Synthesis of Rice Processing Plants. I. Development of Simplified Models

This article, the first of three articles on the synthesis of rice processing plants, focuses on the development of simplified mathematical models necessary for use in optimizing rice processing plants. The second concentrates on the optimal synthesis of a rice plant and the third on the sensitivity of the optimization to uncertainty in model parameters. Existing models for rice processing unit operations are not suitable for flowsheet optimization and new models need to be developed to overcome numerical difficulties that occur in optimization applications, specifically in mixed integer nonlinear programming (MINLP) applications. Simplified models of the drying, cooling, and tempering units are developed. In addition head rice yield models, used as a quality indicator, energy consumption, and economic models were also developed. Naturally, the new models exhibit some mismatch with respect to the existing models from which they were developed. However, a sensitivity analysis, presented in Part III, has shown that the optimal flowsheet structure was not sensitive to a lack of fit between the simplified and complex models. The simplified models were found adequate to be appropriate for use at the synthesis stage.     

Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

A Model for Through Drying of Tissue Paper at Constant Pressure Drop and High Drying Intensity

A mathematical model for through drying of paper at constant pressure drop was developed. The model is based on physical properties; hence, basis weight, pressure drop, drying air temperature, pore size distribution, initial gas fraction, and tortuosity are important input parameters to the model. The model was solved for different combinations of the variables basis weight, drying air temperature, and pressure drop corresponding to industrial conditions and the results were compared with data from bench-scale experiments. The simulations show that the drying rate curve is very sensitive to the air flow rate and that correctly modeling the correlation between pressure drop and air flow rate is the most important factor for a successful model for through drying. The model was tuned by adjusting the parameters initial gas fraction and tortuosity in order to give the best possible fit to experimental data. For a given basis weight and pressure drop, different drying air temperatures resulted in relatively constant values of the fitted parameters. This means that the model can well predict the effects of changes in drying air temperature based on a tuning of the model performed at the same basis weight and pressure drop. However, for a given basis weight, an increase in pressure drop yielded fitted parameters that were somewhat different; i.e., a lower initial gas fraction and a higher tortuosity, a change that increases the resistance to air flow. This implies that the correlation between pressure drop and air flow rate in the model does not quite capture the nonlinear relationship shown by the experiments.     

Evaporation and Evolution of Suspended Solution Droplets at Atmospheric and Reduced Pressures

Thermal history and solute precipitation behavior of suspended solution droplets of sodium chloride (NaCl), magnesium sulphate (MgSO₄), and zirconium hydroxychloride (ZrO(OH)Cl) evaporating at atmospheric and reduced pressures are studied. Experimental measurements on the variation of droplet diameter, solution concentration, and temperature during the evaporation period are presented and discussed. The results of solute precipitation behavior in solution droplets observed under an optical microscope are displayed and discussed. Results indicate that reducing the pressure (∼ 33 kPa) results in a change in the solution droplet evaporation rate, but the thermal histories of a particular solution droplet are similar at the atmospheric and reduced pressures. At atmospheric and reduced pressures used in this study, the d² law for solution droplets is valid at early stages of the evaporation and before the solute precipitation initiates. Drying of MgSO₄ and ZrO(OH)Cl solution droplets results in the formation of spherical particles, whereas drying of spherical NaCl solution droplets results in the formation of cubic particles.     

Effect of the Treatment Temperature on the Surface Drying Set of Sugi Boxed-Heart Square Timber

High-temperature and controlled humidity treatment before drying has proven to be highly effective in preventing surface checks by forming drying sets in the surface layer of boxed-heart square timber in Japan. In this study, we examined the differences of the surface drying sets on sugi timber under different treatment temperatures. As a result, the width of a surface check after drying was much smaller at a treatment temperature of 120°C than at 80°C, and this indicates that the drying set with 120°C treatment would be larger than that with 80°C treatment. Also we observed that treatment temperature had a greater effect on the drying set as the drying advanced.     

