Multiple model-based controller design applied to an electrochemical batch reactor

This study demonstrates the control of an electrochemical batch reactor, that produces the desired product in a competing chemical/electrochemical reaction network, using a multiple model-based controller design. Since this type of control framework requires a process model to provide predictions of the controlled variables, and because batch reactors are highly nonlinear and nonstationary in nature, a bank of linear, dynamic, state-space models rather than a single, linear state-space or convolution model is developed to represent the nonstationary behaviour of the batch process. It is shown that the performance of this model/controller design can provide good reactor performance in the face of known disturbances.     

Some investigations into the anode profile in the transition zone in an electrochemical hole sinking operation

An empirical relationship has been suggested by some researchers to evaluate the overcut,a _o, in the transition zone. But the detailed study of this relationship has revealed that it overestimates the value ofa _o for machining under large equilibrium gap conditions. In this paper, the authors give a simpler equation, based on regression analysis, for the estimation of overcut in the transition zone. Further,a _o has also been found to be a function ofY _e,f, D, r _c andV.     

Some theoretical considerations on the long-term stability of polymer concrete composites in reactive environments

In this report, a theoretical examination is made of the life span of polymer concrete (PC) composites in aggressive environments. Using well known physical chemistry laws, in can be shown that the durability of PC is dependent only on the temperature and concentration of the aggressive environment. This dependence can be extremely useful to potential users of PC materials in aggressive environments since the life span of such materials may be predicted with minimum experimental data.     

Some principles of electrochemical fuel-cell design

This paper considers some electrochemistry and the electrochemical engineering principles for design and optimization of fuel cells.

The mass-transfer processes on the electrolyte side and the gas side of the working electrodes are analyzed and related to the kinetics of the process.

The faradaic efficiencies of individual electrode processes and their relations to the overall material balance are discussed. The design methods are illustrated by an optimization study for a 50-cell hydrogen-oxygen fuel-cell system.     

Effect of gas evolution on dispersion in an electrochemical reactor

Gas evolution at electrodes is encountered in many electrochemical processes, and the resulting gas bubbles affect mixing or dispersion in the neighbouring liquid. Experiments were conducted to study the effect of electrogenerated gas bubbles on dispersion in the fluid close to wall in a parallel-plate electrochemical reactor. Platinum microelectrodes and copper electrodes were used to generate gas (hydrogen or oxygen depending on polarity) bubbles and to measure dispersion, respectively. Estimated void fraction of gas bubbles was less than 0.01. Response curves were modelled using the axially dispersed plug flow model. Results obtained indicate that mean residence time of marked material (i.e. fluid close to wall) is almost unaffected by gas bubbles. Dispersion coefficient, however, increases with gas evolution at low liquid flow rates (say, for Reynolds number less than 100); but it is unaffected at higher flow rates. The effect of hydrogen and oxygen bubbles on dispersion under the range of conditions studied, appears to be similar.     

Effect of gas evolution on mass transfer in an electrochemical reactor

Experiments were conducted to study the effect of gas bubbles generated at platinum microelectrodes, on mass transfer at a series of copper strip segmented electrodes strategically located on both sides of microelectrodes in a vertical parallel-plate reactor. Mass transfer was measured in the absence and presence of gas bubbles, without and with superimposed liquid flow. Mass transfer results were compared, wherever possible, with available correlations for similar conditions, and found to be in good agreement. Mass transfer was observed to depend on whether one or all copper strip electrodes were switched on, due to dissipation of the concentration boundary layer in the interelectrode gaps. Experimental data show that mass transfer was significantly enhanced in the vicinity of gas generating microelectrodes, when there was forced flow of electrolyte. The increase in mass transfer coefficient was as much as fivefold. Since similar enhancement did not occur with quiescent liquid, the enhanced mass transfer was probably caused by a complex interplay of gas bubbles and forced flow.List of symbols A electrode area (cm²) - a constant in the correlation (k = aRe ^m , cm s^–1) - C _{R, bulk} concentration of the reactant in the bulk (mol^–1 dm^–3) - D diffusion coefficient (cm² s^–1) - d _h hydraulic diameter of the reactor (cm) - F Faraday constant - Gr Grashof number =gL ³/² (dimensionless) - g gravitational acceleration (cm s^–2) - i _g gas current density (A cm^–2) - i _L mass transfer limiting current density (A cm^–2) - k mass transfer coefficient (cm s^–1) - L characteristic length (cm) - m exponent in correlations - n number of electrons involved in overall electrode reaction, dimensionless - Re Reynolds number =Ud _h^–1 (dimensionless) - Sc Schmidt number = D ^–1 (dimensionless) - Sh Sherwood number =kLD ^–1 (dimensionless) - U mean bulk velocity (cm s^–1) - x distance (cm) - _N equivalent Nernst diffusion layer thickness (cm) - kinematic viscosity (cm² s^–1) - density difference = (_L – ), (g cm^–3) - _L density of the liquid (g cm^–3) - average density of the two-phase mixture (g cm^–3) - void fraction (volumetric gas flow/gas and liquid flow)     

Some theoretical and practical aspects of polyester whitening from the wash bath

Uptake of fluorescent whitening agents from aqueous and organic systems by polyester fibers and films under various conditions was investigated. Different factors influencing the correlation between uptake of the fluorescent whitening agents and their performance in laundry liquors are discussed on the basis of the presented data. The results indicate that fluorescent whitening agents normally used for whitening other synthetic fibers can also have valuable additional effects on polyester. Furthermore the results are discussed in terms of the possible mechanisms of whitening.     

