Energy consumption in batch thermal processing: model

Journal of Food Engineering 73 (2006) 217–224
www.elsevier.com/locate/jfoodeng
Energy consumption in batch thermal processing:
model development and validation
R. Simpson
a
a,*
, C. Corte´s a, A. Teixeira
b
Departamento de Procesos Quı´micos, Biotecnolo´gicos, y Ambientales, Universidad Te´cnica Federico Santa Marı´a, Casilla 110-V, Valparaı´so, Chile
b
Department of Agricultural and Biological Engineering, Frazier Rogers Hall, P.O. Box 110570, University of Florida, Gainesville,
FL 32611-0570, USA
Received 29 July 2004; accepted 22 January 2005
Available online 14 April 2005
Abstract
Thermal processing is an important method of food preservation in the manufacture of canned foods, retortable pouches, trays
and bowls (retortable shelf-stable foods).
The aim of this research was to develop a mathematical model to estimate total and transient energy consumption during the heat
processing of retortable shelf-stable foods.
The transient energy balance for a system defined as the steam and its water condensate in the retort requires no work term. The
heat transfer terms include radiation and convection to the cook room environment, and heat transfer to the food in the cans. Mass
and energy balance equations for the system were solved simultaneously, and the equation describing heat transfer in the food material was solved numerically using an explicit finite difference technique. Correlations valid in the range of interest (100 C through
140 C) were utilized to estimate the thermodynamic properties of steam, condensate, and food product.
Depending upon selected conditions, retort insulation will account for a 15–25% energy reduction. In addition, initial temperature could reduce the peak energy demand in the order of 25–35%.
These models should be useful in searching for optimum scheduling of retort battery operation in the canning plant, as well as in
the optimising process conditions, to minimize energy consumption.
2005 Elsevier Ltd. All rights reserved.
Keywords: Energy consumption; Batch processing; Retort insulation
1. Introduction
Thermal processing is an important method of food
preservation in the manufacture of shelf-stable canned
foods, and has been the cornerstone of the food processing industry for more than a century. Although the literature in food science and thermal processing is very
extensive, most of the references deal with the microbiological and biochemical aspects of the process.
*
Corresponding author. Tel.: +56 32 654302; fax: 56 32 654478.
E-mail address: ricardo.simpson@usm.cl (R. Simpson).
0260-8774/$ - see front matter 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2005.01.040
The basic function of a thermal process is to inactivate pathogenic and food spoilage causing microorganisms in sealed containers of food using heat treatments
at temperatures well above ambient boiling point of
water in pressurized steam retorts (autoclaves).
Excessive heat treatment should be avoided because it
is detrimental to food quality and underutilizes plant
capacity. Batch processing with a battery of individual
retorts is a common mode of operation in many
food-canning plants (canneries). Although high speed
processing with continuous rotary or hydrostatic retort
systems can be found in very large canning factories
(where they are cost-justified by high volume throughput),
218
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
Nomenclature
A
Cp
E
gc
H
h
m_
M
P
Pm
Q_
R
t
t*
T
T0
T
v
V
area (m2)
specific heat (J/kg K)
energy (J)
universal conversion factor; 1 (kg m/N s2)
enthalpy (J/kg)
heat convection coefficient (W/m2 K)
mass flow rate (kg/s)
mass (kg)
pressure (Pa)
molecular weight (kg/kmol)
thermal energy flow (W)
ideal gas constant 8.315 Pa m3/kmol K (J/
kmol K)
time (s)
time required to eliminate air from retort
temperature (K)
initial temperature
average product temperature (K)
velocity (m/s)
volume (m3)
Greek symbols
q
density (kg/m3)
e
surface emissivity of retort shell at an average
of emitting and receiving temperatures
(dimensionless)
such systems are not economically feasible in the majority of small to medium-sized canneries (Norback &
Rattunde, 1991).
Among problems confronted by canned food plants
with batch retort operations, are peak energy/labour demand, underutilization of plant capacity and underutilization of individual retorts (Simpson, Almonacid, &
Teixeira, 2003). In batch retort operations, maximum
energy demand occurs only during the first few minutes
of the process cycle to accommodate the venting step,
while very little is needed thereafter in maintaining process temperature. In order to minimize peak energy demand it is customary to operate the retorts in a
staggered schedule, so that no more than one retort is
venting at any one time. Similar rationale applies to labour demand, so that no more than one retort is being
loaded or unloaded at any one time.
