Mathematical Modeling and Simulation of Drying Using Two Industrial Concurrent and Countercurrent Rotary Dryers for Ammonium Nitrate

Drying of ammonium nitrate (AN) is accomplished in the Shiraz Petrochemical Complex (SPC) using a concurrent rotary dryer following a countercurrent rotary dryer. A mathematical model for these rotary dryers including heat and mass transfer was developed. The model was checked against industrial-scale data, which showed a good agreement. The average absolute deviation of the simulation results compared to the industrial data for the concurrent dryer was 4.0% for solids moisture, 1.3% for solids temperature, and 1.8% for air temperature and for the countercurrent dryer it was 9.0% for the solids moisture, 2.0% for solids temperature, and 4.6% for air temperature. These simulation results reveal that for outlet solid moisture, inlet AN moisture, and air temperature as well as the outlet temperature of product, the inlet solid and air temperature have major effects for both concurrent and countercurrent flow.     

THE DEVELOPMENT AND VALIDATION OF A SYSTEM MODEL FOR A COUNTERCURRENT CASCADING ROTARY DRYER

An overall system model for a countercurrent rotary dryer has been developed with the ullimale aim of assessing controller pairings in these dryers. This model is based on heat and mass balances within dryer regions combined with two subsidiary models, one describing the equipment (which determines particle transport and heat transfer)and the other describing the behaviour of the material (the drying kinetics). Six partial differential equations have been set up to evaluate six state variables: solids moisture content, solids temperature, gas humidity, gas temperature, solids holdup and gas holdup as functions of time and rotary dryer length. A control-volume method has been used to reduce the six partial differential equations with respect to time and the length of the rotary dryer to six ordinary differential equations in time.

The drying model has been implemented in the SPEEDUP flowsheeting package (with FORTRAN subroutines) The model has been validated by fifteen experiments-in a pilot scale countercurrent-flow rotary dryer (0.2m in diameter and 2m in length)     

THE DEVELOPMENT AND VALIDATION OF A SYSTEM MODEL FOR A COUNTERCURRENT CASCADING ROTARY DRYER

ABSTRACT

An overall system model for a countercurrent rotary dryer has been developed with the ullimale aim of assessing controller pairings in these dryers. This model is based on heat and mass balances within dryer regions combined with two subsidiary models, one describing the equipment (which determines particle transport and heat transfer)and the other describing the behaviour of the material (the drying kinetics). Six partial differential equations have been set up to evaluate six state variables: solids moisture content, solids temperature, gas humidity, gas temperature, solids holdup and gas holdup as functions of time and rotary dryer length. A control-volume method has been used to reduce the six partial differential equations with respect to time and the length of the rotary dryer to six ordinary differential equations in time.

The drying model has been implemented in the SPEEDUP flowsheeting package (with FORTRAN subroutines) The model has been validated by fifteen experiments-in a pilot scale countercurrent-flow rotary dryer (0.2m in diameter and 2m in length)     

On Dryer Energy Performance and Controllability: Generalized Modeling and Experimental Validation

This work presents an approach to compute dryer energy efficiency using air flowrate step responses and establish a link between drying energy efficiency and process controllability. The approach is based on the temperature drop between the dryer inlet and outlet air under adiabatic conditions and so decouples water evaporation from heat loss and product heating effects on dryer temperature drop. As such, the computation is accurate even for dryers with significant heat losses where the traditional use of actual temperature drop measurements is grossly inaccurate. The approach is tested and verified on two experimental case studies involving significant heat losses: the first, a continuous fluidized-bed dryer (from literature); the second, a conventional and zeolite wheel-assisted batch dryer designed in the current study.     

