In this work, a Calcium Looping (CaL) configuration for cement plants using two interconnected circulating fluidized bed (CFB) reactors integrated into the clinker production process, is investigated. In the proposed system, the oxy-fired CFB calciner has a dual task: (i) calcining the finer fraction of the raw meal to feed the rotary kiln of the plant and (ii) calcining the coarser fed raw meal fraction, so as to recirculate part of it to the carbonator to capture CO2 from the flue gases of the kiln. Such arrangement also exploits the known tendency of limestone materials to experience intense attrition and fragmentation under the severe calcination conditions in the oxyfired CFB calciner, so that the calciner also performs the task of an auxiliary mill. The techno-economic study conducted in this work has been carried out by analysing different levels of fragmentation of the raw material, consistent with experimental results from the TRL7 la Pereda CaL pilot plant. Two different configurations were analysed: the first, in which limestone with a larger particle size than the correctives is fed, to be used in CFB reactors; the second, in which no separation of limestone from other solid species is possible and all raw meal is used as CO2-sorbent in the CaL system. The benefits of this approach are confirmed by the estimated specific primary energy consumption for CO2 avoided (SPECCA) of 2.8-3.0 MJLHV/kgCO2 when pure limestone is used in the carbonator and of 3.5-4.6 MJLHV/kgCO2 when the raw meal is used as sorbent. The economic analysis indicates the competitiveness of the novel proposed process compared to other CaL systems, resulting in a cost of CO2 avoided (CCA) between 49.2 to 57.9 €/tCO2, excluding costs for CO2 transport and storage.