar "cup-plate" diffusion procedure has been applied to the
quantitative determination of polygalacturonase (Dingle $3.1. 1953) .
This test has been used by Steele and Yang (1960) and Beavers 323141970)

for polygalacturonase activity determination in cherry brine.

F—2 . Process calculation .

 

The general method, first described by Bigelow _e_t__al. (1920),
was an extension of partial sterilization. Ball _e_t___g.l_. (1957) defined
partial sterilization as follows: if the TSP is t; min at T degrees,
the: heating which lasts for t; min at T degrees, results in steriliza—
tion which is tz/tl complete. Ball proved that sterilities are additive.
In 1928 Ball introduced a hypothetical TUI‘ curve passing through 1 min

at 250°F. Since lethality of a given process is the time in min of an

23

equivalent process at 250°F, then F in Ball's hypothetical TDI‘ curve
is equal to 1, where F is the time required to destroy an organism at
250°F. According to this information equation (32) can be rearranged

as follows:

250—T
Z (35)

 

log t/F =

where t, is the time in min to destroy the organism at T degrees. Since

F is 1 min, equation (35) is reduced to:

 

 

log t = 35%3 (36)

or
t = 10 2524‘ (37)

and
l/t = 10 12250 (38)

where 1/t is defined as the lethal rate (L) at terperature T. Therefore,
for a giver process where Z is fixed and the terperature time relation-
ship is known, the total lettality (degree of inactivation) can be
calculated since lethalities are additive.

Sturbo (1940, 1949, 1953) showed that in the case of conductive
heating, a process with F=4 does not have twice the sterilizing capacity
of another process with F‘r-Zmin.

Deincberfer and Humphrey (1959) introduced the following analytical
method:

By integration of equation (29)
1n 00/0 = I: kdt = v (39)

where V, the design criterion, is a measure of the size of the job to
be accomplished or the degree of inactivation. If k varies in accordance

with the Arrhenius equation, equation (39) gives

7 = A I: exp (-Ea/RT) dt (40)
at constant temperature

V = At exp (-Ea/R!1‘) = -kt (41)

In continuous sterilization processes, where the medium flows through
the heating, cooling, and holding section, V for heating and cooling is
calculated from equation (40) and V for holding from equation (41).

Therefore:
+ V + V (42)

For a certain process, if the terperature—time profiles are known, them
equation (40) results in integrals that can be solved analytically.

The disadvantages of the method are: (a) it assumes that the entire
population consists of spores of the design species, and (b) it requires
heat transfer information for the analytical solution of the integrals.

Another method devimd by Stumbo (1949) , Hicks (1951), and
Gillespy (1962), bases the process time on the probability survival in

the whole container.

25

The following assurption is another approach to the problem: if
it is assured that after a process the slowest point is safe, then the
rest of the fluid which must have a longer heating time must be safe.
Richards (1965) has adopted a graphical solution which provides a
ready means for the determination of the normal sterilization cycle.
The tixne-terperature profile for a batch sterilization is plotted over
the entire cycle. The cumulative values are then determined by stepwise

integration over the complete cycle.

ME’I‘HIBANDPWJRES

A. Instruments and Materials

Instruments

 

Figure 2 shows a diagramatic description of the apparatus used in
the experiment. The pasteurization unit consisted of three sections,
namely, heating, holding, and cooling. The helix in the heater was
5.8 m (19 ft) long, in the cooler 3.97 m (13 ft), and in the holding
section 4.88 m (16 ft). The tubes were made of stainless steel. The
specifications of the writ are given in Table 1.

An open pressure cooker was used to maintain the heating medium
at a constant and controlled temperature. The heating medium was
recirculated using a centrifugal pmp and the flow rate was measured with
a rotameter located in the line downstream from the pump. Tb lessen
scale build up on the outside of the brine coil in the heater the
heating medium was passed through a cOpper coil immersed in a hot water
bath. This enclosed indirect heating system reduced the amount of
scale build up essentially to zero.

The flow rate of the brine was of great importance. Steady-state
condit ions within the pasteurization unit could not have been achieved
with a fluctuating flow rate. A varying flow rate would result in a
fluctuating and unpredictable degree of enzyme inactivation. The
problem was solved by using two pumps and a supply tank positioned four

26

65.5 €020 mo gangs—558 sow Spam mfiaooo o5 gases no same? 0358 .N 0.53m

        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. I assa
$240528
$32559 $2; 5: ES E52032
H1... 523 5: v A 3.2,:
fl 7 . . has:
. . “.285 see.
_
_
s -
“ ¥z<e
35258 H “ 5&3 26:55
Fl. IIIII VIII/ “ Kelp
b
538: ES: 2. x u z.
mmszfiasfl $2; 571/ u $5: $108 Jae; 38
A
3 a a
0
~22; / a a a a so
,I s $2; 38
l A .

 

 

 

BNEBEE :8 02.301

Table l. Specificatiers of Experimental Heat Exchanger.

 

 

Specification Heater Cboler
Srell diameter 22 cm 22 an
Shell height 43 cm 43 cm
Helix diameter 19.05 cm 19.05 cm
Nurber of turns 10 10

Tube length 580 cm 397 cm
Pitch _ 3.18 cm 3.81 cm
Tube I.D 0.635 en 0.635 cm
Tube O.D 0.7937 cm 0.7937 cm

 

Length of tube in holding section: 488 on

feet; above the pumps. The first pump transferred brine to the supply
tank and the second pump pumped the brine from the base of ’the tank
into the heater. The first pump had a higher capacity, therefore, a
small amount of brine overflowed from the tank maintaining a constant
level at 30 en.

The pressure drop through the pasteurization unit was measured
by attaching one end of a mercury manometer in the brine line at the
entrance of the heater and the other at the outlet of the unit . Therefore,
the pressure drop was measured in mm of mercury.

The temperature at several points throughout the system (Figure 3)
was recorded on a Honeywell potentiometer. All thermocouples were

copper—constantan wire of equal length and calibrated in ice water.

29

Petri dishes with dimensions 15 X 85 mm were used for the "cup-
plate" procedure. Small plastic collars (9 mm diameter) were placed in
the center of the dish before the addition of the substrate in order
to provide cups into which the enzyme-brine solution was added using

a syringe.
Materials

Hot and cold water were used for the heating and cooling medium
respectively.

The constant temperature along the holding coil was considered to
be the process terperature, which in turn, determined the hot water
terperature. Because the amount of inactivation desired was determined
by the process temperature, the degree of inactivation was directly
related to the hot water bath terperature. The heating medium was
flowing downward in the heater and the brine upward in the coil as
indicated in Figure 3; therefore, the liquids were in a counterflow
arrangement.

Tap water was selected for the cooling medium, which flowed
upward in the cooler. The brine flowed downward in the cooler to
produce a counterf low arrangerent .

The flow rate of the hot and cold water was adjusted to 3.78 Kg/min
and 5.6 Kg/min respectively, while that of the brine was 1 Kg/min.

Brine of Napoleon variety was chosen for the experimental trials.
The brine was supplied by a plant located in Traverse City, Michigan.
Extraneous matter including color, stare, leaves and seeds were removed

using a reclamation system developed by Athanasopoulos and Heldman.

(TU BE WALL

   
 

WALL SURFACE

THERMO COUPLE
WALL THERMO COUPLE

Attacl'xnert of the bare junction in the wall
and on the wall surface of the tube.

