Permeation reaction calculation method of inorganic gel in porous medium

Abstract

The invention relates to a permeable reaction calculation method for inorganic gel in a porous medium, which comprises the following steps: establishing a pore model of the porous medium, and permeating a first reactant and a second reactant in the porous medium to generate a first reaction product; the first reactant comprises silicate ions, and the second reactant comprises calcium ions; the first reaction product changes the pore structure of the porous medium so as to influence the permeation speed of silicate ions and calcium ions, and a first volume variable of the first reaction product is calculated; establishing a dissolution model of the calcium ions, and calculating a second volume variable of the pore structure of the porous medium caused by the dissolution of the calcium ions according to the mutual influence of the dissolution of the calcium ions and the change of the pore structure of the porous medium; according to the first volume variable and the second volume variable, the change condition of the pore structure of the porous medium is obtained, so that the performance of the capillary crystalline material under different environmental conditions can be dynamically and accurately simulated, and the permeability and the self-healing behavior of the capillary crystalline material can be better predicted.

Description

Technical Field

[0001] The invention relates to a method for calculating the permeation reaction of an inorganic gel in a porous medium, and belongs to the field of simulation and emulation of computational material science and engineering materials. Background Art

[0002] Cement-based materials with excellent self-healing and anti-permeability properties are seeing increasing application in durability and environmental protection. As a functional material with self-healing properties, permeable crystalline materials are widely used in concrete and cement-based materials. Their anti-permeability and crack resistance play a key role in improving building durability.

[0003] Patent CN114689827B, authorized in China, discloses a method for testing the self-healing performance of self-repairing concrete cracks. This method involves conducting an anti-seepage pressure test on cracked concrete self-healing specimens and a baseline concrete self-healing specimen. The anti-seepage pressure of the cracked concrete self-healing specimen and the baseline concrete self-healing specimen are then measured. The self-healing performance of the self-repairing concrete cracks is evaluated using the ratio of the anti-seepage pressures of the cracked concrete self-healing specimen to the baseline concrete self-healing specimen. However, this method fails to demonstrate the impact of post-processing factors on the self-healing performance, nor does it explore the internal factors of self-healing.

[0004] Chinese patent publication number CN114414453A discloses a method for measuring the penetration depth of an inorganic penetrating crystalline material into concrete. The method comprises: applying the inorganic penetrating crystalline material to a known coating density on the surface of a concrete specimen, placing the concrete specimen in a closed chamber with adjustable humidity, temperature, and air pressure, and allowing the inorganic penetrating crystalline material to naturally penetrate under the set humidity, temperature, and air pressure conditions. After a certain period of penetration, the concentrations of Na and K elements are measured in samples taken at different depths from the concrete specimen surface. Based on a graph of Na and K concentration versus depth, the depth at which the Na and K concentrations suddenly drop is determined, and the penetration depth of the inorganic penetrating crystalline material into the concrete specimen surface is determined accordingly. This method eliminates interference caused by Na and K elements inherent in the concrete specimen during direct measurement. This method selects Na and K ions for penetration prediction, providing a new penetration testing method that can provide insights into detecting the penetration of penetrating crystalline materials. However, this method fails to account for the coupled influencing factors, such as the material environment, and does not reflect the complex working conditions found in actual projects.

[0005] Furthermore, traditional methods primarily rely on laboratory testing, using experimental methods such as immersion and pressure penetration testing to obtain data on material permeability and crack resistance. These experiments involve observing the material's permeation behavior in water and chemical reagents, and evaluating its water resistance and durability by measuring metrics such as penetration depth and water absorption. However, this approach is often costly, time-consuming, and difficult to control, and it struggles to simulate the long-term permeability of materials under complex stress environments. Existing finite element simulation methods have been used for material stress analysis and crack prediction. For example, software such as COMSOL and ANSYS are commonly used for porous media permeation simulation of cement-based materials. By adjusting parameters such as the material's permeability coefficient, environmental stress, and temperature and humidity, these methods can simulate internal permeation and microcrack formation in the material. However, due to the limitations of most finite element simulations in accounting for the material's internal crystallization and self-healing properties, it is difficult to accurately predict the dynamic self-healing response of permeating crystallized materials and their contribution to crack resistance. Furthermore, the simulation accuracy is limited by limitations in model establishment, parameter settings, and calculation methods, making it difficult to truly reflect the complex working conditions found in actual projects. Self-healing material technology has been applied to concrete crack healing, but its microstructural simulation capabilities are relatively limited. Traditional methods typically use reaction rate-based models, incorporating the chemical reactions of self-healing materials at the crack site into their calculations to predict the material's strength recovery after crack repair. However, these methods struggle to accurately simulate the permeability changes and self-healing processes of materials under complex stress states. For example, there is currently a lack of dynamic simulations of the response of self-healing materials to changes in environmental stress, or the impact of material crystallization behavior on permeability.

