Simulation of 3D multi-scale wormhole propagation in carbonates considering correlation spatial distribution of petrophysical properties

Abstract

Simulation of wormhole propagation is very critical for predicting stimulation effects of matrix acidizing and acid fracturing in carbonate reservoirs. In this paper, a 3D multi-scale wormhole propagation model is introduced, and the corresponding numerical solution details are described. Meanwhile, a variogram model is introduced to describe the correlation spatial distribution of the rock petrophysical properties, which makes simulation results of the model more realistic and reliable. An optimal parallel algorithm to numerically solve these mathematical models are discussed. Calculation results in this paper have shown that core pore structures and core minerals proportions both do significant effect on acidization simulation results. It is shown that wormholes propagate paths are highly determined by porosity distribution, and the pore-scale heterogeneity has a negative correlation with the acid volume of breakthrough. On the other hand, it is confirmed that mineral dissolution patterns change regularly with the increase of the ratio of dolomite to limestone in carbonate cores. Simulations of 3 cases have also shown that the significance of including the correlation spatial distribution of core petrophysical properties into the simulation in order to achieve a more accurate calculation of acidization effects in production and stimulation of reservoirs.