5. STERILIZATION OF LIQUID MEDIA The liquid media which

1

• 5. STERILIZATION OF LIQUID MEDIA

2

• The liquid media which contains all essential
• nutrients for cell growth is
• ? First heat sterilized with steam, then
• ? Cooled down before introduction into the
  bioreactor vessel

3

• Two types of sterilization
• ? Batch sterilization (see Fig. 5.1, and Table
  5.1 for corresponding temperature profile).
• ? Continuous sterilization (see Fig. 5.2a,
  5.2b)

4

• Two types of continuous sterilization
• Direct steam injection sterilizer (see Fig.
  5.2a)
• ? Plate heat exchanger sterilizer (see Fig. 5.2b)

5
FIG. 5.1 Types of equipment for batch
sterilization of media. Adopted from S. Aiba,
A.E. Humphrey and N.F. Millis. Media
Sterilization. In Biochemical Engineering, 2nd
Ed., Academic Press, Inc., New York (1973) 254.
6
TABLE 5.1. Temperature-Time Profile in Batch
Sterilization. Adopted from S. Aiba, A.E.
Humphrey and N.F. Millis. Media Sterilization.
In Biochemical Engineering, 2nd Ed., Academic
Press, Inc., New York (1973) 254.
7
FIG. 5.2a Direct steam injection type of
continuous sterilization of liquid media.
Adopted from S. Aiba, A.E. Humphrey and N.F.
Millis. Media Sterilization. In Biochemical
Engineering, 2nd Ed., Academic Press, Inc., New
York (1973) 257.
8
FIG. 5.2b Plate heat exchanger type of continuous
sterilization of liquid media. Adopted from S.
Aiba, A.E. Humphrey and N.F. Millis. Media
Sterilization. In Biochemical Engineering, 2nd
Ed., Academic Press, Inc., New York (1973) 257.
9
? Fig. 5.3a and 5.3b show the temperature- time
profiles for the two types of continuous
sterilization.
FIG. 5.3a Sterilization temperature vs. time
profile for direct steam injection continuous
sterilizer. Adopted from S. Aiba, A.E. Humphrey
and N.F. Millis. Media Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 258.
10
FIG. 5.3b Sterilization temperature vs. time
profile for plate heat exchanger sterilizer.
Adopted from S. Aiba, A.E. Humphrey and N.F.
Millis. Media Sterilization. In Biochemical
Engineering, 2nd Ed., Academic Press, Inc., New
York (1973) 257.
11

• 5.1 KINETICS OF THERMAL DEATH OF MICROORGANISMS
• Heat is used to kill
• ? Contaminant microorganisms
• ? Spores
• present in a liquid nutrient medium.
• The destruction of microorganisms by heat means
• ? Loss of Viability of these microorganisms and
  spores.

12

• ? The thermal death of microorganisms follow
  first order kinetics given by Eq. 5.1.
• dN/dt -kN...(5.1)
• Where
• N Number of viable microorganisms
• t Sterilization time, min
• k Thermal death rate constant, min-1
• If at time t0 0, N N0, then integration of
  Eq.
• 5.1 results in Eq. 5.2.
• N N0 e-kt (5.2)
• Also
• ln(N/N0) -kt .(5.3)

13

• The term decimal reduction time, D, is used to
  characterize the death rate constant.
• D is defined as the sterilization time required
  to reduce the original number of viable cells by
  one tenth.
• N/N0 1/10 e-kD
• ln(0.10) -kD
• D 2.303/k.(5.4)

14

• ? Fig. 4.4 and 4.5 shows typical data of N/N0
  vs. sterilization time for spores of Bacillus
  stearothermophillus, one of the hardest spores
  to kill, and vegetative cells of E. coli

15
FIG. 4.4 Typical thermal death rate data for
spores of Bacillus stearothermophilus Fs 7954 in
distilled water where N number of viable spores
at any time, N0 original number of viable
spores. Adopted from S. Aiba, A.E. Humphrey and
N.F. Millis. Media Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 241.
16
FIG. 4.5 Typical death rate data for E. coli in
buffer, where N number of viable spores at any
time, N0 original number of viable spores.
Adopted from S. Aiba, A.E. Humphrey and N.F.
Millis. Media Sterilization. In Biochemical
Engineering, 2nd Ed., Academic Press, Inc., New
York (1973) 241.
17

• The thermal death rate constant k is given by
  Eq. 5.5 and follows the typical Arrhenius
  equation.
• K A e-E/RT..(5.5)
• Where
• A empirical constant
• E Activation energy for thermal death of
  microorganism
• T Absolute temperature, oK
• R Gas constant 1.98 cal/g mole oK

18

• ? Fig. 4.6 and 4.7 shows the Arrhenius plots of
  k for spores of B. stearothermophilus, and
  vegetative cells of E. coli, respectively.

19
FIG. 4.6 Correlation of isothermal death rate
data for spores of Bacillus stearothermophilus Fs
7954, where k reaction rate constant and T
absolute temperature. Value of E (activation
energy) 68.7 kcal/ g mole. Adopted from S.
Aiba, A.E. Humphrey and N.F. Millis. Media
Sterilization. In Biochemical Engineering, 2nd
Ed., Academic Press, Inc., New York (1973) 242.
20
FIG. 4.7 Correlation of isothermal death rate
data with temperature for E. coli, where k
reaction rate constant and T absolute
temperature. Value of E (activation energy) 127
kcal/g mole. Adopted from S. Aiba, A.E. Humphrey
and N.F. Millis. Media Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 243.
21

• For spores of B. stearothermophilus, the
• following kinetic parameters apply
• ? A 7.94 x 1038 min-1
• ? E 68.7 x 103 cal/g mole
• ? The higher the value of E, the more difficult
  it is to kill by thermal denaturation a
  microorganism or spore.

