Abstract
An improved 1D-averaged model for wormhole propagation was developed that considers acid spending and leakoff along wormholes. The 1D-averaged type of model is one of several types that have been developed for predicting wormhole propagation during matrix acidizing treatment in carbonates; other models include discrete models, Darcy-scale 2D and 3D continuum models, and multi-pore-scale network models. Among these models, the 1D-averaged model is commonly applied in acidizing simulation software because of its simplicity.
Most of 1D-averaged models are based on the pore volume to breakthrough correlations developed from core flooding experiments on different rock samples and acid systems. It is also generally assumed that the effect of acid spending is already included in the experimental results. Although this is a reasonable assumption when the wormhole length is shorter than the core length (typically 6 in.), once wormhole penetration is longer than 6 in., the acid spending becomes more significant while acid travels along wormholes due to the reaction between acid and the side walls of wormholes. Meanwhile, acid leak-off through wormhole walls becomes an important factor for longer wormholes. Not considering acid spending and leakoff in relatively longer wormholes may result in overestimation of wormhole penetration depth.
In our model, we adopted an empirical correlation to determine the leak-off velocity profile along wormholes. Then, we developed a numerical model to simulate the non-uniform acid concentration along wormholes. Both the empirical correlation for leak-off velocity profile and the numerical model for acid concentration are validated by comparing to published materials and an independent computational fluid dynamics (CFD) software. As expected, wormhole penetration predicted by the new model shows shorter wormholes than the traditional 1D-averaged model.
We applied the new model to a field case and showed its capability of reasonably matching the downhole pressure during acidizing treatments and PLT data before and after acidizing treatments, which demonstrates the applicability of the model to job design and interpretation in the field.
