Computational modelling of industrial pulp stock chests

Agitated pulp stock chests are the most widely used mixers in pulp and paper manufacture. Stock chests are used for a number of purposes, including attenuation of high‐frequency disturbances in pulp properties (such as mixture composition, fibre mass concentration, and suspension freeness) and are designed using semi‐empirical rules based largely on previous experience. Tests made on both laboratory and industrial‐scale pulp chests indicate that they are subject to non‐ideal flows, including channelling and creation of dead zones. In the present work, a commercial computational fluid dynamic (CFD) software (Fluent) is used to model two industrial pulp stock chests. The first chest is rectangular, agitated using a single side‐entering impeller, and feeds a mixture of chemical pulps at 3.5% mass concentration (C_m) to a papermachine. The second chest has rectangular geometry, with a mid‐feather wall used to direct suspension flow through a U‐shaped trajectory past four side‐entering impellers. This chest is used to remove latency from a C_m = 3.5% thermomechanical pulp suspension ahead of stock screening. For CFD computations, pulp rheology was described using a modified Hershel–Buckley model. Steady‐state simulations were made corresponding to process conditions during mill tests. The calculated steady‐state flows were then used to determine the dynamic response of the virtual chests and then compared with experimental measurements and found to agree reasonably well. The computed flow fields provided insight into mixing processes occurring within the chests, showing cavern formation around the impellers (which reduced the agitated volume available for mixing). Mass‐less particle tracking, using the steady‐state flow field, gave insight into the stagnant regions and bypassing zones created in the vessels. This paper discusses difficulties encountered in characterising the mixing (both experimentally and computationally) and the limitations of the industrial data.     

Effect of time delays in characterizing the continuous mixing of non-Newtonian fluids in stirred-tank reactors

Aqueous xanthan gum solutions are pseudoplastic fluids possessing yield stress. Their continuous mixing is an extremely complicated phenomenon exhibiting non idealities such as channeling, recirculation and dead zones within the stirred-tank reactors. To characterize the continuous mixing of xanthan gum solutions, three dynamic models were utilized: (1) a dynamic model with 2 time delays in discrete time domain, (2) a dynamic model with two time delays in continuous time domain, and (3) a simplified dynamic model with a single time delay in discrete time domain. A hybrid genetic algorithm was employed to estimate the model parameters through the experimental input–output dynamic data. The extents of channeling and fully mixed volume were used to compare the performances of these three models. The dynamic model parameters exerting strong influence on the response predicted by the dynamic model were identified. It was observed that the models with 2 time delays gave a better match with the experimental results.     

Periodic section modeling of convective continuous powder mixing processes

This study aims to develop a general model of the convective continuous mixing process. The main idea is that continuous mixing can be considered as a combination of powder flow and mixing processes. Although powder flow is characterized by the residence time distribution (RTD), powder mixing can be described by a batch mixing process simulated in one periodic section of the continuous mixer. By characterizing the two processes separately, we can calculate the number of sections required to achieve certain homogeneity. In this study, continuous mixing is simulated using the discrete element method, and segregating and non‐segregating mixing cases are tested to investigate the applicability of the model. Results show satisfactory predictions by the model, which is able to characterize the continuous mixing performance of both mixing cases. On the basis of this study, we were also able to suggest a novel method in design and control of continuous powder mixing systems. © 2011 American Institute of Chemical Engineers AIChE J , 2012     

Continuous versus discrete modelling of heat transfer to agitated beds

Heating of free-flowing particles by contact with the wall of a rotary drum without inserts has been simulated in two dimensions by means of the thermal version of the Discrete Element Method (DEM). The results are in qualitative agreement with existing experimental data and with the classical penetration model (PM) for the following limiting cases: heat transfer controlled by a contact resistance at the wall of the drum; heat transfer to agitated beds with significant bed-side resistance; heat transfer to the stagnant bed. The latter can be used to establish an equivalence (calibration) between the discrete (DEM) and the continuous (PM) modelling approach. Thermal mixing times can be derived from asymptotic overall heat transfer coefficients obtained via thermal DEM for agitated beds. They are found to be significantly smaller than purely mechanical mixing times. For the investigated conditions, they are also much smaller than previous recommendations based on the PM. The ability of thermal DEM to provide information not accessible to the penetration model, like temperature distributions, is discussed. It is pointed out that a decrease of the high computational cost of the method is necessary in order to enhance its applicability.     

Description of interaction processes in agitated liquid-liquid dispersions

Phenomenological models are proposed to describe drop breakup and coalescence in a turbulently agitated liquid-liquid dispersion. Based on these models, breakage and coalescence rate functions are developed and used to solve the general population balance equation describing drop interactions in a continuous flow vessel. Parameters of the models are evaluated by comparison with experimental data on drop size distributions and mixing frequencies obtained in a continuous flow vessel over a range of operating conditions. The favorable agreement between experimental observation and the model are encouraging that the model is suitable for predicting dispersion properties such as drop size distributions, interfacial areas and mixing frequencies.     

