# Chemical Engineering Science (v.63, #8)

Modelling of hydrate formation kinetics: State-of-the-art and future directions by Cláudio P. Ribeiro; Paulo L.C. Lage

*(2007-2034)*. Clathrate hydrates have drawn considerable attention in the last few years due to a variety of possible applications, including transportation and storage of natural gas and carbon dioxide sequestration in the ocean. These applications require the development of effective hydrate formation reactors, which, in turn, asks for a comprehensive understanding of hydrate formation kinetics. Contrary to hydrate thermodynamics, hydrate kinetics are still poorly understood. In the present contribution, a critical review of the literature on hydrate kinetics is provided, with special emphasis upon modelling efforts, essential to the design of any reactor. The main features of the models available in the literature for hydrate nucleation and growth are discussed, together with their limitations. In addition, suggestions for further developments are presented.

**Keywords:**Mathematical modelling; Nucleation; Particle formation; Phase change; Hydrate; Natural gas;

Modeling of branching density and branching distribution in low-density polyethylene polymerization by Dong-Min Kim; Piet D. Iedema

*(2035-2046)*. Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties in measurement and computation of scission effect and branchings of polymer. Our previous papers [Kim, D.M., et al., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR. Chemical Engineering Science 59, 699–718; Kim, D.M., Iedema, P.D., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor. Chemical Engineering Science, submitted for publication] are concerned with the scission reaction during ldPE polymerization and its effect on molecular weight distribution (MWD) of ldPE for various reactor types. Here we consider branching distributions as a function of chain length for CSTR and tubular reactor processes. To simultaneously deal with chain length and branching distributions, the concept of pseudo-distributions is used, meaning that branching distributions are described by their main moments. The computation results are compared with properties of ldPE samples from a CSTR and a tubular reactor. Number and weight average branchings and branching density increase as chain length increases until the longest chain length. The concentrations of long chain branching (LCB) are close to those of first branching moment in both CSTR and tubular reactor systems. The branching dispersity, a measure for the width of the branching distribution at a certain chain length, has the highest value at shorter chain length and then monotonously decreases approaching to 1.0 as chain length increases. Excellent agreements in branching dispersities between calculation with branching moments and prediction with assumption of binomial distribution for a tubular reactor and CSTR processes show that the branching distribution follows a binomial distribution for both processes.

**Keywords:**Polymerization; Modeling; Branching; Branching distribution; Reaction engineering; Molecular architecture design;

The density of water in carbon nanotubes by Alessio Alexiadis; Stavros Kassinos

*(2047-2056)*. In this paper, the density of water confined in carbon nanotubes of different sizes and chirality is calculated. Molecular dynamics is used to simulate the spontaneous filling of the nanotube with water molecules coming from an external bath. Three H 2 O filling modes are found and a correlation, which relates the density with the nanotube diameter, is proposed.

**Keywords:**Carbon nanotubes; Confined water; Molecular dynamics;

Modeling and kinetics of tandem polymerization of ethylene catalyzed by bis(2-dodecylsulfanyl-ethyl)amine- CrCl 3 and Et ( Ind ) 2 ZrCl 2 by Junwei Zhang; Hong Fan; Bo-Geng Li; Shiping Zhu

*(2057-2065)*. A mathematical model was developed to describe ethylene–1-hexene copolymerization with a tandem catalysis system. A series of semi-batch polymerization runs catalyzed by a trimerization catalyst bis(2-dodecylsulfanyl-ethyl)amine- CrCl 3 and a copolymerization catalyst Et ( Ind ) 2 ZrCl 2 in toluene at 74 ∘ C were carried out to verify the model. Both experimentation and modeling showed that adjusting the Cr/Zr ratio yielded various branching densities and thus melting temperatures, as well as molecular weights and polydispersities. Broad composition distributions and thus broad DSC curves were observed at high Cr/Zr ratios. Modeling results elucidated that this is due to an accumulation of 1-hexene component and to composition drifting during the copolymerization. It was also found that applying a short time period of pre-trimerization improved homogeneity in chain microstructure and minimized broadening in DSC curves.

