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**Introduction to Bioreactors**

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Biochemical Reactor A device in which living cells or enzyme systems are used to promote biochemical transformation of matter Uses: pharmaceutical industries Chemical industry Waste treatment Biomedical applications

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2 types: Microbial fermenter- cell growth is used to produce metabolites, biomass, transformed substrates, or purified solvents Enzyme reactors (cell free)- immobilized enzymes often used for fluid-fluid and solid-fluid contractors

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**Designing a bioreactor:**

The coupled set of mass balance equations which describe the conversion of reactants to products Ex: Substrate S is converted to cells (X) and Product (P). Growth of cells… (dX/dT)V = (rx) ( V) Consumption of substrate… (dS/dT)V = (rs)(V) Product formation… (dP/dT)V = (rp)(V)

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**Constitutive Rate Expressions for Biological Processes**

Model of Microbial Growth Segregated- cells are different from one another Non-segregated models lump the population into one biophase interacting with external environment and is one species in solution; they are mathematically simple External environment influences cell response and can confer new growth characteristics on the cell

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**Unstructured Growth Models**

Simple relationships that describe exponential growth Kinetics of cell growth are described using cell and nutrient concentration profiles Malthus’s simple model: rx = µX where rx is the increase in dry cell weight and µ(hr-1) is a constant. dX/dt = kX(1-βX) was proposed as a cell concentration-dependent inhibition term by Verhulst, Pearl, and Reed.

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Monod Model Developed by Jaques Monod, exemplifies the effect of nutrient concentration based on E. coli growth are various sucrose concentrations and assumes only the limiting substrate is important in determining the rate of cell proliferation

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**For the Monod Model Cell growth might follow the form**

rx = µX = µmaxSX/Ks + S and batch growth at constant volume dX/dt = µmaxSX/Ks + S µmax is max specific growth rate of cells Ks is value of the limiting nutrient concentration Two limiting forms: At high substrate concentrations S>>Ks, µ= µmax At low substrate concentrations S<<Ks, µ= µmax/KsS

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**Models of Growth and Non-growth Associated Product Formation**

Primary metabolites- growth associated; rate of production parallels growth of cell population; Ex: gluconic acid Secondary metabolites- non-growth associated; kinetics do not depend on culture growth rate; Ex: antibiotics, vitamins Intermediate products- partially growth associated; Ex: amino acids, lactic acid

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**Mass transfer in Bioreactors**

Possible resistances: In a gas film At the gas-liquid interface In a liquid at the gas-liquid interface In the bulk liquid In a liquid film surrounding the solid At the liquid-solid interface In the solid phase containing the cells At the sites of biochemical reactions

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**Definition of Mass Transfer Coefficient**

Relates transfer rates to concentration terms and is defined as a mass balance for a certain reactant or product species in the reactor… Na = kLa(Ci x g – CL) Na= Oxygen transfer rate (through the air bubbles) CL = local dissolved oxygen concentration in bulk liquid at any time Cg= oxygen concentration in the liquid at the gas- liquid interface at infinite time a= interfacial area kL= local liquid phase mass transfer coefficient

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**Bioreactor types and modes**

Bubble Columns Systems with Stationary Internals The above take on this correlation: KLa = constant Vns where n is in the range in the bubble flow regime Stirred-Tank Reactors uses this correlation: KLa = (Pg/V)n (VSr)

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**Power Requirements Air-lift Systems Agitated Un-gassed Systems**

The power input through a reactor can be high in larger reactors The power input is estimated as: Pg = GRT ln (P1/P0) Agitated Un-gassed Systems In the turbulent flow regime, P ~ ρn3D5 In the laminar flow regime, P ~ 1/Re P ~ µN2D3 where P is proportional to viscosity but independent of density Gassed Systems Power required is less than un-gassed with reduction Pg/P given as PgP = f(NA)

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**Scale-Up Scale-up methods based on… Fixed power input**

Fixed mixing time Fixed oxygen transfer coefficient Fixed environment Fixed impeller tip speed

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Scale-up at fixed KLa It may be impossible to maintain equal volumetric gas flow rates since the linear velocity through the vessel will increase differently with the scale It may be possible to decrease the volume of gas per volume of liquid per minute on scale-up while increasing power input by changing reactor geometry and power input per unit volume

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**Scale-up on Flow Basis which becomes: N2 = N1 = (V2/V1)1/3(D1/D2)5/3**

Design based on constant input of agitator power per unit reactor volume : P1/V1 = P2/V2 For constant power input in vessels that are geometrically similar ρN31D51/V1 = ρN32D52/V2 which becomes: N2 = N1 = (V2/V1)1/3(D1/D2)5/3

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Lecture 1: Kinetics of Substrate Utilization and Product Formation

Lecture 1: Kinetics of Substrate Utilization and Product Formation

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