Investigating Acidizing in Carbonate Reservoirs: Global Sensitivity Analysis

Reservoir stimulation is a common technique used to improve the productivity of carbonate reservoirs such as carbonate acidizing. This process involves injecting a reactive fluid to dissolve the rock mineral, creating a conductive path for hydrocarbon flow (i.e., wormhole). With the development of tight and unconventional reservoirs, stimulation has become more critical for optimal economic production. This study aims to simulate carbonate dissolution with a two-scale continuum model and investigate how the uncertainty propagates in that model. The petrophysical properties of carbonate encounter significant uncertainty that affects the predictivity of the model. A simulation model was developed to simulate the initiation and propagation of wormhole in carbonate rock. We investigate the effect of varying the injection rate on the dissolution channel and the efficiency of the acidizing fluid. Next, we utilized design of experiments in a rigorous multi-step methodology to build a surrogate model based on polynomial chaos expansion. The surrogate model is used to perform global sensitivity and uncertainty propagation analysis. We utilize the surrogate model and Sobol indices to identify the most significant parameter affecting stimulation process using dimensionless groups, including the Damkohler, Peclet, and acid capacity number. The results showed that the dissolution channel and pore volume to breakthrough depends on the injection rate. The surrogate model reproduces the simulation model results for the dissolution channel, the pore volume to breakthrough, and the effective permeability. The global sensitivity analysis shows that the acid capacity number is the most significant parameter for the pore volume to breakthrough with the highest value of the total Sobol index. For effective permeability, the initial mean porosity is the primary source of uncertainty. The marginal effect calculated for the individual parameter confirms the results from Sobol indices. This work provides a systematic workflow for uncertainty analysis and optimization applied to the processes of carbonate stimulation.