**Keywords:**Ethylene–1-hexene copolymer; Ethylene trimerization; Tandem catalysis system; LLDPE; Modeling;

Ultra-stability of gas hydrates at 1 atm and 268.2 K by Guochang Zhang; Rudy E. Rogers

*(2066-2074)*. This paper details creation of methane sI hydrates that are much more stable at 1 atm and 268.2 K than any previously reported. Extraordinarily stable natural gas sII hydrates at 1 atm and 268.2–270.2 K are reported for the first time. Test innovations that achieved ultra-stabilities give insight into hydrate self-preservation mechanisms. Water–surfactant liquid solutions were used to nucleate hydrate crystals that adsorbed as extremely small particles on surfaces of high thermal conductivity. The small hydrate particles packed and consolidated symmetrically upon Al or Cu cylindrical surfaces, minimizing internal void spaces and fractures in the accumulated 250–400 g hydrate mass. Resulting hydrate stability window is 268.2–270.2 K at 1 atm. Methane sI, as well as natural gas sII, hydrates exhibit only minimal decomposition upon reducing confining system pressure to 1 atm in the 268.2–270.2 K stability window. Total gas that evolved after 24 h at 1 atm in the stability window typically amounted to less than 0.5% of originally stored gas, and this ultra-stability was shown to persist when the test was allowed to run 256 h before terminating. The entire methane sI or natural gas sII hydrate mass remains stable during pressure reduction to 1 atm, whereas previous reports defined hydrate anomalous stability for only about 50% of fractional hydrate remnants.

**Keywords:**Energy; Nucleation; Particle formation; Surfactant; Hydrates; Gases;

X-ray computed tomography of a gas-sparged stirred-tank reactor by Jason J. Ford; Theodore J. Heindel; Terrence C. Jensen; Joshua B. Drake

*(2075-2085)*. X-ray computed tomography (CT) is used to explore the differences in gas dispersion in a stirred-tank reactor (STR) for different operating conditions by varying the impeller speed and gas flow rate. X-ray imaging has been carried out in a 0.21 m ID acrylic STR equipped with a nylon Rushton-type impeller. From the CT images, major differences in local gas holdup are observed for different operating conditions. Completely dispersed conditions have a relatively uniform holdup profile while flooded conditions show a high gas holdup near the impeller shaft. The high resolution of the X-ray system allowed fine details such as recirculation regions behind the baffles to be visualized.

**Keywords:**Hydrodynamics; Multiphase flow; Stirred-tank reactor; Tomography; Visualization; Voidage;

Sensitivity analysis of adsorption bed behavior: Examination of pulse inputs and layered-bed optimization by T. Grant Glover; M. Douglas LeVan

*(2086-2098)*. A mathematical model is developed to examine the sensitivity of the breakthrough of adsorption beds to system parameters. As the process model is integrated a single time, sensitivities are simultaneously calculated. The impact of mass and energy transfer effects and adsorbent layer thicknesses are determined by calculating the derivatives of the outlet concentration and outlet temperature. Several examples are considered. To establish a basis, the breakthrough of single beds is considered first. The adsorption of hexane on BPL activated carbon is contrasted with the adsorption of nitrogen on carbon molecular sieve, and combined mass and energy effects are considered by studying the adsorption of nitrogen on BPL activated carbon. The sensitivity data are then applied to determine the optimum bed layering of a two-layer, two-bed PSA system. The solution method presented can be adapted for the sensitivity analysis and subsequent optimization of a large number of adsorption systems.

**Keywords:**Adsorption; Mass transfer; Optimization; Mathematical modeling; Sensitivities; Pulse; Layered bed;

Unsteady motion of a single bubble in highly viscous liquid and empirical correlation of drag coefficient by Li Zhang; Chao Yang; Zai-Sha Mao

*(2099-2106)*. The unsteady motion of single bubbles rising freely in a quiescent liquid with high viscosity was measured using a CCD (charge coupled device) camera. Sequences of the recorded frames were digitized and analyzed using image analysis software and the measurements of the acceleration and steady motion of bubbles were obtained. The total drag coefficient was calculated from the accelerating motion to the steady motion with the added mass force and history force included. In virtue of dimensional analysis, the total drag coefficient of single bubbles is correlated as a function of the acceleration number, Archimedes number and Reynolds number based on the equivalent bubble diameter. The proposed correlation represents very well the experimental data of the total drag force in a wide range covering both unsteady accelerating motion and steady motion. The combined added mass and history force coefficient accounting for the accelerating effect on single bubbles was evaluated and correlated.

