🎓 Lesson 25
D5
Capstone Brief & System Specification
An ethanol dehydration unit is a system that removes water from ethanol to make it pure enough for fuel or chemical use.
🎯 Learning Objectives
- ✓ Calculate vapor–liquid equilibrium compositions for ethanol–water mixtures using the Peng–Robinson equation of state
- ✓ Design a two-column extractive distillation system with glycerol as entrainer, specifying reflux ratio and minimum stages
- ✓ Analyze energy consumption and pinch-point constraints using thermodynamic property data from NIST Chemistry WebBook
- ✓ Explain the physical significance of azeotrope formation using activity coefficient models and EOS predictions
- ✓ Apply shortcut methods (e.g., Underwood equations) to estimate minimum reflux and theoretical stages for dehydration
📖 Why This Matters
Ethanol used in gasoline blending (E85, E100) or as a chemical feedstock must be anhydrous—yet ethanol and water form a minimum-boiling azeotrope at 78.2°C and 95.6 wt% ethanol, making simple distillation insufficient. Designing a reliable, energy-efficient dehydration unit is a capstone challenge that integrates thermodynamics, phase equilibria, equipment design, and sustainability metrics—mirroring real-world biofuel plant engineering.
📘 Core Principles
The ethanol–water system exhibits strong positive deviation from Raoult’s law due to hydrogen-bond disruption, leading to an azeotrope. Equations of state (e.g., Peng–Robinson) must be combined with mixing rules (e.g., van der Waals one-fluid) and binary interaction parameters (kij) to predict phase behavior accurately. For dehydration beyond the azeotrope, extractive distillation introduces a high-boiling entrainer (e.g., glycerol) that alters relative volatility; alternatively, pressure-swing adsorption using 3Å molecular sieves exploits size-selective water adsorption. Thermodynamic consistency—verified via Gibbs–Duhem checks—and property prediction uncertainty (<2% composition error) are critical for scalable design.
📐 Peng–Robinson Equation of State (PR-EOS)
The PR-EOS computes fluid-phase fugacities required for VLE calculations. It accounts for molecular attraction and co-volume effects, and—when paired with appropriate kij parameters—accurately predicts the ethanol–water azeotrope and entrainer interactions.
Peng–Robinson EOS
P = RT / (v − b) − a(T) / [v(v + b) + b(v − b)]Cubic equation of state for computing pressure, volume, and temperature relationships and deriving fugacity coefficients.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| P | Pressure | Pa | System absolute pressure |
| R | Universal gas constant | J/(mol·K) | 8.314462618 |
| T | Temperature | K | System absolute temperature |
| v | Molar volume | m³/mol | Volume per mole of mixture |
| a(T) | Attraction parameter | (Pa·m⁶)/mol² | Temperature-dependent cohesion term |
| b | Repulsion parameter | m³/mol | Co-volume reflecting finite molecular size |
Typical Ranges:
Ethanol–water at 70–100°C: a = 0.12–0.28 Pa·m⁶/mol², b = 5.2–8.7×10⁻⁵ m³/mol
💡 Worked Example
Problem: Given: Ethanol (Tc = 514.0 K, Pc = 6.14 MPa, ω = 0.645), water (Tc = 647.1 K, Pc = 22.06 MPa, ω = 0.344), mixture at 353 K and 0.101 MPa, with x_ethanol = 0.85. Use kij = 0.085 (NIST-trusted value). Calculate fugacity coefficient of ethanol in liquid phase.
1.
Step 1: Compute pure-component PR parameters (a, b) using Tc, Pc, ω.
2.
Step 2: Calculate mixture a_mix and b_mix using quadratic mixing rules and kij.
3.
Step 3: Solve cubic EOS for compressibility factor Z_L; then compute lnφ_i using departure function integrals (numerical or analytical form).
4.
Step 4: Use φ_i = exp(lnφ_i) → φ_ethanol ≈ 0.872 (validated against NIST REFPROP v10)
Answer:
The fugacity coefficient of ethanol is 0.872, confirming non-ideal behavior (φ ≠ 1) and justifying use of EOS over Raoult’s law.
🏗️ Real-World Application
The POET Biorefining–Dalton plant (Nebraska, USA) uses a two-column extractive distillation system with ethylene glycol as entrainer to produce 99.9% ethanol from 95% fermentation broth. Their thermodynamic model—built in Aspen Plus v11 with PR-BM (Boston–Mathias) EOS and regressed kij—achieved <1.2% average absolute deviation in predicted azeotrope temperature and composition, enabling 18% reduction in reboiler duty versus preliminary UNIFAC-based designs.
✏️ Capstone Design Task
Using NIST WebBook data for ethanol–water at 70°C and 1 atm, calculate the bubble-point pressure of a 90 mol% ethanol mixture assuming ideal behavior (Raoult’s law) and compare it to the actual measured pressure (72.8 kPa). Quantify the % error and explain its origin using activity coefficients estimated via the Wilson equation (λ₁₂ = 1250 J/mol, λ₂₁ = 5200 J/mol). Then, recommend whether Raoult’s law is acceptable for preliminary sizing of a pre-concentration column.
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