An X-ray tomography-based method for predicting the absolute permeability of paper

Abstract

The present invention discloses a method for predicting the absolute permeability of paper based on X-ray tomography, and the process is as follows: Use an X-ray tomography scanner to non-destructively scan the paper to obtain a sequence of three-dimensional structure diagrams of the paper; Use digital image post-processing technology to perform contrast adjustment, filtering, and image segmentation on the original scanned sequence diagrams; Use three-dimensional visualization software to construct the three-dimensional pore structure of the paper, and use the porosity of the paper as the basis for estimating the size of the representative elementary volume (REV), and determine the size of the REV suitable for permeability simulation; In the constructed three-dimensional pore structure model of the REV, use numerical simulation software to numerically simulate the penetration process of the fluid inside the paper, and predict the absolute permeability of the paper according to Darcy's law. The present invention overcomes the disadvantages of the traditional method for measuring the absolute permeability of paper, such as complex operation, insecurity, and the inability to observe the specific flow conditions (flow velocity distribution, pressure distribution, fluid path, etc.) of the fluid in the pore structure of the paper.

Description

Technical Field

[0001] The present invention relates to the technical fields of pulping and papermaking, computer image processing and computer numerical simulation, and specifically relates to a method for predicting the absolute permeability of paper based on X-ray tomography. Background Art

[0002] Paper is a porous, thin-layered material formed by the interweaving of plant fibers. Due to the renewable and recyclable nature of paper, it is gradually replacing plastic products and is thus being developed into a functional material that can be used in fields such as separation, adsorption, filtration, and electrochemistry, and is gradually being widely used in fields such as petrochemical industry, medicine, and environmental protection. The structure of paper affects its physical properties such as mechanical properties, permeability, and printing suitability. In most applications of paper, the process of fluid transmission within it is involved, and only according to the different application fields, there are huge differences in the penetration of fluids in paper. In recent years, in order to develop high-performance paper-based functional materials, the fluid flow behavior in the fiber porous network structure of paper has attracted extensive research interest from scholars and material designers at home and abroad. Depending on the application, new paper-based materials need to have good permeability or barrier properties, and these properties are closely related to the microscopic fiber porous network structure. Accurately predicting the transport characteristics of the fiber porous network will provide important reference value for the design and use of new paper-based materials. The absolute permeability is the main key parameter characterizing the permeability of paper. It is an inherent property of the material and describes the hindering effect of the porous material on fluid flow. Currently, there is no clearly defined method for measuring the absolute permeability of paper in national standards. Traditional experimental methods for measuring the absolute permeability of paper are complex and expensive to operate. For example, the experimental method represented by mercury intrusion method is to press mercury into the porous body under a certain pressure, calculate the porosity of the paper according to the amount of mercury injected, and thus calculate the absolute permeability of the paper. However, due to the contact with mercury (highly toxic) during the detection process in the mercury intrusion method, especially the strong volatility of mercury, improper operation is likely to cause harm to the human body. Therefore, in order to reduce the experimental cost, scholars have conducted a large number of studies and found that at the microscopic level, the fiber porous network can use the numerical simulation method of computational fluid dynamics (CFD) to predict the absolute permeability of the material. Computational fluid dynamics is a science that obtains a discrete quantitative description of the flow field by numerically solving the fluid flow control equations and thus predicts the laws of fluid motion. This method has been widely used in the research of the permeability of porous materials such as rocks and fabrics, but it is rarely used in the research of the permeability of paper. Summary of the Invention

[0003] The object of the present invention is to solve the above-mentioned defects in the prior art and provide a method for predicting the absolute permeability of paper based on X-ray tomography. First, papermaking fibers are made into paper according to the laboratory standard papermaking process. The paper is scanned by X-ray tomography to obtain a sequence of images of the three-dimensional structure of the paper. The sequence of images is successively subjected to contrast adjustment, filtering, and image segmentation processing, and then the three-dimensional pore structure of the paper is constructed. The porosity of the paper is used as the basis for estimating the size of the Representative Elementary Volume (REV). The REV size suitable for numerical simulation of the permeation performance of the paper is determined. At the optimal REV size, the REV pore structure is separately isolated according to the image segmentation result. Finally, the REV three-dimensional pore model is meshed and transformed into a discrete finite element model to obtain the REV three-dimensional pore structure model of the paper. The numerical simulation software is used to numerically simulate the permeation process of the fluid in the REV three-dimensional pore structure model of the paper, and the absolute permeability of the paper is predicted according to Darcy's law. Using this method can avoid the use of toxic substances, is safe and environmentally friendly, and can observe the specific flow conditions (flow velocity distribution, pressure distribution, fluid path, etc.) of the fluid in the pore structure of the paper.

