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Carbonates invariably have small (micron) to large (centimeter) scale heterogeneities in flow properties that may cause the effects of injected acids to differ greatly from what is predicted by a model based on a homogenous formation. To the best of our knowledge, there are neither theoretical nor experimental studies on the effect of large scale heterogeneities (vugs) on matrix acidizing. The abundance of carbonate reservoirs (60% of the world?s oil reserves) and the lack of a detailed study on the effect of multi-scale heterogeneities in carbonate acidizing are the main motivations behind this study. In this work, we first present a methodology to characterize the carbonate cores prior to the core-flood acidizing experiments. Our approach consists of characterization of the fine-scale (millimeter) heterogeneities using computerized tomography (CT) and geostatistics, and the larger-scale (millimeter to centimeter) heterogeneities using connected component labeling algorithm and numerical simulation. In order to understand the connectivity of vugs and thus their contribution to flow, a well-known 2D visualization algorithm, connected component labeling (CCL), was implemented in 3D domain. Another tool used in this study to understand the connectivity of the vugs and its effect on fluid flow is numerical simulation. A 3D finite difference numerical model is developed based on Darcy-Brinkman formulation (DBF). Using the developed simulator a flow-based inversion approach is implemented to understand the connectivity of the vugs in the samples studied. After multi-scale characterization of the cores, acid core-flood experiments are conducted. Cores measuring four inches in diameter by twenty inches in length are used to decrease the geometry effects on the wormhole path. The post acid injection porosity distribution and wormhole paths are visualized after the experiments. The experimental results demonstrate that acid follows not only the high permeability paths but also the spatially correlated ones. While the connectivity between the vugs, total amount of vuggy pore space and size of the cores are the predominant factors, spatial correlation of the petro-physical properties has less pronounced effect on wormhole propagation in acidiziation of carbonates. The fact that acid channeled through the vugular cores, following the path of the vug system, was underlined with computerized tomography scans of the cores before and after acid injection. This observation proposes that local pressure drops created by vugs are more dominant in determining the wormhole flow path than the chemical reactions occurring at the pore level. Following this idea, we present a modeling study in order to understand flow in porous media in the presence of vugs. Use of coupled Darcy and Stokes flow principles, known as Darcy-Brinkman formulation (DBF), underpins the proposed approach. Several synthetic simulation scenarios are created to study the effect of vugs on flow and transport. The results demonstrate that total injection volume to breakthrough is affected by spatial distribution, amount and connectivity of vuggy pore space. An interesting finding is that although the presence and amount of vugs does not change the effective permeability of the formation, it could highly effect fluid diversion. We think this is a very important observation for designing of multi layer stimulation.