Calcium looping cycles for capturing CO2 from large emission sources will most likely use interconnected circulating fluidized bed reactors. The mass balances that govern the mixed solids in the main reactors of these systems, combined with a description of sorbent reaction and decay in activity, are used in this work to define the average activity of the material as a function of the sorbent recycling and make up flow ratios. The new formulation of the mass balances takes into account the fact that particles during carbonation and/or calcination achieve partial conversion in the respective reactors. In these conditions, average activity is shown to be a function of not only sorbent properties and make-up flow ratios, but also the internal solid circulation rates between the reactors. Explicit equations are obtained for the average activity of the circulating materials. These equations are used to discuss the effect of the key operating variables on CO2 capture efficiency. The equations proposed here for the CaCO3/CaO system may also be valid for other chemical reactor systems that use interconnected circulating fluidized beds. (C) 2009 Elsevier B.V. All rights reserved.