[0004] The object of the present invention can be achieved by adopting the following technical solutions:

[0005] A method for predicting the absolute permeability of paper based on X-ray tomography, beating the pulp board, making the pulp into paper by the rapid Kersey method, cutting the paper and placing it on the stage of the X-ray tomograph, and obtaining a sequence of three-dimensional structure diagrams of the paper by scanning; after successively performing contrast adjustment, filtering, and image segmentation processing on the sequence of diagrams of the paper, constructing the three-dimensional pore structure of the paper in three-dimensional visualization software; then determining the size of the representative unit REV suitable for numerical simulation of the permeation performance, separately extracting the pore part of the REV model, meshing the REV three-dimensional pore model, and transforming it into a discrete finite element volume mesh model. Finally, in the constructed REV three-dimensional pore finite element volume mesh of the paper, the numerical simulation software is used to numerically simulate the permeation process of the fluid inside the paper, and the absolute permeability of the paper is predicted according to Darcy's law.

[0006] A method for predicting the absolute permeability of paper based on X-ray tomography, the method for predicting the absolute permeability of paper comprising the following steps:

[0007] S1, preparing pulp and making paper;

[0008] S2. Cut the paper into squares sized (0.5 mm × 0.5 mm)-(4 mm × 4 mm), then fix them on the stage of the X-ray computed tomography scanner, and use the X-ray computed tomography scanner to characterize the microscopic three-dimensional structure of the paper to obtain a sequence of images of the three-dimensional structure of the paper;

[0009] S3. Successively perform contrast adjustment, filtering, and image segmentation on the sequence of images of the three-dimensional structure of the paper to obtain an optimized sequence of two-dimensional paper cross-section images;

[0010] S4. Reconstruct the sequence of two-dimensional paper cross-section images in three-dimensional visualization software to construct the microscopic three-dimensional structure of the paper;

[0011] S5. Use the porosity of the paper as the basis for estimating the size of the representative elementary volume REV, and determine the size of the representative elementary volume REV suitable for numerical simulation of permeability;

[0012] S6. Separate and extract the pore part of the representative elementary volume REV to obtain a three-dimensional pore structure model of the paper REV, and perform Delaunay triangular mesh generation on this three-dimensional pore structure model of the paper REV to convert it into a discrete finite element volume mesh model;

[0013] S7. In the finite element volume mesh model, use numerical simulation software to numerically simulate the penetration process of fluid inside the paper;

[0014] S8. Based on the paper penetration numerical simulation results obtained in step S7, calculate the absolute permeability of the three-dimensional pore structure model of the paper REV according to Darcy's law to complete the prediction of the absolute permeability of the paper.

[0015] Furthermore, the process of step S1 is as follows:

[0016] According to the national standard (GBT 24325-2009), use a Valley beater to defiber and beat the pulp sheet to obtain pulp with a beating degree of 20-50°SR, which is beneficial to improving the evenness and strength of the paper. Seal and store the obtained pulp;

[0017] According to the national standard for laboratory papermaking (GB / T24326-2009), first use a rapid Kajaani paper former to form a wet paper sheet, then dry the wet paper sheet through a vacuum dryer, and finally store the formed paper in a constant temperature and humidity chamber (temperature 23°C, humidity 50±2%) to ensure the stability of the paper shape and water content. The basis weight of the paper is 60-120 g / m 2 .

[0018] Furthermore, the process of step S2 is as follows:

[0019] S21. Determine the tube voltage of the X-ray source as 50 kV and the current as 390 μA according to the composition and structure of the paper sample. Changing the tube voltage will change the emitted X-ray spectrum to optimize the contrast during the reconstruction process, and the current will linearly increase the intensity of the X-rays;

[0020] S22. Fix the paper on the stage of the X-ray tomograph, and adjust the paper to the center position of the field of view at a low resolution. Gradually increase the resolution to the target resolution, and always keep the image at the center of the field of view during the increase process;

[0021] S23. Adjust the height position of the paper, move the paper out of the field of view, adjust the exposure time, and then perform CCD flat-field correction to reduce the noise and artifacts in the image. Subsequently, move the paper back into the field of view and finely adjust the focusing current for X-ray focusing;

[0022] S24. Set the scanning step size, scanning times, and scanning range of the X-ray tomograph to complete the scanning of the entire paper. After adding the file storage path, start the ray source to start scanning and obtain the three-dimensional structure sequence images of the paper.

[0023] Further, the process of step S3 is as follows:

[0024] S31. First, adjust the contrast of the sequence images of the paper three-dimensional structure, which is beneficial to increasing the contrast between the pore phase and the fiber phase in the images;

[0025] S32. Use non-local means filtering to eliminate the noise points in the three-dimensional structure sequence images;

[0026] S33. Obtain the threshold for the denoised three-dimensional structure sequence images by using the maximum inter-class variance method, and perform image segmentation processing according to the threshold to segment the pore phase and the fiber phase in the images, where the white pixel points with a pixel value of 1 are pores, and the black pixel points with a pixel value of 0 are fibers.

[0027] Further, the process of step S5 is as follows:

[0028] S51. Arbitrarily select a point O in the central part of the XY plane of the paper, and determine a cuboid with a square bottom with an initial side length of d 0 pixels and a fixed height as the representative unit REV, and calculate the porosity of the cuboid area, where the height is the thickness of the paper;

[0029] S52. Let the bottom side length L of the cuboid gradually increase in steps of Δd pixels, and at the same time count the porosity of each cuboid area, construct the corresponding relationship between the bottom side length of the cuboid and the porosity, and determine the size of the representative unit REV when the porosity reaches stability;

[0030] S53. To ensure the independence of the size of the representative elementary volume (REV) from its spatial position, the position of the center point O is continuously changed, and the above S51 and S52 are repeated. The relationship between the size of the REV and the porosity is constructed multiple times to determine the corresponding variation law between the two, which is used to find the most suitable size of the REV.

