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Cu-rich precipitates formation is associated with the precipitation hardening of Fe-Cu based steels and the embrittlement of reactor pressure vessel steels under neutron irradiation. The accurate modeling of the time evolution of Cu-rich precipitates is therefore of fundamental importance for the design of Fe-Cu based steels and the prediction of the irradiation induced shift of the ductile to brittle transition temperature of reactor pressure vessels. This work applies cluster dynamics with mobile Cu monomers and clusters to model Cu precipitation in dilute Fe-Cu alloys at several temperatures. Optimized model parameters can be used to simulate the mean radius, number density, volume fraction, and matrix composition evolution during isothermal annealing with reasonable accuracy. The possible reduction of the mobility of Cu-rich clusters due to additional alloying elements in Fe-Cu based steels is discussed.