ISOTHERMAL REACTOR DESIGN PTT 255 REACTION ENGINEERING ISOTHERMAL REACTOR DESIGN Dr Noor Hasyierah Mohd Salleh Department of Chemical Engineering Technology

OBJECTIVES Students should be able to: Describe the algorithm that allows the reader to solve chemical reaction engineering problems through logic rather than memorization. Size batch reactors, CSTRs, PFRs, and PBRs for isothermal operation given the rate law and feed conditions.

OUTLINE Algorithm for Isothermal Reactors Design Structure for Isothermal Reactors - Batch Reactor - CSTR - Tubular Reactor/PFR Pressure Drop in Reactors Copyright Cheng 05

Algorithm for Isothermal Reactors To design an isothermal reactors, the following sequence is highly recommended. To carry out the evaluation, the following method can be used: Graphically (Chapter 2 plot) Numerical (Quadrature Formulas Chapter 2 and Appendix A4) Analytical (Integral Tables) Software (Polymath)

Steps/Procedure to Design Isothermal Reactor Apply mole balance and design equations of reactors – (chap 1 & 2) Find rate law – (chap 3) Use stoichiometry to express as a function of X – (chap 3) Combine and evaluate to find Volume of CSTR and PFR or reaction time for batch reactor. – (chap 4) Copyright Cheng 05

1. The general mole equation START Algorithm for Isothermal Reactor END 1. The general mole equation 2. Design Equations: Batch CSTR PFR Evaluate the algebraic (CSTR) or integral (PFR) equations 3. Is –rA=f(X) given? YES Copyright Cheng 05 NO 4. Determine the rate law in terms of the concentration of the reacting species 5. Use Stoichiometry to express concentration as a function of conversion Liquid phase or Gas phase Constant Volume Batch Constant P and T 6. Combine steps 4 and 5 to obtain –rA=f(X)

Design Structure for Isothermal Reactors Batch Reactor Analysis on laboratory scale batch reaction are sometimes needed in the scale up of laboratory experiments to pilot plant operation or to full scale production. Data from batch reactor can be used as a references to determined the reaction time, t needed to achieve a conversion, x for specific reaction or sometimes to find the reaction rate constant, k and also to determine the volume, V of reactors.

Batch Reactor – Liquid Phase Operation Case : Calculation of time taken, (t) to achieve a given conversion (X) Elementary irreversible 1st order reaction A  B Step 1: Write the mole balance in term of x Step 2: Write the rate law Step 3: Derive concentration term from stoichiometry

Step 4: Combine equation from step 1,2,3 Step 5: Evaluate by integration The reaction time or tR

Summary : Estimation of reaction time of batch reactor for first and second order Mole Balance Rate Law First order Second order Stoichiometry Combine Evaluate (integrate)

Batch Reactor- Example A  B Calculate the reaction time of the above process to reach 90% conversion in a constant-volume batch reactor scales, if k = 10-4 s-1. For first order

Design Structure for CSTR CSTR can be used for liquid and gas phase reaction but are typically used for liquid-phase reaction Thus CSTR Design covered in this part consists of : -1st order liquid phase Irreversible reaction -2nd order liquid phase Irreversible reaction

Damköhler number Damkohler number (Da) is the ratio of the rate of reaction of A to the rate of convective transport of A at the entrance to the reactor. rate of reaction at entrance entering flow rate of A Damkohler number (Da) gives a quick estimation of the degree of conversion in CSTR

Damköhler number For 1st order irreversible reaction; For 2nd order irreversible reaction; Rule of thumb to estimate degree of conversion : If Da  0.1,  X < 0.1 If Da  10,  X > 0.9

CSTR – Liquid Phase Operation A  B Step 1: Write the mole balance in term of x In term of space time, τ = V/ v0 Elementary irreversible 1st order reaction

tk is often referred to as Damköhler number Step 2: Write the rate law Step 3: Derive concentration term from stoichiometry *Liquid phase: constant volume : v = v0 Step 4: Combine equation from step 1,2,3 Rearrange : tk is often referred to as Damköhler number (for 1st order)

Step 5: Evaluate – Several parameters can be evaluate based on derived equations . For examples: Space time (τ) Conversion (X) Exit concentration (CA)

