On a mathematical model for loop reactors—II. Estimation of parameters

Based on a model of loop reactors with sections of different mixing behaviour and on an approximation formula for its residence time distribution, a procedure is derived to determine the main model parameters, the mean circulation time, the circulation variance and the corresponding values of the individual sections. Finally the results of application of this procedure to RTD-measurements in a laboratory liquid jet loop reactor are presented.     

Jet pulsed filters as chemical gas/solid reactors—Experiment and model prediction

A recently introduced generations filter model [A. Kavouras, G. Krammer, Distributions of age, thickness and gas velocity in the cake of jet pulsed filters—application and validation of a generations filter model, Chem. Eng. Sci. 58 (2003) 223–238] allows one to determine from macroscopic experimental data the distribution of cake thickness versus filter area and in consequence the complete filter behaviour. Based on a simplified assumption this generations filter model is employed in a predictive way to estimate operating points of imperfectly cleaned filters. However, filter behaviour in terms of the fraction of the filter area cleaned when jet pulsed cannot be predicted yet without experimental data. This is due to the variable cleaning properties of the cake, which are dependent on the filter operating parameters.

Combining the predictive filter model and a model for the chemical reactions in the fixed bed of the filter cake [A. Kavouras, B. Breitschaedel, G. Krammer, A. Garea, J.A. Marques, A. Irabien, SO₂ removal in the filter cake of a jet pulsed filter: a combined filter and fixed bed reaction model, Ind. Eng. Chem. Res. 41 (2002) 5459–5469], the filter performance as a gas/solid reactor can also be simulated in a predictive way. It is found that the pressure drop across the filter has a weak influence on filter performance as a gas/solid reactor.     

Fluidization behavior in a circulating slugging fluidized bed reactor. Part I: Residence time and residence time distribution of polyethylene solids

Square nosed slugging fluidization behavior in a circulating fluidized bed riser using a polyethylene powder with a very wide particle size distribution was studied. In square nosed slugging fluidization the extent of mixing of particles of different size depends on the riser diameter, gas velocity, hold up and solids flux in the riser. Depending on the operating conditions the particle residence time distribution of a riser in the slugging fluidization regime can vary from that of a plug flow reactor to that of a well-mixed system.Higher gas velocities cause shorter particle residence times because of a significant decrease in the hold-up of particles in the riser at higher gas velocities. A higher solids flux also shortens the average residence time. Both influences have been quantified for a given polyethylene-air system.Residence time and residence time distribution were determined for different particle size and the influence of gas velocity, solids flux, hold up and riser diameter was studied. When comparing data from segregation and residence time experiments it is clear that segregation data can predict the spread in residence time as a function of overall residence time, particle size and gas velocity. The differential velocity between small and large particles found in the segregation experiments can predict the spread in residence time as found in the residence time distribution experiments with a powder with a broad particle size distribution. Raining of particles through the slugs was studied as a function of plug length, gas velocity and pulse length. It was found that raining is not the determining mechanism for segregation of particles.     

Residence time distribution in a single‐phase rotor–stator spinning disk reactor

A reactor model for the single‐phase rotor–stator spinning disk reactor based on residence time distribution measurements is described. For the experimental validation of the model, the axial clearance between the rotor and both stators is varied from 1.0 × 10^?3 to 3.0 × 10^?3 m, the rotational disk speed is varied from 50 to 2000 RPM, and the volumetric flow rate is varied from 7.5 × 10^?6 to 22.5 × 10^?6 m³ s^?1. Tracer injection experiments show that the residence time distribution can be described by a plug flow model in combination with 2–3 ideally stirred tanks‐in‐series. The resulting reactor model is explained with the effect of turbulence, the formation of Von Kármán and Bödewadt boundary layers, and the effect of the volumetric flow rate. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2686–2693, 2013     

Residence time distribution and oxygen transfer in a novel constructed soil filter

