Objective assesment of safety, sensory, nutrition, shelf life and economics
Jul 08, 2015
A processed food must be “Safe”, have acceptable “Shelf life”, “Sensory qualities”, “Nutrition”, and be “Economic”. An approach to address these issues, for a “particulate” in “fluid”, thermally processed food product, is presented here.
A thermal process constitutes a “time – temperature (T – )” treatment under fluid flow. This is calculated by solving conventional differential element heat balance with appropriate initial and boundary conditions. For fluid flow - equations of motion, continuity and Navier Stokes – in appropriate co-ordinate system are solved to derive velocity profile and its gradient as shear rate. The viscosity is Non-Newtonian and modeled as Power-Law with exponential terms for temperature and moisture dependency. Coupling kinetics for parameters of interest in product and process development gives an objective measure of their value. Industry practice to use “markers” to reflect various effects was followed. Safety – was reflected by microbial metabolism of Cl. Botulism or pasteurization by fruits and vegetables industry practice. Shelf life by per-oxidase enzyme inactivation, Sensory perception of fruit firmness by pectin de-polymerization and Nutrition by Vitamin B1 retention.
This approach can be applied to compare commercially employed equipment, such as scraped surface heat exchanger and helical coils for continuous processing or a kettle for batch processing. Choice of equipment type determine both fixed and variable costs and hence product economics.
Results obtained in practicing this approach for quantitative determinations of “Safety”, “Shelf life”, "Sensory perception”; “Nutrition” and “Economics” are presented here.
The scope, challenges and limitations of this approach are further discussed.
A thermal process constitutes a “time – temperature (T – )” treatment under fluid flow. This is calculated by solving conventional differential element heat balance with appropriate initial and boundary conditions. For fluid flow - equations of motion, continuity and Navier Stokes – in appropriate co-ordinate system are solved to derive velocity profile and its gradient as shear rate. The viscosity is Non-Newtonian and modeled as Power-Law with exponential terms for temperature and moisture dependency. Coupling kinetics for parameters of interest in product and process development gives an objective measure of their value. Industry practice to use “markers” to reflect various effects was followed. Safety – was reflected by microbial metabolism of Cl. Botulism or pasteurization by fruits and vegetables industry practice. Shelf life by per-oxidase enzyme inactivation, Sensory perception of fruit firmness by pectin de-polymerization and Nutrition by Vitamin B1 retention.
This approach can be applied to compare commercially employed equipment, such as scraped surface heat exchanger and helical coils for continuous processing or a kettle for batch processing. Choice of equipment type determine both fixed and variable costs and hence product economics.
Results obtained in practicing this approach for quantitative determinations of “Safety”, “Shelf life”, "Sensory perception”; “Nutrition” and “Economics” are presented here.
The scope, challenges and limitations of this approach are further discussed.
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02/18/12 Ashok Dhruv, [email protected] 2
02/18/12 Ashok Dhruv, [email protected] 3
Physical / ChemicalProcess
Equipment
MathematicalConstitutive Eqn.
Ini. & Boundary cond.
Physical laws
Laws of Math
ProductBy-productsWaste streams
Raw materials Utilities Labor
Physical propertiesOperating conditionsAssumptions
Microbial log cycle reductionEnzyme deactivation. amountObjective sensory quality
Physical form
Mathematical form
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Generic ApproachGeneric Approach
• Derive time - temperature profile
• Derive Viscosity, Velocity, Shear profile
• Select markers
• Apply kinetics– Microbial, Enzymatic, Bio-Chemical
• Integrate over product volume/process step
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θ tc x0, y0, z0,( )p q r
Axp
Ayq
⋅ Azr
⋅ Bx tc( ) p⋅ By tc( ) q⋅ Bz tc( ) r⋅ Cx x0( ) p⋅ Cy y0( ) q⋅ Cz z0( ) r⋅∑∑∑
→:=
Tf tc x0, y0, z0,( ) ta Ti ta−( ) θ tc x0, y0, z0,( )⋅+ 460 R⋅−:=
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 530
50
70
90
110
130
150
170
190
210Time to heat fruit piece in puree
Time of heating, minutes
Tem
pera
ture
, de
g F
130
175
T f tc 0, 0, 0,( ) R1−⋅
T f tcx
in,
y
in,
z
in,
R
1−⋅
TAvgF tc( ) R1−⋅
3 5
tc
12Ashok Dhruv, [email protected]/18/12
Viscosity model for Pear puree based on data from Dr.Steffe's book, page 370.
