HighlightRigorous mathematical techniques and image-based modelling were used to quantify the effect of root hairs on nutrient uptake and to investigate how uptake is influenced by growing root hairs.

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This article examines the CO 2 adsorption−desorption kinetics of bituminous coal under low pressure injection (0.5 MPa) in the context of CO 2 sequestration in shallow level coal seams. This study used two different sizes of intact core samples of bituminous samples from seam no. 30 at the Experimental Mine Barbara (EMB) in Katowice, Poland. Manometric adsorption kinetics experiments were conducted on 50 mm dia. 60 mm long coal core samples (referred to as EMB1) and 50 mm dia. 30 mm long coal core samples (referred to as EMB2). The kinetics of adsorption at injection pressures ranging from 0.1 to 0.5 MPa were compared to those at elevated pressures ranging from 0.5 to 4.5 MPa. For the first time, intact sample adsorption−desorption data were fitted in pseudo first order (PFO), pseudo second order (PSO), and Bangham pore diffusion models. The PSO model fits the data better than the PFO model, indicating that bulk pore diffusion, surface interaction, and multilayer adsorption are the ratedetermining steps. Comparing the equilibrium amount of adsorbed (q e ) obtained for the powdered samples (9.06 g of CO 2 /kg of coal at 0.52 MPa) with intact samples (11.68 g/kg at 0.53 MPa and 7.58 g/kg at 0.52 MPa for the intact EMB1 and EMB2 samples) showed the importance of conducting experiments with intact samples. The better fit obtained with the Bangham model for lower pressure equilibrium pressures (up to 0.5 MPa) compared to higher pressure equilibrium pressures (4.5 MPa) indicates that bulk pore diffusion is the rate-determining step at lower pressures and surface interaction takes over at higher pressures. The amount of CO 2 trapped within the coal structure following the desorption experiments strengthens the case for intact bituminous coal samples' pore trapping capabilities.

This work presents a coupled thermo-hydraulic−mechanical (THM) model to study real gas flow behavior in a deformable coal matrix. The matrix encompasses multiple pore sizes ranging from nanometers to micrometers, and promotes various complex, inter-related mass transport mechanisms. In this model, the adsorbed gas layer at the interface between the solid matrix and the free gas phase is considered as an independent phase. Gas adsorption/desorption and diffusion process are defined separately for individual phase, which are then interacted via mass exchange between the phases. The Knudsen number based flow regimes are adopted to describe bulk gas transport in the matrix of varying pore sizes, and the adsorbed phase transport is described by surface diffusion mechanisms. The thermal effect on gas adsorption and transport behavior is investigated. In addition, the mechanical behavior is included to consider the stress dependency of the porosity and intrinsic permeability of porous rocks. The validity of the proposed model is achieved by comparing numerical solutions with published experimental data. Numerical simulations were performed to investigate the real gas transport processes in a coal matrix of multiple pore sizes. The simulated results show that the times to reach pressure equilibrium and adsorption equilibrium are not the same, and they depend on the pore size, pressure, and surface diffusion. The time required to reach equilibrium is reduced significantly with an increase of pore sizes. Diffusion coefficients in the porous matrix are not constant but vary with pressure and pore sizes, which is important for accurate estimation of coalbed gas production or carbon sequestration.

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