Chemical Reaction Engineering

Chemical reaction engineering combines chemical kinetics with reactor design to transform raw materials into desired products. It's the heart of chemical manufacturing, determining how efficiently and safely chemical transformations occur.

Reaction Kinetics

Rate Laws

The rate of reaction describes how concentration changes with time:

For a reaction: $aA + bB \rightarrow cC + dD$

Where:

• $-r_A$ = rate of disappearance of A
• $k$ = rate constant
• $\alpha, \beta$ = reaction orders
• $C_A, C_B$ = concentrations

Arrhenius Equation

Temperature dependence of rate constant:

Where:

• $A$ = pre-exponential factor
• $E_a$ = activation energy
• $R$ = gas constant
• $T$ = temperature

Reactor Design

Batch Reactor

All reactants added at start, no flow in or out:

Continuous Stirred-Tank Reactor (CSTR)

Perfect mixing, uniform composition:

Plug Flow Reactor (PFR)

No mixing, composition varies along length:

Catalysis

Homogeneous Catalysis

Catalyst and reactants in same phase.

Heterogeneous Catalysis

Catalyst in different phase (usually solid).

Catalyst Properties

• Activity: How fast reaction occurs
• Selectivity: Desired product formation
• Stability: Resistance to deactivation

Advanced Reaction Engineering Concepts

Non-Ideal Reactor Behavior

Real reactors deviate from ideal models due to:

Residence Time Distribution (RTD):

• C-curve: Response to pulse input
• F-curve: Response to step input
• E-curve: Normalized C-curve

Tanks-in-Series Model: For reactors with partial mixing:

Where $N$ is the number of equivalent tanks.

Dispersion Model: For tubular reactors with axial mixing:

Where $Pe$ is the Peclet number.

Multiple Reaction Systems

For complex reaction networks:

Selectivity and Yield:

• Instantaneous selectivity: $S = \frac{r_P}{r_A}$
• Overall yield: $Y = \frac{\text{moles of product formed}}{\text{moles of reactant consumed}}$

Reaction Network Analysis:

• Parallel reactions
• Series reactions
• Complex networks

Heterogeneous Catalysis

Catalyst Effectiveness Factor:

Thiele Modulus: For first-order reaction in spherical catalyst:

Where $D_e$ is the effective diffusivity.

Internal and External Diffusion:

• External mass transfer: Film diffusion
• Internal diffusion: Pore diffusion
• Weisz modulus: Combined criterion

Reactor Stability and Multiplicity

Energy Balance: For non-isothermal reactors:

Multiple Steady States: Some reactors can operate at different temperatures for the same conditions.

Runaway Conditions: When heat generation exceeds heat removal capacity.

Reactor Scale-up

Scale-up Challenges

• Mixing efficiency: Different flow patterns at large scale
• Heat transfer: Reduced surface-to-volume ratio
• Mass transfer: Different gas-liquid contacting
• Safety considerations: Larger inventories, longer response times

Scale-up Methods

• Geometric similarity: Maintaining same shape and proportions
• Constant power per volume: For mixing-sensitive reactions
• Constant mixing time: For fast reactions
• Constant heat transfer coefficient: For temperature-sensitive reactions

Scale-up Criteria

• Chemical similarity: Same reaction pathways
• Physical similarity: Similar flow and mixing patterns
• Thermal similarity: Similar temperature profiles

Real-World Application: Ammonia Production

The Haber-Bosch process for ammonia synthesis demonstrates advanced reaction engineering principles:

Reaction Kinetics

The ammonia synthesis reaction follows Temkin-Pyzhev kinetics:

Catalyst Design

Iron catalyst with promoters:

• Structural promoters: Al₂O₃ (increases surface area)
• Electronic promoters: K₂O (increases activity)
• Stability promoters: CaO (improves stability)

Advanced Reactor Design

Multi-bed adiabatic reactor with interstage cooling:

• Bed 1: High temperature for fast kinetics
• Bed 2: Intermediate cooling and reaction
• Bed 3: Lower temperature for equilibrium shift

# Ammonia synthesis reactor design with advanced kinetics
import numpy as np

# Operating conditions
pressure = 200     # atm
temperature_bed1 = 450  # °C
temperature_bed2 = 400  # °C
temperature_bed3 = 380  # °C

# Kinetic parameters (simplified)
k1 = 0.1  # forward rate constant
k2 = 0.02 # reverse rate constant
alpha = 0.5
beta = 0.5

# TODO: Calculate conversion in each bed using advanced kinetics
# Consider equilibrium limitations and kinetic rates

conversion_bed1 = 0
conversion_bed2 = 0
conversion_bed3 = 0
overall_conversion = 0

print(f"Bed 1 conversion: {conversion_bed1:.3f}")
print(f"Bed 2 conversion: {conversion_bed2:.3f}")
print(f"Bed 3 conversion: {conversion_bed3:.3f}")
print(f"Overall conversion: {overall_conversion:.3f}")

# Calculate equilibrium conversion for comparison
def equilibrium_constant(T):
    # Empirical correlation for ammonia synthesis
    return np.exp(-2.691122 * np.log(T) - 5.519265e-5 * T + 1.848863e-7 * T**2 + 2001.6/T + 2.6899)

K_eq_450 = equilibrium_constant(450 + 273.15)
print(f"Equilibrium constant at 450°C: {K_eq_450:.3f}")

Your Challenge: Reactor Selection and Design

In this exercise, you'll compare different reactor types and select the most appropriate design for a chemical process.

Goal: Analyze and compare CSTR and PFR performance for a second-order reaction.

Reaction System

Consider the liquid-phase reaction: $A + B \rightarrow C$

• Rate law: $-r_A = k C_A C_B$
• $k = 0.1$ L/mol·min
• Feed: $C_{A0} = C_{B0} = 2$ mol/L
• Desired conversion: $X_A = 0.9$
• Volumetric flow rate: $v_0 = 10$ L/min

# Reaction parameters
k = 0.1          # L/mol·min
CA0 = 2.0        # mol/L
CB0 = 2.0        # mol/L
v0 = 10.0        # L/min
X_desired = 0.9  # conversion

# TODO: Calculate reactor volumes for CSTR and PFR
# For second-order reaction with equal initial concentrations:
# -r_A = k CA^2
# CA = CA0(1 - X)

# CSTR volume
CA_out = 0
rate_out = 0
V_CSTR = 0

# PFR volume (integrate design equation)
V_PFR = 0

print(f"CSTR volume required: {V_CSTR:.1f} L")
print(f"PFR volume required: {V_PFR:.1f} L")

# Compare performance
volume_ratio = V_CSTR / V_PFR
print(f"Volume ratio (CSTR/PFR): {volume_ratio:.2f}")

if V_CSTR > V_PFR:
    print("PFR is more volume-efficient for this reaction")
else:
    print("CSTR is more volume-efficient for this reaction")

What factors besides volume efficiency would influence reactor selection? How would the comparison change for a first-order reaction?