Lecture 6, Segment 1: Conversion and Reactor Sizing

Introduction

• Focus on Chapter 2: Conversion and Reactor Sizing
• Definition and development of design equations in terms of conversion

Objectives

1. Define conversion
2. Develop design equations in terms of conversion (X)
3. Size CSTR and plug flow reactors
4. Compare conversions for reactors in series

Reflections on Chemical Reaction Engineering (CRE)

• Originated to describe the process of reactor selection and sizing
• Choosing the proper reactor type: Batch, Plug Flow, Packed Bed, Semi-Batch, Fluidized Bed, CSTR
• Calculating reactor size
• Determining optimal operating conditions

Chapter Recap

• Chapter 1: Derived general mole balance equation and applied to four types of ideal reactors
• Chapter 2: Focus on defining conversion and developing design equations

Defining Conversion

• Basis: Choose limiting reactant for calculations
• Stoichiometry: Use stoichiometric coefficients to rewrite reaction equations
• Conversion (X):
  • Moles of limiting reactant A reacted divided by moles of A fed
  • For irreversible reactions, max conversion = 1
  • For reversible reactions, max conversion = equilibrium conversion (Xe)

Batch Reactor Design Equation

• Conversion and Time: Longer residence time increases conversion until equilibrium or complete consumption
• Conversion Equation:
  • X = (NA0 - NA) / NA0
  • Rearrange to NA = NA0(1 - X)
• General Mole Balance: Derive batch reactor design equation in terms of X

Design Equations for Flow Reactors

• Continuous Flow Systems: Conversion increases with reactor volume
• Conversion (X) Definition:
  • X = (FA0 - FA) / FA0, where FA0 and FA are molar flow rates

CSTR Design Equation

• Derive from general mole balance
• Equation: V = (FA0 * X) / (-RA)
• Rate of reaction evaluated at exit due to well-mixed condition*

Plug Flow Reactor Design Equation

• Plug Flow Assumptions: No radial gradients
• Equation:
  • Differential Form: dFA/dV = RA
  • Introduce X: d(FA0*X)/dV = RA
  • Integral Form: V = FA0 * ∫(dX / -RA)

Packed Bed Reactor Design Equation

• Packed Bed Characteristics: Tubular with catalyst particles
• Equation Similarity: Similar to plug flow reactor but using W instead of V
• Considerations: Pressure drop effects discussed in Chapter 4

Conclusion

• Developed design equations for four ideal reactors using conversion
• Upcoming lectures: How to apply these design equations

This lecture focused on defining conversion, understanding its implications in reactor design, and deriving design equations for various reactor types. The next steps involve applying these equations in practical scenarios.