RU2566726C1 - Method to determine mass-transfer factor of porous permeable materials - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: values included into kinetic laws of mass transfer and convective mass transfer: substance mass, motive force of mass transfer process (difference of medium potentials at both sides of material), material surface, process time. At the same time specified values are determined experimentally under two various speeds (true and auxiliary ones) of the medium washing the material from the side of mass transfer factor determination, with subsequent calculation of the sought-for factor according to the formula produced by the analytical method:

, where ΔM₁ and ΔM₂ - accordingly, moisture mass increment in process of the experiment, kg; Δτ - time increment corresponding to moisture mass increment, s; w₁ and w₂ - accordingly, true and auxiliary speeds of substance flow, m/s; Δ - total motive force of mass transfer process from one medium to another via a permeable wall of the material, Pa; F - sample surface area, m². This formula expresses the quantitative share of potential difference between the surface and the washing medium, i.e. motive force of mass transfer by the mechanism of convective diffusion, from total motive force of mass transfer process from one medium to another via a permeable material.

EFFECT: invention makes it possible to increase accuracy of determination of mass transfer factor of porous materials, by exclusion of potential measurement on material surface contacting with its washing medium.

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Description

The invention relates to a drying and heat-moisture treatment technology for a variety of porous permeable (for example, heat-insulating) materials, including in the textile, light, food industries.

A known method for determining the mass transfer coefficient, based on the kinetic law of mass transfer (convective diffusion) Schukarev-Dalton [1], including determining the potentials of the driving force of the mass transfer process on the wall of the material and in the environment.

The disadvantage of this method is that in practice it is difficult to perform, and sometimes unfeasible, due to the complexity and inaccuracy of measuring potential (partial pressure, concentration, etc.) on a porous or fleecy surface of a permeable solid. The noted complexity gave rise to numerous options for determining the mass transfer coefficient, using various assumptions or indirect solutions, naturally leading to certain limitations, complication of calculation methods and inevitable errors in the results [2-5].

The technical result of the proposed method is its simplification and improving the accuracy of the determined mass transfer coefficient.

This result is achieved by the fact that in the proposed method for determining the mass transfer coefficient of porous permeable materials, including determining the values included in the kinetic law of mass transfer, namely: the mass of the substance, the driving force of the mass transfer process (potential difference of the media on both sides of the material), the surface of the material, time of the process according to the invention, the quantitative fraction of the potential difference between the moving stream and the surface being washed Δ _β is simultaneously expressed, i.e. the driving force of mass transfer by the convection mechanism from the total driving force of mass transfer Δ from one medium to another through a permeable wall.

This allows us to simplify the experiments by eliminating potential measurements on the streamlined surface of the material and to increase the accuracy of the determined mass transfer coefficient.

Accordingly, a distinctive feature of the obtained formula, which gives new information about the process, is that it expresses the quantitative fraction of the driving force of the convective heat transfer process from the medium to the material surface Δ _β of the total driving force of the mass transfer process Δ. Knowing the value of this fraction and the value of Δ, it is possible to accurately determine the value of the mass transfer coefficient without any assumptions and indirect methods.

The proposed method is implemented in a device, a diagram of which is shown in the drawing. The main element of the device is a thermo-hygrostatic chamber 1 with a recirculating flow of moist air. The chamber is divided by a longitudinal horizontal partition 2 into two zones, in which cups 4 with test samples 5 are placed on special supports 3. The chamber has a sorbent (sulfuric acid, zeolite, etc.). The air is circulated by the fan 6 complete with a temperature setter - an electrocontact thermometer 14. The air speed in the zones, and accordingly the fan performance, is determined by the number of revolutions of the impeller and regulated by an autotransformer 7. The air is heated by an electric heater 8, the power of which, and therefore the temperature air regulate autotransformer 9.

Measurement of air temperature is carried out with dry 10 and wet 11 thermometers. According to their testimony, the relative humidity of the air is determined. The speed and circulation of air flows are measured with a portable anemometer 12.

The working volume of the cups 4 is filled with 30-50% water, the test samples 5 are installed in their grooves, the compression is carried out by clamping nut 13. The cups with the samples are numbered, weighed on an analytical balance and loaded into the chamber 1 on the stand 3. Adjusting the load with LATR 7, set the necessary air speed in the chamber 1, and then, constantly increasing the load, set the desired temperature of the circulating air. Air parameters are kept constant throughout the experiment. Every 0.5 ... 1 hour weigh the cups and fix the parameters of the air.

