140904_AUT_CG4017_PART+B

CG4017

Bioprocess Engineering 2

Course Notes, Autumn 2014, Part 2 of 2

Dr Denise Croker, BM-028

[email protected] Office Hours, Wednesday 11- 1.

6. HEAT TRANSFER

6. Heat Transfer

6.1 Heat transfer equipment Two major applications of heat transfer (ht) equipment in bioprocessing, are for

bioreactor temperature control (usually removal of heat by cooling water), and for

the thermal sterilisation (by addition of heat using steam) of substrate media prior

to fermentation.

The rate (and hence efficiency) at which heat is transferred is primarily determined by

two key parameters:

1. The temperature difference between the hot and cold bodies

2. The surface area available for heat exchange

These in turn are influenced by a number of variables, including:

HT system physical size HT system geometry HT system materials used Fluid flow conditions within the HT system

As seen in section 5, energy balance calculations allow us to evaluate the energy

requirement (HT rate) for a particular process/unit. Once this is known, estimating the

heat transfer surface area is the central objective in HT equipment design.

The HT requirements of bioreactors can be quite different depending on their scale of

operation: large fermenters usually require heat removal, whereas small systems lose

heat more easily (higher surface:volume ratio) and may require heating to maintain

operating temperature.

(a) & (b): Dont interfere with mixing in vessel, easy to maintain sterility, but low HT area only really suitable for small/lab-scale vessels.

(c) & (d): High HT area hence good for large reactors, but may have mixing, sterility,

and/or cleaning issues.

(e): Excellent HT area, may have problems with sterility or pumping mechanical

shear degradation of cells. Heat exchanger residence time must be small in

aerobic fermentations to ensure minimal depletion of liquid phase oxygen.

Heat transfer

configurations for

bioreactors: (a) jacketed

vessel; (b) external coil;

(c) internal coil; (d)

baffle-type coil; (e)

external heat exchanger

From Bioprocess Engineering Principles by Pauline M. Doran

The variation of cooling water temperature with distance through the coil in internal coil-

type HT equipment (c) and (d) can be seen below:

The coolant temperature rises as it passes through the coil and takes up heat, whereas

the fermenter temperature remains fairly constant since the contents are well mixed.


The simplest form of HT

equipment for small-scale

external (to the reactor)

operation is the double-

pipe heat exchanger:

Used for HT area

Shell and tube heat exchangers are used for HT area applications >15m2:

Single pass shell and tube heat exchanger


Shell and tube heat exchangers are used for HT area applications >15m2:

Large HT surface area in a small volume.

Shell-side baffles used to decrease flow cross-sectional area (increase linear velocity)

and to promote transverse rather than parallel flow over the pipes.

For increased HT area, without excessively long pipes, multiple pass shell & tube

heat exchangers are used.

Single pass shell and tube heat exchanger


Arrangement (a) is best since it

avoids temperature cross-over of

the heating and cooling fluids, as

seen in (b)

Double pass shell and

tube heat exchanger

Temperature profiles for

different shell side entry

positions


6.2 Heat transfer between fluids

The situation at the heat transfer surface of a heat exchanger pipe wall can be shown:

The stagnant liquid films on both sides of the

solid surface result in the formation of

thermal boundary layers, similar to the

situation for mass transfer at a solid surface.

In general thermal boundary layers are thinner

than the corresponding hydrodynamic

boundary layers for mass transfer.

Heat transfer rate, Qb, across a thermal

boundary layer is given by:

(93)

Where h is the boundary layer heat transfer

coefficient, A is the HT area normal to the

direction of heat flow, and T is the temperature difference between the wall and the

bulk fluid. Here Th = Th-Thw at the hot surface, and Tc = Tcw-Tc at the cold surface.

h values must normally be determined from correlations based on experimental data.

Heat transfer across a solid

heat transfer surface

TAhQb


Thermal boundary layer heat transfer coefficients for

industrial heat exchange fluids


The rate of heat transfer by conduction through the pipe wall, Qw, can be obtained from

Fouriers law: (94)

where k = wall thermal conductivity and y = distance from the hot side.

In this case, integrating eq. (94), with limits of: T=Thw at y=0, and T= Tcw at y=B gives:

(95)

Eq. (95) can be rewritten as: (96)

where Rw is the wall thermal resistance: (97)

In a similar way, we can define the thermal boundary layer resistances:

(98) and (99)

When a system, such as our heat exchanger pipe, contains a number of different heat

transfer resistances in series (thermal boundary layers + pipe wall), the overall

resistance is equal to the sum of the individual resistances.

dy

dTkAQw

wcwhww TB

kATT

B

kAQ

w

ww

R

TQ

kA

BRw

AhR

h

h

1

AhR

c

c

1

Thus for the overall heat transfer rate, Q, we have:

(100)

In eq. (100):

and from eqs. (97)-(99): or (101)

where U = overall heat transfer coefficient. Thus: (102)

Eq. (102) allows quantification of Q knowing U, A and with easily measureable hot and

cold bulk fluid temperatures.

From eq. (101) we can see that the major factors that govern the value of U are the

fluid hydrodynamics at the thermal boundary layers and the thermal conductivity and

thickness of the pipe wall.

cwhT RRRT

R

TQ

ch TTT

AhkA

B

AhR

ch

T

11

UAhk

B

hAR

ch

T

1111

TUAQ

6.3 Heat exchanger fouling factors

HT surfaces in process heat exchangers are almost always subject to dirt and scale

deposition during normal operation. The latter contribute additional resistance to heat

flow and reduce the value of U. Thus:

(103)

where hfh and hfc are the respective

hot- and cold-side fouling factors.

Increasing 1/U obviously decreases U,

and hence HT efficiency decreases with

fouling

It is very difficult to accurately estimate

fouling factors, due to the disparate

nature of such deposits and their

physical properties, as well as their time-

and temperature-dependant nature. Heat transfer across a solid heat transfer

surface with fouling of both surfaces


fcchfh hhk

B

hhU

11111

Fouling factors for typical scale deposits from

industrial heat exchange fluids


6.4 Heat transfer equipment design equations (102)

Calculation of the heat transfer area, A, required for a particular heat exchanger, from

eq. (102), requires that Q, T, and U are known. The former two may be obtained from

energy balance calculations, whilst U is estimated from empirical correlations based on

experimental data.

