The Problem of Formation Destruction in Carbon Dioxide Storage: A Microscopic Model

In the context of the current global transition toward low-carbon energy, the issue of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> utilization has become increasingly important. One of the most promising natural targets for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> sequestration is the terrigenous sedimentary formations found in oil, gas, and coal basins. It is generally assumed that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> injected into such formations can be stored indefinitely in a stable form. However, the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> into subsurface water leads to a reduction in pH, which may cause partial dissolution of the host formation, altering the structure of the subsurface in the injection zone. This process is relatively slow, potentially unfolding over decades or even centuries, and its long-term consequences require careful investigation through mathematical modeling. The geological formation is treated as a partially soluble porous medium, where the dissolution rate is governed by surface chemical reactions occurring at the pore boundaries. In this study, we present an applied mathematical model that captures the coupled processes of mass transport, surface chemical reactions, and the resulting microscopic changes in the pore structure of the formation. To ensure the model remains grounded in realistic geological conditions, we based it on exploration data characterizing the composition and microstructure of the pore space typical of the Cenomanian suite in northern Western Siberia. The model incorporates the dominant geochemical reactions involving calcium carbonate (calcite, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>a</mi><mi>C</mi><msub><mi>O</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>), characteristic of Cenomanian reservoir rocks. It describes the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> in the pore fluid and the associated evolution of ion concentrations, specifically <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>H</mi><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msup><mi>a</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>C</mi><msubsup><mi>O</mi><mn>3</mn><mo>−</mo></msubsup></mrow></semantics></math></inline-formula>. The input parameters are derived from experimental data. While the model focuses on calcite-based formations, the algorithm can be adapted to other mineralogies with appropriate modifications to the reaction terms. The simulation domain is defined as a cubic region with a side length of 1 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">μ</mi></semantics></math></inline-formula>m, representing a fragment of the geological formation with a porosity of 0.33. The pore space is initially filled with a mixture of liquid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and water at known saturation levels. The mathematical framework consists of a system of diffusion–reaction equations describing the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> in water and the subsequent mineral dissolution, coupled with a model for surface evolution of the solid phase. This model enables calculation of surface reaction rates within the porous medium and estimates the timescales over which significant changes in pore structure may occur, depending on the relative saturations of water and liquid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>.