Parametric study on dispersed phase holdup and axial drop size distribution in a pulsed disc and doughnut extraction column

ABSTRACT

A parametric study of the dispersed phase holdup, specific power consumption (P) and axial drop size distribution (ADSD) in a pulsed disc and doughnut column have been carried out with 30% Tri-Butyl Phosphate- 0.01 M nitric acid system. ‘P’ and holdup decreases with increasing percentage duty cycle and increases exponentially with increased pulsation. Whereas ‘P’ remains almost independent of total superficial velocity and phase flow ratio. At the top of the extraction section, the most uniform DSD have been observed. Subsequently, Unified empirical correlations have been developed over much wider range for predicting the holdup and Sauter mean diameter.

KEYWORDS:

• Dispersed phase holdup
• axial drop size distribution
• specific power consumption
• cumulative volume distribution
• unified correlation

Nomenclature

Table

Acknowledgements

The authors are grateful to Professor Dr J. B. Joshi, Emeritus Professor, Homi Bhabha National Institute, for his valuable guidance. The authors also express their sincere gratitude to Dr. M.L Singh, scientific officer, BARC, for helping them understand the techniques of linear regression. Dr. Joti Nath Sharma and Mr. Sukhdeep Singh, scientific officer, BARC, are humbly acknowledged for their valuable guidance in formatting the manuscript.

Disclosure statement

The authors declare no conflict of interest.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Annexure-I.

Specific power consumption calculation:

$\mathrm{P}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}=\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\ast \mathrm{V}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}$

$\begin{array}{rl}& \mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}=\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\\ & \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{d}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{v}\mathrm{e}\left(\mathrm{P}\mathrm{S}\mathrm{I}\right)\ast \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{g}\end{array}$

$\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{g}=\pi {\mathrm{d}}^2/4;\mathrm{d}=0.0508\mathrm{m}$

$\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{g}=3.14\ast 0.25\ast {0.0508}^2{\mathrm{m}}^2=2.025\ast {10}^{-3}{\mathrm{m}}^2$

$\mathrm{V}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}$

$\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}=\mathrm{P}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{d}\mathrm{e}={\mathrm{A}}_{\mathrm{p}}$

Time =$\frac{\mathrm{d}.\mathrm{c}}{\mathrm{f}}$; where d.c = percentage duty cycle; f= frequency of pulsing (Hz)

Liquid mass in the extraction section = Volume of the extration section * Density of the mixed phase = πD²/4 *L * {ρ_dX + ρ_c(1–X)}= 3.14 * 0.25 * 0.075² * 2 * {ρ_dX+ρ_c(1–X)} kg = 0.0088 * {ρ_dX+ρ_c(1–X)}kg

Specific power consumption= Pressure* $2.025\ast {10}^{-3}\ast \frac{{\mathrm{A}}_{\mathrm{p}}\ast \mathrm{f}}{\mathrm{d}.\mathrm{c}\ast 0.0088\ast \{{\rho }_{\mathrm{d}}\mathrm{x}+{\rho }_{\mathrm{c}}\left(1-\mathrm{x}\right)\}}\ast \left(\frac{101325.16}{14.7}\right)$ W/kg;

The factor $\left(\frac{101325.16}{14.7}\right)$ has been used to convert the pressure in PSI to Pascal.

Therefore, Specific power consumption= 1586.12* Pressure* $\frac{{\mathrm{A}}_{\mathrm{p}}\ast \mathbf{f}}{\mathbf{d}.\mathbf{c}\ast \{{\rho }_{\mathbf{d}}\mathbf{x}+{\rho }_{\mathbf{c}}\left(1-\mathbf{x}\right)\}}$ W/kg

Additional information

Funding

This research is funded by the Bhabha Atomic Research Centre, Mumbai, as a part of the doctoral project.