[0006] Therefore, in view of the shortcomings of the above technologies, it is urgent to propose a method for calculating the permeation reaction of inorganic gels in porous media. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for calculating the permeation reaction of inorganic gels in porous media, which can dynamically and accurately simulate the performance of permeable crystalline materials under different environmental conditions to better predict their permeability and self-healing behavior.

[0008] To achieve the above object, the present invention provides the following technical solution: a method for calculating the permeation reaction of an inorganic gel in a porous medium, the method comprising:

[0009] Establishing a pore model of a porous medium, and infiltrating a first reactant and a second reactant into the porous medium so that the first reactant and the second reactant react to generate a first reaction product; wherein the first reactant comprises silicate ions, and the second reactant comprises calcium ions;

[0010] The first reaction product changes the pore structure of the porous medium to affect the permeation rate of the silicate ions and the calcium ions, thereby causing the volume of the first reaction product to change, and calculating a first volume variable of the first reaction product;

[0011] Establishing a calcium ion dissolution model, and calculating a second volume variable of the pore structure of the porous medium caused by the calcium ion dissolution based on the mutual influence between the calcium ion dissolution and the change in the pore structure of the porous medium;

[0012] According to the first volume variable and the second volume variable, the change of the pore structure of the porous medium is obtained.

[0013] In one embodiment, the first reactant and the second reactant react to generate a first reaction product, including:

[0014] The silicate ions and the calcium ions will produce content changes due to reaction rate and ion transport when they penetrate into the porous medium. The reaction control equation is obtained based on the conservation relationship in the fluid transport process to calculate the content change of the silicate ions and the calcium ions penetrating into the porous medium.

[0015] In one embodiment, the reaction control equation is:

[0016]

[0017] where Φ = φ paste =φ capillary +φ gel , its value is 3.2nm~320μm, J is in Ω=-1.5tanh(8.0(φ paste -0.25))+2.5, C represents the concentration of silicate ions and / or the flow rate of water in the voids, and Q is

[0018] In one embodiment, the first volume variable formula of the first reaction product is:

[0019]

[0020] Where, ΔV CSH Represents the volume change of the first reaction product; V CSH represents the volume of CSH when the first reaction product is dissolved to 0; C CSH Indicates the total mol amount of the first reaction product when the first reaction product is dissolved to 0; C solidIndicates the molar amount of the remaining first reaction product.

[0021] In one embodiment, the method further comprises:

[0022] As the concentration of the calcium ions decreases, the dissolution of the third reactant in the porous medium is promoted;

[0023] Based on the first volume variable formula of the first reaction product, an ion transport equation is established, and combined with the pore model of the porous medium to establish the calcium ion dissolution model.

[0024] In one embodiment, the ion transport equation is:

[0025]

[0026] The first term on the left represents the unsteady term, and the second term is the convection term; the first term on the right represents the diffusion term, and the second term represents the source term.

[0027] In one embodiment, the formula for the change in the pore structure of the porous medium is:

[0028]

[0029] where ΔV CH represents the reduction in solid phase volume due to the dissolution of the third reactant (m 3 / m 3 ); Δm CH Indicates the mass of the third reactant dissolved (kg / m 3 );ρ CH represents the density of the third reactant (2.24×10 3 kg / m 3 ); ΔC CH Indicates the reduction of the solid third reactant (mmol / m 3 );M CH represents the molar mass of the third reactant calcium (74.1×10 -6 kg / mmol).

[0030] In one embodiment, the reaction rate formula of the silicate ion is:

[0031]

[0032] The beneficial effects of the present invention are as follows: by establishing a pore model of a porous medium, and infiltrating a first reactant and a second reactant in the porous medium so that the first reactant and the second reactant react and generate a first reaction product; wherein the first reactant includes silicate ions and the second reactant includes calcium ions; the first reaction product changes the pore structure of the porous medium to affect the penetration rate of silicate ions and calcium ions, thereby causing the volume of the first reaction product to change, and calculating a first volume variable of the first reaction product; establishing a calcium ion dissolution model, and calculating a second volume variable of the pore structure of the porous medium caused by calcium ion dissolution according to the mutual influence of calcium ion dissolution and the change in the pore structure of the porous medium; according to the first volume variable and the second volume variable, obtaining the change in the pore structure of the porous medium, thereby simplifying the parameter setting under complex conditions by constructing a model, and being able to quickly simulate the permeability and crack resistance of the material under different environmental parameter settings. Compared with the complex steps of relying on experimental measurement and finite element model setting in the prior art, the present invention reduces the dependence on experimental data, making the model more suitable for various actual working conditions.