The experiment is completed after the loss of moisture in the glass is stabilized. This condition corresponds to 2-3 ^fold repetition of the same moisture loss over the same time intervals.

Thus, the proposed method, due to the exclusion of measurements on the surface of the material, has the following advantages: high accuracy of the determined mass transfer coefficients β _i , the relative simplicity of conducting experiments and processing the results, reducing the duration of processes, eliminating the invasiveness of the material, which means better reproducibility of the results, expanding the class studied materials and the fastest accumulation of experimental data.

The calculated expression is derived based on the laws of mass transfer and convective diffusion [1].

When deriving the desired equation and transformations, the commonly used notation is used in modern literature [1, 2, 4]. In particular, in the textbook A.G. Kasatkina "Basic processes and apparatuses of chemical technology" (the eighth edition, revised, published by "Chemistry", 1971) in Ch. 10 “Fundamentals of mass transfer” describes the concepts, formulations, designations and basic equations of convective mass transfer - p. 413-416, the mechanism of the mass transfer process - p. 417, equations and mass transfer coefficients - p. 420-422, as well as the relationship between the mass transfer coefficients β and mass transfer K - p. 428-430.

We used the following notation: K _m1 , K _m2 - mass transfer coefficients in comparative experiments, kg / (m ² · s · Pa); ΔM ₁ , ΔM ₂ - increment of the mass of moisture in the process of experiment, kg; Δ is the total driving force of the mass transfer process from one medium to another through the wall, Pa; Δ _β is the driving force (potential difference) of the process of convective mass transfer from the wall to the medium, Pa; F is the surface area of the sample, m ² ; Δτ is the increment of time corresponding to the increment of the mass of moisture, s; λ _m is the mass conductivity coefficient of the porous material, kg / (m · s · Pa); β _i - mass transfer coefficients for various experimental conditions, kg / (m ² · s · Pa); w ₁ , w ₂ - true and auxiliary flow rates of the substance from the outside of the sample material, m / s; δ is the thickness of the sample, m

The stationary process of mass transfer of a diffusing substance in homogeneous media separated by a permeable solid wall is considered. Moreover, from the inside, the speed of the medium is unchanged, and from the outside, we take two speed values: true w ₁ and auxiliary w ₂ . Then, in accordance with the kinetic law of mass transfer, we express the increment of the diffused substance over the time Δτ, all other things being equal, for both cases:

Taking into account that

и $$\frac{1}{{\beta }_{н.}}$$

и - соответственно внешние диффузионные сопротивления переносу по обе стороны стенки в первой и второй жидких (газообразных) средах, (м²·с·Па)/кг; $$\frac{\delta }{{\lambda }_m}$$

- диффузионное сопротивление массопроводности проницаемой стенки, (м²·с·Па)/кг. Тогда в изотермических условиях для наружной среды получим:Where $$\frac{\mathrm{one}}{{\beta }_{\mathrm{at}n.}}$$

and $$\frac{\mathrm{one}}{{\beta }_{n.}}$$

and - respectively, external diffusion resistance to transfer on both sides of the wall in the first and second liquid (gaseous) media, (m ² · s · Pa) / kg; $$\frac{\delta }{{\lambda }_m}$$

- diffusion resistance of the mass conductivity of the permeable wall, (m ² · s · Pa) / kg Then in isothermal conditions for the external environment we get:

Here β _int , β _n - mass transfer coefficients in the general case for internal and external environments; β ₁ , β ₂ - mass transfer coefficients of the external environment for modes with speeds w ₁ and w _2, respectively.

From dependences (1) and (2), taking into account (3), it follows:

- сумма диффузионных сопротивлений процесса переноса массы механизмом массоотдачи с внутренней стороны и массопроводностью через стенку (материал).Where $$\Sigma R=\frac{\mathrm{one}}{{\beta }_{\mathrm{at}n.}}+\frac{\delta }{{\lambda }_m}$$

- the sum of the diffusion resistances of the mass transfer process by the mass transfer mechanism from the inside and the mass conductivity through the wall (material).

