Showing papers in "Chemical Engineering & Technology in 2004"

High‐Pressure Homogenization as a Process for Emulsion Formation

Abstract: Emulsions find a wide range of application in industry and daily life. In the pharmaceutical industry lipophilic active ingredients are often formulated in the disperse phase of oil-in-water emulsions. Milk, butter, and margarine are examples of emulsions in daily life. In the metal processing industry emulsions are used in the form of coolants. Emulsions can be produced with different systems. In the following, the process of high-pressure homogenization is briefly compared to other common mechanical emulsification systems. To facilitate the selection of an emulsification system, the influence of the most important parameters of the emulsion formulation on the resulting mean droplet diameter in the most prevalent continuous emulsification systems is outlined. Subsequently, the most common high-pressure homogenization systems are discussed in detail. On the basis of data from the literature and own experimental results the described high-pressure homogenization systems will be compared regarding their attainable mean droplet diameter. It shows that homogenizers with a relatively simple geometry like the patented “combined orifice valve” (Kombi-Blende) attain the smallest mean droplet diameters. The advantage of the “combined orifice valve” compared to other high-pressure homogenization systems is not more efficient droplet disruption but rather more efficient droplet stabilization against coalescence immediately after the droplet breakup. The greatest research potential concerning the development of new high-pressure homogenization systems is still to be seen in improvements of droplet stabilization, i.e., the reduction of coalescence.

A Two-Compartment Fluidized Bed Reactor for CO2 Capture by Chemical-Looping Combustion

Abstract: Chemical-looping combustion (CLC) is a combustion method for a gaseous fuel with inherent separation of the greenhouse gas carbon dioxide. A CLC system consists of two reactors, an air reactor and a fuel reactor, and an oxygen carrier circulating between the two reactors. The oxygen carrier transfers the oxygen from the air to the fuel. The flue gas from the fuel reactor consists of carbon dioxide and water, while the flue gas from the air reactor is nitrogen from the air. A two-compartment fluidized bed CLC system was designed and tested using a flow model in order to find critical design parameters. Gas velocities and slot design were varied, and the solids circulation rate and gas leakage between the reactors were measured. The solids circulation rate was found to be sufficient. The gas leakage was somewhat high but could be reduced by altering the slot design. Finally, a hot laboratory CLC system is presented with an advanced design for the slot and also with the possibility for inert gas addition into the downcomer for solids flow increase.

CFD Simulation of Liquid Film Flow on Inclined Plates

Abstract: A two-phase flow CFD model using the volume of fluid (VOF) method is presented for predicting the hydrodynamics of falling film flow on inclined plates, corresponding to the surface texture of structured packing. Using the proposed CFD model the influence of the solid surface microstructure, liquid properties and gas flow rate on the flow behavior was investigated. From the simulated results it was shown that under the condition of no gas flow the liquid flow patterns are dependent on the microstructure of the plates, and proper microstructuring of the solid surface will improve the formation of a continuous liquid film. It was also found that liquid properties, especially surface tension, play an important role in determining the thin-film pattern. However, there are very different liquid film patterns under the action of gas flow. Thinner liquid films break easily, but thicker liquid films can remain continuous even at higher gas flow rates, which demonstrates that all factors affecting the liquid film thickness will affect the liquid film patterns under conditions of counter-current two-phase flow.

Utilization of Raw and Activated Date Pits for the Removal of Phenol from Aqueous Solutions

Abstract: Activated carbons prepared from date pits, an agricultural waste byproduct, have been examined for the adsorption of phenol from aqueous solutions. The activated carbons were prepared using a fluidized bed reactor in two steps; carbonization at 700 °C for 2 hours in N2 atmosphere and activation at 900 °C in CO2 atmosphere. The kinetic data were fitted to the models of intraparticle diffusion, pseudo-second order, and Lagergren, and followed more closely the pseudo-second-order chemisorption model. The isotherm equilibrium data were well fitted by the Freundlich and Langmuir models. The maximum adsorption capacity of activated date pits per Langmuir model was 16 times higher than that of nonactivated date pits. The thermodynamic properties calculated revealed the endothermic nature of the adsorption process. The uptake of phenol increased with increasing initial phenol concentration from10 to 200 ppm and temperature from 25 to 55 °C, and decreased with increasing the solution pH from 4 to 12. The uptake of phenol was not affected by the presence of NaCl salt.