[0033] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention and implement it according to the contents of the specification, the following is a detailed description of the preferred embodiments of the present invention with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the reaction within the model of the void structure of the porous medium;

[0035] Figure 2 This is a schematic diagram of the penetration testing method;

[0036] Figure 3 Mortar porosity calculation results diagram;

[0037] Figure 4 Calculation results of net slurry porosity;

[0038] Figure 5 Reaction-related parameters affect test results;

[0039] Figure 6 Transmission-related parameters affect test results;

[0040] Figure 7 Quantitative analysis diagram of Ca(OH)2 in the anti-seepage model. DETAILED DESCRIPTION

[0041] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0042] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0043] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0044] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. In the description of the present invention, the axis direction is consistent with the height direction.

[0045] See Figures 1 to 7 In a preferred embodiment of the present invention, a method for calculating the permeation reaction of an inorganic gel in a porous medium includes:

[0046] Step S1: Establish a pore model of a porous medium, and infiltrate a first reactant and a second reactant into the porous medium so that the first reactant and the second reactant react to form a first reaction product (CSH); wherein the first reactant comprises silicate ions and the second reactant comprises calcium ions. In this embodiment, the porous medium is concrete, the first reactant is CaO·SiO2, and the second reactant is Ca(OH)2. In other embodiments, the porous medium may be soil, rock, foam, ceramic, etc., the first reactant may be another compound comprising silicate ions, and the second reactant may be another compound comprising calcium ions. These are not specifically limited here and will be determined based on actual conditions.

[0047] The formula for the first reactant and the second reactant to react and generate the first reaction product is:

[0048] Na2O·nSiO2+nCa(OH)2=nCaO·SiO2+2NaOH+(n-1)H2O

[0049] Among them, n=2.12. The impact of the reaction on the material is mainly through changing the pore structure through the amount and density difference of the reaction products. The volume of 1 mol Ca(OH)2 is: 33.04 mol, and the volume of 1 mol CaO·SiO2 is: 47.54 mol. After the reaction, the volume of 1 mol of material increases and the pores decrease.

[0050] The reaction rate formula of silicate ion is:

[0051]

[0052] The balanced equation for the reaction process is:

[0053]

[0054] The ion transport equation is:

[0055]

[0056] The first term on the left represents the unsteady term, and the second term is the convection term; the first term on the right represents the diffusion term, and the second term represents the source term.

[0057] The ion transport equation represents the conservation relationship in the fluid transport process. Through this equation, the control equation for the reaction calculation can be obtained as follows:

[0058]

[0059] The first term is the rate of change of the unsteady term over time; the first part in the brackets of the second term is the increase rate of the diffusion term, and the second part is the decrease rate of the convection term; the third term is the increase term of the source term.

[0060] For silicate ion penetration, C represents the silicate ion concentration and / or the velocity of water in the pores. The change in silicate concentration is composed of two components: one is the change in concentration (J) due to silicate ion diffusion and movement with pore water, which is the second term in the formula; the other is the consumption R (<0) due to reaction with calcium ions.

[0061] Item Simplified to the governing equation of the J reaction process:

[0062] That is, the above process can be referred to as: the first reactant and the second reactant react to generate a first reaction product, including:

[0063] When silicate ions and calcium ions penetrate into porous media, their contents change due to reaction rate and ion transport. Based on the conservation relationship in the fluid transport process, the reaction control equation is obtained to calculate the content change of silicate ions and calcium ions penetrating into porous media.

[0064] The reaction control equation is:

[0065]

[0066] where Φ = φ paste =φ capillary +φ gel , its value is 3.2nm~320μm, J is in Ω=-1.5tanh(8.0(φ paste -0.25))+2.5, C represents the concentration of silicate ions and / or the flow rate of water in the voids, and Q is

[0067] Step S2: The first reaction product changes the pore structure of the porous medium to affect the penetration rate of silicate ions and calcium ions, thereby causing the volume of the first reaction product to change, and calculating a first volume variable of the first reaction product.