22

• ? The value of activation energy, E, due to
  thermal denaturation (death) for vegetative
  microbial cells and spores is in the range of
  E 50 to 100 kcal/g mole.

23

• ? For the thermal denaturation of enzymes,
  vitamins, and other fragile nutrients, the
  activation energy, E, is in the range of
• E 2 to 20 kcal/ g mole.
• ? For a given liquid medium containing both, it
  is easier (faster) to denature thermally,
  enzymes and vitamins and other nutrients, and
  more difficult (slower) to denature (kill)
  vegetative cells.

24

• ? In order to find the value of k for any system
  (spores and vegetative cells, nutrients) it is
  important to know both A and E in the Arrhenius
  Eq. 5.5.
• ? Sterilization at relatively high temperatures
  with short sterilization times is highly
  desirable because it favours the fast killing
  of vegetative cells and spores with minimal
  denaturation of nutrients present in the liquid
  medium.

25

• 5.2 BATCH STERILIZATION OF LIQUID MEDIA
• During batch sterilization
• ? Both temperature and time change
• ? Also k changes with time, since k f (T)
• Table 4.1 shows the sterilization temperature as
  a
• function of time for batch sterilization using
• different types of heat transfer and cooling.
• dN/dt -kN -Ae-E/RT N..(5.6)

26

• Integrating Eq. 5.6 from t0 0, N N0 to any
• time t t and N N, we get Eq. (5.7).
• ln(N0/N) ?0t kdt A ?0t e-E/RTdt .....(5.7)
• We define
• ? ln (N0/N).(5.8)

27

• In sterilization design
• ? ? Is used as a criterion of design.
• ? ? Specifies the level of sterilization
  required for a liquid nutrient medium.

28

• During batch sterilization, there are three
  periods
• of sterilization
• ? Heating of the liquid medium period
• ? Holding at constant temperature period
• ? Cooling period

29

• During each period, a separate value of ? is
  calculated
• ?Total ln(N0/N) ?heating ?holding
  ?cooling(5.9)
• ? ?heating ln(N0/N1) ?0t1 kdt
• ? ?holding ln(N1/N2) ?t1t2 kdt
• ? ?cooling ln(N2/N) ?t2t3 kdt
• Where
• N No. of contaminants after sterilization
• N0 No. of contaminants before sterilization
• N1 No. of contaminants after heating period
  t1
• N2 No. of contaminants after holding period
  t2
• t1, t2, t3 Sterilization times during,
  heating, holding and cooling.

30

• Total batch sterilization time, t, is given by
  Eq. 5.10.
• t t1 t2 t3 ...(5.10)

31

• EXAMPLE OF BATCH STERILIZATION
• ? Calculate the total degree of batch
  sterilization, ?total, for a liquid medium
  inside a bioreactor vessel, which reaches a
  maximum temperature 120 oC, and then cooled
  off. Assume that the liquid medium contains
  spores of B. stearothermophilus, and the initial
  total number is N0 6 x 1012 spores. The
  temperature vs. time profile during batch
  sterilization is given below.

32

• t (min) T1 (oC)
• 0 30
• 10 50
• 30 90
• 36 100
• 43 110
• 50 120
• 55 120
• 58 110
• 63 100
• 70 90
• 102 60
• 120 44
• 140 30

For spores of B. stearothermophilus k 7.94 x
1038 exp(-68.8 x 103)/RT min-1 R 1.98 cal/g
mole oK
33
FIG. 4.8 Batch sterilization k and T vs. t
example calculation. Area under the curve k vs. t
is total degree of sterilization, ?total.
Adopted from S. Aiba, A.E. Humphrey and N.F.
Millis. Media Sterilization. In Biochemical
Engineering, 2nd Ed., Academic Press, Inc., New
York (1973) 256.
34

• ? Fig. 4.8 shows the temperature-time profile
  and the value of k as a function of T i.e. k
  f (T) as given in the previous slide.

35

• Examining Fig. 4.8, it is also evident that the
  values of k are a function of t i.e. k f
  (t), ranging between 0 to 34 min, and between
  64 to 140 min. Therefore, the area under the
  curve k (min-1) vs. t (min) is the graphical
  integration, which gives
• ? ?total ln(N0/N) ?0140 kdt 33.8
• ? N N0/exp(33.8) 6x1012/4.77698x104
• 1.256x10-2

36

• 5.3 CONTINUOUS STERILIZATION OF LIQUID MEDIA
• ? Fig. 4.2a and 4.2b show the two most common
  types of continuous sterilizers used with steam
  to carry out the sterilization of liquid
  fermentation media.

37

• ? In both systems, the liquid medium is heated
  rapidly the desired high temperature either by
  direct steam injection or by plate heat
  exchangers and then it goes through a holding
  section, which is a tube of given diameter and
  length to give the desired residence (holding)
  sterilization time

38

• The holding tubular section is well insulated
  and it is held at the same sterilization
  temperature along its length.
• ? Fig. 4.3a and 4.3b give approximate
  temperature-time profiles for the steam
  injection and plate heat exchanger types
  respectively.

39

• ? NOTE The direct steam injection gives much
  faster rise in temperature but, the original
  liquid medium is being diluted by the amount of
  the steam condensate during the injection of the
  steam.
• Therefore, an enthalpy and mass balance is
  required at the steam injection nozzle.