State of the Art and Future Trends in CFD Simulation of Stirred Vessel Hydrodynamics

Abstract: Computational fluid dynamics (CFD) has become a widely used tool for analysing, optimising and supporting the design of mixing processes in stirred vessels. The present contribution gives a brief summary of the methods applied for numerically treating the power input by the impeller, such as empirical methods, the multiple frame of reference approach and unsteady methods using sliding or clicking meshes. Thereafter, recent developments and trends in the numerical computation of single phase flows in stirred vessels on the basis of DNS (direct numerical simulations), LES (large eddy simulations) and RANS (Reynolds-averaged Navier-Stokes) approaches are summarised. Since many operations in stirred vessels involve at least two phases, also the methods for modelling these flows, such as the two-fluid method and the Euler/Lagrange approach are briefly described and recent applications are reviewed. Finally, also own calculations for single-phase mixing and particle dispersion in a stirred vessel using the Euler/Lagrange approach are introduced emphasising some recent developments.

Biotreatment of industrial wastewater by selected algal-bacterial consortia

Abstract: A new approach for remediation processes in highly polluted environments is presented. The efficiency of algal-bacterial associations for the remediation of industrial wastewater of a pond in Samara, Russia, was investigated. After screening of algae and bacteria for the resistance to the wastewater the following strains were selected: the algal strains Chlorella sp. ES-13, Chlorella sp. ES-30, Scenedesmus obliquus ES-55, several Stichococcus strains (ES-19, ES-85, ES-86, ES-87, ES-88), and Phormidium sp. ES-90 and the bacterial strains Rhodococcus sp. Ac-1267, Kibdelosporangium aridum 754 as well as two unidentified bacterial strains (St-1, St-2) isolated from the collector pond. All the strains listed above were immobilized onto various solid carriers (capron fibers for algae; ceramics, capron and wood for bacteria) and used for biotreatment in a pilot installation. The results showed that the selected algae and bacteria formed stable consortia during the degradation of the waste, which was demonstrated for the first time for the green alga Stichococcus. Stichococcus and Phormidium cells attached to capron fibers with the help of slime and formed a matrix. This matrix fixed the bacteria and eukaryotic algae and prevented them from being washed off. A significant decrease in the content of the pollutants was observed: phenols were removed up to 85 %, anionic surface active substances (anionic SAS) up to 73 %, oil spills up to 96 %, copper up to 62 %, nickel up to 62 %, zinc up to 90 %, manganese up to 70 %, and iron up to 64 %. The reduction of the biological oxygen demand (BOD 25 ) and the chemical oxygen demand COD amounted to 97 % and 51 %, respectively.

Influence of Physical Properties on Drop Size Distribution of Stirred Liquid‐Liquid Dispersions

Abstract: An experimental investigation was carried out to analyse the influence of coalescence behavior on drop size distributions in stirred liquid-liquid dispersions. An endoscope measurement technique was applied that allowed the determination of drop sizes even with high volumetric dispersed phase fractions φ of up to 0.5. The influence of pH and addition of ions was studied by shaking and stirring experiments. For high coalescence rates, the results show self-similar drop size distributions independent of all other parameters. With low coalescence rates the Sauter diameter d 32 decreases and the distributions become narrower. When phase ratios were increased the common correlation d 32 ∼ (1 + const. (p) We -0.6 did not lead to a reliable description of the mean drop sizes due to coalescence effects.

Steering of Liquid Mixing Speed in Interdigital Micro Mixers – From Very Fast to Deliberately Slow Mixing

Abstract: Very fast mixing in the range of milliseconds as well as deliberately slow mixing was realized by specially adjusted interdigital micro mixers made of glass or stainless steel. The corresponding micro mixers are presented including experimental and theoretical investigations of the respective mixing process. Fast mixing was realized by combination of flow multilamination by interdigital microstructured feeding structures with geometric focusing. Details on the microfabrication, achievable throughputs and hydrodynamics are discussed. To prevent clogging of microsized feeding structures in the case of precipitation reactions, mixing was deliberately slowed down by separating the reactant solutions at the outlet by additional layers of inert liquids.

