The performance of porous solid sorbents for CO₂ capture is strongly influenced by the interplay between adsorption thermodynamics, pore structure, and mass transfer limitations. In materials such as hydrochar zeolite composites, adsorption-induced structural changes can result in swelling or shrinkage that dynamically alters diffusional pathways. To describe this complex coupling, a semi-analytical model is proposed that adapts the matchstick geometry and constant volume theory, which is traditionally applied to coalbed methane reservoirs for modeling CO₂ adsorption under confined conditions. The model assumes that the porous composite consists of rigid matchstick-like matrix blocks separated by transport-accessible pores. Under the constant volume condition, any volumetric expansion of the matrix due to CO₂ adsorption leads to a proportional reduction in accessible pore volume. As CO₂ adsorption in these composites previously showed a better fit for the Freundlich isotherm, the strain is modeled accordingly using this relationship. Unlike traditional models that only focus on equilibrium adsorption capacity, this approach also accounts for how strain affects the rate of gas transport. The effective diffusivity is described as decreasing exponentially with increasing strain, capturing a feedback loop where greater adsorption causes more swelling, which in turn slows down further adsorption by limiting diffusion. Key assumptions include negligible bulk deformation, homogeneous material properties, and isothermal adsorption. The model avoids difficult-to-measure parameters such as cleat compressibility, instead relying on directly measurable quantities including adsorption constants, mechanical strain coefficients, and initial porosity. This work provides a theoretical foundation for understanding how structural responses influence CO₂ mass transfer in advanced sorbent systems.