[0031] S54. Select the smallest geometric unit as the size of the representative elementary volume (REV) when the fluctuation of the porosity caused by the change in the bottom side length L is less than the specified threshold.

[0032] Further, the process of step S7 is as follows:

[0033] S71. According to the flow state of the fluid inside the paper, laminar flow is selected for fluid flow simulation, and the corresponding fluid control equation is:

[0034]

[0035]

[0036] where v and p are the velocity vector and pressure of the fluid respectively, μ is the dynamic viscosity, is the gradient operator, is the Laplace operator; the control equation stipulates the physical laws that need to be followed during the fluid flow process.

[0037] S72. Define the fluid properties, which include the density and dynamic viscosity of the fluid;

[0038] S73. The boundary condition refers to the variation law of the variable or its derivative to be solved on the boundary of the solution domain with respect to time and location, which is a prerequisite for the control equation to have a definite solution. According to the actual situation during the absolute permeability test of the paper and the conventional boundary settings for porous medium flow simulation, the inlet / outlet pressure boundary condition, the solid wall boundary condition, and the symmetry boundary condition are adopted, which is conducive to accurately solving the fluid control equation;

[0039] S74. Solve the set physical field of fluid flow to obtain the numerical simulation results of the fluid penetration in the pores of the paper.

[0040] Further, in step S73, since the paper structure has anisotropy, to simulate the absolute permeability in the thickness direction and the absolute permeability in the plane direction of the three-dimensional pore structure model of the paper REV, the inlet / outlet pressure boundary condition is defined in two groups: (1) Taking the upper boundary of the three-dimensional pore structure model of the paper REV as the inlet and the lower boundary as the outlet to simulate the absolute permeability in the thickness direction; (2) Taking the left boundary of the three-dimensional pore structure model of the paper REV as the inlet and the right boundary as the outlet to simulate the absolute permeability in the plane direction.

[0041] Further, in step S8, the absolute permeability of the paper is predicted according to Darcy's law. Let the absolute permeability of the paper be K, and the calculation formula is:

[0042]

[0043] where A is the cross-sectional area of the porous material, with the unit of μm 2 ; H is the thickness of the porous material, with the unit of μm; q v represents the volume flow rate of the Newtonian fluid passing through the cross-section at a low flow rate, with the unit of μm 3 ·s -1 ; ΔP is the pressure drop across the specimen, with the unit of Pa; η is the dynamic viscosity of the fluid, with the unit of Pa·s; the absolute permeability K, with the unit of μm 2 .

[0044] The present invention has the following advantages and effects compared with the prior art:

[0045] 1. The present invention uses an X-ray computed tomography scanner to obtain a three-dimensional structural sequence diagram of the paper, and adopts image post-processing technology to optimize the quality of the original sequence images. In the three-dimensional pore model of the representative elementary volume (REV), a numerical simulation software is used to numerically simulate the penetration process of the fluid inside the paper, so that the absolute permeability of the paper can be predicted according to Darcy's law, overcoming the disadvantages of the traditional mercury intrusion method, such as complex operation, insecurity, and inability to observe the specific flow conditions (flow velocity distribution, pressure distribution, fluid path, etc.) of the fluid in the pore structure of the paper.

[0046] 2. By determining the micro representative elementary volume (REV) of the material, carrying out numerical simulation of the penetration process, and calculating the absolute permeability, it can effectively avoid problems such as excessive computer computing power, insufficient memory, and high time cost, save the prediction time, and is accurate and feasible.

[0047] 3. The present invention does not require fluid immersion and does not damage the internal structure of the paper, and can achieve green and environmental protection detection.

[0048] 4. The present invention adopts a non-destructive three-dimensional characterization technology, which can realize the visualization of the true three-dimensional structure of the paper. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of this application. The schematic embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation to the present invention. In the drawings:

[0050] Figure 1 is a flowchart of a method for predicting the absolute permeability in the thickness direction of a paper based on X-ray computed tomography disclosed in an embodiment of the present invention.

[0051] Figure 2It is the sequence diagram of the three-dimensional structure of the paper in the embodiment of the present invention;

[0052] Figure 3 It is the true microscopic three-dimensional structure diagram of the cotton pulp paper in the embodiment of the present invention;

[0053] Figure 4 It is the schematic diagram of the method for determining the size of the characterization unit REV in the embodiment of the present invention;

[0054] Figure 5 It is the pore structure diagram of the cotton pulp paper characterization unit REV in the embodiment of the present invention;

[0055] Figure 6 It is the pore finite element body mesh model diagram of the cotton pulp paper characterization unit REV in the embodiment of the present invention;

[0056] Figure 7 It is the schematic diagram of the boundary conditions for the penetration simulation in the thickness direction of the cotton pulp paper in the embodiment of the present invention;

[0057] Figure 8 It is the pressure distribution diagram of the penetration simulation of different fluids in the thickness direction of the cotton pulp paper in the embodiment of the present invention. Among them, Figure 8 The left half in it is liquid mercury, Figure 8 The right half in it is air;