**Keywords:**Bubble; Drag coefficient; Multiphase flow; Added mass force; History force; Correlation;

Gas–liquid flow and bubble size distribution in stirred tanks by G. Montante; D. Horn; A. Paglianti

*(2107-2118)*. This work is aimed at investigating the turbulent two-phase flow and the bubble size distribution (BSD) in aerated stirred tanks by experiments and computational fluid dynamics (CFD) modelling. The experimental data were collected using a two-phase particle image velocimetry technique and a digital image processing method based on a threshold criterion. With the former technique, the liquid and the gas phase ensemble-averaged mean and r.m.s. velocities are measured simultaneously, while with the latter the dimensions of the bubbles dispersed inside the liquid are evaluated. On the modelling side, a CFD approach, based on the solution of Reynolds average Navier–Stokes equations in an Eulerian framework for both phases, is adopted. As for the bubble dimensions modelling, besides the mono-dispersed assumption, a population balance method, named MUSIG, with bubble break-up and coalescence models is considered. The BSD and the axial and radial velocity of the gas and the liquid phase are presented and discussed. The outcomes of the computational work are evaluated on the basis of the experimental results.

**Keywords:**Gas–liquid stirred tank; Two-phase PIV; Bubble size distribution; CFD;

Towards further internal heat integration in design of reactive distillation columns—Part III: Application to a MTBE reactive distillation column by Kejin Huang; San-Jang Wang; Wenming Ding

*(2119-2134)*. According to the principle introduced in the first two papers of this series, seeking further internal heat integration between reaction operation and separation operation during the synthesis, design, and operation of a reactive distillation column synthesizing methyl tertiary butyl ether (MTBE) from methanol and isobutylene is investigated. Although the MTBE reactive distillation column is characterized by complicated thermodynamic properties and multiple steady states, a substantial reduction of energy requirement and capital investment can still be achieved with the consideration of further internal heat integration between the reaction operation and the separation operation in the two existing steady states. Dynamics and operation of the resultant process designs are then examined in terms of static and dynamic analysis and sharp improvement in process dynamics and controllability is clearly identified through intensive comparison against the simple process design without the consideration of further internal heat integration between the reaction operation and the separation operation involved. It is demonstrated that the more synergistic relationship evolved during the reinforcement of internal heat integration should account for the dramatic improvement in process dynamics and controllability.

**Keywords:**Distillation; Internal heat integration; Process synthesis; Process design; Process dynamics; Process control;

Computation of turbulence and dispersion of cork in the NETL riser by Veeraya Jiradilok; Dimitri Gidaspow; Ronald W. Breault; Lawrence J. Shadle; Chris Guenther; Shaoping Shi

*(2135-2148)*. The knowledge of dispersion coefficients is essential for reliable design of gasifiers. However, a literature review had shown that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. This study presents a comparison of the computed axial solids dispersion coefficients for cork particles to the NETL riser cork data. The turbulence properties, the Reynolds stresses, the granular temperature spectra and the radial and axial gas and solids dispersion coefficients are computed.The standard kinetic theory model described in Gidaspow's 1994 book, Multiphase Flow and Fluidization, Academic Press and the IIT and Fluent codes were used to compute the measured axial solids volume fraction profiles for flow of cork particles in the NETL riser. The Johnson–Jackson boundary conditions were used. Standard drag correlations were used. This study shows that the computed solids volume fractions for the low flux flow are within the experimental error of those measured, using a two-dimensional model. At higher solids fluxes the simulated solids volume fractions are close to the experimental measurements, but deviate significantly at the top of the riser. This disagreement is due to use of simplified geometry in the two-dimensional simulation. There is a good agreement between the experiment and the three-dimensional simulation for a high flux condition.This study concludes that the axial and radial gas and solids dispersion coefficients in risers operating in the turbulent flow regime can be computed using a multiphase computational fluid dynamics model.