6.4.1 HT system design: energy balance calculations

For double pipe or shell and tube heat exchangers, the general energy balance

equation (83), under steady-state conditions and in the absence of shaft work,

becomes:

(104)

where M = mass flow rate, Et = specific enthalpy, i = in, o = out.

Applying eq. (104) separately to the hot and cold HT fluids, noting M is the same at

inlets and outlets:

and (105)

where h denotes the hot fluid, and c the cold fluid.

TUAQ

0 QEtMEtM ooii

hhohih QEtEtM ccocic QEtEtM

When there is no heat lost by the heat exchanger, all heat removed from the hot stream

is transferred to the cold stream, thus Qh = Qc = Q , and:

(106)

If sensible heat only is exchanged between the fluids, then the enthalpy differences can

be given in terms of heat capacity, Cp, and temperature change:

(107)

Eq. (107) is used in heat exchanger design to determine Q and inlet and outlet

temperatures of the fluid streams. It can also be used to evaluate the heat removal

requirement from a bioreactor, to maintain a desired reactor temperature. In this case,

at steady state the temperature of the hot fluid (i.e. the fermenter broth) is constant, so

the left hand side of eq. (107) is zero, and:

(108)

Q in eq. (108) can be determined from the energy balance equation for cell bioreactors:

Q = -Hr - Mv.hv - Q + Ws (92)

QEtEtMEtEtM cicochohih

QTTCpMTTCpM cicocchohihh

QTTCpM cicocc

Use of the heat exchanger design eq. (102) requires knowledge of T, the difference in

temperature between the hot and cold heat exchange fluids. As we have seen however

in section 6.1, fluid temperatures, and thus the rate of heat exchange, vary with position

in heat exchangers, even under steady state operation. This problem may be resolved

by including temperature as a positional variable, and subsequently solving the coupled

differential design equations that result, or more often by the use of an average T.

When the temperature of both hot and cold fluids vary in either co- or counter-

current flow, the average taken is the logarithmic mean temperature difference (LMTD),

TL. In eq. (109) T1 and T2 are the

temperature differences between the hot and

the cold fluids at the ends of the exchanger. (109)

These are calculated using the values of Thi,

Tho, Tci, and Tco from the energy balance eq. (108).

Assumptions made in eq. (109): U and Cps are constant; negligible heat loss; steady state operation. Corrections must be applied to eq. (109) for multi-pass exchangers.

When one fluid remains at constant temperature, e.g. in fermenters, the arithmetic

mean temperature difference, TA is used. In

eq. (110), TF is the fermenter temperature, and

T1 and T2 are the inlet and exit temperatures of (110)

the heat exchange fluid.

)/ln( 12

12

TT

TTTL

2

)(2 21 TTTT FA

6.4.2 Evaluation of U, the overall heat transfer coefficient

Eq. (103) shows the constituent components of U, the overall heat transfer coefficient:

(103)

The wall resistance term can be calculated knowing the thickness (B) and thermal

conductivity (k) of the wall material. Fouling factors (hfh and hfc) (if applicable) can be

estimated from typical literature data, as already seen.

Determination of the thermal boundary layer HT coefficients (hh and hc) is more

problematic however, since they are dependent on flow hydrodynamics and fluid

properties adjacent to the wall surfaces. These are normally evaluated using

experimentally determined empirical correlations, expressed in terms of dimensionless

numbers. This is similar to the situation for liquid-solid (external) mass transfer

coefficients (see section 4.3.1).

The Nusselt number, Nu, is the primary means by which hh or hc is calculated:

This dimensionless number represents the ratio of

convective to conductive heat transfer rates. (111)

where D = pipe or tank diameter and kfb =bulk fluid thermal conductivity.

fcchfh hhk

B

hhU

11111

fbk

DhNu

Many empirical correlations exist that allow the determination of the Nu for different

heat exchange situations. These involve other, experimentally-measureable

dimensionless numbers or physical parameters, including:

(112)

(113)

(114)

(Pr represents the ratio of momentum to heat transfer)

D = pipe or tank diameter Di = impeller diameter u = fluid linear velocity

Ni = impeller rotational speed L = pipe length Cp = average heat capacity of fluid

b = bulk fluid viscosity w = wall fluid viscosity = fluid average density

b

DuRenumber,ReynoldsPipe

b

iii

DNRenumber,ReynoldsImpeller

2

fb

bp

k

CPrnumber,Prandl

Some examples of these correlations are given below.

Turbulent flow inside tubes without phase change:

(low viscosity fluids) (115)

when 104 Re 1.2 x 105 and 0.7 Pr 120 and L/D 60.

(high viscosity fluids) (116)

Turbulent flow outside tubes without phase change:

when Remax 6 x 103 (117)

Remax = Re with D = outside pipe diameter and u = maximum linear flow velocity

through the pipe bundle. C = 0.33 for staggered and C = 0.26 for in-line tubes.

Stirred tanks:

(118) (119)

Helical coil hx Jacket hx

4.08.0023.0 PrReNu

14.0

33.08.0027.0

w

bPrReNu

33.0PrReCNu 0.6max

14.0

33.062.087.0

w

bi PrReNu

14.0

33.062.036.0

w

bi PrReNu

7. DOWNSTREAM

SEPARATION PROCESS - 2

31

What is downstream processing?

Unit operations that take place after

the product has been synthesised with

the objective of:

- Recovering the product

- Improving quality and

concentration of the product

- (formulating the product into final

form) not covered here

Post Reaction/Fermentation

Steps

Downstream Separation Processes 1 (CG4003)

Application Unit operation

Isolation of solids and cellular agglomerates Regular filtration

Cell isolation Centrifugation

Separation of intracellular products Cell disruption

Isolation of cells and macromolecular species Microfiltration/ultrafiltration

Isolation of macromolecular species and

soluble products

Dialysis/reverse osmosis

Isolation of soluble products Liquid-liquid extraction

Isolation of soluble products Adsorption

Isolation of soluble products Chromatography

Final purification Crystallisation

Final purification Drying

7.5 Liquid-Liquid Extraction This separation method relies on the different solubility's of mixture components

between two immiscible liquid phases, as a means of isolating the different soluble

components present in the mixture.

7.5.1 Aqueous-Organic Solvent Extraction

This is the conventional type of extraction system used in an organic chemistry lab, for

example when using diethyl ether to extract an organic product from an aqueous

reaction mixture. The basic process involves three parts, done on the lab scale in a

separating funnel:

1.Vigorous mixing of the aqueous and the organic phases to allow transfer of the

product between the phases

2.Settling of the mixture to allow phase separation to occur

3.Removal of heavier, spent aqueous phase (raffinate) from the bottom of the

separating funnel, to leave the lighter, organic, product-containing phase (extract).

