Perfect Mixing Research Articles

Removal of Arsenic from Wastewaters by Airlift Electrocoagulation. Part 2: Continuous Reactor Experiments

Arsenic removal from wastewater is a key problem for copper smelters. Conventional methods either prove to be complicated, expensive, or not sufficiently effective. This work shows the results of electrocoagulation (EC) in aqueous solutions containing arsenic in a newly designed and constructed cylindrical continuous airlift reactor. The residence time distribution measurements showed that the reactor behaved as an ideal continuous stirred tank reactor (CSTR) with perfect mixing. Ten EC experiments were carried out in the continuous airlift reactor with sacrificial iron electrodes. The variables were: initial As(V) concentration, liquid flow rate, and electric current density. The results showed that the airlift EC process could reduce an initial As concentration from 1000 mg L−1 to 220 mg L−1 – corresponding to a reduction of 78%. In addition, a 100 mg L−1 solution was reduced by 88%. The Fe-to-As (mol/mol) ratio, when EC was working properly, was in the range of 1.3–1.5, which is very promising for the future development of the reactor. The arsenic removal is proportional with the electric current, the electric charge and the CSTR residence time. On the other hand, when the flow rate is increased, the arsenic removal decreases.

Two Approximate Methods To Estimate Conversion and Yield in Mixed Chemical Reactors

In many cases, quick methods are needed to evaluate the conversion and yield that may occur in a given reactor with a desired chemical reaction and necessary product. Full experimentation and/or full numerical simulation to evaluate the situation is neither warranted nor needed. In many cases, methods even quicker than computational fluid dynamics (CFD) with closure are needed to approximate yield results for various versions of a reactor. This paper reviews two methods that might be used beyond assuming perfect mixing or perfect plug flow to determine the likely conversion and yield for reactions in tubular reactors with mixing effects and in stirred vessel reactors. These methods can typically be implemented using a simple numerical integration program (such as POLYMATH) and/or a math program (such as MATLAB). In most cases, the results will not perfectly duplicate actual laboratory or pilot results, but simulated comparisons of various reactor setups can be made which are likely to be valid, because th...

Product and by-product formation in electrolysis of dilute chloride solutions

The results of an experimental study on electrochemical disinfection of water are presented. Attention was paid to the behaviour of chlorine compounds during electrolysis of water containing chlorides, with particular regard to the selectivity of the process towards the production of oxidising agents. Two reactor configurations were tested: a stirred tank cell and a filter press cell inserted in a hydraulic circuit. Both cells were equipped with boron doped diamond (BDD) anodes. Experiments were performed in batch and continuous mode. The effect of such operating parameters, current density, stirring rate or recirculating flow rate, on the behaviour of the process was investigated. The results at BDD anodes show that low current densities and perfect mixing of the system should be adopted in order to obtain high values of the concentration of oxidising agents avoiding the formation of such undesired by-products as chlorite, chlorate and perchlorate ions. Runs were also performed in which BDD was substituted by a commercial (Ti/RuO2) DSA anode and the results obtained with the two materials are compared.

A Biological Interpretation of Transient Anomalous Subdiffusion. II. Reaction Kinetics

Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.

Evaluation of membrane bioreactor performance via residence time distribution: effects of membrane configuration and mixing

Unlike conventional wastewater treatment systems that have a single effluent discharge point, membrane bioreactors (MBR) may have multiple extraction points resulting from the location of the membrane element in the reactor. This leads to multiple residence time distributions for an MBR system. One method to characterise the mixing is based on the concept of residence time distribution (RTD). A set of RTDs were generated using the conservative tracer, lithium chloride, for pilot plant MBRs with capacity up to 300 m3/day. Flat sheet and hollow fibre pilot plant MBR systems were operated in parallel on primary effluent collected at the Bedok Water Reclamation Plant in the republic of Singapore. Analysis of the RTD profiles indicated that membrane geometry did not impact on the kinetic conversion associated with nitrification because both MBRs were in well mixed conditions. However, the energy required to achieve perfect mixing with a hollow fibre module MBR, as defined by the velocity gradient, was lower than that with a flat sheet module MBR. The implication is that energy input associated with reactor mixing will depend on the configuration of the membrane. The difference in energy requirements between flat sheets and hollow fibres is such that careful consideration should be given to membrane selection in larger municipal installations.