A limited number of research studies have addressed
and analysed energy consumption in retort processing
(Barreiro, Perez, & Guariguata, 1984; Bhowmik, Vischenevetsky, & Hayakawa, 1985 and Singh, 1977) Most of
these have attempted to quantify total energy consumption but not transient energy consumption. Furthermore, these studies were applied to processes used for
traditional cylindrical cans, and their findings are not
c
r
ratio of specific heat at constant pressure to
specific heat at constant volume (dimensionless)
Stefan–Boltzmann constant, 5.676 · 108
W/m2 K4
Subscripts
a
air
b
bleeder
amb
ambient
c
convection
cv
condensed vapour
cr
critical value
cw
cooling water
e
metal container
in
insulation
p
food product
r
radiation
rt
retort
s
steam
sl
saturated liquid
sv
saturated vapour
rs
retort surface
t
time
v
vapor
w
condensed water
necessarily applicable to processes used for flexible or
semirigid trays, bowls or retort pouches. AlmonacidMerino, Simpson, and Torres (1993) developed a transient energy balance equation for a still-cook retort,
but the model only simulated the holding time and did
not include come up time. Transient energy consumption should be an important factor in deciding retort
scheduling, as well as determining optimum variable
temperature profiles to achieve specified objectives (e.g.
Minimize energy consumption, maximize nutrient retention, or minimize process time) (Almonacid-Merino
et al., 1993).
Many studies have shown that maximum nutrient
retention at constant retort temperature does not differ
considerably from the one obtained from time variable
retort temperature processes (VTRT) when optimising
average quality (Almonacid-Merino et al., 1993; Saguy
& Karel, 1979; Silva, Hendrckx, Oliveira, & Tobback,
1992). However, Almonacid-Merino et al. (1993) have
shown that process time can be significantly reduced,
while maintaining a high quality product with a TVRT
process. Another objective function that has been successfully investigated is the search for maximum surface
retention of a given quality factor (Banga, Martin,
Gallardo, & Casares, 1991). To give a practical use to
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
the TVRT profiles, Almonacid-Merino et al. (1993) included a constraint to determine which of the searched
temperature profiles were feasible and possible to reproduce in a real retort.
In order to optimise food canning plant operating
decisions and to implement optimum TVRT profiles, a
comprehensive mathematical model was developed to
predict transient and total energy consumption for
batch thermal processing of canned foods including
retortable pouches, trays and bowls.
2. Materials and methods
2.1. Model development
The transient energy balance for a system defined as
the retort including cans without their contents, and
the steam and condensate in the retort requires no work
term (Fig. 1). The heat transfer terms—between the system and its environment—include radiation and convection to the plant cook room environment, and heat
transfer to the food within the cans. Equations were
solved simultaneously and the heat transfer equation
for the food material was solved numerically using an
explicit finite difference technique. Correlations valid in
the range of interest (100 C through 140 C) were utilized to estimate the thermodynamic properties of
steam, condensate, and food material.
The process was divided into three steps: (a) venting
period, (b) period after venting to reach process temper-
Fig. 1. Still vertical retort (cross-sectional view of vertical retort used
for study).
219
ature, and (c) holding time. Cooling step was not analysed because no steam is required. First, the mathematical model for the food material is presented and
then a full development of the energy model for the
complete thermal process.
2.1.1. Mathematical model for food material
Food material was assumed to be homogeneous and
isotropic, therefore the heat conduction equation for the
case of a finite cylinder solid could be expressed as
1 oT o2 T o2 T 1 oT
þ
þ 2 ¼
r or or2
oz
a ot
ð1Þ
where T is a function of the position (r, z) and time (t).
The respective boundary and initial conditions are as
follows:
T ðfood material; 0Þ ¼ T 0
where T0 is a known and uniform value through the
food material at time 0.
