Method for analyzing uncertainty of characteristic parameters of three-dimensional porous medium in image data limited scene

Abstract

The invention provides an uncertainty analysis method for characteristic parameters of a three-dimensional porous medium in an image data limited scene. According to the method, image samples of a limited porous medium are used as training data, an amplified generative adversarial network is adopted, local features are captured, and a large number of three-dimensional porous medium images are generated through amplification. And then geometric (porosity, specific surface area, Euler number and the like) and flow (relative permeability, capillary pressure and the like) characteristic parameters of the porous medium are obtained through image analysis and numerical simulation methods, so that the uncertainty of the characteristics of the porous medium is explored. According to the technical scheme, under the condition of limited image data, the three-dimensional porous medium image can be reconstructed, and the fluctuation range of parameters and the error range of related experiments are given, so that reactor design and catalyst development are guided.

Description

Technical Field

[0001] The present invention relates to the field of porous medium image reconstruction and physical property parameter analysis, and in particular to a method for uncertainty and error analysis of characteristic parameters of three-dimensional porous media in a scenario with limited image data. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Porous media are widely used in industrial applications (e.g., homogeneous catalysts, electrodes, and CO2 storage). Evaluating the energy and mass transport processes within the pores of porous media is crucial for reactor design and catalyst development. However, limited research has focused on assessing the uncertainties in geometric and flow properties. This is because repeated experiments on numerous samples are costly and time-consuming. Consequently, most studies focus on analyzing the physical properties of a limited number of samples.

[0004] Digital twinning is another method for studying the properties of porous media. High-resolution three-dimensional X-ray imaging combined with pore-scale modeling can quantify the geometry and flow characteristics of porous media. However, instrument scanning is costly, labor-intensive, and the shooting area is small, making it difficult to obtain a large amount of structure. Therefore, it is usually not feasible to obtain a large amount of porous media structural data through scanning imaging. At the same time, pore-scale simulation of multiple samples is not only limited by the imaging input data, but also by the calculation speed of the pore-scale model. For example, using the lattice Boltzmann method (LBM) and the finite volume method to capture pore-scale flow and calculate characteristics such as relative permeability, even with high-performance computer resources, a single run takes weeks. Therefore, when the structural data of porous media is limited, it is more difficult to assess the uncertainty of the characteristic parameters of porous materials. Summary of the Invention

[0005] The purpose of the present invention is to address the shortcomings of the existing technology and propose a method for capturing local features, amplifying and generating three-dimensional porous medium images, and analyzing the uncertainty of porous medium characteristic parameters when structural image data is limited, so as to solve current problems and guide reactor design and catalyst development.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for uncertainty analysis of characteristic parameters of a three-dimensional porous medium structure in a scenario with limited image data includes the following steps:

[0008] STEP 1: Obtain a 3D scan structure of a larger porous medium as the 3D scan structure of the original porous medium, and cut it to obtain a large number of smaller 3D porous medium sample data as a training data set.

[0009] The image size of the larger-sized porous medium three-dimensional scanning structure is not less than 512×512×512 voxels, and the image size of the small-sized three-dimensional porous medium sample obtained by cutting is not less than 64×64×64 voxels.

[0010] STEP 2: Based on the amplified generative adversarial network, the training dataset obtained in STEP 1 is used to amplify the porous medium and obtain a large amount of porous medium structure image data similar to the 3D scan structure of the original porous medium.

[0011] The amplified generative adversarial network is optimized based on the deep convolutional generative adversarial network. The amplified generative adversarial network specifically includes two parts: a generator and a discriminator. The generator consists of five three-dimensional deconvolution layers. Except for the last layer, each layer in the network is batch normalized. Except for the last layer, which uses the Tahn activation function, all other layers use Leaky ReLU as the activation function. The discriminator consists of six three-dimensional convolution layers. Except for the last layer, each layer in the network is spectral normalized and uses the Leaky ReLU activation function. The Hinge loss function is used as the loss function, and the Adam optimizer is used for backpropagation to update the network parameters.

[0012] During the training process of the amplified generative adversarial network, the generator and discriminator are trained alternately. The discriminator calculates a loss function by comparing the real dataset with the dataset generated by the generator. The parameters of the generator and discriminator are then updated using the chain rule and the Adam optimizer. The size of the output generated dataset is several times the size of the input training dataset.