CSTR – Liquid Phase Operation 2A  B Step 1: Write the mole balance in term of x In term of space time, τ = V/ v0 Elementary irreversible 2nd order reaction

tkCA0 is often referred to as Damköhler number Step 2: Write the rate law Step 3: Derive concentration term from stoichiometry *Liquid phase: constant volume : v = v0 Step 4: Combine equation from step 1,2,3 tkCA0 is often referred to as Damköhler number (for 2nd order)

Step 5 : Evaluate Space time (τ): Conversion (X): Da number *negative sign must be chosen because X cannot be greater than 1

CSTR Design (Gas phase) Example: 2A  B Step 1: Write the mole balance in term of x Step 2: Write the rate law Elementary irreversible 2nd order reaction

Isothermal & no pressure drop Step 3: Write concentration in terms of conversion (from stoichiometry) Step 4 : Combine all the equations   For gas phase v v0 Isothermal & no pressure drop

Exercise 1 Example: The elementary liquid phase reaction 2A  B is carried out isothermally in a CSTR. Pure A enters at a volumetric flow rate of 25 dm3/s and at a concentration of 0.2 mol/dm3. What CSTR volume is necessary to achieve a 90% conversion when k = 10 dm3/(mol*s)? Copyright Cheng 05

Design Structure for PFR Gas and liquid phase reactions generally carried out in tubular reactors. Assume no dispersion and no radial gradients in either temperature, velocity, or concentration and in the absence of pressure drop or heat exchange. Thus PFR Design considers on: -1st order liquid phase Irreversible reaction -1st order gas phase Irreversible reaction -2nd order liquid phase Irreversible reaction -2nd order gas phase Irreversible reaction

Elementary irreversible 2nd order reaction PFR Design Example: 2A  B Step 1: Write the mole balance in term of x Step 2: Write the rate law Elementary irreversible 2nd order reaction

Isothermal & no pressure drop Step 3: Write concentration in terms of conversion (from stoichiometry) Step 4 : Combine all the equations Rearrange For liquid phase v = v0   For gas phase v v0 Isothermal & no pressure drop For liquid phase v = v0

Step 4 :continue   For gas phase v v0

Pressure Drop in Reactors In liquid-phase reactions, the concentration of reactants is insignificantly affected by even relatively large changes in total pressure. Thus, the effect of pressure drop on the rate of reaction can totally be ignored in liquid-phase reactor sizing. However in a gas-phase reactions, the concentration of the reacting species is proportional to the total pressure. This fact is especially true in micro reactors packed with solid catalyst (PBR) whereas the channels are so small that pressure drop can limit the throughput and conversion for gas-phase reactions. Copyright Cheng 05

PBR Design Presence of Pressure Drop Example: 2A  B + C A gas phase reaction is being carried out in a PBR with pressure drop existence. Elementary irreversible 2nd order reaction Step 1: Write the mole balance in term of x Step 2: Write the rate law Copyright Cheng 05

Step 3: Write concentration in terms of conversion (from stoichiometry) Step 4 : Combine all the equations Before evaluation (step 5),we now need to relate the pressure drop to the catalyst weight (W) in order to determine the conversion (X) as a function of W Isothermal T = T0   Pressure drop exist P P0 Copyright Cheng 05

Ergun equation for single reaction The majority of gas phase reaction are catalyzed by passing the reactant through a packed bed of catalyst particles Ergun equation for single reaction Copyright Cheng 05

For isothermal operation, we have two sets of equation with two unknowns, X & P Special case: if ε=0, an analytical solution to Eq.2 is obtained as follows (Eq.1) (Eq.2) Copyright Cheng 05 Used only when ε=0 (Eq.3)

Step 5 : Evaluate by integration Combine Eq. 1 and Eq.3 Step 5 : Evaluate by integration Rearrange to obtain conversion (X) and catalyst weight (W). Copyright Cheng 05

For gas phase reactions, as the pressure drop increases, the concentration decreases, resulting in a decreased rate of reaction, hence a lower conversion when compared to a reactor without a pressure drop Copyright Cheng 05

Thank You Copyright Cheng 05