Chemical Reaction Engineering Dr. Yahia Alhamed Chemical and Materials Engineering Department College of Engineering King Abdulaziz University
General Mole Balance
Batch Reactor Mole Balance
Constantly Stirred Tank Reactor Mole Balance CSTR or MFR
Plug Flow Reactor (PFR) Mole Balance F df The integral form V = A is: A F A0 r A This is the volume necessary to reduce the entering molar flow rate (mol/s) from F A0 to the exit molar flow rate of F A.
Packed Bed Reactor Mole Balance PBR F A0 F A + r A dw = dn A dt The integral form to find the catalyst weight is: W = F A F A0 df A r A
F A0 = C Ao v o Space time and space velocity τ = is called space time (s) = V/v o Space velocity = 1/τ, where; F A0 = Molar feed rate of key reactant A (mol/s) C Ao = Concentration of key reactant A in the feed (mol/m 3 ) v o =Volumetric flow rate of feed to the reactor (m 3 /s) V = volume of the reactor For constant volume systems v = v o where v is volumetric flow rate leaving the reactor
Reactor Mole Balance Summary
Conversion Consider the general reaction: aa + bb - cc + dd We will choose A as bases of calculation (i.e. Key reactant) The limiting reactant is usually taken as the key reactant Then: A + (b/a)b (c/a)c + (d/a)d X A = moles reacted/moles fed
Design Equations The following design equations are for single reactions only Design equations for multiple reactions will be given later
Summary
Batch Stoichiometric Table
Concentration: Batch Systems Constant Volume Batch: Note: if the reaction occurs in the liquid phase or if a gas phase reaction occurs in a rigid (e.g., steel) batch reactor Then etc. If then And we have r A =f(x)
Flow System Stoichiometric Table
Concentration: Liquid Flow System Flow Stystem: Liquid Phase Flow System: etc. If the rate of reaction were then we would have This gives us -r A = f(x). Consequently, we can use the methods discussed in Chapter 2 to size a large number of reactors, either alone or in series.
F υ = υ T P 0 0 F T 0 P F T F T0 Concentration: Gas Flow System = F T0 +δf A0 X F T0 T T 0 = 1+ δy A0 X = ( 1 +εx) F T = C T υ and F T0 = C T0 υ 0 υ= C T0 C T υ 0 C T = P RT and C T0 = P 0 RT 0 THEN C A = F A0 ( 1 X ) υ Note that the reaction is: A + (b/a)b - (c/a)c + (d/a)d IF the reaction rate is given by -r A = k C A2 CB THEN with
Multiple Reactions Use molar flow rates and concentrations; DO NOT use conversion! Types of Multiple Reactions 1. Series Reactions 2. Parallel Reactions 3. Complex Reactions: Series and Parallel 4. Independent
Selectivity and Yield Instantaneous Overall SELECTIVITY YIELD Example: (1) desired product, r D =k 1 C A2 C B A + B k 2 (2) undesired product, r U =k 2 C A C B U 1
Another example about Selectivity and Yield (1) desired product, r D =k 1 C A2 C B (2) undesired product U1, A + B k 2 U 1 r U1 =K2C A C B (3) undesired product U2, A + B k 3 3 U 2 r U 2 = k 3 C B C A then k S D/U1 /U = 1 C 2 A C B 2 k 2 C A C B + k 3 C B C = 3 A k 1 C A k 2 + k 3 C A 2 S D/U1/U2 C A
Mole Balances
Net Rate of Reaction for Species A
Algorithm for Multiple Reactions
Series Reactions, t=0 C A =C A0
Series Reactions dc C dt = k 2 C B, t = 0 C C = 0
Multiple Reactions () 1 A + 2B C () 2 3C + 2A D r 1A = k 1A C A C B 2 r 2C = k 2C C A2 C C 3 r A = r 1A + r 2A r 1A = k 1A C A C B 2 r 2A 2 = r 2C 3 r 2A = 2 3 r 2C = 2 3 k 2C C A 2 C C 3 r A = k 1A C A C B 2 2 3 k 2C C A 2 C C 3 r 1B 2 = r 1A 1 r 1B = 2r 1A r 2B = 0 r B = r 1B + 0 = 2r 1A r B = 2k 1A C A C B 2 r 1A 1 = r 1C 1 r 1C = r 1A 3 r 2C = k 2C C A2 C C r C = r 1C + r 2C = r 1A + r 2C r C = k 1A C A C B 2 k 2C C A 2 C C 3 r 1D = 0 r 2C 3 = r 2D 1 r D = 0 + r 2D = r 2C 3 r D = 1 3 k 2C C C 3 C A 2
Case 1:Liquid Phase Reaction in a CSTR
Case 1:Liquid Phase Reaction in a CSTR
Polymath Solution
Elementary Multiple Reactions
Example: Liquid Phase Reaction
Example: Liquid Phase Reaction
Example: Liquid Phase Reaction
Solution of differential equations
Multiple Reactions Gas Phase Use Molar Flow Rates!!!
The Algorithm
The Algorithm (given)
The Algorithm
Heterogeneous Catalytic Reaction 1-External diffusion of reactants towards the external surface of the catalyst pellet 2-Internal diffusion of reactants into the pores of the catalyst pellet 3- Adsorption of reactants on the active sites 4- Surface reaction 5- Desorption of products from active sites into the pore volume of the catalyst pellet 6- Internal diffusion of products through the pores of the catalyst pellet towards the external surface of the catalyst pellet 7- External diffusion of products to the bulk of the fluid
Molecular Adsorption C A S = K A P A 1+ K A P A
Steps of Catalytic Reaction B B A B C D A B C D B A C + D C + C D + D
Example: Catalytic Reaction to Improve the Octane Number of Gasoline Focusing on the second reaction:
Example: Catalytic Reaction to Improve the Octane Number of Gasoline
Example: Catalytic Reaction to Improve the Octane Number of Gasoline r N = r S = k S C N,S C I S K S C T C V = 1+ K N P N + K I P I
Different Surface Mechanisms