Bodenstein Number (Bo) & Levenspiel Closed-Vessel RTD Variance Formula

Bridging ideal Plug Flow (Bo -> infinity) and ideal CSTR backmixing (Bo -> 0) via tracer RTD variance!

Named after chemical kinetics pioneer Max Bodenstein, the axial mass-peclet / Bodenstein number Bo = (u * L) / D_ax (the reciprocal of Octave Levenspiel’s vessel dispersion number D_ax / (u * L)) measures the ratio of convective plug transport to axial eddy/molecular dispersion across reactor or packed-column length L!

For a closed-closed vessel (no dispersion across the inlet or outlet nozzles—van der Laan, 1958; Levenspiel, Chemical Reaction Engineering), the exact dimensionless tracer residence-time distribution (RTD) variance is sigma_theta^2 = sigma_t^2 / tau^2 = (2 / Bo) - (2 / Bo^2) * (1 - EXP(-Bo))! At interstitial velocity u = 0.15 m/s, length L = 2.4 m, and D_ax = 0.018 m^2/s, Bo = 20.00 (low-to-moderate dispersion) with sigma_theta^2 = 0.09500 (close to 2/Bo = 0.10, vs. Bo = 8.00 when channelling boosts D_ax to 0.045 m^2/s)!

Bodenstein Axial Dispersion Number Bo = (u * L) / D_ax

Computes convective-to-dispersive ratio Bo from interstitial velocity u (B2, m/s), bed length L (B3, m), and axial dispersion coefficient D_ax (B4, m²/s).

=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Axial Dispersion Inputs", ROUND((B2 * B3) / B4, 2))

Van der Laan / Levenspiel Closed-Vessel RTD Dimensionless Variance sigma_theta²

Evaluates exact closed-boundary variance 2/Bo - (2/Bo^2)*(1 - EXP(-Bo)).

=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Axial Dispersion Inputs", ROUND(2 / ((B2 * B3) / B4) - (2 / (((B2 * B3) / B4) ^ 2)) * (1 - EXP(-(B2 * B3) / B4)), 5))

Further reading

• Microsoft Support — EXP function