CEE Joonhong Park Copy Right Environ. Eng. Course Note 9 (Reactor I) Review of Ideal Reactor Models - CMBR - CM(C)FR - PFR Advanced Ideal Reactor Problems

CEE Joonhong Park Copy Right Ideal Reactors Completely Mixed Batch Reactor (CMBR) Completely Mixed Continuous Flow Reactor (CMCFR) Q-In Q-out Plug-Flow Reactor (PFR) Q-InQ-out

CEE Joonhong Park Copy Right General Material Balance Model 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 ± = Molar rate of input of material i across the control volume boundaries Molar rate of output of material i across the control volume boundaries -

CEE Joonhong Park Copy Right Completely Mixed Batch Reactor (CMBR) CMBR Material Balance 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 C: contaminant concentration

CEE Joonhong Park Copy Right Completely Mixed Continuous Flow Reactor (CMCFR) or “CSTR” Q Q Completely Stirred Tank Reactor (CSTR) V = Reactor volume C = concentration in reactor d(CV)/dt = Q * C in – Q * C + r * V C in C dC/dt = Q/V * (C in – C) + r Here V/Q = Θ = hydraulic resistant time 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 * (C in – C) + r = 1/Θ * (C in – C) – k * C C/C in = 1/(1 + k * Θ)

CEE Joonhong Park Copy Right V Q Q C in C out Q C in Q C out V/2 QC1QC1 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 % Example:

CEE Joonhong Park Copy Right Completely Mixed Continuous Flow Reactor (CMCFR) Q Steady State Efficiency of CSTRs in Series V = Overall Reactor Volume C in C 1 /C in = 1/(1 + k * Θ/2) Q C1C1 C2C2 V/2 C 2 /C 1 = 1/(1 + k * Θ/2) C 2 /C in = 1/(1 + k * Θ/2) 2 C out /C in = 1/(1 + k * Θ/n) n When n = large, C out /C in = Exp (-k Θ)

CEE Joonhong Park Copy Right Q Steady State Efficiency of CSTRs in Series V = Overall Reactor Volume C in C1C1 C n-1 V/n C out /C in = 1/(1 + k * Θ/n) n When n = large, C out /C in = Exp (-k Θ) Q CnCn V/n …..

CEE Joonhong Park Copy Right Material Balance in PFR C IN V (water velocity) X ΔXΔX CXCX C X+ΔX Missions: 1.Governing equation (point form) 2.Calculate concentration as a function of distance, X A

CEE Joonhong Park Copy Right Material Balance in PFR Assumptions V and C IN are constant. Reaction rate = - kC (first order rate) Steady State (dC/dt=0).

CEE Joonhong Park Copy Right Comparison of CMFR and PFR HW: Draw the C/C-in versus kΘ plot for 1 st order decay And discuss why the differences occur. (hint: see p. 233 and 229 in your course material)

CEE Joonhong Park Copy Right Point Form of Mass Continuity Relationship Δx ΔzΔz Δy N| X N| X+ΔX N| Z+ΔZ N| X N| y N| y+Δy - (δNx/δx+ δNy/δy+ δNz/δz) + r = δC/ δt Divide all the terms in Eq (text book) by ΔxΔyΔz, and then, Question: Dimension of unit of each term?

CEE Joonhong Park Copy Right Inter-phase Mass Transfer Phase 1 Boundary Layer Inter-phase Mass Transfer X-direction Y-direction Phase 2 CoCo C k: Inter-phase Mass Transfer Coefficient (L/T)

CEE Joonhong Park Copy Right Completely Mixed Batch Reactor (CMBR) CMBR Material Balance 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 C: contaminant concentration When inter-phase mass transfer is involved, Net accumulation rate in reactor, d(CV) reactor /dt =N*A = k m (C-C o ) A Phase j (ex. activated carbon) C: concentration in phase i Co: concentration in phase j A: overall surface area where the interphase mass transfer occurs Phase I (ex. water)

CEE Joonhong Park Copy Right Inter-phase Mass Transfer in PFR V 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 C IN C: VOC concentration in water phase C a : VOC concentration in air phase K a-w : air-water interphase mass transfer rate constant (1/T) A W HW: Get the steady-state analytical solution for when Ca=0 (hint: see p. 235 in your course material)

CEE 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!!)