 

 

 

 

 

 

 

COOLER ‘ HEATER . A
F———__._
COLD HOT WATER
WATER IN
OUT 1
- l
A A

COLD , HOT WATER
WATER OUT
I N

 

A Inlet and outlet hot water stream temperature
A Inlet and outlet cold water stream temperature
0 Wall surface terperature measurerent

0 Wall temperature measurerent

D Brine stream temperature measurement

I Bulk temperature measurement

Figure 3. Thermocouple stations for wall, wall surface and fluid
stream temperature measurement.

31

Reclaimed brine was found to have a pH of 3.1 and 10.5% soluble solids,
thereby eliminating further adjustment or pretreatment .

Purified commercial polygalacturonase (Pectinase’) from isperggllus

 

niggr was used in this study at a concentration of 1 mg of the enzyme
per 1 ml of brine.
The substrate of the enzyme for the "cup-plate" procedure was made

from the following:

Distilled water 1000 ml
Polygalacturonic acid 2.5 g
Ammonium oxalate 2.5 g
Bacto agar 20 g
Potassium acid phthalate 10 g
Thymol 0.25 g

All of the substances were mixed in a 2 liter Erlenmeyer flask and

the mixture was sterilized at 120°C for 5 min.

B. Temperature Measuremnts

The properties of the fluids used in the experiment were determined

at the mean film temperature conditions (Tf) using the equation

T = Tb + Tw
f 2
where Tb = mean bulk terperature (°C)
TW = mean wall terperature (°C)

'Ib obtain the wall terperature a U shaped groove was cut on the inner

part of the tree wall of the helix. The bare junction of the thermocouple

 

lIzhectinase is the trade name for polygalacturonase supplied by SICMA
en. Co.

was placed in the groove in direct contact with the metal wall of the
tube. The groove was then filled with a sticky plastic material in
order to have adequate insulation. Three thermocouples were installed
along the helix, with one at each end and one in the middle. The
average of the three terperatures was considered to represent the
mean wall terperature of the coil on the inner side of the heat
exchanger.

Fbr the shell-side measurements, the following equation was used:
_ TS + T

b

Ti“ 2

where TS = wall surface terperature (°C)

Wall surface terperatures were measured using the same procedure as
described for the wall except the thermocouples were attached on the
surface of the wall instead of the U shaped groove.

The bulk temperature for the streams in each section was measured
by connecting a rubber ttbe on the entrance and the exit of each
stream and placing the bare thermocouple jtmction in the center of
each tube. The mean bulk temperature was considered to be the average
of the inlet and the outlet stream terperatures. For the shell—side
measurements, three individual bulk terperatures were recorded: at the
entrance, the outlet, and the center of the shell. In Figure 3 the
several positions of the attached thermocouples are indicated, while
in Appendix C the recorded temperatures at the various positions for

four differert trials are preserted.

33

C . Pressure Drop and Heat Transfer Determination

The ability of the apparatus to maintain a desired heat treatment
condition was checked with water in place of cherry brine. Nbre than
100 trial runs were made to achieve the desired accuracy. Before
making heat treatment trials on brine, the pH and soluble solids
contert were determined. An ABE refractcmeter and a pH meter were used.
With soluble solids of 10.5% and pH of 3.1 no adjustment was necessary.
The instrumentation was also checked on the brine in the same manner
as was done previously on water. Temperature readings were taken after
steady-state condit ions had been attained in a particular run which

usually required 10 min.

C—l . Pressure drop.

 

The ttbe side or coil side head loss was examined under the

following conditions:

Processed liquid: water
Flow rate: 1-2 Kg/min
Fluid temperature: 11,5-70 °C
Wall terperature: 32.5—60 °C
Reynolds number: 5051-10092
Critical Re: 6700

The properties of the water were evaluated at mean film terperature
conditions. The critical Re was determined by equation (7). Laminar
friction factors were obtained with equation (5), while equation (9) was
used for turbulent flow. Fbr straight tubes f = 16/Re and f = 0.046/RIe°°2

for laminar and turbulent flow respectively. After the friction factors

34

were evaluated, the pressure drop was calculated by applying equation (1).

C-2. Heat transfer calculations.

 

Inside heat transfer coefficients were evaluated under the following

experimental conditions:

Processed liquid: Brine
Brine flow rate: 1 Kg/min
Reynolds number: 5350-7300
Prandtl number: 2.93-4.6

As in pressure drop measurements the properties of the brine were
evaluated at mean film terperature conditions, and they were assmed
to be identical to those of water. Because the present work and that
of Seban _e_1;_a_l. (1963) and Rogers gt__a;_l_. (1964) were carried out under
similar experimental conditions, equation (17) with a constant value of
0.21 was used, for the inside heat transfer coefficiert determination.

The experimental conditions for the outside heat transfer coeffi-

cient estimation were as follows:

Hot water ‘flow rate: 3.78 Kg/min
Cold water flow rate: 5.6 Kg/min
Grashof nurber: 5X105-1 .2X107
Reynolds number: 50-70
Grf/Rez > 40

The ratio Gr f/Re2 > 40 indicates that both natural and forced convection
coexist, the natural being the predominant. Therefore, equation (24)
should be used, where K = 1.7 and C = 0.235. In the cooler, natural

convection did not seem to exist since the water was flowing upward while

the density was increasing downward. It was assured that, because the
velocity of the water was very stall (l m/min), the equations used for
the heater would apply.

Reynolds nurber calculations were based on the maximum velocity.
The maximum velocity was considered to exist in the stallest cross
sectional area. As the water flows upward (cooler) or downward (heater)
two areas are involved: one between the shell wall and the coil
(0.0162 m2) and the other which corresponds to the diameter of the coil
(0.0248 m2). Therefore, the Reynolds nurber was based on an area of
0.0162 m2.

Assuming no scaling deposit exists on the tubes, equation (26)
was used for over-all heat transfer coefficient calculations where
kw for stainless steel equals 16.26 W/m.°C.

The over-all heat transfer coefficient was also predicted by
noting that the wall terperature was found to vary exponentially.
If it is assumed that the stream terperature will vary the same way,

thei according to Deindoerfer et a1. (1959),

T = J (1 + be'Kt) (43)

where T = stream terperature at any time t (°K)

 

U = over-all heat transfer coefficient

W = mass of flowing medium in contact with the
surface area A (Kg)

A = surface area across which heat transfer
occurs

cp= specific heat (KJ/Kg.°C)

After time t, the medium will exit the heater at a certain temperature

Texit‘ Equation (43) gives
T - T .
-Kt = 1n (“pf—j—fg—ui) (443)
H 0
TH’ Texit’ and TO can be measured, while t could be calculated based

on the flow rate and the diameter of the tube. Therefore, K may be
predicted relatively easily. A, W, and cp are also known or predictable.
Then

For the cooling section, b = TO—Tc/Tc, where Tc is the temperature of
the cooling medium (°K). After time t' , the medium will exit the cooler

at temperature T' exit. Equation (43) then is reduced to

T' - T
- t' = 1n (‘Tfexitvr C) (44b)
0 C

37

Where K is based on the U, A, W, and CD of the cooler. The over-all
heat transfer coefficient may be calculated as given previously.

