Multiobjective optimization of an industrial grinding operation under uncertainty

Multiobjective optimization of an industrial grinding operation under various parameter uncertainties is carried out in this work. Two sources of uncertainties considered here are related to the (i) parameters that are used inside a model representing the process under consideration and subjected to experimental and regression errors and (ii) parameters that express operators’ choice for assigning bounds in the constraints and operators prefer them to be expressed around some value rather than certain crisp value. Uncertainty propagation of these parameters through nonlinear model equations is reflected in terms of system constraints and objectives that are treated here using chance constrained fuzzy simulation based approach. Such problems are treated in literature using the standard two stage stochastic programming methodology that has a drawback of leading to combinatorial explosion with an increase in the number of uncertain parameters. This problem is overcome here using a combination of fuzzy and chance constrained programming approach that tackles the problem by representing and treating the uncertain parameters in a different manner. Simultaneous maximization of grinding circuit throughput and percent passing mid size fraction are studied here with upper bound constraints for various performance metrics for the grinding circuit, e.g. percent passing of fine and coarse size classes, percent solids in the grinding circuit final outlet stream and circulation load of the grinding circuit. Uncertain parameters considered are grindability indices of rod mill and ball mill, sharpness indices of primary and secondary cyclones and the respective upper bounds for the constraints mentioned above. The deterministic multiobjective grinding optimization model of Mitra and Gopinath [2004. Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm. Chem. Eng. Sci. 59, 385-396.] forms the basis of this work on which various effects of uncertain parameters are shown and analyzed in a Pareto fashion. Nondominated sorting genetic algorithm, NSGA II, a popular elitist evolutionary multiobjective optimization approach, is used for this purpose.     

Investigation of wear pattern in a complex coal pulveriser using CFD modelling

In this study, we have constructed a commercial-scale pulveriser and simulated motion of air and coal particles inside the pulveriser to investigate the effect of air passage on the wear pattern. Simulations were carried out using Eulerian–Lagrangian approach. The results indicated that the primary air entering into the pulveriser under the bowl via splitters, exited the pulveriser vanes to the left with the highest velocity. This validates the constructed model as the nozzle ring above the bowl has vanes that run clockwise making most of the primary air to exit the vanes to the left. Additional simulations with modified inlet duct geometry led to a possible solution for making the airflow distribution even at the base of the mill, which is expected to reduce the wear pattern. The results presented in the paper provides impetus for the modification of the airflow path using baffle splitters in the primary air duct, which could prove valuable to designers for the optimisation of airflow and the potential reduction of wear on the components within the coal pulveriser.     

Multiphase flow simulation of a simplified coal pulveriser

In coal-fired power plants, the first major component is pulveriser, whose performance dictates the total power station efficiency. Pulveriser is employed to grind the lumped coal and transport the fine coal powder to furnace chamber for an efficient combustion. In this study, we have simulated motion of air and coal particles inside a commercial-scale pulveriser. Multiphase flow simulation of a simplified pulveriser was carried out using a granular Eulerian–Eulerian approach. Due to inclined air-distributor vanes, the flow field within pulveriser was slightly asymmetric. Regions of exceptionally high velocities were predicted close to the outer walls of the pulveriser, indicating a strong probability of particles carryover within these regions. The 100 μm coal particles qualitatively followed the air path-lines. However, the velocity vectors for 500 μm particle deviated significantly from those of airflow. The results presented in the paper provide impetus for the development of a complex pulveriser model, which further could prove valuable to designers for optimisation of components within the mill.     

Experimental and Numerical Study of Grinding Media Flow in a Ball Mill

An experimental and numerical study on the grinding media dynamics inside a baffled ball mill under different solid‐flow regimes, namely, cascading, cataracting, and centrifuging, is described. The Eulerian approach was used for all simulations and the boundary condition at the drum wall was investigated by means of the specularity coefficient parameter. This effort is an important approach in representing the particle‐wall interaction in a ball mill. The restitution coefficient of the balls was experimentally measured using a video camera, and its influence was evaluated by comparing the numerical and experimental outcome of flow patterns. The simulations results proved that the specularity and restitution coefficients effects at the drum wall were more evident at high rotational speeds.     