Dependence (4) can be converted:

and taking into account the expression for K _m present in the form:

where ΔM ₁ and ΔM ₂ are, respectively, the amount of diffused substances in the first and second mass transfer processes for the same period of time Δτ (s), kg

Replacing K _{m1 by} its expression from (1) and carrying out the corresponding transformations, we obtain the necessary calculation formula for the desired mass transfer coefficient:

The kinetic law of Schukarev-Dalton (1) for the conditions of convective diffusion (mass transfer) as applied to the flow in the second medium when it moves with speed will have the form:

Express the amount of flow M ₁ = ΔM ₁ / Δτ (kg / s) of the diffusing substance based on the dependence (6):

Using (1 ′) and (7), the ratio of the driving forces can be expressed as follows:

Thus, the right-hand side of relation (8), expressed only by the mass characteristics of two mass transfer processes and the ratio of the velocities of the second medium, is the fraction of the mass transfer driving force Δβ ₁ of the total mass transfer driving force Δ.

Obviously, under the conditions under consideration, the value of the determined fraction varies in the range 0 <D ₁ <1.

или β₁=(1/D₁)·[М₁/(Δ·F)], где $$D_1\cdot \Delta ={\Delta }_{{\beta }_1}$$

- движущая сила массоотдачи, выраженная через общую долю движущей силы массопередачи. Движению второй среды со скоростью w₂ будет соответствовать своя доля D₂, движущая сила массоотдачи $$\Delta {\text{'}}_{{\beta }_1}=D_2\cdot \Delta$$

и уравнение массоотдачи: $$M_2=\Delta {\text{'}}_{{\beta }_1}\cdot D_2\cdot \Delta \cdot F$$

.We equate (1 ′) and (7) taking into account (8), we obtain: $$M_{\mathrm{one}}={\beta }_{\mathrm{one}}\cdot {\Delta }_{{\beta }_{\mathrm{one}}}\cdot F={\beta }_{\mathrm{one}}\cdot D_{\mathrm{one}}\cdot \Delta \cdot F$$

or β ₁ = (1 / D ₁ ) · [M ₁ / (Δ · F)], where $$D_{\mathrm{one}}\cdot \Delta ={\Delta }_{{\beta }_{\mathrm{one}}}$$

- the driving force of mass transfer, expressed through the total share of the driving force of mass transfer. The movement of the second medium with a speed of w ₂ will correspond to its share D ₂ , the driving force of mass transfer $$\Delta {\text{'}\text{'}}_{{\beta }_{\mathrm{one}}}={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="00000024.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\cdot \Delta$$

and mass transfer equation: $${\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="00000024.png"\; state="\{\{state\}\}">M</figure-callout>}}_2=\Delta {\text{'}\text{'}}_{{\beta }_{\mathrm{one}}}\cdot {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="00000024.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\cdot \Delta \cdot F$$

.

From the comparison it follows that the obtained equation (6) is the kinetic law of mass transfer, in which the driving force is expressed in terms of a fraction of the total driving force of the mass transfer.

From (6), taking into account (8), it also follows:

and this means that under the conditions under consideration, the fraction D1 is numerically equal to the ratio of the diffusion resistance of mass transfer of the second medium at a speed w ₁ to the diffusion resistance of mass transfer.

по уравнению (6).The above dependences are the theoretical justification of the described method, which differs from the already known ones in that the mass transfer coefficient is calculated by the driving force of the mass transfer process, represented through the fraction of the driving force of the mass transfer, accurately and simply measured in the experiment. As follows from the above discussion, the necessary information for determining the value of the fraction D is obtained from the results of two mass transfer processes. Thus, the new method is carried out by carrying out two stationary processes of mass transfer, which proceed sequentially or in parallel, and they differ only in different velocities w ₁ and w _{2 of the} liquid (gaseous) medium from the side of the studied surface of the body, ceteris paribus. And as a result, a combination of only experimental data M ₁ (ΔM ₁ ), M ₂ (ΔM ₂ ), w ₁ , w ₂ without any assumptions and approximations allows us to express the value of the fraction, and therefore, determine the value of the driving force of mass transfer and calculate the coefficients mass transfer β ₁ and $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

by equation (6).

The magnitude of the exponent n at a ratio of velocities w ₁ / w ₂ is determined by the shape of the surface that is in contact with a liquid or gas. From the experience of studying the phenomena of heat and mass transfer for most of the most common forms of surfaces, these indicators are known. For example, when washing with a liquid stream small flat partitions n → 1, when the liquid flows through channels n = 0.8, and when washing with a liquid stream flat forms (fabric, leather, wall) n≈0.6.