An energy balance in each section of the unit can also give a
good approximation of the value of the over-all heat transfer coefficient .
Based on the logarithmic mean temperature difference (IMID) the following

expression can be used:

q=rhcp AT=UAF ATm (440)

rate of heat transfer between the fluids (W)

where q

8‘
ll

mass flow rate (Kg/min)
AT = change in bulk tarperature between entrance and

exit of the tube

ATm IMI‘D (°C)

’11
ll

correct ion factor, dimensionless

The correction factor for the experimental heat exchanger was assumed
to be similar to that of a multiple-pass counterflow heat exchanger.
From charts (Holman, 1976) F was found equal to 0.95 and 0.99 for the

heater and cooler respectively.

D. Performance Calculation

The over-all heat transfer coefficient estimation, for the heater
and cooler was described in the previous sect ion. Inlet and outlet
temperatures of the fluids were recorded on the potentiareter. The fluid

capacity rate was calculated by multiplying the flow rate by the specific

38

heat of each fluid. The surface area through which heat transfer occurred
was calculated based on the logarithmic mean area of the inner and outer
areas of the coils.

The effectiveness, 8, of each section was determined by using

equation (27), while equation (28) was applied for NTU calculation.

E. Degree of Inactivation Measurement and Galculation

Purified polygalacturonase was added to the untreated brine at the
rate of 1 mg of enzyme per 1 m1 of brine. The pasteurized brine was
collected and the degree of inactivation was measured by determining
the concentration of the remaining enzyme. The "cup—plate" procedure
as used by Athanasopoulos (1976) was applied. Tb the cup of each
Petri dish 0.15 ml of enzyme-brine solution was added and incubated for
20 hr at 35°C. The diameter of the clear zone was related to a
standard curve and the amount of inactivation recorded. The standard
curve was prepared by diluting 100, 80, 60, 40, and 20 mg of enzyme to
100 ml of Napoleon brine. This resrlted in 100, 80, 60, 40, and 20% of
enzyme activity. 0.15 ml of each dilution was added to Petri dishes
containing the solidified agar. The dishes were placed in the incubator
together with those containing the pasteurized brine. The diameter of the
clear zone of each dilution was plotted against enzyme concentration
on semi-log paper. The straight line obtained was regrded to be the
standard curve (Figure 4).

The degree of inactivation was calculated by both, the General and

the Analytical methods, as illustrated by the following example.

39

Example Problem

Napoleon cherry brine containing 1 mg polygalacturonase enzyme
per 1 ml of brine was pasteurized in a helically coiled heat exchanger.

Determine the amount of inactivation if the following information is

available: Heater Cooler

Area of coiled tube (m2): 0.129 0.088
Length of coil (m): 5.8 3.96
Brine flow rate (Kg/min): 1
U (W/mz. °C): 1085 1011
Mount of brine in contact with coil (Kg): 0.180 0.124
Time of heat exposure (sec): 10.83 7.45
Specific heat of brine: 4186.9 J/Kg.°C
Constant in Arrhenius equation,

A (sec ‘1): 7.5 x 1039
Velocity constant of polygalacturonase

at 76.66°C: 0.3057 sec"1
Activation energy of polygalacturonase: 64668 cal/mole
A value of polygalacturonase 8.4°C
Temperature—time profile in coils: exponential

A. Analytical Method.
According to equation (40), for both heating and cooling,

7 = A I: em(-Ea/Rl‘)dt

100

‘7» ACTIVITY

 

ZONE DIAMETER, mm

Figure 4. Standard curve for polygalacturonase activity measurement.

41

Since the terperature—time profiles are exponential, carbination of
equation (40) and (43) results in integrals which are first order
exponential integrals that can be numerically evaluated for the various
values of their lower limits or argtments. Thus for exponential

temerature—time profiles in the heating and cooling sections we have:

 

 

 

A a a

v=— E1(-—-—)-E1( ) (45)
K 1+b lib-kt
A -3.
'- E E1( _a)-E1(——§ka-a)
l+b 1+be

co e-x

By definition E1(z) = fz 7 dx (46)

z = lower limit or argument

E1= first order exponential integral function

For positive arguments up to 15, the first order exponential integral
function can be taken from tables (Deindoerfer et a1. 1959). Above this

argument, the following approximation yields a satisfactory value:

.2 .
E (z) = g— (47)

To solve the problem equation (45) and (47) should be used.

Heat ing Sect ion

 

93.9 + 77.5

2 = 84.7°C or 358.9°K

 

J = heat source temperature =

64668

a = 1.987 x 358.9 = 90'68

 

J

T:

 

 

 

K = U A = 1085 WLm2.°C x 0.1294 m2 x 1JjW.sec
cp 0.180 Kg x 4186.9 J/Kg.6C
_—_ 0
To 295.4 K,
T - T
b = 0 H = -0.1769 e‘Kt — 0.147
TH
a a
fig - 110.16 , 1+be-Kt = 93.10
a a
——-a=18.48, ——_——_a=2.42
1H) 1+be Kt
.- e—llO-lo _ -50
E.(110.10)— W - 1.3 x 10

 

E1(93-10) = 3.% X 10-73, E1(18.48) = 5 X 10-10
E1(2.42) = 3.67 x 10‘2

A no Ae”a

K = 4.03 X 10 K = 16.73

Equation (45) becomes,

4.03 x 10"0 [1.30 x 10'50 — 3.96 x 10"“)

= 0.186 sec"1

— 16.73 [5 x 10‘” — 3.67 x 10' ] = -0.01595 + 0.61399

vheat. = 0.59804

Cooling

- _ 13 + 22
c cool1ng medium temerature - ---2——

= 17.5°C = 290.7°K

43

64668

a = 1.9877 290.7 = ”1'95

 

 

_ 1011 x 0.0885 x 1 = -1
K - 0.124 X 4196.9 0.1723 sec
To = 349.86°K , b = 0.2035 , e‘Kt = 0.277

a a
__-_.. = 93.02 , -— = 105.97
1+5 1+be-Kt

a a
———a=-18.93, -——-:—-—a=5.98
1+b 1+be Kt

Ae‘a -

A/K=4.35X10"° , '12—": 1.17x10 °
E1(93.02) = 4.29 x 10‘” , E1(105.97) =-- 8.96 x 10'”
E1(—18.93) = -8791114.3 , E1(-5.98) = -66.12

Equation ( 45) becomes,

4.35 x 10"0 [4.298 x 10‘“3 - 8.96 x 10‘”]
—1.17 x 10"° [—8791114.3 + 66.12] = 0.01869 + 0.10285

V = 0.12154

cool.

.. _._ ‘1 =
Vhold.‘ kt 0.3057 sec X9.02 sec 2.7574
(the brine is exposed in the holding coil for 9.02 sec)
Vtota1'_'vheat. + vcool. + vhold.

= 0.59804 + 0.12154 + 2.7574 = 3.47698

44

V

total = 1n NO/N , (assume N0 = 100)

then, lOO/N = 32.36 and N = 3.09%
or

100 - 3.09 = 96.91% inactivation
B. General Method

A basic requirement in process calculation by the general method
is measurement of the terperature of the sterilized medium during heat
treatment. In the preselt study the temperature of the treated brine
was measured at several points. The temperature between these points
was predicted by using equation (43). Therefore, the following method
may be considered as a modification of the general method.

For the heating section equation (43) becales,

T = 358.9 (l-0.769 e'°'“”5’c

)

t varies from O to 10.83 sec
For the cooling section equation (43) gim,

T = 290.7 (1 + 0.2035 e‘°'1mt

t varies from 0 to 7.47 sec
By giving t several values, the cormpcnding temperatures can be
obtained. A plot of temperatureversus tine results in the temperature
-time profile (Figure 14).