BACKGROUND: The constructed soil filter (CSF), also known as soil biotechnology is a system for water renovation, which makes use of formulated media, culture of soil micro‐ and macro‐organisms, additives and plantation to purify water and wastewater. The process gives benefits in terms of applicability across very small to large scale, natural aeration, absence of moving parts, no biological sludge generation, odor free green aesthetic ambience. RESULTS: Residence time distribution (RTD) studies were carried out using laboratory scale CSF. Pulse potassium bromide tracer tests were carried out to determine RTD, and the Peclet number found to be 9–13 for a 2 m bed, and 2–3 for a 0.30 m bed with oxygen transfer of 0.08 h^?1. CONCLUSION: The two‐channel dispersion model for flow behavior shows a good fit to the experimental data, indicating a reactor Peclet number 9–13 for a 2 m bed and 2–3 for a 0.3m bed. Oxygen transfer studies carried out using various methods gave an oxygen transfer coefficient of about 0.08 h^?1. Wastewater purification studies indicate overall COD removal rate of around 50 mg L^?1 h^?1, suggesting that highly aerobic conditions are prevalent in the CSF system. Copyright © 2009 Society of Chemical Industry     

Residence time distribution of solid particles in a continuous, high-aspect-ratio multiple-impeller stirred vessel

In this paper experimental information on the retention time distribution (RTD) of solid particles in a high-aspect-ratio vessel, stirred by three equally spaced Rushton turbines, is presented. The relevant data were obtained by a special technique named twin system approach (TSA) that greatly simplifies the handling of particle-laden streams and is therefore particularly suited for investigating particle RTD in flow systems. The technique fundamentals are first summarized, together with the data analysis procedure. This lastly requires a numerical deconvolution operation that is easily performed with the help of Z-transforms. Two different approaches for excluding the spurious contributions of the external piping required for the experimentation are tested and discussed.Particle tracing was performed by an effective particle-coating/optical-detection technique that allows particles recovery and reuse after each experimental run.The RTD data obtained indicate that a cascade of ideally mixed tanks with backflow results into very good agreement with experiment, with practically any number of tanks in series but one, provided that the backflow rate parameter is chosen accordingly. In all cases, the recirculation is large enough for the resulting flow model to be quite close to a single perfectly stirred vessel.     

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.     

Residence time distribution and dispersion of gas phase in a wet gas scrubbing system

Residence time distribution (RTD) of exhaust gas in a wet scrubbing system was investigated for application to the removal of SO _x , NO _x or dust included in exhaust gas. The mixing of gas phase in the wet scrubbing system was also examined by considering the axial dispersion coefficient of gas phase. Effects of gas amount (velocity), liquid amount (velocity) and solid floating materials on the residence time distribution (RTD) and axial dispersion coefficient of exhaust gas were discussed. The addition of solid floating materials could change the RTD and thus dispersion of exhaust gas in the scrubbing system. The mean residence time and axial dispersion coefficient of exhaust gas were well correlated in terms of operating variables.     

A mathematical model for pyrolysis of a solid particle — effects of the heat of reaction

A transient analysis of the effects of the heat of reaction in a solid pyrolysis system is presented. Two cases, one characterizing the heat-transfer-controlled reaction and the other self-sustaining reaction, are analyzed. To carry out the numerical simulation, utilization is made of the volume reaction model which takes into account the simultaneous heat and mass transfer phenomena, and the method of line which utilizes the second order centered finite difference scheme for the spatial discretization. Effects of the heat of reaction on the solid conversion, solid reactant, and fluid product concentration profiles, temperature distribution, enthalpy, and average fluid product concentration in the particle are examined. The results are graphically presented and interpreted.     

Residence time distribution and hold-up in a cocurrent upflow packed bed reactor at elevated pressure

The residence time distribution in liquid phase was measured in a cocurrent upflow packed bed reactor for the system methanol-hydrogen at low Reynolds numbers and at elevated pressure. The plug flow with axial dispersion model was used to describe mixing in the system. The imperfect pulse method was used to measure the system response to a tracer pulse input. The parameters were calculated using the weighted moments method. The influence of the weighting factor was investigated. The experimental and theoretical outputs, as calculated by convolution, agreed very well. Different types of correlations were used for the Bodenstein number and liquid hold-up. From these correlations, the optimal one was selected for each parameter. A comparison was made between the ordinary moments and the weighted moments methods which led to the conclusion that the latter method is superior with respect to the accuracy of the estimated parameters and therefore strongly recommended.     

