WO2020048520A1

WO2020048520A1 - A method for determining air drying kinetics of a product and a device used thereof

Info

Publication number: WO2020048520A1
Application number: PCT/CN2019/104637
Authority: WO
Inventors: Xiaodong Chen; Jie Xiao; Aditya Putranto; Nan FU
Original assignee: Soochow University
Priority date: 2018-09-07
Filing date: 2019-09-06
Publication date: 2020-03-12

Abstract

A method for determining air drying kinetics of a product comprise the steps of: S1: constructing a reaction engineering approach; S2: measuring and recording separately the temperature and moisture changed over time; S3: determining the ratio of the heat transfer coefficient to the mass transfer coefficient; S4: calculating the reaction engineering approach parameters: activation energy and rate constant; S5: measuring and obtaining a temperature-moisture relationship equation; S6: establishing a reaction engineering approach drying kinetics. Also, there is a purposely designed and constructed device used for determining air drying kinetics of a product.

Description

A method for determining air drying kinetics of a product and a device used thereof

Related Applications

This application claims priority of the Australian provisional patent application 2018903366 filed on 7 September 2018, the entire content of which is incorporated herein by reference.

Field of the Invention

The present disclosure relates generally to a method for establishing the parameters of air drying of a product, such as vegetables and fruits, in order to establish a fully workable drying kinetics, in the form of an effective mathematical model, which is used for model-based control of drying process. More particularly, the method comprises an analytical procedure for deducing the kinetics model parameters that are independent of the external drying conditions.

The present disclosure also relates to a device that is capable of providing continuous measurements of sample temperature history and moisture content changing with time.

Background of the Invention

Vegetables and fruits are often dried in air or in gas for preservation purposes or in many occasions dried materials themselves are of the product form. Drying process is an energetic process and the product quality is influenced greatly by the drying process. In order to control drying process and to optimize the drying process for the best product quality, it is desirable to have an accurate mathematical model which accounts for the moisture loss and temperature-time history which can then be employed to predict adequate drying process under any air-drying arrangement available for the humankind.

For practical purposes, the product being dried as a whole is most useful for model based control of the drying process. This means that no spatial distribution of temperature and moisture needs to be predicted or simulated. Corresponding to mathematical modeling, the drying of a whole product (subject or sample) is described with a so-called Lumped Drying Rate Model. The lumped drying rate model can be used to predict the temperature and moisture content. How to generate the parameters of a suitable, and most importantly accurate, lumped model for drying rate is of many concerns. The mechanistic models for drying, including the lumped models, must encapsulate the effects of product temperature and product moisture content. They describe the internal transport of moisture and energy leading to the overall effect of product moisture loss and temperature change. To obtain these ‘internal’ models, one has to be able to ‘isolate’ out the influences of the external parameters such as convective mass and heat transfer coefficients which vary greatly in different devices and operating conditions. For a suitable model, the external conditions should not affect the internal model parameters. There are only two kinds of lumped models that qualify the above requirements. One is called the characteristic drying rate curve (CDRC) model and one is called the reaction engineering approach (REA) model. The generation of the parameters for CDRC model is known to be interwind with the external parameters (for determining the critical parameters for benchmarking) . The REA model, on the other hand, is a model that describes all stages of the drying process in a continuous manner, in the sense that it generates a signature plot (the activation energy plot) that covers the whole range of moisture content of the product (sample) . However, both mathematical models of drying require some empirical constants if not all of them to be determined in a laboratory. Therefore, it is desirable to have a drying model approach that is possible to remove the influences of the external transfer processes. Also, it is desirable to have a device which can generate the adequate data which are good enough to be analyzed using a data analysis procedure that can yield the kinetics of drying which is applicable in many hot air-based drying equipments. In other words, it is desirable to have an overall effective method (equipment and data analysis) to produce drying kinetics for fruits and vegetables that is independent of the devices used in industrial scale processing.

Existing procedures usually employ drying equipment to generate drying kinetics which is often described either in empirical time-dependence functions or the diffusion-based models. Usually, the equipment can measure the temperature of the sample of concern (fruits and vegetables) , can measure the weight loss of the sample. The weight loss data is used to establish the drying rate. The temperature of the sample is however not often measured actually but in the current method it must.

Summary of the Invention

In one aspect of the invention, this invention provides a method for determining air drying kinetics of a product, such as vegetables and fruits, comprising the steps of:

S1: constructing a reaction engineering approach;

S2: measuring and recording separately the temperature and moisture changed over time;

S3: determining the ratio of the heat transfer coefficient to the mass transfer coefficient;

S4: calculating the reaction engineering approach parameters: activation energy and rate constant;

S5: measuring and obtaining a temperature-moisture relationship equation;

S6: establishing a reaction engineering approach drying kinetics.

