We present a new averaged model for describing wormhole formation in carbonates. The model presented here captures the reaction and transport mechanisms at the pore scale and couples it to the Darcy scale through the use of two concentration variables, structure property correlations and mass transfer and dispersion coefficients. A salient feature of the model is that it captures both the reaction and mass transfer controlled regimes simultaneously, thus enabling the study of a wide range of stimulation fluids. Three important dimensionless parameters are identified in the model, namely, the Thiele modulus (pore scale parameter), Damköhler number (core scale parameter) and the acid capacity number that depends on the fluid/mineral system. Comparison of model predictions to experimental data shows good agreement. A preliminary analysis is presented on the factors that influence wormhole density.
Acid treatment of carbonates to enhance production of oil is a widely used stimulation technique. A common observation in the experimental studies on carbonate cores1–5 is that dissolution creates patterns that are dependent on the injection rate of the acid. These dissolution patterns were broadly classified into three types: uniform dissolution, wormholing regime and face dissolution corresponding to high, intermediate and low injection rates, respectively. To achieve a fixed increase in the permeability of the core, it is observed that creating wormholes optimizes the acid treatment and reduces the amount of acid required. In the uniform and face dissolution regimes, the volume of acid required is found to be much higher. Though it is well recognized that wormhole formation optimizes the treatment, there is little knowledge about the injection rate at which wormholes are formed, especially when the treatment involves the injection of acid mixtures or complex reactions between the fluid and the mineral etc.
Because the injection rate plays an important role in wormhole formation, several experiments1–7 have been conducted to determine the influence of various factors like temperature, acid concentration, reaction rate, acid diffusion coefficient, length of the core, etc. on the optimum injection rate (Qopt) and the minimum number of pore volumes (PVmin) required for breakthrough. Some of the key observations in those experiments are:
Qopt increases () and PVmin decreases () with increasing reaction rate3,5.
Qopt and PVmin with increasing acid concentration4.
Qopt with increasing temperature5.
Qopt with increasing length4.
PVmin with increasing diameter of the core6.
In addition to the above factors, reaction kinetics, regimes of reaction (mass transfer/kinetic control), heterogeneities and geometry (aspect ratio, linear/radial core) are also found to affect the optimum injection rate.
Numerous models have been developed in the past to explain wormhole formation and to obtain an estimate of the optimum injection rate. However, the reaction and transport mechanisms are not properly accounted for in these models, which limits their applicability. Extension of these models to the case of complex kinetics and systems involving competing reaction and transport processes is also difficult. As a result, the existing models are either valid in a narrow range of parameters or describe only a few aspects of acidization. In this paper, we present an averaged model for describing reactive dissolution in carbonates. The model captures the trends observed in the experiments and could be used to study a wide range of stimulating fluids.