Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate packed bed pressure drop using the Ergun equation from particle size, bed void fraction, fluid properties, and bed height. Apply to fixed-bed reactors, absorption towers, and adsorption systems.
What this calculator is used for
Packed beds are widely used in chemical reactors, adsorption columns, absorption towers,
and dryers throughout the process industry. When fluid flows through packed particles,
it experiences significant pressure loss due to friction and the tortuous flow path
created by the packing material. Accurate estimation of this pressure drop is essential
for blower, compressor, and pump sizing, as well as for verifying operating pressure margins.
Typical engineering use cases
Preliminary design of packed bed reactors and adsorption columns
Blower and compressor pressure requirement estimation
Evaluating the impact of particle size and void fraction on system performance
Assessing pressure drop increases due to fouling or packing degradation
Operating pressure margin verification for existing systems
Governing equation and methodology
This calculator uses the Ergun equation, which combines viscous and inertial loss terms:
This equation is applicable over a wide range of Reynolds numbers and is commonly used
for both gas and liquid flow through packed beds.
Engineering assumptions and limitations
Uniform particle size and packing
Steady-state, single-phase flow
No channeling or maldistribution
Wall effects in small-diameter columns not considered
Practical design notes
In practice, pressure drop tends to increase over time due to fouling or particle breakage.
Apply appropriate design margins for continuous operation. For critical systems, pilot data
or vendor guarantees are recommended to validate the design.
Worked Example
Given:
Spherical packing dp = 5 mm, bed void fraction ε = 0.40
Air (ρ = 1.2 kg/m³, μ = 1.8×10⁻⁵ Pa·s), superficial velocity v = 0.10 m/s
Interpretation: Note how viscous and inertial terms are comparable here (transitional regime). The result is dominated by ε via the 1/ε³ terms — bed settling or fines that drop ε from 0.40 to 0.35 would raise ΔP by roughly 50 %, so specify the as-packed void fraction, not the ideal one.
Common Mistakes & Misuse
Using a guessed void fraction — the Ergun terms scale with (1−ε)²/ε³ and (1−ε)/ε³, so a 0.40→0.35 error can raise ΔP by over 50%.
Plugging in the nominal particle size for irregular packing without a sphericity correction, which biases the effective diameter that drives the viscous term.
Using interstitial velocity in place of superficial velocity — the Ergun equation is written on the empty-tower (superficial) basis.
Applying the correlation to shallow beds or low tube-to-particle ratios (D/dp < ~10) where wall channelling makes the prediction optimistic.
Frequently Asked Questions
What is the Ergun equation?
The Ergun equation combines viscous (Blake-Kozeny) and inertial (Burke-Plummer) terms to predict pressure drop across a packed bed. It is valid for a wide range of Reynolds numbers and is the standard method for fixed-bed design.
How does void fraction affect pressure drop?
Pressure drop is extremely sensitive to void fraction ε. The Ergun equation has terms proportional to (1-ε)²/ε³ and (1-ε)/ε³. A small decrease in void fraction (e.g., 0.40 to 0.35) can increase pressure drop by over 50%.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.