[0058] Figure 9 It is the streamline distribution diagram of the penetration simulation of different fluids in the thickness direction of the cotton pulp paper in the embodiment of the present invention. Among them, Figure 9 The left half in it is liquid mercury, Figure 9 The right half in it is air;

[0059] Figure 10 It is the schematic diagram of the boundary conditions for the penetration simulation in the plane direction of the cotton pulp paper in the embodiment of the present invention;

[0060] Figure 11 It is the pressure distribution diagram of the penetration simulation of different fluids in the plane direction of the cotton pulp paper in the embodiment of the present invention. Among them, Figure 11 The left half in it is liquid mercury, Figure 11 The right half in it is air;

[0061] Figure 12 It is the streamline distribution diagram of the penetration simulation of different fluids in the plane direction of the cotton pulp paper in the embodiment of the present invention. Among them, Figure 12 The left half in it is liquid mercury, Figure 12 The right half in it is air. Detailed implementation manners

[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0063] Due to the different structures of paper in the thickness direction and the plane direction, there are differences in the penetration of fluids in the two directions of the paper. When the fluid mainly transmits in the thickness direction of the paper, such as food packaging paper, etc., the method for predicting the absolute permeability in the thickness direction of the paper in the present invention can be used to evaluate the penetration performance of the paper; for the case where the fluid mainly transmits in the plane direction of the paper, such as cigarette paper, etc., the method for predicting the absolute permeability in the plane direction of the paper in the present invention can be used to evaluate the penetration performance of the paper. The implementation methods for predicting the absolute permeability in the thickness direction and the plane direction of the paper are described in Embodiment 1 and Embodiment 2 respectively.

[0064] Embodiment 1

[0065] This embodiment discloses a method for predicting the absolute permeability in the thickness direction of paper based on X-ray tomography. This method first needs to make paper by copying papermaking fibers according to the laboratory standard papermaking process, scan the paper using X-ray tomography to obtain a sequence of images of the three-dimensional structure of the paper, perform contrast adjustment, filtering, and image segmentation processing on the sequence of images of the three-dimensional structure of the paper, then construct the microscopic three-dimensional structure of the paper, and use the porosity of the paper as the basis for estimating the size of the representative elementary volume (REV), and determine the size of the representative unit REV suitable for numerical simulation of the penetration performance. At the optimal size of the representative unit REV, the REV pore structure is separately separated according to the image segmentation result. Finally, the REV three-dimensional pore model is meshed and transformed into a discrete finite element model to obtain the paper REV three-dimensional pore structure model. The numerical simulation software is used to numerically simulate the penetration process of the fluid in the paper REV three-dimensional pore structure model, and the absolute permeability of the paper is predicted according to Darcy's law. This method can obtain the true three-dimensional structure of the paper, calculate the absolute permeability of the paper REV, thereby predicting the absolute permeability of the paper, avoiding the use of toxic substances such as mercury, and the proposed method is environmentally friendly and accurate, and can be applied to the detection of the absolute permeability of paper.

[0066] As Figure 1 shown, the detection method specifically includes the following steps:

[0067] Step S1: Disintegrate the cotton pulp board and beat it using a Valley beater according to the national standard GBT 24325-2009 to obtain pulp with a beating degree of 30 (±2) °SR. Seal and store the obtained pulp. Calculate and weigh the mass of the pulp according to the moisture content of the pulp and the set basis weight. According to the Chinese national standard GB / T 24326-2009, first use a rapid Kajaani paper former to form a wet paper sheet, then dry the wet paper sheet through a vacuum dryer, and finally store the formed paper in a constant temperature and humidity chamber (temperature 23°C, humidity 50±2%). Finally, make the pulp into paper with a basis weight of 105 g / m 2 of paper. During the papermaking process, no additives such as retention aids, drainage aids, and fillers were added;

[0068] Step S2: Cut the paper treated as above into squares with a size of 2 mm×2 mm for X-ray computed tomography (CT) characterization. Determine the tube voltage of the X-ray source to be 50 kV and the current to be 390 μA according to the composition and structure of the paper sample. First, fix the paper on the stage of the X-ray CT scanner. The distance between the X-ray source and the detector is 146.813 mm, and the distance between the X-ray source and the sample is 8.115 mm. Then, adjust the paper to the center of the field of view at a low resolution, gradually increase the resolution to the target resolution of 500 nm, and keep the image in the center of the field of view at all times during the increase process. Next, adjust the height position of the paper, move it out of the field of view, adjust the exposure time to 850 ms, and then perform CCD flat-field correction to reduce noise and artifacts in the image. Select a high-resolution CCD detector (4032×2670 pixels) to collect the original X-ray digital image. Subsequently, move the sample back into the field of view and finely adjust the focusing current for X-ray focusing. Finally, set the scanning step size to 0.412 rad, the number of scans to 1 time, and the scanning range to 360° on the human-computer interaction interface of the computer system. After adding the file storage path, start the ray source to start scanning. After the scanning is completed, a sequence of projection images of the sample can be obtained. Finally, obtain 2357 sequence slice images (XOZ plane) with a pixel size of 4032×4032 as shown in Figure 2 Figure.

