Disclosed are systems and methods for increasing oil production in an integrated oil and gas production plant including hydrogen sulfide removal and sour-gas injection into an underground formation. Hydrogen sulfide-selective membranes are used to debottleneck known systems and methods by removing hydrogen sulfide from bottlenecked plant process steps including sour gas compression, hydrogen sulfide removal and sour gas injection. A method of retrofitting an integrated plant includes adding a hydrogen sulfide-selective membrane upstream of an amine unit to remove hydrogen sulfide from an associated gas stream and form a permeate stream enriched in hydrogen sulfide and a retentate stream depleted in hydrogen sulfide and enriched in hydrocarbon gases. Less hydrogen sulfide is sent to the amine unit and oil production is higher than in the integrated plant without the hydrogen sulfide-selective membrane.