🧪 Fixed-Bed Adsorption Breakthrough (Thomas & BDST)

Model dynamic packed-bed adsorption breakthrough curves (S-curves), exhaustion times, Bed Depth Service Time (BDST), and Mass Transfer Zone (MTZ) migration.

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

Fixed-Bed Adsorption Breakthrough (Thomas & BDST)

Mass Transfer

📊 Solver Telemetry ● ACTIVE

👁️ Views 33

⚡ Solves 29

💾 Downloads 383 📦 Fortran Code 6.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

🧪 Packed Adsorbent Bed Mass Transfer Wave Front Migration

Real-time visual simulation of solute adsorption gradient wave advancing through porous bed

📝 Configuration & Presets

🪨 GAC Phenol (350 L/h) 🪵 Biochar Heavy Metal (Pb²⁺) 💎 Zeolite PFAS Trace Bed 🎨 Textile Dye Decolorization

📐 Column Dimensions & Adsorbent

Bed Height Z [m]:

Column Diameter D [m]:

Adsorbent Bulk Density ρ_b [g/L]: GAC: ~450–550 g/L, Zeolite: ~700–850 g/L

Equilibrium Adsorption Capacity q₀ [mg/g]:

💧 Fluid Flow & Thomas Kinetics

Liquid Feed Flow Rate Q [L/h]:

Inlet Solute Concentration C₀ [mg/L]:

Thomas Kinetic Rate Constant k_Th [mL/(mg·min)]: Typical range: 0.05 to 0.50 mL/(mg·min)

Thomas & BDST Formulations:
• Thomas S-Curve: C/C₀ = 1 / [ 1 + exp( (k_Th q₀ M / Q) − k_Th C₀ t ) ]
• Breakthrough Time (5%): t_b = t₅₀ − ln(19) / (k_Th C₀)
• Exhaustion Time (95%): t_s = t₅₀ + ln(19) / (k_Th C₀)
• Critical Bed Depth: Z₀ = (u₀ / (k_BA N₀)) · ln(C₀/C_b − 1)

📊 Breakthrough Performance Results

📊 Output Summary
💾 Fortran Source

5% Breakthrough Time (t_b)

t_b = 203.3 hours (8.5 days)

Treated Volume: 10,163 Liters (10.2 m³)

M_ads = 8.8 kg

95% Exhaustion Time (t_s) 219.0 hours Midpoint t₅₀ = 211.1 h

Mass Transfer Zone (MTZ) 0.06 m 7.2 % of bed height

Critical Minimum Bed Depth (Z₀) 0.030 m BDST threshold

Superficial Velocity (u₀) 1.59 m/h Bed Vol = 25.1 L

📈 Thomas Sigmoidal Breakthrough S-Curve C/C₀ (%) vs Time

📉 Bed Depth Service Time (BDST): Service Life vs Bed Height

=================================================================
 THERMOFLUIDCALC — ADSORPTION BREAKTHROUGH ANALYSIS REPORT
=================================================================
Case Title                 : Engineered Biochar Column for Heavy Metal (Pb²⁺) Removal
Bed Dimensions (Z x D)     : 0.80 m x 0.20 m (Volume = 25.1 L)
Adsorbent Mass in Bed      : 8.80 kg (bulk density = 350 g/L)
Liquid Feed Flow Rate (Q)  : 50.0 L/h (superficial u0 = 1.59 m/h)
Inlet Solute Conc (C0)     : 25.0 mg/L
Adsorption Capacity (q0)   : 30.0 mg/g
-----------------------------------------------------------------
5% BREAKTHROUGH TIME (tb)  : 203.26 hours (8.47 days)
95% EXHAUSTION TIME (ts)   : 218.97 hours (9.12 days)
TREATED EFFLUENT VOLUME    : 10,163.2 Liters (10.16 m3)
Mass Transfer Zone (MTZ)   : 0.057 meters
Critical Bed Depth (Z0)    : 0.030 meters (BDST limit)
=================================================================

📘 Calculation Methodology & Adsorption Kinetics Standards

Thomas Column Model

The Thomas model assumes plug flow with second-order reversible Langmuir adsorption kinetics, providing the classic analytical S-curve:

                    C/C₀ = 1 / [ 1 + exp( (kTh q₀ M / Q) − kTh C₀ t ) ]
                

Bed Depth Service Time (BDST)

BDST relates service time linearly to bed depth. The x-intercept represents the critical depth $Z_0$ below which instantaneous breakthrough occurs.

Key Engineering Assumptions

Isothermal operation with negligible axial fluid dispersion.
Breakthrough criterion defined at $C/C_0 = 5\%$ ($0.05$).
Exhaustion criterion defined at $C/C_0 = 95\%$ ($0.95$).

ThermoFluidCalc Engineering Report