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Pore-Scale Study to Analyze the Impacts of Porous Media Heterogeneity on Mineral Dissolution and Acid Transport Using Darcy–Brinkmann–Stokes Method

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Abstract

Inherent pore structure of rocks has a significant impact on the acid–rock interaction during the acidizing process. In this study, a new pore-scale reactive transport model applying Darcy–Brinkmann–Stokes method has been developed based on the open-source computational fluid dynamics platform, OpenFOAM, and validated with experimental results. By solving the mass balance equation and advection–diffusion equation, the developed numerical simulation model could capture the evolving pore structure and track the distribution of transported acid. The impacts of different grain sizes and distributions on the dissolution rate of mineral (calcite), evolving porosity, and the transport characteristics of acid have been investigated. In addition, sensitivity analysis has been conducted with respect to the various Damköhler numbers and Péclet numbers in the digital rock image model of Niobrara formation. The changing volume fraction of pores could be categorized into three patterns with different dimensionless numbers—linear growth, pseudo-linear growth, and a flat S-curve growth. The simulation cases of Estaillades carbonate, Massangis Jaune carbonate models, and Sample X segmentation showed that their inherent grain distribution was highly influential on the mineral dissolution rate, where 3-D simulation showed the same results. The developed pore-scale reactive transport model can be applied to various systems with complex pore structures, in order to provide a guidance to predict the system responses such as dissolution rates, surface area, and porosity changes during acidizing in large-scale continuum model.

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Abbreviations

\(\varepsilon_{f}\) :

Volume fraction of fluid area

\(\varepsilon_{f}\) :

Volume fraction of rock

\(\overline{v}_{f}\) :

Average velocity of fluid

\(\overline{p}_{f}\) :

Average pressure

\(\mu_{f}\) :

Dynamic viscosity

\(\rho_{f}\) :

Fluid density

\(\overline{\omega }_{f,A}\) :

Concentration of acid

\(k\) :

Local permeability

\(k_{0}\) :

Initial local permeability

\(D_{A}^{*}\) :

Effective diffusion coefficient of species

\(\dot{m}_{A}\) :

Mass reaction rate of mineral dissolution by acid

\(D_{A}\) :

Molecular diffusivity of the acid component in liquid

\(\dot{m}\) :

Mass transfer rate on the liquid–solid interface

\(r\) :

Reaction constant

\(a_{v}\) :

Effective surface area

\(\psi\) :

Diffuse-interface function

\(\rho_{s}\) :

Rock density

\(\beta\) :

Stoichiometric coefficient

Ae :

Volume-averaged effective surface area

K :

Absolute permeability

A n :

Normalized effective surface area

f :

Fluid phase

s:

Solid phase

A :

Acid

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Acknowledgements

We greatly appreciate the financial and resources support for this research from National Research University Fund of University of Houston. We are also grateful for Zhuoran Li and Lotanna Ohazuruike at University of Houston for their helpful suggestions for writing.

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  1. Department of Petroleum Engineering, University of Houston, Houston, USA

    Jiahui You & Kyung Jae Lee

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You, J., Lee, K.J. Pore-Scale Study to Analyze the Impacts of Porous Media Heterogeneity on Mineral Dissolution and Acid Transport Using Darcy–Brinkmann–Stokes Method. Transp Porous Med 137, 575–602 (2021). https://doi.org/10.1007/s11242-021-01577-3

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