Steady state inferential modeling of temperature and pressure in an air-swept coal pulverizing ball mill

Mill discharge temperature and differential pressure have a strong effect on efficiency and safety of a coal fired power plant. Therefore, it is imperative that they are closely monitored and controlled during mill operation to keep their levels within a predetermined safe and efficient operating range regardless of the rate at which the raw coal is fed to the mill. One way to achieve this is through a control schedule that compares the value obtained from the process to the stored set-point value to determine if there is any deviation that requires correction. This paper describes a steady state model that could be used alongside conventional controllers as an on-line shadow that provides inferential estimates of desired temperatures and pressure drops in the mill circuit which can be continuously compared with the actual values for adjustment. This would not only help to avoid the difficulties associated with direct measurement but also provide a means for early detection of drifts and failing sensors and serve as a temporal back-up for the out-of-order sensors. The model was tested using industrial data collected from four ball mills at a coal fired power plant in South Africa and the results show a reasonable agreement between the measured data and model predictions both qualitatively and quantitatively within a 5% error margin. The model outputs were found to be highly sensitive to the variation in mill loading, the primary air (PA) flow and the mill channel dimensions. Therefore, for validity of this model, accurate determination of all significant parameters is essential. For now, the model is only valid for the ball mills involved in the current study, but with availability of data it can be reproduced elsewhere.     

CFD modeling of MPS coal mill with moisture evaporation

Coal pulverizers play an important role in the functioning and performance of a PC-fired boiler. The main functions of a pulverizer are crushing, drying and separating the fine coal particles toward combustion in the furnace. It is a common experience that mill outlet pipes have unequal coal flow in each pipe and contain some coarse particles. Unequal coal flow translates into unequal air-to-fuel ratio in the burner, deviating from the design value and thus increasing unburned carbon in fly ash, NO_x and CO. Coarser particles at the mill outlet originate from poor separation and decrease the unit efficiency. In addition, coarser particles reduce burner stability at low load. Air flow distribution at the mill throat, as well as inside the mill, significantly influences the mill performance in terms of separation, drying, coal/air flow uniformity at the mill outlet, wear patterns and mill safety. In the present work, a three-dimensional computational fluid dynamics (CFD) model of the MPS Roll Wheel pulverizer at Alliant Energy's Edgewater Unit 5 has been developed. The Eulerian-Lagrangian simulation approach in conjunction with the coal drying model in Fluent, a commercial CFD software package, has been used to conduct the simulation. Coal drying not only changes the primary air temperature but it also increases the primary air flow rate due to mass transfer from coal. Results of the simulation showed that a non-uniform airflow distribution near the throat contributes significantly to non-uniform air-coal flow at the outlet. It was shown that uniform velocity at the throat improves the air and coal flow distribution at the outlet pipes. A newly developed coal mill model provides a valuable tool that can be used to improve the pulverizer design and optimize unit operation. For example, reject coal rate, which is controlled by the air flow near the mill throat, can be reduced. The model can also be used to further aid in identifying and reducing high temperature or coal-rich areas where mill fires are most likely to start.     

Modeling of a grinding circuit with a swing-hammer mill and a twin-cone classifier

A model was formulated for a continuous, air-swept milling system, assuming the mill to be fully mixed, with all particles leaving the mill in the air stream. The air-sweeping effect was treated as an internal classification which allows fine particles to leave and returns coarse particles for regrinding. The kinetic parameters for the continuous model were estimated using experimental data from a continuous pilot-plant air-swept swing-hammer mill. Functional forms that provide information regarding the power, the internal classification action of the mill, and the action of the external classifier, were deduced for different plant conditions. It was found that the specific rates of breakage could be assumed to vary with particle size according to S_i = a(x_i/x_o)^α, where the value of α was 1.3 for the coal used in the tests. The values of a varied with mill hold-up W, giving a maximum of aW as W became large. The primary breakage distribution values were assumed to be normalized, giving a value of characteristic slope of γ = 0.60.     

Characterization of membrane electrode assembly with hydrogen-hydrogen cell and ac-impedance spectroscopy: Part I. Experimental

A measurement system based on a symmetrical hydrogen-hydrogen cell was developed and presented. The net water flux through and impedance of Gore™ Primea^® Series 58 MEA were measured under different humidity conditions. An equivalent circuit approach was used to analyze impedance measurement data and the dependences of membrane conductivity and reaction kinetics on the humidity were obtained. Modeling work was found necessary to estimate the diffusion coefficient of water in the membrane, because humidity profile inside the cell was uneven and unknown during the net water flux measurements. Gas permeabilities of different cell components and water uptake of the MEA were measured to get parameter values for the modeling work. The actual modeling work was not conducted in this contribution, but is explained in Part II of this paper.     