40

• ? The problem design and size both the
  diameter and length of the tubular holding
  section which is held at a given temperature
  assuming a desired degree of sterilization,
  using the thermal rate constant and its
  Arrhenius relationship for spores of B.
  stearothermophilus, which is one of the hardest
  spores to kill by steam sterilization.

41

• ? NOTE In both the injection type and plate
  exchanger type of continuous sterilizers, it is
  required to design (size-up) the length and
  diameter of the tubular holding section.

42

• DESSIGN OF THE TUBULAR (HOLDING)
• SECTION IN A CONTINUOUS STERILIZER
• ? Consider the tubular holding section in Fig.
  4.9 having length L and diameter dt, which is
  held at constant sterilization temperature T.

43

• ? The number of contaminants entering and
  leaving the tube are N0 and N per mL of
  fermentation liquid medium, which has physical
  properties, viscosity ?, density ?, and specific
  heat Cp, at the given temperature T.

44
FIG. 4.9 Tubular sterilizer

• ? The volumetric flow rate of liquid medium
  through the tube is Q (m3/min).
• ? Depending on the flow rate and diameter of
  the tube and the physical properties of the
  fermentation liquid medium, the radial velocity
  profile of the fluid elements inside the tube
  will change.

45

• ? The velocity profile will also determine the
  residence (sterilization) time each fluid
  element will spend inside the tube of given
  length L.
• ? Therefore, the uniformity of sterilization
  will depend on the velocity profile.

46

• Ideally, we want a plug flow, flat velocity
  profile, to make sure that all fluid elements
  spend exactly the same residence time and
  therefore all have the same sterilization time.
• ? However, in real practice for real fluids the
  velocity profile changes from ideal flat
  profile as the pipe Reynolds's Number changes.

47

• In addition, we need to account for axial
  dispersion (back mixing) of fluid elements
  inside the pipe, which is characterized by the
  Peclet Number (Pe).
• ? The axial dispersion coefficient, Ez, is also
  referred to as eddy diffusivity, which can be
  measured by using dye dispersion techniques.

48

• The axial dispersion is part of the Peclet
  Number and it affects
• ? the mass balance of number of
  contaminants
• ? and their destruction by heat
  sterilization.

49

• ? Fig. 4.10 shows three different types of
  velocity profiles in tubular flow of liquids.
• ? The velocity profile can be measured very
  easily by using a pitot tube and manometer.
• ? As seen from Fig. 4.10 the turbulent flow
  regime is desirable for two reasons

FIG. 4.10 Distribution of axial velocity profiles
in fluiids exhibiting three different types of
flow inside round pipes ? mean velocity of the
fluid. Adopted from S. Aiba, A.E. Humphrey and
N.F. Millis. Media Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 259.
50

• ? First, the velocity profile is fairly flat
• ? Secondly, the turbulence inside the pipe
  gives excellent heat transfer characteristics
  which ensures sterilization temperature
  uniformity in all liquid elements inside the
  pipe.

51

• DIFFERENTIAL MASS BALANCE ON
• CONTAMINANTS COMBINED WITH 1ST
• ORDER THERMAL DEATH KINETICS
• ? Consider a differential length element dZ
  along the length of the tubular sterilizer, as
  shown below

52

• ? First order thermal death kinetics is given
  by Eq. 5.11
• dN/dt -kN . (5.11)
• Making a differential mass balance on the number
• of contaminants, we have the following
• ? Rate in Rate out Rate of disappearance
• Rate of accumulation

53

• At steady-state
• Rate of accumulation 0
• Rate in Convective or bulk flux Diffusive
  (axial dispersion) flux.
• ? Rate out Convective or bulk flux
  Diffusive (axial dispersion) flux.

54

• ? Convective flux u.N
• Diffusive (axial dispersion) flux
• -EZ(dN/dZ)
• where Ez axial dispersion coefficient (m2/s)
• Rate of disappearance of contaminants
• dN/dt -kN

55

• Therefore, for differential fluid element dZ we
• have
• (Axial dispersion in out) (Bulk transport
  in out) (Rate of disappearance) 0
• EZ (d2N/dZ2) - u (dN/dZ) kN 0 .(5.12)

56

• We can transform Eq. 5.12 by introducing the
  following dimensionless variables
• Ñ N/N0 Ž Z/L ? t/?
• PeB uL/EZ Nr kL/u

57

• Where t sterilization time (min)
• mean residence time in the tube
• AL/Q (cross section area of
  tube)(length)/(volumetric flow rate of
  medium)
• u Mean velocity of fluid
• Q/A m3/min/m2

58

• PeB Modified Peclet No. (or Bodenstein No.)
• uL/EZ dimensionless
• EZ Axial dispersion coefficient (m2/min)

59

• When PeB ? 0,
• then EZ ? ?, and therefore we have perfect
  backmixing, as in the case of a perfectly mixed
  stirred tank vessel.
• When PeB ? ?,
• then EZ ? 0, which means we have no backmixing
  at all, i.e., we have a perfect plug flow of the
  fluid through the tube as in the case for
  perfect plug flow tubular vessel.

60

• After introducing all dimensionless parameters in
• Eq. 5.12 then we have
• d2Ñ/dŽ2 - u (dÑ/dŽ) (PeB) (Nr)(Ñ)
  0 .....(5.13)

61

• Using the following boundary conditions, we can
• solve Eq. 5.13
• Ž ? 0
• then dÑ/dŽ (PeB) (1 Ñ) 0
• Ž 1
• then dÑ/dŽ 0
• The solution to Eq. 5.13 using the above boundary
• conditions is shown in section media
  sterilization of the
• book Biochemical Engineering by S. Aiba, A.E.
• Humphrey, N.F. Millis, Academic Press, New York
  (1973).

