Method for calculating the vapor diffusion coefficient of bound water in porous glass sand media

Abstract

This invention discloses a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium, and belongs to the technical field of groundwater hydrodynamics in aeration zones. This method establishes a functional relationship between the vapor diffusion coefficient of bound water and the evaporation rate and equivalent evaporation area of ​​bound water for the vapor diffusion process of bound water in a porous glass sand medium, and further calculates the vapor diffusion coefficient of bound water. By using this method, it is possible to obtain the dynamic change of the vapor diffusion coefficient of bound water in the water evaporation process of a porous glass sand medium. The method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium according to the present invention enables the rapid acquisition of the vapor diffusion coefficient of bound water with high accuracy and reliability.

Description

[Technical Field]

[0001] This invention belongs to the technical field of groundwater hydrodynamics in aeration zones, and more specifically, to a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium. [Background technology]

[0002] The diffusion coefficient is an important parameter representing the water transport capacity in a porous glass sand medium. Experimental and numerical simulation methods are typically used to calculate the water diffusion coefficient of porous glass sand mediums.

[0003] The experimental method calculates the water diffusion coefficient by actually measuring the diffusion rate of water in a medium. This can be achieved using various experimental apparatuses and techniques, such as measuring the water transport rate through the medium. However, the experimental method requires a lot of time and resources because it necessitates performing numerous experiments to obtain sufficient data for analysis. Furthermore, limitations on experimental conditions, such as the control of elements like temperature, humidity, and pressure, also affect the feasibility of the experiment.

[0004] On the other hand, numerical simulation methods use mathematical models and computers to simulate the diffusion process of water in a medium. This method involves establishing mathematical models of the medium structure and water transport, and then using a computer to simulate the water diffusion process and calculate the water diffusion coefficient. However, numerical simulation methods require accurate mathematical models and high-performance computers, resulting in high computational complexity and long computation times.

[0005] Therefore, while these methods all have some use in calculating the water diffusion coefficient, they all ignore bound water, which is the main control factor of vapor diffusion, and the diffusion coefficient calculation is basically performed considering all pore water. Furthermore, problems such as limited experimental conditions, significant consumption of time and resources, and high computational complexity are particularly significant. Therefore, in order to solve these problems, further research and development of more efficient and accurate calculation methods are necessary. [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] The objective of the present invention is to provide a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium, thereby solving the technical problems of conventional techniques, which cannot take into account the dynamic changes in the vapor diffusion coefficient of bound water, resulting in low accuracy and low reliability. [Means for solving the problem]

[0007] Regarding the technical solutions, in order to solve the above technical problems, the present invention proposes a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium. Specifically, Step 1 calculates the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 2 calculates the equivalent evaporation area of ​​bound water in the porous glass sand medium based on the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 3 involves establishing a dynamic relationship between the evaporation rate of bound water in a porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium, and constructing a functional relationship where the vapor diffusion coefficient of bound water in the porous glass sand medium is the dependent variable and the evaporation rate of bound water and the equivalent evaporation area of ​​bound water in the porous glass sand medium are the independent variables. The method includes step 4, which calculates the vapor diffusion coefficient of bound water based on the functional relationship between the vapor diffusion coefficient of bound water and the vaporization rate of bound water and the equivalent area of ​​vaporization of bound water, by giving the vaporization rate of bound water and the equivalent area of ​​vaporization of bound water.

[0008] Furthermore, in step 1, the method for calculating the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium is as follows: e = V(∂θ / ∂t) e b =V(∂θ b / ∂t) and e is the total evaporation rate, b V is the evaporation rate of bound water, V is the volume of the glass sand porous medium, θ is the total volume water content, and θ b θ is the bound water volume water content, t is the evaporation time, ∂θ / ∂t is the change in total volume water content with respect to evaporation time, and ∂θ b / ∂t represents the change in bound water content with respect to evaporation time.

[0009] Furthermore, in step 2, the calculation of the equivalent evaporation area of ​​bound water in the porous glass sand medium is performed.

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[0010] Furthermore, in step 3, the method for establishing the dynamic relationship between the evaporation rate of bound water in the porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium is as follows:

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[0011] A method for constructing a functional relationship with the vapor diffusion coefficient of bound water in the glass sand porous medium as the dependent variable and the evaporation rate of bound water in the glass sand porous medium and the evaporation equivalent area of bound water in the glass sand porous medium as the independent variables is [Number] as follows.

