Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

DRYING OF SHRINKING MATERIALS : MODELLINGS WITH SHRINKAGE VELOCITY

An attempt is proposed to modelize the coupling effects between heat transport, mass transport and solid shrinkage during the drying of like gels products.

A special attention is laid upon the different ways to determine the solid displacement.

Some experimental results are presented to validate the modelling approach.     

EVALUATION OF PENG ROBINSON EQUATION OF STATE IN CALCULATING THERMOPHYSICAL PROPERTIES OF COMBUSTION GASES

A set of simple equations of the thermodynamic and transport properties of the combustion gases of a gas turbine have been derived based upon the critically evaluated data and two equations of state: The virial equation of state and Peng-Robinson (PR) equation of state.

The properties which have been considered were, density, specific heat at constant pressure, enthalpy, entropy, viscosity and thermal conductivity.

The temperature range was (200-2600 K) theoretically while the pressure range was (0.3-1.2 MPa).

A computer program, to evaluate the departure of thermophysical properties using virial and PR equations of state, was used.

The Peng Robinson (PR) equation of state gave better estimated accuracy than the virial equation of state especially in evaluating the departure of thermodynamic properties.     

HEAT AND MASS TRANSFER DURING DRYING OF GRANULAR PRODUCTS BY COMBINED CONVECTION AND CONDUCTION

Numerical simulation of grain drying in a vertical cylindrical bed has been carried out with an imposed hot air flow and a conductive heat flux at the wall.

The model equations are numerically solved using a finite volume method. The numerical simulation gives the time and space evolution of temperature when the lateral area of the cylinder is heated by a constant density flux and a constant temperature. The influence of different parameters (essentially the ratio of heat flux to the heat capacity of flow, and the dryer geometry) on the relative moisture content and the drying time is examined.     

SIMULATION OF TRANSPORT DYNAMICS IN FLUIDIZED-BED DRYERS

A mathematical model for predicting three-dimensional, two-phase flow, heat and mass transfer inside fluidized-bed dryers has been developed. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum and energy for both phases inside the dryer, and is coupled with correlations concerning interphase momentum-, heat-, and mass-transfer.

It is shown that the model can predict the most important engineering aspects of a fluidized-bed dryer including pressure drop, particle holdup, temperature distribution in both phases as well as drying efficiency all over the fluidized-bed. Plug-flow conditions are predicted for the gas phase, while back-mixing is predicted for the particles.

The effect of particle mass-flow-rate on fluidized-bed dryer performance is evaluated. It is shown that the lower the particle mass flow-rate, the more intense the horizontal moisture gradients, while the higher the particle rate the more uniform the moisture distribution throughout the bed.     

CONTROL OF A PULSED LIQUID-LIQUID EXTRACTION COLUMN BASED ON A MULTILEVEL SYSTEM OF AUTOMATA

This paper presents the real-time application of the learning control theory to the control of a chemical pilot plant: a pulsed liquid-liquid extraction column.

The behaviour of an agitated liquid-liquid extraction column can be related to random mechanisms such as the phenomena of droplets breakage and coalescence. Previous studies on hydrodynamic and mass transfer aspects showed that a pulsed liquid-liquid extraction column had an optimal behaviour for operating conditions close to flooding. These results led to choose the following strategy to control the column in its optimal behaviour zone:

- the measure of the conductivity of the liquid medium below the distributor which gives a good information about flooding, is the controlled variable

-the pulse frequency is the control action.

The learning control algorithm is based on a multilevel system of automata which operates in a random environment. By means of an evaluation unit of the performances of the column which generates either penalty (inaction) or reward on the basis of heuristic rules, the automaton chooses a value of the pulse frequency. This approach is essentially connected to artificial intelligence in so far as human knowledge on the plant is included in these rules.

This algorithm has been implemented on a microcomputer for control purposes. The experimental results presented show the good performances of the approach.     

AN ANALYSIS OF CELLULAR FLOW OBSERVED ON THE INTERFACE OF A PARTIALLY FORMED DROPLET†

In [16], during an experiment designed to model the internal circulation of a forming droplet, secondary surface flows were observed on the droplet interface.

After summarizing the experimental results of [16], we present one possible mechanism, based on the surface surfactant mass transport equation of Levich and the surface stress-strain boundary conditions at a free surface, that provides a good qualitative explanation of the origins and the nature of the secondary motion observed in [16]. The critical hypotheses in this mechanism are that the normal component of ihe vorticity at the free surface is determined primarily by the components of the velocity field tangential to the level lines of the surface surfactant density, near the maxima and minima of that density function and that the normal component of the fluid stress does not vanish at such points.

The consequent analysis of the mass transport equation in the interface shows that the resulting surface motion may be viewed as arising from a resonance phenomenon analogous to the forced vibrations of a spring at resonance.

