A mathematical model for the unsteady-state behaviour of an activated sludge unit

Based on a steady state model for biological purification of waste-water in an aeration basin with little backmixing, a model was developed for simulation of the unsteady state. An excellent fit was achieved by including the adsorption of parts of the substrate at the contact of the recycled sludge and the fresh waste water. Furthermore the assumption of an inert—biological non degradable-part was obvious. Special terms help describing the slow response of the systems to peak in the properties of the influent.

Including also a dynamic model for the secondary settler, a model for the biological stage of the waste-water purification plant was developed, with which it is possible to test various control strategies.     

A model of zinc-nickel alloy electrodeposition in an industrial-scale cell

This paper analyses continuous alloy plating of steel strip with the use of a rate model that accounts for migration and homogeneous equilibria in the mass-transport boundary layer adjacent to the cathode. The model predicts the effect of bath composition, temperature, electrolyte velocity, and current density on the alloy composition and current density distribution within the cell. The effect of a slight taper of the interelectrode gap was also considered. The results were used to evaluate which of several currently used electrogalvanizing cells are most likely to succeed in producing coats of uniform zinc-nickel alloy composition. It is demonstrated that mass-transfer of the zinc is a critical factor under typical industrial conditions and that electrolyte injection counter to the strip movement is important for application of an electrodeposit uniform in composition.     

Plantwide control for optimal operation of industrial-scale crude distillation unit processes

In this article, a combination of the wavelet neural network framework and the line-up competition algorithm is used to solve the economic optimization algorithm for an industrial-scale atmospheric distillation column (ADC) process. Compared to the relevant measuring data from Sinopec Wuhan Petroleum Group Company, China, the first optimal operating conditions show that the increments of the duties of furnace and pump-arounds of the ADC can effectively improve oil production. In our approach, the preflash column (PFC) coupled with ADC is denoted as an industrial-scale crude distillation unit (CDU) process. Since the PFC can produce light naphtha and reduce the furnace duty and steam consumption of ADC, it is verified that the CDU process provides the higher economic potential than ADC. Based on the second optimal operating conditions, the plantwide control strategy is employed to operate the system safely as well as regulate the outputs of the plant in the presence of inlet perturbations. Within the plantwide control framework, the inventory control aims to keep the controlled variables close to the desired operating condition and the quality control loops use a combination of inferential predictions and feedforward ratios to effectively suppress the temperature spikes of trays and furnaces. Finally, the simulations show that the product quality is guaranteed due to no offset ASTM D86 distillation temperature responses.     

Membrane fouling in electrodialysis: a model and experiments

Membrane fouling is a common cause for poor performance in electrodialysis systems, usually because it reduces the limiting current. Fouling may be caused by deposits of either neutral matter or colloidal matter with ion exchange properties. In the present paper a model for membrane fouling is developed and expressions are derived for the reduction in limiting current caused by both neutral fouling films and films having ion exchange properties. The effect of fouling is shown to depend not only on the properties of the fouling film, but also on the hydrodynamic conditions in the channels and in the case of ion exchange fouling films on the salt concentration in the dialysate channel. Ion exchange fouling films are shown to be much more effective in reducing the limiting current than neutral films. Some experimental data are presented which confirm the trend of the theory for fouling with ion exchange films.     

Designing of an electrodialysis desalination plant

The design and operation of an electrodialysis desalination process are based on a set of fixed and variable parameters such as stack construction, feed and product concentration, membrane properties, flow velocities, current density, recovery rates, etc. These parameters are interrelated and may be rather different for different applications. For an efficient operation of an electrodialysis desalination plant, the process has to be optimized in terms of overall costs considering component properties and operating parameters. In this study the design and optimization of an electrodialysis plant to be used for brackish water desalination has been treated. The required equations were derived or, as in the case of the limiting current density, were experimentally determined. As an example, an electrodialysis plant with a sheet-flow stack construction and given feed solution composition was designed and optimized in terms of overall costs and the sensitivities of the different parameters are analyzed.     

