Method for calculating bound water vapor diffusion coefficient of glass sand porous medium

Abstract

The present invention belongs to the technical field of dynamics of groundwater in an aeration zone. Disclosed is a method for calculating a bound water vapor diffusion coefficient of a glass sand porous medium. In the method, for a bound water vapor diffusion process of a glass sand porous medium, a functional relationship of a bound water vapor diffusion coefficient with regard to a bound water evaporation rate and a bound water evaporation equivalent area is established, and then the bound water vapor diffusion coefficient is calculated. By using the method, dynamic changes in the bound water vapor diffusion coefficient during a water evaporation process of the glass sand porous medium can be calculated. The method for calculating a bound water vapor diffusion coefficient of a glass sand porous medium provided in the present invention can rapidly acquire a bound water vapor diffusion coefficient with high precision and high reliability.

Description

A calculation method for the water vapor diffusion coefficient of glass sand porous media Technical Field

[0001] The invention belongs to the technical field of groundwater dynamics in aeration zones, and particularly relates to a method for calculating a glass sand porous medium combined with water vapor diffusion coefficient. Background Art

[0002] The diffusion coefficient is an important parameter that describes the water transport capacity in glass sand porous media. When it comes to the calculation of the water diffusion coefficient of glass sand porous media, experimental methods and numerical simulation methods are usually used.

[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 setups and techniques, such as measuring the water transmission rate through the medium. However, the experimental method is time- and resource-intensive, as numerous experiments are required to obtain sufficient data for analysis. Furthermore, experimental limitations, such as the need to control temperature, humidity, and pressure, can also affect the feasibility of the experiment.

[0004] Numerical simulation, on the other hand, utilizes mathematical models and computers to simulate the water diffusion process in a medium. This method calculates the water diffusion coefficient by establishing a mathematical model of the medium structure and water transport, then using a computer to simulate the water diffusion process. However, numerical simulation requires accurate mathematical models and high-performance computers, resulting in high computational complexity and long computation times.

[0005] Therefore, while these methods have some application in calculating water diffusion coefficients, they all ignore bound water as the primary controlling factor in vapor diffusion and primarily calculate the diffusion coefficient for the entire pore water volume. Furthermore, they are particularly susceptible to limitations in experimental conditions, significant time and resource consumption, and high computational complexity. Therefore, further research and development of more efficient and accurate calculation methods are needed to address these issues.

[0006] Summary of the Invention

[0007] Purpose of the invention: The present invention provides a method for calculating the diffusion coefficient of water vapor in combination with glass sand porous media, so as to solve the technical problems in the prior art that the dynamic changes of the diffusion coefficient of water vapor cannot be considered, the accuracy is low, and the reliability is poor.

[0008] Technical solution: In order to solve the above technical problems, the present invention proposes a method for calculating the water vapor diffusion coefficient of glass sand porous media, which specifically includes the following steps:

[0009] Step 1: Calculate the total evaporation rate of the glass sand porous medium and the evaporation rate of the bound water in the glass sand porous medium;

[0010] Step 2: Calculate the equivalent evaporation area of ​​bound water in the glass sand porous medium based on the total evaporation rate of the glass sand porous medium and the evaporation rate of bound water in the glass sand porous medium;

[0011] Step 3: Establish a dynamic relationship between the evaporation rate of water bound to the glass sand porous medium and the equivalent area of ​​water evaporation bound to the glass sand porous medium, and construct a functional relationship with the diffusion coefficient of water vapor bound to the glass sand porous medium as the dependent variable and the evaporation rate of water bound to the glass sand porous medium and the equivalent area of ​​water evaporation bound to the glass sand porous medium as the independent variables;

[0012] Step 4: According to the functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, the bound water vapor diffusion coefficient is calculated given the bound water evaporation rate and the bound water evaporation equivalent area.

[0013] Furthermore, in step 1, the method for calculating the total evaporation rate of the glass sand porous medium and the evaporation rate of the bound water of the glass sand porous medium is as follows:

[0014] Where, e is the total evaporation rate, e b is the bound water evaporation rate, V is the volume of the glass sand porous medium, θ is the total volume water content, θ b is the volumetric water content of bound water, t is the evaporation time, is the change in total volume water content relative to evaporation time, It represents the change of bound water volume content relative to evaporation time.

[0015] Furthermore, in step 2, the equivalent area of ​​glass sand porous medium combined with water evaporation is calculated as follows

[0016] Among them, A v is the equivalent area of ​​combined water evaporation, A is the actual surface area of ​​the glass sand porous medium, is the porosity of the glass sand porous 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, ρ w is the density of water, g is the acceleration due to gravity, is the average free water pore diameter, is the change in capillary rise height.

