Structuring case-study Crystallization · PDF fileStructuring case-study Crystallization Graciela ALVAREZ, H. BENKHELIFA, M. ARELLANO, D. LEDUCQ, D. FLICK , Irstea,APT,CSIC, UCL, UNIROMA

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Structuring case-studyCrystallization

Graciela ALVAREZ, H. BENKHELIFA, M. ARELLANO, D. LEDUCQ, D. FLICK ,

Irstea,APT,CSIC, UCL, UNIROMA

Workshop CAFE EFFOST 20th November 2012

[email protected]

2

Workshop CAFE EFFOST 20th November 2012 [email protected]

Process and industrial problem

Pasteurization 85°C

Storage

MixMix Ripening 4°C

12 to 24 hrs

Packaging, Moulding

55°°CC

-- 55°°CC

Initial Freezing Initial Freezing -- Freezer Freezer

Exit TExit T°°C C --5 to 5 to --66°°CC

Mixture 60°C Ingredients

Refrigerant fluid entry

Scraper blades

Refrigerant fluid

exit

Sorbet

mix

entry

Sorbet exit

30-50% ice

Ice crystal size < 50µm to

avoid undesirable quality:

coarse, grainy texture.

Homogenization

60°C - 200 bars

3


On-line sensors

Freezing

MixMix

SorbetSorbet

Water %Water %

Sugar %Sugar %

Gum %Gum %

Ice CreamIce Cream

Energy Energy

ConsumptionConsumption

•• Ice crystal sizeIce crystal size

•• ViscosityViscosity

••TemperatureTemperature

Mix flow rateMix flow rate

[kg/s][kg/s]Dasher rotation speed Dasher rotation speed

[rpm][rpm]

Raw

material

Process

SSHEProduct

TT°°C Evap.C Evap.

[[°°C]C]

Sorbet crystallization : Water/ Sugar/ Gum without air

Controlled variables

Actuators

minmax and φφφφφφφφ ≥≥≥≥≤≤≤≤ iceice ddwithObjective function :

==== .min

ice

elec

m

Wj

&

Objectives

4


Experimental Device

1 - Refrigerated storage tank

2 - Volumetric piston pump

3 - SSHE or Freezer

4 - Outlet pipe

5 - Exit temperature - Pt100 probe

6 - Ice crystal size - FBRM probe

7 - Product exit

FBRM

Probe

Pt100

Probe

Lemon

Sorbet

Lemon

sorbet mix

Frozen sorbet

exit

Pilot-scale SSHE or freezer WCB MF50 - Nominal capacity: 0.007 to 0.021 kg/s

5


Focused beam reflectance measurement

Probe Window

principle Enlarged view

Path of Focused

Beam

Chord length = time period of

reflection light * laser beam

tangential speed

6


Experimental Device

Rheology experimental study

1 - Refrigerated tank

2 - Piston pump

3 - SSHE or freezer

4 - Pt100 probe at inlet

5 - Pipe rheometer

6 - Pressure manometers

7 - Pt100 probe at inlet

8 - Product exit

7


Ice crystallization study

Operating Conditions Coded Values

Factors Unity - αααα -1 0 +1 + αααα

X1 - Mix flow rate (kg/s)kg/h

0.00725

0.01035

0.01450

0.01865

0.02175

X2 - R22 Temperature (°°°°C) -10.60 -12.50 -15.25 -18 -19.90

X3 - Dasher speed(rad/s)

rpm57.07545

62.83600

78.54750

94.25900

104.721000

∑ ∑∑∑= =<=

+++=3

1

3

1

23

10

ˆi ji

jiijiiii

ii XXXXY ββββ

0β iβ iiβ ijβ

ji XX

Interception, linear, quadratic, interaction effect

Experimental conditions

Effect of 3 operating conditions on 2 responses:mean chord length - draw (exit) temperature of sorbe t

Y Predicted response

8


Effect of process on exit temperature

78.54 rad/s (750 rpm)

↘↘↘↘↘↘↘↘ TeTe↘↘↘↘↘↘↘↘ Draw temperature Draw temperature ↗↗↗↗↗↗↗↗ XiceXice

MFR (MFR (↗↗↗↗↗↗↗↗ residence times) residence times) ↘↘↘↘↘↘↘↘ Draw Draw

temperaturestemperatures

Process ResultsProcess Results

DS and Te effect

↗↗↗↗↗↗↗↗ Dasher speed results in a slightly warming of Dasher speed results in a slightly warming of

the draw temperaturethe draw temperature

Te and MFR effect

(50 kg/h)

9


Effect of process conditions on mean chord lengthEffect of process conditions on mean chord length

78.54 rad/s (750 rpm) = cte

↘↘↘↘↘↘↘↘ TeTe↘↘↘↘↘↘↘↘ CL (Chord lenght)CL (Chord lenght)