SPRAY DRYING DYNAMIC MODELING WITH A MECHANISTIC MODEL

In this work we suggest the dynamic modeling of a spray dryer considered as a series of well-stirred dryers. That is, a series of dryers in which the output variables are equal to the state variables. The state equations were obtained from the heat and water mass balances in product and air. Additionally, heat and water mass balances in interface jointly with water equilibrium relation between product and air were considered. A pilot spray dryer was modeled assuming one, two, five and 20 well stirred steps. Low-fat milk with 10-20% of solids was dried at different inlet air temperatures (120-160°C), air flow rate of 0.19 kg dry air s^-1 and different feed rates (1.4 - 4.2 × 10^-4 kg dry solids s^-1). Stationary result showed that the model predicts the experimental air outlet temperature, at different inlet conditions with a maximum deviation of 6°C. The dynamic simulation reproduce the experimental one with moderate accuracy. Experimental dynamic showed that the pilot plant spray dryer has a well-stirred process behavior. The model represents a method for estimate outlet product moisture as function of the outlet air temperature. This has application for automatic control because there is not an easy way to measure on-line measure the outlet product moisture content.     

Experimental Investigation and Modeling of Plug-Flow Fluidized Bed Drying Under Steady-State Conditions

In this study, a model for a plug-flow fluidized bed dryer under steady-state conditions was presented. The model was based on differential equations; thus the bed of the dryer was divided horizontally and vertically into major and minor control volumes, respectively. Each control volume was composed of two thermodynamic systems: solid and gas. The mass and energy balances of the particles in the major control volume based on the axial dispersion were developed to derive the axial profiles of solid moisture content and temperature. To derive the variation of gas humidity and temperature along the bed height and hence the axial profiles of outlet gas humidity and temperature, the mass and energy balances in the gas over the minor control volume, considering the plug flow of gas through the bed, were developed. The model was validated by comparing the simulation results with the experimental data obtained by drying the long-grain rough rice under steady-state conditions in a laboratory-scale, plug-flow fluidized bed dryer. A very satisfactory agreement between the simulation and the experimental data of solid moisture content, solid temperature, and outlet gas humidity and temperature was achieved. Also, the effects of inlet gas temperature, weir height, and inlet dry solid mass flow rate on the simulated axial profiles of solid moisture content and temperature, humidity difference between inlet and outlet gas, and outlet gas temperature were investigated.     

A Study of the Limitations to Spray Dryer Outlet Performance

The concept of the product moisture locus was tested in this work using a pilot-scale modified Niro spray dryer (diameter 0.8 m, height 2 m), where the residence time of the particles inside this spray dryer is lower compared with larger industrial spray dryers. The moisture contents of skim milk powder produced from spray drying skim milk (solids content 8.8% w/v) at different operating conditions, namely different swirl vane angles (0°, 25°, 30°), inlet air temperatures (170°C, 200°C, 230°C) and process fluid flowrates (1.4 kg h^-1, 1.6 kg h^-1, 1.8 kg h^-1), were compared with the predicted equilibrium moisture contents. In addition, the residence time of the particles was also increased in the spray dryer by decreasing the inlet air mass flowrate from 0.016 to 0.013 kg s^-1. The outlet moisture contents of the skim milk powder for all the 23 runs carried out in this work were within 0.4% of the equilibrium values. Thus, the skim milk powder particles were in close equilibrium with the gas inside the drying chamber. These equilibrium limitations are confirmed by other literature data (Boonyai, P. Comparative Evaluation of Soymilk Drying in a Spray Dryer and Spouted Bed of Inert Particles. M.Sc. Thesis. Asian Institute of Technology: Bangkok, Thailand, 2000; 90 pp; Harvie, D.J.E.; Langrish, T.A.G.; Fletcher, D.F. A computational fluid dynamics study of a tall-form spray dryer. Trans IChemE 2002, in press). The use of this finding to predict spray dryer performance is demonstrated by mass and energy balance calculations.     

Coupled simulation of the flue gas and process gas side of a steam cracker convection section

A coupled simulation of the flue gas and process gas side of the convection section of a steam cracker is performed, making use of the CFD software package Fluent. A detailed overview of the operating mode of the different heat exchangers suspended in the convection section is obtained. The asymmetric inlet flow field of the flue gas in the convection section, and the radiation from the convection section walls leads to large differences in outlet temperatures of the tubes located in the same row. The flow fields and temperature fields in the tubes of a single heat exchanger differ significantly with e.g., outlet temperatures of the hydrocarbon‐steam mixture ranging from 820 K to 852 K. Moreover, the simulations reveal the presence of hot spots on the lowest tube row, possibly causing fouling. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

