CHE-26

Ergun packed-bed pressure drop

Blake–Kozeny plus Burke–Plummer: viscous and inertial losses.

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Packed bedsErgun 1952

Governing equation

\dfrac{\Delta P}{L}=150\dfrac{\mu(1-\varepsilon)^2 u}{\varepsilon^3 d_p^2}+1.75\dfrac{\rho(1-\varepsilon)u^2}{\varepsilon^3 d_p}

where

\mu: Viscosity (Pa·s)
\varepsilon: Void fraction (—)
u: Superficial velocity (m/s)
d_p: Particle diameter (mm)
\rho: Fluid density (kg/m³)
L: Bed length (m)
\Delta P: Pressure drop (kPa)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-26 — Ergun packed-bed pressure drop) is the form associated with Ergun 1952. Working symbols: $\mu$ , $\varepsilon$ , $u$ , $d_p$ , $\rho$ , $L$ $\rightarrow$ $\Delta P$ . Ergun added the laminar Kozeny and turbulent Burke–Plummer terms to correlate ΔP through packed beds of spheres.

Purpose

Purpose: compute

\Delta P

from

\mu

\varepsilon

u

d_p

\rho

L

in Chemical engineering via

\dfrac{\Delta P}{L}=150\dfrac{\mu(1-\varepsilon)^2 u}{\varepsilon^3 d_p^2}+1.75\dfrac{\rho(1-\varepsilon)u^2}{\varepsilon^3 d_p}

Blake–Kozeny plus Burke–Plummer: viscous and inertial losses. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.001\,\mathrm{Pa·s}

\varepsilon = 0.400\,\mathrm{—}

u = 0.200\,\mathrm{m/s}

d_p = 3.000\,\mathrm{mm}

\rho = 1000.000\,\mathrm{kg/m^{3}}

L = 1.000\,\mathrm{m}

, the governing relation

\dfrac{\Delta P}{L}=150\dfrac{\mu(1-\varepsilon)^2 u}{\varepsilon^3 d_p^2}+1.75\dfrac{\rho(1-\varepsilon)u^2}{\varepsilon^3 d_p}

yields

\Delta P = 237.50\,\mathrm{kPa}

. A packed column, a ΔP arrow, two loss bars. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Viscosity \mu0.001 Pa·sVoid fraction \varepsilon0.4 —Superficial velocity u0.2 m/sParticle diameter d_p3 mmFluid density \rho1000 kg/m³Bed length L1 m

Outputs

Pressure drop \Delta P237.50 kPa

Reading speed

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Narration of this film

A packed column, a ΔP arrow, two loss bars.

Ergun added the laminar Kozeny and turbulent Burke–Plummer terms to correlate ΔP through packed beds of spheres.

Reading speed

Watch on YouTube