nµ m1
3:= Estimate from data @ 26.6 C or 80 F
T :Temperature in degrees Fm: Moisture content in %kµ m T m,( ) e( )
6.24−3.118 10
3⋅T 460+
+ 11.357 1 m−( )⋅+
Pa⋅ s
nµ m⋅:=
µ PPTm T m, γ,( ) kµ m T m,( ) γnµ m 1−
⋅:= µ PPTm 80 m,6
s,
18.422poise=
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Velocity profileVelocity profile
vz r( )∆P
2 kµm
tfavg
Rmc,
⋅ L
1
nµm nµm
nµm 1+⋅ Ri
nµm 1+
nµm r
nµm 1+
nµm−
⋅:=
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0.015 0.01 0.005 0 0.005 0.01 0.0150
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
trace 1
Velocity in z direction
Radial distance, in
Vel
ocit
y, f
t /
sec
3
0
v z r( )
ft
s
R iR i− r
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1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3110
60
10
40
90
140
190
240
Shear rate, radiallyShear rate, axially
Shear rate as afunction of radius, SSHE
Radial distance, inches
She
ar r
ate
in p
er sec
ond
240
110−
γ θ r in⋅( ) s⋅
γ z r in⋅( ) s⋅ 10⋅
31.5 r
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LogRedClB 1.044 10 4−×=LogRedClB log e 10,( ) LncitocfClB⋅:=
CitoCfClB 1.00024=CitoCfClB eLncitocfClB:=
LncitocfClB 2.403 10 4−×=LncitocfClB0
τmin
θKClB θ( )⌠⌡
d min⋅:=
KClB 7( ) 3.534 10 3−× min 1−=KClB θ( ) K0ClB e
∆EClB
Rgas TAvg θ( ) 460 R⋅+( )⋅
−
⋅:=
TAvg 8( ) 196.762R=Exp 101.745=Exp∆EClB
Rgas TAvg 15( ) 460 R⋅+( )⋅:=
∆EClB
Rgas3.73 104× K=∆EClB 3.73 104⋅ Rgas⋅ K⋅:=K0ClB 2 1040⋅ s 1−⋅:=
Calculation of Microbial kill :
FTPast 37.228s=FTPast0
τmin
θ10
TAvg θ( ) TRef−
z
⌠⌡
d min⋅:=
τ 4.359min=z 10 R⋅:=TRef 180 R⋅:=
Calculation of extent of Pasteurization :
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0 1 2 3 4 50
20
40
60
80
100
120
140
160
180
200Peroxidase activity drop in heat period
Time in heating MC tube, minutes
Act
ivit
y ra
tio,
; A
vg T
emp
deg
F
200
00
Ratio POD θ( )
%
T Avg θ( )
R
50
τmin
θ
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
10
20
30
40
50
60
70Temp, Firmness and PG Conc. of peaches
Time, minutes
Tem
p F,
Firm
ness
, N, P
G C
once
ntar
tion
70
0
T MW θ( )
R
Firm θ( )
PG θ( ) 100⋅
10 θ
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Calculation of Nutrition destruction :
Based on Vitamin B1 - Thiamin, Kinetics
K0B1 2.19 109⋅ s 1−⋅:= ∆EB1 1.18 104⋅ Rgas⋅ K⋅:=∆EB1
Rgas1.18 104× K=
Exp∆EB1
Rgas TAvg 15( ) 460 R⋅+( )⋅:= Exp 32.187= TAvg 8( ) 196.762R=
KB1 θ( ) K0B1 e
∆EB1
Rgas TAvg θ( ) 460 R⋅+( )⋅
−
⋅:= KB1 7( ) 1.074 10 3−× min 1−=
LncitocfB10
τmin
θKB1 θ( )⌠⌡
d min⋅:= LncitocfB1 7.046 10 4−×=
CitoCfB1 eLncitocfB1:= CitoCfB1 1.000705=
LogRedB1 log e 10,( ) LncitocfB1⋅:= LogRedB1 3.06 10 4−×=
20Ashok Dhruv, [email protected]/18/12
tc 0 5, 300..:=Pdrip =Percent drip lossPdrip 4 60 FractionMyoDe⋅+:=
FractionMyoDe =FractionMyoDe 1 Convratio−( ):=
Convratio =Convratio eLnConv:=LnConv =LnConv0
160
tcKrate tc( )−⌠⌡
d min⋅:=
Conv 160( ) =Conv tc( )0
160
tcKrate tc( )−⌠⌡
d:=
Krate 7( ) min 1−=Krate tc( ) K0 e
∆E
Rgas TAvg tc( )⋅
−
⋅ 101.3− pH tc( )⋅⋅:=
TAvgF 45( ) R=Exp =Exp∆ E
Rgas TAvg 5( )⋅:=
∆ E 43500 454⋅cal
mole⋅:=K0 2.13 1034⋅ 60⋅ min 1−⋅:=pH 160( ) =pH tc( ) 7.0
.01
mintc⋅ min⋅−:=
Calculation of Myosin denaturation :
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Value generation - Increased Value generation - Increased RevenuesRevenues
• Revenues - Growth– Elasticity of demand
• Sensory perceptions - Product Appeal• Nutrition - Satiating, Health• Shelf life - Convenience• Price, Advertising,
• Satisfy Consumer
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Value Generation - Minimize Value Generation - Minimize CostsCosts
• Fixed Costs– Equipment - Sized to Scope– Facilities - 3 to 5 X of Equipment
• Variable costs - Function of process conditions
– Utilities– Labor– Yield– Capacity
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Capital cost optimization - Capital cost optimization - ExampleExample
80 90 100 110 120 130 140 150 160 170 1800.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
Refrigeration system costFacility cost, @ 50 $/sq ftTotal cost, FC @ 40 $/Sq.Ft.Total cost, FC @ 50 $/Sq.Ft.Total cost, FC @ 60 $/Sq.Ft.
Capital cost minimization
Time in chiller, minutes
Inst
alle
d co
sts,
$ i
n M
illi
ons
2.5
0.5
RC t( ) 106−⋅
FC 50 t,( ) 106−⋅
TC 40 t,( ) 106−⋅
TC 50 t,( ) 106−⋅
TC 60 t,( ) 106−⋅
18080 t
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SummarySummary
• Application of Basic– Heat & Momentum transfer principles with– Kinetics: Microbial, Enzymatic, Bio-Chemistry– Mathematical models, IT Tools
• Results in Objective Measures of– Safety, Sensory, Shelf life, Nutrition– Yield, Capacity, Quality
• Capital and Global Cost Optimization
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