The first colum of the following table represeits the midpoint time

for time intervals 1 sec. The second colum is the temperature that

45

corresponds at each time, and is taken from Figure 14. From equation (38)

T-250

Z (F=1min)

In the problem the process terperature is 170 F(76.66°C) 76 250°F,

therefore, Fun + 1 min. Thus the above equation will become

T — 76.66
Z

Since the time intervals = 1 sec, the third colum, which represents

the time interval lethality

T - 76.66

=LXAt=1X10 Z sec

Table 2. Calculation of cumulative lethality.

 

 

T - 76.66
Midpoint Time Midpoint Temp. 10 Z
sec °C
0.5 27.5 1 x 10"’_
1.5 37.8 2.3 x 10 5
2.5 46.0 0.00022
3.5 52.5 0.00132
4.5 58.0 0.0060
5.5 62.5 0.020619
6.5 66.4 0.06005
7.5 69.5 0.14048
8.5 72.5 0.31971
9.5 75.0 0.63442
10.5 76.5 0.95708
11.5 76.66 1.0
12.5 76.66 1.0
13.5 76.66 1.0
14.5 76.66 1.0
15.5 76.66 1.0
16.5 76.66 1.0
17.5 76.66 1.0
18.5 76.66 1.0
19.5 76.66 1.0
20.5 70.0 0.16117
21.5 61.6 0.01611
22.5 54.5 0.00230
23.5 48.7 0.00046
24.5 43.6 0.00011
25.5 36.2 0.00001
26.5 35.5 -

 

Tbtal = 11.3200 sec
Cumulative lethality = 11.3200

 

The cumlative lethality represents the equivalent process time at
temperature 76.66°C. Since k = 0.3057 sec'1 , equation (30) becures,

1n C/Co = - kt -0.3057 sec-1 X 11,3200 sec
If 00 = 100, then C = 3.14%
Thus, the process resulted in

100 - 3.14 = 96.86% inactivation.

REalLT‘S AND DISCUSSKN
A. Pressure Drop

The frictional losses in a pipe are higily dependent on the fluid
films that exist on the metal walls. Since the fluid flow pattern
(laminar or turbulent) effects these boundary layers, the degree of
turbuleice determines the amount of pressure drop through a pipe.

Figure 5 illustrates the effect of Reynolds nmber on the friction factors
in laminar and turbulent flow, for straight and coiled pipes. The
friction factors are affected to a greater extent by the Re in the laminar
flow conditions than in turbulent flow. This holds for both straight

and coiled pipes. The fact that, in the laminar flow the friction

factor is inversely proportional to Re (equation 2) while in the turbulent
region it is inversely proportional to Re°°2 (fs = 0.046/me°'2), which
explains the previously mentioned effect on the friction factors. There-
fore, with an increasing Re, the friction factors fall more gradually in
the turbulent flow than in the laminar flow region.

The centrifugal force which exists in a curved pipe produces a
pressure gradient in a cross section. This pressure gradient yields
a pair of secondary flows which cause a larger anomt of pressure drop
in coiled pipes than in straigit 1313368. The curvature ratio (di/Dh) may
be ceisidered as an expression of the magnitude of the centrifugal force.

The coil diameter is the factor that determines the value of this force

47

48

 

Iamfinar

Turbulent

0.01-

 

 

0.001 . ill, . .4, l L l_ll, .

 

 

1 2 3 4 5 6 7 8 9 10 XI103

Re

Figure 5. Effect of Reynolds number on friction factor in straight
and.coiled tubes for laminar and.turbulent flow.

49

for a certain inside tube diameter. Snall coil diameters contribute to
a larger centrifugal force and larger pressure gradient. Figure 6 shows
the variation in the friction factors among coils with different
diameters. Under a constant Re, smaller coil diameters result in
friction factors of higher values.

Probably the most important factor that influences the pressure
drop in a tits is the flow rate. The relationship between frictional
pressure losses and flow rate is shown in Figure 7. The pressure losses
increase gradually with small flow rates (low fluid velocity), whereas
the pressure drop increases rapidly at high flow rates (high fluid
velocities). Such a relationship may be expected since, according to
equation (1), the pressure drop is directly proportional to the square
of the fluid velocity. Table 3 and Figure 7 give a canparison between
the calculated and the measured pressure drop. The calculated values
were found to deviate from -l.3 to 49.2% from the measured ones. Actually,

equation (9) was developed for isothermal conditions. The use of mean

film tenperature may give a good approximation.

The shell-side pressure drop was measured. Seven trials gave values
from 689 N/mz (0.1 psi) to 1034 N/mz (0.15 psi). The enall velocities
that were encountered in the shell-side in both sections contributed to
the lower pressure drop . Therefore, it may be concluded that under the
conditions carried out in the experiment the shell-side pressure drop

is of no significance.

 

 

 

 

2 x 10" -
10" L
P
p
Re:
- o di/D = 0.043
. 0 Straight tube
a di/D = 0.033
I di/D - 0.058
.007 .0075 .008 .0085 .009 .0095

Figure 6. Effect of curvature ratio on frictional factors in
coils.

5x10“

PRESSURE DROP, Wm2

51

 

X Measuredpressuredrop

 

 

 

p

‘H ‘ -
O 0.5 1 1.5 2

FLOW RATE, Kglmin

 

Figure 7. Effect of flow rate on calculated total pressure
drop in the coils of the pasteurization unit .

52

Table 3. Calculated and measured total internal pressure drop in the
pasteurization unit, at several flow rates.

 

 

Flow rate Calculated Measured Difference
(Kg/min) AWN/m2) ANN/m”) %

l .0 12769 13858 -7 . 85

l . 2 16915 17161 -1 . 43

l . 5 24483 22414 +9 . 23

2 . 0 42196 42754 -1 . 30

 

B. mat Transfer

The influence of the curvature ratio on the inside heat transfer
coefficient is similar to that of the pressure drop described previously.
The straight lines in Figure 8 are derived from equation (17) using
different (ii/DI1 values. The centrifugal force promotes mixing in the
coiled pipe and this results in higher heat transfer coefficients in coils
than in straight tubes. Figure 8 also shows how high Re contributes to
high heat transfer coefficients as a result of increasing turbulence with
increasing Re. Coils with the same tlbe diameter but different coil
diameter will give different heat transfer coefficients urnder the same
conditions. Those with a smaller diameter give the higher values. When
the influence of the coil diameter on the centrifugal force and the effect
of coil diameter on the heat transfer coefficients are considered, the
values given in Figure 8 are valid and reasonable. Also illustrated
in Figure 8 the higher Nu of coils when canpared with th0se in straignt
tubes.

o di/D = 0.058
. di/D = 0.043
g di/D = 0.033

I Straight tube

 

-0.4
Nu1,Prf
5‘2

 

 

o
01
5"
01
63b

6.5 7

Figure 8. Inside heat transfer coefficients in coils for
different Re and different curvature ratio.