MFR (MFR (↗↗↗↗↗↗↗↗ residence times) residence times) ↘↘↘↘↘↘↘↘not not

significant effect on CLsignificant effect on CL

Process ResultsProcess Results

DS and Te effect

↗↗↗↗↗↗↗↗ DS slightly warming of the exit temperatureDS slightly warming of the exit temperature

Te and MFR effect

(50 kg/h)= cte

↘↘↘↘↘↘↘↘ TeTe↘↘↘↘↘↘↘↘ CL (Chord lenght)CL (Chord lenght)

10


Apparent viscosity measurementsApparent viscosity measurements

1 - Refrigerated tank

2 - Piston pump

3 - Freezer

4 - Outlet pipe

5 - Pt100 probe

6 - FBRM probe

7 - Product exit

8 - Tube viscometer

Lemon

sorbet mix

Laboratory scale pilot freezer WCB MF50

8

Frozen sorbet

exit stream

11


Tube viscometerTube viscometer

w

w

d

dn

γσ&ln

ln=

; 2

)(

L

PRstressshearWall w

∆=σ

P∆

Slope:

Correction factor of wall

shear rate

3

4

R

VrateshearWall w π

γ&

& =

V&

12


1napp *K −= γη &

w

w

d

dn

γσ&ln

ln=

n

K

Slope:

flow behaviour index

Intercept:

consistency index

Tube viscometerTube viscometer

3

4*

4

13

R

V

n

ncorrectedw π

γ&

&+=

13


Sorbet characterisation Sorbet characterisation withoutwithout airair

91.0

*66.12

54.0

=

=

R

w γσ &

94.0

*88.32

45.0

=

=

R

w γσ &

5% Ice 5% Ice contentcontent


92.0

*81.72

41.0

=

=

R

w γσ &


14


Sorbet characterisation Sorbet characterisation withoutwithout airair

Sorbet becomes more shear-thinning and more viscous

with the increase in the ice volume fraction within sorbet.

↗ Ice volume fraction ↘ Flow behaviour index ↗ Ice volume fraction ↗ Consistency index

15


Sorbet characterisation with airSorbet characterisation with air

1

10

100

1 10 100

Sh

ear

stre

ss

(Pa)

Shear Rate (1/s)

Xv.a.=0.5 - Xv.i.=0.23

Xv.a.=0.335 - Xv.i.=0.23

Xv.a.=0.2 - Xv.i.=0.23

Xv.a.=0 - Xv.i.=0.23

airmix

air

VV

V.a.Xv

+= 100

V

VO%

mix

air ×=

shear-thinning behaviour

increases in the air volume

fraction

Fig. 2. Flow behaviour of sorbet at -3.9°C (Xv.i. = 0.23) as a function of the air volume fraction (Xv.a.) at mix flow rate of

0.007 kg.s-1 and rotational speed of 78.5 rad.s-1.

n=0.397

n=0.312

n=0.269

n=0.257

Air volume fraction % Overrun

100 %

50%

25%

No Overrun

16


Sorbet characterisation with airSorbet characterisation with air

App viscosity as a function of the shear rate for sorbet at -3.9 °C

(Xv.i. = 23%), 0.007 kg.s -1 and rotational speed of 78.5 rad.s -1.

0

10

20

30

40

50

1 10 100Shear rate 1/s

App

aren

t vis

cosi

ty (

Pa.

s) Sorbet NoOverrun

Sorbet 100%Overrun (50%v/v)

= 0.8 Pa.s without air

airwithapp ....η = 1.6 Pa.s with air

appη

17


Flow rate kg/h

Rotation speed rpm

Tsortie ºC

Fat content Fat content % %

Overrun %

n K (Pa.s) n ηηηη app (Pa.s) à10s-1

25 600 -5 66 75 0,395 48,423 12.00

25 400 -5 66 75 0.463 38.249 11.11

25 600 -5 1212 75 0.431 81.648 22.03

25 400 -5 1212 75 0.594 60.129 23.61

Ice cream characterisation with air Ice cream characterisation with air

+ + fat globulesfat globules

↗ Fat content % ↗ Apparent viscosity

Ice cream becomes more viscous with the increase in the fat

content.

18


18

Ice Crystallisation modelling in the freezerIce Crystallisation modelling in the freezer

z=

r

• Plug flow in axial direction z : t resid = V/ Mix flow rate

• Crystallisation and heat transfer studied in functi on of

radial and axial position (t = z / v axial )

• Output variables : T out , Dmean, µout at steady state

Ri

Re Tmean

ωmean

at the scale of a REVRepresentative Elementary Volume

di

Dm

19


19

Ice Crystallization modelling in the freezer

Equations : Population balance equation

+ Energy balance equation

+ State equation (u,T,ϕi)