The electrochemical recovery of iron in a two-compartment batch electrochemical reactor

A model has been developed for a two-compartment batch electrochemical reactor in which simultaneous iron deposition and hydrogen evolution occur at the cathode, the anodic reaction being the production of hydrogen ions. The model incorporates ionic diffusivities through the diaphragm and a composite kinetic parameter for the cathodic reactions. In order to apply the model to data from a small batch reactor, the diffusivities have been obtained under conditions in which hydrogen alone is evolved at the cathode. The value of the kinetic parameter has been chosen to provide the best agreement between the model predictions and the experimental results. Satisfactory predictions of the current efficiency for iron deposition and the final concentrations in the reactor has been obtained, the largest discrepancies between predicted and actual concentrations being at high anolyte hydrogen ion concentrations. Reasons for these discrepancies are discussed.     

The electrochemical production of hydrogen using a carbonaceous fuel as an anode depolarizer

Carbon depolarized water electrolysis using the ferrous/ferric redox cycle as a mediator is discussed. Complete combustion of non-celulosic fuels by this process is not a realistic goal, though substantial voltage reduction over conventional water electrolysis can be achieved and unique by-product materials of possible upgraded value over feedstocks are produced.     

Characterization of an electrochemical reactor for the ozone production in electrolyte-free water

The filter-press electrochemical ozonizer is characterized as a function of the applied electric current, temperature, and linear velocity of the electrolyte-free water. Lead dioxide electroformed on surface of a non-platinized fine mesh stainless steel support was used as anode. Electrolysis of the electrolyte-free water was carried out using the membrane electrode assembly (MEA) adequately compressed by means of a specially designed clamping system. Electrochemical characterization studies were carried out galvanostatically as a function of temperature and linear velocity of the circulating water. It was verified that the electrochemical ozone production (EOP) taking place at the reacting zones formed at the solid polymer electrolyte (SPE)/mesh electrode interface is not considerably affected by circulating water when the linear velocity inside the distribution channels is higher than 1.20 cm s⁻¹. A current efficiency for the EOP of 13% and a specific electric energy consumption of 70 Wh g⁻¹ were obtained when an electric current of 130 A was applied at 30 °C. The reactor service life test revealed that the MEA using the lead dioxide fine mesh electrode as anode and a fine mesh stainless steel electrode as cathode, pressed against the SPE, is stable for the ozone production.     

The shape of the cohesive arch in hoppers and silos — Some theoretical considerations

Models of the cohesive arch have been developed in order to predict arch shape and test the circular arc hypothesis first proposed by Enstad [‘On the theory of arching in mass flow hoppers’, Chem. Eng. Sci., 1975, 30, 10, 1273-1283].A 2-dimensional arch was modelled. Vertical and horizontal force balances described the system, with 2 unknown: arch stress, σ_arc, and vertical arch co-ordinate y. A rotationally symmetrical system was also modelled and included the azimuthal stress σ_az. σ_az was related to σ_arc by a Mohr-Coulomb yield type of equation. These equations were solved numerically by an Euler method.A least squares fit was used to predict the equivalent circular arc radius R and circular arc co-ordinate y_circ. The square of deviation from the circle Σ(y − y_circ)² was used as a statistical measure of the goodness of fit to the circular arc.The arch shape was generally an excellent approximation to the circular arc. However, the arch diverged from the circular as arch span increased.A dimensionless group was defined: the Stress-Radius Number, N_SR, which incorporates the ratio of equivalent circular arc radius to the arch stress at the apex. N_SR was constant for a given set of conditions and was ideally equal to 1 for a 2-dimensional arch and 2 for a rotationally symmetrical arch with no overpressure.Arch thickness models had little effect upon arch shape but had a great influence upon stress. This affected the critical outlet dimension for flow.Rotationally symmetrical arches were very sensitive to the relation between azimuthal and arch stresses. This affected both arch shape and stresses.A critical outlet dimension was calculated and showed great variation dependent upon assumptions made. Jenike's approach of an arch of constant thickness with no overpressure yielded a conservative value.     

Performance of a multipurpose research electrochemical reactor

This paper reports on a multipurpose research electrochemical reactor with an innovative design feature, which is based on a filter press arrangement with inclined segmented electrodes and under a modular assembly. Under bipolar connection, the fraction of leakage current is lower than 4%, depending on the bipolar Wagner number, and the current distribution is closely uniform. When a turbulence promoter is used, the local mass-transfer coefficient shows a variation of ±10% with respect to its mean value. The fluidodynamics of the reactor responds to the dispersion model with a Peclet number higher than 10. It is concluded that this reactor is convenient for laboratory research.     