7.5 x 103

8

95998989 9035 hows; u a. 0.358969 “03:0 05.5 a one

H3

5.55.2333 soda noes: u . 9 1092.893 soda .9qu u Be

 

 

as- 22 82 «.2 a: 4.8 m8
9:- 82 «8.2 4.8 ado. 98 «.««
«2+ 82 22 o.«« o2 can 2.2
o.«. 22 82 out. ozmo s2 «.««
92 ea: 82 m2 o2 «.«m at.
on- 22 22 was 2.8 o.«s «.««
«8+ 82 3.2 o.o« an m2 :8
«.2 82 82 «.«s 25 cos m.m«
I- senescence 85.898 one is one Es
on. Co
85423, .528 51.2sz seam BE .6 as:

 

. maoH peonoo garage H8833 noon:
.80 {:55 3822358 nonhuman some 86288 386vo can 83958 no 339.8 .4 23

55

The Grashof and the lbynolds nurber of the shell-side varied from
5 x 106 to 1.2 x 107 and 50 to 70 respectively. This indicates that
natural convection was the precbminant force in the heat transfer
mechanism in the stell—side. Outside heat transfer coefficients were
calculated by equation (24). They were also predicted through equations
(44a) and (44b) for heating and cooling respectively. In Table 4 the
difference between the predicted and calculated values is illustrated.
They were found to vary from -3.0 to +ll.6%. Actually, in the cooler,
natural convection did not seen to exist because the water was flowing
upward while the density was increasing downward. The assurption that
natural convection equations can be applied to the shell—side of the
cooler due to the low velocities of the water (lm/min), seems to be
correct as illustrated in Table 4. The outside heat transfer coefficients
were found to be smaller than those in the inside. The lower inlet to
outlet velocities in the shell—side than those inside the coils may have
contributed to the lower heat transfer coefficients.

The most important heat transfer parameter in designing a heat
exchanger is the over—all heat transfer coefficient. Equations (25),
(44c), and (44a) or (4411) for heating and cooling respectively, were
used to calculate the over-all heat transfer coefficient. In Table 5
the results of the three approaches are presented. The three methods
were found to be in satisfactory agreenent. Figure 9 and 10 illustrate
the relationship between over-all heat transfer coefficients and the
logarithmic temperature difference ratio. The straight line in Figure 9
is the solution of equation (44a) and in Figure 10 the solution of
equation (44b). Both figures indicate that for constant heating or

cooling medium temperatures the difference between inlet and outlet

g

85.2098”? #0350 .0983 u m.

H3

gage p038 05.5 n

one

8858.888 822 can u Be

 

 

0.858893 822 scene 1 e
82 22 82 «.2 T: 4.8 m8
22 82 8: 4.2. 8.8. 98 «.««
2o :2 «82 o.«« o2 o8 H2
««2 82 so: miss 8.8 e2. «.««
men 48 to o2 o2 «.«m at
man «o2 82 is 2.8 o.«e «.««
«8 Re 88 o2 a: new 58
o2. .82 mSH «.«e 28 0.2 m.m«
888m 8.82 $8 8888 348 .8 88$ :2 85cm 9se 8e one Be

0

O
EHUHPHHU a: g alas a; .6 gm.

 

. mace p.380 0922098» H3000 soon:
.0850: panacea. cones. .3 89892.8 .60 was: 822.808 88qu some 281.88 02. .m passe

 

57

 

8 9 10 11 12 13 x 103

u, Wlmz. °c

0 Predicted by equation (44a)
A Calculated from the total resistance

D Calculated fran energy balance

Figure 9. Effect of teuperature difference ratio of the
two fluids in the heater, on the over-all heat

transfer coefficient .

-O.45

 

 

8 8.5 9 9.5 10 10.5 x 102

U, w1m2. °c

. Predicted by equation (44b)
A Calculated from the total resistance

[3 Calculated fran energy balance

Figure 10. Effect of temperature difference ratio of
the fluicb in the cooler on the over—all
heat transfer coefficient .

temperature of the fluid in the coils determines the nagnitude of the over-
all heat transfer coefficient. 'Ihus, large tarperature differences
contribute to high U values, while snall talperature differences result

in suall U values.

C. Performance of the Emerinental Heat Exchanger

Figures 11 and 12 illustrate the tenperature distribution of the fluids
in the heating and cooling section. The brine inlet and outlet temperature
was measured, while the tenperature change with time was predicted by
equation (43). The distribution is very similar to that of a double pipe
counterflow heat exchanger. Therefore, the mm of the experimental heat
exchanger my be calculated in a manner similar to that of a double pipe
heat exchanger. Since the IMP!) can be calculated the over-all heat
transfer coefficient can be calculated by using equation (44c).

The difference between inlet and outlet tenperatures of the hot and
cold water is effected by the flow rate of each stream. The larger the
flow rate the smaller the tenperature difference. 'Ihe drop in the hot
water curve is larger than the rise of the curve of the cold water as shown
in Figures 11 and 12. Different flow rates (3.8 Kg/min for the hot water
and 5.6 Kg/min for the cold water) accmmt for the variation.

Table 6 indicates that the effectiveness of the experimental heat
exchanger varied from 73 to 78% for the heating section and 63 to 68%
for the cooling sect ion. The lower effectiveness of the cooling section
uny'be due to the lower over-all heat transfer coefficients of the cooler.

Generally the temperature for both fluids was lower than that in the heater.

DISTANCE FROM INLET, m 0

 

 

 

 

0.43 -
#L3A
77.5 7
Hot Water
or
o
Lu.
1
'2 Erin
< ' e
n:
Lu
0.
2
Lu
I-
22.

 

 

 

5.8

 

DISTANCE FROM INLET, m

Figure 11. 'Deuperature profiles in the heater of
the experinental heat exchanger.

 

61

DISTANCE FROM INLET , m

 

 

 

 

 

 

9.43 O
81
Brine
o0 9

Lu.
:2
E
<
a
I.”
%
Lu 34.4
|-

‘ 11. 1

6 5.13

 

DISTANCE FROM INfEr, m

Figure 12. Termerature profiles in the cooler of
the experinmtal heat exchanger.

 

mN.H mo.N mm vb o.Hw

 

mNH Hod .5 E. m6»
mm . H 3. H so mm o . mm
mm . H mm . H mm mm o . on
.HmHooo House: .8300 powwow 0o
PE 9... . mmccmSH powwwm chafing wwdoong

 

68.33%”, wmcoona Hagen as 553— H 90 open 2.on a. we 2am. gnu
mfinflnsmpmmm now homage pawn Hanna—nag 23 .3 PE 28 wmmemfi Beam .0 cHnflH.

63

The NI‘U of the heat exchanger is a function of the over-all heat
transfer coefficient and the heat transfer area (equation 28) . Higher

NTU values also occurred in the heater as shown in Table 6.

D. Polygalacturonase Heat Treatment

The D values of an organisn increases very rapidly with small increases
in temperature. An increase in tenperature also results in a sharp decrease
in the velocity constant, k, of a reaction. Therefore, the percentage of
inactivation is highly temperature dependent . By increasing the temperature
from 70 to 72°C the anmmt of inactivation increases fran 44 to 63%, as
shown in Table 7. The effect of teaperature on the degree of inactivation
is illustrated in Figure 13. At lower tarperatures the increase is
relatively sharp and asynptot ical 1y approaches the value of 100% inactiva-
tion. The temperature-time profiles in Figure 14, as predicted by
equation (43) , were used for calculating the inactivation at several
process tanperatures or constant tarperatures along the holding coil .
Because of the exponential nature of the heating and cooling portions,
the enzyme was subjected to higher tanperatures for a longer period in
the heater than in the cooler for the sane range of tarperature. Thus,
the heating section contributed more to the total inactivation than the
cooling section, as in Table 8 is shown. The three methods which were
used for the inactivation determination, nanely plating, analytical,
and general , gave results in close agreement with each other, as shown
in Table 7. If it is assured that plating is the more accurate method,
the analytical and the general were found to vary fran the plating values
from -l.9 to +2.34% (Table 7). Therefore, use of either the general or

7o INACTIVATI ON

70

Figure 13.

