🧬 Gas Permeation Membrane Separation

Design hollow fiber and spiral-wound gas separation membranes for CO2/CH4 biogas upgrading, H2 recovery, and N2 enrichment using cross-flow permeation models.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 28

⚡ Calculs faits 23

💾 Téléchargements 282 📦 Code Fortran 6.4 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🔬 Hollow Fiber Membrane Shell-and-Lumen Gas Permeation

Real-time visual simulation of fast gas molecules diffusing across hollow fibers into permeate lumen

📝 Configuration & Presets

🌱 Biogas (CO₂/CH₄, α=35) ⚡ H₂ Syngas Recovery (α=60) 💨 N₂ Air Separation (O₂/N₂) 🏭 Carbon Capture (Vacuum Perm)

🧪 Membrane Permeance & Selectivity

Fast Gas Permeance Q_A [GPU]: 1 GPU = 10⁻⁶ cm³(STP)/(cm²·s·cmHg)

Ideal Selectivity α_A/B (Q_A/Q_B):

⚡ Operating Pressures & Flow Rates

Feed Shell High Pressure P_h [bar a]:

Permeate Lumen Pressure P_l [bar a]:

Feed Flow Rate F [Nm³/h]:

Feed Fast Gas Fraction x_f [mol/mol]:

Stage Cut θ (Permeate / Feed): Industrial range: 0.20 to 0.60

Gas Permeation Formulations:
• Flux: J_i = Q_i · (P_h x_i − P_l y_i) [mol/(m²·s)]
• Selectivity: α = Q_A / Q_B
• Stage Cut: θ = Permeate / Feed
• Membrane Area: A_m = (P · y_p) / [ Q_A · ΔP_lm ] [m²]

📊 Membrane Sizing Results

📊 Output Summary
💾 Fortran Source

Required Membrane Surface Area

A_m = 637.0 m²

Permeate Purity: 45.1 % Fast Gas | Retentate: 98.7 % Slow Gas

θ = 45 %

Permeate Stream Flow Rate 135.0 Nm³/h y_p = 0.451 (Recovery = 96.6 %)

Retentate Product Flow Rate 165.0 Nm³/h x_r,slow = 98.7 % (Recovery = 68.7 %)

Transmembrane Pressure Ratio 0.125 ΔP = 7.0 bar

Specific Membrane Productivity 0.21 Nm³/(m²·h) Per unit membrane area

📈 Permeate Purity (%) vs Stage Cut θ (%)

📉 Required Area A_m (m²) vs Feed Pressure P_h (bar)

=================================================================
 THERMOFLUIDCALC — GAS PERMEATION MEMBRANE ANALYSIS REPORT
=================================================================
Case Title                 : Industrial Nitrogen Gas Generation (O2/N2 Air Separation)
Feed Flow Rate (F)         : 300.00 Nm3/h (3.718 mol/s)
Feed / Permeate Pressure   : 8.00 bar a / 1.00 bar a (ratio = 0.125)
Permeance & Selectivity    : 80.0 GPU (alpha = 6.5)
Feed Fast Gas Mole Fraction: 0.210
Target Stage Cut (theta)   : 45.00 %
-----------------------------------------------------------------
REQUIRED MEMBRANE AREA (Am): 636.96 m2
Permeate Flow Rate         : 135.00 Nm3/h (Fast Gas Purity = 45.06 %)
Retentate Flow Rate        : 165.00 Nm3/h (Slow Gas Purity = 98.69 %)
Fast Gas Recovery in Perm  : 96.56 %
Slow Gas Recovery in Retent: 68.71 %
Specific Permeate Flux     : 0.212 Nm3/(m2.h)
=================================================================

📘 Calculation Methodology & Membrane Technology Standards

Solution-Diffusion Mechanism

Gas transport through dense polymeric membrane skins is governed by Fickian diffusion driven by partial pressure gradients between the shell and fiber lumen:

                    JA = QA · (Ph xA − Pl yA)
                

Purity vs Recovery Trade-Off

Increasing stage cut $\theta$ increases fast-gas recovery but dilutes permeate purity as local driving force decreases along the fiber length.

Key Engineering Assumptions

1 GPU = $10^{-6}\,\text{cm}^3(STP)/(\text{cm}^2\cdot s\cdot\text{cmHg}) = 3.348\times 10^{-10}\,\text{mol/(m}^2\cdot\text{s}\cdot\text{Pa)}$.
Ideal gas behaviour ($22.414\,\text{L/mol}$ at STP).
Cross-flow hollow fiber configuration with negligible lumen pressure drop.

ThermoFluidCalc Engineering Report