A pure oxygen combustion technology is crucial in Carbon Capture and Storage (CCS) technology especially in capturing of $CO_2$, where CCS will reduce 9 $GtCO_2$ by 2050, which is 19% of the total $CO_2$ reduction amount. To make pure oxygen combustion feasible, a regenerative system is required to enhance the efficiency of pure oxygen combustion system. However, an existing air combustion technology is not directly applicable due to the absence of nitrogen that occupies the 78% of air. This study, therefore, investigates the heat and fluid flow in a regenerative system for pure oxygen combustion by using commercial CFD software, FLUENT. Our regenerative system is composed of aluminium packed spheres. The effect of the amount of packed spheres in regenerator and the effect of presence or absence of a bypass of exhaust gas are investigated. The more thermal mass in regenerator makes the steady-state time longer and temperature variation between heating and regenerating cycle smaller. In the case of absence of bypass, the regenerator saturates because of enthalpy imbalance between exhaust gas and oxygen. We find that 40% of exhaust gas is to be bypassed to prevent the saturation of regenerator.