Wherein, the step of S1 comprises:

S11: based on the mass balance of a product being dried, deducing and obtaining an overall drying rate equation in REA approach by data reduction procedure;

S12: based on the energy balance of a product being dried, deducing and obtaining a lumped energy balance equation;

S13: resulting in the reaction engineering approach by dividing the overall drying rate equation of S11 with the lumped energy balance equation of S12.

In another aspect of the invention, the activation energy may be resulted by rearranging the equation form of the reaction engineering approach of S13.

In another aspect of the invention, the temperature-moisture relationship is obtained by using a programmed relative humidity reduction while keeping constant gas temperature.

In a further aspect of the invention, the temperature-moisture relationship is obtained by very dry gas and change temperature during a drying test.

In a further aspect of the invention, the mass and heat transfer coefficients may be obtained through the reaction engineering approach drying kinetics on the basis of having obtained the surface area of the product.

In yet a further aspect of the invention, the surface area of the product may be evaluated as a function of water content on the basis of having obtained transport coefficients.

In many aspects of the invention, the products are preferably fruits and vegetables.

In one aspect of the invention, it provides a device for determining air drying kinetics of a product, comprising:

- heaters for making hot air stream for drying;

- flow straighteners, which are positioned downstream of the heaters, configured to make the airflow parallelly flowing into the test section;

- a plurality of temperature sensors;

- a product holder for supporting product samples;

- an electronic balance which is linked to a computer and connected to the product holder;

- a temperature measurement arrangement connected to the product holder for measuring temperatures of the product sample in real-time;

- a camera for observing the size and appearance changes of the product sample;

- a blower for providing stable drying airflow.

In a further aspect of the invention, the temperature measurement arrangement is one or more thermocouples.

The reaction engineering approach of the present invention is new in the field of obtaining air drying kinetics of products, especially for fruits and vegetables, as they are in many cases non-standard shapes. By using the proposed derivations of the reaction engineering approach to drying kinetics modeling, without knowing the detailed heat and mass transfer correlations, and without knowing the detailed surface changes and size changes during drying, one can use the new approach to obtain the drying kinetics parameters: activation energy and rate constant. And then it is possible to establish a procedure, without carrying out experiments under constant drying conditions, to measure the reaction engineering approach parameters under variable drying conditions, and further to obtain the reaction engineering approach drying kinetics.

Brief Description of the Drawings

The objects and features of the invention can be better understood with reference to the drawings described below. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the drawings, like numerals are used to indicate like parts throughout the various views.

Fig. 1 is a schematic diagram of the device for determining air drying kinetics of a product according to one embodiment of the invention;

Fig. 2 is typical experimental data on moisture-time obtained from the trials carried out using the device shown in figure 1: (a) Initial water content of the sample is 9.75 kg. kg ^-1 (on dry basis) ; (b) Initial water content of the sample is 11.09 kg. kg ^-1 (on dry basis) ;

Fig. 3 is typical experimental temperature-time curves obtained from the trials carried out by using the device shown in figure 1: (a) Initial water content of the sample is 9.75 kg. kg ^-1 (on dry basis) ; (b) Initial water content of the sample is 11.09 kg. kg ^-1 (on dry basis) ;

Fig. 4 is typical records of the sample images obtained by using the camera disposed in the device shown in figure 1, showing highly deformable nature of the carrot samples which are typical of fruits and vegetables;

Fig. 5 is the activation energy plots obtained by conventional approach and the current claimed approach of the present invention, showing the high consistency of the current approach.

DETAILS OF THE INVENTION

As discussed above, this invention provides a method for determining air drying kinetics of a product, comprising the steps of:

S1: constructing a reaction engineering approach;

S5: measuring and obtaining a temperature-moisture relationship equation;

S6: establishing a reaction engineering approach drying kinetics.

Wherein, the step of S1 comprises:

Detailed equation deduction and construction procedures of S11 to S12 are generally described in the following sections.

S11: Overall drying rate equation

The reaction engineering approach (REA) is an application of chemical reactor engineering principles to model drying kinetics. A lumped parameter model where the overall drying rate of a product (sample) (flux multiplied by surface area) of the moist materials can be expressed as the following:

Where, m _s is the dried mass of thin layer material (kg) , X is moisture content on dry basis (kg. kg ^-1) and

is the mean water content on dry basis (kg. kg ^-1) , t is time (s) , ρ _v, sis the vapor concentration at interface (kg. m ^-3) , ρ _v, ∞is the vapor concentration in the drying medium (kg. m ^-3) , h _m is the mass transfer coefficient (m. s ^-1) and A is surface area of the material (m ²) .

