Numerous carbonate matrix acidizing models have been developed to study the flow and reaction of Hydrochloric acid (HCl) in calcite, but there is a significant gap in the literature for models built to investigate wormhole propagation by alternative acidizing fluids such as organic acids and chelants. In this work, a model is developed to study wormhole propagation by these alternative fluids, using the two-scale carbonate acidizing model approach with Navier-Stokes formulation for fluid-flow description.

The reaction kinetics used for acetic acid (HAc) in the model is modified to account for the slight dissociation of the weak acid in aqueous solution and a fractional order of reaction. The output from the model is compared with available experimental data in the literature for qualitative and quantitative validation. This study extends the linear first-order reaction kinetics used for HCl in previous two-scale models for the chelating agents ethylenediaminetetraacetic acid (EDTA) and diethylenetriaminepentaacetic acid (DTPA), with updated dissolution rate constants and dispersion coefficients, and the output compared with experimental data for qualitative validation.

The acid efficiency curves generated from the model for acetic acid compares qualitatively and quantitatively with reported experimental data, and the numerical simulations show that a higher amount of acid will be required to reach breakthrough for acetic acid than for HCl, as expected. The model output for the chelating agents does not match quantitatively with experimental data, but the qualitative trend can be observed from the numerical simulation results. The updated reaction kinetics for acetic acid is extendable to formic acid, which is the other commonly used organic acid in carbonate matrix acidizing, to obtain an equally dependable model output. However, a more complex reaction kinetics will be required to model the multi-step chemistry that occurs in the dissolution of carbonate by chelating agents.

The model developed in this study accurately captures the wormholing phenomena by acetic acid, and it can also be used to predict optimum injection rates for organic acids. The simulation results also show that the model, based on Navier-Stokes momemtum formulation, is computationally less expensive than previous models with the Darcy-Brinkman formulation, and simulations at very high injection rates with this model require less computational time than models developed with the Darcy formulation.

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