An Evaluation of Factors Influencing the Energy-Efficient Operation of Well-Mixed Fluidized Bed Dryers

This article describes the results of calculations of specific energy consumption, E_s, performed on a well-mixed fluidized bed dryer simulator. Exhaust air temperature-humidity loci required to yield a specified outlet moisture content were also determined. Most of the calculations related to solids whose drying rate was gas-film controlled. Six model drying curves were employed to examine the effects of drying rate and hygroscopicity in addition to the normal operating parameters. The results indicated that E_s was highest for slow-drying hygroscopic solids and lowest for fast-drying, non-hygroscopic solids. Specific energy consumption increased with decreasing bed temperature and outlet moisture content and with increasing heat loss but was independent of solids loading and airflow rate. For both the aforementioned solids and a much slower drying material (wheat), there was close agreement between the zero heat loss data and a single theoretical curve approximating the performance of an ideal adiabatic dryer. Distinct differences between the behavior of well-mixed and plug flow fluidized bed dryers are reported.     

微粒群算法在干燥器多变量优化设计中的应用

建立了以具有废气循环的回转干燥系统年总费用为目标函数的优化设计数学模型,在此基础上探讨了惯性权因子对微粒群算法性能的影响,并应用微粒群算法求解干燥器优化设计数学模型,对干燥器出口废气温度与循环比进行优化设计。结果表明,带动态非线性惯性因子的微粒群算法对求解多变量的干燥优化设计问题具有方法简单、所需微粒群规模小、收敛速度快等特点;采用部分废气循环并进行优化设计对干燥系统的节能具有十分重要的意义,对湿空气出口温度和废气循环比进行优化设计,其年总费用比无废气循环的常规设计节省18．2%,比循环比为0．2时的常规设计节省12．6%。     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

ABSTRACT

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

CFD Modeling of Microwave-Assisted Fluidized Bed Drying of Moist Particles Using Two-Fluid Model

The drying behavior of moist spherical particles in a microwave-assisted fluidized bed dryer was simulated. The two-fluid Eulerian model incorporating the kinetic theory of granular flow was applied to simulate the gas–solid flow. The simulations were carried out using the commercial computational fluid dynamics (CFD) package Fluent 6.3.26. The effects of different levels of microwave power densities as well as initial gas temperature on the prediction of solids moisture content, gas temperature, and gas absolute humidity were investigated. The effect of microwaves was incorporated into calculations using a concatenated user-defined function (UDF). The simulation results were compared with experimental data obtained from drying of soybeans in a pilot-scale microwave-assisted fluidized bed dryer and reasonable agreement was found. The mean relative deviation for prediction of solids moisture content, gas temperature, and gas absolute humidity were less than 3, 10, and 5%, respectively. Further work is needed to validate the proposed model for large-scale plants.     

Bibliography of Literature on Fundamentals and Applications of Vibration in Particle Processing

This article describes the results of calculations of specific energy consumption, E _s , performed on a well-mixed fluidized bed dryer simulator. Exhaust air temperature–humidity loci required to yield a specified outlet moisture content were also determined. Most of the calculations related to solids whose drying rate was gas-film controlled. Six model drying curves were employed to examine the effects of drying rate and hygroscopicity in addition to the normal operating parameters. The results indicated that E _s was highest for slow-drying hygroscopic solids and lowest for fast-drying, non-hygroscopic solids. Specific energy consumption increased with decreasing bed temperature and outlet moisture content and with increasing heat loss but was independent of solids loading and airflow rate. For both the aforementioned solids and a much slower drying material (wheat), there was close agreement between the zero heat loss data and a single theoretical curve approximating the performance of an ideal adiabatic dryer. Distinct differences between the behavior of well-mixed and plug flow fluidized bed dryers are reported.     