In previous studies, the mass transfer coefficient (h _m) was determined based on either the established Sherwood number correlations (Incropera and Dewitt, 1990) or that obtained experimentally for the drying conditions involved. A can be a function of the moisture content if the material shrinks during the drying process. Equation 1 is basically correct for all cases where water leaves solid in vapor form. Even in the case of the lumped approach, there is no assumption of uniform moisture content in this REA approach. It was characterized with the mean moisture content.

The surface vapor concentration (ρ _v, s) can be correlated in terms of saturated vapor concentration of water (ρ _v, sat) by the surface relative humidity (RH _s) in the following equation (Chen and Chen, 1997; Chen and Xie, 1997) :

One can see that the surface RH is represented in an Arrhenius form. ΔE _v represents the increasing difficulty to remove moisture from materials as moisture content reduces (in addition to the free water effect) . Being a semi-empirical model, ΔE _v is ideally to be the mean moisture content

dependent. T _s is the surface temperature of the material being dried (K) . For many products, T _s may be replaced by an average temperature of the product (sample) measured.

For a small temperature range, such as from 0℃ to just over 100℃, ρ _v, sat (kg. m ^-3) can in fact be approximated with the following equation (Chen, 1998) :

Where, K _v was found to be 1.61943 x 10 ⁵ (kg. s ^-1) and E _v was found to be 38.99 kJ. mol ^-1 which is basically the latent heat of water vaporization illustrating the physics involved for evaporating free water (Chen, 1998) .

For a broader range of temperature, one may use the following formula which correlates the entire range of the data (such as from 0℃ to about 200℃) summarized by Keey (1992) :

ρ _v, sat=4.844×10 ^-9 (T-273) ⁴-1.4807×10 ^-7 (T-273) ³+2.6572×10 ^-5 (T-273) ²-4.8613×10 ^-5 (T-273) +8.342×10 ^-3 Equation4

Where, T is temperature (K) based on the given data (Putranto et al, 2010) .

Nevertheless, the idea of an REA approach is a valid one.

The rate of drying, in REA approach, is then expressed as:

Noting that the above equation has a parameter that is the surface temperature (T _s) for the moist porous material being dried, it can be troublesome to measure under certain circumstances.

It has been found, based on many previous practical experiences of using the REA approach, that drying experiments for generating the REA parameters need to be conducted where the air (or gas) humidity is very low in order to cover the widest possible range of ΔE _vversus

The dependence of the additional activation energy on moisture content can then be normalized as:

Where, ζ is a function of moisture content difference (the current moisture content less the final equilibrium one) , ΔE _v, ∞is the maximum when the moisture concentration of the sample approaches relative humidity and, for convective drying, the temperature of the drying air (gas) :

ΔE _v, ∞=-RT _∞ln (RH _∞) Equation7

Where, X _∞is the equilibrium moisture content corresponding to RH _∞and T _∞, which can be related to one another using the equilibrium isotherm (Keey, 1992) .

Equation 6 is not affected by the external drying conditions and is thus a unique character of the internal moisture transfer and is a fingerprint of the product.

In the current approach, it is important to note that so far the experiments for gaining the relevant equation 7 has to be under the very dry condition so the final water content attained in experiments is usually very small.

When the temperature of concern is average product temperature based on Equation5, the REA can be expressed as:

Where,

and

are average product temperature and moisture content respectively.

By rearranging the Equation 8, the activation engery ΔE _v can be written as:

If the surface area A and the mass transfer coefficient h _m are known, or measured in separated experiments, one good run of drying experiment under the same drying air (gas) condition is sufficient for establishing equation 6, as mentioned in the above description.

It is noted that in order obtain data to calculate the above activation energy, one has to have the “external parameters” , such as the surface area (changing with time or water content) and the mass transfer coefficient which is dryer dependent for most of the times.

S12: Lumped energy balance equation

When the temperature of the moist material being dried does not vary much within the material, a uniform temperature may be considered (more quantitative assessment of this assumption can be found with the ideas of the modified Biot number and modified Lewis number) . The lumped expression for the energy balance of a product (sample) being dried is written as the following:

Where the mass of the material being dried is expressed as:

And C _p can be calculated as:

The heat of drying, H _drying (J. kg ^-1) , can be taken as the latent heat of water vaporization.