[0068] The first volume variable formula of the first reaction product is:

[0069]

[0070] Where, ΔV CSH Represents the volume change of the first reaction product; V CSH represents the volume of CSH when the first reaction product is dissolved to 0; C CSH Indicates the total mol amount of the first reaction product when the first reaction product is dissolved to 0; C solid Indicates the molar amount of the remaining first reaction product.

[0071] Therefore, step S3: establishing a calcium ion dissolution model (CALC-model), and calculating the second volume variable of the pore structure of the porous medium caused by the calcium ion dissolution based on the mutual influence between the calcium ion dissolution and the change of the pore structure of the porous medium.

[0072] Step S4: Obtaining the change of the pore structure of the porous medium according to the first volume variable and the second volume variable.

[0073] The method also includes:

[0074] As the concentration of calcium ions decreases, the dissolution of the third reactant in the porous medium is accelerated;

[0075] Based on the first volume variable formula of the first reaction product, an ion transport equation is established, and combined with the pore model of the porous medium to establish a calcium ion dissolution model. In this embodiment, the third reactant is calcium hydroxide.

[0076] That is, the formula for the change of the pore structure of porous media is:

[0077]

[0078] where ΔV CH represents the reduction in solid phase volume due to the dissolution of the third reactant (m 3 / m 3 ); Δm CH Indicates the mass of the third reactant dissolved (kg / m 3 );ρ CH represents the density of the third reactant (2.24×10 3 kg / m 3 ); ΔC CH Indicates the reduction of the solid third reactant (mmol / m 3 );M CH represents the molar mass of the third reactant calcium (74.1×10 -6 kg / mmol).

[0079] In addition, the effect of calcium hydroxide dissolution on porosity in the model is caused by the reduction of the solid phase volume of concrete due to the dissolution of solid calcium hydroxide and the first reaction product. The dissolution of the first reaction product is not considered in the sodium silicate infiltration, and the dissolution of the first reaction product is ignored.

[0080] The saturation concentration of calcium ions C satu , the calculation takes into account the influence of hydroxide, that is, the hydroxide ions in each step are accumulated, according to the formula K sp =[Ca 2 +][OH - ] 2 , the saturated calcium ion concentration can be calculated (the inhibitory effect of high pH value on calcium ion dissolution).

[0081] The calcium ion dissolution model (CALC-model) can be used to calculate the penetration and dissolution of calcium ions and their impact on the pore structure of porous media. The calculation assumes a calcium ion deficiency, so the amount of calcium silicate generated is determined by the amount of calcium ion dissolution. Taking into account the amount of calcium ions that penetrate externally, the reaction of all calcium ions with silicate ions to form calcium silicate is incorporated into the calcium ion dissolution model (CALC-model). The way in which this model alters pore structure is modeled after the way calcium ion dissolution alters pore structure, transferring the volume (mass) increase to the HYGR-model (the original thermodynamic coupling model).

[0082] The above process completes the calculation of silicate ion transport and its impact on the internal structure of concrete.

[0083] From the above, we can know that the reaction rate formula of silicate ions is:

[0084]

[0085] The reaction rate k directly affects the change of product content over time and further affects the development of pores and the transport of water and ions.

[0086] Therefore, to determine the magnitude of the rate, a constant boundary concentration boundary was used to test the specimens, and the corresponding porosity was measured at 3, 7, and 14 days to calibrate the K value. The results showed that when k = 0.1, the porosity calculation results and experimental values were in good agreement, which can better reflect the changes in pores. The reaction rate with K = 0.1 was used to calculate the changes in Ca(OH)2 content at different depths over time.

[0087] 1. During the spraying stage, the Ca(OH)2 at a depth of 0-2mm is consumed first, followed by 2-4mm and 4-6mm. All Ca(OH)2 at a depth of less than 6mm is consumed, while Ca(OH)2 at a depth of 6-8mm is partially consumed. After 8-10mm, the consumption is very small.

[0088] 2. The average consumption of Ca(OH)2 at the depth where the Ca(OH)2 content changes (0-10mm) at 14 days can be calculated to be approximately 65.8% of Ca(OH)2 consumed, which is close to the consumption of 52.5% deduced from the pore test value.

[0089] In order to determine the penetration depth of sodium silicate, blank and sprayed samples were taken and the content of Na element was measured along the penetration depth using an electron probe. The method is as shown in the attached figure. Figure 2 shown.