The effects of adsorbtion-desorbtion and surface dilational viscosity may be incorporated in this mechanism. A method for the experimental measurement of surface dilational viscosities is proposed.     

GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.     

VACUUM DRYING OF OAKWOOD :MOISTURE STRAINS AND DRYING PROCESS

After presenting the characteristics and the data acquired in an industrial evacuated kiln, a simplified analysis of heat and mass transfers is proposed. This analysis is based on the existence of a evaporization front determining two zones in the longitudinal direction :

-a dried zone in which moisture is less than 30 %

-a wet zone in which moisture is still at its initial value.

Such a hypothesis allows to study transfers transversally first, then longitudinally. Both equation systems ore linked by conditions of continuity for mass and energy.

This study allows to determine the shapes of the temperature and pressure curves in the longitudinal direction. The linearity of the variation of the average drying velocity versus the average moisture content of the board is also proved. Finally, the modeling of mechanical phenomena thanks to a finite element program shows the rupture zones appearing during the drying process.     

STEAM DRYLNG OF WOOD FUELS

The objective of this work is to investigate some of the important aspects in the design of a steam band dryer for wood fuels. For this purpose the drying of the material in a bench-scale fixed bed dryer has been studied.

Drying times and thermal efficiencies for experiments conducted under different conditions are compared. The investigated materials are soft-and hardwood chips and softwood bark.

The thermal efficiency, the part of the sensible heat which is used during one passage of the steam through the bed, increases with increasing mass load (mass of dry matter per unit area) and with decreasing steam mass flux. At a mass load of 30 kg/m the thermal efficiency is about 0.85 even at steam mass fluxes as high as 0.6 kg/m² s (1.2 m/s). The thermal efficiency proves to be almost independent of pressure and temperature of the steam.

Due to the very inhomogeneous materials the steam mass flow distribution was uneven. This causes a decreased thermal efficiency. When bark     

DYNAMICS OF FRACTIONATORS WITH STRUCTURED PACKING

A generalized dynamic mode! of a distributed staged (packed) fractionator is developed in this work. In particular we consider the dynamics of fractionators which employ structured packings as a means of achieving mass and heat transfer in multi-component systems.

The mathematical model is described by a large set of partial and ordinary differential equations coupled with non-linear algebraic constraints (PODAEs). These equations arise from the mass and energy balances on a distributed column-section together with the fluid dynamic relations. A computational algorithm is developed which employs a polynomial approximation leading to a large differential-algebraic equation (DAE) system. This is solved using standard implicit DAE algorithms.

In this work, the liquid holdup and transfer coefficients (both mass and heat) are computed from established correlations and detailed thermodynamic relations. This differs from most of the previous work reported, which used very simple correlations based on a single variable such as liquid or vapour rate. The results show that the more rigorous computation of transfer coefficients is essential to the veracity of the model.

The model has been applied to the case of an industrial depropanizer which uses a Mellapak 250Y structured packing. The generalized model can be used to study the control and optimization of such fractionators, which are becoming more prolific in the petroleum and related industries.     

Fracture Toughness of Adhesive Joints

To define the influence of the processing variables on the resistance of epoxy joints to brittle crack extension during short loading times, the fracture toughness, g_ic, of the joints was measured as a function of the following variables:

1. Hardener type (TEPA vs. HHPA)

2. Ratio of hardener to resin content

3. Post-cure temperature

and 4. Joint geometry (thickness and width)

It was found that the toughness of the TEPA hardened system varied by a factor of four-to-one as the ratio of hardener to resin content and post-cure temperature varied within what might be considered reasonable limits for manufacturing. The toughness of the HHPA hardened system varied only over the middle half of this same range.

For both systems, toughness increased with joint thickness over the range of 2 to 50 mils.     

SUBLIMATION OF PURE SUBSTANCES IN GAS FLUIDIZED BEDS AT ATMOSHPERIC PRESSURE.

This paper deals with the sublimation of large bodies, or “objects”, made up from a pure substance in a bubbling gas fluidized bed of considerably smaller particles, or “fines”. The influence of such parameters as the gas velocity, the bed temperature, the size and the adsorption capacity of the fines has been investigated.

The results obtained clearly show that the rate of sublimation in fluidized beds is far higher than in air alone. It increases with increasing bed temperature, decreasing particle size, increasing powder mass capacity, and roughly varies as a parabolic function of time. It has also been observed that the temperature difference between the bed and the object surface, or “temperature depression”, depends on the fines characteristics as well as on bed temperature, but is independent of gas velocity when good solid mixing conditions are achieved.

Bed-to-object heat and mass transfer coefficients have been deduced from data points and attempts have been made to provide a reasonable theory to account for them. After a complete examination, the idea of interpreting transport phenomena based on a well-adapted “surface renewal model” has been proposed.     

