Adsorbent Bed Pressure Drop Ergun Equation — What It Actually Is (And What It Is Not)

If you design, specify, or troubleshoot a fixed-bed adsorber - PSA oxygen, compressed air dryer, natural gas dehydration, hydrogen purification - the bed pressure drop directly sets compressor power, sieve attrition, and operating cost. This guide walks through the Ergun equation step by step, runs four worked examples on real industrial conditions, and gives the practical particle size trade-offs that decide whether your bed runs clean for five years or chokes on fines after eighteen months.

Every fixed-bed adsorber has a pressure drop. Feed gas enters the top of the tower at high pressure, percolates down through the packed bed of beads, and exits at the bottom at slightly lower pressure. That pressure difference (delta P) is not free - it costs compressor work, generates heat that the sieve must dissipate, and at extreme levels it can fluidize the bed or crush particles into fines.

In a typical industrial adsorber the design targets for total bed pressure drop are:

If pressure drop exceeds 8 percent of feed pressure, two things start to go wrong: (1) the compressor or feed blower must work harder, raising operating cost by 5 to 15 percent over the unit lifetime; (2) the bed begins to vibrate and shift under the higher differential pressure, accelerating sieve attrition and dust generation. In extreme cases fines accumulate in the lower part of the bed, drop rises another 20 to 30 percent within months, and the tower has to be opened for sieve replacement.

Designing the bed pressure drop correctly up front avoids all of this. The tool for that is the Ergun equation, published in 1952 and still the workhorse correlation for any packed bed of solid particles - adsorbent beads, catalyst pellets, sand, even grain in a silo.

In 1952, Sabri Ergun at the Carnegie Institute of Technology published a correlation that combined two physical effects - viscous energy loss (the laminar term) and kinetic energy loss (the inertial term) - into a single equation for pressure drop across a packed bed:

dP 150 * (1 - eps)^2 mu * v 1.75 * (1 - eps) rho * v^2 --- = ----------------- * -------- + ----------------- * --------- L eps^3 dp^2 eps^3 dp Where:

Adsorbent Bed Pressure Drop Ergun Equation — The Hidden Defect / Failure Mode

The first term dominates at low Reynolds number (Re_p below 10), where flow is essentially laminar. The second term dominates at higher Re_p (above 100), where inertial effects take over. Most industrial adsorbers run at Re_p between 1 and 1000, which is exactly the regime where Ergun is most accurate - within plus or minus 20 percent against experimental data, validated against more than 2,000 measurements across particle sizes from 0.05 mm to 50 mm.

Ergun fit his equation to two earlier correlations - the Kozeny-Carman equation for viscous flow in porous media and the Burke-Plummer equation for turbulent packed bed flow - and showed that a single weighted sum reproduces both. The 150 constant for the viscous term and the 1.75 constant for the inertial term are empirical but well-validated across decades of catalysis and adsorption engineering. They appear unchanged in every major chemical engineering textbook (McCabe, Smith and Harriott; Perry's Chemical Engineers' Handbook; Coulson and Richardson) and are the basis for the equivalent diameter concept used in packed tower design.

• Compressed air dryer (heatless desiccant): 0.3 to 0.5 bar (5 to 7 percent of 7 bar feed)
• Natural gas dehydration (TSA): 0.2 to 0.5 bar (1 to 3 percent of 40 to 70 bar feed)
• PSA oxygen concentrator: 0.05 to 0.12 bar (3 to 8 percent of 1.4 bar adsorption)
• Hydrogen PSA: 0.10 to 0.30 bar (1 to 3 percent of 20 bar feed)

Adsorbent Bed Pressure Drop Ergun Equation — Measured Numbers Across Grades

Step 1: convert flow to superficial velocity. Cross-sectional area = pi * (1.50/2)^2 = 1.767 m2. Operating density at 40 bar (g) (41 bar absolute) and 35 degrees C: rho = (41 * 1e5 * 16e-3) / (8.314 * 308) = 25.6 kg/m3. Actual volumetric flow = (15000 * 1.013e5 / (41e5 + 1.013e5)) * (308 / 273) = 1245 m3/h = 0.346 m3/s. Superficial velocity v = 0.346 / 1.767 = 0.196 m/s.

Step 2: compute Re_p. Methane viscosity at 40 bar 35 degrees C is approximately 1.30e-5 Pa.s. Re_p = rho * v * dp / mu = 25.6 * 0.196 * 0.004 / 1.30e-5 = 1544. This is well into the inertial-dominated regime, where the second Ergun term dominates.

Where Adsorbent Bed Pressure Drop Ergun Equation Earns Its Premium — Core Chemistry

Step 2: Re_p. Air viscosity at 25 degrees C: 1.85e-5 Pa.s. Re_p = 2.81 * 0.0447 * 0.00075 / 1.85e-5 = 5.1. This is at the upper edge of the laminar-dominated regime, where both Ergun terms contribute roughly equally.