Effect of an AC perturbation on a desalination electrodialysis process

The influence of an alternating (AC) sinusoidal perturbation, of known frequency and small amplitude, superimposed to the usual applied continuous (DC) signal in a desalination electrodialysis process has been studied. The experiments were carried out with two types of ion-exchange membranes and sodium chloride aqueous solutions of two initial concentrations and at different frequencies of the AC signal. The results show that the presence of the AC perturbation favours the desalination process, mainly at the lowest frequencies. This fact is considered as a consequence of that the electroosmotic transport accompanying ion transfer during the process is affected by the AC perturbation. This behaviour suggests that the presence of an AC perturbation may influence on the efficacy of the desalination process.     

Effective separation of magnetite nanoparticles within an industrial-scale pipeline reactor

ABSTRACT

Within the field of wastewater treatment, nano-adsorbents are a significant emerging technology; however, separation of the nano-scale particles after loading has proved to be an impediment to widespread industrial implementation. Magnetic collection of nanoparticles is a potential strategy for effective separation. Nano-scale magnetite is an effective adsorbent, is sufficiently magnetically susceptible, and is superparamagnetic, allowing re-dispersion following magnetic collection.

In this work, an in-line, water-cooled magnetic collection module was developed with collection efficiencies regularly exceeding 98%. Models were developed over various flow regimes. The role of cooperative magnetophoresis was demonstrated and a physical model has been proposed for adsorption upon particle agglomerations about magnetic core wires.     

Using hybrid neural networks in scaling up an FCC model from a pilot plant to an industrial unit

The scaling up of a pilot plant fluid catalytic cracking (FCC) model to an industrial unit with use of artificial neural networks is presented in this paper. FCC is one of the most important oil refinery processes. Due to its complexity the modeling of the FCC poses great challenge. The pilot plant model is capable of predicting the weight percent of conversion and coke yield of an FCC unit. This work is focused in determining the optimum hybrid approach, in order to improve the accuracy of the pilot plant model. Industrial data from a Greek petroleum refinery were used to develop and validate the models. The hybrid models developed are compared with the pilot plant model and a pure neural network model. The results show that the hybrid approach is able to increase the accuracy of prediction especially with data that is out of the model range. Furthermore, the hybrid models are easier to interpret and analyze.     

Improvement in steam stripping of sour water through an industrial-scale simulation

Sour water containing hydrogen sulfide, carbon dioxide, hydrogen cyanide, and ammonia is mainly purified by steam stripping. Increased concern in recent times over effluent water quality and energy saving has caused sour water stripping to attract considerable attention. However, the development of the operation methodology and structure of this process has not been systemic, leading to inefficiencies in the systems commonly used. In this paper, the characteristics of a sour water stripping column are investigated by using an industrial-scale simulation. From these results, we propose several guidelines (high feed temperature, low composition of CO₂ in the feed, need of rectifying section, low mass flow rate of the second recycle stream, high reflux ratio, and modified structure using a pump-around side cooler) for improving stripper performance through changes in the operating condition and process structure. The proposed structure and guidelines can be applied not only to reduce steam consumption and lower the ammonia concentration in the effluent water but also to operate the system stably.     

Crystal growth dispersion in an MSMPR crystallizer — a mathematical model

According to the literature, one of the formation mechanisms of crystal growth rate dispersion consists in each individual crystal growing at an adequate constant rate, with different rates however for different crystals. In the present paper, this case has been described on the basis of a population density of nuclei, making use of the classical exponential dependence amongst others. Differences between n and n have been interpreted. The dependencies describing the population density of crystals n have been presented and a simplified method for their calculation proposed.     

