Self-diverting acids are commonly used in matrix acidizing treatments of carbonate formations, not only to increase permeability by generating wormholes, as with conventional acids such as HCl, but also to self-divert into zones of lower injectivity, in the goal of optimizing zonal coverage. In this paper, a new model for wormhole propagation is proposed, which describes both stimulation and diversion processes.

A preliminary model is presented, which predicts wormhole propagation under radial-flow conditions for conventional acids. Then, a new set of parameters characterizing the reactive flow of self-diverting acids is developed, and the above model is extended to include self-diverting mechanisms. In particular, it is shown how the new parameters related to wormhole growth and those to diversion can be assessed from linear core-flood experiments and integrated into a new radial-flow model for field-scale prediction. Using this model, a new criterion is developed for diverter efficiency as a function of permeability contrast. Finally, the model is validated against radial flow experiments.

It is found that self-diverting acids are characterized by two new parameters which, when combined with the model for wormhole propagation, can be used to predict the performance of self-diverting acids, both in terms of wormhole penetration and in terms of zonal coverage. Some criteria are also developed to assess the diversion ability of acids.


Models for predicting wormhole propagation have been widely discussed in the literature. Various types of modeling techniques have been used to describe the wormholing phenomenon:

  1. 1D-averaged models 1,2,3,4,5

  2. Discrete models 6,7,8

  3. Darcy-scale 2D and 3D continuum models 9,10

  4. Multi-pore scale network models 2,11

In this work, we will partly review types 1 and 3 as they encompass most of the existing literature, and as we believe they constitute the most effective and tractable way to describe the wormholing process. All the literature related to wormhole modeling known to the authors refers to conventional acids, i.e., acids whose rheological properties do not change significantly with time. Self-diverting acids have been developed in order to achieve drastic changes in their rheological properties as acid spends.

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