tepn Papcek Faculty of Mechatronics and Interdisciplinary Engineering Studies, Technical University

1
tepán Papácek Faculty of Mechatronics and
Interdisciplinary Engineering Studies, Technical
University of Liberec Institute of Physical
Biology, University of South Bohemia, Nove Hrady
OPTIMAL DESIGN OF MICROALGAL
BIOREACTOR METHODOLOGY BASED ON GROWTH MODELLING
AND SIMULATION
PBR in N.Hrady
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Aim of the project New methodology proposal for
PBR design

• Outline
• Introduction Algal biotechnology basics
• Modelling of algal growth in PBR and Model
  implementation
• Experimental verification of model structure and
  parameters
• Concluding remarks and Future prospects

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ALGAL PHOTOBIOREACTORS (PBR)

• Stirred Tank R, OBR
• Bubble Column R
• PBR with recycle
• tubular flat panel

• Open vers. Closed
• outdoor indoor

PBR in N.Hrady
MBU Trebon
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MICROORGANISM ALGAE CYANOBACTERIA eukaryotic
- prokaryotic
Spirulina (Arthrospira)

• Chlorella, Chlamydomonas,

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PRODUCT BIOMASS, HVC, H2 production,

• Biomass for
• Nutritional additives
• and animal feed
• HVC (High-value compounds aseptic and
  sterilisable PBR is requiered) Bioactives comp.
  (e.g. antiviral, anticancer activity), fine
  chemicals (karotenoids, aminoacids, PUFA, etc.)
• H2 production
• CO2 secuestration

www.spirulina.com
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PROCESS PHOTOSYNTHESIS (in microalgae)
8 hn
Calvin-Benson cycle of carbon fixation (Nobel
Prize, 1961)
2 NADPH2 3 ATP
2H2O Enzymes O2
CO2 Enzymes (CH2O) carbohydrates
Light reactions
Dark reactions
Theoretical limits of algal productivity
Specif.growth rate m0.2 h-1 5.5 x 10-5 s-1
doubling time ln2/m 3.5 h Implication for
industrial cultivation (i) special designed
devices, (ii) genetic modification of algae
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Motivation (from scientific point of view)
Optimal design of PBRHow?

• Decoupling principal phenomena influencing algal
  growth in PBR
• Light supply and distribution Fluid flow
  (i.e. Light regime parameters L/D cycles)
• Cell damage due the hydrodynamic (shear) stress
• Mass transfer (Nutrient and CO2 supply,
  Accumulation of photosynthetic O2 )
• Process scalling from single cell level to the
  mass culture

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PBR Modelling multidisciplinary multiscale pb.
O 50 mm
5 m
Time scales Convection / Process 10-3
50 mm
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Modelled phenomena and its spatial and temporal
dependency

• Microlalgal growth in a PBR as a function of
• Light distribution fluid flow (Light regime)
• Hydrodynamic stress (Shear stress Shear rate)
• Mass transfer (gas-liquid, cell-suspension)

• Distributed parameters gt PDE(e.g.
  Navier-Stokes eq. system)

• Lumped parameter model - LPM (Assumpion of well
  mixed unit) gt ODE (e.g. 1st order ODE - reaction
  kinetics)
• Time dependency
• Stationary vers. Non-stationary problems

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Light distribution in PBR cross sections
Lambert-Beer law 3D, 2D, 1D Alternatives Six
flux model (Cassano)
I
Continuous vers. Discrete description
Zone I PFD lt I1 (darkno grown zone) Zone
II PFD(I1, I2) (photolimitation
suboptimal) Zone III PFD(I2, I3)
(photolimitation supra-opt.) Zone IV PFD gt I3
(photoinhibition)
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Lagrangian approach
1/2
Coupling Algal cell trajectory and Irradiance
distributiongt Irradiance history record for an
individual cell How manage one million cell per
ml3 ? Random walk?
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Reaction kinetics Semi-empirical steady-state
models Common principle Light averaging
Monod kinetics
Aiba kinetics with Me term (Meendogenous
metabolism)
Other kinetic models exponencial, logistic, etc.
Other way Specific growth rate averaging (an
example for 1D case flat panel of thickness b,
illumin. from one side) WHAT TO DO in case of
COMPLEX GEOMETRY?
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How introduce the flashing light effect into the
model? Productivity enhancement due to light
integration
Experimental finding For some frequencies the
light is integrated over whole period (Terry
1986)

m(1/2 I) gt1/2 m(I)
If the distribution of L/D cycles is not
sharp? What to do?
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Multicompartment(Eulerian)approach
2 alternatives for state variables selection
1st Concentrations 2nd 3 States of PSF
Multiscale pb. gt stiff system, loss of
sensitivity?
fi,j,k flow rates among compartments k index
directions N,S,E,W(back mixing)
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Numerical scheme for algal growth calculation
(using FEMINA) 1/2
Transport theorem growth model gt System of
(NxM)2 ODE for biomass concentration.
Continuity eq. Euler backward method (E-A
?t)X(t1)X(t) Assumption of well mixing Cx is
homog., i.e. constant during one passing through
the PBR gtonly one term (1-m?t) will stay in the
main diagonal (I.e. no dependency on L/D cycles)
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Numerical scheme for algal growth calculation
(using FEMINA)
2/2
Transport theorem PSF model gt System of
2(NxM)2 ODE for states X1, X2 of PSF
Calculations for one time step 1st Initial
conditions (States X1,2 i,j(t), Cx(t),incident
Irradiance), 2nd New I distribution (comps.
re-definition), 3rd Re-calculation of flowrates
among comps. fi,j,k (t), 4th ODE solution gt New
States X1,2 i,j(t1), 5th Overall concentration
Cx(t1).
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A dynamic 3-state model of Photosynthesis with
photoinhibition (Eilers Peeters, Wu Merchuk)

