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Carbon capture and sequestration in subsurface porous formations is a key technology to reduce CO2 emissions to reach the world net-zero emissions by 2050. Modelling studies to identify injection conditions which do not imply fault reactivation and induced seismicity are mandatory to support project implementation. Fault stability analysis requires to couple full-physics reservoir and geomechanical simulations, limiting the possibility to run multiple sensitivities due to the high computational cost. In this work, a cost-efficient workflow suitable for optimization and uncertainty quantification based on Functional Kriging (FK) surrogate models is proposed. Two different FK techniques are implemented and applied to two synthetic models, simulating CO2 sequestration in a depleted sweet gas reservoir using a compositional model with CH4 and CO2 as components. Field gas injection rate, fault modelling parameters but also geomechanical properties are considered as key variables to study fault reactivation. The proxies are trained on output from few simulations to estimate the time dependent Coulomb Failure Function on each element of the fault triangular mesh monitoring the fault behavior during the fluid injection. The results show that FK proxies accurately replicate fault stability indicators with low average errors on a set of blind simulations.