Abstract: Three dimensional (3-D) simulation of wormhole propagation is crucial for predicting stimulation effects of acidizing or acid fracturing in carbonate reservoirs.This paper presented a 3-D multiple-scale wormhole propagation model built based on the double-scale model,and its solving details.Meanwhile,geological modeling method was used to establish the geology model of porosity correlation distribution in 3-D space,which deals with the saltation of porosity successfully and makes the simulation results more realistic and reliable.Through the simulations,we found that the injection rate is the key factor affecting wormhole patterns.With the increase of the injection rate,five dissolving patterns may be observed,namely face dissolution,conical wormhole,dominant wormhole,ramified wormhole and uniform dissolution.When the convection and dispersion are comparable,the dominant wormhole may form with a thick root and a thin tip.The do-minant wormhole propagation can be divided into the following successive four stages,including competition stage,dominant stage,breaking stage and broadening stage.Most importantly,we found that the wormhole propagation pathway is highly correlated with the spatial correlation of porosity,since the wormhole breaks the core through those large pores with well connectivity.Finally,the field simulation results verified that the models and methods proposed in this paper are feasible and reliable for wormhole simulation of acidizing and acid fracturing in carbonate reservoirs.Those works could provide theoretical support for fine simulation and prediction in the relevant research areas.

Key words: porous medium, acidizing wormhole, 3D simulation, numerical model, carbonate rock, EOR