[0017] Furthermore, in step 3, the dynamic relationship between the evaporation rate of the glass sand porous medium combined with water and the equivalent area of ​​the glass sand porous medium combined with water evaporation is established as follows:

[0018] Where D is the diffusion coefficient of bound water vapor, C1 is the initial vapor concentration during evaporation, and C∞ is the vapor concentration at the end of the evaporation process, A v is the equivalent area of ​​combined water evaporation, and H is the height of the glass sand porous medium.

[0019] A functional relationship was constructed with the glass sand porous medium combined water vapor diffusion coefficient as the dependent variable, and the glass sand porous medium combined water evaporation rate and the glass sand porous medium combined water evaporation equivalent area as the independent variables:

[0020] Furthermore, in step 4, by constructing a functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, under the conditions of given bound water evaporation rate and bound water vapor diffusion area, the bound water vapor diffusion coefficient of the glass sand porous medium can be obtained by substituting them into the calculation.

[0021] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0022] (1) The method for calculating the water vapor diffusion coefficient of the glass sand porous medium provided in the embodiments of the present application theorizes the calculation of the dynamic change of the water vapor diffusion coefficient, making the method generalizable. The method realizes the calculation of the dynamic change of the water vapor diffusion coefficient, and only requires the evaporation rate, vapor concentration, surface area, porosity and other parameters to calculate. This solves the technical problems of the prior art that the dynamic change of the water vapor diffusion coefficient cannot be considered, the accuracy is not high, and the reliability is poor, and the results can be obtained quickly.

[0023] (2) The method for calculating the diffusion coefficient of bound water vapor in porous media provided by the present invention is based on the precise measurement of bound water in the evaporation process of glass sand porous media. By establishing a physical process model of the diffusion of bound water vapor, the diffusion coefficient of bound water vapor is calculated, which makes up for the defect that the diffusion coefficient cannot be calculated for the diffusion process of bound water vapor in the existing technology. It has high accuracy and strong reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG1 is a flow chart of a method for calculating a glass sand porous medium combined with water vapor diffusion coefficient provided by an embodiment of the present invention.

[0025] FIG2 shows the dynamic change of the combined water vapor diffusion coefficient provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are only used 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.

[0027] As shown in FIG1 , the present invention proposes a method for calculating the water vapor diffusion coefficient of a glass sand porous medium, which specifically includes the following steps:

[0028] Step 1: Calculate the total evaporation rate of the glass sand porous medium and the evaporation rate of the bound water in the glass sand porous medium;

[0029] Step 2: Calculate the equivalent evaporation area of ​​bound water in the glass sand porous medium based on the total evaporation rate of the glass sand porous medium and the evaporation rate of bound water in the glass sand porous medium;

[0030] Step 3: Establish a dynamic relationship between the evaporation rate of water bound to the glass sand porous medium and the equivalent area of ​​water evaporation bound to the glass sand porous medium, and construct a functional relationship with the diffusion coefficient of water vapor bound to the glass sand porous medium as the dependent variable and the evaporation rate of water bound to the glass sand porous medium and the equivalent area of ​​water evaporation bound to the glass sand porous medium as the independent variables;

[0031] Step 4: According to the functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, the bound water vapor diffusion coefficient is calculated given the bound water evaporation rate and the bound water evaporation equivalent area.

[0032] Furthermore, in step 1, the method for calculating the total evaporation rate of the glass sand porous medium and the evaporation rate of the bound water of the glass sand porous medium is as follows:

[0033] Where, e is the total evaporation rate, e b is the bound water evaporation rate, V is the volume of the glass sand porous medium, θ is the total volume water content, θ b is the volumetric water content of bound water, t is the evaporation time, is the change in total volume water content relative to evaporation time, It represents the change of bound water volume content relative to evaporation time.

[0034] Furthermore, in step 2, the equivalent area of ​​glass sand porous medium combined with water evaporation is calculated as follows:

[0035] Among them, A v is the equivalent area of ​​combined water evaporation, A is the actual surface area of ​​the glass sand porous medium, is the porosity of the glass sand porous 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, ρ w is the density of water, g is the acceleration due to gravity, is the average free water pore diameter, is the change in capillary rise height.

[0036] Furthermore, in step 3, the dynamic relationship between the evaporation rate of the glass sand porous medium combined with water and the equivalent area of ​​the glass sand porous medium combined with water evaporation is established as follows:

[0037] Where D is the diffusion coefficient of bound water vapor, C1 is the initial vapor concentration during evaporation, and C ∞ is the vapor concentration at the end of the evaporation process, A v is the equivalent area of ​​combined water evaporation, and H is the height of the glass sand porous medium.