Industrially, extractions are usually carried out in some sort of mixer-settler equipment.

33

http://www.halwachs.de/solvent-extraction.htm

34

http://www.cheresources.com/liquid_extractor_design5.gif

35

Aqueous-organic solvent extractions are used to isolate many pharmaceutical and

biopharmaceutical products:

Product Extractive solvent

Antibiotics

Penicillin Butyl acetate, amyl acetate, or methyl isobutyl ketone

Erythromycin Pentyl acetate or amyl acetate

Steroids N-hexane, pentane, or heptane

Vitamins

Vitamin B12 Isopropanol

Alkaloids

Morphine Butanol or benzene

Codeine Trichloroethylene

Organic solvents are not suitable however for the isolation of proteins and other

sensitive biopolymers, since denaturation can occur.

36

Aqueous Two-Phase Extraction

Aqueous solutions that form two distinct phases can provide favourable conditions for

separation of proteins, polysaccharides, nucleic acids, cell fragments, and organelles,

with protection of their structure and biological activity.

These two-phase aqueous systems comprise two incompatible polymers or a polymer

and a salt dissolved in water above certain concentrations. These liquid mixtures

partition into two immiscible phases, each containing more than 75% water.

37


Ficoll = hydrophilic polysaccharide Dextran = branched glucose polysaccharide

38

Aqueous Two-Phase Extraction

Aqueous solutions that form two distinct phases can provide favourable conditions for

separation of proteins, polysaccharides, nucleic acids, cell fragments, and organelles,

with protection of their structure and biological activity.

These two-phase aqueous systems comprise two incompatible polymers or a polymer

and a salt dissolved in water above certain concentrations. These liquid mixtures

partition into two immiscible phases, each containing more than 75% water.

Cell fragments and biomolecules, when added to these systems, partition between the

two phases. By choosing appropriate conditions, it is possible, for example, to confine

cell fragments to one phase, while a product protein partitions to the other phase.

This is particularly useful as a product isolation step from cell debris produced by cell

disruption.

39

Quantification of Liquid-Liquid Extraction

The extent of partitioning of a solute component, i, between the two phases is

determined by the phase equilibrium or partition coefficient for the system, K:

(17)

where L and H refer to the light and heavy phases respectively.

If K>1, then component i favours the light phase, and vice versa.

In many systems K is constant over a wide range of solute concentrations, provided

that the molecular nature of the solvent phases are not changed. There are many

factors that determine the value of K for a particular system, including:

Size, electric charge, and hydrophobicity of the solute molecules/particles Biospecific affinity of the solute for one of the solvent phases Surface free energy and ionic composition of the solvent phases

For these reasons it is not possible to predict K from molecular properties. In some

cases it is possible to produce an empirical correlation (from lab-scale experiments)

that allows quantification of K for a particular system.

H

L

i

iK

][

][

40

For example for extraction of soluble proteins with some polyethylene glycol (PEG)

containing aqueous two phase systems, the following empirical correlation can be

used:

(18)

where M = protein molecular weight, T = absolute temperature, and A is an empirically

determined constant for the aqueous two phase solvent system used.

For a single stage extraction, K should be 3, otherwise multiple stage extraction must

be performed.

The product recovery or % yield, Y, of a solute component can be defined as:

(19) for the light phase

and: (20) for the heavy phase

where V refers to the respective phase liquid volumes.

Thus it is possible to increase the product recovery by using a large volume of the

preferred (extracting) phase.

T

MA

eK.

K

VV

VY

HL

LL

HL

HH

VKV

VY

41

From Bioprocess Engineering by M. L. Shuler & F. Kargi

42

Partition coefficient

increases with

potassium phosphate conc. ,

resulting in

more efficient separation of

enzyme A

The concentration or purification factor, c, is also used to characterise two phase

partitioning. This is defined as the ratio of product concentration in the preferred phase

to that in the extractor feed liquid, [i]o:

(21) (when the product partitions to the light phase)

(22) (when the product partitions to the heavy phase)

In the PEG-salt two phase aqueous system, proteins can be effectively separated from

cell debris, with the proteins partitioning into the light phase and the debris into the

heavy phase. It is only usually necessary to use a single mixer-settler stage since the

partition coefficient, K, is high for this system.

In many cases however phase separation equilibrium is not achieved in a single stage

and multistage operation is required.

o

Lc

i

i

][

][

o

Hc

i

i

][

][

43

Industrial Applications of Liquid-Liquid Extraction

The time required for mass transfer to occur and the ease of mechanical separation of

the two phases are important considerations when performing liquid-liquid extraction

on an industrial scale. Each of these ultimately determine the respective sizes of the

mixer and the settler.

Interphase mass transfer depends on the interfacial surface area available for

exchange between the phases, which in turn is maximised by efficient mixing.

Phase separation in the settler is dependent on having a high interfacial surface

tension between the phases, and is best achieved under calm conditions with no

mixing.

44

http://www.halwachs.de/mixersettler.gif

45

http://www.rousselet-robatel.com/images/products/Mixer-Settler-pic-3lg.jpg 46

Rousselet Robatel 8 stage mixer-settler

http://www.rousselet-robatel.com/products/laboratory-mixer-settlers.php 47

http://images.vertmarkets.com/crlive/files/Images/92F9B851-C50C-11D3-9A82-00A0C9C83AFB/pod2.jpg

Tower extractors: general design

48

(a) Oldshue-Rushton extractor; (b) Scheibel-York extractor ; (c) Rotating-disk extractor ; (d) Pulsed extractor

http://accessscience.proxy.mpcc.edu/content.aspx?id=636100

Types of tower extractors with mechanical agitation

(a) (b) (c) (d)

49

Industrial Applications of Liquid-Liquid Extraction

The time required for mass transfer to occur and the ease of mechanical separation of

the two phases are important considerations when performing liquid-liquid extraction

on an industrial scale. Each of these ultimately determine the respective sizes of the

mixer and the settler.

Interphase mass transfer depends on the interfacial surface area available for

exchange between the phases, which in turn is maximised by efficient mixing.

Phase separation in the settler is dependent on having a high interfacial surface

tension between the phases, and is best achieved under calm conditions with no

mixing.