Effect of Temperature, Pressure and Volume of Reacting Phase on Photocatalytic CO2 Reduction on Suspended Nanocrystalline TiO2

The effect of temperature, pressure and volume of reactant solution on the photocatalytic reduction of CO2at suspended TiO2was studied in an annular batch photoreactor. Reaction products in the liquid phase (methanol, formaldehyde) and in the gas phase (methane, ethane, carbon monoxide, molecular oxygen and hydrogen) were analysed by gas chromatography. The photocatalytic reduction of CO2was not sensitive significantly to small temperature variations within 10 K. The CO2pressure at carbonation of the solution influenced the selectivity of the CO2conversion to methane and methanol, while the dihydrogen yield was higher by two orders of magnitude and independent of the pressure. The dependence of the product yields on the volume of the liquid phase confirmed the fact that the requirement for perfect mixing was difficult to fulfil for the annular configuration of the reactor.

The response of natural displacement ventilation to time-varying heat sources

We examine transients caused by sudden changes in heat load in a naturally ventilated chamber. The space we consider has an isolated heat source, modeled as an ideal plume, and is connected to the exterior via openings at the top and bottom. Pressure differences between the exterior and interior that arise due to the buoyancy in the space drive a natural ventilation flow through the space that generates a two-layer system with buoyant (warm) fluid in the upper layer and ambient fluid in the lower layer. We develop two mathematical models, one assuming perfect mixing of each layer, the other accounting for stratification. We compare both models to small scale laboratory experiments. Neither model is significantly better than the other, and both give good agreement with the experiments. Using these models we identify many appealing features of the type of natural ventilation studied here. These include the fact that a well designed system is self-controlling. The manner in which it controls itself is very robust, because the larger the change in heat load the faster the system will readjust. Also there is a resistance against the interface penetrating deeply into the occupied zone, even for very large changes in heat load.

Impact on groundwater of concurrent leakage and diffusion of dichloromethane through geomembranes in landfill liners

Although intact geomembranes are excellent barriers to fluid flow, there are still two possible pathways for the transport of organic contaminants into the environment: leakage through defects in the geomembrane, and diffusion through the intact geomembrane. Analytical, semi-analytical and numerical techniques for calculating leakage rates have been developed. However, no previous attempt has been made to rigorously model the interaction between leakage through a hole in a wrinkle and diffusion. To address this shortcoming, finite-element analyses in two-dimensional space are performed to simulate the transport of dichloromethane (DCM) through a leaking HPDE geomembrane (GM) for eight cases involving composite liners, including both compacted clay liners and geosynthetic clay liners. Equations of steady-state seepage and time-dependent diffusion-advection in saturated soils are solved. Transport through the GMs is simulated by a novel, mass-conserving equivalent boundary condition that renders the problem computationally more tractable. Results are compared with those obtained from widely used one-dimensional methods, namely the Rowe equation for leakage through a wrinkle and the POLLUTEv7 program for mass transport. It is shown that predictions of leakage and transport by the one-dimensional method (POLLUTEv7) are within a maximum 30% of two-dimensional values under conditions of perfect mixing in the aquifer. When no horizontal mixing is present, concentrations of DCM are found to increase by up to 43% in two-dimensional analyses. It is concluded that one-dimensional analyses are adequate for most practical purposes.

Continuous flushing of contaminants from ballast water tanks

The transport of non-indigenous species (NIS) with ship ballast water is a major environmental problem. The International Maritime Organisation (IMO) have recommended that ballast tanks are flushed through with sea water to remove NIS contaminants. The flushing efficiency is studied using mathematical models and a scaled experimental model of a ballast tank. The density contrast between the ballast water and water used for flushing is important when the Froude number Fr w = U w / | g ′ | H ≪ 1 (defined in terms of average horizontal flow U w , reduced buoyancy g′, and H the vertical dimension in the tank). When denser water is used to flush a ballast tank, from below, it efficiently displaces lighter ballast water; but flushing through with light water creates a buoyant gravity current which effectively short circuits part of the tank. When Fr w ≫ 1, the density contrast between the ballast water and water used for flushing is not important and flushing is controlled by a bulk Péclet number, Pe w . For Pe w ≪ 1 perfect mixing occurs, while for Pe w ≫ 1 displacement flushing occurs. Laboratory experiments of flushing were performed using a model two-dimensional ballast tank employing dye attenuation to measure the whole concentration field and these experiments confirm the essential features of the mathematical models. The results of this study are discussed in the context of current IMO flushing protocols.