62

• Figure 4.11 is a graphical solution of equation
  5.13
• for continuous sterilization in a tube at a
  constant
• temperature, T.
• This Figure shows the degree of sterilization,
  N/N0
• As a function of the dimensionless number,
• Nr at different modified Peclet numbers PeB
• shown on different straight lines for PeB 10 to
• 1000, and PeB ?.
• Please, note that Nr kL/u.

63

• k thermal death rate constant min-1
• L length of tubular sterilizer m
• u average velocity of fluid medium in the
  tubular sterilizer of length L m/min.
• Also, u volumetric flow rate of
  medium/cross-section area of the tubular
  sterilizer.
• For adequate sterilization design we assume a
  modified Peclet number PeB 1000, which is close
  to PeB ?

64

• Fig. 4.11. Degree of sterilization, N/N0, as a
  function
• of Nr kL/u at different PeB numbers for
  tubular
• continuous sterilizer.

65
(No Transcript)
66

• For a given
• degree of sterilization N/N0,
• Peclet No. PeB,
• Flow rate Q,
• dimensions of the tubular sterilizer (L and dt),
• we can find the thermal death kinetic constant
  k,
• and from the Arrhenius equation we can find the
• required sterilization T, at which the tubular
• sterilizer must be held constant.

67

• For a given
• Tube diameter dt
• and volumetric flow rate of liquid medium Q

68

• we can
• calculate the tube Reynolds No. and then
• calculate the axial dispersion coefficient EZ
  from Fig. 4.12 (shown as DZ rather than EZ),
  and then
• calculate the modified Peclet No. and thus
• locate the PeB straight line in Fig. 4.11

69

• If sterilization temperature is specified, then
  we
• can
• Calculate k and then
• Using Fig. 4.11 we can find the length of the
  tubular sterilizer.

70

• ? Depending on what is given and assumed, there
  are different solutions (including trial and
  error) to sterilization design problems using
  Fig. 4.11.

71

• Fig. 4.12 shows the correlation for axial
  dispersion as a function of Reynolds Number in
  pipes, where
• D/udt is plotted against pipe Reynolds Number
  Re u?dt/?.
• In this figure, D EZ dispersion coefficient
• (m2/min)
• u u m/min, and dt tube diameter m.
• For sterilization design we make sure that we
  have turbulent flow conditions, where the
  Schmidt Number is not a variable.

72
FIG. 4.12 Dimensionless correlation for axial
dispersion of fluids flowing in pipes at
different Reynolds Numbers.
73

• 5.4 EXAMPLE OF DESIGN FOR
• CONTINUOUS LIQUID MEDIUM
• STERILIZATION IN A TUBULAR STERILIZER
• A tubular sterilizer is available that has 50 m
  length and
• 0.155 m diameter, and it is required to sterilize
  a liquid
• medium originally at 40 oC with flow rate of
  45,000 kg/hr
• (45 m3/hr). A direct steam injector is used at
  the entrance
• of the tubular sterilizer, which raises the
  liquid
• temperature almost instantly to temperature T and
  is held
• constant throughout the 50 m length using proper
• insulation. The required degree of sterilization
  assuming
• spores of Bacillus stearothermophilus is

74

• N/N0 1.67 x 10-16
• N0 105 spores/mL
• The physical properties of the liquid medium at
• the temperature of sterilization T are assumed to
• be as follows
• Density ? 103 kg/m3
• Viscosity ? 3.6 kg/m.hr
• Specific heat Cp 1 kcal/kg oC

75

• Calculate the following
• The thermal death rate constant k, assuming the
  liquid medium is contaminated with spores of B.
  stearothermophilus.

76

• The temperature T of sterilization to meet the
  above conditions and sterilization criteria.
• 3. The nominal sterilization residence time of
  the liquid medium inside the 50 m long tubular
  sterilizer.

77

• Find the steam flow rate required (kg/hr) at the
  direct injection nozzle, assuming steam at 9
  kg/cm2 gauge pressure, having a latent heat of
  condensation, ? 481.7 kcal/kg.
• 5. Find the dilution ( increase in volume) of
  original liquid medium resulting from the
  addition of steam condensate at the injection
  nozzle. Does the increase affect significantly
  the Reynolds Number and thus the axial dispersion
  coefficient EZ?

78

• SOLUTION
• Assume spores of B. stearothermophilus
• k 7.94 x 1038 exp(-68.7 x 103/1.98T) min-1
• Cross sectional area of tubular sterilizer
• A ?dt2/4 (?/4) (0.155 m)2 1.88 x 10-2 m2
  

79

• Ave. fluid velocity, u Q/A
• (45 m3/hr)/(1.88 x 10-2 m2)
• 2.393 x 103 m/hr 39.89 m/min 0.655 m/s
• Reynolds No. Re u?dt/?
• (2.393 x 103 m/hr)(103 kg/m3)(0.155 m)/(3.6
  kg/m.hr)
• 1.030 x 105

80

• Using the above Reynolds number, which is in the
• turbulent flow regime, we can find the axial
• dispersion coefficient EZ (D) from Figure 4.12.
• At Re 1.030 x 105 We get D/udt 0.2
• Therefore, EZ (0.2)(2.393 x 103 m/hr)(0.155 m)
  74.18 m2/hr

81

• We can calculate the modified Peclet number
• PeB uL/EZ (2.393 x 103 m/h)(50
• m)/(74.18 m2/hr) 1,613
• From Figure 4.11, the straight line that
• corresponds to PeB 1,613 is very close
• to PeB ? (plug flow), i.e. we have a
• fairly flat velocity profile across the pipe
• diameter, which means all fluid elements
• of the liquid medium have almost

82

• the same residence time and thus we
• Have a uniform sterilization.
• It is normally a good sterilization practice to
• use PeB ? 1,000, since this line is very close to
• PeB ? (Figure 4.11).
• Use figure 4.11 to find the corresponding
• value of Nr kL/u, since we know N/N0 1.67
• x 10-16, and the straight line at PeB 1,613.

