New Approaches for Prediction of Flow Regime Boundaries and Overall Gas Holdups in a Bubble Column Operated with Aqueous Solutions of 2-Pentanol

Figures & data

Figure 1. GP fluctuations in an aqueous solution of 2-pentanol (0.5 vol.%) at two U_g values.

Table 1. Physicochemical properties of the various mixtures of DW and 2-pentanol.

Mixture of DW and 2-pentanol	σL (N/m) Start	σL (N/m) End	µL (Pa s) Start	µL (Pa s) End	ρL (kg/m^3) Start	ρL (kg/m^3) End
0.5 vol.% 2-pentanol	55.35 × 10^–3	57.65 × 10^–3	0.86 × 10^–3	0.86 × 10^–3	998.25	998.35
1.0 vol.% 2-pentanol	48.12 × 10^–3	51.06 × 10^–3	0.88 × 10^–3	0.87 × 10^–3	997.70	998.35
1.5 vol.% 2-pentanol	43.19 × 10^–3	47.49 × 10^–3	0.89 × 10^–3	0.88 × 10^–3	997.11	998.04
2.0 vol.% 2-pentanol	40.07 × 10^–3	43.01 × 10^–3	0.91 × 10^–3	0.90 × 10^–3	996.50	997.40

Start: before the first run at the highest U_g; end: after the last run at the lowest U_g.

Figure 2. NHI profiles as a function of U_g in a BC operated with a mixture of DW and 2-pentanol (0.5 vol.% and 1.0 vol.%) aerated with a compressed air.

Figure 3. FR identification based on the information amount in a BC operated with a mixture of DW and 2-pentanol (0.5 vol.%) aerated with a compressed air.

Figure 4. Gas holdup (based on a removal of the foaming layer height) profile as a function of U_g in a mixture of DW and 2-pentanol (0.5 vol.%) aerated with a compressed air.

Figure 5. FR identification based on the information amount in a BC operated with a mixture of DW and 2-pentanol (1.0 vol.%) and aerated with a compressed air.

Figure 6. Illustration of: (a) the gas maldistribution (at U_g = 0.035 m/s) and (b) complete foaming state (at U_g = 0.076 m/s) in DW and 2-pentanol (1.0 vol.%) system aerated with air at ambient conditions.

Figure 7. Gas holdup (based on a removal of the foaming layer height) profile as a function of U_g in a mixture of DW and 2-pentanol (1.0 vol.%) aerated with air.

Figure 8. Prediction of overall gas holdups in a BC operated with a mixture of DW and 2-pentanol (0.5 vol.%) and aerated with a compressed air. Mean d value was fitted at 7.48 × 10⁻³ m.

Figure 9. Prediction of overall gas holdups in a BC operated with a mixture of DW and 2-pentanol (1.0 vol.%) and aerated with a compressed air. Mean d value was fitted at 8.96 × 10⁻³ m.

Figure 10. Prediction of overall gas holdups in a BC operated with a mixture of DW and 2-pentanol (1.5 vol.%) and aerated with a compressed air. Mean d value was fitted at 1.53 × 10⁻² m.

Figure 11. Prediction of overall gas holdups in a BC operated with a mixture of DW and 2-pentanol (2.0 vol.%) and aerated with a compressed air. Mean d value was fitted at 2.214 × 10⁻² m.

Table 2. Values of d and MRE for the various mixtures studied.

Volume conc. of 2-pentanol in DW	d (m)	MRE (%)
0.5vol.%	7.48 × 10^–3	6.2
1.0vol.%	8.96 × 10^–3	2.3
1.5vol.%	1.531 × 10^–2	3.6
2.0vol.%	2.214 × 10^–2	3.7

Figure 12. Variations of overall gas holdups as a function of U_g in a BC operated with different mixtures of DW and 2-pentanol and aerated with a compressed air.

Table 3. Comparison of the errors among the different approaches.

Correlation	ARE (%)	MRE (%)
Equation (5)(5) $${\epsilon }_G=129{\left(\frac{U_g{\mu }_L}{{\sigma }_L}\right)}^{0.99}{\left(\frac{{{g\mu }_L}^4}{{\rho }_L{{\sigma }_L}^3}\right)}^{-0.123}{\left(\frac{{\rho }_G}{{\rho }_L}\right)}^{0.187}{\left(\frac{{\mu }_G}{{\mu }_L}\right)}^{0.343}{\left(\frac{d}{D}\right)}^{-0.089}$$(5) with fitting d	2.12	6.25
Equation (5)(5) $${\epsilon }_G=129{\left(\frac{U_g{\mu }_L}{{\sigma }_L}\right)}^{0.99}{\left(\frac{{{g\mu }_L}^4}{{\rho }_L{{\sigma }_L}^3}\right)}^{-0.123}{\left(\frac{{\rho }_G}{{\rho }_L}\right)}^{0.187}{\left(\frac{{\mu }_G}{{\mu }_L}\right)}^{0.343}{\left(\frac{d}{D}\right)}^{-0.089}$$(5) without fitting d (original form)	25.52	36.63
εG = f(Ug)	3.52	9.86