[0013] Specifically, the training process of the generator is to input the random variable z into the generator and introduce the increment factor α to increase the size of the random variable z of the generator input. This can generate images with the same probability distribution as the training dataset. The minimum sample generated is the same size as the image in the training dataset, and the image can be increased to any size by changing the size of α:

[0014] λ=z+(α-1)×16

[0015] Where λ is the size of the generated image; α is the increment factor, which is an integer greater than or equal to 1; z represents the input image size;

[0016] The image G(z) generated by the generator is then input into the discriminator for discrimination to obtain the probability D(G(z)) that G(z) belongs to the training dataset, and D(G(z)) is substituted into the generator loss function to minimize the generator loss function through training.

[0017] The process of discriminator training is to input the training data set x into the discriminator for discrimination, obtain the probability D(x) that x comes from the training data set, substitute D(x) and D(G(z)) into the discriminator loss function and minimize the loss function through training. Since the dimensions of the training data set and the generated data set are inconsistent, conventional loss functions are difficult to make the model converge. Therefore, the loss used in the network architecture of the present invention is Hinge Loss, which is used to process data sets of different dimensions. The discriminator loss function is:

[0018]

[0019] Where x is the training data, z is a random variable, D(x) is the probability that x comes from the training data set, and θ d is the discriminator parameter, θ g is the generator parameter, is the mathematical expectation of the training data set, is the mathematical expectation of the random variable. The generator loss function is:

[0020]

[0021] Here, G(z) is the generated image; D(G(z)) is the probability that G(z) belongs to the training data.

[0022] The training process is done by adjusting the generator parameters θ g and the discriminator parameters θ d Minimize the generator loss function and the discriminator loss function respectively. The discriminator and generator are trained alternately, and θ is updated in each iteration. g and θ d .

[0023] STEP 3. Calculate the characteristic parameters (specifically structural parameters and transport parameters) of a large number of generated porous media structures through image analysis and numerical simulation methods, perform statistics on the structural parameters and transport parameters, conduct uncertainty analysis, and provide the parameter fluctuation range (experimental error range).

[0024] The structural parameters include porosity, specific surface area and Euler number, which are calculated based on image analysis and Minkowski Functionals (MFs) are used to calculate porosity. Specific surface area S V , Euler number Euler, the specific calculation formula is as follows:

[0025]

[0026] where M0, M1, and M3 are the zero-order, first-order, and third-order Minkowski functionals, respectively; V is the volume of the porous medium; dv is the infinitesimal element of the pore space; ds is the infinitesimal element of the pore surface; R1 and R2 are the principal and secondary curvature radii, respectively.

[0027] The transport parameters include absolute permeability, relative permeability and capillary pressure, and their calculation can be achieved by using numerical simulation methods (DNS, PNM, etc.).

[0028] The absolute permeability is calculated using the Darcy formula. The specific calculation method is shown in the following formula:

[0029]

[0030] Where Q is the flow rate of the fluid through the porous medium under the action of the pressure difference ΔP (m 3 / s); A is the cross-sectional area of ​​the porous material perpendicular to the flow direction (m 2 ); L is the length of the porous medium (m); μ is the viscosity of the fluid (Pa·s); ΔP is the pressure difference between the two sides of the fluid flowing through the porous medium (Pa); K is the absolute permeability of the porous medium (m 2 ).

[0031] The calculation formula for relative permeability is:

[0032]

[0033] Among them, K r is the relative permeability of the porous medium; K is the absolute permeability of the current fluid in the porous medium; K max It is the maximum permeability of a specific fluid in a porous medium under saturated conditions.

[0034] The definition of capillary pressure is:

[0035]

[0036] Among them, P c is the capillary pressure, P nw is the pressure of the non-wetting phase, P w is the pressure of the wetting phase, γ is the surface tension of the fluid, and r is the pore radius.

[0037] The structural parameters and transport parameters are statistically analyzed to perform uncertainty analysis and provide the fluctuation range of the parameters. The specific method is as follows:

[0038] The distributions of porosity, specific surface area, Euler number and absolute permeability are fitted to normal distribution, the standard deviation and mean value are calculated, and a box plot is drawn to determine the fluctuation range of the parameters. The capillary pressure curve is drawn with capillary pressure as the ordinate and saturation as the abscissa, and the relative permeability curve is drawn with relative permeability as the ordinate and saturation as the abscissa. The maximum, minimum and average values ​​of the capillary pressure and relative permeability at each saturation are calculated to obtain the error range of the capillary pressure curve and the relative permeability curve, and the fluctuation range of the parameters is given. The uncertainty of the characteristic parameters of the porous medium can be determined.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] The present invention cuts a large-scale 3D scan of a porous medium to obtain a large number of smaller 3D porous medium sample data as a training dataset. Based on an amplified generative adversarial network, the smaller 3D porous medium sample training dataset is used to amplify the porous medium, generating a large amount of porous medium structure image data similar to the original larger 3D scan of the porous medium. Structural and transport parameters of the generated porous media structures are then calculated and statistically analyzed using image analysis and numerical simulation methods. This allows for uncertainty assessment of the characteristic parameters of porous materials when limited porous media structural data is available. Using numerical simulation methods for transport parameter calculation is faster and more efficient than experimental methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which constitute a part of the present disclosure, are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation to the present disclosure.