Then the following lumped energy balance can be constructed by inducing Equation 9 and 10 into Equation 8:

S13: The Reaction Engineering Approach (REA)

After all the above deduction, on both sides, dividing Equation 13 with the rate of drying expressed in equation 8 leads to:

Subsequently, one can obtain the following equation:

Therefore, apparently as long as the temperature versus time and the moisture contents over time are recorded accurately, the activation energy expressed in Equation 15 can be worked out.

Of course, the condition for that is the ratio of the heat transfer coefficient to the mass transfer coefficient (h/h _m) needs to be knownprior.

Here in the context of the present invention, the surface area effect is actually canceled out to make the obtainment of the activation energy without the complication of the prior known surface area.

The significant advantages in using Equation 15 to work out the REA drying kinetics parameters is that one can conduct experiments under non-constant drying conditions as long as one can obtain the temperature-moisture content relationship reliably.

It is then interesting to note that for many heat and mass transfer scenarios, the ratio of heat transfer coefficient to mass transfer coefficient is either not dependent on gas velocity or insensitive to velocity change, and is a ratio of thermal physical properties of the gas medium determined at the film temperature denoted with f (the average of the sample temperature and gas temperature) as traditionally noted in boundary layer transport.

For instance, for flat sample geometry and for parallel flow, one can have:

The index m and n and the constant C are in general known to literature which have been established many years ago reliably. Thus one has:

The ratio of the transfer coefficients would involve the drying gas properties only. These can be made known prior to the experiments and the data reduction outlined in the current application.

However, Equations 16-18 are not necessarily essential for the validity of the approach of the invention, as long as the effect of Reynolds number can be removed or approximately neglected.

Exemplary embodiments of the device of the invention

When modeling a drying process, the experiments may be carried out under constant drying conditions: constant temperature and constant humidity. Usually, it is required that the material should have its own surface area and mass transfer coefficient known prior to the establishment of the REA parameters such as the activation energies. Usually, in these experiments, the drying air/gas relative humidity is kept near zero (essentially dry air/gas) in order to cover the entire range of the activation energy as a function of water content.

The following description illustrates a purposely designed and constructed device for determining air drying kinetics of a product. The device is a tunnel device (also named as a dryer) which is schematically illustrated in Fig. 1. It is able to measure the required temperature history and the required moisture loss history for establishing the drying kinetics model parameters as outlined in the present invention.

On the other hand, the current device has been constructed so that it can operate with changing air temperature as well. This time-varying condition would not affect the obtainment of the REA kinetics parameters as mentioned in the Summary of the Inventions.

According to one embodiment of the invention, the schematic structure of the device for determining air drying kinetics of a product is shown in Fig. 1. As can be clearly seen from this drawing, a plurality of heaters 5 is provided for making hot air stream 2 by heating the airflow 2 from the blower 1, which is used to provide stable drying air intake to the device. A plurality of flow straighteners 6, which are positioned downstream of the heaters 5 along the airflow direction 2, configured to make the airflow parallelly flowing into the test section. A plurality of temperature sensors is provided for detecting the temperature for control purposes, these sensors are separately positioned on both sides of the gas exit 9 which is placed downstream of the flow straighteners 6 and used when the by-pass is on. Aproduct holder 13 for supporting product samples is provided and connected to a temperature measurement arrangement 12 and an electronic balance 11 which is linked to a computer (not shown in Fig. 1) . The temperature measurement arrangement 12 is used for measuring temperatures of the product sample in real-time, such as thermocouples or similar elements commonly having these functions. A camera 10 is placed under the product holder 13 for observing the size and appearance changes of the product sample over time. Also, the device is provided with a flow metering and control means positioning between the heaters 5 and the blower 1, and a support structure 3 with wheels is provided to hold the whole device and to provide mobility of the equipment.

During the drying experiment, the product (sample) to be dried is placed in the holder, its mass and temperature changes can be recorded over the duration of each experiment. The data are captured through a data-logger connected to a computer for further analysis.

Example

In the embodiment of the invention, an example of drying a highly shrinkable material, carrot tissues (cut into uniform cubes) , is given to illustrate the effectiveness of the current approach. Experiments were conducted in the drying facility designed and constructed for a parallel flow drying scenario which is accurate for the purposes outlined earlier (see Figures 2-4) .

The calculated activation energy can be plotted against the water content (here X _b is the final equilibrium water content achieved in the experiments) (see Figure 5) . It can be seen that the new approach explained above gives excellent agreement to the conventional approach. This means without knowing the detailed heat and mass transfer correlations, and without knowing the detailed surface changes and size changes during drying, one can use the new approach to measure the reaction engineering approach parameters under variable drying conditions and further to obtain the reaction engineering approach drying kinetics.