**Keywords:**Gas-particle flow; Fluidization; Computational fluid dynamics; Reynolds stress;

Modelling and simulation of hydrogen permeation through supported Pd-alloy membranes with a multicomponent approach by Alessio Caravella; Giuseppe Barbieri; Enrico Drioli

*(2149-2160)*. Hydrogen transport in Pd-based supported membranes was described by means of a model considering several elementary steps of the permeation process, improving what done by Ward and Dao [1999. Model of hydrogen permeation behavior in palladium membranes. Journal of Membrane Science 153 (2), 211–231] for self-supported membranes. The model includes the external mass transfer in the multicomponent gaseous phases on both sides of the membrane, described by the Stefan–Maxwell equations. The transport of the multicomponent mixture in the multilayered porous support was also considered and described by means of the dusty gas model, which takes into account Knudsen, Poiseuille and ordinary diffusion. The diffusion in the Pd-alloy layer is modeled by the irreversible thermodynamics theory, taking the hydrogen chemical potential as the driving force of the diffusion in the metallic bulk. The interfacial phenomena (adsorption, desorption, transition from Pd-based surface to Pd-based bulk and vice-versa) were described by the same expressions used by Ward and Dao (1999). Thicknesses of 1 and 10 μ m are considered for the Pd-alloy layer. The asymmetric support consists of five layers, each one characterized by a specific thickness and mean pore diameter. The model separates the permeation steps and consequently their influence, quantifying the relative resistances offered by each of them. Comparison with some experimental data in several conditions in the literature shows a good agreement. The developed tool is able to describe hydrogen transport through a supported Pd-based membrane, recognizing the rate-determining steps (e.g., diffusion in the metallic bulk or in the porous support) involved in the permeation.

**Keywords:**Hydrogen permeation; Pd-based supported membranes;

Response of slot coating flows to periodic disturbances by O.J. Romero; M.S. Carvalho

*(2161-2173)*. Slot coating is a common method in the manufacture of a wide variety of products. It belongs to a class of coating method known as

*premetered coating*: in a steady-state operation, the thickness of the coated liquid layer is set by the flow rate fed to the die and the speed of the substrate moving past, and is independent of other process variables. Thus premetered methods are ideal for high precision coating. However, even the best designed slot coating operations are subjected to small oscillations on the process conditions, such as flow rate, vacuum pressure and gap fluctuations. These oscillation may lead to unacceptable variation on the thickness of the deposited liquid layer. The effect of process condition disturbances on the coated layer has to be minimized to assure a wet thickness as uniform as possible.The effect of an imposed periodic perturbation on the liquid flow rate or on the gap clearance in the coated layer thickness is explored in this work by computer-aided analysis. The amplitude of the thickness variation is determined at different process conditions and die configurations by solving the transient, two-dimensional, viscous free surface liquid flow in the coating bead. The system of equations, with appropriate boundary conditions, was solved by the Galerkin/finite element method, and an implicit time integration. The results show the response as a function of the imposed perturbation frequency and of the die geometry. They indicate that the die geometry may be optimized in order to minimize the film thickness oscillation of a slot coating operation.**Keywords:**Slot coating; Periodic disturbances; Galerkin/finite element method; Transient response; Free surface flow;

Some curious observations of soap film contact lines by Peter M. Ireland

*(2174-2187)*. Contact lines between soap films and solid surfaces have been studied comparatively little. This is surprising, as a network of these contact lines constitutes the contact between an aqueous foam and an imperfectly wetted surface, and is critical for understanding foam slip on this type of surface. Data on the tension at a ‘creeping’ soap film contact line are presented. Surprisingly, given that viscous interactions were shown to be unimportant at these low velocities, this was substantially less than the sum of the ‘creeping’ tension for one wetting and one de-wetting contact line on the same surfaces. A possible explanation for this observation is presented, involving a free energy analysis of the deformed lamellae.

**Keywords:**Wetting; Foam; Dynamic contact angle; Contact angle hysteresis; Surface tension;

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models by Anders Darelius; Anders Rasmuson; Berend van Wachem; Ingela Niklasson Björn; Staffan Folestad

*(2188-2197)*. In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian–Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366–2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas–solid particle flow in a 90 ∘ bend. A.I.Ch.E. Journal, 41, 2187–2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian–Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well.

