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.     

Characterization of the Residence Time Distribution in Spray Dryers

In this work it is presented a study on the residence time distribution (RTD) of particles in a co-current pilot-plant spray dryer operated with a rotary atomization system. A nuclear technique is applied to investigate the RTD responses of spray dryers. The methodology is based on the injection of a radioisotope tracer in the feed stream followed by the monitoring of its concentration at the outlet stream. The experiments were performed during the drying of aqueous suspensions of gadolinium oxide. The RTD responses obtained experimentally presented good reproducibility, indicating that the technique applied is well suited to investigating fluid-dynamics of spray dryers. In addition to the experimental investigation, a mathematical model was used to describe the RTD experimental curves.     

Mean residence time of gas in mechanically agitated gas–liquid contactors

In the present study of gas–liquid contactors, mean residence/contact time was calculated from knowledge of superficial velocity and the gas phase hold-up, for various gas rates and impeller geometry and speeds, and compared with values obtained from RTD measurements. A new correlation, involving Flow Number, Froude Number, system geometry and the physical properties, is proposed. This uses the authors data and those available in literature.     

Shallow Linear Action Graphs and their Embeddings

Action calculi, which generalise process calculi such as Petri nets, π-calculusand ambient calculus, have been presented in terms of action graphs. We here offer linear action graphs as a primitive basis for action calculi. This paper presents the category of embeddings of undirected linear action graphs without nesting, using a novel form of graphical reasoning which simplifies some otherwise complex manipulations in regular algebra. The results are adapted in a few lines to directed graphs. This work is part of a long-term search for a uniform behavioural theory for process calculi. Received October 2000 / Accepted in revised form April 2001     

Spare parts inventory management with demand lead times and rationing

We study an inventory system that consists of two demand classes. The orders in the first class need to be satisfied immediately, whereas the orders in the second class are to be filled in a given demand lead time. The two classes are also of different criticality. For this system, we propose a policy that rations the non-critical orders. Under a one-for-one replenishment policy with backordering and for Poisson demand arrivals for both classes, we first derive expressions for the service levels of both classes. The service level for the critical class is an approximation, whereas the service level for the non-critical class is exact. We then conduct a computational study to show that our approximation works reasonably, the benefits of rationing can be substantial, and the incorporation of demand lead time provides more value when the demand class with demand lead time is the critical class. The research is motivated by the spare parts service system of a major capital equipment manufacturer that faces two types of demand. For this company, the critical down orders need to be satisfied immediately, while the less critical maintenance orders can be satisfied after a fixed demand lead time. We conduct a case study with 64 representative parts and show that significant savings (as much as 14% on inventory on hand) are possible through incorporation of demand lead times and rationing.     

The Gas-to-Particle Heat Transfer and Hydrodynamics in Spouted Bed Drying of Sawdust

This article presents experimental results for spouted bed drying of sawdust, carried out in a full-scale as well as in a laboratory-scale dryer using air as well as steam as drying media. The aim is to present design parameters for a spouted-bed sawdust dryer that can be used by the industry in designing full-scale dryers. A hydrodynamically stable spouted jet spouted bed was obtained. The heat transfer characteristics of the bed were represented in terms of a volumetric heat transfer coefficient (VHC). When sawdust is dried in a spouted bed, the mean VHC is increasing up to fiber saturation level (20-25% wb) from 40 to 110 W/m³ K. The VHC decreases with the residence time and with an increased static bed height. Gas temperature profiles are also presented for the bottom part of the drying chamber.     

Optimal size,hydraulic retention time and volatile solids loading rate of biogas unit using water hyacinth

With a view to evaluate the effects of hydraulic retention time and volatile solids loading rate on methane production using water hyacinth, experiments were conducted in a 160 dm³ capacity, well-mixed continuous digestion unit at ambient temperature. The optimal design of biogas plant using water hyacinth was elucidated, to provide a unit giving a maximum methane yield of 0.16 nm³ kg^?1 volatile solids added, which was 60% greater than the conventional plant using cowdung. The calculations of optimal design factors were based on reactor size, hydraulic retention time and volatile solids loading rate; considerations were made of capital cost, running costs and operational revenue.