Fast mixing and settling can be combined in centrifugal liquid-liquid separators such as

the Pod (Podbielniak). This equipment is very important in fermentation product

separations, such as in penicillin production. Speed of extraction is important in such

cases as the product is unstable in the pH-adjusted broth. A Pod separator can

achieve extraction and separation within minutes, with rapid return of the product into

another more stable aqueous phase (e.g. a phosphate buffer).

50

http://images.vertmarkets.com/crlive/files/Images/92F9B851-C50C-11D3-9A82-00A0C9C83AFB/pod2.jpg

Podbielniak (Pod) centrifugal L-L extractor

51

7.2 Adsorption This involves the concentration of component(s) of a fluid phase (in bioprocessing,

usually a liquid) on the surface or in the pores of a solid adsorbent material. The

adsorbed fluid component is called the adsorbate.

Adsorption serves to isolate products from dilute fermentation liquors or to remove

trace liquid phase impurities during product purification.

The adsorbate-adsorbent interaction is caused by attractive sorption forces between

the liquid component and the solid surface/pore. These can include:

Electrostatic forces Van de Waals (weak physical) Chemical bonding

Three main types of adsorption can be distinguished:

1.Ion exchange (involves electrostatic forces)

2.Physisorption (involves surface weak physical interactions)

3.Chemisorption (involves surface chemical bond formation)

All three are found in bioprocessing applications of adsorption. 52

Liquid mixturecontaining

adsorbate, A

A-free liquid

Packed bed adsorber

A

Step 1A

Adsorbent pelletcross-section

Adsorbent surfacestagnant liquid film(external boundary layer)

A

Catalyst pore

Step 2Adsorption

site

Adsorption site surface

A (liq)

A (ads)

Step 3

Mass transfer and adsorption steps during adsorption of a liquid phase adsorbate, A

External mass transfer

Internal mass transfer

(pore diffusion)

Adsorption (and desorption)

53

Sequence of steps during adsorption/desorption of a fluid phase component

1. Mass transfer (external diffusion) of adsorbate from the bulk fluid to the

external surface of the adsorbent pellet

2. Mass transfer (internal diffusion) of adsorbate from the external pellet

surface through the pores to the adsorption site

3. Adsorption of adsorbate onto the adsorption site

4. Desorption of concentrated adsorbate from the adsorption site

5. Internal diffusion of concentrated adsorbate through the pores to the external

surface of the adsorbent pellet

6. External diffusion of concentrated adsorbate from the pellet surface into the bulk

fluid

54

\\\\\\

Adsorbents

High surface area porous materials. Typical surface areas: 1 to 1000 m2/g.

Typical pore diameters: 1 to 50 nm. Pore size chosen to accommodate adsorbate component molecular/ionic size.

Activated carbons, synthetic polymeric resins based on styrene, divinylbenzene or acrylamide:

Styrene DVB Acrylamide

55

Applications in bioprocessing

Ion exchange adsorption is widely used for the recovery from fermentation broths of: amino acids, proteins, antibiotics, and vitamins.

Removal of coloured impurities e.g. during citric acid production.

Removal of organic chemicals during water purification and wastewater treatment.

Adsorption generally has higher removal selectivity but smaller removal capacity

than liquid-liquid extraction methods.

56

Industrial Adsorption

Operation steps

1. Contacting/adsorbing: removal of target solute from the liquid phase.

2. Washing: to remove any residual unadsorbed material from the adsorbent.

3. Desorption/elution of the concentrated adsorbate with a suitable solvent, e.g. of

different ionic strength or pH.

4. Washing to remove residual eluant.

5. Regeneration of the adsorbent to its original, active condition (inevitably this is

never 100% effective, and as a result most adsorbents must be replaced after a

limited number of adsorption/desorption cycles).

Equipment types

Adsorption operations are normally carried out in fixed, packed adsorbent beds.

Other equipment types sometimes found include moving beds, fluidised beds and

stirred-tank contactors.

57

http://www.cee-environmental.com/public/data/companyProduct1231011370.jpg

Moving bed adsorber

58

Quantification of Adsorption

Adsorption/desorption is an equilibrium process and the extent of adsorption of a

component on a solid surface is determined by the adsorption equilibrium

relationship. Since a number of different driving forces and types of adsorption may

be involved in a given adsorbate-adsorbent system, no single quantification model is

universally applicable.

Adsorption equilibrium relationships are usually expressed as adsorption isotherms

(adsorbed amount versus amount present in the fluid phase under equilibrium

conditions at constant temperature).

A typical scenario found is that amount adsorbed increases with increasing amount

present in the fluid phase, up to a maximum. At this loading no further adsorption can

occur and the adsorbent surface is essentially saturated with adsorbate.

The Langmuir adsorption isotherm has been used to quantify gas-solid adsorption:

(23)

where: C*AS is the amount adsorbed per unit adsorbent, CASm is the maximum

amount adsorbed giving compete coverage of all adsorption sites with monolayer

coverage, C*A is the equilibrium concentration of adsorbate in the fluid phase, and KA

is a constant.

*

**

1 AA

AAASmAS

CK

CKCC

59

***

1 AA

AAASmAS

CK

CKCC

nAFAS CKC

1**

Langmuir isotherm:

Freundlich isotherm:


60

For liquid-solid systems, the Freundlich isotherm has been found to be more

applicable:

(24)

where KF and n are constants for a particular system. If adsorption is favourable n >1

and vice versa.

This adsorption isotherm applies well for the adsorption of many antibiotics,

hormones, and steroids.

There are many other adsorption isotherms, each applicable only to certain systems.

Since the exact adsorption mechanisms vary from system to system, adsorption data

cannot generally be predicted from theory, but must be determined by laboratory

experiment.

nAFAS CKC

1**

61

Fixed Bed Adsorber Characteristics

A fixed bed adsorber is in its simplest form, a vertical column packed with the

adsorbent particles.

These are normally operated industrially as unsteady-state processes, where:

1. The mixture containing the solute is continuously passed through the bed and

amount adsorbed increases with time.

2. Eventually the bed becomes fully loaded/saturated.

3. Desorption of concentrated solute is carried out.

4. Regeneration of the adsorbent is performed, prior to restarting the cycle.

When step 2 occurs, the unadsorbed solute breaks through the adsorbed bed, as observed by an increase in the effluent solute concentration.

62


63

Fixed Bed Adsorber Characteristics

A fixed bed adsorber is in its simplest form, a vertical column packed with the

adsorbent particles.

