A fluid dynamic model for a gas-solid circulating fluidized bed(CFB) designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab.The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process.Because of the high computational costs required to resolve the three-dimensional phenomena,a model representing a trade-off between computational time requirements and accuracy is developed.For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers,a dynamic one-dimensional two-fluid model is sufficient.A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase,and an algebraic turbulence model is applied to the gas phase.The numerical model implementation is based on the finite volume method with a staggered grid scheme.The exchange of solids between the reactor units constituting the circulating fluidized bed(solid flux) is implemented through additional mass source/sink terms in the continuity equations of the two phases.For model validation,a relevant experimental analysis provided in the literature is reproduced by the numerical simulations.The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system.The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors.Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.