Bed Depth Profile Research Articles

Development and analyses of data-driven models for predicting the bed depth profile of solids flowing in a rotary kiln

Soft computing data-driven modeling (DDM) techniques have attracted the attention of many researchers across the globe as they do not require deep knowledge of the complex physical process. In the present research, data-driven based models have been developed using support vector regression (SVR), multilayer perceptron neural network (MLP), radial basis function neural network (RBFNN) and general regression neural networks (GRNN) techniques for predicting the bed depth profile of solids flowing in a rotary kiln. The performances of the developed models were compared and evaluated against the experimental results in terms of statistical measures such as coefficient of determination (R2), and average absolute relative error (AARE). The obtained results and findings from this research have revealed that data-driven models can predict the bed depth profile of solids flowing in a rotary kiln quite accurately. The SVR-based model exhibited the lowest AARE value of 1.72% and highest R2 value of 0.9981 while GRNN, RBFNN, and MLP models gave corresponding values of AARE as 3.69%, 55.13%, 98.15% and those of R2 as 0.9898, 0.0052 and 0.0081, respectively. Moreover, the developed DDM-based models i.e. GRNN, RBFNN, and MLP models overcame the limitations of the existing solutions which involved iterative numerical procedure entailing high degree of computational complexity.

Wood chips flow in a rotary kiln: Experiments and modeling

Rotary kilns are well suited for processing woody biomass by torrefaction to produce bioenergy. One of the key issues for process design lies in the flow pattern modeling. The Saeman model is classically used to predict the mean residence time (MRT) and the bed depth profile of powder materials in rotary kilns. Its ability to describe wood chips flow arises. In the present study, residence time distribution (RTD) experiments are conducted with raw and torrefied wood chips. Effects of operating parameters – kiln slope, rotational speed and inlet flow-rate – on the average residence time, the variance and the mean solid hold-up are discussed. A plug flow with small extent of dispersion is emphasized, even if some segregation phenomena are highlighted. Torrefaction did not evidence any significant influence on the flow pattern. With a discrepancy of 20% between the measured and computed mean residence time, the predictive capacity of the classical Seaman model proved to be insufficient. The model is adapted to predict accurately the load profile and the mean residence time of particles with parallelepiped form. The discrepancy between experimental and calculated results is so reduced from 20% to 5% for the MRT and from 25% to 5% for the mean solid hold-up.

Modeling of Bed Depth Profile of Materials in Rotary Drums Using Support Vector Regression (SVR): Comparison with a Well-Structured Parametric Model

Modeling of Bed Depth Profile of Materials in Rotary Drums Using Support Vector Regression (SVR): Comparison with a Well-Structured Parametric Model

Numerical investigation of bed depth height, axial velocity and mean residence time of inert particles in steady state industrial cement rotary kiln: Case of Figuil Plant in Cameroon

In order to simulate the structure of granular materials in a rotary kiln under the steady-state regime, mathematical models have been developed by different authors. Experimental data are used to test the equations predicting the bed depth profile, the axial velocity profile and the mean residence time of granular particles in the kiln. The Ghirelli and Leckner (2004) [1] formulation is used for the first time to evaluate the residence time. Comparisons show that this formulation gives a satisfactory shape although it underestimates the mean residence time. For bed depth and axial velocity profiles, the Saeman (1951) [5] mechanistic model which has good agreement with experimental data found in literature, is used to predict these characteristics in the Figuil industrial cement kiln. The Lee and Shun (1999) [22] phenomenological relation which gives good agreement with experimental data is used for the prediction of mean residence time.

Modeling and Simulation of Oil Sludge Pyrolysis in a Rotary Kiln with a Solid Heat Carrier: Considering the Particle Motion and Reaction Kinetics

In this study, a dynamic model of oil sludge pyrolysis in a rotary kiln with a solid heat carrier was developed. In the proposed model, both the particle motion in the rolling mode and oil sludge pyrolysis were taken into consideration. Saeman’s model and a multiple-reaction model were involved to simulate the bed depth profile inside the rotary kiln based on the solid motion and the volatile evolution, respectively. Furthermore, the temperature profiles of three phases (solid carrier, oil sludge, and gaseous phase) in diverse conditions were predicated by combining pyrolysis kinetics, heat transfer, and motion equations. In the proposed model, the yields of CxHy, H2, CO, and CO2 were successfully stimulated and predicted. The validity of the model was verified from both aspects of solid axial velocity and gas yields by comparing numerical values to literature reports and experimental data, respectively. This simulation practice was expected to provide an alternative approach to obtain helpful parameters for the designing of an industry-scale rotary kiln pyrolyzer.