[0090] The measurement objects can be divided into two types according to the boundary conditions during production:

[0091] a) Quantitative spraying of 1.4g on the surface;

[0092] b) The penetration boundary is immersed in the spraying liquid for 8 hours.

[0093] To measure the material's effectiveness, we compared the porosity of blank and spray-coated specimens within different pore size ranges. We also pre-set different cracks to simulate the structural degradation experienced in actual engineering applications, and used a program to quantify the crack repair effect of silicate ions.

[0094] In summary: by establishing a pore model of a porous medium, and infiltrating a first reactant and a second reactant into the porous medium, so that the first reactant and the second reactant react and generate a first reaction product; wherein the first reactant includes silicate ions and the second reactant includes calcium ions; the first reaction product changes the pore structure of the porous medium to affect the penetration rate of silicate ions and calcium ions, thereby causing the volume of the first reaction product to change, and calculating the first volume variable of the first reaction product; establishing a calcium ion dissolution model, and calculating the second volume variable of the pore structure of the porous medium caused by the calcium ion dissolution according to the mutual influence of the calcium ion dissolution and the change in the pore structure of the porous medium; according to the first volume variable and the second volume variable, the change in the pore structure of the porous medium is obtained, thereby simplifying the parameter setting under complex conditions by constructing a model, and being able to quickly simulate the permeability and crack resistance of the material under different environmental parameter settings. Compared with the complex steps of relying on experimental measurement and finite element model setting in the prior art, the present invention reduces the dependence on experimental data, making the model more suitable for various actual working conditions.

[0095] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0096] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for calculating the permeation reaction of an inorganic gel in a porous medium, characterized in that: The method comprises: Establishing a pore model of a porous medium, and infiltrating a first reactant and a second reactant into the porous medium so that the first reactant and the second reactant react to generate a first reaction product; wherein the first reactant comprises silicate ions, and the second reactant comprises calcium ions; The first reaction product changes the pore structure of the porous medium to affect the permeation rate of the silicate ions and the calcium ions, thereby causing the volume of the first reaction product to change, and calculating a first volume variable of the first reaction product; Establishing a calcium ion dissolution model, and calculating a second volume variable of the pore structure of the porous medium caused by the calcium ion dissolution based on the mutual influence between the calcium ion dissolution and the change in the pore structure of the porous medium; According to the first volume variable and the second volume variable, the change of the pore structure of the porous medium is obtained.

2. The method according to claim 1, wherein The first reactant and the second reactant react to generate a first reaction product, comprising: The silicate ions and the calcium ions will produce content changes due to reaction rate and ion transport when they penetrate into the porous medium. The reaction control equation is obtained based on the conservation relationship in the fluid transport process to calculate the content change of the silicate ions and the calcium ions penetrating into the porous medium.

3. The method according to claim 2, wherein In the low power consumption mode, the reaction control equation is: where Φ = φ paste =φ capillary +φ gel , its value is 3.2nm~320μm, J is in Ω=-1.5tanh(8.0(φ paste -0.25))+2.5, C represents the concentration of silicate ions and / or the flow rate of water in the voids, and Q is 4. The method according to claim 1, wherein The first volume variable formula of the first reaction product is: Where, ΔV CSH Represents the volume change of the first reaction product; V CSH represents the volume of CSH when the first reaction product is dissolved to 0; C CSH Indicates the total mol amount of the first reaction product when the first reaction product is dissolved to 0; C solid Indicates the molar amount of the remaining first reaction product.

5. The method according to claim 4, wherein The method further comprises: As the concentration of the calcium ions decreases, the dissolution of the third reactant in the porous medium is promoted; Based on the first volume variable formula of the first reaction product, an ion transport equation is established, and combined with the pore model of the porous medium to establish the calcium ion dissolution model.

6. The method according to claim 5, wherein The ion transport equation is: The first term on the left represents the unsteady term, and the second term is the convection term; the first term on the right represents the diffusion term, and the second term represents the source term.

7. The method according to claim 5, wherein The formula for the change in the pore structure of the porous medium is: where ΔV CH represents the reduction in solid phase volume due to the dissolution of the third reactant (m 3 / m 3 ); Δm CH Indicates the mass of the third reactant dissolved (kg / m 3 );ρ CH represents the density of the third reactant (2.24×10 3 kg / m 3 ); ΔC CH Indicates the reduction of the solid third reactant (mmol / m 3 );M CH represents the molar mass of the third reactant calcium (74.1×10 -6 kg / mmol).

8. The method according to any one of claims 1 to 7, characterized in that The reaction rate formula of the silicate ion is:

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