Acidizing of carbonate reservoirs is a common technique used to restore and enhance production by dissolving a small fraction of the rock to create highly conductive channels. Literature review reveals that most acidizing studies are focused on acid injection at a constant volumetric rate (CVR) instead of at a constant injection pressure (CIP). Therefore, the primary objective of the present work is to investigate the benefits and recommended applications of each technique. The study analyzes dissolution patterns and wormhole propagation rate. A coreflood study was conducted using different Indiana limestone cores to assess both techniques. Additionally, a two-dimensional (2D) wormhole model was used to mathematically describe the acidizing phenomena. The algorithm is based on a 2D radial flow system that iterates time to quantify wormhole propagation and injection rate. Wormhole velocity is calculated by an empirical laboratory model that depends on two parameters measured from core flow testing. Therefore, the algorithm captures the essential physics and chemistry of the acid reaction in a carbonate porous medium. The study confirmed that conical, wormhole, and branched types of acid dissolution patterns exist for both techniques (CVR or CIP). Unlike in the CVR technique, dissolution patterns during the CIP technique can change and tend toward a branched dissolution regime. The CIP technique required a lower acid volume to achieve a breakthrough in the conical dissolution regime and a higher acid volume to achieve a breakthrough in the branched dissolution regime compared to the CVR technique. In a dominant wormhole pattern, both techniques required nearly the same acid volume for a breakthrough. A computed tomography (CT) scan confirmed that the CIP technique developed a uniform wormhole at a low initial injection rate. For the CIP technique, the acid injection rate increased exponentially with the volume of the acid injected. The CIP technique is recommended for a low-permeability reservoir where acid injection at a high rate is not possible to avoid face dissolution wormhole patterns. On the other hand, the CVR technique is recommended for a medium—to the high-permeability reservoir where high acid injection rate can be achieved.