The present invention provides an acid catalyzed isoparaffin-olefin alkylation process which improves process stability and safety by storing the acid in an excess of an additive which reduces the fuming tendency of the mixture, for example, a sulfone. Acid is stripped from the additive and concentrated prior to charging the acid to the alkylation reaction zone. Specifically, because the stored solution of acid in the additive is more dilute than can be effectively used for isoparaffin-olefin alkylation, the acid is concentrated prior to charging the catalyst mixture to the reaction zone. The invention solves the problem of conjunct polymer accumulation by diluting the conjunct polymer with a relatively large volume of the additive and continuously regenerating a slipstream of the dilute acid/additive mixture.