Objective assesment of safety, sensory, nutrition, shelf life and economics

02/18/12 Ashok Dhruv, [email protected] 2


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



Thaw

Blend

Heat

Cool

FillHold




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



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⋅−:=


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=


Velocity profileVelocity profile

vz r( )∆P

2 kµm

tfavg

Rmc,

⋅ L

1

nµm nµm

nµm 1+⋅ Ri

nµm 1+

nµm r

nµm 1+

nµm−

⋅:=


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


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


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 :


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


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


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 :


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


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


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


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

Objective assesment of safety, sensory, nutrition, shelf life and economics

Economy & Finance

Objective assesment of safety, sensory, nutrition, shelf life and economics