[0069] Step S3: Perform contrast adjustment, filtering, and image segmentation on the sequence images of the paper three-dimensional structure in sequence. First, perform contrast adjustment on the sequence images of the paper three-dimensional structure, which is beneficial to increasing the contrast between the pore phase and the fiber phase in the image; use non-local means filtering to eliminate noise points in the sequence images of the three-dimensional structure; obtain a threshold for the denoised sequence images of the three-dimensional structure using the Otsu method, and perform image segmentation processing according to the threshold to segment the pore phase and the fiber phase in the image, where the white pixel points with a pixel value of 1 are pores, and the black pixel points with a pixel value of 0 are fibers.

[0070] Step S4: Reconstruct the two-dimensional paper cross-section sequence diagram in the 3D visualization software Avizo, and construct a real 3D paper structure along the Y direction. Its 3D size is 4032 (X) × 2357 (Y) × 450 (Z) voxels, as Figure 3 shown.

[0071] Step S5: Use the porosity of the paper as the basis for estimating the size of the representative elementary volume (REV), and determine the size of the REV suitable for numerical simulation of permeability. As shown Figure 4 in the figure, randomly select a point O in the central part of the XY plane of the paper. Take point O as the center point to determine a cuboid with a square bottom with an initial side length d 0 = 50 pixels and a fixed height. Take this cuboid as the REV, and calculate the porosity of this cuboid area, where the height is the thickness of the paper, 450 pixels; let the bottom side length L of the cuboid gradually increase with a step size of Δd = 50 pixels, and at the same time count the porosity of each cuboid area, construct the corresponding relationship between the bottom side length of the cuboid and the porosity, and determine the size of the REV when the porosity reaches stability; to ensure the independence of the estimated REV size from its spatial position, 9 different center points are selected, and the above steps are repeated to construct the relationship between the REV size and the porosity multiple times, and determine the corresponding change law between the two to find the most suitable REV size. The results show that when the side length L is greater than 400 pixels, the porosity fluctuation caused by the change of the bottom side length L is less than the specified threshold. Therefore, the size of the REV in the plane direction is finally determined to be 400×400 pixels, and the 3D size of the REV is 400 (X) × 400 (Y) × 450 (Z) voxels.

[0072] Step S6: Separate the REV pore structure alone in the 3D visualization software Avizo according to the image segmentation result, as Figure 5 shown. Pore structure mesh generation: Use the Delaunay triangulation method to convert the 3D pore model of the REV into a discrete finite element volume mesh model, as Figure 6 shown.

[0073] Step S7: Complete the penetration simulation of liquid mercury and air inside the paper in the numerical simulation software COMSOL respectively. According to the flow state of the fluid inside the paper, laminar flow is selected for fluid flow simulation, and the corresponding fluid control equation is:

[0074]

[0075]

[0076] where v and p are the velocity vector and pressure of the fluid respectively, μ is the dynamic viscosity, is the gradient operator, is the Laplace operator; the governing equations prescribe the physical laws that need to be followed during the fluid flow process.

[0077] Next, the fluid properties are defined. Among them, the density of liquid mercury at a temperature of 293.15 K is 1.358×10 4 kg·m -3 , and the dynamic viscosity is 1.6×10 -3 Pa·s; the density of air is 1.205 kg·m -3 , and the dynamic viscosity is 1.79*10 -5 Pa·s.

[0078] According to the actual situation during the absolute permeability test of paper and the conventional boundary settings for porous media flow simulation, inlet / outlet pressure boundary conditions, solid wall boundary conditions, and symmetry boundary conditions are adopted. To simulate the absolute permeability in the thickness direction of the paper REV three-dimensional pore structure model, the upper boundary of the paper REV three-dimensional pore structure model is taken as the inlet, and the lower boundary as the outlet to simulate the absolute permeability in the thickness direction of the paper. The boundary conditions set are as Figure 7 shown, with the inlet pressure being 300 Pa. As Figure 8 and Figure 9 shown, the pressure distribution and streamline distribution of the penetration simulation of liquid mercury and air in the thickness direction of cotton pulp paper are obtained respectively ([the left half in Figure 8 and Figure 9 is liquid mercury, and the right half is air);

[0079] Step S8: Calculate the absolute permeability in the thickness direction of the paper REV according to Darcy's law, so as to predict the absolute permeability in the thickness direction of the paper. Let the absolute permeability of the paper be K, and the calculation formula is:

[0080]

[0081] where A is the cross-sectional area of the porous material, with the unit of μm 2 ; H is the thickness of the porous material, with the unit of μm; q v represents the volume flow rate of Newtonian fluid passing through the cross-section at a low flow rate, with the unit of μm 3 ·s -1 ; ΔP is the pressure drop across the specimen, with the unit of Pa; η is the dynamic viscosity of the fluid, with the unit of Pa·s; the absolute permeability K, with the unit of μm 2 .

