Supercritical carbon dioxide (sCO2) cycles are considered to provide a faster response to load change owing to their compact footprint. sCO2 cycles are generally highly recuperative, therefore the response time is mainly dictated by the heat exchanger characteristics. This study model the transient behaviour of a recuperator in 10 MWe simple recuperative Brayton cycle. The response for the variation of inlet temperature and mass flow boundary conditions were investigated using two approaches based on temperature and enthalpy. The performance of these two approaches are compared and the numerical schemes were discussed along with the challenges encountered. The simulation results were validated against the experimental data available in the literature with a fair agreement. The characteristic time of the heat exchanger for a step change of the boundary conditions is reported that supports the recuperator design process. Compact recuperator responded in less than 20 seconds for the changes in the temperature boundary condition whilst it can take upto 1.5 minutes for mass flow change. In order to reduce the computational effort, a logarithmic indexed lookup table approach is presented, reducing the simulation time by a factor of 20.