A Cross-Flow Model for Continuous Plug Flow Fluidized-Bed Cross-Flow Dryers

Plug flow fluidized bed cross-flow dryers have been used in drying of particulate solids such as paddy and other grains for many years. However, simulation of the performance of any particular design of the dryer has always been problematic due to the inadequate overall empirical models used that are too inflexible and too specific to the particular design. In addition, previous theoretical models of the plug flow fluidized bed cross-flow dryer did not model the gas cross flow properly and had difficulty in modeling the moving solid bed. A new steady-state cross-flow model of the dryer that models the gas cross-flow is proposed. The profiles for the solids and air moisture contents and temperatures were found to be dependent on the gas-solid flow ratio, G/F, the specific heat demand, C_PY(T_I - T_A)/(Y_E - Y_I), the total number of a transfer units, N_T = Gε/KφaSL and the specific drying load, (X_I - X_P)/ (Y_E - Y_I). The model was validated by comparing the simulated data with experimental data that were obtained by drying paddy in a plug flow fluidized bed cross-flow dryer pilot plant. The model was found to estimate very well the solids moisture content and temperature, the gas moisture content and temperature profiles, and the driving force profile.     

INFLUENCE OF SOLIDS MOISTURE CONTENT ON THE AVERAGE RESIDENCE TIME IN A ROTARY DRYER

The solids mean residence time in a rotary dryer is influenced by several variables such as dryer dimensions and solids characteristics. One of these characteristics, usually not taken into account in correlations proposed to estimate the mean residence time, is the solids feed moisture content. Although it is well known that the solids moisture content has a major impact on the ability of the solids to move along the rotary dryer, it does not enter as a parameter in available correlations. In this investigation, numerous experiments were performed in a pilot-scale rotary dryer to study the influence of solids moisture content and drying gas temperature on the mean residence time. Sand employed in cement makeup was used to perform these experiments. Results show that the mean residence time for a moisture content in the range of 8% to 12% is four times higher than for dry solids. The moisture content and the drying gas temperature influence significantly the shape of the residence time distribution curve.     

CO2跨临界热泵系统特性再分析

在原有研究的基础上,结合实际系统,本文对CO₂跨临界热泵系统的特性进行再分析,通过参数计算,分析回热温度、气体冷却器出口温度、运行压力三种因素如何影响系统性能,提出提高CO₂热泵运行效率的方法。分析结果表明：回热器并不总有效,而是与气体冷却器出口温度有关,当温度小于某临界值时回热会降低系统运行制热性能系数COP_h,当温度大于此临界值时回热则有助于提高COP_h;对应气体冷却器出口温度存在最优压力,但实际压缩机的可承受压力是有限的,导致系统在某些气体冷却器出口温度下不能在最优压力下运行,同时在不同的排气压力下,存在气体冷却器出口温度最高限定值,否则COP_h不合理也不可接受;热泵出水温度以及气体冷却器出口温度共同影响系统排气压力的选择。     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

Drying characteristics of millet in a continuous multistage fluidized bed

The effects of gas velocity, inlet gas temperature and the solid feed rate on the drying efficiency, the outlet solid moisture content, bed temperature in each stage, the outlet gas humidity and temperature in a rectangular acryl multistage fluidized bed (0.172 m×0.192 m×1.5 m-high) with a downcomer (0.04 m-I.D.) were investigated. The experiments were performed by using 1.9 mm millet particles. The final moisture contents of the solids increased with increasing the solid feed rate. The drying efficiency increased with increasing the wetted solid feed rate but decreased with increasing the inlet gas temperature. The drying performance of the multistage fluidized bed was compared with the single-stage fluidized bed and found to be superior under identical operation conditions. The model predicted values were well matched with the experimental data in the multistage fluidized bed dryer. This paper is dedicated to Professor Dong Sup Doh on the occasion of his retirement from Korea University.     

Modeling of Drying in Moving Bed

The aim of this work is to study the simultaneous heat and mass transfer between air and soybean seeds in moving bed dryers with parallel flow (concurrent and countercurrent), by means of an experimental and simulation work, verifying the validity of classical assumptions. The numerical solution of a one-dimensional boundary value problem was obtained by means of a computational code based on axial integration through DASSL code. Deviations from flat air velocity profile were taken into account considering empirical and mechanistic equations found in the literature that describes air profile as function of radius. The experimental data of air humidity, temperature, and seed moisture content and temperature at the dryer outlet were compared to the simulated values.