In-situ gelling acids are used in carbonate reservoir stimulation to reduce the leakoff rate of the acid and to divert acid to low-permeability zones. Understanding the mechanism of flow diversion and the impact of fluid rheological properties on diversion is critical to developing good matrix stimulation designs. A literature review shows that few studies present models for stimulation with in-situ gelling acids. Specifically, there are no theoretical or empirical rheological models for gelling acids that describe the effects of pH on viscosity and hence flow diversion. The objective of this work is to develop, analyze, and validate a model to represent carbonate acidizing with gelling acids.
In this work, a semi-empirical rheological model based on experimental data for gelling acids that accounts for viscosity as a function of temperature, shear rate, and pH is presented. A two-scale continuum model is developed for non-Newtonian fluids, such as gelling acids. Using the model, the effect of rheological parameters on flow diversion is analyzed and the conditions for maximum diversion are identified. The predicted results are compared with the available experimental data and field observations. A scaling analysis is also presented that leads to a criterion for the optimum injection rate for attaining maximum stimulation for a fixed amount of acid (or a minimum in pore volumes to breakthrough (PVBT)). It is shown that the optimum injection rate for gelling acids depends strongly on rheological parameters of the acid. It is found that the presence of gel leads to more branching of wormholes and more uniform stimulation compared to Newtonian acids.