Methods may include circulating a first wellbore fluid into a wellbore, wherein the first wellbore fluid contains: a non-aqueous continuous phase, and a polyester internal breaker; wherein the first wellbore fluid generates a filter cake in at least a section of the wellbore; circulating a second wellbore fluid into the wellbore, wherein the second wellbore fluid contains an acid source and a surfactant; and allowing the second wellbore fluid to degrade at least a portion of the filter cake. Other methods may include circulating a wellbore fluid into a wellbore drilled with an oil-based mud containing a polyester fluid loss additive, wherein the wellbore fluid comprises one or more surfactants and an acid source.