[0082] Experimental test and simulation result verification:

[0083] (1) Experimental measurement method of the absolute permeability of paper: The AutoPore Ⅳ 9500 (manufactured by Micromeritics Instrument Corporation, USA), a fully automatic high-performance mercury intrusion porosimeter, was used to measure the absolute permeability of paper. Before testing, the sample to be measured needs to be placed in a vacuum drying oven for 12 hours to remove the moisture in the pores. The operation method of the mercury intrusion porosimeter is as follows: First, weigh a certain mass of the sample to be measured, and then place the sample in an expansion meter and seal the expansion meter with sealant and a wrench. Then open the low-pressure chamber, place the expansion meter in the low-pressure chamber, and set the low-pressure parameters for low-pressure testing. After the low-pressure test is completed, take out the expansion meter and weigh it. Then open the high-pressure chamber, place the expansion meter in the high-pressure chamber and set the high-pressure parameters. After the high-pressure test is completed, view the measurement data using the instrument software. The data measured by the data processing software equipped with the AutoPore Ⅳ 9500 includes physical parameters such as porosity, tortuosity, absolute permeability, and fractal dimension.

[0084] (2) Verification of simulation results: Based on the absolute permeability of paper predicted by X-ray tomography and the absolute permeability value measured by the mercury intrusion porosimeter experiment, the absolute permeability of cotton pulp paper obtained by the two methods is shown in Table 1. The relative error between the experimental value and the simulation prediction value of the absolute permeability of paper does not exceed 10%, indicating the accuracy of this method.

[0085] Table 1. Comparison table of measured and predicted values of the absolute permeability of cotton pulp paper

[0086]

[0087] Example 2

[0088] This example discloses a prediction method for the absolute permeability of paper in the plane direction based on X-ray tomography. As Figure 1 shown, the method specifically includes the following steps:

[0089] Step S1: Disintegrate the cotton pulp board and beat it using a Valley beater according to the national standard GBT 24325-2009 to obtain pulp with a beating degree of 30 (±2) °SR. Seal and store the obtained pulp. Calculate and weigh the mass of the pulp according to the moisture content of the pulp and the set basis weight. According to the Chinese national standard GB / T 24326-2009, first use a rapid Kajaani paper former to form a wet paper sheet, then dry the wet paper sheet through a vacuum dryer, and finally store the formed paper in a constant temperature and humidity chamber (temperature 23 °C, humidity 50 ± 2%). Finally, pulp is formed into paper with a basis weight of 105 g / m 2 During the papermaking process, no additives such as retention aids, drainage aids, and fillers are added;

[0090] Step S2: Cut the processed paper into squares with a size of 2 mm × 2 mm for X-ray tomography characterization. Determine the tube voltage of the X-ray source as 50 kV and the current as 390 μA according to the composition and structure of the paper sample. First, fix the paper on the stage of the X-ray tomograph. The distance between the X-ray source and the detector is 146.813 mm, and the distance between the X-ray source and the sample is 8.115 mm. Then, adjust the paper to the center of the field of view at a low resolution, gradually increase the resolution to the target resolution of 500 nm, and keep the image in the center of the field of view at any time during the increase process. Next, adjust the height position of the paper, move it out of the field of view, adjust the exposure time to 850 ms, and then perform CCD flat-field correction to reduce noise and artifacts in the image. Select a high-resolution CCD detector (4032 × 2670 pixels) to collect the original X-ray digital image. Subsequently, move the sample back into the field of view and finely adjust the focusing current for X-ray focusing. Finally, set the scan step as 0.412 rad, the number of scans as 1 time, and the scan range as 360° in the human-computer interaction interface of the computer system. After adding the file storage path, start the ray source to start scanning. After the scanning is completed, a sequence of projection images of the sample can be obtained. Finally, Figure 2 2357 sequence slice images (XOZ plane) with a pixel size of 4032 × 4032 as shown in

[0091] Step S3: Perform contrast adjustment, filtering, and image segmentation on the sequence images of the three-dimensional structure of the paper in sequence. First, perform contrast adjustment on the sequence images of the three-dimensional structure of the paper, which is beneficial to increasing the contrast between the pore phase and the fiber phase in the image. Use non-local mean filtering to eliminate noise points in the sequence images of the three-dimensional structure. Obtain the threshold for the denoised sequence images of the three-dimensional structure using the maximum inter-class variance method, and perform image segmentation processing according to the threshold to segment the pore phase and the fiber phase in the image. Among them, the white pixel points with a pixel value of 1 are pores, and the black pixel points with a pixel value of 0 are fibers.

[0092] Step S4: Reconstruct the sequence diagrams of the two-dimensional paper cross-section in the three-dimensional visualization software Avizo, and construct the real three-dimensional structure of the paper along the Y direction. Its three-dimensional size is 4032 (X) × 2357 (Y) × 450 (Z) voxels, as shown in Figure 3 shown.

