## 1 Introduction  
The calcium looping cycle is an important process which can reduce greenhouse gases emissions into the atmosphere through a variety of applications. Research into the use of calcium looping (CaL) has found the system to be highly suitable for processes such as thermochemical energy storage (TCES) [1; 2; 3; 4] and carbon capture and storage (CCS) [1; 5; 6; 7; 8; 9]. The CaL cycle consists of two reactions, which are theoretically reversible. In the endothermic decomposition (calcination) reaction, calcium carbonate (CaCO3) absorbs energy to produce a metal oxide (CaO or lime) and CO\({}_{2}\). The exothermic carbonation reaction occurs at a lower temperature and/or higher CO\({}_{2}\) partial pressure and releases thermal energy, which can be used to drive a power cycle [1; 10]. The reactions are described by the following expression:  
\[\text{CaCO}_{3}\ (\text{s})\rightleftharpoons\text{CaO}\ (\text{s})+\text{CO}_{2}\ ( \text{g}) \tag{1}\]  
where the reaction enthalpy at standard conditions is \(-178.4\) kJ mol\({}^{-1}\). The study of reaction kinetics is highly applicable to the practical implementation of the CaL cycle for use in energy storage or carbon capture. Reaction kinetics are needed for the design of reactors for CaL, for which several system configurations exist. A typical configuration consists of two interconnected circulating fluidized bed reactors, a calciner and carbonator [11; 12; 13; 14]. Kinetic reaction models suitable for the conditions of interest in CaL have been specifically studied [12; 15; 16; 17; 18; 19] and have helped in the design of reactors [11; 13; 14; 20; 21; 22]. There are two key challenges associated with performing a kinetic analysis of CaL systems, although the reactions have been extensively studied (i.e., [23; 24; 25; 26; 27]). The first is the disparity in the activation energies suggested for both calcination and carbonation [28], and the second is the lack of consensus on the reaction mechanisms [29; 30]. The calcination of CaCO\({}_{3}\) has been studied using a variety of kinetic analysis methods, including the Coats-Redfern method, the [PERSON] and Sivasubramanium method, the Friedman (isoconversional) method, and generalized methods such as pore models and grain models [30]. Calcination activation energies varying between 164 and 225 kJ mol\({}^{-1}\) have been obtained for various forms of limestone and synthetic CaCO\({}_{3}\) under inert atmospheres [30], while studies carried out under CO\({}_{2}\) have produced values of activation energy (\(E_{a}\), kJ mol\({}^{-1}\)) which are as high as 2105 kJ mol\({}^{-1}\)[31]. A consensus on the reaction mechanism has not been established. The intrinsic chemical reaction is considered to be the rate-limiting step by most authors [30]. However, some consider the initial diffusion of CO\({}_{2}\) as a rate-limiting step [32] and some studies indicate that mass transport is significant [33; 34; 35]. Numerous studies suggest that the carbonation reaction takes place in two stages: An initial rapid conversion (kinetic control region) followed by a slower plateau (diffusion control region) [29; 30]. The most commonly applied reaction models which are used to determine kinetic parameters include the so-call generalized methods, which include shrinking core models, pore models, grain models, and apparent (semi-empirical) models [36; 37; 28; 30]. Modeling of the carbonation reaction considers several mechanisms, such as nucleation and growth, impeded CO\({}_{2}\) diffusion, or geometrical constraints related to the shape of the particles and pore size distribution of the powder [26]. For the initial kinetic control region of carbonation, typical values of \(E_{a}\) are 19-29 kJ mol\({}^{-1}\) in synthetic CaO or natural lime [30], although slightly larger values (i.e., [39; 40; 41; 42; 43; 44; 45; 46; 47; 4  
This system conducts both calcination and carbonation under pure CO\({}_{2}\) and has been tested in a small number of studies [23; 24; 41].