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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).