A Control-Volume procedure compared with the Finite-Element method for calculating Stress and Strain during Wood Drying

This paper proposes a suitable method for calculating drying stresses. This is an application of the finite element method (FE) and the so-called control volume (CV) method. The latter has been chosen because most of coupled heat and mass transfer codes are based on CV.

A parallel between the resulting formulation and a particular case of FE method (quadrilateral four-nodes element and Galerkin's method) has been established Both analytical expressions and numerical results were compared. Furthermore, it is shown how to choose interpolation coefficients in CV procedure in order to get exactly the results obtained with FE.

Such a stress calculation has been added to the code TRANSPORE in order to obtain a complete drying code which, in addition to heat and mass transfers, solves stress and strain due to shrinkage, Interesting and promising simulations of non-symmetric convective drying are presented. Indeed, for this drying configuration, the stresses induce a global curvature of the section.     

ON THE INFLUENCE OF SEVERE INTERNAL DIFFUSIONAL LIMITATIONS ON OPTIMUM TEMPERATURE OPERATIONS CRITERION AND POLICIES IN DEACTIVATING FIXED-BED AND BATCH REACTORS

During the forming of glass articles by a variety of different processes, it is important to be able to accurately measure the temperature of the glass. Also, to be practical for production applications, the temperature measuring technique must not interfere with the process or disturb the product. Only infrared radiation pyrometry is capable of meeting these requirements.

Narrow-band radiation pyrometers are non-contacting sensors that (depending on the operating wavelength) either measure the surface temperature or some weighted average of the surface and internal temperatures of semi-transparent glass objects without significantly affecting the product or its heat exchange with the environment. When attempting pyrometer temperature measurements on glass, it must be recognized that the incident radiation originates not only from the surface, but also from the interior which may be at a different temperature. However, a knowledge of the directional spectral volume emissive power of the glass object can be used to determine a "best" operating wavelength for the desired results and/or to help interpret indicated temperature measurements.

A sophisticated mathematical model of coupled radiation and conduction heat transfer in glass has been formulated to calculate the apparent temperature indicated by a hypothetical narrow-band infrared pyrometer receiving radiation emitted by glass plates of specified thickness and non-uniform temperature distribution. These results are presented for a wide range of operating wavelengths, covering the three distinct regions of the transmission spectrum of a typical soda-lime-silica glass.     

ATMOSPHERIC CONTACT DRYING OF GRANULAR BEDS WETTED WITH A BINARY MIXTURE

When regarding the atmospheric contact drying of granular beds wetted with a liquid mixture, both the drying rate and the selectivity of the process, i.e. the change of moisture composition, are of interest. The batch drying of a free flowing ceramic substance, wetted with a 2-propanol-water mixture, is investigated in a rotary dryer with heated wall and air flow.

The theoretical analysis is based on physical models for heat and mass transfer, moisture migration and particle transport, which are presented in examples.

The experimental and theoretical results show that higher selectivities can be achieved by reducing the particle size because of the lower liquid-phase mass-transfer resistance. An increase of the rotational speed leads to a higher drying rate with slightly decreased selectivity if the particles are sufficiently small, since contact heat transfer is enhanced.     

DRYING OF CARROTS. I. DRYING MODELS.

Three models of different complexity are proposed to describe the falling rate period of the carrot drying process with shrinkage. A moving or fixed boundary problem as well as a constant or local moisture and temperature dependent effective diffusivity are considered. The moving boundary problem is solved by an explicit finite difference method. Heat transfer coefficient and effective diffusivity identification were carried out. The results of the heat transfer coefficient show a good agreement with other sources. Using experimental data and the models. describing the heat and mass transfer three different expressions for the effective diffusivity are established. Two of them are only temperature dependent considering or not particle shrinkage. The third one takes into account temperature and local moisture as well as shrinkage.

Drying of foods is a complicated process involving simultaneous coupled heat and mass transfer phenomena which occur inside the material being dried (Chiang and Petersen, 1987). Several models are found in the literature, representing mass and energy transfer which take place during food drying (King, 1968; Sokhansanj and Gustafson, 1980). Usually, approximate solutions are obtained with these     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

HEAT TRANSFER IN TRICKLE-BED REACTORS

The mechanism of radial heat transfer in two-phase flow through packed beds is examined. A model with 2 parameters: an effective radial thermal conductivity in the bed, k_e, and a heat transfer coefficient, h_w, at the wall, give a satisfactory interpretation of the radial temperature profile.

k_e was expressed in terms of a stagnant contribution, due to the heat conduction through the solid and the fluid in the void space, and a radial mixing contribution of the gas and liquid phases, due to the radial component of the velocity of both fluids. The radial mixing contribution of the liquid ( k_e)_L was compared with radial mass dispersion data, and a satisfactory agreement was obtained.

Moreover, ( k_e)was much higher than the gas mixing and the stagnant contributions.

Correlations for hw and k_e)_L have been proposed in accordance with the hydrodynamic regimes of the two-phase flow.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.