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Highlights • N photobioreactors in series modelled with 3N ODEs having Monod and Droop kinetics. • State variables: concentrations of algea and substrate, and internal cell quota. • Results: existence, uniqueness, stability and conditions for steady states. Abstract A photobioreactor (PBR) contains microalgae which under illumination consume carbon dioxide and substrate dissolved in water, and produce oxygen. The process is used in water recovery resource facilities with a continuous flow of wastewaster through the PBR. With several PBRs in series the reduction of substrate can be improved. This paper contains a thorough analysis of a model of PBRs in series, where each PBR is modelled with a system of three ordinary differential equations for the concentrations of dissolved substrate and biomass (algae), and the internal cell quota of substrate to biomass. Each PBR has a certain volume and irradiation. The absorption rate of substrate into the cells is modelled with Monod kinetics, whereas the biomass growth rate is modelled with Droop kinetics, in which both a minimum and a maximum internal cell quota are assumed. The main result is that the model has a unique stable steady-state solution with algae in all PBRs. Another stable steady-state solution is the wash-out solution with no algae in the system. Other steady-state solutions are combinations of these two with no algae in some of the first PBRs and algae in the rest of the PBRs in the series. Conditions on the illumination, volumetric flow and volumes of the PBRs are given for the respective solution. Numerical solutions illustrate the theoretical results and indicate further properties. [ABSTRACT FROM AUTHOR]

Underground coal bed reservoirs naturally contain methane which can be produced. In parallel of the production of this methane, carbon dioxide can be injected, either to enhance the production of methane, or to have this carbon dioxide stored over geological periods of time. As a prerequisite to any simulation of an Enhanced Coal Bed Methane recovery process (ECBM), we need state equations to model the behavior of the seam when cleats are saturated with a miscible mixture of CH 4 and CO 2 . This paper presents a poromechanical model of coal seams exposed to such binary mixtures filling both the cleats in the seam and the porosity of the coal matrix. This model is an extension of a previous work which dealt with pure fluid. Special care is dedicated to keep the model consistent thermodynamically. The model is fully calibrated with a mix of experimental data and numerical data from molecular simulations. Predicting variations of porosity or permeability requires only calibration based on swelling data. With the calibrated state equations, we predict numerically how porosity, permeability, and adsorbed amounts of fluid vary in a representative volume element of coal seam in isochoric or oedometric conditions, as a function of the pressure and of the composition of the fluid in the cleats. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order nonlinear mathematical model describing the dynamics of atmospheric concentration of CO 2 is investigated and studied through the application of a semi-analytical homotopy scheme combined with Sumudu transform and homotopy polynomials. This study examines the consequences of the variations of forest biomass and human population on the dynamics of the concentration of CO 2 gas in the atmosphere. The Caputo fractional derivatives are engaged in this study. The computational work shows that the evaluated iterative terms are adequate for the refined approximations of the solutions for a fractional model of dynamics of atmospheric concentration of CO 2 , and thus authenticate the computational strength of the employed scheme. The variational behavior of concentration of CO 2 , forest biomass, and human population are demonstrated through the graphical presentation regarding the changing values of fractional order derivatives and time t. Moreover, this study also examines the analysis of obtained solutions for a fractional model in view of uniqueness and convergence. [ABSTRACT FROM AUTHOR]

In this paper, we model breathing at the level of a human alveolus by developing a novel mathematical framework that links pulmonary mechanics and gas exchange. Unlike previous models, the developed alveolar model comprises the alveolar gas mixture, capillaries perfused in the alveolar wall, pulmonary surfactant lining the alveolus and the pleural cavity. The inclusion of the multiple compartments affords interested researchers the chance to study the effect of several respiratory factors on breathing. Here, we investigate the effect of holding breath, breathing at different altitudes and frequencies, and varying cardiac output. The important role of pulmonary surfactant in breathing is also highlighted. In addition, we propose a new method to model the transport of oxygen and carbon dioxide between the alveolus and perfused capillaries, and provide a Lagrangian description of surfactant dynamics. Finally, the mechanical work of breathing at the level of the alveolus is derived and implemented to compare the required breathing effort in different scenarios. Numerical results are consistent with published experimental and computational work. [ABSTRACT FROM AUTHOR]