[0042] Figure 1 Schematic diagram of the process of the present invention;

[0043] Figure 2 This is a diagram of the architecture of the amplified generative adversarial network in the embodiment;

[0044] Figure 3 The typical porous medium three-dimensional scanning structure (512 3 voxels) and generated structures (512 3 voxels) cross-sectional comparison;

[0045] Figure 4 Comparison of porosity, specific surface area, Euler number and absolute permeability between the three-dimensional scanned structure and the generated structure of a typical porous medium in the embodiment. DETAILED DESCRIPTION

[0046] Example

[0047] A method for uncertainty analysis of characteristic parameters of three-dimensional porous media structures under image data-limited scenarios is proposed. A typical porous media material, such as Figure 2 , for example, to conduct 3D porous media structure reconstruction and uncertainty analysis of characteristic parameters for scenarios with limited image data. The image size is 1000×1000×1000 voxels, with a resolution of 3.58μm. One image of 512×512×512 voxels was cut from the image as the original limited structure image data, and 20 images of 512×512×512 voxels were cut from the image as comparison data.

[0048] The original large-scale structural data of scanned three-dimensional porous media with a size of 512×512×512 voxels were cut with a cutting position interval of 24. A total of 6859 three-dimensional porous media structure images with an image size of 64×64×64 voxels and a resolution of 3.58μm were obtained as a training dataset for deep learning.

[0049] Based on the Python programming language, the deep convolutional generative adversarial network is optimized to establish an amplified generative adversarial network. A three-dimensional porous media structure image training dataset with an image size of 64×64×64voxels is used to amplify the porous media structure. 1000 three-dimensional porous media structures with an image size of 512×512×512voxels similar to the original three-dimensional scanned structure are obtained. The generated images are compared with the original images. Figure 3 .

[0050] The Minkowski functional was used to calculate the 1000 generated three-dimensional porous media structure images and 20 comparison data images, and the zero-order, first-order, second-order and third-order Minkowski functionals M0, M1, M2 and M3 were obtained respectively. Then the porosity, specific surface area and Euler number were calculated by formula.

[0051] Numerical simulations were used to simulate 1,000 generated 3D porous media structure images and 20 comparative data images, and transport parameters were calculated. Taking a supercritical CO₂ (scCO₂) brine system with an interfacial tension of 35 mN / m as an example, the numerical simulation method was used to simulate capillary pressure-dominated two-phase flow. The contact angle in the system was 0° during drainage and randomly distributed between 15-30° during imbibition, allowing the calculation of absolute permeability, relative permeability, and capillary pressure.

[0052] The porosity, specific surface area, Euler number and absolute permeability of the generated structure were statistically analyzed and compared with the comparative data image. The average values ​​of the porosity, specific surface area, Euler number and absolute permeability of the generated image and the comparative data image are similar, but the standard deviation is larger, e.g. Figure 4 By plotting the frequency distribution histogram and fitting the normal distribution curve, we can get the fluctuation range of the parameters. The results show that the parameter fluctuation of the generated data set can contain the parameter fluctuation of the training data set, which shows that this method has high accuracy.

[0053] The relative permeability and capillary pressure of the 1,000 generated three-dimensional porous media structures were calculated. A capillary pressure curve was plotted with capillary pressure as the ordinate and saturation as the abscissa. A relative permeability curve was plotted with relative permeability as the ordinate and saturation as the abscissa. The maximum, minimum, and average values ​​of the capillary pressure and relative permeability at each saturation were calculated. The error ranges of the capillary pressure and relative permeability curves were obtained, giving the fluctuation range of the parameters. The error ranges of the capillary pressure and relative permeability curves were plotted.

[0054] In summary, the method of the present application can reconstruct three-dimensional porous media images when image data is limited and provide the fluctuation range of parameters and the error range of related experiments, thereby guiding reactor design and catalyst development.