83

• Nr 36, from which we can get k (36)(39.89
• m/min)/(50 m)
• Therefore, k 28.72 min-1
• The corresponding sterilization temperature for k
• 28.72 min-1 can be found from the Arrhenius
• equation for B. stearothermophilus, T 401.5oK
• 129.5oC.
• Nominal sterilization residence time (50
  m)/(39.89
• m/min) 1.25 min

84

• To find the flow rate of steam required we
  perform
• an enthalpy balance at the injection nozzle.
• The heat of condensation from steam is used to
• raise the temperature of the liquid medium from
• 40oC to 129.5oC under pressure of 9 kg/cm2 gauge.
• GS?S GLCp(?T) where
• GS mass flow of rate of steam kg/hr.
• ?S heat condensation of steam at 9 kg/cm2
  gauge,
• kcal/kg steam

85

• GL mass flow of liquid medium, kg/hr
• Cp specific heat of liquid medium, kcal/kg oC
• ?T temperature rise of liquid medium, oC
• GS (GLCp? T)/ ?S
• GS (45,000 kg/hr)(1 kcal/kg oC)(129.5 -
• 40oC)/(481.7 kcal/kg)
• 8,361 kg Steam/hr

86

• increase in volume due to steam condensate
• addition to the liquid medium ( dilution)
• 8,361 kg Steam/hr/45,000 kg/hr 18.58
• New u (45 m3 8.361 m3 medium)/hr
• /(1.88 x 10-2 m2) 2,838 m/hr
• Therefore, New Reynolds Number is
• Re (2.838 x 103)(103)(0.155)/(3.6)
• 1.22 x 105

87

• From Fig. 4.12 we find the corresponding
• approximate value of DZ/udt 0.2, which gives
  the same value of axial dispersion coefficient
  EZ 74.18 m2/hr. Therefore, the steam injection
  diluted the original liquid medium by 18.58
  while the axial dispersion coefficient EZ
  remained the same.

88

• 6. AIR STERILIZATION BY FIBROUS BED FILTERS

89

• In aerobic fermentation systems sterile air
• must be provided
• ? To the bioreactor vessel as the source of
  oxygen for the metabolic activity and growth of
  the microorganisms.
• ? For the aseptic operation of a bioreactor
  system.
• The ambient air contains
• ? Dust and other inert particles
• ? Bacteria, spores and other undesirable
  contaminant microorganisms.

90

• Table 6.1 shows representative species of
  bacteria and spores that may be present in the
  air and their approximate size.
• Current Methods used for Air Sterilization
• ? Packed-beds with glass wool fibers that
  act as filters, and
• ? Filtration membranes of specified pore
  sizes less than the size of contaminants
  which prevents the contamination of the
  liquid medium the bioreactor.

91

• Aseptic operation of the bioreactor means that
  there are no contaminating microorganisms. This
  is very important.

92

• Table 6.1 Representative sizes of air-borne
  bacteria and spores.
• __________________________________________________
  ________
• Species Width (?m) length (?m)
• __________________________________________________
  ________
• Vegetative cells
• Aerobactor aerogenes 1.0 1.5 1.0 2.5
• Bacillus cereus 1.3 2.5 1.1 25.8
• Bacillus licheniformis 1.5 0.7 1.8 3.3
• Bacillus megaterium 0.9 2.1 2.0 10.0
• Bacillus mycoides 0.6 1.6 1.6 13.6
• Bacillus subtilis 0.5 1.1 1.6 - 4.8
• Micrococcus aureus 0.5 1.0 0.5 1.0
• Proteus vulgaris 0.5 1.0 1.0 3.0
• Bacterial Spores
• Bacillus megaterium 0.6 1.2 0.9 1.7
• Bacillus mycoides 0.8 1.2 0.8 1.8

93

• Membrane air filters are usually made of the
• following materials
• 1. Ceramic materials
• ? are durable
• ? can be backwashed
• ? are steam sterilizable
• ? can be used many times
• ? are economical

94

• 2. Many other polymeric materials, such as
• ? polyvinyl alcohol (PVA)
• ? cellulose acetate
• Polysulfone
• Other composite polymeric materials
• 3. A pre-filter is used before the main
  filtration
• membrane to remove large size particles and other
• contaminants. This protects the main membranes
• from plugging. Most membranes are steam
• sterilizable.

95

• 6.1 MECHANISMS OF AIR FILTRATION AND DESIGN OF
  FIBROUS PACKED BEDS

96
FIG. 6.1 Schematic diagram of an air filtration
cylinder packed with glass fibers. Typical glass
fiber diameter is 10 to 20 ?m. N1 and N0 is the
number of contaminating particles per m3 entering
and leaving the air filter. Q volumetric air
flow rate L length of bed DT diameter of
bed.
97

• ? These fibers usually range in diameter from10
  to 20 ?m.
• ? Assuming a typical microbial cell or spores
  size of about 1 ?, the glass fiber diameter is
  about 10 to 20 times larger.
• ? Depending on the degree of solid packing
  fibers, the void (air) volume fraction, ?, in a
  packed bed is usually about 0.955 to 0.975,
  corresponding to solid fiber volume fraction,
  (1 - ?), of 0.045 to 0.025.

