kinetics and rates of reactions - stanford universitycgong/cee373/documents/cee373lecture04.… ·...
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Kinetics and Rates ofReactions
CEE 373
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Roadmap
SANDBOX
Modeling concepts,scales and approaches
SANDBOXProgramming
languages, softwareengineering &
numerical methods
DESIGN
IMPLEMENTATION
Examination ofEquilibrium-based
Code
IMPLEMENTATION
Examination ofReaction Rate-based
Code
IMPLEMENTATION
Examination ofExisting Models forComplex Systems
Project Proposal
IMPLEMENTATION
Visualization, InterfaceDesign and Usability
READINESS
Internal Testing andCode Freeze
RELEASE
Final Presentations("Rollout")
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KINETICS AND RATE LIMITED REACTIONS
OBJECTIVES1. Build a modeling framework for reaction rate-
limited chemistry.2. Examine and understand computer code.3. Produce model results and interpret critically.
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KINETICS AND RATE LIMITED REACTIONS
1. Rate-Limited Reactions2. Kinetics of Nitrification in a Batch Reactor
• Derivation of expressions used in model• Temperature effect on rate constant• Implementation in computer code
3. Kinetics of Nitrification in a Column Reactor• Expressions used in model
4. Michaelis-Menten Kinetics• Substrate-limited reaction rates
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Rate-Limited ReactionsSIMPLE IRREVERSIBLE REACTION EXAMPLES
FirstA ➞ B
ZeroA ➞ B
€
−d[A]dt
= k0
€
−d[A]dt
= k1[A]
€
t1/2 =[A]0
2k0
€
[A] = [A]0 − k0t
€
t1/2 =1k1
ln2
€
ln[A][A]0
= k1t
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Reaction MechanismsThe Added Complexity of Reality
A0
A1
A2
A0 A1 A2
A0 A1 A0 A1 A2
A0
A11
A21
A12 A13
A22 A23
A0
A11
A21
A12 A13
A22 A23
CONSECUTIVE IRREVERSIBLE PARALLEL IRREVERSIBLE
REVERSIBLE CONSECUTIVE REVERSIBLE
PARALLEL CONSECUTIVE PARALLEL CONSECUTIVE
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Nitrification Kinetics
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Nitrification in a Batch ReactorDERIVATION
€
NH4
+ k1,nitrosomonas → NO2
− k2 ,nitrobacter → NO3
−
Pair of irreversible, first order kinetic reactions
€
d[NH4
+]
dt= −k1[NH4
+]
€
[NH4
+] = [NH4
+]0e−k1t
€
d[NO2
−]
dt= k1[NH4
+]− k2[NO2
−]
€
[NO2
−] =
k1[NH4
+]0
k2 − k1
e−k1t − e−k2t{ }
€
[NO3
−] = [NH4
+]0 − [NH4
+]− [NO2
−]
First order rate law for step 1
Integrated form for step 1
First order rate lawexpression for consecutivefirst order steps
Integrated formfor consecutivesteps
Mass balance expression
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Nitrification in a Batch ReactorRELATING TO COMPUTER CODE
TC = TC + (TB / 10)S = S + 1DA = Exp(-K1 * TC)DB = Exp(-K2 * TC)N1(S) = CA * DAJ = K1 * CA / (K2 - K1)N2(S) = J * (DA - DB)N3(S) = CA - N1(S) - N2(S)
K1 = LA * Exp(A * (TA - 20))K2 = LB * Exp(B * (TA - 20))
€
[NH4
+] = [NH4
+]0e−k1t
€
[NO2
−] =
k1[NH4
+]0
k2 − k1
e−k1t − e−k2t{ }
€
[NO3
−] = [NH4
+]0 − [NH4
+]− [NO2
−]
Temperature Effect Adjustments
€
′ k i = kiea(T−20)
20°C Reference StateConstant
€
where a =Ea
RT1T2
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Nitrification in a ColumnNUMERICAL SOLUTIONS (STEADY STATE)
€
v =QθA
Velocity in porous media
€
x = vtSimple Transport
€
[NH4
+] = [NH4
+]0e− ′ K 1x
€
[NO2
−] =
′ K 1[NH4
+]0
′ K 2 − ′ K 1e− ′ K 1x − e− ′ K 2x{ }
€
[NO3
−] = [NH4
+]0 − [NH4
+]− [NO2
−]
€
where Ki =ki
v
€
′ K i = ′ K iea(T−20)Temperature Effect Adjustments
where Q = application rate, v = porewater velocity, θ = volumetric watercontent, A = cross-sectional area
where x = distance, v = velocity, t = time
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Reaction MechanismsThe Added Complexity of Reality
A0
A1
A2
A0 A1 A2
A0 A1 A0 A1 A2
A0
A11
A21
A12 A13
A22 A23
A0
A11
A21
A12 A13
A22 A23
CONSECUTIVE IRREVERSIBLE PARALLEL IRREVERSIBLE
REVERSIBLE CONSECUTIVE REVERSIBLE
PARALLEL CONSECUTIVE PARALLEL CONSECUTIVE
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Biologically Controlled ReactionsGrowth, Decay, and Biodegradation
Michaelis-Menten Kinetics
E + S ES P + Ek1
k-1
kp
€
µ =µmax[S]Km + [S]
Examples• Biodegradation of pesticides• Algal growth
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Numeric Types: Visual BASIC