Step 3: Ergun calculation. Viscous term: (150 * 0.60^2 / 0.40^3) * (1.85e-5 * 0.0447 / 0.00075^2) = 1378 Pa/m. Inertial term: (1.75 * 0.60 / 0.40^3) * (2.81 * 0.0447^2 / 0.00075) = 439 Pa/m. Total = 1817 Pa/m = 1.82 kPa/m = 0.018 bar/m.

Step 4: total drop across the bed. 0.018 * 0.25 = 0.0046 bar. As a percentage of 1.4 bar (g) feed: 0.33 percent. This is well below the 8 percent ceiling. The fine 0.75 mm LiLSX beads generate only modest pressure drop because the bed is short and the flow is small. The actual constraint on this design is sieve life (LiLSX water sensitivity), not pressure drop.

Adsorbent Bed Pressure Drop Ergun Equation — Dosing Across Service Conditions

Step 3: Ergun. Sphericity for alumina beads is approximately 0.85, so effective dp = 0.0035 * 0.85 = 0.00298 m. Viscous term: (150 * (0.58)^2 / (0.42)^3) * (1.88e-5 * 0.0442 / (0.00298)^2) = 1576 Pa/m. Inertial term: (1.75 * 0.58 / (0.42)^3) * (9.06 * 0.0442^2 / 0.00298) = 422 Pa/m. Total = 1998 Pa/m = 2.00 kPa/m = 0.020 bar/m.

Step 4: bed pressure drop. 0.020 * 0.5 = 0.010 bar. As percent of 7 bar (g) feed: 0.14 percent. Tiny. So the design is over-conservative on pressure drop. Either the bed could be shortened to 250 mm and still meet 0.07 percent drop, or the tower diameter could be reduced. In practice compressed air dryers are usually sized for breakthrough time (6 to 8 hours minimum cycle), not pressure drop.

Hydration Kinetics, Set Control, and Working Time

Step 4: total bed drop. 0.0076 * 3.5 = 0.0266 bar. As percent of 20 bar (g) feed: 0.13 percent. Almost negligible. The design is pressure-drop limited by other things - probably bed sizing for adsorption kinetics and cycle time, not Ergun.

This is typical of high-pressure hydrogen PSAs: pressure drop is rarely the binding constraint because the feed gas has low density and viscosity. The binding constraint is hydrogen recovery, which favors slow cycles and tall beds.

1. Step 1: Kinetics - smaller beads have shorter diffusion paths. A 1 mm bead reaches 90 percent of equilibrium in roughly 25 percent of the time a 2 mm bead needs in the same application. Faster kinetics means shorter cycles, higher recovery, smaller beds.
2. Step 2: Attrition and dust - smaller beads break more easily during loading and thermal cycling. Aluminaworld attrition test (ASTM D4058) shows that 1.6 to 2.5 mm molecular sieve loses 0.05 to 0.10 wt% per test cycle, while 0.5 to 1.0 mm beads lose 0.15 to 0.30 wt%. Fines end up at the bottom of the bed, partially blocking the support grid, raising pressure drop over time.
3. Step 3: Liquid contamination tolerance - larger beads tolerate occasional liquid slugs (compressor condensate, process upsets) better than small beads because the void space is larger. A 3 mm bead bed can survive a 50 mL water slug without waterlogging; a 1 mm bed cannot.

• dP/L = pressure drop per unit bed length (Pa/m)
• eps = bed void fraction (dimensionless, 0.35 to 0.45 typical)
• mu = gas dynamic viscosity (Pa.s)
• v = superficial gas velocity (m/s)
• dp = particle diameter (m)

Procurement Specification — What to Demand on the COA

If you scale a process from a 50 mm pilot column to a 1 m production tower, you cannot simply multiply pressure drop by the diameter ratio. Wall effects in small columns force the flow to redistribute near the wall, where the void fraction is higher (less compaction near the rigid wall). This actually reduces the average pressure drop, but the prediction gets less reliable.

The standard rule: vessel-to-particle diameter ratio D/dp must be greater than 20 for the Ergun equation to apply within 10 percent. For dp = 2 mm, D must be at least 40 mm - so a 50 mm pilot column is acceptable. For dp = 0.5 mm, D must be at least 10 mm, but most pilot work at this size uses 25 to 50 mm columns, so the rule is comfortably met.

• Non-spherical particles (extrudates, crushed granules): Multiply particle diameter by sphericity factor phi (0.6 to 0.9 typical). Most engineered adsorbents are near-spherical and phi approaches 1.0.
• Wall effects in small-diameter columns: If vessel diameter D is less than 20 * dp, increase pressure drop by 5 to 15 percent over the Ergun prediction.
• Heat of adsorption effects: Temperature rise of 5 to 20 degrees C is common in the mass transfer zone. Use viscosity and density at average bed temperature, not inlet temperature.
• Multicomponent adsorption: Ergun is purely hydrodynamic. Actual cycle time and breakthrough depend on the adsorption equilibrium and kinetics, not just pressure drop.

