A method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device.

Abstract

This invention discloses a method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device. Its main feature is the use of a multi-segment function to fit the wet flow-pressure curve piecewise, followed by analysis of the dry flow-pressure curve and the optimized wet flow-pressure curve data to calculate the optimized pore size distribution data. By optimizing and analyzing the data to obtain the optimal fitted curve, researchers and engineers can better understand, analyze, and summarize the pore size distribution characteristics of membrane elements. The data processing and optimization method involved in this invention indirectly reduces the impact of instrument errors on test results while improving the rationality of pore size distribution test results.

Description

Technical Field

[0001] This invention belongs to the field of data analysis, specifically relating to a method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device. Background Technology

[0002] Porous materials are a class of structural-functional integrated materials with wide industrial applications and significant research value, playing an important role in petrochemical, metallurgical, and environmental protection fields. Taking metal membrane materials as an example, their pore size parameters mainly include key indicators such as maximum pore size, flow-pressure curve, and pore size distribution. Pore size distribution is the most critical and representative core parameter. Currently, the commonly used gas-liquid displacement method is based on wet and dry flow-pressure curve data of porous materials, according to standards ASTM-F316 and GB / T 32361-2015. The obtained pore size distribution results can reflect the concentration and consistency of pore size in porous materials. Its rational design and accurate characterization are of great significance for optimizing the performance of porous materials in applications such as liquid filtration, gas separation, and automated equipment measurement.

[0003] Besides the aforementioned gas-liquid displacement method, other methods used for pore size distribution testing include mercury intrusion porosimetry and gas adsorption. While mercury intrusion porosimetry can obtain a wide range of pore size distributions, the high-pressure conditions may damage the original pore structure of the material. Gas adsorption is sensitive to micropores and mesopores, but has limited ability to characterize macropores and is highly model-dependent. Therefore, the gas-liquid displacement method has become the simplest and most suitable pore size distribution detection technique for practical engineering applications. The core of the gas-liquid displacement method for pore size distribution detection is based on wet and dry flow-pressure curve data of porous materials, combined with different analytical calculation models. Currently, the analytical methods that have been applied include the Soviet Ishkin method, the German Zager method, and the American ASTM-F316 method. Among them, ASTM-F316 is an internationally recognized analytical method that combines practicality, authority, and consistency. The core principle of the ASTM-F316 method stems from the physical balance between capillary suction and surface tension. Before testing, the porous material must be thoroughly wetted to fill the pores with wetting liquid. During testing, the gas pressure is gradually increased. When the applied pressure overcomes the surface tension and capillary resistance, the liquid inside the pores of the porous material is expelled. By comparing the gas flow rates through dry and wet samples at the same pressure, the percentage of flow rate passing through pores of a specific size can be determined. The difference between the dry and wet film flow rates can be used to quantitatively calculate the flow rate proportion within a certain pore size range, ultimately yielding the pore size distribution data.

[0004] In the actual testing of porous materials using the ASTM-F316 method, the measured flow-pressure curve data comes from the real-time response of the sensor and can reflect the dynamic characteristics of the system. However, it is easily affected by environmental interference and sensor errors, and is prone to problems such as strong fluctuations and high dispersion. Especially when using small pressurization steps for high-precision automated testing, due to the large number of data acquisition points, adjacent data are prone to "oscillation" due to instrumentation, external environment and other reasons. This results in insufficient stability and resolvability of the obtained flow-pressure curve measured data. The pore size distribution data obtained from this analysis will have "negative" points, which have no practical and physical meaning in characterizing the pore size distribution.

[0005] To address the aforementioned issues, this invention patent provides a method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device. The core innovation of this method lies in: dividing the wet flow-pressure curve data into three regions for segmented fitting, including the zero flow region, transition region, and saturation region; proposing the use of a Logistic function to fit the wet flow-pressure curve data in the transition region, resulting in a fitted wet flow-pressure curve that reflects the S-shaped nonlinear growth characteristics of porous materials in the wet state, characterized by "low-speed growth → rapid growth → low-speed growth," with a smooth and stable fitted curve. This method can eliminate the "negative value" phenomenon in the pore size distribution calculation results caused by large fluctuations in the data collected in the transition region during the testing of the wet flow-pressure curve, indirectly reducing the impact of instrument errors on the test results while improving the rationality of the pore size distribution test results. Summary of the Invention

[0006] The purpose of this invention is to provide a method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device. The method is characterized by using a multi-segment function to fit the wet flow-pressure curve piecewise, and then analyzing the dry flow-pressure curve and the optimized wet flow-pressure curve data to calculate the optimized pore size distribution data.

