Modeling adsorption with lattice Boltzmann equation

Lattice Boltzmann method for adsorption under stationary and transient conditions: Interplay between transport and adsorption kinetics in porous media

A numerical method based on the Lattice Boltzmann formalism is presented to capture the effect of adsorption kinetics on transport in porous media. Through the use of a general adsorption operator, canonical models such as Henry and Langmuir adsorption as well as more complex adsorption mechanisms involving collective behavior with lateral interactions and surface aggregation can be investigated using this versatile model. By extending the description of adsorption phenomena to kinetic regimes with any underlying adsorption model, this effective technique allows assessing the coupled dynamics resulting from advection, diffusion, and adsorption in pores not only in stationary conditions but also under transient conditions (i.e., in regimes where the adsorbed amount evolves with time due to diffusion and advection). As illustrated in this paper, the development of such an approach provides a simple tool to determine the reciprocal effect of molecular flow and dispersion on adsorption kinetics. In this context, the use of a Lattice Boltzmann-based approach is important as it allows considering porous media of any morphology and topology. Beyond fundamental implications, this efficient method allows treating real engineering conditions such as pollutant dispersion or surfactant injection in a flowing liquid in soils and porous rocks.

Image-based modeling of gas adsorption and deformation in porous media

Understanding adsorption of CO₂ in porous formations is crucial to its sequestration in geological formations. We describe a model for adsorption of CO₂ and the deformation that it induces in a sandstone formation over wide ranges of temperature and pressure. The model couples the thermodynamics of sorption with elastic deformation of the solid. Finite-element computations are then used in order to compute CO₂ adsorption isotherms along with the induced strain in the formation. We also compute the Darcy permeability of the porous medium using the lattice-Boltzmann method. All the computations are carried out with a three-dimensional image of a core sample from Mt. Simon sandstone, the target porous formation for a pilot CO₂ sequestration project that is currently being carried out by Illinois State Geological Survey. Thus, no assumptions are made regarding the shape and sizes of the pore throats and pore bodies. The computed CO₂ sorption isotherm at 195 K is in excellent agreement with our experimental data. The computed permeability is also in good agreement with the measurement. As a further test we also compute the sorption isotherm of N₂ in the same formation at 77.3 K, and show that it is also in good agreement with our experimental data. The model is capable of predicting adsorption of CO₂ (or any other gas for that matter) in porous formations at high pressures and temperatures. Thus, it is used to study the effect of hydrostatic pressure on adsorption and deformation of the porous formation under various conditions. We find that the effect of the confining pressure is more prominent at higher temperatures. Also computed is the depth-dependence of the capacity of the formation for CO₂ adsorption, along with the induced volumetric strain.

Adsorción de acetaminofén sobre carbones activados a diferente pH. Entalpía y entropía del proceso

Se analizaron los cambios entálpicos y entrópicos derivados del proceso de adsorción de acetaminofén sobre carbones activados con química superficial modificada. Se realizó, además, una variación del pH para determinar los cambios en las propiedades termodinámicas cuando existen cargas en el adsorbato y en el adsorbente. Se encontró que la máxima capacidad de adsorción (1,172 mmoles g -1) corresponde al proceso llevado a cabo en el carbón activado denominado CAR en este estudio a pH 7; los valores de las funciones termodinámicas de entalpía de inmersión y entropía de adsorción fueron -36,02 J g-1 y 0,123 J g-1 K-1, respectivamente. Así, el cambio de entropía de adsorción para el acetaminofén en los carbones activados estudiados dependió del pH. Se encontró que esta función termodinámica varía en el siguiente orden pH 2 > pH 11 > pH 7. Este comportamiento se relaciona con el número de especies presentes en la solución capaces de interactuar con la superficie del carbón activado.  

Kinetic Accessibility of Porous Material Adsorption Sites Studied through the Lattice Boltzmann Method

We present here a computational model based on the lattice Boltzmann scheme to investigate the accessibility of active adsorption sites in hierarchical porous materials to adsorbates in a flowing liquid. By studying the transport and adsorption of tracers after they enter the pore space of the virtual sample, we characterize their kinetics as they pass through the pore space and adsorb on the solid-liquid interface. The model is validated on simple geometries with a known analytical solution. We then use it to investigate the influence of regular grooves or disordered roughness on the walls of a slit pore geometry, looking at the impact on adsorption and transport. In particular, we highlight the importance of adsorption site accessibility, which depends on the shape and connectivity of the pore space as well as the fluid flow profile and velocity.