🧬 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 = 136.6 m²

Permeate Purity: 75.6 % Fast Gas | Retentate: 80.4 % Slow Gas

θ = 40 %

Permeate Stream Flow Rate 240.0 Nm³/h y_p = 0.756 (Recovery = 72.0 %)

Retentate Product Flow Rate 360.0 Nm³/h x_r,slow = 80.4 % (Recovery = 83.2 %)

Transmembrane Pressure Ratio 0.069 ΔP = 14.9 bar

Specific Membrane Productivity 1.76 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                 : Biogas Upgrading Polyimide Hollow Fiber Module (CO2/CH4)
Feed Flow Rate (F)         : 600.00 Nm3/h (7.436 mol/s)
Feed / Permeate Pressure   : 16.00 bar a / 1.10 bar a (ratio = 0.069)
Permeance & Selectivity    : 120.0 GPU (alpha = 35.0)
Feed Fast Gas Mole Fraction: 0.420
Target Stage Cut (theta)   : 40.00 %
-----------------------------------------------------------------
REQUIRED MEMBRANE AREA (Am): 136.63 m2
Permeate Flow Rate         : 240.00 Nm3/h (Fast Gas Purity = 75.60 %)
Retentate Flow Rate        : 360.00 Nm3/h (Slow Gas Purity = 80.40 %)
Fast Gas Recovery in Perm  : 72.00 %
Slow Gas Recovery in Retent: 83.17 %
Specific Permeate Flux     : 1.757 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