 

 

75 8)

TEMPERATURE °c

Effect of tenperature on the degree of enzyne
inactivation.

65

.HHoo 3H0: on» wcoHa £3.3ch psmpmcoo .33 as @3395 assuage mars 6338.5

mm

.8300

.02 as:

2 m

0.. o2

0.. cap

o. 6.2.

o. 96
:8
2:28

I000

acumen

.2 as

 

a.“

.b

30 ‘3an1vaadwar

66

 

 

0200+ 0200+ 2.00.00 000.00 000.00 00.20
002+ 002+ 00.00 20.00 00.00 00.02.
00.2- 002+ 00.00 00.00 8.00 8.00
0.2- 00.0.. 02.00 00.00 00.00 00.00
20.8000 2.8202205 20.20000 282002000 0:2 0.020 00
62.202000 0 722.002.6022 0. .0202.

 

2202 #03020 9:00.209 20220

0020020 882 008008 2820.22.20 000 20.20000 002 .20

0000002 00.200 002 an 00258.00 82 002 20002 280.200 .0 0200.2.

67

5:00.200 H.003 05 Ho 09322092022 0n» 2200022202 000058.200 222 0.2085: 0202. 2

 

 

 

AwdtdeN. 2333.0 AvaHodH 30380.8 o.Hw
8.0020060 3.88.0 $033.3 8033.8 0.00
20.000000 20.00002 200002.02 202000.00 0.00
23.00:..8 3.820202 Ammvewd 3030060. 0.00
0000.20.22 00092022 2222092022 2:00.209 0..
H28 ozHQHom mag. a 295.2. .252.
.228 0020200 03 00020
0.222020202222200 02:30:00 0 0.220: 60508 0002033220 023 3 60003030 .20w220nox0
B002 Hang—92.20920 05 .20 22020000 22000 22 05.2.2380 820.038.0222 000209222ng0me2~2 .m 02020.2.

68

the analytical method for determining the polygalacturonase inactivation
in the pasteurization 1mit may give a satisfactory approximation. The
analytical may be more advantageous if adequate heat transfer data is
available, since it is faster than the general method. It should also be
noted, that the variation becomes smaller as the degree of inactivation
increases. A temperature of 81°C along the holding eon resulted in a
4.7D process, which may be considered adequate to prevent softening of the
cherries. Such an inactivation is difficult to determine by plating if
the diameter of the collar is higher than 1 on, because the diameter of
the clear zone that the enzyme creates, is less than 1.2 cm. Therefore,
collars with a very snall diameter unst be used.

In general inactivation in the holding coil is not difficult to
predict, because of the isothermal nature of the pm. Application of
equation (41) under iSothermal conditions gives the degree of inactivation.
The case is unre conplicated where tamerature varies with time. At
tenperatures of 76.66 and 81°C the degree of inactivation was as follows:

Holding coil: 76.4 and 79.16%

Heating and cooling section: 19.89 and 20.16%
In the experimental heat exchanger treating cherry brine at a rate of
1 Kg/min, an approxinate degree of inactivation at a teuperature range
between 76.66 - 81°C, may be determined by,

(a) Calculating the degree of inactivation in the holding

section.

(b) Adding 20% to the above value.

'lhe total inactivation, calculated in (b) will be :t 0.16% fran the

actual inactivation .

69

In order to treat an enzyme, other than polygalacturonase, the rate
constants must be known. Suparath (1976) found that pectinase fran

Penicillimn janthinellum, which causes softening in brined pickles, is the

 

most heat resistant enzyme in cucumber brine. From Suparath's data the

k and Z values of pectinase from P. janthinellun were calculated. 'Ihey

 

were compared with those of polygalacturonase, which were determined by
Athanasopoulos (1976). The Z value of the pickle pectinase was found to
be 4.592°C. Polygalacturonase has a Z value equal to 8.4°C. Figure 15
illustrates the thermal resistance curves of the two enzymes. Because

pectinase from P. Qanthinellun has smaller Z value than polygalacturonase,

 

it is more sensitive to temperature changes, as illustrated in Table 9.

At low temperatures the pickle enzyme is Here heat stable than poly-
galacturonase. At temperatures higher than 80°C, polygalacturonase

is considered more heat resistant. The Arrhenius plots of the two enzymes
are presented in Figure 16. In Figure 16 the sharper increase or decrease
of the k values of the pickle pectinase can be seen.

Suparath's data were inadequate because the D values for the pickle
pect inase were detennined for two tameratures only. In the comparison
between polygalacturonase and the pickle enzyme, it was assmed that the
two D values determined by Suparath are points on the straight line shown
in Figure 15. If the assunption is correct, then the experimental heat
exchanger used for polygalacturonase inactivation may be used for pickle
brine pasteurization since at temperatures above 80°C polygalacturonase
has higher D and lower k values (Table 9). 'Ihe carposition of the pickle
brine should also be considered. Usually the soluble solids of the pickle
brine is aromd 12% which is very close to the cherry brine as indicated

in Table A—1.

100

388

D , VALUES , sec

10

O P. Janthinellun

I A. nige' rl

 

 

/ Z 8.45 °C
/ Z 4.592 °C
68 7O 72 74
TEMPERATURE, °c

Figure 15. 'Ihemal resistance curves for pectinase fmn
"llus' n (PG) at pH 3.0 and for pectinase
fmn Penicilliun Janthinellun at pH 3.3

 

1From Athanasopoulos (1976)

 

0.10 ,

 

 

0.05

0 P. lanthinellun

. A. niggr1
0.02

   

2. .80 2.35 2.90 2.95 x 10’3

1 o
T 0
Figure 16. Arrhenius plot for polygalacturonase at pH

3.0 and pectinase fran P. lanthinellum at
3.7.

K

 

 

‘me Athanasopoulos (1976)

883 fig same
883 000832 Ea

 

 

 

 

 

finds Sn 08.3. 25 8
0033. 86. Show 8.0 we
«8.8. mod . Sad 8.8 me
@323 «0.3 mama. 8.00 as
ohms 8.8 000; 8.02 me
name when $0.0 8.8m 2.
Venn Ba x a 8a .033, d Teen 62 x a. new .935 .o 00
8283020038 .Sfiefifiaan .c 02E.
.asd u we ea

 

5303550.... .m EH 000230?” was ~06 n mm as 0m§98dww§oa How 38398 0....dm .m 0H3

E. Qxarational Cost of the Pasteurization Process

To evaluate the economics of the pasteurization of cherry brine,
several factors must be considered including:
Labor
Fuel
Punping
and cold water needs.
Because the heat exchanger was designed to be in line with the reclamation
system, labor cost for the heat treatment itself is difficult to evaluate.
Thus, in the following calculations labor will be excluded.
The operational cost will be based on the following assumptions:

Amount of brine for pasteurization: 1000 gallons

Degree of inactivation desired: 99.985%

Flow rate of brine: 1 Kg/min

Hot water flow rate: 2.7 Kg/min

Cold water flow rate: 5.6 Kg/min

Temperature drop in the heater: 40°F or 22.2°C

Cost of fuel: $2.26 per 1,000,000 B’I‘U1
Cost of the water: $2.50 per 1000 fts‘2

The system includes three pumps with 20 ft or 6 m total length of tubing.
Under these conditions, heating of the water requires
14016 BTU/hr
which will cost