[0007] Furthermore, a method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device is characterized by the following operational steps:

[0008] Step 1: Divide the wet flow-pressure curve data into three parts: zero flow zone, transition zone, and saturation zone. The zero flow zone corresponds to the initial stage of the wet flow-pressure curve test, where the flow rate does not respond to pressure changes, and the critical pressure difference at the endpoint is the maximum bubble point pressure. In the transition zone, different sized channels are penetrated by gas in descending order of size, gradually forming a continuous conductive path. The saturation zone corresponds to the steady-state seepage after the channels are fully connected, where the flow rate is not constrained by capillary force and the channel opening process, and the wet and dry flow-pressure curves coincide.

[0009] Step 2: In the zero-flow region, the applied pressure difference of the material is less than the interfacial tension of the wetting liquid in the pore, and the gas flow rate is zero. The mathematical expression is:

[0010] 𝑄 𝑊 (𝑃) = 0 (𝑃 < 𝑃 𝑚𝑎𝑥 )

[0011] Among them, 𝑄 𝑊 (x) represents the gas flow rate through the sample at pressure P on the wet flow-pressure curve. 𝑚𝑎𝑥 This is the maximum bubble point pressure.

[0012] Step 3: The internal channels of the material in the transition zone are gradually connected, exhibiting a strong nonlinear S-shaped upward characteristic with a rapid jump from near zero. The wet flow-pressure curve approaches the dry flow-pressure curve until the two coincide. The transition zone uses the Logistic function to fit the wet flow-pressure curve data, and the mathematical expression is:

[0013]

[0014] in, This represents the maximum upper limit of the flow rate within the interval. The growth rate of the wet flow-pressure curve within the interval is calculated using a univariate linear regression model; P0 is calculated by combining the dry gas half-flow curve. Calculations were performed by combining dry gas flow curves.

[0015] Step four: The wet flow-pressure curve in the saturated zone follows a linear seepage law and is fitted using a direct proportional function. The mathematical expression is:

[0016]

[0017] Where k is the linear regression coefficient:

[0018]

[0019] in, When pressure is The gas flow rate through the sample at that time.

[0020] Step 5: Calculate the orifice distribution by combining the optimized wet flow-pressure curves from Steps 2, 3, and 4. The mathematical expression is:

[0021]

[0022] In the formula: F(P) is the cumulative proportion of orifices that have been opened under pressure P; Q W Q is the flow rate through the wet sample. dTo determine the flow rate through the dry sample, As the test site; It represents the ratio of wet flow rate to dry flow rate under a certain pressure.

[0023] As an improvement, the wet flow-pressure curve data is divided into three regions for segmented fitting, including the zero flow region, the transition region, and the saturation region. The zero flow region corresponds to the initial stage of the wet flow-pressure curve test, the transition region corresponds to the middle stage of the wet flow-pressure curve test, and the saturation region corresponds to the later stage of the wet flow-pressure curve test.

[0024] As an improvement, the transition zone uses the Logistic function to fit the wet flow-pressure curve data. The fitted wet flow-pressure curve can reflect the S-shaped nonlinear growth characteristics of the transition zone of porous materials in the wet state, which is "low-speed growth → rapid growth → low-speed growth". The fitted curve is smooth and stable.

[0025] As an improvement, the method can eliminate the "negative value" phenomenon in the pore size distribution calculation results caused by large fluctuations in the data collected in the transition zone during the testing of wet flow-pressure curves. This indirectly reduces the impact of instrument errors on the test results while improving the rationality of the pore size distribution test results.

[0026] The key innovation of this invention lies in proposing to fit the wet flow-pressure curve data using a Logistic function in the transition zone, and then analyze the dry flow-pressure curve data with the optimized wet flow-pressure curve data to calculate the optimized pore size distribution data. The pore size distribution data processing and optimization method involved in this invention solves the problem of abnormal fluctuations in detection results caused by random noise and errors during the actual flow-pressure data measurement process of automated testing devices, achieving smoothing and correction of the wet flow-pressure relationship and pore size distribution data. By optimizing and analyzing the optimal fitting curve, the accuracy and stability of the detection results are significantly improved, facilitating the understanding, analysis, and summarization of membrane element pore size distribution characteristics by scientific researchers and engineers.