Mathematical model for waste minimization of a bleach plant in paper industry

AbstractIn the present investigation a steady‐state mathematical model is developed for a typical four stage CEHH bleaching sequence in Indian Pulp and Paper Industry. Each stage of the sequence is composed of chemical additions and mixing, reaction in a retention tower, and washing. Unit operation models were formulated using mass balances on liquor, fibres, kappa number, chemicals and COD based on the assumption of perfect mixing and quasi steady‐state. The COD is used in this paper as an indication of the amount of effluent coming out from four bleaching stages. In order to validate the model, the simulated results are compared with the literature data; a good agreement is achieved between the simulated results with the literature data. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A general correlation to predict axial dispersion coefficients in aerated channel reactors

Tracer studies have been widely applied to characterize the flow behavior in activated sludge reactors. The channel reactor with bottom aerators is one of the widespread designs in large wastewater treatment plants. Its flow behavior is well modeled either as a plug flow reactor with axial dispersion or as the perfect mixing cells in series. Several correlations have been developed to estimate the dispersion coefficients as a function of operating and geometrical parameters. These correlations fit properly the data derived from a given reactor in the range of operating and geometrical parameters for which they have been determined. Unfortunately they cannot be applied straightforwardly with a sufficient level of confidence to scale-up industrial units or scale-down laboratory pilots. Recently, two papers have proposed more general correlations [Makinia, J., Wells, S.A., 2005. Evaluation of empirical formulae for estimation of the longitudinal dispersion in activated sludge reactors. Water Res. 39, 1533–1542; Potier, O., Leclerc, J.-P., Pons, M.-N., 2005. Influence of geometrical and operating parameters on the axial dispersion in an aerated channel reactor. Water Res. 39, 4454–4462] but they are still not able to represent the whole set of data from the literature. This paper proposes a general correlation, which can represent all the available and usable sets of data from the literature and more than 170 experimental results obtained in our laboratory with a precision of 18%.

Wastewater treatment in a hybrid activated sludge baffled reactor

A novel hybrid activated sludge baffled reactor (HASBR), which contained both suspended and attached-growth biomass perfect mixing cells in series, was developed by installing standing and hanging baffles and introducing plastic brushes into a conventional activated sludge (CAS) reactor. It was used for the treatment of domestic wastewater. The effects on the operational performance of developing the suspended and attached-growth biomass and reactor configuration were investigated. The change of the flow regime from complete-mix to plug-flow, and the addition of plastic brushes as a support for biofilm, resulted in considerable improvements in the COD, nitrogen removal efficiency of domestic wastewater and sludge settling properties. In steady state, approximately 98 ± 2% of the total COD and 98 ± 2% of the ammonia of the influent were removed in the HASBR, when the influent wastewater concentration was 593 ± 11 mg COD/L and 43 ± 5 mg N/L, respectively, at a HRT of 10 h. These results were 93 ± 3 and 6 ± 3% for the CAS reactor, respectively. Approximately 90 ± 7% of the total COD was removed in the HASBR, when the influent wastewater concentration was 654 ± 16 mg COD/L at a 3 h HRT, and in the organic loading rate (OLR) of 5.36 kg COD m −3 day −1. The result for the CAS reactor was 60 ± 3%. Existing CAS plants can be upgraded by changing the reactor configuration and introducing biofilm support media into the aeration tank.