To estimate the temperature at food surface at any
time t, a finite energy balance was developed at the surface (Fig. 2).
kA
oT
oT
þ hAoT ¼ MCp
or
ot
ð2Þ
In most practical cases, it can be assumed that Biot
number is well over 40, meaning that the temperature
of the surface of the food material could be equalized,
at any time, with retort temperature (Almonacid-Merino et al., 1993; Datta, Teixeira, & Manson, 1986; Simpson, Aris, & Torres, 1989; Simpson, Almonacid, &
Torres, 1993; Teixeira, Dixon, Zahradnik, & Zinsmeiter,
1969). The aforementioned statement is not necessarily
applicable for retortable pouch or semi rigid trays and
bowls processing (Simpson et al., 2003). The model
(Eq. (2)) considers the possibility of a Biot number less
than 40, but is also suitable for a Biot number equal
to or larger than 40.
Fig. 2. Finite energy balance at the food surface (infinite slab).
220
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
2.1.2. Mass and energy balance during venting
Before expressing the energy balance, it is necessary
to define the system to be analysed: Steam-air inside
the retort—at any time t (0 6 t 6 t*), during venting—
was considered as the system (Fig. 1).
Global mass balance
ð12Þ
dM
m_ s m_ sv m_ a ¼
dt
ð3Þ
Mass balance by component
Air: m_ a ¼
dM a
dt
ð4Þ
Vapour: m_ s m_ sv m_ w ¼
Condensed water: m_ w ¼
m_ w ¼
dM sv
dt
The mass flow of condensate was estimated from the
energy balance as
m_ w ðH sv H sl Þ ¼ dQ_
¼ hAðT in T amb Þ þ reAðT 4in T 4amb Þ
dT p
dT rt
þ M rt C prt
dt
dt
dT e
dT in
þ M in C pin
þ M e C pe
dt
dt
þ M p C pp
ð5Þ
dM w
dt
ð6Þ
dT p
dT rt
dT e
dT in
þ M rt C prt
þ M e C pe
þ M in C pin
dt
dt
dt
dt
ðH sv H sl Þ
hAðT in T amb Þ þ reAðT 4in T 4amb Þ þ M p C pp
M ¼ M a þ M sv þ M w ;
m_ ¼ m_ sv þ m_ a
ð7Þ
General energy balance
½H s m_ s IN ½H sv m_ sv þ H a m_ a OUT þ dQ_ dW_
dEsystem
dt
ð8Þ
where
dQ_ ¼ dQ_ c þ dQ_ r þ dQ_ p þ dQ_ e þ dQ_ rt þ dQ_ in
ð9Þ
dW_ ¼ 0
ð10Þ
Replacing the respective terms into Eq. (9), the term
dQ in Eq. (8) can be quantified as
d Q ¼ hAðT in T amb Þ þ reAðT 4in T 4amb Þ
dT p
dT rt
dT e
þ M rt C prt
þ M e C pe
dt
dt
dt
þ M in C pin
dT in
dt
ð11Þ
The following expression shows how the cumulative
term of Eq. (8) was calculated. Because of the system
definition, changes in potential energy as well as kinetic
energy were considered negligible:
ð14Þ
Therefore the steam mass flow demand during venting
should be obtained replacing Eqs. (5), (6), (7), (11),
(12), and (14) into Eq. (8).
2.1.3. Mass and energy consumption between venting and
holding time (to reach process temperature)
As was mentioned before, first, it is necessary to define the system to be analysed: Steam and condensed
water inside the retort were considered as the system
(Fig. 1).
Global mass balance: m_ s m_ b ¼
and
þ M p C pp
ð13Þ
Therefore,
where
¼
dEsystem
dH sv
dM sv
dV sv
dP sv
¼ M sv
þ H sv
P sv
V sv
dt
dt
dt
dt
dt
dH a
dM a
dV a
dP a
þ Ha
Pa
Va
þ Ma
dt
dt
dt
dt
dH w
dM w
dV w
dP w
þ Hw
Pw
Vw
þ Mw
dt
dt
dt
dt
Vapour: m_ s m_ b m_ w ¼
Condensed water: m_ w ¼
dM
dt
dM sv
dt
dM w
dt
Energy balance on the bleeder
System: Steam flow through the bleeder.
