Under the terms limited knowledge of the kinetics of the processes of chemisorption of sulfur oxides, an approach to qualitative determination of the chemisorption capacity of limestone-based adsorbents is proposed, which allows to optimize the hardware-technological design of the sulfur oxide capture process at the design stage. To take into account the high cost of effective fine adsorbents, it is proposed to recycle part of the source product, which contains an adsorbent with a residual adsorption capacity. Dependences for calculation of economy of fresh adsorbent are resulted. To reduce the effect of CaSO4 ballast product on the efficiency of sulfur oxide capture and reduce energy costs for recycling, it is proposed to segregate the recycle stream into unreacted or partially unreacted adsorbent and completely converted into calcium sulfate, followed by recirculation of the adsorbent only.