In practice, the new method is implemented quite simply using a laboratory experimental setup (see drawing). For example, it is necessary to determine the mass transfer coefficient of moisture vapor between the barmony surface of the skin and the surrounding air of the chamber. As in the case of vapor permeability experiments, in the upper part of a glass partially filled with distilled water, a leather sample is tightly strengthened with a bakhtarmany surface outward. Then the glass is placed in the flow chamber, in which the speed of movement w ₁ , temperature t and relative humidity φ are already stabilized. After reaching the stationary mode of mass transfer (two to three times the data on moisture loss from the glass), the moisture loss ΔM _{1 is} measured over time Δτ and the temperature of the water in the glass is t _c . Then only the air velocity in the chamber is changed and stabilized to a value of w ₂ at a constant temperature and relative humidity. After reaching the stationary mode, ΔM _{2 is} measured for the same period of time Δτ, the temperature of the water in the glass t _in and the relative humidity φ are checked (using dry and wet thermometers). The measured data determine the partial pressure of moisture vapor in the glass P _article = (0.95 ÷ 0.98) P _n (P _n - saturation pressure at t _in ), in the chamber R _to and the driving force of mass transfer, expressed through the partial pressure of moisture vapor , Δ = P _st -P _to , mm Hg The experimental data of two stationary processes are used to calculate the mass transfer coefficient β ₁ according to the formula (6).

Example: we use the experimental data [5] obtained for skin with a fringed surface: w ₁ = 2 m / s, w ₂ = 2, 3 m / s, n = 1, Δτ = 1 hour, the driving force of the mass transfer process is Δ = 23 mmHg Art., skin surface F = 4.9 · 10 ^-4 m ² . Moisture loss: at the first stage of the process with w ₁ = 2 m / s ΔМ ₁ = 49 · 10 ^-6 kg, at the second stage ΔМ ₂ = 49.845 · 10 ^-6 kg. The following values of the mass transfer coefficients were obtained, which is in good agreement with the experimental data:

кг/(м²·ч·мм рт. ст.). Погрешность - в пределах 5-7%.β ₁ = 3.336 · 10 ^-2 kg / (m ² · h · mm RT.article); $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}=\mathrm{3,784}\cdot {10}^{-2}$$

kg / (m ² · h · mm RT. Art.). The error is within 5-7%.

An important circumstance of the proposed method and its new feature is the comparison of two modes of the same process, differing only in the speed of movement of one of the media (in this case, external). This makes it possible to find the quantitative fraction of the driving force of the convective mass transfer process Δ _β , which is very difficult and sometimes impossible to determine in experiment, unlike the quantities easily and accurately measured in experiment: ΔM ₁ ; ΔM ₂ , w ₁ , w ₂ , Δ.

Information sources

1. Kasatkin A.G. Basic processes and apparatuses of chemical technology. - M .: Chemistry, 1971

2. Dubnitsky V.I. Methodology for determining moisture coefficients. - M.: Energoizdat, 1954.

3. Nikitina L. M. Thermodynamic parameters and mass transfer coefficients in wet bodies. - M .: Energy, 1968

4. Rudobashta S.P. Mass transfer in solid phase systems. - M.: Chemistry, 1980.

5. Chesunov V. M., Zakharova A. A. Optimization of drying processes in light industry. - M .: Legpromizdat, 1985 .-- 112 p.

Claims (1)

A method for determining the mass transfer coefficient of porous permeable materials, including determining the quantities included in the kinetic laws of mass transfer and convective mass transfer, namely: the mass of the substance, the driving force of the mass transfer process (potential difference of the media on both sides of the material), the surface of the material, the process time, characterized in that these values are determined experimentally at two different speeds (true and auxiliary) of the medium washing the material from the side of determining the mass coefficient success, with the subsequent calculation of the desired coefficient according to the analytically obtained formula:

where ΔM ₁ and ΔM ₂ - respectively, the increment of the mass of moisture during the experiment, kg; Δτ is the increment of time corresponding to the increment of the mass of moisture, s; w ₁ and w ₂ - respectively, the true and auxiliary flow rates of the substance, m / s; Δ is the total driving force of the mass transfer process from one medium to another through the permeable wall of the material, Pa; F is the surface area of the sample, m ² , while in this formula the quantitative fraction of the potential difference between the surface and the washing medium is expressed, i.e. the driving force of mass transfer by convective diffusion mechanism, from the general driving force of the mass transfer process from one medium to another through permeable material.

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