14016 BTU X 63 hr X $2.26/1,000,000 BTU = $1.99

 

‘From Rippen (1977)
2From Rippen (1977)

74

During the process. 734.12 ft of cold water is needed in the cooler.
This will cost,
734.12 ft3 x $2.5/1ooo ft3
= $1.83
The pumping requirements were calculated to be
$0.10
Therefore, the cost for pasteurizing 1,000 gallons is
1.99 + 1.83 + 0.10 = $3.92

The~above operational cost could be lowered by having a regenerative
unit connected after the holding coil where the pasteurized brine would
preheat untreated brine. The preheated brine after the regenerative
unit would be pumped directly into the heating section. Thus, regeneration
‘would save both fuel and cold water since the untreated brine would.exit
the regenerative unit at a temperature higher than that of the roomy while
the pasteurized brine would exit the regenerative unit at a temperature
lower than that of the holding coil. For example, if the designed percent
of regeneration would be 50%, the amount of heat added to the brine in
the heater and that removed from the brine in the cooler would be
reduced by 50%. This will further reduce the amnunt of fuel and cold
water required by 50%. Thus, the operational cost may be reduced
approximately 50%.

A serious corrosion problem could occur with regeneration because
a large surface area is in contact wdth the brine. Cherry brine is
considered to be a highly corrosive material. The metals that should be
used in the manufacture of a pasteurization unit must be of high quality
in order to resist corrosion of the metal surfaces in contact wdth brine.
Such a requirement will affect the initial and installation cost of the

pasteurization unit .

75

Cucumber brine is probably as corrosive as cherry brine. Using the
following information the cost of pasteurizing 1000 gallons is estimated

as follows:

Labor cost @ $4.00/hr 2.641
Propane 1.29
Pumping 0.79
Chemicals 24.4.1.
Total operational cost: $7.05

Pasteurizer 5 yr depreciation $8915/yr: $10.51

The above indicates that the initial cost of the pasteurization unit
is higher than the operational cost ($10.51 vs $7.05). Therefore, a less
expensive heat exchanger may contribute in cost reduction of the pasteuri-

zat ion process.

 

lFrom McFeeters et al. (1977)

(IDNCLUS IONS

The degree of inactivation of polygalacturonase present in spent cherry
brine can be measured by the agar "cup plate" technique after pasteuri-
zation of the spent cherry brine in a helically coiled heat exchanger.
Application of the general and analytical methods for predicting the
degree of polygalacturonase inactivation can give satisfactory results.
If adequate heat transfer information is available, the analytical
method is more advantageous since the computations are more rapid

than the general method.

Predicted inactivation and that measured by the agar "cup plate"
procedure were found to vary from —l.9 to +2.34%. The variation
becomes smaller as the degree of inactivation increases.

When the constant temperature along the holding coil is 81°C and the
brine is held 9 sec at this temperature, polygalacturonase is
inactivated by 99.985%.

Shell-side convective heat transfer coefficients in a helical heat
exchanger can be calculated by considering coexistence of natural

and forced convection.

The MD of a helical heat exchanger and further the over-all heat
transfer coefficient can be estimated in a manner similar to that

of a multiple—pass counterflow heat exchanger.

The thermal effectiveness of the heater was 77% and that of the cooler

68%. The pasteurization process under these conditions resulted

76

77

in 99.985% polygalacturonase inactivation.
9. A regeneration unit that would give 50%:regeneration in the heating
and cooling sections, may contribute to approximately 50% reduction

of the operational cost of the pasteurization unit.

BIBLICXERAPHY

BIBLICXRAPHY

Athanasopoulos, P. E. and Heldman, D. R. 1976. Pilot Plant for Cherry
Brine Reclamation. Paper presented in the First International
Congress on Engineering and Food. Boston, Mass.

Athanasopoulos, P. E. 1976. Kinetics of Thermal Inactivation of
Polygalacturonase in Spent Cherry Brine. Ph.D. Thesis, Michigan
State University, East Lansing, Mich.

Ball, C. O. 1928. Mathematical Solution of Problems on Thermal Processing
of Canned Food. Univ. Calif. (Berkeley). Public Health 1 (2): 15.

Ball, C. 0., Olson, F. C. W. 1957. Sterilization in Food Technology.
McGraw Hill Co., N. Y.

Beavers, D. L., Payne, C. H., Soderquist, M. R., Hildrun, K. L. and
Cain, R. F. 1970. Reclaiming used Cherry Brine. A.E.S. Oregon
State University. T. B. III.

Berg, R. R. and Bonilla, C. F. 1950. Heating of Fluids in Coils.
Trans. N. Y. Acad. Sci., 13, 12.

Brekke, J. E., Watters, G. 6., Jackson, H., and Powers, M. J. 1960.

Texture of Brined Cherries. U. S. Department of Agr. Res. Serv.
74-34.

Bigelow, B. W., Bohart, G. S., Richardson, A. L., and Ball, C. 0. 1920.
Heat Penetration in Processing Canned Foods. NCA, Bull. 16—L.

Dean, w. R. 1927. Note on Motion of Fluid in a Curved pipe. Phill.
Mag., 4,208.

Deindoerfer, F. H. 1957. Calculation of Heat Sterilization Times for
Fermentation Media. Appl. Microbiol. , 5, 221-228.

Deindoerfer, F. H. and Hmphrey, A. E. 1959. Analytical Method for
Calculating Heat Sterilization Times. Appl. Microbiol., 7, 256-264.

Deincberfer, F. H. and Hurphrey, A. E. 1959. Principles in the Design
of Continuous Sterilizers. Appl. Microbiol . , 7, 264—270.

Dingle, J. and Raid, W. W., and Solomons, G. L. 1953. The Enzymatic
Degradation of Pectin and other Polysuccharites II. Application
of the "Cup-Plate" Assay to the Estimation of Enzymes. J. Sci.
Agri. a, March, 149.

79

80

Edney, H. G. S., Edwards, M. F., and Marshall, V. C. 1973. Heat Transfer
to a Cooling Coil in an Agitated Vessel. Trans. Instn. men.

Engrs. , 51, 4-9.

Gillespy, T. C. 1962. The Principles of Heat Sterilization. ”Recent
Advances in Food Science". Butter work. Iondon.

Hankin, L., and Anagnostakis, S. L. 1975. The Use of Solid Media for
Detection of Enzyme Production by Fangi. Mycologia, Vol. LXVII,
N0. 3, 597.

Hicks, E. W. 1951. (h the ENaluation of Canning Processes. Food
Technology. 5, 134.

Iblman, J. P. 1976. Heat transfer. 4th Ed. McGraw Hill 00., New York,
N. Y.

Ito, H. 1959. Memoirs of the Institute of High Speed Mechanics.
Tonoku Univ. (Japan)., 14, 137.

Ito, H. 1959. Friction Factors for Turbulent Flow in Curved Pipes.
Trans. ASME, J. Basic Engrs., D81, 123.

Kays, W. M. and London, A. L. 1955. Compact Heat Exchangers. The
National Press, Palo Alto, CA.

Kern, D. Q. 1950. Process Heat Transfer. McGraw Hill 00., New York, N. Y.

Kertesz, Z. I. 1951. The Pectic Substances. International Publiéaers,
New York, N. Y.

Kreith, F. 1961. Principles of Heat Transfer. International Textbook
Co. , Scranton, PA.