98

• Fig. 6.1 As the air passes through the voids of
  the
• packed bed filter, the microbial particles and
• spores are trapped within the bed, and the exit
  air becomes free of any contaminants.

99

• Several mechanisms used for the entrapment of
• micron-sized contaminants depends on
• ? the air flow rate (specifically the air
  velocity)
• ? Velocity of the particles around the each
  fiber

100

• To appreciate the different mechanisms by
  which micron-sized solid particles are
  collected by single fibers, consider the single
  fiber shown in Fig. 6.2.
• ? Consider the cross-section of a solid fiber of
  
• diameter df, and the flow patter of air around
  the fiber shown as solid lines along which a
  solid particle of diameter dp is carried. The
  broken flow lines show the path of solid
  particles as they approach the solid fiber. Let
  b be the width of the air stream that flows
  around the fiber.

101
FIG. 6.2 Cross-section of flow patterns around a
single cylindrical fiber of diameter df, with air
flow lines having width b, and a particle of
diameter dp intercepted by the fiber. Laminar air
flow is assumed around the fiber cross-section.
Broken flow lines indicates the flow patter of
particle. Adopted from S. Aiba, A.E. Humphrey
and N.F. Millis. Air Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 280.
102
Five different mechanisms of collection of air
born particles by fibrous beds 1. Inertial
impaction 2. Direct interception 3. Diffusion
4. Settling by gravitational force
5. Collection of solid particle by
electrostatic forces.
103

• Mechanism no. 4 can be neglected because
• ? the solid particles are extremely small in
  the order of 1?, and
• ? the gravitational force is not a significant
  contribution to the overall total collection
  efficiency.

104

• Studies on electrostatic charge of Bacillus
  substilis spores in air have shown that
• 1. About 70 have positive charge
• 2. 15 have negative charge
• 3. 15 are neutral

105

• The most important three mechanisms for
  particle collection by fibrous beds
• 1. Inertial impaction
• 2. Direct interception
• 3. Diffusion
• All three are shown in Fig. 6.3.

106
FIG. 6.3 The three mechanisms of particle
collection by a single fiber of diameter df.
Particle diameter dp, and b width of air stream.
Dotted lines show path of particle. (1) inertia
of particle results in impact of fiber (2)
direct particle interception by the fiber,
particle moving outside b will not be
intercepted (3) particle moves by diffusion and
touches fiber. Adopted from S. Aiba, A.E.
Humphrey and N.F. Millis. Air Sterilization. In
Biochemical Engineering, 2nd Ed., Academic Press,
Inc., New York (1973) 280.
107

• 6.1.1. INERTIAL IMPACTION
• Inertial impaction is due to
• The impact contact with the fiber of the solid
  particle moving with a velocity u which deviates
  from the air stream line velocity due to the
  particles inertia.

108

• For the particle inertial impaction on single
  fibers
• of different diameters there is
• A particular critical air velocity, Vc, below
  which the inertial impaction can be neglected.
• The critical air velocity Vc is a function of
• ? Air viscosity ?g,
• ? Particle density ?p
• ? Particle diameter dp
• ? Fiber diameter df

109

• Eq. 6.1 gives the critical air velocity, which is
• based on
• The motion of particle dp following Stokes
  Law, and
• ? Using the Cunninghams correction factor C
  for slip velocity.

110

• VC (1.125) ?df/C?pdp2 ..(6.1)
• Where
• VC critical air velocity below which inertial
  impaction of particle may be neglected
• ?g air viscosity 1.80 x 10-4 g/cm.sec at
  20 oC
• df fiber diameter
• C Cunninghams correction factor
• ?p particle density, typical density of
  bacteria and spore particles 1 g/cm3
• dp particle diameter

111

• Substituting the appropriate values of ?g for
  air, C from an empirical correlation, and ?p,
  then equation 6.1 becomes
• VC (constant) (df/dp2) ....(6.2)

112

• The results of Eq. 6.2 are shown graphically
  in Fig. 6.4, where the critical velocity VC is
  plotted against particle diameter dp at
  different diameters df of single fibers.
• Inertial impaction of a particle will take
  place only when the particle is within the air
  stream of width b.
• ? If the particle is outside width b there will
  be no inertial impaction.

113
FIG. 6.4 Critical velocity of air, Vc, as a
function of particle diameter dp, using different
diameters df of single fibers. Air at 20 oC and
particle density ?p 1 g/cm3. Adopted from S.
Aiba, A.E. Humphrey and N.F. Millis. Air
Sterilization. In Biochemical Engineering, 2nd
Ed., Academic Press, Inc., New York (1973) 281.
114

• The theoretical value of collection efficiency of
• single fibers due to inertial impaction is ?o/
  and is
• given by equation 6.3.
• ?o/ (b/df) .(6.3)
• where
• ?o/ collection efficiency of single fiber due
  to inertial impaction, (-)
• b width of air stream (Fig. 6.2 and 6.3)
• df diameter of single fiber

115
6.1.2. INTERCEPTION OF PARTICLE ? As shown
in Fig. 6.2 and 6.3, physical interception of
the particle by the fiber is possible when the
air streamline is at a distance dp/2 from the
fiber surface at a location ? ?/2, which is a
limiting condition for the deposition of the
particle on the fiber surface.
116

• According to Langmuir the single fiber collection
• efficiency, ?o//, is a function of two
  dimensionless
• numbers
• ? The Reynolds Number of the air based on
  fiber diameter df, and
• ? The interception parameter, Nr dp/df,
  and it is given by Eq. 6.4.

