THE INFLUENCE OF PRESSURE AND TEMPERATURE ON THE KINETICS OF VACUUM DRYING OF KETOPROFEN

ABSTRACT

This paper explores the influence of temperature and pressure on drying kinetics of 2-(3-benzoylphenil propionic acid) ketoprofen, in a vacuum dryer on laboratory scale, Experimentally determined relations between moisture content and drying rate vs time, were approximated with an exponential model. Model parameters were correlated with drying conditions (temperature, pressure) and defined by functions of their potentions.

From an energy balance of the process, a mathematical model for simulating dependence of sample temperature vs drying time, and moisture content of material, has been developed.

Simulation of the drying kinetics and sample temperature, by use of those functional dependencies shows good agreement with experimental results.     

KINETICS OF DRYING IN CYCLICALLY SHIFTED SPOUTED BED

This paper presents kinetics of batchwise drying in a spouted bed apparatus with cyclically shifted gas stream, i.e. drying medium flowrate is changed cyclically along inlet cross-section of a bed during operation time.

Such an apparatus provides advantages of both spouted and oscillating beds which include: good hydrodynamic conditions within the bed and energy savings. Two types of particulate materials, i.e. beet and wheat seeds, which differ largely in physical properties were used in experiments.

Based on the results of this investigation formulae for reduced moisture content (X^red) in dependence on drying time and air temperature were developed.     

DRYING KINETICS FOR SOME FRUITS: PREDICTING OF POROSITY AND COLOR DURING DEHYDRATION.

Drying kinetics of four fruits (prune, quince, fig and strawberry) were studied by using a simple mass transfer mathematical model involving a characteristic parameter (K) as a function of process variables. The model was tested with data produced in a laboratory air dryer, using non-linear regression analysis. The investigation involved three values of sample thickness (5, 10, 15mm) and three different air temperatures (50, 60, 70 °C).

The parameters of the model were found to be greatly affected by sample thickness and air temperature. The effect of moisture content on the porosity of three fruits (namely avocado, prune and strawberry) was also investigated. A simple mathematical model was used to correlate porosity with moisture content. It was found that porosity increased with decreasing moisture content.

Samples of three fruits (avocado, prune and strawberry) were investigated to estimate color changes during conventional drying at 70 °C. A first order kinetic model was fitted to experimental data with great success. It is found that the color of avocado and strawberry change while the color of prune remains the same.

Furthermore, the water sorption isotherms of three fruits (avocado, prune and strawberry) at 25° temperature were determined experimentally and the parameters at the GAB equation were evaluated by means of non-linear regression analysis. The use of the above equation produced a very good fit.     

MODELISATION PRINCIPLES FOR DRYING OF GELS

When one wants to understand and model the drying of high water content gels, one needs to gather all thermal physical parameters and to derive a physical model based on independently measured parameters. We chose to work experimentally and theoretically on water diffusion and drying of spheres of polyacrylamide gel.

We have demonstrated the strong influence of vitreous transition on the relationship of water diffusivity with moisture content. Values of the diffusion coefficient and temperature shift factor for diffusion have been proposed.

Convective and micro-wave drying kinetics show the presence of a drying phase purely specific to radiation absorption. Finally, we have proposed a mathematical model containing independent physical parameters, which' not only predicts mass fluxes but also analyses critical physical phenomena.     

CHANGE IN VIABILITY OF MAIZE DURING HIGH-TEMPERATURE DRYING

Germination and moisture content loss data were collected of maize with a moisture content ranging from 15 to 32% (w.b.), an air temperature from 40 to 75°C, and an exposure time from 0.5 to 180 minutes.

A germination-retention model was developed based on the normally distributed death-rate theory (NDD). The NDD model was combined with a concurrent-flow (CCF) dryer model, and tested against viability data of maize dried in a commercial two-stage CCF dryer. Acceptable agreement between the predicted and experimental viabilities was obtained.

The effect of the CCF dryer design, and of several operating parameters, on the loss of maize-seed viability was analyzed. Simulation with the NDD-CCF dryer model shows that high quality seed can be produced by drying at air temperatures well above 100°C.     

Determination of Spray-Drying Kinetics in a Small Scale

The main aim of the study presented in this article was to develop and test a method to determine spray-drying kinetics in a laboratory scale. A special measuring tunnel to obtain evaporation rate similar to the conditions observed in a spray-drying column was designed, built and tested.

Extensive studies of drying kinetics for maltodextrin were performed for different air flow rates and air temperatures. Test runs to determine repeatability of this technique showed satisfactory agreement between subsequent measurements, which confirms accuracy of the developed measuring method.

An effect of the initial moisture content on the critical moisture content was observed which is related to a decrease of the equilibrium vapor pressure over the solution and a decrease of the driving force of evaporation and drying rate of the process.