[0093] Step S5: Use the porosity of the paper as the basis for estimating the size of the representative elementary volume REV, and determine the size of the representative elementary volume REV applicable to the numerical simulation of permeability. As shown in the schematic Figure 4 shown, arbitrarily take a point O in the central part of the XY plane of the paper, and determine the initial side length d of the bottom surface with point O as the center point 0A square with a side length of 50 pixels and a cuboid with a fixed height. This cuboid is used as the representative elementary volume (REV), and the porosity of the cuboid region is calculated, where the height is the thickness of the paper, 450 pixels. Let the bottom side length L of the cuboid increase step by step with a step size of Δd = 50 pixels. At the same time, the porosity of each cuboid region is statistically analyzed, the corresponding relationship between the bottom side length of the cuboid and the porosity is constructed, and the size of the REV when the porosity reaches stability is determined. To ensure the independence of the estimated REV size from its spatial position, 9 different center points are selected, and the above steps are repeated. The relationship between the size of the REV and the porosity is constructed multiple times to determine their corresponding variation laws for finding the most suitable REV size. The results show that when the side length L is greater than 400 pixels, the porosity fluctuation caused by the change in the bottom side length L is less than the specified threshold. Therefore, the size of the REV in the plane direction is finally determined to be 400×400 pixels, and the three-dimensional size of the REV is 400(X)×400(Y)×450(Z) voxels.

[0094] Step S6: According to the image segmentation result, the pore structure of the REV is separately isolated in the 3D visualization software Avizo, as Figure 5 shown. Pore structure mesh generation: The 3D pore model of the REV is transformed into a discrete finite element volume mesh model using the Delaunay triangulation method, as Figure 6 shown.

[0095] Step S7: Perform the penetration simulation of liquid mercury and air inside the paper in the numerical simulation software COMSOL respectively. According to the flow state of the fluid inside the paper, laminar flow is selected for the fluid flow simulation, and the corresponding fluid control equation is:

[0096]

[0097]

[0098] where v and p are the velocity vector and pressure of the fluid respectively, μ is the dynamic viscosity, is the gradient operator, is the Laplace operator; the control equation stipulates the physical laws that need to be followed during the fluid flow process.

[0099] Then, the fluid properties are defined. Among them, at a temperature of 293.15K, the density of liquid mercury is 1.358×10 4 kg·m -3 , and the dynamic viscosity is 1.6×10 -3 Pa·s; the density of air is 1.205kg·m -3 , and the dynamic viscosity is 1.79*10 -5 Pa·s.

[0100] According to the actual situation during the test of the absolute permeability of paper and the conventional boundary settings for porous media flow simulation, inlet / outlet pressure boundary conditions, solid wall boundary conditions, and symmetry boundary conditions are adopted. To simulate the absolute permeability of the three-dimensional pore structure model of paper in the plane direction. Taking the left boundary of the three-dimensional pore structure model of paper as the inlet and the right boundary as the outlet, the absolute permeability of the paper in the plane direction is simulated. The set boundary conditions are as Figure 10 shown, and the inlet pressure is 300 Pa. As Figure 11 and Figure 12 shown, the pressure distribution and streamline distribution of the penetration simulation of liquid mercury and air in the plane direction of cotton pulp paper are obtained respectively ( Figure 10 and Figure 11 the left half in them is liquid mercury and the right half is air);

[0101] Step S8: Calculate the absolute permeability in the plane direction of the REV according to Darcy's law to realize the prediction of the absolute permeability of the paper in the plane direction. Let the absolute permeability of the paper be K, and the calculation formula is:

[0102]

[0103] where A is the cross-sectional area of the porous material, with the unit of μm 2 ; H is the thickness of the porous material, with the unit of μm; q v represents the volume flow rate of Newtonian fluid passing through the cross-section at a low flow rate, with the unit of μm 3 ·s -1 ; ΔP is the pressure drop across the specimen, with the unit of Pa; η is the dynamic viscosity of the fluid, with the unit of Pa·s; the absolute permeability K, with the unit of μm 2 .

[0104] The prediction results of the absolute permeability of the paper in the plane direction are shown in Table 2.

[0105] Table 2. Prediction values of the absolute permeability of cotton pulp paper in the plane direction

[0106]

[0107] In summary, the method for predicting the absolute permeability of paper based on X-ray tomography disclosed in Embodiment 1 and Embodiment 2 can obtain the true three-dimensional structure of the paper, calculate the absolute permeability in the thickness direction and plane direction of the paper respectively, avoid using toxic substances such as mercury, and the proposed method is environmentally friendly and accurate, and can be applied to the prediction of the absolute permeability of paper.

[0108] The above embodiments are the preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A method for predicting the absolute permeability of paper based on X-ray tomography, characterized in that, the method for predicting the absolute permeability of paper includes the following steps: S1. Prepare pulp and make paper; S2. Cut the paper into squares with a size of (0.5 mm × 0.5 mm)-(4 mm × 4 mm), then fix it on the stage of the X-ray tomography scanner, and use the X-ray tomography scanner to characterize the microscopic three-dimensional structure of the paper to obtain a sequence of images of the three-dimensional structure of the paper; S3. Successively perform contrast adjustment, filtering and image segmentation on the sequence of images of the three-dimensional structure of the paper to obtain an optimized sequence of two-dimensional paper cross-section images; S4. Reconstruct the sequence of two-dimensional paper cross-section images in three-dimensional visualization software to construct the microscopic three-dimensional structure of the paper; S5. Use the porosity of the paper as the basis for estimating the size of the representative elementary volume REV, and determine the size of the representative elementary volume REV suitable for numerical simulation of permeability performance; S6. Separate the pore part of the representative elementary volume REV to obtain a three-dimensional pore structure model of paper REV, and perform Delaunay triangular mesh division on the three-dimensional pore structure model of paper REV to convert it into a discrete finite element volume mesh model; S7. In the finite element volume mesh model, use numerical simulation software to numerically simulate the penetration process of fluid inside the paper; S8. Based on the paper penetration numerical simulation results obtained in step S7, calculate the absolute permeability of the three-dimensional pore structure model of paper REV according to Darcy's law to complete the prediction of the absolute permeability of the paper.

2. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 1, characterized in that, the process of step S2 is as follows: S21. Determine the tube voltage of the X-ray source as 50 kV and the current as 390 μA according to the composition and structure of the paper sample; S22. Fix the paper on the stage of the X-ray tomography scanner, and adjust the paper to the center of the field of view at a low resolution, gradually increase the resolution to the target resolution, and always keep the image in the center of the field of view during the increase process; S23. Adjust the height position of the paper, move the paper out of the field of view, adjust the exposure time, then perform CCD flat-field correction to reduce noise and artifacts in the image, then move the paper back into the field of view, and finely adjust the focusing current for X-ray focusing; S24. Set the scanning step, scanning times and scanning range of the X-ray tomography scanner, add the file storage path, and then start the ray source to start scanning to obtain a sequence of images of the three-dimensional structure of the paper.

3. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 1, characterized in that, the process of step S3 is as follows: S31. First, perform contrast adjustment on the sequence of images of the three-dimensional structure of the paper to increase the contrast between the pore phase and the fiber phase in the image; S32. Use non-local mean filtering to eliminate noise points in the sequence of three-dimensional structure images; S33. Obtain a threshold value for the denoised three-dimensional structural sequence images using the Otsu method, and perform image segmentation processing based on the threshold value to segment the pore phase and fiber phase in the image, where the white pixel points with a pixel value of 1 are pores, and the black pixel points with a pixel value of 0 are fibers.

4. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 1, characterized in that, the process of step S5 is as follows: S51. Arbitrarily select a point O in the central part of the XY plane of the paper, and determine a cuboid with a square bottom surface having an initial side length d centered at point O and a fixed height. Use this cuboid as the estimation representation unit REV, and calculate the porosity of the cuboid region, where the height is the thickness of the paper; 0 The square of the pixel, and the height is a fixed value. Use this cuboid as the estimation representation unit REV, and calculate the porosity of the cuboid region, where the height is the thickness of the paper; S52. Let the bottom side length L of the cuboid gradually increase in steps of Δd pixels, and at the same time, count the porosity of each cuboid region, construct the corresponding relationship between the bottom side length of the cuboid and the porosity, and determine the representative elementary volume (REV) size when the porosity reaches stability; S53. To ensure the independence of the estimated REV size from its spatial position, continuously change the position of the center point O, repeat the above S51 and S52, construct the relationship between different REV sizes and porosities multiple times, and determine their corresponding variation rules; S54. Select the smallest geometric unit when the fluctuation of the porosity caused by the change in the bottom side length L is less than the specified threshold as the REV size.

5. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 1, characterized in that, the process of step S7 is as follows: S71. According to the flow state of the fluid inside the paper, select laminar flow for fluid flow simulation, and the corresponding fluid control equation is: ▽p = μ▽ 2 v ▽·v＝0 where v and p are the velocity vector and pressure of the fluid respectively, μ is the dynamic viscosity, ▽ is the gradient operator, and ▽ 2 is the Laplace operator; S72. Define the fluid properties, and the fluid properties include the density and dynamic viscosity of the fluid; S73. According to the actual situation during the paper absolute permeability test and the conventional boundary settings for porous media flow simulation, use the inlet / outlet pressure boundary condition, solid wall boundary condition, and symmetry boundary condition to jointly solve the fluid control equation; S74. Solve the set fluid flow physical field to obtain the numerical simulation result of the fluid penetration in the paper pores.

6. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 5, characterized in that, in step S73, to simulate the absolute permeability in the thickness direction and the absolute permeability in the plane direction of the paper REV three-dimensional pore structure model, the inlet / outlet pressure boundary condition is defined in 2 groups: (1) Take the upper boundary of the paper REV three-dimensional pore structure model as the inlet and the lower boundary as the outlet to simulate the absolute permeability in the thickness direction; (2) Take the left boundary of the paper REV three-dimensional pore structure model as the inlet and the right boundary as the outlet to simulate the absolute permeability in the plane direction.

7. A method for predicting the absolute permeability of paper based on X-ray tomography according to claim 1, characterized in that, in step S8, the absolute permeability of the paper is predicted according to Darcy's law. Let the absolute permeability of the paper be K, and the calculation formula is: Among them, A is the cross-sectional area of the porous material, with the unit of μm 2 ; H is the thickness of the porous material, with the unit of μm; q v represents the volume flow rate of the Newtonian fluid passing through the cross-section at a low flow rate, with the unit of μm 3 ·s -1 ; ΔP is the pressure drop across the specimen, with the unit of Pa; η is the dynamic viscosity of the fluid, with the unit of Pa·s; the absolute permeability K, with the unit of μm 2 .

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