• PSF - photosynthetic factory
• X1 open state X2 closed X3
  inhibited X1X2X31
• Growth kgX2 Me
• Me-maintenance rate (order 10-4)
• k-photosynthesis production yield (order of kg
  10-4)

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Transient Steady state of PSF
Initial C. X1(0)1,X2(0)0 a1000ß, ?1000d

• Steady state X1, X2,
• Specific growth rate mgkX2-Me
• In steady state is PSF model equivalent with Aiba
  kinetics...

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Numerical simulator FEMINALGA

• Implementation of growth eq.just proposed scheme
  in code FEMINA

Time course of biomass concentration
productivity
Design parameters
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Optimal design Problem definition and solution
Optimization Algorithm
PBR Design parameters constraints
PBR optimal param.
PBR process model
Operating conditions constr. (I,flow rate)
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Flashing light effect Growth enhancement due to
the light integration

• L/D cycles induced by
• Light supply (LED array)
• Flow regime (Taylor vortices in C-T BR)

Couette-Taylor BR, MBU Trebon
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Hydrodynamic (shear) stress Growth impediment
mechanical dammage
Microalgal cell fragility Damage caused by 1.
Flow regime, 2. Pumping device
Identification of model parameters
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A typical growth experiments Aibas model
Productivity (dimensionless)
For low Cx , Plt0 due to photoinhibition For high
Cx , Plt0 due to Me
Increasing Irradiation
Normalised concentration
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• Proposal of a new methodology for PBR design
  (full scale modelling)
• New modelling framework for PBR modelling
  (multicompartment approach)
• Experimental verification of PSF model
  implemented into compartments
• Evaluation of shear stress damage (in
  Couette-Taylor BR)
• Future prospects
• Sensitivity analysis of predicted overall
  productivity to changes of PBR design and
  operating parameters
• Numerical stability analysis of implemented
  model(with special attention to stiff)

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Thanks for your kind attention

• A za podporu a konzultace
• dekuji svým kolitelum Doc.J.Marykovi a
  Dr.K.Peterovi (CVUT), kolegum z VÝZKUMNÉHO CENTRA
  FOTOSYNTÉZY, z dílen MBÚ (T.Machovi a
  P.Hofhanzlovi) a BÚ Trebon, Doc.R.itnému a
  Ing.R.Prokýkovi (CVUT), Dr.P.Strasákovi
  (Techsoft Engineering), Dr.P.Polachovi a Dr.
  M.Schusterovi (koda Výzkum s.r.o.),
  Dr.M.Holeckovi (ZcU Plzen) a kolegum z KMO,
  Fakulty mechatroniky, TU Liberec a také celé mé
  rodine.

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Optimization modelling framework proposal
State estimation MPC
Two level modelling
PBR - real system
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Parametrické buzení of PSF
Budou nucené oscilace? Vlastní frekvence,
rezonance, apod. Pro I I0/2I0/2exp(iwt)

• Flashing light effect enhancement takes place in
  PSF model?
• IIo vers. Iharmonic
• Ratio of Specific growth rates m1/m2...

Why is stiff pb. for states X1,X2,X3 well
resolved?
Calculations-averaging for time course of Biomass
concentr. 1st States X in every comp. 2nd m from
X2gtmean conc. Cx 3rd Next time step.
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Reengineering PBR designed for making suspension
flow uniform and light source optics make the
rest

• Static mixers
• (Ugwu, Ogbonna Tanaka,2002),see fig. 1
  Twister-tape
• Flow invertors
• (Strasák,Zitny,2002) see fig. 2,
• Swirling flow
• (Muller-Feuga et al., 2003)

Fig. 1
Fig. 2
heureka
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Lagrangian approach
2/2
Coupling Algal cell trajectory and Shear stress
maximal value gt Shear stress history record for
an ind. cell How evaluate it? Shear stress dose
is determining or the SS maximal value?
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Why is stiff pb. for states X1,X2,X3 of PSF model
well resolved ?
Transport theorem PSF model gt System of
2(NxM)2 ODE for states X1, X2 of PSF
Numerical properties of ODE Condition number of
matrix A,
Some ideas Averaging takes place in microscale
Then the scale jump for the concentration takes
place Could be (how is) the matrix A for our
model (PSF fluid flow) sensitive to fi,j,k
? Transition rates between states are of the same
order as fi,j,k ?