Results of the experiments proved that the generalized drying curve obtained from small-scale experiments could be used to describe spray-drying kinetics if the critical moisture content of the material is known.     

NONDESTRUCTIVE MEASUREMENT OF MOISTURE DIFFUSION COEFFICIENT IN WOOD DRYING

The computer tomography(CT image of wood was analyzed to estimate the moisture content from CT number. Comparing moisture contents, densities and CT numbers, moisture distributions were nondestructively determined by CT numbers detected with the scanner.

By periodically measuring CT images of the same cross section of specimens in drying, change of moisture distribution was computed. The coefficients of moisture movement at given positions inside the specimen were directly calculated from Fick's Law with known values of moisture content change, distance and drying time.

The diffiion coeficient was described as a function of various driving forces of moisture content, partial vapor pressure and chemical potential of moisture in wood. The results were comparable to data in the literature. Furthermore, it is shown that diffusion coefficients based on moisture content varies as a curve with the maximum value at about 15% m.c. during drying, and that the moisture content is actually adaptable to the driving force for moisture movement in wood because of capability over wide moisture content range.     

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.     

Vacuum Drying of Oak Wood

Vacuum drying, j,e drying under absolute gas pressure of about 10⊃ Pa. is an efficient means of reducing the process period and of producing good quality wood. We will examine here continuous vacuum drying where the plank surfaces are kept at a constant temperature, which remains above the boiling point, and moisture flowing to the surface is extracted from the kiln.

We have carried out an experimental study of oak drying under such conditions. The drying rate and moisture content profile of the sample (40 mm thick) are recorded during the whole drying period.

A model of continuous drying is established from general conservation equations with the main approximation that the air is rapidly extracted. The two constitutive equations of the model which describe temperature and water content fields are of a diffusive type and coupled through coefficients. The adequate boundary equation is not a convective one, but expresses a hygroscopic equilibrium between the vapour in the chamber and the wood surface. The mass diffusive coefficient can be adjusted to the drying rates through capillary pressure and bound water diffusion functions. The wood heterogeneity (seasonal growth) is the main factor of discrepancy in these functions. The simulated drying rates correspond with the experimental ones.     

DEACTIVATION OF DRIED SUBBITUMINOUS COAL

Deep drying of inherent moisture from subbituminous coal produces a dried product which is friable and very reactive to oxygen in air. The major problems in handling dried coal, which are unique to deep drying of low-rank coal, are: (1) avoidance of spontaneous combustion, (2) prevention of moisture reabsorption, and (3) control of dust. Atlantic Richfield has developed, and successfully demonstrated, technologies which solve all three problems. However, this paper will be confined to the spontaneous combustion problem

Low-temperature 'oxidation may result in spontaneous combustion' of the coal during storage or transit. The increased reactivity to low-temperature oxidation of dried coal is due to two factors: (1) the reduction in moisture content, and (2) the increase in temperature. A laboratory technique was developed to measure the coal reactivity to low-temperature oxidation at temperatures near ambient. Laboratory data was then used to develop a pseudo-first order kinetics model for dried subbituminous coal as a function of temperature and moisture content. The influence of particle size was also determined

A one-dimensional spontaneous heating model was formulated to evaluate the effects of wind velocity, coal pile porosity, thermal conductivity of crushed coal, and geometry of coal piles on the dried coal's tendency to spontaneous combustion. This model was validated against two large-scale spontaneous heating tests. Each test consumed about 800 pounds of dried coal.

Based on a selected combination of three deactivation methods and predictions of the computer model, a special product treatment procedure was developed and successfully demonstrated in pilot plant tests in 1983. Dried coal stockpiles (about 100 tons per pile) were monitored for four months under severe weather conditions with no evidence of either moisture reabsorption or spontaneous combustion.     

EFFECT OF CREEP AND MECHANO-SORPTIVE EFFECT ON STRESS DEVELOPMENT DURING DRYING

Constitutive equations to quantify wood deformation under combined mechanical loading and moisture content change (1] were coupled with the moisture distribution developed during drying to predict stress and strain in 50 by 190-mm Douglas-fir heartwood lumber.

Two combinations of temperature and relative humidity were used to dry the wood. The overall board shrinkage and the immediately released and set strains were measured as a function of time. Those strains were compared with analytic results, which showed good agreement.

The roles that four strain components played in the development of stress-both at board surface and center were compared for different drying conditions. The significance of creep and mechano-sorptive strain in relieving the stress was demonstrated by varying the model parameters.     