Solubility of CO2 in Aqueous Piperazine and its Modeling using the Kent-Eisenberg Approach

Abstract: A systematic investigation of the equilibrium solubility of CO2 in aqueous piperazine solutions was conducted in a double-jacketed stirred cell reactor The solubilities of CO2 in the solution were measured at 20, 30, 40, and 50 °C with CO2 partial pressures ranging from 04–95 kPa Generally the aqueous piperazine solution exhibits the same characteristics as conventional alkanolamines Increasing the CO2 partial pressure increases the gas loading, however increasing the temperature or concentration decreases the CO2 loading The values of the CO2 loading obtained confirm that the piperazine forms stable carbamates The equilibrium solubility data were analyzed using a Kent-Eisenberg approach Representation of the model is generally in good agreement with that of the experimental data, especially at high temperature

Microwave‐Assisted Heterogeneous Gas‐Phase Catalysis

Abstract: This article reviews microwave-assisted heterogeneous gas-phase catalysis. To date, this special means of non-classical energy input by microwave radiation is still a fringe area of catalysis research, and alternative reaction engineering in chemistry and chemical engineering. However, microwave-assisted heterogeneous gas-phase catalysis is expected to gain significant popularity in academia and industry in the near future. Experimental set-ups that have been described in literature are critically reviewed, and concepts for the design of improved experimental set-ups are provided in this article. Historical developments, current tendencies, and a short introduction to the theory of dielectric heating are discussed.

Product Design of Cohesive Powders – Mechanical Properties, Compression and Flow Behavior

Abstract: The fundamentals of cohesive powder consolidation and flow behavior are explained using a reasonable combination of particle and continuum mechanics. By the model stiff particles with soft contacts, universal models are presented which include the elastic-plastic and viscoplastic particle contact behavior with adhesion, load-unload hysteresis and thus energy dissipation, a history-dependent and a nonlinear adhesion force function. With this as the physical basis, incipient powder consolidation, yield and cohesive steady-state flow, consolidation and compression functions, compression and preshear works are explained. As an example, the flow properties of an ultrafine limestone powder are shown. These constitutive models are used to evaluate shear cell test results for apparatus design to ensure reliable powder flow. Finally, conclusions are drawn concerning particle stressing, powder handling behavior and product quality assessment in processing industries.

Effects of plant growth promoting rhizobacteria (PGPRS) on the biological nitrogen fixation, nodulation, and growth of Lupinus albus l. cv. multolupa

Abstract: The effects of five plant growth promoting rhizobacteria on the biological nitrogen fixation (BNF), nodulation, and growth promotion of plants of Lupinus albus cv. Multolupa were investigated. The plants were selected for their capacity to use 1-aminocyclopropane-1-carboxylic acid (ACC) as the sole source of nitrogen. Four strains belonged to the genus Pseudomonas (Luc 1, Luc 2, Luc 3, and Luc 4) and one (Luc 5) belonged to the genus Bacillus. Three patterns of inoculation were examined. In the first pattern, PGPRs were inoculated seven days before being inoculated with B. japonicum. In the second pattern, PGPRs and B. japonicum were co-inoculated, and in the last pattern, PGPRs were inoculated seven days after being inoculated with B. japonicum. The plants were sampled 30 and 45 days after being inoculated with B. japonicum (T1 and T2). In the first pattern of inoculation, Luc 5 significantly increased the biological nitrogen fixation compared to the control at the first sampling time, as did Luc 1 and Luc 4 at the second sampling time. In the second pattern of inoculation, Luc 5 negatively effected the biological nitrogen fixation at both sampling times. In the third pattern of inoculation, all PGPRs caused a decrease in the nitrogen content of the plants compared to the control. The results obtained according to the patterns of inoculation showed that the mechanisms of action of the effects and routes used by Gram-negative and Gram-positive strains were clearly different. Competition between PGPRs and B. japonicum, competition for the niches in the rhizoplane, production of auxins, and induction of systemic resistance (ISR) by the production of siderophores or by lipopolysaccharides present in the outer membrane (LPS) are discussed as probable reasons for the effects observed.

