Open Bed — Chromatography Calculator

How it works: Enter your process parameters and open-bed test measurements (bed height, pressure drop ΔP, and flow velocity). The engine automatically curve-fits an exponential pressure–flow model and a bed-compression model to predict Critical, Packing and Running parameters. Uncheck any unstable data points and the fit updates automatically.

Process Parameters

Bed height, L

Column inner diameter, ID

Aspect ratio L / ID

Particle diameter (reference)

µm

Viscosity @ 20°C, cp₂₀

Temperature

°C

Total viscosity, cp (auto, water-corrected)

Models

cp(T) = [µ_water(T)] × cp20

x = ΔP × L ÷ bedH (normalised pressure)

y = fa(1 − fbx) ÷ (L·cp) (flow)

bedH(P) = fe + fce−f_dP + ffe−f_gP²

Aspect ratio — wall support

L / ID ≥ 2.0 ➜ Significant

1.0–2.0 ➜ Moderate

0.5–1.0 ➜ Marginal

< 0.5 ➜ Negligible

Open-Bed Test Data

Need at least 6 data points.

Use	#	Bed height (cm)	ΔP (bar)	Flow	Flow (cm/h)	x̄, Bar comp (calc)	ŷ, estim (cm/h)	Del

Tick a row to include it in the fit. The first row (ΔP = 0) anchors bed compression (self-sedimentation height); the flow model ignores zero-flow rows. x̄ is pressure normalised to bed height L; ŷ is the fitted flow estimate. Enter the volumetric flow (ml/min, unit selectable in the column header); Flow (cm/h) is the calculated linear velocity = volumetric × 60 ÷ [π·(ID/2)²], using the column inner diameter from Process Parameters.

Fitted Parameters

Flow model — y = f_a(1−f_b^x)/(L·cp)

f_a

—

f_b

—

SSR

—

Compression model — bedH = f_e+f_ce^−f_dP+f_fe^−f_gP²

f_c

—

f_d

—

f_e

—

f_f

—

f_g

—

SSR

—

Enter data to fit.

Legend

f_a asymptotic flow (cm/h)

f_b rise rate (exponent base)

f_c primary compressible amplitude (cm)

f_d primary compression decay rate

f_e incompressible baseline height (cm)

f_f secondary compressible amplitude (cm)

f_g secondary compression decay rate

SSR sum of squared residuals (goodness of fit)

Predicted Operating Parameters

Parameter	Pressure (bar)	Flow (ml/min)	Flow (cm/h)
Critical	—	—	—
Packing (70%)	—	—	—
Running (70% of packing)	—	—	—

Packing flow / Critical

—%

Running flow / Critical

—%

Bed compression

Self-sedimentation height

—cm

Bed height @ packing P
—cm

Compression factor

—%

Packing factor

—

Fitted Curves

Pressure – Flow (open bed)

Exponential-rise-to-maximum model with measured points.

Model Measured Critical Packing Running

Bed compression

Bed height versus pressure (double-exponential model).

Model Measured Packing P

References

Nelder, J.A. & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4), 308–313. — The derivative-free optimisation algorithm used throughout this calculator for all curve fits.

Stickel, J.J. & Fotopoulos, A. (2001). Pressure-flow relationships for packed beds of compressible chromatography media at laboratory and production scale. Biotechnol. Prog., 17, 744–751. — Empirical model linking critical velocity to aspect ratio (L/D); wall support decreases linearly with inverse diameter.

Keener, R.N., Maneval, J.E. & Fernandez, E.J. (2004). Toward a robust model of packing and scale-up for chromatographic beds: 1. Mechanical compression. Biotechnol. Prog., 20, 1146–1158. — Janssen-Walker continuum-mechanics model of stress attenuation by wall friction; characteristic length scale proportional to column diameter.

Guiochon, G., Drumm, E. & Cherrak, D. (1999). Evidence of a wall friction effect in the consolidation of beds of packing materials in chromatographic columns. J. Chromatogr. A, 835, 41–58. — Definitive experimental characterisation of mechanical wall support in packed beds.

Physical Analysis (Blake–Kozeny)

Cross-checks the empirical fit against rigid-bed theory

This panel estimates the effective porosity of the packed bed from the compression model and compares the empirical exponential fit with the Blake–Kozeny equation (the laminar term of Ergun) to assess whether the bed is in a compressible or critical/incompressible regime (Stickel & Fotopoulos, 2001). Adjust the gravity-settled porosity ε₀ to match your media.

Settled porosity ε₀

Sphericity φ

Solid density ρₛ (g/mL, optional)

ε @ packing pressure

—

Compressibility index

—

Blake–Kozeny flow @ ε

—

Empirical / BK ratio

—

Bed regime

—

Scale-up prediction (Stickel–Fotopoulos)

Wall support reduces bed compression in narrow columns. When scaling to a wider column, the bed compresses more, increasing flow resistance. Enter the target production-column diameter to see the predicted shift.

Lab L/D ratio

—

Target col. ID (cm)

Target bed H (cm, optional)

Predicted flow @ target

—

Blake–Kozeny: ΔP/L = 150·μ·(1−ε)²·v / (ε³·dp²·φ²). The compressibility index measures how much the bed compacts from its gravity-settled state to the packing pressure. Ratios close to 1.0 mean the empirical fit matches rigid-bed theory (your bed is in the critical/incompressible regime). Ratios ≪ 1.0 indicate additional flow resistance from bed compression that Blake–Kozeny alone cannot capture — your bed is in the compressible regime.