Evaluation of Textile Bobbins Drying Processes: Experimental and Modelling Studies

Drying of textile bobbins was carried out on two kinds of laboratory-scale dryers: in a cross circulation drying rig, atmospheric pressure heating air is used, while in the through circulation drying apparatus, the heating air is pressurized before the drying process takes place. In both cases, a bobbin was fitted with seven thermocouples, placed in a plane normal to the bobbin axis but at different radial distances, in order to provide temperature data during the drying process. In cross circulation drying, plots of temperature against time indicated the presence of two moving fronts, one starting from inside the bobbin, another from the outside, while in through circulation drying, similar plots showed the presence of an evaporation front, moving from inside the bobbin to the outside. In both canes, numerical models were developed to simulate the drying processes.     

Integration of a Malt Drying Model into a Malt Plant Scheduling Software

Malting is a very intensive, energy-consuming process and, from the point of view of energy, green malt drying is one of the most important operations. Double-deck kiln drying, a variant of single-deck kiln drying, is the most commonly used process, but it is usually manually controlled under empirical control actions. These are the reasons why a research project was carried out based on the computer modeling of these process operations including a software tool named CIMFOOD. A knowledge-based system (KBS) allowing the entire processing-plant dynamic behavior simulation and scheduling concerning thermal energy requirements was developed.     

The Change of Body Temperature During Convective Drying of Cube-Shaped Apple Pieces

When using the convective drying method, the mass transfer between drying air and moisture diffusion of the material is very important. The moisture moves inside the material because of the volume change caused by the increased temperature. This movement is additionally affected by the texture of the material. According to the research dealing with colloid capillary porous texture of vegetables and fruit, the humidity migration inside the material occurs in both fluid and steam condition at the same time. This migration is stimulated by the heating and decreasing humidity along with the flow. In this research, winter varieties of apples (Jonathan, Golden Delicious, and Idared) were studied by heating of a 20 × 20 × 20 piece of apple with a thermocouple in it. On the basis of the measurements it can be stated that for the fruits with a high percentage of moisture (75-90%), when making the drying condition, the moisture gradient is influenced by the fractured cells of the cut area. It was found that the variety of apple is very important in relation to the heating and water loss gradient. According to the results, the wet volume change due to the heating highly influences the water loss. The models that describe the temperature of the material have a connection with the water loss.     

Comparison of Two Drying Schedules for European Hophornbeam (Ostrya carpinifolia Scop.) Lumber

Two types of conventional kiln-drying schedules (mild and harsh) based on moisture content (MC) were compared with regard to time, drying quality, and energy cost. The results were evaluated according to the classification of the European Drying Group. Proper drying periods of mild and harsh schedules were found to be 550 and 514 h, respectively. Evaluations in terms of drying quality indicated that better results were achieved with the mild schedule, especially when comparing drying defects and final MC. From an energy efficiency point of view, the harsh schedule, by saving 36 h of drying time, reduced electricity by 594 KWh and was therefore found to be $65 more profitable in this trial.     

A Mass Transport Model for Drying Wood under Isothermal Conditions

Mass transport in wood during drying can have different mechanisms at different periods of drying. Depending on the current moisture content (MC) and the structure of the wood, the driving forces for the mass transport are essentially different. Above the fiber saturation point (FSP), the lumens are partially saturated and the transport of liquid (free) water occurs as a consequence of capillary action. On the other hand, below the FSP, bound water within the cell walls is conveyed by diffusion, and water vapor in the lumens moves under influence of pressures gradient. Based on these considerations, a unified model is presented that takes into account the transport of the different moisture phases. Simulation of the drying of a Norway spruce sample at 50°C from about 135 to 7% MC is carried out using the finite element method (FEM). Comparison between the simulated average MC and the experimental observations obtained from X-ray computed tomography (CT) shows reasonable agreement. Possible simplifications in the model are briefly discussed as well as some aspects of the numerical implementation. Finally, the influence of absolute permeability on the average MC is studied.