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments: The automated detection device used in the embodiments is derived from the utility model patent "An Automated Detection Device for Membrane Element Aperture", patent application number: 202521853802.7. Attached Figure Description

[0028] Figure 1 The measured flow-pressure curves for dry and wet membrane element samples are shown.

[0029] Figure 2 The dry and wet flow-pressure fitting curves for the membrane element samples;

[0030] Figure 3 The pore size distribution of the membrane element sample is calculated based on the dry and wet flow-pressure fitting curves.

[0031] Figure 4 The image shows the pore size distribution of the membrane element sample calculated based on the measured flow-pressure curves of dry and wet flow. Detailed Implementation

[0032] The following detailed description, in conjunction with embodiments and accompanying drawings, is provided. It should be emphasized that the following description is merely exemplary and not intended to limit the scope of the invention or its application.

[0033] In this embodiment, a stainless steel powder sintered porous membrane element with a thickness of 2 mm and a diameter of 30 mm was used as the test sample. The testing device described in utility model patent 202521853802.7 was used for testing, with a pressure step of 0.1 kPa. The measured dry and wet flow-pressure curves of the membrane element sample obtained by the automated pore size detection device are shown below. Figure 1 As shown.

[0034] Step 1: Determine the zero-flow region. Using the path trajectory of the measured curve, perform analytical fitting calculations using the Matlab embedding algorithm to obtain the piecewise function analytical expression of the wet flow-pressure fitting curve for the membrane element sample:

[0035] 𝑄 𝑊 (𝑃) = 0 (𝑃 < 𝑃 𝑚𝑎𝑥 )

[0036] Among them, 𝑄 𝑊 (x) represents the gas flow rate through the sample at pressure P on the wet flow-pressure curve of the membrane element sample. 𝑚𝑎𝑥 The value is obtained directly through testing with an automated pore size detection device, corresponding to the maximum bubble point pressure of the membrane element sample. In this embodiment, the value is 22.06 kPa.

[0037] Step two, determine the transition zone. The wet flow-pressure curve data is fitted using the Logistic function; the mathematical expression is:

[0038]

[0039] in, The maximum upper limit of the flow rate within the transition zone is determined by the intersection of the dry and wet flow-pressure measured curves obtained by the automated pore size detection device. In this embodiment, this value is 1.07 L / min. P0 is the median average bubble point pressure of the membrane element sample, determined by the intersection of the dry half-flow rate curve obtained by the dry flow-pressure curve and the wet flow-pressure measured curve. In this embodiment, this value is 47.22 kPa. The minimum bubble point pressure of the membrane element sample is determined by the intersection of the dry and wet flow-pressure measured curves obtained by the automated pore size detection device. In this embodiment, this value is 73.92 kPa. The growth rate of the wet flow-pressure curve of the membrane element sample within the transition zone was calculated using a univariate linear regression model. The calculation process is as follows:

[0040] 1) Determine the maximum upper limit value 'a' of the flow rate within the transition zone;

[0041] 2) The transition zone data set is denoted as (p i q i Let i be the ordinal number of the data points, and let i be the permutation number of the data set. After calculation, a new transition zone data set (p) was obtained. i Q i );

[0042] 3) New transition zone data group (p i Q i Linear fitting yields a linear function Q = ꭓP + λ, where ꭓ is the slope of the linear function obtained from the new transition zone data set, and λ is the intercept of the linear function, i.e., the flow rate value corresponding to a pressure of 0 kPa. Finally, the growth rate b in the transition zone wet flow-pressure curve fitting function is ꭓ, which in this embodiment is b = 1.07. The obtained transition zone wet flow-pressure curve fitting function is:

[0043]

[0044] Step 3: Determine the saturation zone. The wet flow-pressure curve follows a linear seepage law and is fitted using a direct proportional function. The mathematical expression is:

[0045]

[0046] Where k is the linear regression coefficient:

[0047]

[0048] in, When pressure is The gas flow rate through the sample is k = 0.013 in this embodiment. The resulting wet flow-pressure curve fitting function in the saturated region is:

[0049]

[0050] Based on the above fitting calculations, the wet flow-pressure fitting curve of the membrane element sample is obtained as follows: Figure 2 As shown.

