Optimal acid-injection rate is critical information for carbonate-matrix-acidizing design. This rate is currently obtained through fitting acidizing-coreflood experimental results. A model is needed to predict optimal acid-injection rates for various reservoir conditions.
A wormhole forms when larger pores grow in the cross-sectional area at a rate that greatly exceeds the growth rate of smaller pores caused by surface reaction. This happens when the pore growth follows a particular mechanism, which is discussed in this paper. We have developed a model to predict wormhole-growth behavior. The model uses the mode size in a pore-size distributionthe pore size that appears most frequently in the distributionto predict the growth of the pore. By controlling the acid velocity inside of it, we can make this particular pore grow much faster than other smaller pores, thus reaching the most-favorable condition for wormholing. This also results in a balance between overall acid/rock reaction and acid flow. With the introduction of a porous-medium model, the acid velocity in the mode-size pore is scaled up to the interstitial velocity at the wormhole tip. This interstitial velocity at the wormhole tip controls the wormhole propagation. The optimal acid-injection rates are then calculated by use of semiempirical flow correlations for different flow geometries.
The optimal injection rate depends on the rock lithology, acid concentration, temperature, and rock-pore-size distribution. All these factors are accounted for in this model. The model can predict the optimal rates of acidizing-coreflood experiments correctly, compared with our acidizing-coreflood experimental results. In addition, on the basis of our model, it is also found that at optimal conditions, the wormhole-propagation velocity is linearly proportional to the acid-diffusion coefficient for a diffusion-limited reaction. This is proved both experimentally and theoretically in this study. Because there is no flow-geometry constraint while developing this model, it can be applied to field scales. Applications are presented in this paper.