Secondary current distribution in a two-dimensional model cell composed of an electrode with an open part

On the assumption that the relation between the overpotential and the current density is expressed by linear and Butler-Volmer equations, secondary current distributions were obtained in a two-dimensional model cell in which a working electrode with an open part serving to release gas bubbles to the back side of the electrode is located parallel to a counter electrode or a separator. Cell resistances or cell voltage in the model cell were evaluated for various combinations of geometrical parameters and heterogeneous kinetic parameters by means of the finite element method. As a result, when the kinetic equation was the linear approximation, the cell resistance or cell voltage varied mainly with two geometrical parameters (the interelectrode distance and the electrode surface ratio) and the kinetic parameters. On the other hand, when the kinetic equation was of the Butler-Volmer type the cell voltage varied with the kinetic parameters and the percentage of open area instead of the electrode surface ratio. In order to facilitate estimation of cell voltage for an industrial productiontype cell composed of electrodes with voids or holes, the computed cell voltages were expressed as functions of these parameters in simple approximate equations. A criterion for estimating whether the cell voltage is controlled by the overpotential or the ohmic drop is presented.     

Primary current distribution in a two-dimensional model cell composed of an electrode with an open part

A two-dimensional model for industrial production-type cells in which electrodes have holes for releasing gas bubbles to the back side of the electrodes and a separator located between the working- and counter-electrodes is proposed in conjunction with some geometrical parameters of the electrode and the cell. The primary current distribution in this model was calculated for a series of values of the parameters by the finite element method. The current distribution in the cell with the separator is quite different from that without the separator. Variations of the ohmic potential drop with the parameters reveal that the cell resistance is determined not only by the interelectrode distance but also by the per cent open area and in some cases by the superficial surface area. The partitions of the total current into the currents on the front, the back and the intermediate sides of the working-electrode are obtained as functions of the per cent open area and the superficial surface area. These results may be useful for estimating the performance of the electrode.Nomenclature b distance from the back wall to the back side of the working-electrode - d ₁ distance between the front side of the working-electrode and the separator (or the counter electrode when cell has no separator) - d ₂ width of the separator - I total current per half pitch - L length of a real electrolysis cell - n coordinate perpendicular to the boundary of the model cell - o _p per cent open area, given by Equation 1 for the present model - p pitch, i.e. twice the length of the unit cell - R equivalent unit-cell resistance defined by Equation 13 - R _t total cell resistance - r ratio of the average current density on each side of the working-electrode to that of the counter-electrode - s superficial surface area, given by Equation 2 for the present model - t thickness of the working electrode - u _k function defined by Equation 10 - test function - w width of the working electrode - x abscissa located on the cell model - y ordinate located on the cell model - d infinitesimal length on the boundary - ₁ resistivity of the solution phase - ₂ resistivity of the separator - potential - ^* potential at the working electrode - linear integration contour along I0, AH or EFDH - double integration space in the solution or the separator phase     

Development of a mathematical model for a secondary reformer

A rigorous one-dimensional heterogeneous model is developed for a secondary reformer in an ammonia plant with special emphasis on the catalyst particle models. These are based on the effective diffusivity model and the Stefan-Maxwell model in the catalyst pore and the film around the catalyst particle. The performance of these four models is evaluated for the data collected from a commercial reformer in the complete operating range and recommendations are made regarding the use of appropriate particle models. The models for the catalyst particle show considerable deviations at the particle level but the reformer simulations produce almost identical results at the global level for all the four particle models. The need for a rigorous treatment of interphase resistance to mass transfer has been clearly demonstrated by comparison of the present model with the model of Singh and Saraf.     

A mathematical model of a spouted bed gasifier

A mathematical model of the spouted bed gasifier has been constructed based on simplified first order reaction kinetics for the gasification reactions and the stream tube hydrodynamic model of Mathur and Lim. This two region model treats the spout as an isothermal plug flow reactor with cross flow into a series of streamtubes forming the annulus. Each streamtube is considered as a plug flow reactor. The effects of kinetic and hydrodynamic parameters on model predictions are illustrated, and a comparison made with experimental gas composition profiles obtained in a 0.30-m dia. gasifier.     