Kubair, V. and Kuloor, N. R. 1966. Heat Transfer to Newtonian Fluids
in Coiled Pipes in laminar Flow. Int. J. Heat Mass Transfer. g. 63.

McAdams, W. H. 1942. Heat Transmission. 2nd Ed. McGraw Hill 00., New
York, N. Y.

McAdams, W. H. 1954. Heat Transmission. 3rd Ed. McGraw Hill 00., New
York, N. Y.

McCready, R. M. and Mchb, 0. A. 1954. Texture Changes in Brined Cherries.
Western-Packer, 46, 17.

McFeeters, R. F., Palnitkar, M. R., Velting, M., Fehringer, N., and Coon,
W. 1977. Reuse of Brines in Camercial Cuculber Fermentation.
Unpublished. Michigan State University, East Lansing, MI.

Messa, C. J., Foust, A. L. and Phoehlein, G. W. 1970. Slell-Side Heat
Transfer Coefficients in Helical Coil Heat Exchanger. I.E.C.
(Proc. Des. Dev.), 8, 344-347.

81

Mari, Y. and Nakayama, W. 1965. Study on Forced Convection Heat Transfer
in Curved Pipes. (lst report, laminar region). Int. J. Heat Mass
Transfer. 8, 67.

Mori, Y. and Nakayama, W. 1967. Study on Forced Convection in Curved
Pipes. (2nd report, turbulent region). Int. J. Heat Mass Transfer.
10, 37-59.

Panasiuk, 0., Sapers, G. M. and Ros, L. R. 1975. Recycling Bisulfite
Brines in Sweet Cherry Processing. Unpublished. E.R.S.C.
Philadelphia, PA.

Richards, J. W. 1965. Br. Chem. Eng. 10, 116.

Rippen, A. L. 1977. Survey of Energy Utilization in Dairy Plants in
Michigan. Unpublished. Michigan State University, East Iansing,
MI.

Rippen, A. L. 1977. Methods, Concerns and Plants for Handling Dairy
Plant Wastes in Michigan, Unpublished, Michigan State University,
East Iansing, MI.

Rogers, G. F. C. and Mayhew, Y. R. 1964. Heat Transfer and Pressure Drop
in Helically Coiled Tubes with Turbulent Flow. Int. J. Heat Mass
Transfer. 7, 1207-1216.

Runkhlyadeva, M. R., and Korchagina, G. I. 1975. Interferometric
Determination of the Activity of Pectinoloytic Enzymes of Fungal
Origin. Applied Bioch. and Microbiol. June, p. 782. (Translated
from Russian: original Nov-Dec., 1973).

Seban, R. A. and McLaughlin, E. A. 1963. Heat Transfer in Tube Coils
with laminar and Turbulent Flow. Int. J. Heat Mass Transfer. 6, 378.

Soderquist, M. R. 1971. Activated Carbon Renovation of Spent Cherry Brine.
J. WPCF. 43:1600.

Stumbo, C. R. 1948. Bacteriological Considerations Relating to Process
Evaluation. Food Technol. 2, 115.

Stumbo, C. R. 1949. Further Considerations Relating to Evaluation of
Thermal Processes for Foods. Food Technol. 3, 126.

Sturbo, C. R. 1953. New Procedures for Evaluating Thermal Processes
for Foods in Cylindrical Containers. Food Technol. 7, 309. ‘

Srinivasan, P. S., Nandapurkan, S. S., and Holland, F. A. 1968. Pressure
Drop and Heat Transfer in Coils. Trans. Chem. Engrs., 46, CE113.

Suparath, C. 1976. Thermal Inactivation of Pectinase in Cucurber Brine.
M.S. Thesis, Michigan State University, East Iansing, MI.

82

Watters, G. G., Brekke, J. E., Powers, M. J., and Yang, H. Y. 1961.
Brined Cherries Analytical and Qiality Control Methods. ARS Bull.
74—23.

White, C. M. 1929. Steamline Flow through Curved Pipes. Proc. R. Soc.
A128, 243.

White, C. M. 1932. Fluid Friction and its Relation to Heat Transfer.
Trans. Inst. (hem. Engrs., London. 10, 66—80.

Wiegand, E. H. 1955. Brine Cherry Breakdown. In. Proc. Oregon Hort. Soc.

APPENDICES

Table A—1. Brine composition for certain cherry varieties in Michigan.1

 

 

Cherry variety pH SCz Ca Soluble
(%) (%) Solids (76)
Schmid 3.1 0.345 0.312 10.5
Windsor 3.4 0.355 0.374 11.1
Bing 3.5 0.414 0.414 10.1
Napoleon 3.1 0.330 0.286 10.5

 

lFran Panasiuk et al. (1975).

Length

Area

Volume

velocity

Density

Force

Mass

Pressure

Energy, heat

Heat flow

Heat flux per unit area
Energy per unit mass
Specific heat
Thermal conductivity

Convective heat transfer
coefficient

Dynamdc viscosity (v)
Kinematic Viscosity (v)
Volumetric flow

Power

Thermal diffusivity

Thnmeuature

85

APPENDIX B

Units Conversions

1 Kg/mesec
1.mF/sec

l.mfi/sec

l.mF/sec

 

1°K = °C + 273.15
°R = °F + 459.67

ENGLISH

3.2808 ft

10.

35

[000

00000000

0.

.2248 lb

7639 ft2

.3134 ft3
.2808 ft/sec

.06243 lbw/ft3

f

.2046 10m

.45 x 10'“psi
.9478 Btu

.4121 Btu/hr

.317 Btu/hr—ft2
.4299 Btu/lbm
.2388 Btu/lbmr°F
.5778.Btu/hrbft-°F

.1761 Btu/hrbft2—°F

672 Ibm/ft-sec

10.764 ftZ/sec

35.3134 ft3/sec

1.

34 hp

10.764 ftz/sec

5 /9( °r+32>

5/9(°R)

86

APPENDIX C

Recorded temperatures at various posit ions within the pasteurization

1mit for four different trials (°C).

 

 

TRIAL

PCBITION OF THE 1 2 3 4
THERMXIJUPIE

Temperature along the holding coil

70 72 76.7 81
Brine inlet (Heater) 23.3 22.2 22.2 22.2
Brine outlet (Heater) 70.3 72.2 77.2 81.7
Brine inlet (Cooler) 69.7 71.7 76.1 80.5
Brine outlet (Cooler) 33.3 32.2 34.0 34.4
Hot water inlet 87.8 86.1 93.9 98.9
Hot water outlet 72.2 74.4 77.5 76.6
Hot water stream 81.5 79.4 84.4 87.5
Cold water inlet 11.7 13.0 13.0 11.1
Cold water outlet 25.6 19.5 22.0 19.2
Cold water stream 18.0 16.5 18.0 15.0
Upper wall (Heater) 73.3 74.4 78.8 84.4
Middle wall (Heater) 66.6 68.3 72.8 77.0
Lower wall (Heater) 37.2 38.9 40.0 40.5
Upper W311 (Cooler) 53.3 54.4 57.2 58.6
Middle wall (Cooler) 32.2 34.0 36.5 37.2
Lower wall (Cooler) 24.1 23.3 25.0 25.8
Upper wall surface (Heater) 72.2 75.0 80.5 85.8
lower wall surface (Heater) 37.0 37.7 40.5 42.5
Upper wall surface (Cooler) 48.8 42.0 45.0 47.0
Icwer wall surface (Cooler) 25.5 19.5 22.0 20.0