Growth

G = ββββ (Tsat – T)γγγγ

Breakage

Nucleationheterogeneous nucleation at wall

(((( ))))δδδδ−−−−αααα==== esat TTN

Assumptions

Non equilibrium approach

Equilibrium curve

-16

-14

-12

-10

-8

-6

-4

-2

0

2

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Sugar fraction

Fre

ezin

g P

oint

(°C

)

mix lemon

sucrose solution

Tsat for the mix obtained experimentally

νννν••••

ϕϕϕϕεεεε==== iscrapNB

20


Model building, and model reduction

(((( ))))(L)B )RR()LL( N))t,L(.G(

Ltt,L

bec ++++−−−−δδδδ−−−−δδδδ====ψψψψ∂∂∂∂∂∂∂∂++++

∂∂∂∂∂ψ∂ψ∂ψ∂ψ� Population balance equation (without radial mixing)

2020

� PBE multiplied by Lj and integrated to obtain the moments� Balance equation for the moment given by:

(((( )))) 1j3/j1j

c1jj M.B.12NLM.G.j

dt

dM++++

−−−−−−−− −−−−++++++++====

� Ordinary equations :

dMo/dt = N + B M1

dM1/dt = G.Mo + N.Lc + B (22/3-1) M2

dM2/dt = 2.G.M1 + N. Lc2 + B (21/3-1) M3

dM3/dt = 3.G.M2 + N.Lc3 With

(((( ))))2

ee TTShdtdu ••••

γγγγµµµµ++++−−−−====

νννν••••

ϕϕϕϕεεεε==== iscrapNB

21


Crystallization Model

Moments model

Energy balance

Growth, Nucleation and Breakage

Viscosity

The Parameters to be identified

22


WP4: Model building, process dynamics and model reduction

22

Model parameters range

hehe alphapalphap betabeta xixi epsilonepsilon chichi LcLc

1400 1400 -- 32003200

W.mW.m--11.K.K--11

4.e8 4.e8 –– 1.5.e91.5.e9

ss--11.m.m--33.K.K--11

3.e3.e--7 7 –– 8.e8.e--77

m.sm.s--11.K.K--11

2020--3535 10 10 –– 50 50

mm--11

1.5 1.5 -- 33 4 4 –– 8 8

µµmm

Wall heat transfer coefficient heHeterogeneous Nucleation coefficient alphap

Growth coefficient beta

Adjustment parameter of sorbet viscosity xiViscous dissipation parameter chi

Initial crystal size Lc

Breakage constant epsilon

Results steady state approach

23


Parameter identification WP6Parameter identification WP6

� Heterogeneous Nucleation coefficient α = 11.34 108 s-1m-2K-1

� Wall heat transfer coefficient h = 2894 Wm-2K-1

� Growth coefficient ββββ = 6.37 .10-7 ms -1K-1,

�Viscous dissipation parameter X= 25,82

�The initial crystal size Lc= 6.98 µm

�Viscosity coefficient ξξξξ = 3.85

CSIC : Eva Balsa, Carlos Vilas, Antonio Alonso

AMIGO Tools optimisation and IdentificationAMIGO Tools optimisation and Identification

24


Parameter estimation

Weighting cost function

Fit quality (mean relative residual in %):> Temperature at the output: 6.9%> Chord length: 5.1%> Viscosity: 24.1%

he : 2.89428e+003� : 1.13448e+009� : 6.37008e-007�:25.82076Lc : 6.98353e-006 : 3.85328

5 10 15 20 25 30 35 40-40

-20

0

20

Rel pred error: 100*(Tdata-T)/Tdata). Mean error output:6.91630765477107

5 10 15 20 25 30 35 40

-505

1015

Rel pred error: 100*(Lcdata-Lc)/Lcdata). Mean error:5.09405012728256

2 4 6 8 10 12 14 16-80-60-40-20

020

Rel pred error: 100*(mudata-mu)/mudata). Mean error:24.0936050368514

CSIC : Eva Balsa, Carlos Vilas, Antonio Alonso

AMIGO Tools optimisation and AMIGO Tools optimisation and IdentificationIdentification

25


Evaporation temperature results Experimental vs simulation

2525

(mix flow rate = 35 kg/h, dasher speed = 750 rpm)

steady state approach

26


Effet of evaporation temperature on Chord lenght .. Exp vs simulated

262626

(mix flow rate = 35 kg/h, dasher speed = 750 rpm)

27


WP5: Sensors

University of RomaResults of Electronic Nose Experiment at Irstea

� 6 experimental conditions created varying the following parameters:� Flow ice-cream machine (from 25 to 35 l/h)� Tevap refrigerant liquid (from -9 °C to -16.2 °C)� Mix flow rate (from 25 to 35 l/h(?))

� 36 measurements in two consecutive days.� Target parameters:

� Size crystals [µm]� Model estimated viscosity [Pa s]

28


WP7 : Process monitoring and controlCeline Casenave (INRA) & Denis Dochain (UCL)

29


Thank you for you attentionThank you for you attention

The research leading to these results has received funding from the European Community‘s Seventh Framework Programme

Documents

Structuring case-study Crystallization · PDF fileStructuring case-study Crystallization Graciela ALVAREZ, H. BENKHELIFA, M. ARELLANO, D. LEDUCQ, D. FLICK , Irstea,APT,CSIC, UCL, UNIROMA