Mass transfer in an electrochemical reactor with two interacting jets

An electrochemical reactor operated with two identical solution streams injected in opposite directions on the same axis, and leaving it at a normal direction was studied by measuring local and global mass transfer coefficients and visualization of solution flow patterns. This flow configuration was compared to a case where a single stream enters the reactor and leaves it on the same axis. It was found that only the data obtained for the single stream mode can be correlated by the Chilton-Colburn relation, indicating a near laminar boundary layer flow. Global mass transfer coefficients for the single stream mode were found to be slightly higher than those for the interacting jets mode. However, when comparing the two modes by taking into account the dimensionless ratio of the mass transfer coefficient (Sh) to the energy consumption (Eu), it was found that the interacting jets (IJ) mode exhibits a better performance as compared to the single stream mode. The superiority of the IJ mode increases with increasing Reynold's number (Re).Nomenclature A, B adjustable parameters - b half width of channel - C electrolyte ion concentration - d inlet pipe diameter - d microelectrode diameter - D diffusion coefficient - maximum value of mean deviation - E pumping energy - Eu Euler number - F Faraday number - i current to a single microelectrode on an active wall - i current to a single microelectrode in an inert wall - I global diffusion current - k mass transfer coefficient to a single microelectrode in an active wall - k mass transfer coefficient to a single microelectrode in an inert wall - K global mass transfer coefficient - Q volumetric flow rate - Q _T total volumetric flow rate - R radius of the electrochemical reactor - Re Reynolds number - s surface area of a microelectrode - S surface area of the working electrode - Sc Schmidt number - Sh Sherwood number - V _x axial flow velocity alongx-axis - V flow velocity at large distance from the leading edge - V mean flow velocity - x axis tangential to the surface - y axis normal to the surface - z number of electrons transferred in the reaction (z=1 in the present case) Greek letters viscosity - specific gravity - kinematic viscosity (/) - P pressure drop across the reactor - V voltage drop across the reactor Abbreviations ST single stream - IJ interacting jets     

The analysis of an isothermal batch electrochemical reactor with a secondary cathodic reaction

An analysis has been made to examine the effect of a constant applied electrolysing voltage on the performance of an isothermal batch electrochemical reactor in which the rate of the cathodic reaction is limited by mass transfer of a reactant to the electrode surface, a simultaneous secondary reaction occurring at higher cathode potentials.Numerical solutions are presented for a hypothetical process study to show how average production rates for various percentage conversions of reactant are influenced by the magnitude of the electrolysing voltage and the corresponding electrical energy requirement. The most noticeable effect is that the electrical energy requirements for a given production rate are very strongly influenced by both the degree of conversion of reactant and by the extent to which the secondary reaction occurs.     

Entrance effect on mass transfer in a parallel plate electrochemical reactor

The influence of different fluid inlet types, slits or tubes, on mass transfer in a rectangular reactor was studied. Measurements of mass transfer coefficients were made using the limiting diffusion current technique based on ferricyanide ion reduction at a large nickel electrode located downstream of abrupt expansions. The overall mass transfer coefficients obtained were 3 to 13 times greater than those obtained in fully developed flows. Overall mass transfer coefficients were correlated for Reynolds numbers ranging from 400 to 3500 by a unique equation by introducing a nondimensional expansion factor defined by the ratio of the fluid inlet cross-section to that of the reactor. The correlation equation obtained was compared with literature data.     

An experimental study of a single layer packed bed cathode in an electrochemical flow reactor

Experimental measurements are reported for a packed bed electrode consisting of a single planar layer of uniform copper plated spheres located between platinum anodes and restrained by two plane porous PVC diaphragms. Two mass transfer controlled reactions, namely the reductions ofm-nitrobenzene sulphonic acid and copper sulphate, were investigated and the electrochemical mass transfer data in the range 23 <Re < 520 correlated by the equationShSc ^?1/3 = 0-83Re ^0.56, the Reynolds and Sherwood numbers being defined in terms of a particle diameter. Variations of electrode potential throughout the bed were found to be small enough to ensure reaction selectivity in the system.     

Simulation of an extractive electrochemical reaction operated under limiting current conditions in a parallel-plate reactor

An extractive electrochemical reaction, which uses an extractive liquid (β) to separate the adherent product (S) on the electrode surface (e) in order to allow the continuation of the reaction (R) occurring electrochemically in a reacting phase (α), was investigated with the aim of studying the kinetics and reactor design. A kinetic model based on the competitive surface coverage (θ) by the reactant and the product, was developed to describe the performance in a parallel-plate reactor. The electrochemical reaction rate, defined asKmAX _α/e(1-θ)(C _R/α-C _R/e), is equal to the extraction rate, defined asKdAX _β/Seθ(C _S ^β/sat -C _S/β) under steady-state conditions whereX is the dispersion function andA is the specific surface area. Simulation under limiting current conditions reveals that this system is dependent on the volume ratio of the two liquids, the dispersion effect and the reactor geometry and diffusion coefficients. Three dimensionless parametersΦ _k(=K _m/K _d),Φ _x (=X _α/e/X _β/Se) andΦ _v ( =X _β/X _α) were used to describe this extractive electrochemical reaction.