5.4 Results and discussion
5.4.1 Variations of frictional pressure drop with different variables
In the previous chapter, the effect of superficial gas velocity on the gas holdup in the presence of water-paraffin liquid and water-kerosene in the gas-liquid-liquid downflow contactor was reported (Goshika and Majumder, 2018). It was observed that the gas holdup of the downflow contactor increases with an increase in the concentration of water-paraffin liquid and water-
kerosene systems with varying gas superficial velocity. In this chapter, the effect of the gas holdup on a three-phase frictional pressure drop in the presence of water-paraffin liquid and the water-kerosene is analyzed. The impact of the gas holdup on a three-phase frictional pressure drop with varying superficial gas velocity for 15% (v) paraffin liquid is shown in Figure 5.1a. It is observed that frictional pressured drop increases with an increase in the gas holdup and superficial gas velocity. As the gas holdup of the system increases, the contact among the paraffin droplets generates more friction and turbulence with an increase in the gas-liquid-liquid mixture velocity. The frictional pressure drop variation with the gas holdup with kerosene of 15% (v) at a different gas flow rates is shown in Figure 5.1b. The frictional pressure drop increases with an increase in overall gas holdup (ɛg). But the frictional pressure drop in case of kerosene is less than that of the paraffin liquid. This is due to the lower viscosity of the kerosene than that of the paraffin liquid.
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 5
10 15 20 25 30 35
usg= 0.84 × 10- 2 m/s usg= 1.70 × 10- 2 m/s usg= 2.55 × 10- 2 m/s usg= 3.40 × 10- 2 m/s
∆PfT (Pa)
εg (-)
(a)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0
5 10 15 20
usg = 0.84 × 10- 2 m/s usg = 1.70 × 10- 2 m/s usg = 2.55 × 10- 2 m/s usg = 3.40 × 10- 2 m/s
εg (-)
∆PfT (Pa)
(b)
Figure 5.1: Variations of frictional pressure drop with gas holdup at different gas velocity (a) for 15% (v) of paraffin liquid, (b) for 15% (v) of kerosene
Figure 5.2a and Figure 5.2b represent the deviation of a frictional pressure drop along with the
corresponding gas holdup of dispersed liquid, paraffin liquid, and kerosene of 35% volume. The frictional pressure drop rises with a rise in overall gas holdup (ɛg), but the frictional pressure drop in case of dispersed liquids of higher volume (35%) is more than that at the lower volume (15%) due to the higher resistance of the fluids as the liquid-liquid mixture viscosity increases with the volume of dispersed liquid.
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0
10 20 30 40
usg = 0.84 × 10- 2 m/s usg = 1.70 × 10- 2 m/s usg = 2.55 × 10- 2 m/s usg = 3.40 × 10- 2 m/s
∆PfTP (Pa)
εg (-)
(a)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0
5 10 15 20
usg = 0.84 × 10- 2 m/s usg = 1.70 × 10- 2 m/s usg = 2.55 × 10- 2 m/s usg = 3.40 × 10- 2 m/s
∆PfTP (Pa)
εg (-)
(b)
Figure 5.2: Variations of frictional pressure drop with gas holdup at different gas velocity (a) for 35% (v) of paraffin liquid-water, (b) for 35% (v) of kerosene-water
5.4.1.2 Effect of gas and liquid-liquid mixture Reynolds number on frictional pressure drop The frictional pressure drop variation with gas and liquid-liquid mixture Reynolds number is shown in Figure 5.3a. The frictional pressure drop rises with a rise in liquid-liquid mixture and gas Reynolds number. By increasing the superficial gas velocity, the flow area of the liquid- liquid mixture inside the column decreases due to higher gas holdup, which led to a rise in the frictional pressure drop. A similar trend is also reported by many researchers (Kundu et al., 1995;
Babu et al., 1999; Sivaiah and Majumder, 2012; Majumder, 2016). At a fixed superficial gas velocity, with the increase in liquid velocity, the intensity of liquid-liquid mixture inside the
column leads to the coalescence of drops to generate bigger size drops which cause a rise of friction in the column. The frictional pressure drop variation with liquid-liquid mixture and gas Reynolds number at 15% (v) kerosene is shown in Figure 5.3b. It is seen that the frictional pressure drop rises with a rise in liquid-liquid mixture Reynolds number. The frictional pressure drop of kerosene is less than that for the paraffin liquid.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 5 10 15 20 25 30 35 40
Reg= 27.82 Reg= 55.64 Reg= 83.46 Reg= 111.28
∆PfT (Pa)
Redl-cl ×10-3 (-)
(a)
2 3 4 5 6 7
0 5 10 15 20
Reg= 27.82 Reg= 55.64 Reg= 83.46 Reg= 111.28
∆PfT (Pa)
Redl-cl× 10-3 (-)
(b)
Figure 5.3: Variations of frictional pressure drop with liquid-liquid mixture Reynolds number (a) for 15% (v) of paraffin liquid, (b) for 15% (v) of kerosene
The variations of frictional pressure drop with mixture (liquid-liquid) Reynolds number for a certain holdup of paraffin and kerosene are shown in Figures 5.4a and 5.4b, respectively. It is observed that the frictional pressure drop rises with an increase in the volume of liquid-liquid mixture Reynolds number. However, the frictional pressure drop of dispersed liquids of higher volume (35%) is more than that for the lower volume (15%). This is owed to the higher resistance of the fluid as the liquid-liquid mixture viscosity increases with the amount of dispersed liquid.
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 5
10 15 20 25 30 35
Reg= 27.82 Reg= 55.64 Reg= 83.46 Reg= 111.28
∆PfT (Pa)
Redl-cl× 10-3 (-)
(a)
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
0 5 10 15 20
Reg= 27.82 Reg= 55.64 Reg= 83.46 Reg= 111.28
∆PfT (Pa)
Redl-cl×10-3 (-)
(b)
Figure 5.4: Variations of frictional pressure drop with liquid-liquid mixture Reynolds number (a) for 35% (v) of paraffin liquid, (b) for 35% (v) of kerosene
5.4.1.3 Effect of different dispersed liquid volume on frictional pressure drop
The variation of frictional pressure drop with dispersed liquid volume (for paraffin liquid) is shown in Figure 5.5a. It is found that the increase in dispersed liquid volume increases the frictional pressure drop and the viscosity of the gas-liquid-liquid mixture. Those mentioned above hindered the movement of drops which leads to a decrease in column friction. As increasing the dispersed liquid concentration, the interstitial liquid velocity decreased by the higher friction losses between drops and the viscous liquid medium. The variation of frictional pressure drop with dispersed liquid volume for kerosene is shown in Figure 5.5b. The frictional pressure drop rises with a rise in dispersed liquid volume. The frictional pressure drop is higher for kerosene than that for the paraffin liquid due to the lower viscosity of kerosene.
20 40 60 80 100 120 0.5
1.0 1.5 2.0 2.5 3.0
5% paraffin liquid 15% paraffin liquid 25% paraffin liquid 35% paraffin liquid uj = 4.24 m/s
Reg (-)
∆PfT (Pa)
(a)
20 40 60 80 100 120
0.7 0.8 0.9 1.0 1.1 1.2
5% kerosene 15% kerosene 25% kerosene 35% kerosene at uj= 4.24 m/s
Reg (-)
∆PfT (Pa)
(b)
Figure 5.5: Variations of frictional pressure drop with gas Reynolds number at different dispersed concentrations of (a) paraffin liquid, (b) kerosene
5.4.2 Analysis of frictional pressure drop by different models