[0038] A functional relationship was constructed with the glass sand porous medium combined water vapor diffusion coefficient as the dependent variable, and the glass sand porous medium combined water evaporation rate and the glass sand porous medium combined water evaporation equivalent area as the independent variables:

[0039] Furthermore, in step 4, by constructing a functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, under the conditions of given bound water evaporation rate and bound water vapor diffusion area, the bound water vapor diffusion coefficient of the glass sand porous medium can be obtained by substituting them into the calculation.

[0040] Actual example:

[0041] In the experiment, glass sand with a mesh size of 30 and a particle size range of 0.6-0.8 mm was selected as the sample preparation material. Given the physical property parameters of the sample, glass sand porous medium samples with saturations of 100%, 80%, 60% and 40% were prepared to carry out evaporation experiments. According to a method for calculating the diffusion coefficient of bound water vapor in a glass sand porous medium provided by the present invention, the dynamic change of D is obtained as shown in Figure 2. Generally speaking, when describing vapor diffusion according to Fick's law, D is considered to be a constant, but according to the method provided in this embodiment, D is not constant during the evaporation process, but increases slightly with the increase of evaporation time. Despite this, the overall change of D during the evaporation process is very small. Therefore, it is feasible to regard D as a constant when describing the diffusion process of bound water vapor. However, in order to accurately describe the migration law of the diffusion process of bound water vapor, the change of D must be taken into account. The higher the degree of unsaturation, the larger the corresponding D. This shows that the increase in the degree of unsaturation promotes the migration of bound water through vapor diffusion.

[0042] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to 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 be included in the scope of protection of the present invention.

Claims

1. A method for calculating the diffusion coefficient of glass sand porous medium combined with water vapor, characterized in that: The method comprises the following steps: Step 1: Calculate the total evaporation rate of the glass sand porous medium and the evaporation rate of the combined water of the glass sand porous medium; Step 2: Calculate the evaporation equivalent area of ​​the glass sand porous medium combined water according to the total evaporation rate of the glass sand porous medium and the evaporation rate of the glass sand porous medium combined water; Step 3: Establish a dynamic relationship between the evaporation rate of glass sand porous media combined with water and the equivalent area of ​​glass sand porous media combined with water evaporation, and construct a functional relationship with the glass sand porous media combined with water vapor diffusion coefficient as the dependent variable and the glass sand porous media combined with water evaporation rate and the glass sand porous media combined with water evaporation equivalent area as the independent variables; Step 4: According to the functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, the bound water vapor diffusion coefficient is calculated given the bound water evaporation rate and the bound water evaporation equivalent area.

2. The method for calculating the diffusion coefficient of glass sand porous medium combined with water vapor according to claim 1, characterized in that: In step 1, the method for calculating the total evaporation rate of the glass sand porous medium and the evaporation rate of the combined water of the glass sand porous medium is as follows: Where, e is the total evaporation rate, e b 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 is the volumetric water content of bound water, t is the evaporation time, is the change in total volume water content relative to evaporation time, It expresses the change of bound water volume content relative to evaporation time.

3. The method for calculating the diffusion coefficient of glass sand porous medium combined with water vapor according to claim 2, characterized in that: In step 2, the method for calculating the equivalent area of ​​evaporation of combined water of the glass sand porous medium according to the total evaporation rate of the glass sand porous medium and the evaporation rate of combined water of the glass sand porous medium is as follows: Among them, A v is the equivalent area of ​​combined water evaporation, A is the actual surface area of ​​the glass sand porous medium, is the porosity of glass sand porous media, ξ is the empirical reduction coefficient, σ is the interfacial tension of water, α is the contact angle between water and glass sand surface, ρ w is the density of water, g is the acceleration due to gravity, is the average free water pore diameter, is the change in capillary rise height.

4. The method for calculating the diffusion coefficient of glass sand porous medium combined with water vapor according to claim 3, characterized in that: In step 3, the dynamic relationship between the evaporation rate of the glass sand porous medium combined with water and the equivalent area of ​​the glass sand porous medium combined with water evaporation is established as follows: Where D is the combined water vapor diffusion coefficient, C1 is the initial vapor concentration during evaporation, and C ∞ is the vapor concentration at the end of the evaporation process, A v is the equivalent area of ​​combined water evaporation, H is the height of the glass sand porous medium; The functional relationship is constructed with the glass sand porous medium combined with water vapor diffusion coefficient as the dependent variable, the glass sand porous medium combined with water evaporation rate and the glass sand porous medium combined with water evaporation equivalent area as the independent variables as follows:

5. The method for calculating the diffusion coefficient of glass sand porous medium combined with water vapor according to claim 4, characterized in that: In step 4, by constructing the functional relationship between the bound water vapor diffusion coefficient and the bound water evaporation rate and the bound water evaporation equivalent area, under the conditions of given bound water evaporation rate and bound water vapor diffusion area, the bound water vapor diffusion coefficient of the glass sand porous medium can be obtained by substituting them into the calculation.

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