**Keywords:**Fluid mechanics; Kinetic theory of granular flow; Frictional stress models; Powder technology; Granulation; Multiphase flow;

A new discretization of space for the solution of multi-dimensional population balance equations by Mahendra N. Nandanwar; Sanjeev Kumar

*(2198-2210)*. In this work, a novel radial grid is combined with the framework of minimal internal consistency of discretized equations of Chakraborty and Kumar [2007. A new framework for solution of multidimensional population balance equations. Chemical Engineering Science 62, 4112–4125] to solve

*n*-dimensional population balance equations (PBEs) with preservation of ( n + 1 ) instead of 2 n properties required in direct extension of the 1-d fixed pivot technique of Kumar and Ramkrishna [1996a. On the solutions of population balance equation by discretization-I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332]. The radial grids for the solution of 2-d PBEs are obtained by intersecting arbitrarily spaced radial lines with arcs of arbitrarily increasing radii. The quadrilaterals obtained thus are divided into triangles to represent a non-pivot particle in 2-d space through three surrounding pivots by preserving three properties, the number and the two masses of the species that constitute the newly formed particle. Such a grid combines the ease of generating and handling a structured grid with the effectiveness of the framework of minimal internal consistency. A new quantitative measure to supplement visual comparison of two solutions is also introduced. The comparison of numerical and analytical solutions of 2-d PBEs for a number of uniform and selectively refined radial grids shows that the quality of solution obtained with radial grids is substantially better than that obtained with the direct extension of the 1-d fixed pivot technique to higher dimensions for both size independent and size dependent aggregation kernels. The framework of Chakraborty and Kumar combined with the proposed 2-d radial grid, which offers flexibility and achieves both reduced numerical dispersion and the ease of implementation, appears as an effective extension of the widely used 1-d fixed pivot technique to solve 2-d PBEs.**Keywords:**Population balance modelling; Discretization methods; Multi-dimensional population balance equations; Modelling and simulation;

Oxygen sorption and desorption properties of Sr–Co–Fe oxide by Qinghua Yin; Jay Kniep; Y.S. Lin

*(2211-2218)*. SrCoFeO x has been investigated as a new sorbent for air separation and oxygen removal at high temperatures. X-ray diffraction analysis of a SrCoFeO x sample prepared by liquid citrate method reveals that the sample contains an intergrowth ( Sr 4 Fe 6 - x Co x O 13 ± δ ) , perovskite ( SrFe 1 - x Co x O 3 - δ ) , and spinel ( Co 3 - x Fe x O 4 ) phase. Both oxygen vacancies ( V O ¨ ) and interstitial oxygen ions ( O i ″ ) are involved in the oxygen adsorption and desorption process for SrCoFeO x . Compared with the perovskite-type oxide La 0.1 Sr 0.9 Co 0.9 Fe 0.1 O 3 - δ , SrCoFeO x has stronger structure stability in a reducing environment and it also exhibits a larger oxygen sorption capacity at temperatures higher than 800 ∘ C . Meanwhile, unlike La 0.1 Sr 0.9 Co 0.9 Fe 0.1 O 3 - δ which shows a fast adsorption rate and a slow desorption rate at 900 ∘ C , SrCoFeO x shows a fast desorption rate and slow adsorption rate at the same temperature. X-ray diffraction data reveals that SrCoFeO x samples sintered at 1140 ∘ C have a higher amount of the intergrowth phase than samples sintered at 950 ∘ C due to slow formation kinetics. X-ray diffraction and thermogravimetric analysis of SrCoFeO x samples prepared by the citrate and solid state method show that the synthesis method strongly influences the amount of the three phases in a sample.

**Keywords:**Air separation; Mixed-conducting oxides; Defect chemistry; Adsorption;

Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles by Anthony G. Dixon; M. Ertan Taskin; Michiel Nijemeisland; E. Hugh Stitt

*(2219-2224)*. Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tube-to-particle diameter ratio ( N ) equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185–5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order:

*solid cylinders*>*one-hole particles*>*multi-hole particles*. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study.**Keywords:**Computational fluid dynamics; Catalyst design; Heat transfer; Packed bed; Chemical reactors; Reaction engineering;

Thin film flow over spinning discs: The effect of surface topography and flow rate modulation by O.K. Matar; G.M. Sisoev; C.J. Lawrence

*(2225-2232)*. We examine the effect of disc topography and time modulation of the liquid flow rate at the inlet on the dynamics of a thin film flowing over a spinning disc. We use a combination of boundary-layer theory and the Kármán–Polhausen approximation to derive coupled equations for the film thickness, and radial and azimuthal flow rates. Substrate patterning is taken into account in the limit of small-amplitude topography. Our numerical results indicate that the combined effects of flow rate modulation at the inlet and disc patterning can lead to a significant increase in interfacial waviness, which greatly exceeds that associated with the constant flow rate, smooth disc case.