Considering an adiabatic steam flow:
v2
½H sv m_ b IN H b þ
¼0
m_ b
2gc
OUT
ð15Þ
ð16Þ
ð17Þ
ð18Þ
where the bleeder is assumed to be operating in steady
state condition, with no heat, no work, and negligible
potential energy effects, the energy balance around the
bleeder reduces to (Balzhizer, Samuels, & Eliassen,
1972)
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
ðH b H sv Þ þ
v2b v2sv
¼0
2gc
ð19Þ
For a gas that obeys the ideal gas law (and has a Cp
independent of T),
ðH sv H b Þ ¼ C p ðT sv T b Þ
ð20Þ
Neglecting v2sv in relation to v2b , and replacing Eq. (20)
into Eq. (19), it reduces to
Tb
2
vb ¼ 2gc C p T sv
1
ð21Þ
T sv
Considering an isentropic steam flow in the bleeder
which obeys the ideal gas law, Eq. (21) could be re-written as
!
ðc1
c Þ
2gc P sv
c
Pb
2
vb ¼ 1
ð22Þ
c1
qsv
P vs
where the continuity equation is
m_ b ¼ qvb A
ð23Þ
221
If Ps is bigger than Pc, substituting Eq. (25) into Eq.
(24), the expression for the mass flow is as follows:
cþ1
c
2ðc1Þ
c1
P s Ab
2
P amb
2
m_ b ¼ qffiffiffiffiffiffi
for
<
ð27Þ
RT s c þ 1
cþ1
Ps
c
2.1.4. Mass and energy balance during holding time
System: Steam inside the retort (Fig. 1).
Global Mass balance: m_ s m_ b ¼
Vapour: m_ s m_ b m_ w ¼
Condensed water: m_ w ¼
dM
dt
dM sv
dt
dM w
dt
ð28Þ
ð29Þ
ð30Þ
Energy balance on the bleeder
The steam flow through the bleeder was estimated as
previously mentioned, therefore:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!ffi
c
c1
u
ðc1
c Þ
P s Ab P amb u
2
P
2
P amb
amb
t
if
6
<1
m_ b ¼ rffiffiffiffiffiffiffiffi
1
c1
cþ1
Ps
Ps
RT s P s
c
cþ1
c
2ðc1Þ
c1
P s Ab
2
P amb
2
if
<
m_ b ¼ rffiffiffiffiffiffiffiffi
cþ1
Ps
RT s c þ 1
c
dT p
dT rt
dT e
dT in
þ M rt C prt
þ M e C pe
þ M in C pin
hAðT in T amb Þ þ reAðT 4in T 4amb Þ þ M p C pp
dt
dt
dt
dt
m_ w ¼
ðH sv H sl Þ
Therefore, combining Eqs. (22) and (23):
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!ffi
u
ðc1
u
c Þ
P s Ab P amb t
2
P amb
m_ b ¼ qffiffiffiffiffiffi
1
RT s
c1
Ps
Ps
Therefore the steam mass flow was estimated as
m_ s ¼ m_ w þ m_ b
ð24Þ
3. Results and discussion
c
The maximum velocity of an ideal gas in the throat of a
simple converging nozzle is identical to the speed of
sound at the throat conditions. The critical pressure is
Pc (Balzhizer et al., 1972)
P c ¼ P amb
2
cþ1
c
c1
ð25Þ
Then Eq. (23) will be valid for Ps in the following range:
2
cþ1
c
c1
6
P amb
<1
Ps
ð31Þ
ð26Þ
3.1. Preliminary validation
The developed model was tested using bibliographic
data (Barreiro et al., 1984), as a preliminary means of
validation. The following data were utilized for the following calculations:
Retort: mrt: 163.6 kg, crt: 500 J/kg C, Ab:
7.94 · 106 m2, Art: 2.97 m2, Vrt: 0.356 m3.
Containers: Cans dimensions: 307 · 409, number of
cans inside the retort: 180, me: 0.06 kg, ce: 500 J/kg C.
Product: Pea puree with a thermal diffusivity of
1.70 · 107 m2/s.
222
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
Table 1
Comparison between data obtained from Barreiro et al. (1984) and
calculations from the developed procedure in this study
Temperature
(C)
Process time
(min)
Energy
(MJ)
(Barreiro et al., 1984)
Energy
(MJ)
(this research
study)
104.4
110.0
115.6
121.1
126.7
132.2
196
113
85
66
56
50
118.0
100.8
97.0
93.1
95.0
100.4
114.6
103.6
103.0
106.7
109.4
114.8
Processing conditions: The time–temperature requirements were calculated for the thermal sterilization of the
pea puree in 307 · 409 cans reaching an integrated lethal
value Fc of 2.52 min for Clostridium Botulinum at
121.1 C (Barreiro et al., 1984). Tpo: 37.8 C, Tcw:
26.7 C.
Surface heat transfer coefficient and emissivity: h:
5.77 w/m2 C, e: 0.94.