These are normally operated industrially as unsteady-state processes, where:

1. The mixture containing the solute is continuously passed through the bed and

amount adsorbed increases with time.

2. Eventually the bed becomes fully loaded/saturated.

3. Desorption of concentrated solute is carried out.

4. Regeneration of the adsorbent is performed, prior to restarting the cycle.

When step 2 occurs, the unadsorbed solute breaks through the adsorbed bed, as observed by an increase in the effluent solute concentration.

Efficient operation of a fixed bed adsorber is greatly dependent on the shape of the

breakthrough curve and on the exact effluent solute concentration at which

adsorption operation is stopped:

Waiting until high effluent solute concentrations are reached means losing a large amount of solute unadsorbed.

Stopping adsorption at too low effluent solute concentration means having a large amount of the adsorbent bed unused. 64


65

7.3 Process Chromatography This involves the separation of the components of a mixture by differential component

migration as the mixture (mobile phase) moves through a chromatography column

packed with a solid (stationary phase).

Component-stationary phase interactions can be of an adsorptive (surface adhesion)

or a partitionary (dissolution in an adsorbed solvent located on the stationary phase)

nature.

This product separation/purification method is widely used industrially in

bioprocessing:

Isolation of recombinant products from genetically engineered organisms Recovery of high-purity theraputics and biopharmaceuticals Purification of proteins, peptides, amino acids, nucleic acids, alkaloids,

vitamins, and steroids.

Like adsorption, this technique has high selectivity but relatively low capacity for

product isolation, compared to e.g. liquid-liquid extraction. Hence it is normally used for

low production volume/high value added biochemical products.

The theory and quantification of chromatography will be covered in analytical

chemistry modules and will not be covered here. 66


67

The following types of chromatographic separation methods are important industrially:

1.Adsorption chromatography (ADC): based on solute adsorption onto a porous solid

adsorbent (as in section 7.6).

2.Liquid-liquid partition chromatography (LLC): based on different partition coefficients

(solubility) of the solute molecules between a stationary adsorbed liquid phase and a

passing solution. The adsorbed liquid is often non-polar, e.g. wax-type materials.

3.Gel filtration chromatography (GFC): Based on the molecular sieving effect when

solute molecules penetrate into the small pores of column packing materials to

different extents. Separation occurs on the basis of solute molecular size and shape.

A.k.a size exclusion chromatography.

4.Ion exchange chromatography (IEC): Based on adsorption of ions or electrically

charged biomolecules on an ion exchange resin by electrostatic forces.

5.Hydrophobic chromatography (HC): Based on hydrophobic interactions between

solute molecules (e.g. proteins) and functional groups (e.g. alkyl residues) on the

column packing material surface.

6.Affinity chromatography (AFC): Based on specific chemical interactions between

solute molecules and packing material surface ligands. Ligand-solute interaction is

very specific and governed by solute molecule size, shape and polarity. Lock and key type interaction akin to an enzyme-substrate binding.

7.High pressure liquid chromatography (HPLC): Can be any of the above, except high

liquid pressure through column gives fast separation with high resolution. Very

important in the pharma/biopharma industry, so get experience with it!!

68

Process Scale Chromatography Columns

7.4 Precipitation and Crystallisation Precipitation is usually the first step in the purification of intracellular proteins after cell

disruption and refers to the transition of one component of a solution mixture from the

liquid phase to the solid phase. The resulting solid may be in a disordered form

(amorphous precipitate), or the molecules/ions may be in an ordered three

dimensional lattice (crystallised form).

Precipitation

In bioprocessing, there are three major methods used for precipitation.

1. Salting out by adding inorganic salts such as sodium sulphate at high ionic

strength. The added ions interact with the water more strongly, causing the

protein molecules to precipitate. The relationship between protein solubility, S,

and solution ionic strength, I, can be given by:

(25)

where So is the protein solubility when I = 0, and KS is the salting out

coefficient, which is a function of temperature and pH, and

where Z = ionic charge

IKS

SS

o

.log

2].[5.0 iZiI71

From Bioprocess Engineering by M. L. Shuler & F. Kargi

72

2. Solubility reduction at reduced temperatures (

Lysine isoelectric point

http://upload.wikimedia.org/wikipedia/commons/7/7e/Lysine_pI.png

74

7.8.2.1 Nucleation & Growth

Nucleation first formation of a solid - nucleus

Growth subsequent size enlargement of that nucleus to the final crystal product

Nucleation governs the final product size:

High nucleation rate lots of nuclei existing solute has a large surface area to deposit upon resulting crystals will be small

Low nucleation rate few nuclei existing solute has less area to deposit on resulting crystals will be larger

Driving force for nucleation/growth Supersaturation

76

The Solubility Curve

Supersaturation

Saturated Solution

Undersaturated

Supersaturated

The amount of solute dissolved

in the solution is greater than

the solubility

Generating Supersaturation

Supersaturation

The Metastable Zone

Nucleation

The Metastable Zone

Spontaneous

Nucleation

Possible

& Growth

can occur

No Nucleation

But

Growth is Possible

No Nucleation

No Growth

cb

ci

cs

Crystal face Bulk solution

cb - ci

ci - cs

Concentration

85

7.8.2.2

86

(27)

(28)

Combining to eliminate ci:

87

(29)

88

Solu

bilit

y

Temperature

MX.yH2O (hydrated salt)MX (anhydrous salt)

NaCl

KNO3

89

7.8.2.3 Variation of solubility with temperature

Increasing temperature normally increases the solubility of a solute

(positive temperature coefficient) since dissolution is normally

endothermic.

However in some cases increasing temperature may have little effect on

solubility, or may even decrease the solubility (i.e. dissolution may be

exothermic).

Solutes with large temperature coefficients are easily crystallised by cooling, whereas those with small coefficients must be crystallised by

evaporation.

Careful temperature control must be used with negative temperature coefficient solutes. Thus for example the hydrated salt shown above

can only be crystallised out at low temperatures (by vacuum

crystallisation). 90

7.8.2.4 Industrial crystallisation equipment

Crystallisers can be classified in various ways: batch/continuous,

cooling/evaporative, linear/stirred. The most important feature is the method by

which crystal size is controlled, i.e. control of nucleation rate. Crystallisers are

generally simple in design, the only moving parts being agitators and/or scrapers.