Neural Network Based Control of the Acrylonitrile Polymerization Process

AbstractAcrylic fiber is commercially produced by free radical polymerization, initiated by a redox system. Industrial production of polyacrylonitrile is a variant of aqueous dispersion polymerization, which takes place in a homogenous phase under isothermal conditions with perfect mixing. The fact that the kinetics are a lot more complicated than those of ordinary polymerization systems makes it difficult to control the molecular weight. On the other hand, abundant data is being gathered in industrial polymerization systems, and this information makes the neural network based controllers a good candidate for managing such a difficult control problem. Multilayer neural networks have been applied successfully in the identification and control of dynamic systems. In this work, the neural network based control of continuous acrylonitrile (ACN) polymerization is studied, based on a previously developed new rigorous dynamic model for the polymerization of acrylonitrile. Two typical neural network controllers are investigated, i.e., model predictive control and NARMA‐L2 (Nonlinear Auto Regressive Moving Average) control. These controllers are representative of the variety of common ways in which multilayer networks are used in control systems. The results present a comparison of the two common neural network controllers, and indicate that the model predictive controller requires a larger computational time.

Mixing characteristics of industrial columns in rougher circuit

The rougher circuit at Miduk Copper Concentrator, Iran, includes five Microcel™ flotation columns in parallel, each 12 m in height and 4 m in diameter. The main objective of this communication was to describe the mixing conditions of rougher columns using residence time distribution (RTD) data. A liquid radioactive tracer was employed to trace the material reported to tailing and concentrate. External scintillation detectors were used to record the tracer intensity without disturbing the flow pattern. Data analysis showed that large and small tank-in-series and N perfect mixers in series were the best models to present the flow pattern of liquid transferred to tailing and concentrate, respectively. Solids mean residence time from a theoretical model for counter-current columns was estimated. A 1.4:1 ratio between the residence time of liquids and solids was achieved. In order to complete the diagnosis, solid content and grade profiles along the collection and froth zone of one of the columns were also measured. The results of the present study showed that despite the presence of vertical baffles, the mixing conditions of industrial rougher columns were close to well mixed ones. The possible causes for mixing in industrial columns were described. As expected by increasing gas flow rate, the mean residence times of liquid transferred to both tailing and concentrate streams reduced and the mixing degree increased.

The Interaction of Reactions and Transport Part III: Asymptotes, Approximations, and Generalizations

Asymptotes, approximations, and generalizations are presented for homogeneous reactions in a round tube. The well-known solutions for plug flow and laminar flow are first reinterpreted as asymptotes for perfect and negligible radial mixing, respectively, for non-energetic reactions. The use of integrated-mean terms to derive asymptotes and approximate solutions for a wide range of behavior, including energetic reactions in adiabatic flow, is then illustrated.Generalized solutions analogous to those for thermal convection in terms of Re and Pr appear to be impossible to formulate for systems involving multiple reaction mechanisms because of the many parameters, including for energetic reactions the frequency factor, energy of activation, and heat of reaction for each mechanism. However, generalization appears to be feasible in terms of differential formulations and numerical methods of solution.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove ‘fixation’, i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume.

Effect of fuel mixing phenomena on the kinetic behavior of molten salt reactors

This paper deals with the significance of the effects of fuel mixing phenomena on the kinetic behavior of molten salt reactors. The point kinetic system of equations is applied with 1‐D resolution of the precursor equations. Dispersion is modeled by including diffusion into the precursor equations and by assuming perfect mixing in certain parts of the primary circuit of the reactor. Results are presented on the oscillating behavior of the reactor and the influence of fuel mixing phenomena on the amplitude of the accillations.

Weak trophic interactions and the balance of enriched metacommunities

Weak trophic interactions have been shown to promote the stability of ecological food webs characterized by perfect mixing. However, their importance at the landscape level and response to enrichment has not been extensively examined. In this paper we examine the food-web model explored by McCann et al. [1998. Weak trophic interactions and the balance of nature. Nature 395, 794–798]. The model is expanded into a metacommunity construct where local communities are coupled through global or local dispersal. We analyze global and local stability, as well as spatial synchrony in relation to trophic interaction strength and dispersal regimes. Results reveal that weak interactions can operate through two scale-dependent mechanisms: (i) under low local dispersal regimes, local stabilization of each community under weak interactions directly scales-up to global stability. (ii) Under high local dispersal, asynchronous local destabilization associated with weak interactions proves the driver behind global stability. In the face of enrichment, weak trophic interactions are shown to be instrumental in promoting global stability when dispersal is local. These results demonstrate how the importance of weak trophic interactions can be generalized at the landscape level despite contrary local predictions.

