"Wormholes", which are characteristic shapes resulting from the acidizing of carbonate formations have been considered in the past as fractals. In previous publications, analytical relationships of the area penetrated by wormholes, the wormhole porosity and the fractal dimension have been presented. Local mineral compositional heterogeneities and structures result in uneven reaction profiles when acid reacts with carbonate rocks. This, coupled with permeability heterogeneities, leads to microscopic flow instabilities which may evolve into macroscopic wormhole patterns.

The understanding of the physics of acidizing is becoming a serious issue with the emergence of horizontal wells, where massive volumes of acid may be needed for effective stimulation. The stochastic nature of the wormholing process has been a limiting factor for a physical interpretation. The simulation of this unstable growth process is the purpose of this paper.

The impacts of permeability anisotropy, heterogeneous distribution of the properties of the formation, such as microfractures and zones of different permeabilities, are investigated. A simulation model, the permeability driven fingering model (PDF) is presented. This technique is a new approach to diffusion limited growth, which traditionally has been simulated with diffusion limited aggregation models (DLA). The randomness of fractal growth is changed by introducing a bias representing the permeability anisotropy and the preferential reaction kinetics of lithologic heterogeneities.

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