Study of holdup and slip velocity in an L-shaped pulsed sieve-plate extraction column

International Journal of Industrial Chemistry https://doi.org/10.1007/s40090-018-0167-y RESEARCH Study of holdup and slip velocity in an L‑shaped pulsed sieve‑plate extraction column Elham Mohammadi1 · Jafar Towfighi1 · Jaber Safdari2 · Mohammad H. Mallah2 Received: 28 April 2018 / Accepted: 26 December 2018 © The Author(s) 2019 Abstract High-end applications require a very tall vertical extraction column in some cases which deteriorates protection against radiation and cannot be employed for indoor applications. On the other hand, horizontal extraction columns offer higher efficiency and pretension, but lower maximum throughput. In order to address this issue, the L-shaped pulsed extraction column is a new type of extractors which were recently introduced for such applications with area constraints. The objective of this study is to evaluate the effects of operating parameters and physical properties on the variation of holdup and slip velocity in this type of extractors for three liquid systems including toluene–water, butyl acetate–water and n butanol–water without and under mass transfer condition. A comprehensive investigation on the determination of predictive ability of available correlations for the holdup and slip velocity in pulsed plate columns has been conducted. Finally, new correlations are proposed for prediction of these parameters regarding operational conditions and physical properties. Keywords L-shaped pulsed plate column · Slip velocity · Holdup · Pulsation intensity · Mass transfer List of symbols A Amplitude of pulsation, m Af Pulsation intensity, m/s D Column diameter, m d Hole diameter, m f Frequency of pulsation, Hz g Acceleration due to gravity, = 9.81 m/s2 h Plate spacing, m H Column length, m Q Volumetric flow rate, m3/s Vc Superficial velocity of continuous phase, m/s Vd Superficial velocity of dispersed phase, m/s Vs Slip velocity, m/s Greek symbols 𝛼 Fractional free area 𝜑 Holdup 𝜇 Viscosity, N s/m2 𝜌 Density, kg/m3 * Jaber Safdari 1 Chemical Engineering Department, Tarbiat Modares University, P.O. Box: 14115‑143, Tehran, Iran 2 Materials and Nuclear Fuel Research School, Nuclear Science and Technology Research Institute, Tehran, Iran Δ𝜌 Density difference between two phases, kg/m3 𝜎 Interfacial tension between two phases, N/m Introduction Solvent extraction is one of the methods applied in separation industry. There are numerous types of extractors including mixer-settlers, columns, and centrifugal extractors [1]. Pulsed columns are a class of solvent extractors which offer various advantages such as high throughput, simple design, low space requirement, and with no internal moving parts [2]. Various internals have been used so far in pulsed columns such as packing, perforated plates and disc and doughnuts. However, pulsed columns can be classified in two structural groups: 1. Vertical pulsed columns. 2. Horizontal pulsed columns. Each kind has its own advantages and disadvantages. It is revealed that the mass transfer efficiency is comparable in both types of columns, whereas area limitations are influential variables that affect the industrial use of these columns. Moreover, the need time to start up the vertical columns is less than the horizontal ones, whereas in vertical 13 Vol.:(0123456789) International Journal of Industrial Chemistry columns, the throughput capacity is higher than the horizontal columns. According to previous investigations on the main features of the horizontal and vertical types of extraction columns, it is observed that the advantages of vertical pulsed columns are more than the horizontal ones [3–6]. It is believed that an L-shaped pulsed plate column has the potential to obviate some of the main disadvantages of the horizontal and vertical types in industrial applications as follows: 1. Throughput of the L-shaped pulsed sieve—plate column is less than the vertical types and more than the horizontal types. 2. Height for installation and requirement surface area of an L-shaped column as indoor is less than that of the vertical or horizontal columns. 3. The energy consumption in the L-shaped column is somewhat between that in the horizontal columns and the vertical columns. In this regard, various efforts have been made. Amani et al. [7] studied the effects of operating parameters on the two-phase pressure drop in an L-shaped pulsed plate column. They also examined the throughput of the column and proposed new correlations for prediction of pressure drop and flooding points. A particular approach for preventing flooding has been developed as well. Akhgar et al. [8]. investigated the flow regime transitions in an L-shaped column and determined the values of characteristic velocities in the column under different steady-state operating conditions. In this study, the transition from dispersion to emulsion regime in the horizontal section and the transitions from mixer-settler to dispersion regime in the vertical section have been correlated, characterizing the minimum and maximum operating capacity of the column. In another study, the measurement of mean drop size and drop diameter distribution has been focused by Amani et al. [9, 10]. The drop behavior in different operating regimes has been evaluated and new correlations have been proposed for prediction of mean drop size in terms of operating parameters and physical properties of the chemical systems. Moreover, the drop size distribution is found to be well correlated using the log-normal probability density function. Regarding the well description of extraction column operation, it is essential to evaluate the variation of drop population characteristics such as holdup and drop size [11]. In fact, pulsation improves the column performance due to providing higher drop breakage and consequently increasing the interfacial area between two phases. However, because of the entrainment of small drops and thereby increasing axial mixing, the column performance might be affected by pulsation [12]. Thus, investigation of hydrodynamic parameters including holdup and slip velocity is crucial for design 13 and scaling up of an extraction column to determine the drag coefficients, [13–16] and mass transfer performance [17–20]. The dispersed phase holdup (φ) can be defined as volume fraction of the column which is occupied by the dispersed phase: 𝜑= 𝜐d , 𝜐c + 𝜐d (1) where 𝜐d and 𝜐c represent the volume of the dispersed and continuous phases, respectively. Moreover, the slip velocity is the relative velocity with respect to the continuous phase, which can be characterized by Eq. (2), as the sum of the linear actual velocities of the continuous and dispersed phases under condition of countercurrent flow: [21] Vs = Vc Vd + , 𝜑 1−𝜑 (2) where Vd and Vc are the superficial velocities of the dispersed and continuous phases and can be obtained by Eq. (3) as follows: V= Q . A (3) Various investigations have been implemented on the dete (...truncated)