[0012] Furthermore, in step 4, according to the functional relationship between the constructed vapor diffusion coefficient of bound water and the evaporation rate of bound water and the evaporation equivalent area of bound water, the vapor diffusion coefficient of bound water in the glass sand porous medium can be obtained by substitution calculation under the given conditions of the evaporation rate of bound water and the vapor diffusion area of bound water.

[0013] Regarding the beneficial effects, compared with the prior art, the technical solution of the present invention has the following beneficial technical effects.

[0014] (1) The calculation method of the vapor diffusion coefficient of bound water in the glass sand porous medium according to the embodiment of the present application theorizes the calculation of the dynamic change of the vapor diffusion coefficient of bound water, thereby generalizing the method. The method can realize the calculation of the dynamic change of the vapor diffusion coefficient of bound water and can be calculated only by parameters such as evaporation rate, vapor concentration, surface area, and porosity. In the prior art, the dynamic change of the vapor diffusion coefficient of bound water cannot be considered, and there are technical problems of low accuracy and low reliability, which are solved, and the results can be obtained quickly.

[0015] (2) The method for calculating the vapor diffusion coefficient of bound water in a porous medium according to the present invention calculates the vapor diffusion coefficient of bound water by establishing a physical process model of vapor diffusion of bound water based on accurate measurement of bound water in the evaporation process of a glass sand porous medium, thereby compensating for the drawback in the prior art that it is not possible to calculate the diffusion coefficient for the vapor diffusion process of bound water, and is highly accurate and reliable. [Brief explanation of the drawing]

[0016] [Figure 1] Figure 1 is a flowchart showing a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium according to an embodiment of the present invention. [Figure 2] Figure 2 shows the dynamic change in the vapor diffusion coefficient of bound water according to an embodiment of the present invention. [Modes for carrying out the invention]

[0017] Specific embodiments of the present invention will be described in more detail below with reference to the drawings and examples. The following embodiments are used solely to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0018] As shown in Figure 1, the present invention proposes a method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium, specifically, Step 1 calculates the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 2 calculates the equivalent evaporation area of ​​bound water in the porous glass sand medium based on the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 3 involves establishing a dynamic relationship between the evaporation rate of bound water in a porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium, and constructing a functional relationship where the vapor diffusion coefficient of bound water in the porous glass sand medium is the dependent variable and the evaporation rate of bound water and the equivalent evaporation area of ​​bound water in the porous glass sand medium are the independent variables. The method includes step 4, which calculates the vapor diffusion coefficient of bound water based on the functional relationship between the vapor diffusion coefficient of bound water and the vaporization rate of bound water and the equivalent area of ​​vaporization of bound water, by giving the vaporization rate of bound water and the equivalent area of ​​vaporization of bound water.

[0019] Furthermore, in step 1, the method for calculating the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium is as follows: e = V(∂θ / ∂t) e b =V(∂θ b / ∂t) And, e is the total evaporation rate, b V is the evaporation rate of bound water, V is the volume of the glass sand porous medium, θ is the total volume water content, and θ b θ is the bound water volume water content, t is the evaporation time, ∂θ / ∂t is the change in total volume water content with respect to evaporation time, and ∂θ b / ∂t represents the change in bound water content with respect to evaporation time.

[0020] Furthermore, in step 2, the calculation of the equivalent evaporation area of ​​bound water in the porous glass sand medium is performed.

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[0021] Furthermore, in step 3, the method for establishing the dynamic relationship between the evaporation rate of bound water in the porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium is as follows:

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[0022] A method for constructing a functional relationship where the vapor diffusion coefficient of bound water in a porous glass sand medium is the dependent variable, and the evaporation rate of bound water in the porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium are the independent variables is:

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[0023] Furthermore, in step 4, the constructed bound water vapor diffusion coefficient can be obtained by substituting the values ​​given the bound water evaporation rate and the bound water vapor diffusion area, based on the functional relationship between the bound water evaporation rate and the equivalent evaporation area of ​​the bound water.

