Environ. Eng. Week 12 (Reactor I) Review of Ideal Reactor Models - CMBR - CM(C)FR - PFR Advanced Ideal Reactor Problems 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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 = 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

CEE3330-01 Joonhong Park Copy Right Q 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. 99.96% 2018-05-19 CEE3330-01 Joonhong Park Copy Right

Steady State Efficiency of CSTRs in Series Q 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 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

Material Balance in PFR CX CX+ΔX Missions: Governing equation (point form) Calculate concentration as a function of distance, X CIN V (water velocity) A X ΔX 2018-05-19 CEE3330-01 Joonhong Park Copy Right

Material Balance in PFR Assumptions V and CIN are constant. Reaction rate = - kC (first order rate) Steady State (dC/dt=0). 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

Point Form of Mass Continuity Relationship N|Z+ΔZ N|y+Δy Divide all the terms in Eq. 2-17 (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 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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) 2018-05-19 CEE3330-01 Joonhong Park Copy Right

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!!) 2018-05-19 CEE3330-01 Joonhong Park Copy Right