Estimation of Performance with the Two Truncated Probability Density Functions, Case Study: Using Mixco Column to Extract Samarium and Gadolinium

ABSTRACT

A hydrodynamic performance by the variation in the droplet size and distribution was moreover considered in the recording of experimental data for the extraction of rare-earth ions. The percentage of stripping and extraction efficiency for rare earth ions increases directly proportional to rotation speed. The identification of a suitable probability density function is carried out by utilizing the mixture of two normal probability density functions. By separation factor exceeding 5.9, extraction efficiency and percentage of stripping up to 95% could be achieved in the continuous Mixco column, which has superior hydrodynamic characteristics with a great prospect of application.

Graphical Abstract

KEYWORDS:

• Rare Earth Ions
• d2ehpa
• stripping
• extraction
• drop Diameter and Distribution

Symbols

AARE	=	average absolute relative error (-)
D	=	distribution ratio (-)
d32	=	Sauter mean diameter (m)
dR	=	rotor diameter (m)
E	=	extraction efficiency (-)
g	=	acceleration due to gravity (m/s2)
M	=	concentration ions (mg/L)
N	=	rotor speed (1/s)
Qc	=	continuous phase flow rate (m3/s)
Qd	=	dispersed phase flow rate (m3/s)
R	=	reaction parameter (-) in Eq. (6(6) ${\mathrm{d}}_{32}=5.42\times {10}^{-4}{R}_1{\left(\frac{{\rho }_{\mathrm{c}}{\mathrm{N}}^4{\mathrm{d}}_{\mathrm{R}}^4}{\mathrm{g}\sigma }\right)}^{-0.311}{\left(\frac{{\mu }_{\mathrm{c}}^4\mathrm{g}}{\mathrm{\Delta }\rho {\sigma }^3}\right)}^{-0.258}{\left(1+\frac{{\mathrm{V}}_{\mathrm{c}}}{{\mathrm{V}}_{\mathrm{d}}}\right)}^{-0.075}$(6) )
S	=	stripping efficiency (-)
V	=	Volume (m3)
Vc	=	continuous phase velocity (m/s)
Vd	=	dispersed phase velocity (m/s)
w	=	weight function

Greek Letters

∆ρ	=	density difference between phases (kg/m3)
β	=	separation factor (-)
μ	=	viscosity (Pa.s)
ρ	=	density (kg/m3)
σ	=	interfacial tension (N/m)

Subscripts

c	=	continuous phase
d	=	dispersed phase

Highlights

• The feasibility of pilot-scale multistage extraction column for REE ions was investigated.

• Larger drop size and wider drop size distribution are obtained in the stripping stage.

• A mixture of two truncated probability density functions is proposed for drop size distribution.

• The results indicated that rotation speed imposed more influence on %E and %S.

• High values for extraction efficiency, stripping percent, separation factor were obtained.