I got about the same results as you with Henry's law at 20 deg C.
Following environmental regulations hydrocarbons and H2S may have to be absorbed from the tank vent gases, as you are planning to do.
Assuming you are referring to an oil refinery sour water tank (as an upstream storage to feed a stripper) here are some additional precautions taken by some refiners, for example:
a. Leaving about 2 ft of hydrocarbons floating on top of the sour water for odor reduction, taking care of removing the hydrocarbons before emptying the tank to prevent their being fed to the stripper.
b. Providing an inert (nitrogen) blanket for more efficient odor control and to prevent the formation of explosive atmospheres.
The tank is supposed to be operated at about 60% full, maximizing residence time to homogeinize the composition of the sour water due to fluctuating refinery operations considering the need of a -more or less- stable stripping operation, as well as to permit the efficient removal of hydrocarbons.
Would you prefer to carry out a lab bench experiment to measure the H2S in the vent gases assuming the above procedures ? Kindly comment.