Frequency Domain Estimation of Continuous Time Cointegrated Models with Mixed Frequency and Mixed Sample Data

Recent work by the author on mixed frequency data analysis has focused on the estimation of cointegrated systems in continuous time based on a fully specified dynamic system of equations, while the estimation of cointegrating vectors in a discrete time system has been approached using a semiparametric frequency domain estimator. We extend the latter approach to cover the continuous time case, establishing the asymptotic properties of the frequency domain estimator and explore, in a simulation study, the effects of misspecifying the continuous time dynamic model in discrete time compared to treating the dynamics non‐parametrically. An empirical illustration is also provided.     

Residence time distributions in discrete recycle systems with crossmixing

An analysis is given of the moments and residence time distributions of a discrete recycle-crossflow model which can be used to account for departures from perfect mixing in stirred tank reactors. The model, which includes the continuous recycle-crossflow model of Hochman and McCord [2] as a special case, contains the number of stages N as an additional parameter. It is particularly useful in situations in which N is small or is known from prior information. Residence time distribution functions of the discrete recycle-crossflow model are also synthesized from known distribution functions of its components using a network decompositions approach. The problem structure disclosed in the analysis and sysnthesis can greatly facilitate conversion and yield calculations at a later stage. Model verification and parameter estimation are briefly discussed in this paper.     

Modeling of Contact Dryers

Contact drying of stagnant or agitated beds can be reliably described by the penetration model under vacuum or inert conditions. However, the penetration model has disadvantages in the consideration of granular mechanics and statistics due its continuous nature. The fact that such disadvantages can be avoided by discrete approaches is illustrated by application of the discrete element method to the problem of heating of particles in a rotary drum. Important limiting cases are treated, along with conditions for equivalence between continuous and discrete model. Time constants and scaling aspects are addressed and opportunities of combined product and process engineering are pointed out.     

The measurement of mixing efficiency of continuous mixers

A radiotracer method for testing the mixing characteristics of industrial continuous mixers in actual process conditions is described. The tracer is fed into the input of the mixer at a constant rate and the radiation in the output is measured by two properly collimated radiation detectors. The measurement yields data in the form of two time series which contain information about the radial and axial homogeneity of the tracer in the measuring point. The formulas connecting the information in the measurement data and the axial and radial concentration variation of tracer are derived by the methods of statistical mathematics. The values for experimental parameters are obtained by computer simulation of the radiation measurement geometry.The method was tested by measuring the increase of the homogeneity as a function of mixing distance in a static tube chlorine mixer in a pulp bleaching plant. Also some results obtained on another type of mixers showing the effect of pulp type on mixing are given.     

散相液滴在搅拌萃取塔内的停留时间分布

A resident time model is proposed to evaluate the performance of agitated extraction columns. In this model, the resident time of dispersed drops is simulated with the discrete phase modeling, where the continuous phase and the dispersed phase （drops） are described by the single-phase Navier-Stokes （turbulence） model and Lagrangian model, respectively. The interaction of dispersed phase and continuous phase is neglected for the low concentration of drop in the cases studied. The statistical parameters of drops （the average resident time and standard deviation） under different operation conditions are computed for four columns. The relation of the above statistical parameters with the performance of columns is discussed and the criterions for an optimal compartment are outlined. Our results indicate that the resident time model is useful to evaluate the performance and optimize the design of extraction columns.     

Independent block identification in multivariate time series

In this‐30 work we propose a model selection criterion to estimate the points of independence of a random vector, producing a decomposition of the vector distribution function into independent blocks. The method, based on a general estimator of the distribution function, can be applied for discrete or continuous random vectors, and for i.i.d. data or dependent time series. We prove the consistency of the approach under general conditions on the estimator of the distribution function and we show that the consistency holds for i.i.d. data and discrete time series with mixing conditions. We also propose an efficient algorithm to approximate the estimator and show the performance of the method on simulated data. We apply the method in a real dataset to estimate the distribution of the flow over several locations on a river, observed at different time points.     

A New Type of Agitated Liquid/Liquid Extraction Column with Enhanced Coalescence Plates

Abstract

A new type of stator plates for the separation of mixing cells in agitated extractors is presented. These plates consist of thin vertical elements made of materials wetted by the dispersed phase. These elements form a lattice with an extremely high free area (over 90%) which hinders all flows other than the axial one. In this way, mixing cells are effectively separated while at the same time, the phases can flow through the column without flooding. The dispersed phase coalesces on the plate surfaces and occupies part of its free area, so that only the part necessary for the flow of the continuous phase remains free. Very high throughput and good separation efficiency were obtained during the preliminary experiments in a broad range of phase throughputs and ratios. The results were better than those achieved by comparable conventional columns.     