Experimental and Simulated Performances of a Batch-Type Longan Dryer with Air Flow Reversal Using Biomass Burner as a Heat Source

This article presents experimental performance of a batch-type longan dryer using a biomass burner with air flow reversal and also presents modeling of the longan dryer for drying of whole longan. The dryer essentially consists of a biomass burner and a drying bin with an arrangement for periodic air flow reversal. Three drying runs with loading capacity of 2,000, 1,500, and 1,000 kg of whole longan were carried out. There was no significant difference in temperatures in different positions (except inlet and outlet) inside the dryer (p < 0.05) or moisture content inside the dryer (p < 0.05). Whole longan was dried from an initial moisture content of 74% (wb) to a final moisture content of 14% (wb). The drying time of whole longan in the longan dryer was 60, 54, and 48 h for 2,000, 1,500, and 1,000 kg loading, respectively. The quality of dried product was also good in comparison to the high-quality product in markets.

To simulate the performance of the longan dryer for drying of whole longan, a set of partial differential equations was developed and the equations were solved using the finite difference technique. The numerical solution was programmed in Compaq Visual FORTRAN version 6.5 (Compaq Computer Corp., TX). The simulated moisture contents agreed well with the experimental data. This model can be used to provide the design data and it is also essential for optimal dryer design.     

Experimental and numerical studies on the gas flow surrounding a single cluster applied to a circulating fluidized bed

The term cluster or streamer is commonly applied to a collection of particles held together by hydrodynamic forces. Inside a circulating fluidized bed a single cluster has a significant effect on the gas that flows around it. Recent experiments have suggested that large scale gas fluctuations occur as the air flows around the cluster body. This paper examines the effect a single cluster has on the surrounding gas flow. Experimental work focuses on a small riser with the ability to release a single cluster. A specially designed probe measures the gas velocity as the cluster travels by. Numerical work simulates the effect of airflow around a porous body. The fluctuation levels observed are comparable to the experiments. Both results show that large scale velocity fluctuations occur in the gas in the vicinity of a cluster. This has a large impact on gas and particle modeling and mixing inside a circulating fluidized bed.     

Numerical Simulation of Open‐Circuit Continuous Mills Using a Non‐Linear Population Balance Framework: Incorporation of Non‐First‐Order Effects

Population balance modeling has been used as a tool for simulating, optimizing, and designing various particulate processes, including milling. A fundamental tenet of the traditional models for milling processes is the first‐order breakage kinetics. Ample data obtained from batch milling studies show that this assumption is not necessarily valid for certain milling systems. In the present theoretical investigation, an attempt has been made to incorporate these experimentally observed non‐first‐order effects into continuous mill models within the context of a novel non‐linear population balance framework. In view of two idealized flow regimes, i.e., perfect mixing and plug‐flow, continuous mills operating in the open‐circuit mode are numerically simulated. The simulations indicate that not only does the product size distribution depend on the degree of mixedness in a continuous mill, but also on the non‐first‐order effects arising from multi‐particle interactions.     

Binder jetting additive manufacturing of silicon carbide ceramics: Development of bimodal powder feedstocks by modeling and experimental methods

A limitation of binder jetting additive manufacturing is the low density of fabricated parts. Mixing powders with different sizes is a promising approach to increase powder bed packing density and, hence, printed part density. However, in previous studies mixed powder feedstock was prepared by trial and error method. In this research, both modeling and experimental methods were used to prepare the bimodal powder feedstocks. Analytical packing model was introduced for irregular powders. A bimodal powder was prepared by mixing two different-sized silicon carbide powders (i.e. coarse and fine) using ball mill, and their tap densities were measured. Silicon carbide plates were printed using the coarse and bimodal powders by a commercial binder jetting system. Results showed that the modeling method could predict the tap density of bimodal powders with high accuracy. The printed parts from bimodal powder achieved higher green densities than those from the unimodal powder.     

A short-lived radioactive tracer method for the measurement of closed circuit ball mill residence time distributions

This paper describes an extension of the short-lived radioactive tracer method to the on-stream measurement of residence time distributions of ball mills in closed circuit with a classifier. In essence, the method calls for tracing a size of irradiated circuit feed particles for which the classifier behaves as a simple splitter. By assuming that the mill RTD is particle size independent and that there is negligible tracer dispersion in the classifier, tracer data obtained in the mill product are mathematically treated to give the mill RTD. The extended method is derived, developed and demonstrated on a closed circuit test loop and on a pilot-plant scale ball mill in closed circuit with a hydrocyclone.     

