A natural gas stream with a total volumetric flow rate of 880 standard cubic meters (SCM) per hour (std m³/h), temperature of 40°C, and total system pressure of 405 kPa is contaminated with 1.0 mole % hydrogen sulfide (H₂S). A packed-bed gas absorption tower of 2.0 m diameter is used to lower the H₂S concentration in the natural gas down to 0.050 mole% so that the H₂S will not poison a steam-reforming catalyst used to convert the natural gas to hydrogen gas. Since H₂S is not very soluble in water, the chelating agent monoethanolamine (MEA, molecular weight 61 g/gmole) is added to water to increase the equilibrium solubility of the H₂S in aqueous solvent systems. In the present problem, an aqueous, 15.3 wt % MEA solvent containing no H₂S at a total flow rate of 50 kgmole/h is added to the top of the tower to selectively remove the H₂S from the natural gas stream. The tower packing height is 10.0 m.
a. From a process material balance, determine mole fraction composition of H₂S in the liquid scrubbing solvent exiting the tower.
b. Using the equilibrium distribution data in the table provided below, provide a plot of y_Avs. x_Afor the process, showing the equilibrium and operating lines.
c. Determine the minimum solvent flow rate L_S,min.
d. Back out the required overall mass-transfer coefficient of the operating tower, K_Ga, given that the packing height (z) is 10.0 m.
Equilibrium distribution data at 40°C for 15.3 wt% MEA in water (A = H₂S)^*:

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PA (mm Hg) 9.1 0.96 143 3.0 43.1 59.7 106 0.642 0.814 0.842 mole H2S/mole MEA 0.125 0.208 0.362 0.729