[0024] Actual calculation example

[0025] In the experiment, glass sand with a mesh count of 30 and a particle size range of 0.6 to 0.8 mm was selected as the sample manufacturing material. The physical property parameters of the sample were given, and porous glass sand media samples with saturation rates of 100%, 80%, 60%, and 40% were manufactured, and evaporation experiments were conducted. The dynamic change of D obtained according to the calculation method for the vapor diffusion coefficient of bound water in the porous glass sand media according to the present invention is shown in Figure 2. Generally, when describing vapor diffusion according to Fick's law, D is considered to be a constant, but according to the method in this embodiment, D is not constant during the evaporation process and increases slightly with increasing evaporation time. Nevertheless, the overall change of D during the evaporation process is very small. Therefore, when describing the vapor diffusion process of bound water, it is possible to treat D as a constant. However, in order to accurately describe the movement law of the vapor diffusion process of bound water, the change in D must be considered, and the higher the degree of unsaturation, the larger the corresponding D. This indicates that the movement of bound water by vapor diffusion is promoted by increasing the degree of unsaturation.

[0026] The above-described specific embodiments further illustrate the object, technical solution, and beneficial effects of the present invention. However, these are merely specific embodiments of the present invention and do not limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should all be included within the scope of protection of the present invention.

Claims

1. A method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium, Step 1 involves calculating the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 2 calculates the equivalent evaporation area of ​​bound water in the porous glass sand medium based on the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. Step 3 involves establishing a dynamic relationship between the evaporation rate of bound water in a porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium, and constructing a functional relationship where the vapor diffusion coefficient of bound water in the porous glass sand medium is the dependent variable and the evaporation rate of bound water and the equivalent evaporation area of ​​bound water in the porous glass sand medium are the independent variables. A method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium, comprising step 4, which involves calculating the vapor diffusion coefficient of bound water based on a functional relationship between the vaporization rate of bound water and the equivalent area of ​​evaporation of bound water, by giving the vaporization rate of bound water and the equivalent area of ​​evaporation of bound water.

2. Step 1 involves calculating the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium. e = V(∂θ / ∂t) e ｂ = V(∂θ) ｂ / ∂t) and e is the total evaporation rate, and e ｂ V is the evaporation rate of bound water, V is the volume of the porous glass sand medium, θ is the total volume water content, and θ ｂ θ is the bound water volume water content, t is the evaporation time, ∂θ / ∂t is the change in total volume water content with respect to evaporation time, and ∂θ ｂ The method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium according to claim 1, characterized in that / ∂t is the change in bound water volume water content with respect to evaporation time.

3. Step 2 is a method for calculating the equivalent evaporation area of ​​bound water in a porous glass sand medium based on the total evaporation rate of the porous glass sand medium and the evaporation rate of bound water in the porous glass sand medium, [Math 11] And, A ｖ ρ is the equivalent area of ​​bound water evaporation, A is the actual surface area of ​​the porous glass sand medium, ψ is the porosity of the porous glass sand medium, ξ is the empirical reduction coefficient, σ is the interfacial tension of water, α is the contact angle between water and the glass sand surface, and ρ ｗ g is the density of water, and g is the acceleration due to gravity. [Math 12] This is the average pore size of free water, [Number 13] The method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium according to claim 2, characterized in that is the amount of change in capillary rise height.

4. Step 3 involves establishing a dynamic relationship between the evaporation rate of bound water in a porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium. [Number 14] And, D is the vapor diffusion coefficient of the bound water, and C １ is the initial vapor concentration in the evaporation process, and C ∞ is the vapor concentration at the end of the evaporation process, and A ｖ is the evaporation equivalent area of the bound water, and H is the height of the glass sand porous medium, A method for constructing a functional relationship where the vapor diffusion coefficient of bound water in a porous glass sand medium is the dependent variable, and the evaporation rate of bound water in the porous glass sand medium and the equivalent evaporation area of ​​bound water in the porous glass sand medium are the independent variables is: [Number 15] The method for calculating the vapor diffusion coefficient of bound water in a porous glass sand medium according to claim 3.

5. Step 4 is characterized in that the constructed vapor diffusion coefficient of bound water can be obtained by substituting values ​​into a porous glass sand medium, given the conditions that the evaporation rate of bound water and the vapor diffusion area of ​​bound water are specified, so that the vapor diffusion coefficient of bound water can be obtained by the function relationship between the evaporation rate of bound water and the equivalent evaporation area of ​​bound water.

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