117

• ? o// 1/2 (2.00 - lnNRe)PR ...(6.4)
• where
• ?o// single fiber collection efficiency due
  to interception, dimensionless
• NRe Reynolds Number of air based df
• V?df/?,
• where ? and ? the density and viscosity of air,
• V velocity of air, df fiber diameter
• PR 2(1 NR)ln(1 NR) (1 NR) 1/(1 NR)
• NR interception parameter dp/df

118

• 6.1.3. DIFFUSION OF THE PARTICLE
• ? Small particles such as bacteria and spores of
  about 1? in diameter and small densities of
• about 1 g/cm3 display Brownian motion in the
• air, and may be collected by diffusion on the
• surface of fibers as shown in Fig. 6.3.

119

• The diffusivity of light and very small
  micron particles is given by Eq. 6.5.
• DBM C kT/(3??dp)....(6.5)
• Where
• DBM diffusivity of particle due to
  Brownian motion (BM), cm2/sec.
• k Boltzman constant 1.38 x 10-16 cm2
  g/s2 oK
• T Absolute air temperature, oK
• dp Particle diameter, cm

120

• The single fiber collection efficiency, ?o/// due
  to
• diffusion only, is given by Eq. 6.6.
• ?o/// 1/2(2.00 lnNRe)(a b- c).(6.6)
• Where
• ?o/// single fiber collection efficiency due
  to diffusion, dimensionless
• NRe Reynolds Number of air based fiber
  diameter df
• Xo effective radius of displacement of
  particle due to diffusion

121

• a 2(1 2Xo/df)ln(1 2Xo/df)
• b (1 2Xo/df)
• c 1/(1 2Xo/df)
• The value of 2Xo/df is given by Eq. 6.7.
• 2Xo/df (1.12)(2)(2.00 - lnNRe)(DBM)/Vdf..(6.7)
  

122

• Where
• NRe V?df/? Reynolds Number of air
• V air velocity through the filter bed
  superficial air velocity/void fraction of
  bed (i.e. V Ug/?)
• DBM Particle diffusivity (Eq. 6.5)

123

• 6.1.4. OVERALL PARTICLE COLLECTION EFFICIENCY BY
  THE FIBROUS BED FILTER
• For a single fiber, the total particle
  collection efficiency, ?o is the sum of the
  three efficiencies due to inertial impaction,
  ?o/ (Eq. 6.3), interception ?o// (Eq. 6.4), and
  diffusion ?o/// (Eq. 6.6).
• ?o ? o/ ? o// ? o/// ( 6.7)
• Please, note that Eq. (6.7) shows the total
  collection
• efficiency for a single fiber only.

124

• ? In practice, the collection efficiency for
  inertial impaction ?o/ may be neglected.
• The overall single fiber efficiency, ?o is the
  sum of interception, ?o// and diffusion, ?o///.
• Fig. 6.5 shows all single fiber collection
  efficiency
• data in literature correlated with dimensionless
• parameters.

125
FIG. 6.5 Dimensionless correlation of total
collection efficiency for single fibers, ?o, due
to to interception and diffusion. The ordinate
and abscissa are ?oNRNPe and NRNPe1/3NRe1/18
respectively, NR interception parameter, NPe
Peclet number, and NRe Reynolds number.
Adopted from S. Aiba, A.E. Humphrey and N.F.
Millis. Air Sterilization. In Biochemical
Engineering, 2nd Ed., Academic Press, Inc., New
York (1973) 284.
126

• In order to calculate the total pressure drop ?P
• over the fibrous packed bed of length L, Fig. 6.6
• can be used, where, the modified drag coefficient
• CDM is plotted against the Reynolds number of the
• air flowing through the packed bed.

127
FIG. 6.6 Dimensionless between the modified drag
coefficient, CDM, and the Reynolds number of air.
The total pressure drop across the fibrous bed
filter is ?P. The length of the fibrous bed is L
128

• ? NOTE The air velocity V is equal to the
  superficial air velocity Ug based on the
  cross- sectional area of the bed divided by the
  void volume fraction, ?, occupied by the air
  (i.e. V Ug/ ?).

129

• 6.1.5. CALCULATION PROCEDURE
• FOR THE DESIGN OF FIBROUS
• FILTER BEDS USED FOR AIR
• STERILIZATION
• The following steps are used to calculate the
  single
• fiber and overall fibrous bed efficiency, and
  total
• pressure drop across the fibrous bed.

130

• STEP 1 Find overall fibrous bed particle
  remova removal efficiency
• ? (Ni N0)/Ni...............................
  .....(6.9)
• Where Ni and N0 are the number of particles per
• m3 entering and leaving the fibrous bed,
• respectively.

131

• STEP 2 Calculate the following parameters
• NR dp/df interception parameter(6.10)
• NRe V?df/?...(6.11)
• NSc (?/?)/DBM..(6.12)
• NPe NScNRe..(6.13)
• Then use Fig. 6.5 to find the value of ?o, the
  single fiber particle
• collection efficiency.

132

• STEP 3 Calculate ?? given by
• ?? ?o(1 4.5?)..(6.14)
• Where
• ? void volume fraction of fibrous bed.
• (1 - ?) ?, for 0 lt ? lt 0.1

133

• STEP 4 Find the length of fibrous bed, L,
• ?? ?(1 - ?) df/4?Lln1/(1 -
  ?)..(6.15)
• STEP 5 Find pressure drop per unit bed length
  (?P/L) by using Fig. 6.6.