Transient Material Accumulation in Rotary Drums

An empirical start-up transient model was developed for rotary drums using the data obtained from a pilot scale apparatus. The structure of the model is composed of dimensionless groups which reflect the effects of important operational variables on transient material filling-up inside the drum. The model is composed of two parts. One for predicting the displacing time of the material apex to any specified length of drum in an initially empty drum. The other one predicts the variations of the bed depth of material during filing-up period. It was shown that the model can be used, also, for steady state condition of material bed depth profile inside rotary drums.

A hydrodynamic model for flighted rotary kilns used for the conversion of cohesive uranium powders

The axial and transverse solid distribution of a cohesive powder in flighted rotary kilns was calculated from an original method based on the lifter discharge law previously determined, geometrical calculations and supplementary measurements (in particular the fall velocity of the powder at high temperature). At a given axial position, the quantity of powder falling through the gas, the total quantity of flighted powder as well as the quantity remaining in the bulk are thus calculated; the axial bed depth profile is obtained from the Saeman–Kramers–Afacan model.

Exact analytical solution for the bed depth profile of solids flowing in a rotary kiln

Abstract In this communication exact analytical solution of the well known Saeman's model equation, which is used to find the bed depth profile of the granular material flowing in a rotary kiln, has been obtained. Mathematically this model equation is characterized by a first order nonlinear ordinary differential equation and the exact analytical solution has been obtained in terms of an implicit form of elementary transcendental function by following the methods of separation of variables and partial fraction decomposition. To the best of the authors' knowledge, this is perhaps the first attempt towards obtaining the exact analytical solution for the above model equation. The results obtained by using the exact analytical solution have been successfully verified against those obtained by using the numerical method and are found to be superior to those obtained by using the existing approximate analytical solutions. Besides, the exact analytical solution has also been fruitfully employed to simulate various experimental results available in literature. Furthermore, the effects of various parameters on the bed depth profile have also been briefly analyzed.

Axial transport and residence time of MSW in rotary kilns: Part I. Experimental

Experiments on the influences of operational variables on the axial transport of both heterogeneous municipal solid waste (MSW) and homogenous sand are conducted in a continuous lab-scale rotary kiln cold simulator. Compared with sand, the residence time of MSW has a relatively large discrepancy with the ideal normal distribution due to the trajectory segregation of MSW components. The residence time at different axial zone is quite different due to the varied bed depth profile along the kiln length. MSW has a longer mean residence time (MRT) and a lower material volumetric flow (MVF) than sand because of the higher θ d than sand. The increment of both rotating speed and kiln slope reduces MRT, and increases MVF. Exit dam has a significant impact on the MRT and the influence of internal structure group consisting of various axial ribs and circular ribs is mainly determined by the height of circular ribs. Inside wall roughness also has effect on MRT through changing the bed regimes. For a case with the certain inlet and exit bed depths, the product of MRT and MVF holds at a constant within the limits of experimental errors in spite of the changing experimental variables.

95/06316 Experimental study of residence time, particle movement and bed depth profile in rotary kilns

95/06316 Experimental study of residence time, particle movement and bed depth profile in rotary kilns

Experimental study of residence time, particle movement and bed depth profile in rotary kilns

AbstractExperiments were performed in a pilot scale rotary kiln with coal and coke particles to study their mean residence time, residence time distribution, bed depth profile and time spent at the bed surface. The influence of filling ratio on residence time was studied with a uniform bed depth in the kiln. Residence time distribution and bed depth profile measurements were performed in a kiln without end constriction, at different rotational speeds and different solid inputs. The residence time fraction corresponding to the passage of the particles at the bed surface was measured with a photographic study of the movement of a coloured particle.Various equations were tested to represent the experimental results. The equations of Kramers and Croockewit (1952) and Ronco (1965) were adequate to calculate mean residence times, while only the former could represent correctly the bed depth profile. An equation is proposed which turns out to be quite accurate in predicting the fraction of the residence time spent in the upper layer of the bed.

Residence time distribution and material flow studies in a rotary kiln

Experiments were conducted in a rotary kiln containing ilmenite particles to study the residence time distribution (RTD) of low-density particles, holdup, and bed depth profile. The variables include feed rate of solids, slope and rotational speed of the kiln, type and size of the tracer, and dam height. Correlations are presented for mean residence time, dispersion number, holdup, and steady-state throughput of solids in terms of the process variables. A simple method is proposed to estimate the dam height that gives rise to a flat profile of solids bed along the length of the kiln.