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Preparing for the PE Exam
Biological Systems(10% of exam)
Cady R. Engler, P.E.Bio & Ag Engineering Dept.
Texas A&M University
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Topics Biological Processes
~5 questions Principles of organic and biochemistry Aerobic and anaerobic processes Ergonomics
Environmental and Ecological Systems ~3 questions Environmental assessment techniques Awareness of ecological processes
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Topics Principles of organic and biochemistry
Thermal properties – food and biomaterials Mass and energy balances Heat and mass transfer Kinetics
Enzyme reactions Growth Death
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Topics Aerobic and anaerobic processes
Bioreactor systems Oxygen transfer Anaerobic treatment
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Topics Ergonomics
Human/machine interaction physical capabilities visual requirements
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Topics Environmental assessment techniques
Measurement of organic matter Measurement of other nutrients Effect of scale
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Topics Ecological processes
Mass and energy balances Limiting nutrients
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Thermal properties Water
psychrometrics
Biomaterials
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Mass and energy balancesHeat and mass transfer
These may appear in several different sections of the exam.
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Enzyme Kinetics
Michaelis-Menten model
s = substrate concentration v = reaction velocity vmax = maximum reaction rate
KM = Michaelis-Menten (saturation) constant
d s
d tv
v s
K sM
m a x
Michaelis-Menten enzyme kinetics
KM
First order
Zero order
d s
d tv
v s
K sM
m a x
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Michaelis-Menten Kinetics Example 1
An enzyme that follows simple Michaelis-Menten kinetics has the following parameter values:
vmax = 116 mg/L·s
KM = 5.2 mg/L
Determine the initial reaction rate with a substrate concentration of 100 mg/L.
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Michaelis-Menten Kinetics Example 1 (cont.)
vv s
K s
v
M
m ax
1 1 6 m g
L s
1 0 0 m g
L
L
5 .2 1 0 0 m g1 1 0 m g / L s
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
0.5
1
1.5
2
2.5
3
3.5
M-M Kinetics – Example 2 The figure below shows reaction rates as a function of substrate
concentration for an enzyme catalyzed reaction. Estimate vmax and KM for the enzyme.
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M-M Kinetics – Example 2 From inspection of the plot:
vmax ≈ 3.25 mol/L·min
KM = s @ v = 0.5 vmax = 0.025 mol/L
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Enzyme Kinetics May use reciprocal (Lineweaver-Burk) plot for
evaluation of parameters
1 1 1
v
K
v s vM
m ax m ax
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Evaluating kinetic parameters Lineweaver-Burk plot
1/v
1/s-1/KM
1/vm
slope = KM/vm
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M-M Kinetics – Batch Reaction
Substrate concentration as a function of time can be found by integrating the kinetic equation with s = s0 at t = 0:
s
sKsstv
sK
sv
dt
dsv
00max
max
lnM
M
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Enzyme Kinetics Inhibition of enzyme reactions
Competitive Non-competitive Substrate Other
Immobilized enzymes – diffusion effects Surface Internal (porous particles)
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Growth Kinetics Exponential growth of microorganisms
Monod model for dependence of growth rate on substrate concentration
d x
d tx
m ax s
K ss
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Monod growth kinetics
m ax s
K ss
m ax
s
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Growth Kinetics Maintenance requirements of organisms must
be considered in many systems (equivalent to adding a death term):
Growth rates may be subject to inhibition – similar to enzyme kinetics
d x
d tx k xd
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Yield Coefficients Yield of cell mass per mass of substrate
consumed:
Other yield coefficients can be defined in a similar manner.
Yx
sx s/
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Bioreactor Systems
Batch reactor:
for Monod kinetics(note that both s and xvary with time)
dx
d tx
sx
K sS
m ax
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Batch Reactor Generally, μ = μmax for batch growth since s >> KS
for most of the growth period
dx
d tx m ax
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Bioreactor Systems
Continuous stirred tank reactors (CSTR) (assuming no maintenance requirement)
µ = specific growth rate
D = dilution rate
θ = mean residence time
washout occurs when D ≈ µmax
D1
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CSTR – Monod Kinetics
D
DKsYssYx
D
DKs
sK
sD
Ssxsx
S
S
max0/0/
max
max
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CSTR – Monod Kinetics
When grown under a specific set of conditions, an organism has the following growth characteristics:
μmax = 0.3 h-1
KS = 0.45 g/LThe feed to a CSTR has a substrate concentration of 100 g/L. Determine the maximum dilution rate if the substrate concentration in the effluent is not to exceed 1 g/L.