Table 1 shows a comparison between calculations (total energy consumption) obtained from Barreiro et al.
(1984) and the ones obtained with the model developed
in this study. Although estimations are in the same
range and compare well, values obtained with the model
developed in this research study are higher except at
TRT 104 C. One potential explanation lies in the fact
that the procedure developed by Barreiro et al. (1984)
clearly underestimates the steam mass flow during venting. One of the main contributions of this research study
was to develop a complete transient energy model, but
also to approach the critical behaviour of energy demand during venting.
3.2. Model applications
To analyse the effect and the impact of different process variables in total and transient energy consumption,
the following variables were studied (most data for the
simulation purposes were obtained from Barreiro
et al., 1984):
(a) Retort insulation: Fig. 3 compares the transient
and total steam consumption for insulated (3.8-cm thick
layer of asbestos cement) and non-insulated retort.
Using the insulated retort the total steam consumption
reduction was in the order of 19% when compared to
non-insulated retort (Fig. 3). Insulation did not play a
significant role in terms of reducing peak energy consumption (Fig. 3).
(b) CUT: Fig. 4 compares the transient steam consumption for different come up times (CUT) (5, 10
and 15 min). Fig. 4 shows that if CUT increases the
maximum peak of steam consumption is reduced. As
an example, if CUT increases from 5 to 15 min the
Fig. 3. Transient and total steam consumption rate profiles for
insulated and non-insulated retort.
Fig. 4. Process temperatures and transient steam consumption rate
profiles for different CUT times.
Fig. 5. Transient and total steam consumption rate profiles for
different initial food temperatures.
R. Simpson et al. / Journal of Food Engineering 73 (2006) 217–224
reduction in peak energy consumption is in the order of
12%.
(c) Initial food temperature (T0): Fig. 5 compares the
transient steam consumption for different initial food
temperatures (27.8 and 75 C). Fig. 6 shows that for
the high temperature the maximum peak and the total
steam consumption are reduced 30% and 29% respectively. Clearly the most important variable to reduce
peak energy consumption was the initial temperature
of the food material.
(d) Retort size: Fig. 6 compares the steam consumption per processed can for different retort size with the
same ratio product/retort volume (0.47).
Case 1: Retort dimensions: mrt: 163.6 kg, Art: 2.97 m2,
Vrt: 0.356 m3, Containers: cans dimensions: 307 · 409,
number of cans inside the retort: 180.
223
Case 2: Retort dimensions: mrt: 230.4 kg, Art: 3.50 m2,
Vrt: 0.6 m3 (Bhowmik et al., 1985), Containers: cans
dimensions: 307 · 409, number of cans inside the retort:
303.
Fig. 6 shows that for the larger retort size the ratio of
steam consumption [kg]/mass product [kg] is reduced
(13%) but the maximum steam consumption is increased
(85%). Possibly the main reason behind this result is that
the area over volume ratio decreases as the retort
increases.
Previous analyses can be extended to figure out the
impact of process temperature in relation to total energy
demand for a given process. As an example, Fig. 7
shows the effect of insulation and processing temperatures (104.4, 110.0, 115.6, 121.1, 126.7, and 132.2 C)
on energy consumption during retorting of pea puree
in 307 · 409 cans (Barreiro et al., 1984).
4. Conclusions
Fig. 6. Transient steam consumption rate profiles and ratio product
mass/steam consumption mass for different retorts sizes.
A complete mathematical model to predict transient
and total energy consumption was developed and tested
against published data for a preliminary validation.
The transient energy consumption in batch operations shows that maximum energy demand occurs only
during the first few minutes of the process cycle to
accommodate the venting step, while very little is needed
thereafter in maintaining process temperature.
Depending upon selected conditions, retort insulation
will account for a 15–25% energy reduction. In addition,
initial temperature could reduce peak energy demand in
the order of 25–35%.
The model can be used to identify those improvements
in facility and product handling with the highest impact
on total and transient energy consumption, but also to
identify feasible variable retort temperature profiles.
Acknowledgment
We kindly appreciate the contribution made by Mr.
He´ctor Patin˜o.
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