Question 31.7: Examples 3 to 5 have focused on gas absorption processes. In......
Examples 3 to 5 have focused on gas absorption processes. In the final example of this chapter, we will consider a liquid stripping process, focusing on determination of the minimum and operating carrier gas flow rate.
A liquid stream containing dissolved ammonia (NH_{3}, solute A) in water must be reduced in composition from 0.080 moles A/mole solvent to 0.020 moles A/mole solvent, using air as the stripping gas at 293 K and 1.0 atm to transfer the volatile NH_{3} from the liquid to the gas phase. The process will be carried out in a packed tower with countercurrent flow of gas and liquid. If inlet liquid flow rate fed to the top of the tower is fixed at 0.010\,\mathrm{kgmole}/\mathrm{m^{2}}\cdot{\mathrm{s}}, determine the minimum inlet gas flow rate of air fed to the bottom of the tower, and the mole ratio of NH_{3} in the exiting stripping gas at an operating rate of 2.0 times the minimum gas flow rate. Equilibrium distribution data were provided in Example 3.
The equilibrium distribution curve in mole ratio coordinates for the ammonia-water-air system at 293 K and 1.0 atm is provided in Figure 31.24. At the bottom of the tower, Y_{A_{1}}=0\ \mathrm{and}\ X_{A_{1}}=0.020. Based on the shape of the operating curve, the pinch point will occur at the top of the tower where the gas exits and the feed liquid enters. Consequently, at {{X}}_{A_{2}}=0.080, we see that Y_{A,\operatorname*{min}}=0.071, which is on the equilibrium line, as shown in Figure 31.24.
The minimum carrier gas flow rate at this Y_{A,\operatorname*{min}} is determined by material balance. First, the solvent flow rate is
L_{S}=L_{2}(1-x_{A_{2}})={\frac{L_{2}}{1+X_{A_{2}}}}={\frac{0.010\,{\mathrm{kgmole}}/{\mathrm{m}}^{2}\cdot{\mathrm{s}}}{1+0.080}}=0.00926\,{\mathrm{kgmole}}/{\mathrm{m}}^{2}\cdot{\mathrm{s}}
The minimum carrier gas flow rate is
G_{S,{\mathrm{min}}}=L_{S}{\frac{(X_{A_{2}}-X_{A_{1}})}{(Y_{A_{2},{\mathrm{min}}}-Y_{A_{1}})}}=(0.00926){\frac{(0.080-0.020)}{(0.071-0.0)}}=0.0078\;{\mathrm{kgmole}}/{\mathrm{m}}^{2}\cdot{\mathrm{s}}
and the operating carrier gas flow rate is
G_{S}=2\cdot G_{S,\mathrm{min}}=2(0.0078\;\mathrm{kgmole}/\mathrm{m}^{2}\cdot{\mathrm{s}})=0.0156\;\mathrm{kgmole}/\mathrm{m}^{2}\cdot{\mathrm{s}}
Finally, the mole ratio composition of NH3 in the outlet gas at the operating carrier gas flow rate is
Y_{A_{2}}=Y_{A_{1}}+\frac{L_{S}}{G_{S}}(X_{A_{2}}-X_{A_{1}})=0.0+\frac{(0.00926)}{(0.0156)}(0.080-0.020)=0.0356\frac{\mathrm{mole~NH}_{3}}{\mathrm{mole~air}}
The operating line at Y_{A_{2}} is also shown in Figure 31.24.