**Keywords:**Spinning disc; Fluid mechanics; Interfaces; Process intensification; Mass transfer; Topography; Waves; Hydrodynamics;

A Laplace transformation based technique for reconstructing crystal size distributions regarding size independent growth by Shamsul Qamar; Gerald Warnecke; Martin Peter Elsner; Andreas Seidel-Morgenstern

*(2233-2240)*. This article introduces a technique for reconstructing crystal size distributions (CSDs) described by well-established batch crystallization models. The method requires the knowledge of the initial CSD which can also be used to calculate the initial moments and initial liquid mass. The solution of the reduced four-moment system of ordinary differential equations (ODEs) coupled with an algebraic equation for the mass gives us moments and mass at the discrete points of the given computational time domain. This information can be used to get the discrete values of size independent growth and nucleation rates. The discrete values of growth and nucleation rates along with the initial distribution are sufficient to reconstruct the final CSD. In the derivation of current technique the Laplace transformation of the population balance equation (PBE) plays an important role. The proposed technique has dual purposes. Firstly, it can be used as a numerical technique to solve the given population balance model (PBM) for batch crystallization. Secondly, it can be used to reconstruct the final CSD from the initial one and also vice versa. The method is very efficient, accurate and easy to implement. Several numerical test problems of batch crystallization processes are considered here. For validation, the results of the proposed technique are compared with those from the high resolution finite volume scheme which solves the given PBM directly.

**Keywords:**Population balance models; Crystallization processes; Laplace transformation; Model reduction; Mathematical modeling; Reconstruction technique;

High-performance protein separation by ion exchange membrane partitioned free-flow isoelectric focusing system by Jiuhua Cheng; Yi Li; Tai Shung Chung; Shing-Bor Chen; William B. Krantz

*(2241-2251)*. The objective of this study is to investigate a combination of ion exchange membranes and free-flow isoelectric focusing (FFIEF) technology for high-selectivity and high-flux protein separation, in which ion exchange membranes are used as the separation media. An FFIEF device has been designed and extensive experiments have been conducted to prove its effectiveness in enhancing the protein separation performance. Three types of membranes were employed in this work and they were commercial microfiltration (MF) ion exchange membranes, commercial neutral UF cellulose membranes, and home-made ultrafiltration sulfonated polysulfone (UF SPSf) ion exchange membranes. The protein separation results show that the home-made UF SPSf membranes have the superior selectivity and flux to other membranes. This is due to the fact that a stable pH gradient across the membranes as well as the interaction between the protein molecules and membrane surface plays an important role in the high-performance protein separation. By applying a semi-batch separation process and optimizing various experimental conditions, a high-purity ( > 90 % ) and concentrated target protein is obtained at the permeation side of the home-made UF SPSf membranes with a high flux.

**Keywords:**Membrane; Separation; Electrophoresis; Polymers; Protein mixture; IEM-FFIEF (ion exchange membrane partitioned free-flow isoelectric focusing);

Nonlinear multiscale modelling for fault detection and identification by Sang Wook Choi; Julian Morris; In-Beum Lee

*(2252-2266)*. In order to detect abnormal events at different scales, a number of multiscale multivariate statistical process control (MSPC) approaches which combine a multivariate linear projection model with multiresolution analysis have been suggested. In this paper, a new nonlinear multiscale-MSPC method is proposed to address multivariate process performance monitoring and in particular fault diagnostics in nonlinear processes. A kernel principal component analysis (KPCA) model, which not only captures nonlinear relationships between variables but also reduces the dimensionality of the data, is built with the reconstructed data obtained by performing wavelet transform and inverse wavelet transform sequentially on measured data. A guideline is given for both off-line and on-line implementations of the approach. Two monitoring statistics used in multiscale KPCA-based process monitoring are used for fault detection. Furthermore, variable contributions to monitoring statistics are also derived by calculating the derivative of the monitoring statistics with respect to the variables. An intensive simulation study on a continuous stirred tank reactor process and a comparison of the proposed approach with several existing methods in terms of false alarm rate, missed alarm rate and detection delay, demonstrate that the proposed method for detecting and identifying faults outperforms current approaches.

**Keywords:**Multiresolution analysis; Kernel principal component analysis; Fault detection and diagnosis; Multivariate statistical process control; Multiscale kernel principal component analysis;

CFD simulation of bubble columns incorporating population balance modeling by M.R. Bhole; J.B. Joshi; D. Ramkrishna

*(2267-2282)*. A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a k – ε model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485–1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201–9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas–liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071–5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359–6365] also show a good agreement for liquid velocity and gas hold-up profiles.

