In this study, a time dependent model for a regenerative hydrogen-vanadium fuel cell is introduced. This lumped isothermal model is based on mass conservation and electrochemical kinetics, and it simulates the cell working potential considering the major ohmic resistances, a complete Butler-Volmer kinetics for the cathode overpotential and a Tafel-Volmer kinetics near mass-transport free conditions for the anode overpotential. Comparison of model simulations against experimental data was performed by using a 25 cm 2 lab scale prototype operated in galvanostatic mode at different current density values (50 − 600 A m −2 ). A complete Nernst equation derived from thermodynamic principles was fitted to open circuit potential data, enabling a global activity coefficient to be estimated. The model prediction of the cell potential of one single charge-discharge cycle at a current density of 400 A m −2 was used to calibrate the model and a model validation was carried out against six additional data sets, which showed a reasonably good agreement between the model simulation of the cell potential and the experimental data with a Root Mean Square Error (RMSE) in the range of 0.3-6.1% and 1.3-8.8% for charge and discharge, respectively. The results for the evolution of species concentrations in the cathode and anode are presented for one data set. The proposed model permits study of the key factors that limit the performance of the system and is capable of converging to a meaningful solution relatively fast (s-min). Redox flow batteries are considered to be an exceptional candidate for grid-scale energy storage. One attractive feature is their capability to decouple power and energy.1-4 All-Vanadium Redox Flow Batteries (VRFBs) have been considered a promising system due to the limited impact of cross-contamination. However, they have faced challenges related to cost, scale-up and optimization. Current research is also focused on improvement of electrolyte stability for use over a wider temperature window and concentrations, development of electrode materials resistant to overcharge, and mitigation of membrane degradation.1,2 Cost dependency with regarding to vanadium can be mitigated through utilization of new systems that employ only half of the vanadium.1 Recently, a Regenerative Hydrogen-Vanadium Fuel Cell (RHVFC) based on an aqueous vanadium electrolyte V(V) and V(IV) and hydrogen has been introduced 5 and is illustrated schematically in Figure 1. This system contains a porous carbon layer for the positive electrode reaction, membrane and catalyzed porous carbon layer for the negative electrode reaction. Hydrogen evolution, which is an adverse reaction in VRFBs, is here the main anodic process. During discharge, V(V) is reduced to V(IV) and H 2 is oxidized, while the reverse process occurs during charge and H 2 is stored. The vanadium reaction takes place in the positive electrode (cathode), while the hydrogen reaction occurs in the catalyst layer (CL) of the negative electrode (anode). The redox reactions that occur ...
A hydrogen-vanadium electrochemical system was characterized using extensive experimental tests at different current densities and flow rates of vanadium electrolyte. The maximum peak power density achieved was 2840 W m −2 along with a limiting current density of over 4200 A m −2. The cycling performance presented a stable coulombic efficiency over 51 cycles with a mean value of 99.8%, while the voltage efficiency decreased slowly over time from a value of 90.3% to 87.0%. The capacity loss was of 5.6 A s per cycle, which could be related to crossover of ionic species and liquid water. A unit cell model, previously proposed by the authors, was modified to include the effect of species crossover and used to predict the cell potential. Reasonable agreement between the model simulations and the experimental charge-discharge data was observed, with Normalized Root-Mean-Square Errors (NRMSEs) within the range of 0.8-5.3% and 2.9-19.0% for charge and discharge, respectively. Also, a good degree of accuracy was observed in the simulated trend of the polarization and power density, with NRMSEs of 3.1% and 1.0%, and 1.1% and 1.9%, for the operation at a flow rate of vanadium electrolyte of 100 and 50 mL min −1 , respectively, while the voltage efficiency during the cycling test were estimated within a Root-Mean-Square Error (RMSE) of 1.9%. A study of the effect of the component properties on the cell potential was carried out by means of a model sensitivity analysis. The cell potential was sensitive to the cathodic transfer coefficient and the cathode porosity, which are directly related to the cathodic overpotential through the Butler-Volmer equation and the cathodic ohmic overpotential. It was recognized that a kinetic study for the cathodic reaction is needed to obtain more reliable kinetic parameters at practical vanadium concentrations, as well as reliable microstructural parameters of carbon electrodes.
This paper compares two deconvolution methodologies used to estimate residence time distributions (RTD) in industrial closed-circuit ball mills. Parametric and non-parametric deconvolution techniques were evaluated. Both techniques allowed for direct RTD estimates from inlet and outlet tracer measurements in the mills, with no need for mass balances nor assumptions to correct the effect of the tracer recirculation in the grinding circuits. Measurements of inlet and outlet concentrations were conducted by radioactive solid tracers and on-stream detectors. The parametric deconvolution was applied assuming the N-perfectly-mixed-reactors-in-series model, whereas the non-parametric deconvolution consisted of a constrained least squares estimation subject to non-negativity. The shapes of the estimated RTDs were consistent between these methodologies, showing mound-shaped distributions in all cases. From the parametric approach, mixing regimes described by 2–4 perfect mixers in series were observed, which indicated significant differences regarding perfect mixing. The mean (τmean) and median (τ50) residence times were more consistent with the RTD shapes when applying the parametric deconvolution. The non-parametric approach was more sensitive to noise, a disadvantage leading to mean residence times significantly higher than the median, and less consistent with the RTD locations. From the comparisons, the estimation strategies proved to be applicable in industrial closed-circuit ball mills. The parametric deconvolution led to better overall performances for τ50 = 1.7–8.3 min, given a suitable model structure for the RTDs.
This paper studies the effect of moderate deviations with respect to perfect mixing on the estimated kinetic parameters in industrial flotation banks. Radioactive tracer tests and mass balance surveys were performed to characterize the mixing regimes and Cu kinetic responses. For three models (Single Rate Constant, Rectangular and Gamma), two approaches to incorporate the residence time distributions (RTD) in the kinetic characterizations of rougher banks were compared: (i) RTDs measured from the radioactive tracer tests; and (ii) pure perfect mixing in each flotation machine. The measured RTDs did not present significant bypass in the evaluated banks. In all cases, comparable model fitting was obtained with both RTD approaches, which indicates that the kinetic models add sufficient flexibility to compensate for moderate biases in the mixing regime. The studied kinetic models showed non-significant differences in the estimated maximum recoveries (R∞), mean (kmean) and median (k50) rate constants when comparing the process modelling from measured RTDs and pure perfect mixing. However, the Gamma model was more sensitive to the RTD assumption in terms of the shapes of the flotation rate distributions. From the results, kinetic characterizations focused only on model fitting, or on R∞ and kmean (or k50) estimations have low sensitivity to the assumption of perfect mixing when the RTDs present moderate deviations with respect to this regime. Special attention must be paid when characterizing floating components as the perfect mixing assumption may bias the shapes of the flotation rate distributions.
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