THIN-LAYER DRYING CHARACTERISTICS OF ROUGH RICE AT LOW AND HIGH TEMPERATURES

Thin-layer drying characteristics of rough rice were determined at temperature ranging from 11.8 to 51 °C and for relative humidities ranging from 37.1% to 91.3%, with initial moisture contents in the range of 24.7 to 41.6% dry basis. An oven, a self contain air conditioning unit, recently developed in Japan, was used for this experiments. With this apparatus, very smooth drying curves were obtained. The data of sample weight, and dry and wet bulb temperatures of the drying air were recorded continuously throughout the drying period for each test. The drying process was terminated when the moisture content change in 24 h was less than 0.2 % d.b. (weight change was less than 0.05 g). The final points were recorded as the dynamic equilibrium moisture contents.

The drying data were than fitted to the Page model. The model gave a very good fit for the moisture content with an average standard error of 0.294 % d.b¨ Both the drying parameters, K and N, are function of drying air temperature and relative humidity. The effect of variable initial moisture content was also described effectively by the empirical Page model. The drying time employed had a large effect on the K and N values. The results presented here, over typically 5 day drying, will be useful in the long term moisture transfer process occurring during ventilated storage.     

THE SELECTION OF DRYING TECHNOLOGY PROCESS PARAMETERS

Drying by heating is the most common method that has as its primary objective the removal of moisture, with the attendant structural, mechanical, thermal, biological and other property changes being significant as well. The extent to which these objectives are achieved is a function of the design process parameters such as the material, temperature, moisture content, and the duration of the process.

To date, drying process parameters have been mainly selected with the help of empirical critical criteria that differentiate between the occurrence and non-occurrence of various phenomena. The mentioned criteria and drying kinetics and dynamics parameters are rarely interrelated, demanding extensive time-consuming experimentation yielding results of limited reliability.     

KINETICS OF THE CLAY ROOFING TILE CONVECTION DRYING

Kinetics of the convection drying process of flat tile has been investigated experimentally in an industrial tunnel dryer. Several velocities of wet tile movement through the dryer were tested to obtain maximum allowable drying rate curve. As there are various models to describe the kinetics of convection drying, finding a model that would fairly well approximate the kinetics of the whole drying process was part of the research. Especially the polynomial and exponential models were tested.

It was found that exponential model of the type: B(t) = (a-B_e. EXP(-bt²) +B_et (-dB(t)/dt) = 2bt(B(t)-B_e significantly correlates the kinetics of the whole tile drying process.

Applying the maximum allowable drying rate curve obtained for flat tile in the first period of drying, a grapho-analytic model for the optimal conducting of the process has been developed.     

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.     

DEHYDRATION KINETICS AND MODELLING

This paper presents a study on the kinetics of dehydration of carrot parallelepipeds which may be useful for a new method which consists in applying a freezing pretreatment. followed by a vacuum dehydration after sample defreezing.allowing instant products to be produced in terms of rehydration ( about 2 minutes rehydration). in this paperare examined effects of effects of pressure (2.6 to 75 kPa). heating conditions (single and double face heating), temperature (50 to 100°c) and sample thickness (3 to 20 mm thick) on dehydration rate.

Dehydration curves allow the identification of two main periods with variation of sample temperature during drying. The first period is a quasi-isothermal. falling-rate period characterized by a large quantity of moisture removal through diffusional transfer. Then. can be observed a second period with increase in product temperature while drying rate is governed by heat diffusion. A drying model accounting for sample shrinkage is proposed and discussed.     

Drying of Transformer Board

The internal insulation in shell type power transforms is usually ensured by the stacking of plates of board impregnated with oil. A board is in equilibrium with the atmosphere at a moisture content varying from seven to eight percent by weight, but, when the insulating function is required, the water content must be lower than 0.5 %. The aim of the present work is the understanding and the modelling of transformer boards drying.

The first part of this work presents experimental studies showing that the drying of transform board follows two regimes :

- a fast regime in the fim period

- a slow regime, up to 99 percent of dryness.

The effect of heating and the influence of the board thickness on the drying rate also studied. In the second part of this paper, we presnt a model capable to represent the observed kinetics of transformer board drying. This model is based on the diffusion of water vapour in the gaseous phases combined with the transfer of water vapor from the fibres to the -us phase. The due of the average global transfer coefficient can be deduced from the slope of the curve 1 f(drying time), where x     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

DRYING OF PARTICULATE SOLIDS: DETERMINATION OF THE CHARACTERISTIC CURVE OF BROWN COAL.

Variation on the rate of drying of brown coal powder as a function of environmental and intrinsic properties has been studied in a gravimetric laboratory-scale drier.

Raw data have been treated to correlate the constant rate of drying and the equilibrium moisture content as a function of flow rate and temperature of the gas phase, particle size and surface additives. The characteristic drying curve occurs when the reduced rate of drying is plotted as a function of a dimensionless moisture potetial.