Acidic fluid flow in geologic formations leads to mineral dissolution and, under certain circumstances, to localized dissolution forming a dendritic pattern, known as wormhole. Such patterns of conduits and caves are often observed in karstic aquifer and deliberately engineered in oil and gas well stimulation with acid injection. Experimental studies suggest that various parameters such as fluid velocity or material heterogeneity control the wormhole formation. While many numerical and experimental studies found the acid flow velocity to play a controlling role, most models need to randomly seed material heterogeneities to induce wormholes. Here we show that a phase-field approach, which diffuses a sharp interface in a continuous manner, is capable of simulating wormhole without random seeds by accounting for the energy expenditure in the dissolution topology. We verified the model against the sharp interface counterpart in one-dimensional simulations. We then performed the two-dimensional simulations to qualitatively validate wormhole formation and growth patterns against acid injection experiments on carbonate rocks under radial flow conditions. The simulation results indicate that the injected acid is rapidly consumed near the acid entry point at low injection rates while the live acid becomes available at the tip of the dissolved cavity under high rates and thus wormhole starts to grow resulting in much faster acid breakthrough.