MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES (Modellistica matematica dei processi dell

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MATHEMATICAL MODELING OF PROCESSES IN FOOD
INDUSTRIES(Modellistica matematica dei
processi dellindustria alimentare)

• Prof. Michele MICCIOProf. Gianpiero PATARO
• a.a. 2013-14

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Course Syllabus
Modeling
General Classification of models
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Course Syllabus
Mathematical Modeling
General Classification of Mathematical Models
Examples of mathematical models of interest for
Food Engineering
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Course Syllabus
Mathematical Modeling
Solution of Mathematical Models

• Numerical Methods for parabolic PDEs
• Finite differences
• Finite elements
• Collocation Methods

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Course Syllabus
Optimization
Mathematical modeling and optimization

• Intro to Optimization
• General definitions

• Linear Programming (LP)
• theory
• examples

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Course Syllabus
Optimization
Mathematical modeling and optimization
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Objectives of the Course

• To provide the basic knowledge, methods and
  software instruments in order to
• discriminate the complexity of the systems of
  process engineering and meet the possibilities of
  abstract representation
• classify the models, particularly the ones
  related to processes
• handle the Matlab software to solve some simple
  models and understand the results
• numerically solve the parabolic partial
  differential equations
• understand and solve Linear Programming problems.

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Recommended readings and Study materials

• Textbook
• Himmelblau D.M. e Bischoff K.B., Process
  Analysis and Simulation, John Wiley Sons Inc.,
  1967 (Collocazione 660.281 HIM 1)
• Consultation book
• Snieder R., A Guided Tour of Mathematical
  Methods For the Physical Sciences, 2nd Edition,
  Cambridge University Press, ISBN-13
  9780521834926, ISBN-10 0521834929, 2004
  (Collocazione 515 SNI - Inv 19569 Ing. Bcode
  00118373 )
• Other
• Teaching aids provided by the lecturer
• Lecture slides, course handouts and past
  examination texts can be retrieved from the web
  http//comet.eng.unipr.it/miccio

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Assessment method
software-based test ½ score oral colloquium ½
score
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WHAT WILL students LEARN?WHAT can students
do for thesis?
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Salami Simulationand Optimal Operation of a
ripening chamber
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Example
Stazione Sperimentale per lIndustria delle
Conserve Alimentari (Parma/Angri)
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Example
Stazione Sperimentale per lIndustria delle
Conserve Alimentari (Parma/Angri)
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progetto di Ricerca e Sviluppo Safemeat
(PON01_1409)
TITLE Process and product innovations aimed at
increasing food safety and at diversifying
pork-based products (SAFEMEAT) OR 2.7
Simulazione, ottimizzazione e controllo
automatico delle celle di stagionatura nella
preparazione dei prodotti carnei stagionati
innovativi (DICA-UniSA, SSICA, Dodaro SpA)
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Optimization study for salami ripening
OPTIMIZATION MODEL Aim Drying salamis to a
given final moisture content in the minimum
process time. Initial salami data All known.
Objective Function C c1Wbatcht c2Wbatch
/t min! where C is the overall cost for the
production of an industrial salami batch c1
/(kg day) and c2 ( day)/kg are cost
coefficients NOTE C(t) is a non-linear function!
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Optimization study for salami ripening
OPTIMIZATION MODEL Total cost optimum
conditions at the intersection of two mechanisms
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Optimization study for salami ripening
Independent variable (decision variable) t
days is the overall industrial ripening time
for a salami batch t is a function of the main
Operating Variables of the ripening chamber
through a suitable math model of salami
drying where ti is the process time in the i-th
phase or step in industrial ripening.
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Optimization study for salami ripening
Operating Variables Air Velocity ( vair ) Air
Temperature ( Tair ) Relative Humidity of Air (
RHair ) No. of phases or process steps ( N ) in
industrial ripening NOTE As an initial trial, N
may fixed, e.g., N2 Constraints Air
Velocity natural convection ? vair 0 forced
convection ? vair,low lt vair lt vair,up Air
Temperature Tair,low lt Tair lt Tair,up Relative
Humidity of Air RHair,low lt RHair lt RHair,up
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Fluidized Systems.Application of Fluidization
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Typical fluidized bed systems
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Video of a lab-scale fluidized bed
videos_katia_ing_02.wmv
? http//www.fluidizacao.com.br/ing/home.php
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Animationof a Fluidized (bubbling) bed
borb_med.swf
? http//www.fluidizacao.com.br/ing/home.php
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Animationof Liquid-Solid Fluidization
FBRMov.avi
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Gas-Fluidized bed bubbling bed phenomenology
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Fluidized bed dryer of bubbling type
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Fluidized bed dryeran example (1)
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Fluidized bed dryeran example (2)
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Fluidized bed features Liquid-like behavior
? Kunii and Levenspiel, Fluidization Engineering
(1991)
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Fluidized bed features Liquid-like behavior
from Galdos project work (2008)
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Fluidized-bed systems

• When a fluid flows upward through a bed of
  solids, beyond a certain fluid velocity (minimum
  fluidization velocity) the solids become
  suspended. The suspended solids
• have many of the properties of a fluid,
• seek their own level (bed height),
• assume the shape of the containing vessel.
• Bed height typically varies between 0.3m and 15m.
• Particle sizes vary between 1 mm and 6 cm. Very
  small particles can agglomerate. Particle sizes
  between 10 mm and 150 mm typically result in the
  best fluidization and the least formation of
  large bubbles. Addition of finer size particles
  to a bed with coarse particles usually improves
  fluidization.
• Superficial gas velocity Q/S (based on cross
  sectional area of empty bed) typically ranges
  from 0.15 m/s to 6 m/s.

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Fluidized bed uses

• Fluidized beds are generally used for gas-solid
  contacting in process industry (chemical, food,
  petroleum, power production, etc.). Typical uses
  include
• Chemical reactions
• Catalytic reactions (e.g., hydrocarbon cracking)
• Non-catalytic reactions (both homogeneous and
  heterogeneous) ? biomass gasification
• Physical contacting
• Heat transfer to and from fluidized bed between
  gases and solids temperature control between
  points in bed.
• Solids mixing.
• Gas mixing.
• Drying (solids or gases).
• Size enlargement or reduction.
• Classification (removal of fines from gas or
  fines from solids).
• Adsorption-desorption.
• Heat treatment.
• Coating.

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Gas-solid Fluidization basic calculationsintera
ctive webpage
http//asp.dica.unisa.it/MCS/miccio/fluidizzazione
/fluidizzazione.asp
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ERGUN sw for fluidized bed design
installed in the PC lab No. 134
http//www.utc.fr/ergun/
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EXTRA
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• PARABOLIC PDE SOLVER

A project by Ugo AVAGLIANO and Caterina SOMMA