Coaxial Mixer Hydrodynamics with Newtonian and non-Newtonian Fluids

Abstract: The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter- and co-rotating mode were assessed with Newtonian and non-Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co-rotating mode were found to be a better choice for Newtonian and non-Newtonian fluids. The hybrid impeller-anchor combination was found to be the most efficient for mixing in counter-rotating or co-rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N js ) was also determined. It was found that N js had lower values with the impellers having the best axial pumping capabilities.

Kinetic Studies of the Electrochemical Treatment of Nitrate and Nitrite Ions on Iridium‐Modified Carbon Fiber Electrodes

Abstract: Electrochemical reductions of nitrate and nitrite ions in neutral solution were studied using an Ir-deposited carbon fiber electrode. The objective of the study was to set up a process to remove nitrate and nitrite ions from industrial and municipal wastes as well as from the nitrate and nitrite ion enriched water supplies. Since nitrate and nitrite ion reduction kinetics is very slow on plain carbon, the iridium-modified fibers showed a significant reduction of nitrate and nitrite ions. Nitrogen and ammonia were identified as the two major gaseous products of the reduction process. A first-order inhibition kinetics model is proposed and was used to analyze the nitrate and nitrite ion reduction kinetics. The reduction rates of nitrate and nitrite ions were favored at higher cathode potential (cf. -950 mV and -850 mV) in a solution of pH = 7.0 with hydrogen evolution efficiency increasing with cathodic potential. A simple model for the batch re-circulation process was developed for the reduction of nitrate ion at surface-modified fiber electrode. There was a good agreement between the model predictions and experimental results.

Silo Discharge: Measurement and Simulation of Dynamic Behavior in Bulk Solids

Abstract: This paper deals with the experimental investigation and the numerical simulation of silo discharge processes, including dynamic interactions between the silo filling and the elastic silo walls. The discharge process is described by a system of nonlinear differential equations. Via the Finite Element Method (FEM) based on an EULERian reference frame, the deformation rate, the velocity field, the porosity, and the stress distribution can be calculated without the need of re-meshing the FE-grid. To compare simulation results with measured data, the numerical simulation examples are chosen to be similar to an experimental test-silo of the Institute of Mechanical Process Engineering at the Technical University of Braunschweig. Optical measurement techniques are applied to investigate the flow profile, and load cells on the silo walls register the stress evolution, e.g., a stress peak (switch) moving from the outlet to the transition from hopper to shaft.

Modular simulation of fluidized bed reactors

Abstract: Simulation of chemical processes involving nonideal reactors is essential for process design, optimization, control and scale-up. Various industrial process simulation programs are available for chemical process simulation. Most of these programs are being developed based on the sequential modular approach. They contain only standard ideal reactors but provide no module for nonideal reactors, e.g., fluidized bed reactors. In this study, a new model is developed for the simulation of fluidized bed reactors by sequential modular approach. In the proposed model the bed is divided into several serial sections and the flow of the gas is considered as plug flow through the bubbles and perfectly mixed through the emulsion phase. In order to simulate the performance of these reactors, the hydrodynamic and reaction submodels should be integrated together in the medium and facilities provided by industrial simulators to obtain a simulation model. The performance of the proposed simulation model is tested against the experimental data reported in the literature for various gas-solid systems and a wide range of superficial gas velocities. It is shown that this model provides acceptable results in predicting the performance of the fluidized bed reactors. The results of this study can easily be used by industrial simulators to enhance their abilities to simulate the fluidized bed reactor properly.

Macro- and Micromixing in a Taylor-Couette Reactor with Axial Flow and their Influence on the Precipitation of Barium Sulfate

Abstract: A new set-up for precipitation experiments capable of independent adjustment of micromixing and macromixing conditions is presented. The setup consists of a Taylor-Couette (TC) reactor serving as the reaction zone and an external loop where the slower stages of precipitation processes take place. Micromixing in the TC reactor has been investigated with a chemical reaction system and with PIV-measurements. Micromixing times range between 6·10–3 and 8·10–2 s. Tracer experiments reveal the macromixing performance of the whole set-up which has been compared with the behavior of ideal reactors. Precipitation experiments with barium sulfate show some influence of micromixing intensity on the particle size and of macromixing on particle morphology.