Modeling of the Separation of Propene/Propane Mixtures by Permeation through Membranes in a Polymerization System

In the bulk, catalyzed polymerization of propene in an industrial-scale recycle reactor, propane is an important contaminant, and for this reason it is necessary to remove it from the reaction medium in order to maintain high process productivities. In a typical industrial operation, unreacted propene/propane mixtures are purged from the recycle stream and vented to a flare, causing a significant negative impact on the process economics. Despite the potential economic advantages that membrane-based propene recovery may represent industrially, a comprehensive analysis based on a detailed mathematical model of the system is not available yet. The main purpose of this study is presenting a mathematical model to simulate the separation of propene/propane mixtures in a polymerization system using membrane modules. The model developed takes into account two extreme levels of macromixing that may be observed in the permeation module (namely, perfect mixing and plug flow), the diffusion of the gaseous mixture through the polymeric membrane, and the effect of operational variables such as temperature, pressure, flow rates, composition, and membrane area on the separation performance. It is shown that polyimide-based membranes, such as 6FDA−TMPPD (2,2-bis(3,4-decarboxyphenyl)hexafluoropropane dianhydride and 2,3,5,6-tetramethyl-1,4-phenylenediamine), may be used in permeation modules to deliver up to 5% gains in the effective propene concentration at the reactor feed, therefore increasing significantly the reactor productivity. An economic analysis shows that an economic gain of up to U.S.$1.5 million per year per polymerization plant may be attained.

Solids mixing in the riser of a circulating fluidized bed

Gas/solid and catalytic gas phase reactions in CFBs use different operating conditions, with a strict control of the solids residence time and limited back-mixing only essential in the latter applications. Since conversion proceeds with residence time, this residence time is an essential parameter in reactor modelling. To determine the residence time and its distribution (RTD), previous studies used either stimulus response or single tracer particle studies. The experiments of the present research were conducted at ambient conditions and combine both stimulus response and particle tracking measurements. Positron emission particle tracking (PEPT) continuously tracks individual radioactive tracer particles, thus yielding data on particle movement in “real time”, defining particle velocities and population density plots. Pulse tracer injection measurements of the RTD were performed in a 0.1 m I.D. riser. PEPT experiments were performed in a small ( ∼ 0.05 m I.D.) riser, using 18F-labelled sand and radish seed. The operating conditions varied from 1 to 10 m/s as superficial velocity, and 25– 622 kg / m 2 s as solids circulation rate. Experimental results were compared with fittings from several models. Although the model evaluation shows that the residence time distribution (RTD) of the experiments shifts from near plug flow to perfect mixing (when the solids circulation rate decreases), none of the models fits the experimental results over the broad ( U , G ) -range. The particle slip velocity was found to be considerably below the theoretical value in core/annulus flow (due to cluster formation), but to be equal at high values of the solids circulation rate and superficial gas velocity. The transition from mixed to plug flow was further examined. At velocities near U tr the CFB-regime is either not fully developed and/or mixing occurs even at high solids circulation rates. This indicates the necessity of working at U > approx. ( U tr + 1 ) m / s to have a stable solids circulation, irrespective of the need to operate in either mixed or plug flow mode. At velocities above this limit, plug flow is achieved when the solids circulation rate G > approx . 200 kg / m 2 s . Solids back-mixing occurs at lower G and the operating mode can be described by the core/annulus approach. The relative sizes of core and annulus, as well as the downward particle velocity in the annulus ( ∼ U t ) are defined from PEPT measurements. Own and literature data were finally combined in a core/annulus vs. plug flow diagram. These limits of working conditions were developed from experiments at ambient conditions. Since commercial CFB reactors normally operate at a higher temperature and/or pressure, gas properties such as density and viscosity will be different and possibly influence the gas–solid flow and mixing. Further tests at higher temperatures and pressures are needed or scaling laws must be considered. At ambient conditions, reactors requiring pure plug flow must operate at U > approx . ( U tr + 1 ) m / s and G > approx . 200 kg / m 2 s . If back-mixing is required, as in gas/solid reactors, operation at U > approx . ( U tr + 1 ) m / s and G < approx . 150 kg / m 2 s is recommended.