A stochastic model is presented of two coupled fluidised-bed reactors with a steady circulation of particles between them. The particles undergo reaction in each fluidised bed. The model uniquely accounts for the full conversion history of particles as they are circulated. Chemical looping combustion (CLC) is an example of such a process. We have previously used the model, in a general form, to understand the sensitivity of a CLC process to factors such as the nature of the gas-solid reactions or the residence time distribution of the particles in the reactors. To demonstrate that the stochastic model is also valuable for simulating and optimising specific configurations of CLC, it is applied in this paper to simulate CLC with methane as the fuel gas, conducted in a laboratory-scale circulating fluidised bed. Under the operating conditions of the circulating fluidised bed, it was found that the oxidation and reduction reactions were limited by the intrinsic chemical kinetics of the oxygen carrier particles. It was possible to conduct experiments in a packed bed reactor for reduction and a thermogravimetric analyser for oxidation where the reaction was also limited by the intrinsic chemical kinetics. This enabled a single particle model, for inclusion in the stochastic model, to be developed independently of the experiments in the circulating fluidised bed. The resulting stochastic model was able to simulate the performance of the circulating fluidised bed with reasonable accuracy. (C) 2019 Elsevier B.V. All rights reserved.