Solar desalination with a humidification-dehumidification cycle: mathematical modeling of the unit

Solar desalination is gradually emerging as a successful renewable energy source of producing fresh water. Solar Multi-Effect Humidification (MEH) units based on the humidification-dehumidification principle are considered as the most viable among solar desalination units. A simulation study of these units leads to a better understanding of the performance of such type of desalination units. This study therefore focuses on studying and analysing the effects and performance of various components involved in the process along with the study of the effect of water feed flow rate on the desalination production. To our knowledge, there is no such comprehensive model available in the literature. This study could lead a step further in the commercialisation of solar desalination units based on the humidification-dehumidification principle.     

Mass transfer and shear in an airlift bioreactor: Using a mathematical model to improve reactor design and performance

Several studies have shown a strong relationship between morphology and agitation ( [Cui et al., 1997] and [Berzins et al., 2001] ). The shear stress distribution and mass transfer are the important parameters which can improve the performance of bioreactor. In this work, a mathematical model using computational fluid dynamics (CFD) techniques is used to study the gas–liquid dispersion in an airlift reactor. Multiple rotating frame (MRF) technique is used to approximate the movement of the impeller in the stationary reactor. Population balance modeling (PBM) is used to describe the dynamics of the time and space variation of bubble sizes in the reactor. The PBM equation is solved using an approximate method known as the class method (CM) and the bubble sizes are approximated through a discrete number of size ‘bins’, including transport, and different bubble phenomena. These equations of the CM are then written as scalar transport equations and added to the multiphase fluid mechanical equations describing the dynamics of the flow. All these equations are solved using control volume formulation through the use of an open-source CFD package OpenFOAM. The model is used to analyze an existing geometry of an airlift bioreactor and validate the modification on the initial design. The new design of airlift gives a clear performance by the increase of the global and local mass transfer and the decrease of the shear stress.     

Use of the electrodialysis process to concentrate a formic acid solution

Our previous work clearly showed that electro-eletrodialysis was an efficient way to concentrate a formic acid solution. Electro-electrodialysis can be easily scaled up as electrodialysis, but the equipment cost is higher. Accordingly, an electrolysis process with a new cation-exchange membrane was tested in this work. The effects of concentration, electric current density, and concentration difference between the concentrated side and the dilute side were studied. The experimental results indicated that electrodialysis was also an effective method to concentrate formic acid solution. For the high concentration system the overall current efficiency was larger than 100%. The overall current efficiency for a low concentration system would be up to 90%. But the concentrated ratio is not as much as desired, which is limited by the operating system and conditions. In general, the overall current efficiency was increased to a maximum value with an increase of the current density. After a certain value, the overall current efficiency would begin to drop. The increase of the initial concentration helped to increase the overall current efficiency, but led to a decrease in the concentrated ratio. The volume change of the concentrated solution is seriously affected by the current density and the ratio of the initial concentration in the concentrated compartment compared to that in the dilute compartment.     

Development of a mathematical model for the pultrusion process

A mathematical model has been developed to simulate the pultrusion process, namely the profiles of temperature and the degree of cure in both the axial and radial directions in a pultrusion die of cylindrical shape. For the study, the equations of continuity and energy transport, coupled with a kinetic expression for the curing reaction, were solved numerically, using a finite difference method. For the kinetic expression, we used an empirical expression of the form dα/dt = (k₁ + k₂α^m)(1 ? α)ⁿ to describe the curing behavior of both unsaturated polyester and epoxy resins. Differential scanning calorimetry (DSC) was used to investigate the curing behavior of the following systems: unsaturated polyester resin/glass fiber, epoxy resin/glass fiber, and epoxy resin/carbon fiber. The results of DSC runs were used to determine the kinetic parameters, which enabled us to predict the effects on the pultrusion characteristics of the following variables: (1) the type of initiator; (2) the type of fiber reinforcement; (3) the type of resin; and (4) the pulling speed and hence the residence time.