Batch crystallisation

These most often take the form of an open tank with agitation, heating/cooling and

evaporation at the free surface. Agitation helps ensure uniform crystal size

distribution. The major difficulty with this type of unit is fouling of the heat exchange

surfaces by product crystals.

Vacuum crystallisers are commonly used for evaporative cooling where it is

necessary to achieve supersaturation by evaporation. These usually take the form of

tall vertical cylinders. Flash evaporation is used to cool the liquor and to increase the

solute concentration.

91

Continuous crystallisation equipment

From: Chemical Engineering, vol. 2 Coulson & Richardson, p673-681

Continuous crystallisation equipment

End view

Votator crystalliser

92

http://www.labx.com/v2/adsearch/morepics.cfm?chpics=1&chback=

1&adzone=431000&pic=431030&cn=0&adnumber=431030

Votator crystalliser

93


Oslo cooler crystalliser

Supersaturation

Nucleation &

growth

94


Oslo evaporative crystalliser

Supersaturation

Nucleation &

growth

Vacuum

95

8. BIOREACTOR DESIGN &

SCALE-UP

8. Bioreactor Design, Scale-up & Operation

This section will comprise a review of key quantitative reactor design methods,

together with an overview of bioreactor control methodologies.

Many different types, most commonly used is the stirred tank bioreactor:

Major design challenges lie in achieving adequate mixing/aeration

Typically 70-80% filled with liquid, rest is headspace

Foam breaker or chemical antifoam agents often used

Various aspect ratios (height:diameter) used: low (1:1) for anaerobic, higher for aerobic

fermentations

Not used in plant and animal cell culture due to high level of shear damage to sensitive cells

Most suitable type for viscous media


8.1 Bioreactor design

Fed batch (no external mass transfer limitations)

For single cell fermentation reactions, time dependence of

Reaction mixture volume, V: (120)

Cell concentration: (121)

Substrate concentration: (122)

Product concentration: (123)

where F = volumetric feed rate, D = dilution rate(=F/V), other parameters as in section 2.

Fed batch

bioreactor

Fdt

dV

)( Dxdt

dx

xmY

q

YssD

dt

dsS

PS

P

XS

i

pDxqdt

dpp

FB bioreactor, quasi-steady state* operation:

Total cell mass in reactor, Mx: (124)

where Mx,o = cell mass at start of substrate feeding and tfb = time from start of feeding

Reactor substrate concentration: s 0 (125)

Product concentration: p YPSsi (126)

* Quasi-steady state operation involves operating the reactor in batch mode until a

high cell density is achieved and where substrate is virtually exhausted, and then

commencing substrate feeding. Under such conditions the large cell mass present

ensures that the substrate is consumed as fast as it is supplied in the feed, hence

giving s 0.

fbiXSoxx tFsYMM )(,

7.1.2 Chemostat / MFR / CSTR (anaerobic reactions, low viscosity media)

Here the reactor liquid volume is maintained constant by setting inlet and outlet flows

equal and constant. Steady state is achieved by the reactor concentrations adjusting

themselves to the feed rate. At steady state = D.

For enzymatic reactions,


Effectiveness factor, = 1 for cell free enzymes in solution. Since [substrate] is

constant at steady state in continuous flow reactors, then is also normally constant

and can be calculated.

For single/suspended cell culture,


Cell concentration: (129)

Product concentration: (130)

sK

sssD

m

i

max

D

DKs S

max

D

xqpp

p

i

s

PS

p

XS

i

mY

q

Y

D

ssDx

Steady state cell and substrate concentrations

as a function of dilution rate in a chemostat

Cell washout: D > MAX


From eq. (129), assuming no product formation or maintenance requirement:

(131)

The critical dilution rate condition, Dcrit, for cell washout can now be obtained by

substituting from eq. (128) for s, letting x = 0, and solving for D:

(132)

Usually Ks

Cell washout: Dcrit Dopt

Chemostat biomass productivity


The value of D for maximum Qx, Dopt, can be obtained by differentiating eq. (134) with

respect to D and equating to zero:

(135)

iS

Sopt

sK

KD 1max

Chemostat with immobilised cells.

Assuming:

No product formation No maintenance requirement Cells produced by immobilised cell reproduction are released into the medium and ultimately removed in the

product flow. Immobilised cell particles stay in reactor.

Steady state biomass balance:

(136)

where xS = released/suspended [cell], xim = immobilised [cell], and T = total

effectiveness factor from eq. (79).

Dividing by V and expressing F/V as dilution rate: (137)

Steady state limiting substrate balance:

(138)

or

(139)

Chemostat with

immobilised cell

particles 0 VxVxFx imTss

S

imT

x

xD

1

0 VY

xV

Y

xFsFs

XS

imT

XS

si

imTSXS

i xxY

ssD

Combining eqs. (137) and (139) and substituting the Monod equation (3) for gives:

(140)

Eq. (140) graphically:

imTXSi

XSi

S xYss

YssD

sK

s

max


Immobilised cell

chemostat

Plug flow (packed bed) bioreactors

The major industrial application of this bioreactor type

is for immobilised enzyme reactions.

Differential steady-state substrate balance across a reactor section:

(141)

A = reactor cross-sectional area

z = distance along reactor length from the entrance

Minimal attrition damage to biocatalyst particles c.f. stirred reactors.

Good liquid-solid mass transfer due to high flow rate in bed. Liquid recycle also improves this.

Used commercially for immobilised cells and enzymes for production of aspartate and fumarate, and for resolution of

amino acid isomers.

Plug flow

bioreactor with

immobilised

enzyme packing

z

F

A

sK

s

dz

ds

m

T max

For aerobic reactions, aeration is done in a separate vessel to avoid liquid

maldistribution in bed due to trapped air bubbles:

Unsuitable for processes that evolve large amounts of gas, e.g. CO2, since gas

bubbles can become trapped in bed.


Plug flow bioreactor with external medium aeration

Bubble column reactors

Do not require mechanical agitation for mixing and aeration:

Gas sparging causes aeration & mixing

Require less energy than mechanical mixing

Aspect ratios from 2:1 to 6:1 common

Perforated horizontal plates sometimes installed to break up/redistribute

coalesced bubbles

Few moving parts: low capital costs

Foaming can be a problem

Used industrially for production of: bakers yeast, beer, & vinegar, and in wastewater treatment.


Bubble column reactor

Flow regimes in bubble column reactors:

1.Homogeneous flow low gas flow rates, uniform bubble size and velocity, poor gas and liquid mixing.