While the principle of the invention has been described in connection with specific drawings and embodiments, it should be understood clearly that these descriptions are made only by way of example and are not intended to limit the scope of the invention. What has been disclosed herein has been provided for the purpose of illustration and description. It is not intended to be exhaustive or to limit what is disclosed to the precise forms described. Many modifications and variations as are apparent to a person skilled in the art are intended to be within the spirit and scope of the invention. The invention is limited only as defined in the following claims and equivalents thereto.

NOTATION

X Moisture content on dry basis, kg. kg ^-1

Mean moisture content on dry basis, kg. kg ^-1

A Surface area of single droplet or particle, m ²

D Diffusivity, m ². s ^-1

D _v Vapor diffusivity in air, m ². s ^-1

E Activation energy, J. mol ^-1

f Relative drying rate function

g Gravitational acceleration, m. s ^-2

H _drying Heat of drying/wetting, J. kg ^-1

h Heat transfer coefficient, W. m ^-2K ^-1

h _m Mass transfer coefficient, m. s ^-1

k Thermal conductivity, W. m ^-1. K ^-1

M Molecular weight, g. mol ^-1

m _s Mass of solids, kg

Nu Nusselt number (Nu=hL/k) (k here is that of the fluid thus differing from that for Biot number calculation)

Pr Prandtl number (Pr=ν/α, whereνis the kinematic viscosity, m ². s ^-1)

R Ideal gas law constant

Re Reynolds number (Re=ρuL/μ)

RH Relative humidity

Sc Schmidt number (Sc=ν/D)

Sh Sherwood number (Sh=h _mL/D) (D here is that in the fluid thus differing from that for Biot number for mass transfer calculation)

T Temperature, K

t Time, s

T _s Surface temperature, K

T _sat Adiabatic saturation temperature of drying air, K

u Gas velocity, m. s ^-1

X _∞ Equilibrium moisture content on dry basis, kg. kg ^-1

Symbols

ρ Density or concentration, kg. m ^-3

μ Dynamic viscosity, Pa. s

δ Thickness, m

τ Dimensionless time

ρ _v Vapor concentration, kg. m ^-3

Relative activation energy function

Subscripts

∞ Bulk, surrounding or equilibrium

air Air properties

c Critical conditions

e Evaporation

eff Effective

L Thickness

m Mass transfer

o Initial

s Solid, surface

sat Saturated

v Water vapor

Claims

A method for determining air drying kinetics of a product, comprising the steps of:

S1: constructing a reaction engineering approach;

S2: measuring and recording separately the temperature and moisture changed over time;

S3: determining the ratio of the heat transfer coefficient to the mass transfer coefficient;

S4: calculating the reaction engineering approach parameters: activation energy and rate constant;

S5: measuring and obtaining a temperature-moisture relationship equation;

S6: establishing a reaction engineering approach drying kinetics.
The method of claim 1, wherein the step S1 comprises:

S11: based on the mass balance of a product being dried, deducing and obtaining an overall drying rate equation in REA approach by data reduction procedure;

S12: based on energy balance of a product being dried, deducing and obtaining a lumped energy balance equation;

S13: resulting the reaction engineering approach by dividing the overall drying rate equation of S11 with the lumped energy balance equation of S12.
The method of claim 2, wherein the activation energy may be resulted by rearranging the equation form of the reaction engineering approach of S13.
The method of claim 1, wherein the temperature-moisture relationship is obtained by using a programmed relative humidity reduction while keeping constant gas temperature.
The method of claim 1, wherein the temperature-moisture relationship is obtained by very dry gas and change temperature during a drying test.
The method of claim 1, wherein the mass and heat transfer coefficients may be obtained through the reaction engineering approach drying kinetics on the basis of having obtained the surface area of the product.
The method of claim 1, wherein the surface area of the product may be evaluated as a function of water content on the basis of having obtained transport coefficients.
The method of claim 1, wherein the products are preferably fruits and vegetables.
A device for determining air drying kinetics of a product, comprising:

- a plurality of heaters for making hot air stream for drying;

- a plurality of flow straighteners, which are positioned downstream of the heaters, configured to make the airflow parallelly flowing into the test section;

- a plurality of temperature sensors;

- a product holder for supporting product samples;

- an electronic balance which is linked to a computer and connected to the product holder;

- a temperature measurement arrangement connected to the product holder for measuring temperatures of the product sample in real-time;

- a camera for observing the size and appearance changes of the product sample;

- a blower for providing stable drying airflow.
A device of claim 9, wherein the temperature measurement arrangement is one or more thermocouples.