Process for hydrotreating a feed stream comprising a biorenewable feedstock with treatment of an off-gas stream

A process for hydrotreating a feedstock, the process comprising:

• hydrotreating a feed stream comprising a biorenewable feedstock in the presence of a hydrotreating hydrogen stream and hydrogen sulfide and a hydrotreating catalyst to provide a hydrotreated stream;
• separating said hydrotreated stream into a hydrotreated liquid stream and a hydrotreated gas stream;
• passing the hydrotreated liquid stream to a stripper column to provide an overhead gaseous stream and a bottoms stream comprising diesel product;
• condensing the overhead gaseous stream to provide a stripper off-gas stream and a stripper overhead liquid stream;
• contacting at least a portion of the stripper off-gas stream with a caustic stream to provide a sulfur-lean gas stream and a sulfur-rich spent caustic stream;
• combusting sulfur in the sulfur-rich spent caustic stream to provide a flue gas stream comprising sulfur oxide;
• and
• treating the flue gas stream with a scrubbing reagent to produce salts and provide a treated gas stream,
• wherein the step of contacting the at least a portion of the stripper off-gas stream with the caustic stream comprises selectively removing a greater proportion of hydrogen sulfide from the stripper off-gas stream than carbon dioxide in the sulfur-rich caustic stream.