2.Heterogeneous flow high gas flow rates, large, chaotic oscillatory liquid flow cells occur. Upward movement of

liquid & gas in centre of reactor, downflow of liquid at

walls. Good mixing of liquid & gas.

For non-viscous reaction media in heterogeneous flow, kLa

can be correlated with gas flow rate:

(142)

where uG = gas linear flow rate

Not suitable for high viscosity reaction media.

Heterogeneous flow

in a bubble column


Airlift reactors:

(a) and (b) internal

loop vessels,

and (c) external loop


Airlift reactors

Airlift reactors also do not require mechanical agitation for mixing and aeration:

Liquid flow pattern more defined c.f. bubble column reactor since there is physical separation of the up-flowing and down-flowing streams.

Fewer gas bubbles entrained in the downcomer, so liquid flow is faster.

Better liquid mixing c.f. bubble columns, but gas hold-up (and hence gas-liquid mass transfer) not as good: kLa < 0.32uG

0.7 (143)

External loop reactors have even greater gas-liquid disentrainment in the downcomer, c.f. internal loop airlift vessels.

Performance is significantly affected by the details of the vessel internal structure, e.g. size and position of the draft tube can drastically affect kLa.

Very large capacity (>1000m3 volume) airlift reactors have been built. Very tall vessels (aspect ratios up to 100:1), called deep-shaft reactors have been built

underground. These have very good gas-liquid mass transfer.

Used for single cell protein production from methanol and gas oil, for plant and animal cell culture, and in municipal/industrial waste treatment.

Fluidised bed reactors

Upward flow of liquid through a particulate biocatalyst bed is the basis of operation.

Particles must have a suitable size and density in order to fluidise.

Constant motion of particles avoids bed clogging and allows

direct air injection in aerobic

processes.

Particle damage by mechanical attrition can be a problem.

Used in waste treatment (microbes supported on sand particles) and

with microbial flocs for brewing and

vinegar production.


Fluidised bed reactor

for aerobic processes

Trickle bed reactors

Involve spraying the liquid onto the top of a packed bed:

Liquid trickles down over the bed in small rivulets.

Suitable for aerobic processes: air can be injected at the bottom of the

bed without significantly affecting

the liquid distribution.

Good gas-liquid mass transfer due to large G-L interfacial area.

Liquid hold-up is low, so liquid reaction capacity is relatively low.

Limited liquid flow rates: prone to bed flooding at high liquid flows.

Widely used for aerobic wastewater treatment.


Trickle bed reactor for aerobic processes

8.2 Scale-up

Overview of a complex and evolving field

From our discussions thus far, it is obvious that biochemical processes can involve

numerous mass transfer and biochemical reaction steps, depending on their exact

nature.

Whereas the latter (biochemical reaction) steps are intrinsically independent of

the scale of the process, mass transfer steps by their very nature, are very sensitive to

the physical scale and hydrodynamic environment of the process.

For these reasons, scale-up of a biochemical or chemical reaction is often a complex

and demanding task, yet one that is critical to the commercial success of any process.

Treatment of this topic in textbooks and the process engineering literature is often

limited, focussing on relatively isolated cases, with the lack of a comprehensive

overview of scale-up methods and their ranges of application. In part, this may be due

to the fact that scale-up methodologies are currently in the process of undergoing a

major evolution, with the advent of computational fluid dynamics (CFD) applied to

reaction systems.

This section attempts to give my overview of the field as it stands at the time of writing.

Biochemical & Chemical Reactor Scale-up Methods Overview

Method Used for Requires Good points Bad points

Scale-up from lab

data (recipe),

based on overall

reaction time.

Reactions in

low viscosity,

well mixed

media.

Throughput,

yield, and

reaction time or

space time (V/F).

Simple method. No good for poorly

mixed/viscous reaction

media. Unreliable if reaction

conditions other than those of

the original recipe are

chosen.

Ideal reactor

design equations.

Reactions in

low viscosity,

well mixed

media.

Throughput and

reaction kinetic

data. i if

immobilised

/catalyst.

Accurate method.

Can be used for

various reaction

conditions.

No good for poorly

mixed/viscous reaction

media.

Scale-up based

on empirical

mass transfer

correlations.

Multiphase

reactions or

high viscosity,

poorly mixed

media.

Throughput,

medium rheology,

and empirical

mass transfer

correlation.

Relatively simple

to use.

Unreliable if reaction

conditions other than those of

the original mass transfer

correlation are chosen.

Non-ideal reactor

models.

Any type of

reaction.

Throughput,

medium rheology,

and reaction

kinetic data.

Powerful,

accurate method.

Works for

multiphase or

poorly mixed,

viscous reaction

media

Complex to use. Requires

use of CFD (computational

fluid dynamics) methods and

significant computational

power. New: only developed

post-2005.

Scale-up from lab (recipe) data

Simplistic approach, only really useful for low viscosity, homogeneous reactions with no

variation of reaction conditions. Only needs throughput and reaction time:

Reactor sizing example

A batch enzymatic reaction time has been found to be 3.0 hours. Given a required

processing rate of 240kg per day of S at [S]o = 100g/litre , and assuming 18 hours per

day reactor operation, then we can size the reactor volume V as follows:

1. Number of batches per day = 18/3 = 6

2. Mass S required to be processed per batch = 240/6 = 40kg = 40000g

3. Since there is 100g of S in each litre of reaction mixture,

then volume of solution containing 40000g of S = 40000/100

= 400 litres = Reactor volume*

*Notes:

1. Normally 20% extra would be added to this to allow reactor headspace for stirring.

2. This calculation assumes no down time for filling/emptying/cleaning the reactor. If reactor down time is

significant, then it must be added to the reaction time for calculation purposes.

Ideal reactor design equations

Use of equations from sections 7.1.1-7.1.3 (or CG4003 section 5.5.1 for batch reactor)

to get reaction time, tR, or space time, (=V/F=1/D), together with throughput.

Need to know details of the biochemical/chemical kinetics (and i if an immobilised

species or heterogeneous catalyst is involved).

Can handle variations in reaction conditions, but no good for poorly mixed/viscous

reaction media or aerobic/low solubility gas-liquid reactions.

Once tR or is known, similar reactor sizing method used as in example in sect. 7.2.2.

