Methods and machinery are described for combining methane with sulfur trioxide to make MSA, in a system that sustains optimal concentrations of reactants in the main reactor for high yields, efficiency, and profitability. Rather than simply making MSA and then removing it, this design uses a “continuous loop system” with: (i) a “rich acid” stream containing a high concentration of MSA, mixed with sulfuric acid, which will emerge from the main reactor, and (ii) a “reduced acid” stream containing a low concentration of MSA (still mixed with sulfuric acid), from an extractor unit (such as a distillation unit) which removes some but not all of the MSA from the “rich acid”. Additional subassemblies are described which enable the main reactor to work efficiently, at a sustained high flow-through capacity. This system also can be scaled up or down, for any daily MSA production rate.