A THREE-DIMENSIONAL MEASUREMENT TECHNIQUE FOR TURBULENT FLOWS

An experimental technique is presented which will help resolve the nature of bulk motions occurring in turbulent flow. The technique is based upon photogrammetric analysis of stereoscopic motion pictures of the flow Held containing small neutrally buoyant tracer particles. The resulting data essentially consist of discrete sets of three-dimensional particle paths which characterize the bulk motions. The data obtained from the particle paths can also provide such information as point velocity measurements, velocity profiles and estimates of fluid accelerations. Furthermore the technique provides this information at a number of locations simultaneously and with time. In this work, the technique has been specifically applied to the study of flow phenomena occurring in an agitated tank.     

Measurement of concentration profiles in a liquid-liquid extraction column

A novel experimental technique for withdrawing uncontaminated samples of each phase from a highly agitated two liquid phase system (primary dispersion) is presented. The technique has been applied in the study of the continuous and dispersed phase axial mixing characteristic of a mechanically agitated liquid Scheibel extraction column operating under different conditions treating the chemical system acetone-toluene-water. The column mixing compartments were separated by a mixed stainless steel-polypropylene knitted mesh packed bed which was completely ‘wetted’ by the organic dispersed phase. Several concentration profiles are presented and the non-ideal flow parameters as well as the mass transfer coefficients for the column and system under study are reported.     

Application of Central Composite Rotatable Design for Mixing Time Analysis in Mechanically Agitated Vessels

Central composite rotatable design (CCRD) was applied for analyzing and optimizing the effects of impeller rotational speed, gas flow rate, probe location, and tracer injection point on the gas‐liquid two‐phase mixing time in an agitated vessel with a dual six‐blade Rushton turbine. Knowledge of the effects of independent factors on the mixing time is necessary in order to optimize the mixing process. The mathematical relationship between mixing time and four significant independent variables can be approximated by a nonlinear polynomial model. The obtained results demonstrate that CCRD could efficiently be applied for modeling mixing time. It requires fewer experimental runs and provides sufficient information as compared to a factorial design.     

Alternative mixed-integer linear programming models of a maritime inventory routing problem

A single product maritime inventory routing problem is addressed in this paper by exploring the use of continuous and discrete time models. We first present a continuous time model based on time slots for single docks, which is enhanced by reformulating the time assignment constraints. Next, we present a model based on event points to handle parallel docks. A discrete time is also presented based on a single commodity fixed-charge network flow problem (FCNF). All the models are solved for multiple randomly generated instances of different problems to compare their computational efficiency, and to illustrate the solutions obtained.     

CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model

A two-compartment model has been developed for calculating the droplet/particle size distribution in suspension polymerization reactors by taking into account the large spatial variations of the turbulent kinetic energy and its dissipation rate in the vessel. The two-compartment model comprised two mixing zones, namely an impeller zone of high local energy dissipation rates and a circulation zone of low kinetic energy. Computational fluid dynamics (CFD) was employed for generating the spatial distribution of energy dissipation rates within an unbaffled mixing vessel agitated by a flat two-blade impeller. A general methodology was developed for extracting, from the results of the CFD simulations, the volume ratio of the impeller over the circulation zone, the ratio of the average turbulent dissipation rates in the two zones, and the exchange flow rate between the two compartments. The effect of agitation rate, continuous phase viscosity, impeller diameter, and mixing vessel scale on the two-compartment model parameters was elucidated. The two-compartment model was then applied to a non-homogeneous liquid-liquid dispersion process to calculate the time evolution of the droplet size distribution in the mixing vessel. An excellent agreement was obtained between theoretical and experimental results on droplet size distributions obtained from a laboratory-scale reactor operated over a wide range of experimental conditions.     

Age distribution and the degree of mixing in continuous flow stirred tank reactors

New development of mean age theory is discussed for quantitative analysis of mixing and age distribution in steady continuous flow stirred tank reactors. A new relationship between the moments of age and the moments of residence time are derived. With this new relationship the variance of residence time distribution can be computed much more efficiently and accurately. The relationships of three existing variances of age are described and a new set of variances and the degree of mixing are defined. The theory is used to characterize mixing performance in a CFSTR with different layouts of an inlet and an outlet. Mean age and higher moments of age in the reactors are obtained from CFD solutions of their steady transport equations. The spatial distribution of mean age reveals details of the spatial non-uniformity in mixing. Variances of age and the degree of mixing discussed by Danckwerts and Zwietering are computed for the first time in the literature for non-ideal stirred tank reactors. It is found that although these measures are useful, certain key features in non-uniform mixing are not reflected accurately. Results show that the new set of variances and the degree of mixing more accurately characterize the non-uniform mixing in the reactors.