*3.2. Column Study*

#### 3.2.1. Operational Parameters

The LSCFB was designed and fabricated to run for two cycles, namely, the adsorption and desorption cycle, operated for a total duration of 50 min per cycle and maintaining a primary flow rate of 1100 L/h and a secondary flow rate of 750 L/h. The operating feed volume was maintained at 35% of the total volume of the riser, whose dimensions were 1.5 m in height and 0.04 m in diameter. All the experiments were carried out at a room temperature of 30 ◦C. The solid holdup was estimated by the pressure gradient in the riser. On eliminating any kind of effects due to wall friction, the average solid holdup (ε*s*) was determined using Equations (6) and (7).

$$-\frac{\Delta P}{\Delta L} = (\varepsilon\_s \rho\_s + \varepsilon\_1 \rho\_1)\mathbf{g} \tag{6}$$

$$
\varepsilon\_s + \varepsilon\_1 = 1 \tag{7}
$$

where <sup>Δ</sup>*<sup>P</sup>* <sup>Δ</sup>*<sup>L</sup>* , <sup>ε</sup><sup>s</sup> <sup>ε</sup>l, <sup>ρ</sup>*s*, <sup>ρ</sup><sup>l</sup> and *<sup>g</sup>* are the pressure drop gradient (N/m3), solid holdup, liquid holdup, density of the solid (kg/m3), density of the liquid (kg/m3) and acceleration due to gravity (m/s2), respectively.

The value of the terminal velocity (*utr*) of the particle is theorized to be estimated from Equation (8). This value tends to be greater than the minimum fluidization velocity of the particle for the liquid.

$$u\_{tr} = \left[\frac{4(\rho\_s - \rho\_l)^2 \mathbf{g}^2}{225 \rho\_l \mu}\right]^{\frac{1}{3}} d\_p \tag{8}$$

where *dp* and μ are the solid diameter (m) and the liquid viscosity (kg/m s).

The cumulative flow rate of the primary and the secondary inlet pipes provided the total net liquid flow rate. The critical velocity being greater than the terminal velocity of the particle is given by Equation (9) [32,33]:

$$u\_{cr} = 1.2 \ast u\_{tr} \tag{9}$$

The column was operated above the terminal velocity and below the critical transition velocity. The operational conditions of the LSCFB are enlisted in Table 2 [18].

#### 3.2.2. Adsorption Cycle

From the experimental data achieved, it was evident that the LSCFB facilitated a better adsorbate-adsorbent interaction. This was corroborated from the results presented in Figure 5a that showed that the phenol-removal efficiency in the LSCFB was 98%, which was 18% more than the phenol-removal efficiency achieved by 2.5 g of adsorbent dosage in the batch study; also, this enhancement in the phenol-removal efficiency was achieved in a very short operation time of 25 min, as compared with the 3 h contact time of the batch mode.


**Table 2.** Operational parameters for the liquid-solid circulating fluidized bed (LSCFB) column.

**Figure 5.** (**a**) The % phenol removal vs. time in an LSCFB; and (**b**) % phenol desorption vs. time in an LSCFB.

#### 3.2.3. Desorption Cycle

An adsorbent dosage of 2.5 g in the batch study produced a maximum of 56% desorption. Under the same conditions, the continuous column study using the LSCFB resulted in a 64% desorption in a lesser time of 20 min, as shown in Figure 5b. Hence, it was primarily evident that a continuous flow system enriched the desorption level of the adsorbent compared to the batch mode. Additionally, it was also interpreted that on increasing the ethanol concentration, better desorption rates can be achieved in a lesser period.

#### 3.2.4. Column Adsorption Models

On plotting the breakthrough curve for the column [34], a skewed S-shaped curve was obtained, as shown in Figure 6a, which signified the different packing densities in the bed provided by the solid and liquid voidage, thus maintaining the heterogeneity of the bed.

Further modeling was carried out using the Yoon-Nelson, Adam-Bohart and modified-dose response models. The results for the analysis of various column models are presented in Figure 6b–d. The Yoon-Nelson model for column adsorption is described by Equations (10,11) [35]:

$$\ln\left[\frac{\mathcal{C}\_t}{\mathcal{C}\_0 - \mathcal{C}\_t}\right] = k\_{YN}t - \quad k\_{YN}t \tag{10}$$

$$q\_{\rm YN} = \frac{C\_0 \, Q \tau}{1000 \, w} \tag{11}$$

where, *kYN*, τ, *Q*, *w* and *qYN* are the rate constant (1/min), time required for 50% adsorbate breakthrough (min), flow rate (L/min), weight of the adsorbent (g) and Yoon-Nelson adsorptive capacity of the bed (mg/g).

The Adam-Bohart model is based on the theory that the concentration of the feed solution is weak with the speed of adsorption limited by external mass transfer [36]. The model is explained by Equation (12), which relates the value of *C*0/*Ct* with time (t) in an open system. It has been formulated as follows:

$$\ln\left[\frac{\mathcal{C}\_0}{\mathcal{C}\_t} - 1\right] = \left(\frac{k\_{AB}N\_0Z}{\mu}\right) - \left.k\_{AB}\mathcal{C}\_0t\right|\tag{12}$$

where, *kAB*, *Z*, *N*<sup>0</sup> and *u* are the kinetic constant (L/g/min), bed depth in the column (m), Adam-Bohart adsorptive capacity of the bed (mg/g) and outlet velocity of the bed (m/min).

The modified dose-response (MDR) model is a topical fit variant for the column adsorption studies. It is a non-linear logistic fit mostly used to describe the column adsorption behavior of heavy metals. The model is described by the non-linear correlation as specified in Equations (13) and (14) [37].

$$\frac{C\_t}{C\_0} = 1 - \frac{1}{\left(\frac{\mu t}{\mathcal{V}} + 1\right)^a} \tag{13}$$

$$q\_{\rm MDR} = \frac{\mathcal{C}\_0 \, b}{w\_a} \tag{14}$$

where *a* and *b* (mL) are the characteristic factors of the MDR model.

**Figure 6.** (**a**) Phenol-activated carbon breakthrough curve analysis; (**b**) Yoon-Nelson fit model; (**c**) Adam–Bohart fit model; and (**d**) modified-dose response model.

Table 3 presents the characteristic column adsorption capacity obtained for the experimental studies as well as using various theoretical models examined for the column adsorption. The higher correlation coefficient of *R*<sup>2</sup> = 0.8987 indicated that the column adsorption studies obeyed the Adam-Bohart model. The adsorbent capacity predicted by this model was also very close to that of the experimental values. This showed that the column adsorption of phenol onto the activated-carbon-coated glass beads involved a quasi-chemical interactions along with the absence of the internal diffusion effects of the bulk phase on the solid phase [36].