Storage, Shelf Life, and Inventory Hygiene

For engineers who want to run their own numbers, here is a step-by-step worksheet that you can replicate in Excel or Python in 10 minutes:

Inputs: D_vessel (m) = ? L_bed (m) = ? dp_particle (m) = ? (sieve mean size) phi_sphericity = 0.85-0.95 eps_void_fraction = 0.38-0.45 T_feed (K) = ? P_feed_abs (Pa) = ? MW_gas (g/mol) = ? Q_flow (Nm3/s) = ? mu_gas (Pa.s) = ? Convert dp to effective: dp_eff = dp * phi Compute operating density: rho = P * MW / (8.314 * T) Compute operating flow: Q_op = Q_flow * 1.013e5 / P * T / 273 Compute superficial vel: v = Q_op / (pi * (D_vessel/2)^2) Compute Re_p: Re_p = rho * v * dp_eff / mu Ergun: dP_visc_L = 150 * (1-eps)^2 / eps^3 * mu * v / dp_eff^2 dP_inert_L = 1.75 * (1-eps) / eps^3 * rho * v^2 / dp_eff dP_total_L = dP_visc_L + dP_inert_L [Pa/m] dP_total = dP_total_L * L_bed [Pa] Convert: dP_bar = dP_total / 1e5 dP_percent = dP_bar / (P_feed_abs/1e5 - 1.013) * 100 Check: - dP_percent < 8%? -> OK - v < 0.6 * Umf? -> OK - D_vessel / dp_eff > 20? -> OK Aluminaworld can run this calculation on your specific lot of sieve and feed gas composition free of charge. Just send us your operating conditions (vessel dimensions, flow, pressure, temperature, gas composition) and the sieve grade and we will return a pressure drop and fluidization analysis within two business days.

• Vessel inside diameter: 1.50 m
• Bed height: 4.00 m
• Particle size: 3 to 5 mm beads (4 mm average)
• Feed gas: methane at 40 bar (g), 35 degrees C, 15,000 Nm3/h
• Void fraction: 0.38

• Bed inside diameter: 40 mm
• Bed height: 250 mm per bed
• Particle size: 0.5 to 1.0 mm beads (0.75 mm average)
• Feed air at 1.4 bar (g) (2.4 bar absolute), 25 degrees C, 8 LPM per bed
• Void fraction: 0.40

Total Cost of Ownership — Why Premium Pays for Itself

For uniform spherical beads poured randomly into a vertical vessel, the bed void fraction (eps) is 0.38 to 0.42. For 1.6 to 2.5 mm molecular sieve beads the typical design value is 0.40. For irregular crushed particles like 1 to 3 mm activated alumina, expect 0.42 to 0.46 due to poorer packing geometry. Pellets and extrudates (3 to 5 mm cylinders) pack at 0.36 to 0.40. Always measure the actual poured density of the specific sieve grade and back-calculate void fraction rather than using textbook numbers.

Yes. The same equation applies in both directions. During TSA regeneration of a compressed air dryer the purge gas is hot (180 to 220 degrees C) and at near-atmospheric pressure. Viscosity of air at 200 degrees C is roughly 2.6e-5 Pa.s (about 25 percent higher than at 25 degrees C) and density drops to 0.75 kg/m3. Re_p drops by roughly 60 percent compared to room-temperature adsorption. Bed pressure drop during regeneration is therefore typically 30 to 50 percent lower than during adsorption at the same volumetric flow rate. Be aware that the much lower gas density in regeneration can also push the system into the laminar-dominated regime, which is the worst case for fine-particle pressure drop.

The math: a 5-10% longer service life plus lower thermal-cycling spalling plus reduced replacement-frequency combine to deliver 12-25% lower TCO over a single cell-stack replacement cycle, even before the safety/insurance argument for eliminating thermal-shock microcracks. The 8-15% raw-material premium pays back 1.5-2.5x over the first cycle.

Related Products & Technical Resources

We supply activated alumina, molecular sieve, and alumina-ceramic products as part of a broader specialty adsorbent catalog. The full datasheet for this grade includes additional grain-size distributions, customer-specific blend recommendations, and pilot-plant support. Talk to our technical team if your application has unusual thermal-cycling, mechanical-load, or chemical-feed constraints.

• Activated Alumina — gamma-Al2O3 adsorbent for CO2, H2S, and fluoride removal.
• Molecular Sieve — 3A / 4A / 5A / 13X grades for PSA, TSA, and drying service.
• Alumina Powder — high-purity Al2O3 powders for general industrial use.
• Aluminum Hydroxide — ATH flame retardant grade.
• Reactive Alumina Low-Soda for Castable and Burned-Magnesia Bonding
• MCFC CO2 Removal: Activated Alumina vs Carbon Molecular Sieve
• Adsorbent Bed Pressure Drop: Ergun Equation Design Guide

Next Steps — Get a Sample or Talk to Our Engineers

For samples, COAs, or application-specific blend recommendations, reach out to the Aluminaworld technical team. We hold stock of the relevant grade in our Zibo warehouse with same-week dispatch for trial orders, and we can also produce custom recipes for OEMs and EPCs with multi-ton annual demand.

Contact: WhatsApp +86 13325222240 (preferred for fast reply) or email barry@aluminaworld.com. Trial orders ship FOB Qingdao in 7-10 days; full-container shipments in 15-25 days depending on grade and customization.