Summary This paper describes a model where wormholes, the primary feature of carbonate acidizing, are considered as fractals. The influences of acid volume, injection rate, fractal dimension, porosity, and the ratio of undamaged to damaged permeabilities on well performance are studied. Exact expressions of post-treatment skin effects are developed for vertical and horizontal wells. Introduction In the recent past, the industry viewed many studies describing the physics of matrix acidizing and its impact on treatment design and post-treatment well performance as simply interesting. The economics of matrix stimulation of common reservoir thicknesses (<100 ft) in vertical wells precluded wide application of these findings. However, the emergence of horizontal wells, penetrating formations with lengths up to 8,000 ft and more, and the need for massive volumes of stimulation fluids necessitated re-examination and extension of the understanding of the physics of these proc esses. This is especially true if treatment optimization is to be undertaken. Matrix stimulation and the stimulation method vary significantly among common reservoir lithologies. In matrix acidizing of sandstones, the stimulation fluids primarily attack the particles plugging the pore spaces; thus, the treatment may result in a stimulated "collar" around the well if insufficient acid is injected to remove all damage. In this paper, we deal with stimulation of carbonate formations, where treatment relies on reaction kinetics and where new flow paths, or wormholes, are created. The dendritic wormhole patterns have been identified to be fractals. Their shape and extent and the resulting post-treatment skin effect can be quantified with the model presented in this paper.
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