🎓 Lesson 16
D5
Parallel, Consecutive, and Series-Parallel Networks
Parallel, consecutive, and series-parallel networks describe how chemical reactions are arranged in a reactor system—like choosing whether reactions happen all at once, one after another, or in a mix of both—to control product selectivity.
🎯 Learning Objectives
- ✓ Explain how network topology (parallel, consecutive, series-parallel) influences instantaneous and overall selectivity
- ✓ Calculate concentration-time profiles and selectivity ratios for first-order parallel and consecutive reactions
- ✓ Design an ideal CSTR or PFR sequence to maximize desired product yield in a series-parallel network
- ✓ Analyze rate-limiting steps and optimal temperature profiles using Arrhenius dependencies across reaction branches
📖 Why This Matters
Selectivity determines economic viability in industrial processes—from pharmaceutical synthesis (where unwanted isomers reduce purity) to petrochemical cracking (where over-cracking wastes feedstock). Understanding how reactions are interconnected—whether they compete, cascade, or hybridize—is essential to avoid costly separations, meet regulatory specs, and minimize waste. Real-world examples include selective oxidation of ethylene to ethylene oxide (suppressing total combustion) and catalytic reforming in refineries.
📘 Core Principles
Parallel reactions occur when a single reactant partitions into multiple pathways with distinct rate constants (k₁, k₂), making selectivity dependent on relative rates and residence time. Consecutive reactions introduce intermediate accumulation and decay: early termination favors intermediates (e.g., B in A→B→C), while long residence times drive toward final products. Series-parallel networks (e.g., A ⇄ B → C and A → D) require matrix-based analysis or lumped kinetic models; here, selectivity becomes a function of reactor type (CSTR vs. PFR), mixing quality, and thermal management due to differing activation energies across branches.
📐 Selectivity in First-Order Parallel Reactions
For parallel irreversible reactions A → B (k₁) and A → C (k₂), selectivity S_{B/C} = C_B / C_C = k₁ / k₂ — independent of concentration but highly sensitive to temperature via Arrhenius dependence. This ratio holds for both PFR and CSTR under first-order kinetics, though conversion differs.
💡 Worked Example
Problem: Ethylbenzene dehydrogenates to styrene (k₁ = 0.15 min⁻¹) and undergoes cracking to benzene + ethylene (k₂ = 0.05 min⁻¹) at 630°C. Calculate S_{styrene/cracking} and determine if increasing temperature by 20°C (with Eₐ₁ = 125 kJ/mol, Eₐ₂ = 142 kJ/mol) improves selectivity.
1.
Step 1: Compute initial S = k₁/k₂ = 0.15 / 0.05 = 3.0
2.
Step 2: Use Arrhenius to estimate new k values: k = A exp(−Eₐ/RT); assume identical pre-exponential factors (A), so k₁'/k₂' = exp[(Eₐ₂ − Eₐ₁)/R × (1/T₁ − 1/T₂)]
3.
Step 3: Plug in R = 8.314 J/mol·K, T₁ = 903 K, T₂ = 923 K → exponent = (142,000 − 125,000)/(8.314) × (1/903 − 1/923) ≈ −0.51 → ratio = exp(−0.51) ≈ 0.60
4.
Step 4: New S = 3.0 × 0.60 = 1.8 — selectivity decreases with temperature rise due to higher Eₐ for undesired path.
Answer:
The initial selectivity is 3.0; raising temperature reduces it to 1.8, confirming that lower temperature favors styrene despite slower overall rate—a classic selectivity–rate tradeoff.
🏗️ Real-World Application
In the production of nitric acid via the Ostwald process, ammonia oxidizes over Pt-Rh gauze: 4NH₃ + 5O₂ → 4NO + 6H₂O (desired), but competes with total oxidation: 4NH₃ + 3O₂ → 2N₂ + 6H₂O (undesired). This is a parallel network where NO selectivity drops above 900°C due to N₂ pathway dominance. Industrial practice uses short-contact-time PFRs at ~900°C and 7–9 bar, with precise O₂/NH₃ ratio control (1.7–2.0) to maintain >95% NO selectivity—demonstrating how reactor choice and operating conditions override intrinsic kinetics.
🔧 Interactive Calculator
🔧 Open Reaction Engineering and Kinetics Calculator📋 Case Connection
📋 Bioethanol Fermentation Bioreactor Scale-Up with Inhibition Kinetics
Ethanol inhibition caused premature cessation at large scale despite matching nominal conditions
📋 Nitric Acid Absorption Tower Design for Tail-Gas Treatment
Incomplete absorption of NO and NO₂ due to slow liquid-phase oxidation kinetics and poor gas distribution