The optimum design of matrix acidizing treatments in carbonate reservoirs requires accurate modeling of wormhole propagation. While there are several wormhole correlation models available, most are developed based on small core scale experiments, and result in significant deviation when upscaled to field treatment design. There also exists simulation models (e.g. Two-Scale Continuum or Pore Network models). These models are not practical for field design because of the extensive computation effort involved. Large variations in the wormholing behavior are observed in laboratory experiments using different core sizes and geometries (radial flow versus linear flow). This variation is not captured in the previous models. This work proposes a new multiscale wormhole model that represents the physics of wormholing behavior in matrix acidizing of carbonates both at core and field scales.

The derivation of the new semi-empirical model is formulated to represent the experimental data for different core dimensions and flow geometries, as well as field results. In core flooding experiments with different core sizes, the obtained pore volumes to breakthrough and optimal injection velocity are different for each core size. The same behavior is observed in numerical simulations using the Two-Scale Continuum model. That behavior is correctly calculated with the proposed model, which accounts for the dimensions in a function with dependence of the correlation parameters on the wormholed region scale and geometry. Upscaling procedures to linear, radial, elliptical, spherical, and ellipsoidal geometries are presented.

The model's results are validated by the Two-Scale Continuum numerical simulations for both linear and radial flow and verified with experimental results with different core sizes and geometries (both linear and radial flow). We further developed the model for field application, and procedure of using the model is illustrated in the paper. The different flow geometries allow predicting the acidizing behavior in common completions, such as openhole, cased and perforated, and limited entry. The model prediction compares very well to the outcome of field cases.

The new model reproduces the fractal behavior of the dominant wormhole growth above optimal injection rate, and predicts the injection pressure dependence on time as measured experimentally. The model correctly captured the physics of wormhole propagation phenomenon.

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