Claims

1. A method for uncertainty analysis of characteristic parameters of three-dimensional porous media in a scene with limited image data, characterized in that: The characteristic parameters include structural parameters and transport parameters, and the method includes the following steps: 1) Obtain the 3D scanned structure of the original porous medium and cut it to obtain a large number of smaller 3D porous medium sample data as training data sets; 2) Based on the amplified generative adversarial network, the training data set described in step 1) is used to amplify and generate the porous medium, so as to obtain a large amount of porous medium structure image data similar to the three-dimensional scan structure of the original porous medium; 3) Calculate the structural parameters and transport parameters of a large number of generated porous media structures, conduct statistics on the structural parameters and transport parameters, perform uncertainty analysis, and provide the fluctuation range of the parameters.

2. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1 is characterized in that: In step 1), the image size of the three-dimensional scanning structure of the original porous medium is not less than 512×512×512 voxels, the image size of the three-dimensional porous medium sample of smaller size is not less than 64×64×64 voxels, and the images of the three-dimensional porous medium samples of smaller size are allowed to overlap.

3. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1 is characterized in that: In step 2), the amplified generative adversarial network includes a generator and a discriminator; the generator is composed of five three-dimensional deconvolution layers, each layer uses an activation function and normalization processing; the discriminator is composed of six three-dimensional convolution layers, each layer uses an activation function and normalization processing; the generator and the discriminator both use the Hinge loss function as the loss function; and the Adam optimizer is used to update the network parameters.

4. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 3 is characterized in that: In the training process of the amplified generative adversarial network, the generator and the discriminator are trained alternately, and the generator parameters θ are updated in each iteration. g and the discriminator parameters θ d ; The generator loss function is: Among them, G(z) is the generated image and z is a random variable; is the mathematical expectation of the random variable; D(G(z)) is the probability that G(z) belongs to the training data; The discriminator loss function is: Where x is the training data, D(x) is the probability that x comes from the training dataset, G(z) is the generated image, is the mathematical expectation of the training data set.

5. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1, characterized in that: The amplified generative adversarial network is based on the training data set described in step 1) to amplify the porous medium, which is specifically expressed as: λ=z+(α-1)×16 Among them, λ is the size of the generated image; α is the increment factor, which is an integer greater than or equal to 1; z represents the input image size.

6. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1, characterized in that: In step 3), the structural parameters of the porous medium structure include porosity Specific surface area S V , Euler number Euler, Minkowski functional is used to calculate the structural parameters, the specific formula is: Where M0, M1, and M3 are the zero-order, first-order, and third-order Minkowski functionals, respectively; V is the volume of the porous medium; dv is the infinitesimal element of the pore space; ds is the infinitesimal element of the pore surface; R1 and R2 are the principal and secondary curvature radii, respectively.

7. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1, characterized in that: In the step 3), the transport parameters of the porous medium structure include absolute permeability, relative permeability and capillary pressure, which are calculated by numerical simulation method; The absolute permeability is calculated using Darcy's formula, as follows: Where K is the absolute permeability of the porous medium, m 2 ; μ is the viscosity of the fluid, Pa·s; Q is the flow rate of the fluid through the porous medium under the pressure difference ΔP, m 3 / s; L is the length of the porous medium, m; A is the cross-sectional area of ​​the porous material perpendicular to the flow direction, m 2 ; ΔP is the pressure difference between the two sides of the porous medium (Pa); The calculation formula of relative permeability is: Among them, K r is the relative permeability of the porous medium; K is the absolute permeability of the current fluid in the porous medium; K max It is the maximum permeability of a specific fluid in a porous medium under saturation conditions; The formula for calculating capillary pressure is: Among them, P c is the capillary pressure, P nw is the pressure of the non-wetting phase, P w is the pressure of the wetting phase, γ is the surface tension of the fluid, and r is the pore radius.

8. The uncertainty analysis method of characteristic parameters of three-dimensional porous media in a scene with limited image data according to claim 1, characterized in that: In the step 3), the structural parameters and transport parameters are statistically analyzed to perform uncertainty analysis and provide the fluctuation range of the parameters. The specific method is as follows: The distributions of porosity, specific surface area, Euler number, and absolute permeability were fitted to normal distributions, the standard deviation and mean were calculated, and box plots were drawn to determine the fluctuation range of the parameters; The capillary pressure curve is plotted with the capillary pressure as the ordinate and the saturation as the abscissa; the relative permeability curve is plotted with the relative permeability as the ordinate and the saturation as the abscissa; and the maximum, minimum and average values ​​of the capillary pressure and relative permeability at each saturation are calculated to obtain the error range of the capillary pressure curve and the relative permeability curve, and give the fluctuation range of the parameters.

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