Abstract
Matrix acidizing is an extensively used stimulation technique to improve oil recovery in carbonate reservoirs. The interplay between transport and reaction of acid is highly affected by heterogeneity at different scales. The existing experiments and models have difficulties to capture effect of heterogeneities across pore-scale, core-scale and field-scale. The objective of this paper is to provide an efficient multiscale model using continuous time random walk approach to predict acidizing behavior at macroscopic scale considering the effect of microscopic scale heterogeneity.
Instead of solving traditional advection-diffusion-reaction equation (ADRE), the continuous time random walk (CTRW) incorporating with particle tracking (PT) is a probabilistic approach to model fluid transport in heterogenous porous media. Here, the CTRW-PT describes motion of acid particles as random spatial and temporal increments at pore scale which follow independent distributions whose characteristic probability density functions (PDF) are derived. The transport of acid particles is simulated by particle tracking first and chemical reaction is included using the midflight approach. CTRW-PT simulation yields macroscopic plume of acid which creates wormholes at core scale. The core-scale wormhole propagation at different injection rate and concentration agrees qualitatively with the experimental results. Nevertheless, CTRW-PT also demonstrates the effect of heterogeneity that may increase the minimum pore volume to breakthrough. Using CTRW-PT approach is more efficient than solving ADRE in large-scale modeling.
The utilization of CTRW-PT approach on acidizing modeling captures the wormhole propagation of hydrochloric acid in limestone cores. This probabilistic and stochastic approach provides an efficient way to model carbonate acidizing and one can consolidate the lab-scale understanding with field prediction to optimize the acidizing treatment design.
