A volume element model (VEM) for energy systems engineering

Dilay, E.; Vargas, J.V.C.; Souza, Jeferson Ávila; Ordóñez, Juan C.; Yang, Sam; Mariano, André Bellin

doi:10.1002/er.3209

Cited by 26 publications

(17 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The PBR systems shown in Figure were mathematically modeled with the volume element (VE) method that has been previously proposed for systems engineering . The methodology consists of dividing the engineering system under analysis in VEs with uniform properties, which are evaluated at the VE center.…”

Section: Methodsmentioning

confidence: 99%

The experimental validation of a large-scale compact tubular microalgae photobioreactor model

et al. 2017

Self Cite

View full text Add to dashboard Cite

Summary A dynamic mathematical model is developed to estimate microalgae growth in medium‐ and large‐scale compact tubular photobioreactors (PBRs). Besides cell and other chemical species concentrations, temperature and local solar irradiation are important variables to be assessed. Three different experiments were conducted to adjust and validate the mathematical model for which a methodology based on the coefficient of determination is introduced. The first experiment was performed in a 100 L prototype PBR, the second in a column 78.5 L air‐lift PBR, and the third in a 12,000 L compact tubular PBR. Initially, cell growth numerical simulation curves were directly compared with data from the first experiment, which resulted in a coefficient of determination R2 = 0.4043, showing that model adjustment was needed. As a result, 3 adjustment parameters were defined: (i) local solar irradiation (Ψ1); (ii) medium CO2 concentration (Ψ2); and (iii) nutrient concentration (Ψ3). Then, the first experiment data set was used to solve an inverse problem of parameter estimation, obtaining Ψ1 = 1.05, Ψ2 = 0.95, and Ψ3 = 0.18, which resulted in R2 = 0.98584. Next, cell growth numerical simulation curves were compared with measured data from the second and third experiments, obtaining R2 = 0.9862 and R2 = 0.82969, respectively. With the experimentally validated model, a 29 day (or 696 hours) simulation of microalgae cultivation was conducted to calculate the 12,000 L PBR microalgae‐derived oil production, which allowed for the projection of the microalgae species Acutodesmus obliquus oil productivity as approximately 2300 L ha−1 yr−1, considering 11.4% microalgae dry biomass lipid content. Such low production demonstrates that achieving an economically viable process for microalgae‐derived biofuels will require more technological advances and the development of highly optimized processes.

show abstract

Section: Methodsmentioning

confidence: 99%

The experimental validation of a large-scale compact tubular microalgae photobioreactor model

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…A simplified modeling and simulation approach for energy systems engineering that is capable of providing quick and accurate responses during system design was utilized to write the single AMFC mathematical model, namely, a volume element model [23,24]. The fuel cell is divided into seven control volumes (CV) that interact energetically with each other and with the environment as shown schematically in Figure 1a [10].…”

Section: Mathematical Modelmentioning

confidence: 99%

“…All the flow phenomena that are present are taken into account. The result is a volume element model [23,24] with unidirectional internal flow that contains additional three-dimensional features such as the electrode-wetted area, heat transfer between the cell, fuel, oxidant, and the surroundings, and pressure drops in the gas channels. The approach is cross disciplinary and pursues simultaneously (i) the local optimization of components and processes with (ii) the optimal global integration and configuration of the system.…”

Section: Introductionmentioning

confidence: 99%

The maximization of an alkaline membrane fuel cell (AMFC) net power output

Sommer

Vargas

Martins

et al. 2016

Int. J. Energy Res.

Self Cite

View full text Add to dashboard Cite

This study optimizes numerically the relative sizes, spacings (internal structure), and aspect ratios (external configuration) of a single alkaline membrane fuel cell for maximum net power. The alkaline membrane fuel cell (AMFC) cellulosic membrane brings new light to the possibility of having alkaline fuel cells that are nontoxic and asbestos free as compared with static electrolyte cells that use an asbestos separator and ammonium-based alkaline anion-exchange membranes. A dimensionless dynamic mathematical model is utilized in the process, and the results are presented in normalized charts for generality. Two degrees of freedom are considered as follows: (i) the relative thicknesses of two reaction and diffusion layers and the membrane space (internal structure); and (ii) the external aspect ratios of a square section plate that contains all single alkaline membrane fuel cell components (external configuration). The optimized internal and external configurations result from the optimal balance between electrical power output and pumping power to supply fuel and oxidant to the AMFC. A third level of optimization is found, that is, the KOH mass fraction in the electrolyte that leads to a 3-way-maximized net power output. A sixfold variation in AMFC net power output is observed as the internal and external configurations, and KOH mass fraction are changed. Such effect stresses the importance of pinpointing the optimal AMFC configuration in order to avoid poor performance. New algebraic correlations are derived to indicate in dimensionless form, the optimal configurations for the internal and external structure, and resulting maximum net power output, which are important for scaling up and down the AMFC design with ease, without having to perform new simulations.

show abstract

“…A simplified modeling and simulation approach for energy systems engineering that is capable of providing quick and accurate responses during system design was utilized to write the single AMFC mathematical model namely a volume element model [12,13]. The fuel cell is divided into seven control volumes (CV) that interact energetically with each other and with the environment as shown schematically in Fig.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…All the flow phenomena that are present are taken into account. The result is a volume element model (VEM) [12,13] with unidirectional internal flow that contains additional three-dimensional features such as the electrode wetted area, heat transfer between the cell, fuel, oxidant and the surroundings, and pressure drops in the gas channels. The approach is cross-disciplinary and pursues simultaneously: (i) the local optimization of components and processes with (ii) the optimal global integration and configuration of the system.…”

Section: Introductionmentioning

confidence: 99%

Constructal alkaline membrane fuel cell (AMFC) design

Sommer¹,

Vargas²,

Martins³

et al. 2016

IJHT

View full text Add to dashboard Cite

This paper introduces a structured procedure to optimize the internal structure (relative sizes, spacing) and external shape (aspect ratios) of a single alkaline membrane fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the single alkaline membrane fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, electrolyte solution concentration (KOH), geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels of optimization: (i) the internal structure, which basically accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, and (ii) the external shape, which accounts for the external aspect ratios of a square section plate that contains all single alkaline membrane fuel cell components. The available volume is distributed optimally through the system so that the net power is maximized. Temperature and pressure gradients play important roles, especially as the fuel and oxidant flow paths increase. The optimized internal structure and external shape are a result of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the gas channels. In the process, a third level of optimization was found with respect to the KOH concentration in the electrolyte solution that leads to a 3-way maximized net power output. The numerical results show that the maxima found are sharp, since a variation of up to 600% in net power was observed within the tested range of AMFC external aspect ratios, what emphasizes the importance of finding the optimal AMFC parameters, no matter how complex the actual design might be. It is also shown that the three times maximized net power increases monotonically with total volume raised to the power 0.7 (~3/4), similarly to metabolic rate and mass in animal design. Due to the fact that precision and low computational time are combined, it is expected that the model could be used as an important tool for AMFC design, control and optimization at the fuel cell stack level.

show abstract

A volume element model (VEM) for energy systems engineering

Cited by 26 publications

References 26 publications

The experimental validation of a large-scale compact tubular microalgae photobioreactor model

The experimental validation of a large-scale compact tubular microalgae photobioreactor model

The maximization of an alkaline membrane fuel cell (AMFC) net power output

Constructal alkaline membrane fuel cell (AMFC) design

Contact Info

Product

Resources

About