**Keywords:**Bubble column; CFD; Population balance model; Coalescence; Break-up;

Shortstopping and jet mixers in preventing runaway reactions by D. Dakshinamoorthy; J.F. Louvar

*(2283-2293)*. Runaway reactions are continuing to be a major problem in the chemical industry (26% of major accidents). One of the main reasons for runaways is power failure. Runaway reactions could be inhibited in two ways: by the addition of cold diluents and by the addition of an inhibitor (chemical reaction stopper). This technology is called shortstopping. After a power failure, the process of adding an inhibiting agent and mixing it with the reactor contents becomes a major problem in the shortstopping process. Jets or impellers, driven by a small generator, however, can be used for mixing the inhibitor with the reactor contents.Dakshinamoorthy et al. [2006. CFD simulations of shortstopping runaway reactions in vessels agitated with impellers and jets. Journal of Loss Prevention in the Process Industries 19, 570–581] compared the efficiency of using jet mixers versus impeller stirred vessels in shortstopping runaway reactions. On the basis of equal power consumption, this comparative study showed that jet mixers are ineffective when used for shortstopping. One needs to identify additional factors, to effectively shortstop when using jet mixers.Due to the hazardous nature of runaway reactions, these factors cannot be determined with lab scale or pilot plant scale experiments. Recent developments with CFD make it possible to carry out virtual experiments. The computational model is solved using FLUENT. Shortstopping studies via the addition of a reaction inhibitor and cold diluent are discussed in detail. The results reported in this study identify the major and minor factors, which contribute to effective shortstopping; i.e., power requirements, locations for adding the inhibitor, the quantity of inhibitor added, rate of the inhibition, the use of cold diluent and the use of multiple nozzles. These results especially demonstrate the value of using CFD simulations in situations that are experimentally prohibitive.

**Keywords:**Mixing; Safety; Reaction engineering; CFD Simulation; Runaway; Shortstopping;

Length scale dependence of effective inter-phase slip velocity and heterogeneity in gas–solid suspensions by Junwu Wang

*(2294-2298)*. High-resolution Eulerian simulations are carried out to explore the problem of length scale dependence or filter size dependence in heterogeneous gas–solid two-phase flows. It was found that, with the extension of the simulated domain, the average inter-phase slip velocity or inter-phase drag coefficient and the index of heterogeneity increased initially and then approached asymptotic values, which demonstrates the existence of a scale-independent or filter-size-independent plateau for these properties.

**Keywords:**Hydrodynamics; Fluidization; Multiphase flows; Sub-grid scale model; Scale separation; Powder technology;

Stochastic population balance modeling of influenza virus replication in vaccine production processes. II. Detailed description of the replication mechanism by Y. Sidorenko; A. Voigt; J. Schulze-Horsel; U. Reichl; A. Kienle

*(2299-2304)*. In a recent paper a segregated stochastic model was proposed for influenza virus replication in vaccine production processes [Sidorenko, Y., Schulze-Horsel, J., Voigt, A., Reichl, U., Kienle, A., 2008. Stochastic population balance modeling of influenza virus replication in vaccine production processes. Chemical Engineering Science 63, 157–169]. The model used a simple segregated, unstructured approach for the description of the virus replication. In particular, effects arising from limited internal cellular resources and detailed cell physiology were not taken into account. The degree of infection—corresponding to the number of virus equivalents per cell—was used as the only internal coordinate. The model was successful in describing the integral dynamics of the process, however, revealed some discrepancies with respect to the “internal dynamics” of the virus replication. Therefore, in a second step, a much more detailed description of the virus replication process is considered in this paper. Again, cell physiology is described in terms of global growth and death events. Limitations of the intracellular resources are not taken into account. It is shown that this type of model does not contribute significantly to an improvement of the prediction of the internal dynamics. Hence, it is concluded that limited intracellular resources or a detailed description of the cell physiology is required for a more realistic modeling of virus replication dynamics.

**Keywords:**Population balance; Mathematical modeling; Dynamic simulation; Bioreactors; Influenza virus; Vaccine production;

Corrigendum to “A dynamic object-oriented model for efficient simulation of fluid dispersion in turbulent flow with varying fluid properties” by Tomas Skoglund; Petr Dejmek

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