134

• NOMENCLATURE
• DBM particle diffusivity, cm2/sec CkT/(3??dp)
• df fiber diameter, cm
• dp particle diameter, cm
• Dt diameter of fibrous bed, cm
• L length of fibrous bed, cm

135

• m empirical exponent 1.45
• Ni Number concentration of particles before
  filter, particles/cm3
• N0 Number concentration of particles after
  filter, particles/cm3
• NPe Peclet number Vdf/DBM
• NR Interception parameter dp/df
• NRe Reynolds number V?df/?

136

• NSc Schmidt number ?/?DBM
• ?P pressure drop of air flow mm H2O kg/m2
• V Air velocity Ug/(1 - ?), cm/sec
• Ug Superficial air velocity, cm/sec Q (cm3
  air/sec)/(?DT2)/4
• volume fraction of solid fibers in packed bed
• void fraction, (1 - ?), occupied by air in
  packed bed

137

• ?o total collection efficiency of single fiber
  due to interception and diffusion
• ?o overall collection efficiency of filter bed
  packed with fibers
• viscosity of air, g/cm.sec
• density of air, g/cm3
• gc 32.2 ft/sec2 x lbm/lbf 980 cm/sec2 x gm/gf

138

• 1 gf 980 dynes
• 1 dynes 1 gm x 1 cm/sec2
• 1 p.s.i 6.895 x 104 dynes/cm2 5.17 cm Hg

139

• CALCULATION OF PARTICLE DIFFUSIVITY, DBM IN AIR
• The particle diffusivity in air due to their
• Brownian motion is given by the following
• equation
• DBM CkT/(3??dp)
• where

140

• DBM particle diffusivity in air, cm2/sec
• C 1.16, the Cunninghams correction factor for
  
• slip velocity of particle
• k Boltzmans constant 1.38 x 10-16
  cm2.g/sec2.oK
• T air temperature, oK
• viscosity of air at T, g/cm.sec.
• (at 20 oC, ?air 1.8 x 10-4 g/cm.sec)
• dp particle diameter, cm. (assume particle
  density ?p 1 g/cm3)

141

• 6.2 EXAMPLE OF DESIGN FIBROUS BED FILTER FOR AIR
  STERILIZATION
• A packed bed of glass fibers (fiber diameter
  19?m, solid fiber volume fraction ? 0.033) is
  used to sterilize air which then enters a
  bioreactor system where an aerobic microorganism
  is grown for the production of an extracellular
  enzyme. The superficial air velocity required
  based on the volumetric air flow rate and
  cross-sectional area of the packed bed is Ug 5
  cm/sec. The air is at 20 oC and before it enters
  the filter is

142

• assumed to contain 104 microbial particles/m3,
• each particle is assumed to have 1?m diameter.
• Calculate the following
• The relationship between the overall collection
  efficiency of the fibrous packed bed ? and the
  length L of the bed.
• Calculate the pressure drop per unit length of
  fibrous packed bed, ?P/L.

143

• SOLUTION
• NRe df?Ug/?(1 - ?) (19 x 10-4)(1.20 x
  10-3)(5) /(1.80 x 10-4)(1 0.033)
• 6.54 x 10-2
• NR dp/df 1.0 x 10-4/19 x10-4 5.26 x 10-2
• DBM CkT/3??dp (1.16)(1.38 x 10-16)(273 20)
  /(3)(3.14)(1.8 x 10-4)(1.0 x 10-4)
• 2.78 x 10-7 cm2/sec
• NSc ?/?DBM (1.80 x 10-4)/(1.20 x 10-3)(2.78
  x 10-7)
• 5.40 x 105

144

• NPe NScNRe (5.4 x 105)(6.54 x 10-2) 3.53 x
  104
• NRNPe1/3NRe1/18 (5.27 x 10-2)(3.53 x
  104)1/3(6.54 x 10-2)1/18
• 1.49
• From Fig. 6.5, we find
• ?oNRNPe 3.5 x 10
• ?o 3.5 x 10/(6.27 x 10-2)(3.53 x 104) 1.581 x
  10-2
• From Eq. 6.13
• ?? (1.581 x 10-2)(1 4.5 x 0.033) 1.8158 x
  10-2

145

• From Eq. 6.15
• L ?dp(1 -?)/4??? x 2.303log 1/(1 ?)
• 3.14(19 x 10-4)(1 0.033) x 2.303/4 x
  (1.8158 x
• 10-2) x 0.033 log 1/(1 - ?)
• Therefore, the length of the fibrous bed L is
  given
• by the following equation
• L 18.29 x 10-2log 1/(1 - ?)

146

• In Fig. 6.6 the parameter CDm is plotted as a
  function of the fiber Reynolds number NRe.
• CDm ?gcdf?P/2?LV2(1 -?)m
• From Fig. 6.6
• For NRe 6.54 x 10-2,
• the corresponding value of CDM 7.5 x 102

147

• CDM ?gcdf?P/2?LV2(1 -?)m
• In this case m 1.35
• For df 19 x 10-6
• ? 1.20 x10-3 g/cm3 (20 oC) air
• Ug 5 cm/s 5 x 10-2 m/s
• (1 - ?) ? 0.033 solid fraction

148

• void fraction of fibrous bed
• 1.000 0.033 0.967
• ?P/L (CDM)2?V2(1 -?)m/(?gcdf) 5.472 x 10-1
  
• Therefore from the above equation we calculate
  the
• pressure drop per unit length of fibrous bed for
  the
• given conditions specified in the problem
• statement.

149

• This is the end of the course
• notes.