Mixing of viscoelastic fluids with helical-ribbon agitators. I — Mixing time and flow patterns

Batch mixing of viscous fluids with helical-ribbon agitators in 2.4 liter and 13 liter vessels has been studied for agitator speeds up to 200 RPM. Seven different agitators of different dimensions were employed in this work. Mixing times were measured using a decoloration technique and circulation times were determined by the tracer bead method. In addition, velocity profiles were obtained from streak photographs using selective illumination of the vessel and PVC powder as tracer particles. It was found that the mixing times of Newtonian fluids, which agreed with previously published data, were considerably (3 to 7 times) shorter than those of the viscoelastic fluids. The mixing time was strongly affected by the fluids' elasticity; increasing as the fluid elasticity increased. The velocity profiles were qualitatively similar for all the fluids but showed decreased axial circulation and increased circumferential flow as fluid elasticity increased. However, mixing is not only a function of the axial circulation (impeller pumping rate) but also is a function of the perturbations superimposed on the main flow. A simple, first approximation model based on the impeller geometry and flow patterns is proposed to correlate the circulation capacity and mixing time data for the various geometries studied.     

Filling of a complex-shaped mold with a viscoelastic polymer. Part I: The mathematical model

A model for the filling stage of injection molding of viscoelastic thermoplastics in cavities of complex shape is presented. The model considers two-dimensional melt flow, with converging and diverging flow patterns induced by complex boundary shape and by the presence of an obstacle. The model is non-isothermal (with the melt loosing heat to the mold walls as it travels into the cavity) and handles a viscoelastic (following the White-Metzner model) material with properties that vary with temperature, shear rate, and pressure. The numerical method is based on finite differences, with boundary fitted curvilinear coordinates used in the mapping of the flow field (which has an arbitrary shape that evolves with time) into a time invariant rectangle. The numerical results reveal geometry-induced asymmetries in the flow and thermal fields as well as the effect of various process parameters on the pressure and temperature profiles in the cavity. The model admits variable cavity thickness, thus allowing for a treatment of the cavity thickness as a process parameter in the simulations.     

A model for resin flow during composite processing: Part 1—general mathematical development

A generalized three-dimensional model for resin flow during composite processing has been developed. The model is based on a theory of consolidation and flow through a porous medium, which considers that the total force acting on a porous medium is countered by the sum of the opposing forces, including the force due to the spring-like effect of the fiber network and the hydrostatic force due to the pressure of the liquid within the porous medium. The flow in the laminate is described in terms of Darcy's Law for flow in a porous medium, which requires a knowledge of the fiber network permeability and the viscosity of the flowing fluid. Unlike previous resin flow models, this model properly considers the flows in different directions to be coupled and provides a unified approach in arriving at the solution. Comparison of numerical solutions with the closed form analytical solution shows good agreement. Resin pressure profiles show that the pressure gradients in the vertical and horizontal directions are not linear, unlike the assumption of linearity made in several previous resin flow models. The effects on the resin pressure of both linear and nonlinear stress-strain behavior of the porous fiber network were considered. The nonlinear behavior simulates a rapidly stiffening spring and the resin pressure decreases much more rapidly after a given initial period compared to the linear stress-strain behavior.     

Measurement of smoke in fires—a review. I —characteristics of smoke

The Complexity of the behavior of smoke at fires can lead to great difficulties in obtaining measurements from instruments which are both reliable and correlatable with human observations. The first article in this two-part review considers the principal characteristics of smoke, the factors which influence its behaviour at fires, the basic theory of light transmission through smoke, and the behaviour of the eye in smoky conditions. This information will be used in the second article to assess the performance and limitations of various types of smoke measuring instruments.     

Towards a quasilinear process simulator—I. fundamental ideas

Process simulation in the steady state is approached by setting up a global set of nonlinear algebraic equations to represent the plant. These equations are solved by a quasi-linear method, whereby a series of linearised systems are solved whose limiting solution is identical to that of the original set of nonlinear equations. With proper care in the formulation of the linearised approximations, second-order convergence can be achieved in a region sufficiently close to the solution. The Newton-Raphson method falls into this category. However, in general, precautions have to be taken in order to get within the convergent region. Precautions necessary to assure satisfactory solution of the equations are described, but the possibility of multiple solutions is not excluded.