1. Environ. Eng. Week 12 (Reactor I)
Review of Ideal Reactor Models
- CMBR
- CM(C)FR
- PFR
Advanced Ideal Reactor Problems
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2. Ideal Reactors Q-In Q-out Q-In Q-out
Completely Mixed Batch Reactor (CMBR)
Completely Mixed Continuous Flow Reactor (CMCFR)
Q-In
Q-out
Plug-Flow Reactor (PFR)
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3. General Material Balance Model
Molar rate of input of material i across the control volume boundaries
Molar rate of output of material i across the control volume boundaries
Net rate of transformation of material i within the control volume -
Net rate of change (either accumulation or depletion) of material i within the control volume =
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4. CMBR Material Balance C: contaminant concentration
Net accumulation rate in reactor, d(CV)reactor/dt
= net transformation rate (dC/dt)reaction V
When V = constant,
[dC/dt]reactor = [dC/dt]reaction = r
V: reaction
volume
Completely Mixed Batch Reactor (CMBR)
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5. Completely Stirred Tank Reactor (CSTR)Q
Cin Q
V = Reactor volume
C = concentration in reactor C
d(CV)/dt = Q * Cin – Q * C + r * V
dC/dt = Q/V * (Cin – C) + r
Here V/Q = Θ = hydraulic resistant time
Completely Mixed Continuous Flow Reactor (CMCFR) or “CSTR”
Example: When the reaction is a first order decay, what will be the efficiency
in the reactor under steady state conditions?
dC/dt = 0= 1/Θ * (Cin – C) + r = 1/Θ * (Cin – C) – k * C
C/Cin = 1/(1 + k * Θ)
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6. CEE3330-01 Joonhong Park Copy RightQ C1
Example: Q Q Q
Cin
Cin Q
Cout
Cout
V/2
V/2 V
Assumptions: stead state conditions
Ideal CSTR
the first order decay reaction with a rate constant, k.
Givens: V=10,000 L, Q=100L/h, k=1.0/h
Mission: Compare the treatment efficiencies (1- Cin/Cout),
and discuss the effect of sectionization of the reaction on
the treatment efficiencies.
Answers: (1- 1/101) vs (1-1/2601) = 99.00% vs %
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7. Steady State Efficiency of CSTRs in SeriesQ
Cin Q C2 C1
V/2
V/2
Completely Mixed Continuous Flow Reactor (CMCFR)
V = Overall Reactor Volume
C1/Cin = 1/(1 + k * Θ/2)
C2/C1 = 1/(1 + k * Θ/2)
Cout/Cin = 1/(1 + k * Θ/n)n
When n = large, Cout/Cin = Exp (-k Θ)
C2/Cin = 1/(1 + k * Θ/2)2
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8. CEE3330-01 Joonhong Park Copy Right
Steady State Efficiency of CSTRs in Series
Cn-1 Cn C1 Q
…..
Cin Q
V/n
V/n
V/n
V = Overall Reactor Volume
Cout/Cin = 1/(1 + k * Θ/n)n
When n = large, Cout/Cin = Exp (-k Θ)
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9. Material Balance in PFRCX
CX+ΔX
Missions:
Governing equation (point form)
Calculate concentration as a function of distance, X
CIN
V (water velocity) A X ΔX
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10. Material Balance in PFR
Assumptions
V and CIN are constant.
Reaction rate = - kC (first order rate)
Steady State (dC/dt=0).
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11. Comparison of CMFR and PFR
HW: Draw the C/C-in versus kΘ plot for 1st order decay
And discuss why the differences occur.
(hint: see p. 233 and 229 in your course material)
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12. Point Form of Mass Continuity Relationship
N|Z+ΔZ
N|y+Δy
Divide all the terms in Eq (text book) by ΔxΔyΔz, and then, Δz
N|X+ΔX
N|X Δy Δx
N|y
- (δNx/δx+ δNy/δy+ δNz/δz) + r = δC/ δt
Question: Dimension of unit of each term?
N|X
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13. Inter-phase Mass Transfer
Y-direction
k: Inter-phase Mass Transfer Coefficient (L/T)
Phase 2 C
Inter-phase Mass Transfer
Boundary Layer Co
Phase 1
X-direction
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14. CMBR Material Balance C: contaminant concentration
Net accumulation rate in reactor, d(CV)reactor/dt
= net transformation rate (dC/dt)reaction V
When V = constant,
[dC/dt]reactor = [dC/dt]reaction = r
V: reaction
volume
When inter-phase mass transfer is involved,
Net accumulation rate in reactor, d(CV)reactor/dt
=N*A = km (C-Co) A
Completely Mixed Batch Reactor (CMBR)
Phase I
(ex. water)
C: concentration in phase i
Co: concentration in phase j
A: overall surface area where
the interphase mass transfer occurs
Phase j
(ex. activated
carbon)
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15. Inter-phase Mass Transfer in PFR
A volatile organic compound is steadily discharged into the river.
It undergoes first-order chemical decay within the water and
interphase mass transfer across the water-air surface. x ∆x W
CIN V A
C: VOC concentration in water phase
Ca: VOC concentration in air phase
Ka-w: air-water interphase mass transfer rate constant (1/T)
HW: Get the steady-state analytical solution for when Ca=0
(hint: see p. 235 in your course material)
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16. HW#5 Study the solutions for:
Example 5.A.14 (p. 238)
Example 5.A.15 (p. 239)
Example 5.A.16 (p. 240)
Example 5.A.17 (p. 242)
Example 5.A.18 (p. 243)
(Hint: I will use some of them for the final examination. I will do it absolutely!!)
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