Scale-up based on empirical mass transfer correlations

Three methodologies here, according to the type of reaction involved:

1) Mixing time-Reynolds number correlations

Scale-up is on the basis of achieving a desired mixing time, tm. Suitable for

homogeneous (liquid phase) reactions in viscous media. No good for multiphase or

heterogeneous reaction systems.


Concentration response after tracer is injected into a stirred tank

Mixing time, tm

Rei, Impeller Reynolds No.,

( = NiDi2/ )

Ni.t

m, D

ime

nsio

nle

ss

Mix

ing T

ime

, 3

1.54( )i m min i

i

VN t at high Re

D

Typical scenario:

Given a mixing time Rei correlation: estimate one

of V, Di, Ni, or tm, from the

equation, given values for

the other three.

Method needs: Lab/pilot

reactor physical

dimensions and stirrer

speed. Viscosity/rheology

data, medium density. tm.

(144)

2) Scale-up based on principles of geometric & dynamic similarity

Geometric similarity seeks to retain the same relative physical proportions (both internal

and external) of the small-scale (lab) reactor in the production reactor.

Dynamic similarity seeks to retain the hydrodynamic (fluid flow) characteristics on

scale-up, via correlations with appropriate dimensionless numbers and the stirrer power

input.

Suitable for heterogeneous liquid-solid catalyst reactions in viscous media. No good for

aerobic/gas-liquid reactions.

The single most important operating parameter which can maintain geometric and

dynamic similarity is impeller power input, P. Comparison of power input magnitudes in

different sized vessels is facilitated by use of the power number, Np:

(145)

where the first and second terms inside the brackets are the Reynolds and Froude

numbers respectively, and the latter three terms are associated with vessel geometry:

D = impeller diameter, DT = tank diameter, W = baffle width, and H = tank height.

etc

D

H

D

W

D

D

g

DNNDf

DN

PN Tp .....,,,,,

22

53

For geometric similarity, eq. (145) reduces to:

Np = f*(Rei , Fr) (146)

A simple power law function is often used to quantify this function, f*:

Np = K' . Reia . Frb (147)

where the values of K', a, and b must be determined by experiment and curve fitting.

Method needs: lab/pilot reactor physical dimensions, stirrer speed and power

consumption, viscosity/rheology data, medium density.

(from Chemical Engineering, Vol. 1 by Coulson & Richardson)

3) Scale-up on basis of maintaining desired kLa.

When gas-liquid mass transfer is the limiting factor in the overall reaction, this approach

is often used. Based on achieving the same kLa on the production scale as that which

gives best results on the lab scale, by using kLa - impeller power - operating variable

correlations.

Suitable for multiphase gas-liquid or gas-liquid-solid catalyst reactions (including

aerobic fermentations) in viscous media.

Method needs: kLa and stirrer power correlations. Viscosity/rheology data, medium

density.

7.2.5 Non-ideal reactor models

Based on solving the Navier-Stokes equations for fluid motion in tandem with

biochemical or chemical kinetic equations. Still essentially a research tool, but rapidly

coming into mainstream use in process engineering.

Can be applied to almost any system. Complex to use, heavily reliant on computational

power.

Method needs: Throughput, medium rheology, and reaction kinetic data.

Two mutually interdependent sets of parameters to evaluate:

Physical properties of the reactor contents: e.g. localised mass flow velocities,

viscosities, and temperatures.

Chemical/biochemical-originating properties of the reactor contents: e.g. changes in

composition, localised component flow rates, density and temperatures changes as a

result of chemical/biochemical reaction, and, reaction kinetics.

Assessing the physical property parameters involves solution of the Navier-Stokes

equations:

(148)

(149)

(150)

where: = density

t = time

x, y, and z are distance

u, v, and w are linear flow rates in the x, y, and z directions respectively

g = gravitational constant

P = pressure

= viscosity.

2

2

2

2

2

2

z

u

y

u

x

u

x

Pg

z

uw

y

uv

x

uu

t

ux

2

2

2

2

2

2

z

v

y

v

x

v

y

Pg

z

vw

y

vv

x

vu

t

vy

2

2

2

2

2

2

z

w

y

w

x

w

z

Pg

z

ww

y

wv

x

wu

t

wz

Determination of the reactor chemical property parameters requires the use of the ideal

reactor design algorithm (mole balance, energy balance, kinetics, stoichiometry, etc.,)

on a localised basis for different regions within the reactor, each of which is assumed

to be ideally mixed, but with different space time values.

Sequential solution of the Navier-Stokes equations and the reactor design algorithms

gives, on convergence, a detailed quantitative picture of mixing within the reactor and

allows prediction of non-ideal reactor conversion and product distribution.

Example of application of a CFD method (from PhD project of Dan Lane, UL)

A computational fluid dynamics (CFD) package such as FLUENT is used to build a physical simulation model of the reactor.

An advanced reaction engineering package such as gPROMS Multizonal is used to construct a chemical simulation model of the different mixing zones

within the reactor.

Both packages are then used sequentially and if necessary, iteratively, to solve the Navier-Stokes equations (FLUENT) and the reactor design

algorithms (gPROMS) for a given set of operating conditions.

Non-ideal reactor model

Ideal mixing model:

Polymath + Excel

Reactor design algorithms

Reaction

kinetics Rheology

data

gPROMS

Multizonal

CFD (FLUENT):

Navier-Stokes eqns

Reactor mixing pattern, predicted conversion and product distributions

Application of a CFD calculation method for non-ideal reactor simulation

Reactor physical model Feed

External recycle

Internal recycle stream

Outflow

Direction of

rotation

Tank

volume

1362 m3

CFD Velocity profile

Velocity decreases

Results: concentration profiles

950m3 of 1362m3

tank used

~31% of tank

not used!

0 200 400 600 800 100020

25

30

35

40

45

50

ideal

non-ideal

Un

reac

ted

ka

oli

n (

g/L

)

Time (mins)

0 200 400 600 800 1000210

220

230

240

250

Ca

us

tic (

g/L

)

Time (mins)

0 200 400 600 800 10000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Time (mins)

Dis

so

lve

d s

ilic

a (

g/L

)

Time (mins)

0 200 400 600 800 10000

5

10

15

20

25

30

So

da

lite

(g

/L)

One small impeller vs. three

Velocity contours

Intermig impeller: velocity vectors

One small impeller vs. large intermig impeller

Velocity contours

9. RECAP & REVISION

140904_AUT_CG4017_PART+B

Documents

Transcript of 140904_AUT_CG4017_PART+B