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CSTR – Monod Kinetics
1-
max
h07.2
g/L10.45
g/L1
h
3.0
D
sK
sD
S
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Bioreactor Systems
CSTR with recycle (e.g., activated sludge) D > µmax when washout occurs
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Bioreactor Systems Plug flow reactors (PFR)
Behave as batch reactors with reaction time equal to residence time
r ud c
d z
d c
d tc c = concentration of component Cu = linear velocity of fluid
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Microbial Death
First order death (decay) kinetics
N = number of viable organisms Assumes constant temperature Sterilization time depends on size of system since
the number of viable organisms is proportional to size
N t N e k td 0
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Food Sterilization
ktN
N
0
ln
D
tkt
N
N
303.2
log0
D = decimal reduction time = time to kill 90% of viable organisms
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Food Sterilization D is a function of T (temperature) Over range of T used for sterilization
where z is the change in T required to change D by a factor of 10
z
TT
D
D 0
0
log
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Food Sterilization – example 1 For food spoilage organisms, a typical value for z
is 10°C. If D = 0.22 min at 121°C, determine D at 137°C.
min0055.0
60.110
137121
22.0log
137
137
D
D
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Food Sterilization F is the thermal death time or time required to
obtain a stated reduction in the population of organisms or spores usually expressed as a multiple of D often written with subscript denoting T and superscript
denoting z:
10121FF z
T example for
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Food Sterilization – example 2 An acceptable economic spoilage rate for a
particular food product was obtained with a process having F0 = 7 min. Determine the processing time required at 115°C.
Note that F0 is defined using typical values for food spoilage organisms and sterilizing conditions:
FC 18250
101210 FFF
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Food Sterilization – example 2
min28min798.3
98.310
6.010
115121log
log
115
6.0
0
115
0
115
0
0
115
115
115
0
00
F
F
F
D
D
z
TT
D
D
D
F
D
F
N
N
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Food Sterilization – example 3 A food product contains an average of 10 spores
per can prior to sterilization. If a spoilage rate of 1 can in 100,000 is the target, determine F280 for the process. D250 = 1.2 min and z = 18°F.
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Food Sterilization – example 3
min16.0min0259.06
610
10log
min0259.0min2.110
67.118
280250log
280
280
2805
67.1280
250
280
F
D
F
D
D
D
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Oxygen Transfer
Oxygen transfer must balance oxygen uptake at steady state:
kLa = volumetric mass transfer coefficient
cL* = O2 concentration at saturation
cL = O2 concentration
qO2 = oxygen demand of cell mass x = cell mass concentration
k a c c q xL L L O*
2
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Oxygen Transfer Oxygen transfer rate affected by
temperature solute concentrations type of aerator mixing intensity
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Anaerobic Treatment
Anaerobic digestion converts organic matter to methane and carbon dioxide Composition typically 60% CH4, 40% CO2
Trace amounts of H2S also formed
Biogas yield 3 – 8 SCF/lb VS (0.2 – 0.5 m3/kg VS)
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Anaerobic Treatment Anaerobic processes generally slower than
aerobic with retention times >50 days for anaerobic lagoon 10-30 days for mesophilic digester <10 days for thermophilic digester
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Anaerobic Treatment Anaerobic lagoon design (similar refs)
ANSI/ASAE EP 403.3 JUL99, Design of Anaerobic Lagoons for Animal Waste Management, ASAE Standards
Agricultural Waste Management Field Handbook, USDA-NRCS, Chapter 10, Agricultural Waste Management System Component Design:
ftp://ftp.wcc.nrcs.usda.gov/downloads/wastemgmt/
AWMFH/awmfh-chap10.pdf
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Organic matter measurement BOD (5 day)
oxygen consumed by microbial growth BOD5 = [DOt=0-DOt=5]sample - [DOt=0-DOt=5]blank
COD oxygen consumed by chemical oxidation
VS (volatile solids) loss of mass after thermal oxidation
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BOD Example Given the following data, determine the BOD for
a waste water sample that was diluted by a factor of 10:
Dissolved oxygen (mg/L)
Time (d) Diluted Sample Seeded sample
0 8.55 8.75
5 2.40 8.53
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BOD Example
mg/L3.59
1053.875.840.255.8mg/L
5
5
BOD
BOD
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Other nutrients Nitrogen
Total Kjeldahl nitrogen Ammonia nitrogen Nitrate and nitrite
Phosphorus Orthophosphate Total phosphorus
Mass balances, limiting nutrients, eutrophication
References Shuler, Michael L., and Fikret Kargi, Bioprocess
Engineering Basic Concepts, 1st or 2nd Edition, Upper Saddle River, NJ: Prentice Hall, 1992 or 2002.
Heldman, D.R., and D.B. Lund, Handbook of Food Engineering,New York: Marcel Dekker, 1992.
Toledo, R.T., Fundamentals of Food Process Engineering, 2nd Edition, New York: Van Nostrand Reinhold, 1991.
Metcalf & Eddy’s Wastewater Engineering: Treatment, Disposal, and Reuse, 3rd or 4th Edition, New York: McGraw Hill, 1991 or 2002.
ANSI/ASAE EP 403.3 JUL99, Design of Anaerobic Lagoons for Animal Waste Management, ASAE Standards
Midwest Plan Service, Livestock Waste Facilities Handbook (MWPS – 18).