年产100万t矿渣微粉生产线立磨系统热工计算及配置

介绍了某年产100万t矿渣微粉生产线立磨粉磨系统工艺流程,在给定设计原始资料的情况下,利用Excel软件进行了热风炉和立磨系统的热平衡和气流平衡计算,分析了计算关键点。在此基础上,介绍了系统中关键设备如热风炉、收尘器、风机选型依据。     

A simulation model for an air-swept ball mill grinding coal

The conventional model for grinding in tumbling ball mills was modified to allow for air-sweeping, for the case where all the material is carried out of the mill in the air stream. It was shown that this type of mill can be treated as a single fully mixed reactor. The values of the internal classification numbers given by the air-sweeping were determined for a 1 m by 1.5 m pilot-scale mill grinding coal. The results showed that only 1 to 2% of the mill charge are exposed to the sweeping action per mill revolution. S and B values determined in a laboratory mill were scaled-up for use in the continuous mill model and the simulations gave product size distributions and mill capacities which agreed with the pilot-scale mill data within the experimental accuracy of the pilot-scale data.     

Improvement of bioavailability of water insoluble drugs: Estimation of intrinsic bioavailability (Short Communication)

A series of attempts to enhance the bioavailability of water insoluble drugs have been made by the fine grinding technique using a planetary ball mill in wet milling process. Here, the possibility of improving the dissolution properties of water insoluble drugs such as ursodeoxycholic acid (UDCA), diphenyl hydrantoin (phenytoin) and biphenyl dimethyl dicarboxylate (DDB) based on ultra-fine grinding process has been discussed with comparison to experimental data. Also examined was the intrinsic bioavailability estimated based on a molecular modeling approach and thermophysical data.     

Study of model application for drying of pulp fruit in spouted bed with intermittent feeding and accumulation

In the present study, we applied and improved a model to describe the behavior of a spouted bed dryer with intermittent feeding for suspension drying, considering suspension accumulation inside the device. This model is important in macroscopic heat and mass balances, represented by a system of ordinary differential balances, implemented and resolved numerically using Fortran routines, in which the influence of process variables on drying dynamics were assessed. The results obtained in modeling and mathematical simulations were compared with experimental data, indicating that the model fits the process well, based on outlet air temperature and moisture.     

Double-sensor conductivity probe applied in a flotation system

This study proposed a new approach for measuring bubble size distribution, bubble mean diameter, Sauter mean bubble diameter, and gas holdup using a double-sensor conductivity probe in an air/water two-phase system bubble column. The results for the two-phase system were compared and calibrated using analyses from bubble images taken by a digital camera from the side of the column wall. Good agreement was observed between the two techniques. The same double-sensor conductivity was used in an air/water/solids three-phase system. The conductivity probe captured the change in bubble dynamic behaviour inside the pulp phase; however, the presence of the solids made it more challenging to measure. As a result, the VisioFroth commercial package, using images taken from the top of the froth layer, could be used in conjunction with the double-sensor conductivity probe to show the dynamic evolution of mineralized bubbles from the pulp zone to the froth zone in a flotation process.     

The effect of interstitial gas on milling. Part 2

In a previous paper results were presented on the effect of interstitial gas on the milling characteristics of one specific fine powder in a ball mill. This second paper gives more data on two other powders, cracking catalyst and hematite, together with those on the powder used in the earlier experiments, quartz sand. The effects found are similar for each of the three powders: increasing gas pressure or viscosity of the gas or both inside the mill increases the rate of breakage and decreases the fineness of the daughter particles of a milling event. The overall milling speed or production rate as well as the ultimate fineness of the product are both improved by increasing pressure or viscosity.On the basis of these results a comparison is made with wet milling. It appears that pressurized milling, pressure around 10 bar, is a good alternative for the milling of fine powders.     

Steady-State Modeling of Multi-Cylinder Dryers in a Corrugating Paper Machine

In this study, a steady-state model was developed to describe the paper drying process and to analyze pocket dryer conditions for a multi-cylinder fluting paper machine in Iran's Mazandaran Wood and Paper Industries. The machine has 35 cylinders grouped in three drying groups and the cylinders are heated from the inside by steam. The model is based on the mass and energy balance relationships written for fiber, air, and water in the drying section. In this research, the heat of sorption and its variations with paper temperature and humidity changes have been taken into account. Temperature and moisture variation of the paper web and cylinder surface temperature in the machine direction were predicted by the proposed model. Also, temperature and humidity of air in the drying pockets and hood exhaust were estimated by the proposed model. Moreover, the model can predict the evaporation rate and specific drying rate with sufficient accuracy in comparison with the TAPPI standard. Finally, the main modeling parameters were compared with the available operating data and the effectiveness of the developed model was verified through validations.