Mechanistic Model for In-Situ Diverting Acids Flow in Carbonate Formations: From Lab to Field Treatment Optimization

Abstract In-situ diverting acids are commonly used in carbonate acidizing treatments to improve acid coverage by redirecting acid to lower injectivity formation. Most of the models to represent the flow of these in-situ diverting acids, in literature are semi-empirical with very limited predictive capability. Some studies use numerical simulations to accurately capture the physics and dynamics of the process, however, they are computationally intensive, even on lab scale. This study presents a computationally fast physics-based model to simulate and predict the pressure response of in-situ diverting acids. The model divides the formation into three zones, namely, wormhole, disturbance, and virgin zones. The change in acid concentration is tracked in the wormhole and porous media by calculating the overall reaction rate and acid velocities. An abrupt increase in viscosity occurs as pH rises above 1 or 2, which generates disturbance/turbulence in the flow. A Forchheimer-like equation is used to account for the increase in pressure due to flow turbulence. Core flow experiments were conducted at 175°F and 250°F using limestone and dolomite cores treated with in-situ gelled acid (ISGA) and VES-based acid to validate the model. The comparison with linear experiments revealed that, unlike semi-empirical models, the current model captures the complete pressure response observed experimentally. Additionally, it scales very well with the injection rate. Radial experiments from the literature were used to validate the radial version of the model. Remarkably, the model is not only in agreement with radial experiments but also scales well with radial core dimensions. Synthetic one-layer and two-layer radial models were built, and both models revealed that the initial permeability and permeability range have a strong effect on divergence. A multi-layer example is presented to shed light on the model's ability to capture the impact of diversion on fluid distribution. This study describes the development of a mechanistic model for in-situ diverting acid flow under linear and radial geometries. The model specifies the effect of formation permeability contrast, temperature, mineralogy, and wellbore diameter on chemical diverter selection and on acid strength, volume, and injection rate optimization. This study provides useful recommendations on how to design the placement of in-situ diverting acids and the critical factors that need to be considered.