[0051] Step four: Analyze the dry flow-pressure curves and the fitted wet flow-pressure curves according to ASTM-F316 and GB / T 32361-2015 to obtain the pore size distribution map of the membrane element sample, as shown below. Figure 3 As shown.

[0052] Finally, the unoptimized version (see...) Figure 4 By comparing the optimized pore size distribution data, it was found that the pore size distribution data processing and optimization method proposed in this invention can eliminate the "negative value" phenomenon in the pore size distribution calculation results caused by large fluctuations in the data collected in the transition zone during the testing of wet flow-pressure curves. Therefore, the method proposed in this invention can indirectly reduce the impact of instrument errors of the testing device on the test results while improving the rationality of the pore size distribution test results.

[0053] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device, characterized by using a multi-segment function to fit the wet flow-pressure curve piecewise, then analyzing the dry flow-pressure curve and the optimized wet flow-pressure curve data to calculate the optimized pore size distribution data. The specific operation steps are as follows: Step 1: Divide the wet flow-pressure curve data into three parts: zero flow zone, transition zone, and saturation zone. The zero flow zone corresponds to the initial stage of the wet flow-pressure curve test, where the flow rate does not respond to pressure changes, and the critical pressure difference at the endpoint is the maximum bubble point pressure. In the transition zone, different sized channels are penetrated by gas in descending order of size, gradually forming a continuous conductive path. The saturation zone corresponds to the steady-state seepage after the channels are fully connected, where the flow rate is not constrained by capillary force and the channel opening process, and the wet and dry flow-pressure curves coincide. Step 2: In the zero-flow region, the applied pressure difference of the material is less than the interfacial tension of the wetting liquid in the pore, and the gas flow rate is zero. The mathematical expression is: 𝑄 𝑊 (𝑃)=0 (𝑃<𝑃 𝑚𝑎𝑥 ) in, 𝑄 𝑊 (x) represents the gas flow rate through the sample at pressure P on the wet flow-pressure curve. 𝑚𝑎𝑥 This is the maximum bubble point pressure. Step 3: The internal channels of the material in the transition zone are gradually connected, exhibiting a strong nonlinear S-shaped upward characteristic with a rapid jump from near zero. The wet flow-pressure curve approaches the dry flow-pressure curve until the two coincide. The transition zone uses the Logistic function to fit the wet flow-pressure curve data, and the mathematical expression is: in, This represents the maximum upper limit of the flow rate within the interval. The growth rate of the wet flow-pressure curve within the interval is calculated using a univariate linear regression model; P0 is calculated by combining the dry gas half-flow curve. Calculations were performed by combining dry gas flow curves. Step four: The wet flow-pressure curve in the saturated zone follows a linear seepage law and is fitted using a direct proportional function. The mathematical expression is: Where k is the linear regression coefficient: in, For when pressure is The gas flow rate through the sample at that time. Step 5: Calculate the orifice distribution using the optimized wet flow-pressure curves from Steps 2, 3, and 4. The mathematical expression is: In the formula: F(P) is the cumulative proportion of the holes that have been opened under pressure P; Q W Q is the flow rate through the wet sample. d To determine the flow rate through the dry sample, As the test site; It represents the ratio of wet flow rate to dry flow rate under a certain pressure.

2. The method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device according to claim 1, characterized in that... The wet flow-pressure curve data is divided into three regions for segmented fitting: the zero flow region, the transition region, and the saturation region. The zero flow region corresponds to the initial stage of the wet flow-pressure curve test, the transition region corresponds to the middle stage of the wet flow-pressure curve test, and the saturation region corresponds to the later stage of the wet flow-pressure curve test.

3. The method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device according to claim 1, characterized in that: The transition zone was fitted with the wet flow-pressure curve data using the Logistic function. The fitted wet flow-pressure curve can reflect the S-shaped nonlinear growth characteristics of the transition zone of porous materials under wet conditions, which is "low-speed growth → rapid growth → low-speed growth". The fitted curve is smooth and stable.

4. The method for processing and optimizing pore size distribution data based on an automatic membrane pore size detection device according to claim 1, characterized in that... The method described above can eliminate the "negative value" phenomenon in the pore size distribution calculation results caused by large fluctuations in the data collected in the transition zone during the testing of wet flow-pressure curves. While indirectly reducing the impact of instrument errors on the test results, it also improves the rationality of the pore size distribution test results.

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