A Theoretical Approach to Pressure Drop across Cyclone Separators

Abstract: Based on investigation of the flow pattern in cyclone separators, a new theoretical model was developed for the prediction of pressure drop across cyclone separators. This model includes the effect of the geometrical dimensions and flow parameters, and assumes that the total pressure drop consists of four main partial pressure drops due to gas expansion at the separator entrance, wall friction within the separator, swirling motion of the gas, and gas flow through the outlet pipe. The availability of the method is verified by the comparison of calculated values with experimental data and with other models for different dimensions of cyclones.

Investigation of Fluid and Coarse‐Particle Dynamics in a Two‐Dimensional Spouted Bed

Abstract: The aerodynamics of particles and gas flow in a two-dimensional spouted bed (2DSB) with draft plates is investigated with the aid of the discrete element method. The geometry of the 2DSB with draft plates is set as close as possible to the experimental apparatus of Kudra [1] and Kalwar [2]. The physical properties of the coarse particles are similar to those of shelled corn. The calculated minimum spouting velocity and pressure drop agree well with the correlations of Kudra [1] and Kalwar [2]. In the spout region, the particle vertical velocities are found to decrease as the height increases. The fluid velocity in the downcomer region decreases as the superficial gas velocity increases. The particle circulation rate increases when the friction coefficient decreases or the separation height increases. At the minimum spouting velocity, the bed height does not affect the particle circulation rate in the 2DSB with draft plates. The draft plates not only reduce the minimum spouting velocity and pressure drop but also increase the maximum spoutable bed height. The effect of taking out the draft plates on the spouting phenomenon is investigated and the effect of putting in a deflector on the possible breakage of the particles is also estimated.

Semi‐Empirical Equations for the Residence Time Distributions in Disperse Systems – Part 1: Continuous Phase

Abstract: Residence time distributions (RTD) are often described on the basis of the dispersion or the tanks in series models, whereby the fitting is not always good. In addition, the underlying ideas of these models only roughly characterize the real existing processes. Two semi-empirical equations are presented based on characteristic parameters (mean, minimum, maximum residence time) and on an empirical exponent to permit better fitting. The determination of the parameters and their influence on the RTD are discussed. The usefulness of the models is shown in this first part for single-phase systems and for the continuous phase of multiphase systems using data from literature for laminar and turbulent flows in different apparatuses. A comparison with the results of other models is also done.

Large Eddy Simulation of Turbulent Flow in a Rushton Impeller Stirred Reactor with Sliding-Deforming Mesh Methodology

Abstract: The unsteady turbulent flow in a mixing vessel stirred by a Rushton impeller is predicted using the Large Eddy Simulation technique. The interaction between the moving impeller and the static baffles is accounted for explicitly through a sliding-deforming mesh methodology, thus, eliminating approximations used to account for the effect of the moving impeller. Large-scale structures associated with the trailing vortices are assessed via the vorticity and the turbulent kinetic energy distributions. The phase-resolved predictions are compared with measurement data obtained by laser-Doppler anemometry and favourable agreement is reported both for mean as well as turbulence quantities.

Modeling of the Wall Effect in Packed Bed Adsorption

Abstract: A model developed for catalytic packed bed reactors and consistently accounting for the influence of the tube wall on porosity, flow and transport phenomena is used in order to simulate the operation of packed bed adsorbers. By comparison of simulation results with reduced versions of the model the influence of the wall on the adsorber performance is worked out and found to be major at low ratios between tube and particle diameter. The interaction between maldistribution, thermal effects and intraparticle resistances in such adsorber tubes is discussed.

New developments in chemical engineering for the production of drug substances

Abstract: The pharmaceutical industry is moving towards a profitability gap between increasing costs and decreasing prices. Finally, management has understood that mergers and acquisitions, high throughput screening, and biotechnology alone will not save the companies' earnings. Therefore, classical approaches like the optimization of production technologies for drug substances, that might help to increase profitability, are receiving increasing attention. This paper shows how the combination of innovative components will guide the way to very efficient and cost-effective production. The first component is the design and manufacturing of production facilities. The second component is a process streamlining of the production process. The key technologies discussed here are process control and miniplant technology. For these technologies a brief outlook on future trends is given.

