In carbonate acidizing, the injected acid reacts with the rock to create a high conductivity channel called wormhole in order to improve the damage in near wellbore zone. Different from experimental conditions, the acid flow is radial flow and the formation pressure increases due to fluids being compressed under reservoir condition. Both of them can influence wormhole propagation to a great extent, it is very necessary to study the wormhole propagation under reservoir condition. We use a 2D two-scale continuum model coupled with a compressed zone model to study it. The results show that the wormhole propagation velocity under reservoir condition is slower than that under experimental condition. Under constant pressure condition, the smaller the compressibility coefficient of formation fluid, the slower the propagation velocity of wormhole, and vice versa. Under constant rate condition, the smaller the compressibility coefficient of formation fluid, the slower the inlet pressure declines and the faster the outlet pressure increases, and vice versa. Due to the effect of compressed zone and implementation condition, the wormhole length has a maximal value under reservoir condition. We also develop a skin factor model to study on an example. It is found that both wormhole propagation velocity and skin factor decline velocity under constant rate condition are higher than those under constant pressure condition before wormhole breaks through the damaged zone, but both of them are very close after wormhole breaks through. Note that, the acid injection volume has an optimal value.