Adsorption Equilibrium and Adsorption Kinetics: A Unified Approach

Abstract: Conventional methods for the characterization of adsorption systems (determination of equilibrium and kinetic parameters) have been discussed. It is shown that the kinetic parameters determined by conventional methods are completely inconsistent with the equilibrium parameters. This inconsistency is due to the application of completely different models for equilibrium and kinetic study. In the present study adsorption is viewed as a Langmuir type physico-chemical reversible process and a three-parameter model is proposed which describes an adsorption system from both equilibrium and kinetic viewpoints. The model satisfactorily describes the kinetic and the equilibrium data reported by previous authors.

A Semi‐continuous Process for the Synthesis of Methyl Carbamate from Urea and Methanol

Abstract: A semicontinuous process for the synthesis of methyl carbamate from urea and methanol was investigated in the autoclave without the catalyst. Some significant parameters were determined in terms of the methyl carbamate yield. The optimal reaction conditions were found at an initial molar ratio of methanol/urea of 6:1, a reaction temperature of 423 K, a flow rate of fresh methanol at 4 mL/min, a stirring speed of 800 rpm and a reaction time of 6 hours, respectively. A MC yield of 98.7 % was obtained at the optimal reaction conditions. Furthermore, the kinetics of this reaction were researched and the reaction activation energy was obtained as 110.498 kJ/mol. It was demonstrated that removing methanol containing ammonia from the autoclave and replacing it with continuously feeding fresh methanol resulted in a higher reaction rate and a high MC yield.

Large Bubble Sizes and Rise Velocities in a Bubble Column Slurry Reactor

Abstract: The results are reported of an experimental study of the gas holdup, EG, large bubble diameter, d Lb , and large bubble rise velocity, V Lb , in a 0.1 m wide, 0.02 m deep and 0.95 m high rectangular slurry bubble column operated at ambient temperature and pressure conditions. The superficial gas velocity U was varied in the range of 0-0.2 m/s, spanning both the homogeneous and heterogeneous flow regimes. Air was used as the gas phase. The liquid phase used was C 9 -C 11 Paraffin oil containing varying volume fractions (e s = 0, 0.05. 0.10, 0.15, 0.20 and 0.25) of porous catalyst (alumina catalyst support, 10% 0.05 and U > 0.1 m/s. The measured large bubble rise velocity V Lb agrees with the predictions of a modified Davis-Taylor relationship.

A Multi‐Block Approach to Obtain Angle‐Resolved PIV Measurements of the Mean Flow and Turbulence Fields in a Stirred Vessel

Abstract: Two-dimensional Particle Image Velocimetry (PIV) measurements have been used to characterize the complex turbulent flow generated by a T/3 45° pitched-blade down-flow turbine, operated at Re 5 . 10 4 , in a fully turbulent stirred vessel. To maintain high spatial resolution when viewing the whole vessel, a multi-block approach has been developed, which combines data from different fields of view into a composite flow map. Using 500 measurements of instantaneous u and v velocity fields, angle-resolved mean velocity maps and turbulence properties, such as the RMS velocities and the turbulence kinetic energy, have been estimated near to the blade, as well as in the bulk of the vessel, at a spatial resolution of between 1 and 2 mm. Vorticity maps have also been calculated to help visualize the trailing vortex structures close to the impeller blades and integral length scales have been estimated from the two-dimensional spatial auto-correlation function. It is shown than the common assumption that the integral length scale is about half the blade width is an overestimate close to the impeller and an underestimate far from the impeller.

Optimal Production Planning for Chemical Processes under Uncertain Market Conditions

Abstract: Due to lack of a systematic reliability analysis, intuitive decisions can often be made in production planning under uncertainty. These decisions will lead to either conservative or aggressive production. In this work, we propose a novel analysis and optimization framework to address this problem, with which the relationship between the profitability and reliability of a planned operation can be quantified. By using probabilistic programming, the solution of the problem provides comprehensive information on the economical achievement as a function of the desired confidence level of satisfying process constraints. The feasible region will shrink and the profit will decrease when increasing the confidence level. For complex plant operations under multiple uncertainties, the sources of risk that have the most significant impacts on the profitability can be identified. Through this approach, an optimal as well as reliable decision for operations can be made, from which a suitable compensation between the profit and the probability of constraints violation can be received. The approach is applied to three problems of production planning under uncertainty and various issues in planning these operations are discussed.