An apparatus and method for measuring the pore size distribution of porous media by harmonic analysis

Abstract

This invention discloses an apparatus and method for measuring the pore size distribution of porous media through harmonic analysis. The apparatus includes a signal application system, pressure and displacement measuring instruments, a signal processing instrument, and a sample and fluid storage container. The invention applies an oscillating flow to the sample through the signal application system, and the signal processing instrument collects pressure and displacement signals and performs harmonic analysis on the signals. Based on the harmonic analysis results, the frequency response of the porous media's admittance is calculated, thereby obtaining its pore size distribution. This method has the advantages of low cost, no pollution, and rapid accuracy, and is of great significance for a deeper understanding of the pore structure of porous media.

Description

Technical Field

[0001] This invention relates to the field of porous media pore size distribution measurement technology, specifically to an apparatus and method for measuring the pore size distribution of porous media through harmonic analysis. Background Technology

[0002] Natural porous materials are widely found in sedimentary rocks, volcanic rocks, plants, and any form of organic matter, and have broad applications and research in earth sciences, chemistry, biology, and medicine. The pore size distribution of porous materials directly affects their permeability, thus significantly influencing various aspects such as the migration and diffusion of pollutants in soil, soil seepage stability, oil extraction efficiency, ion exchange efficiency of chemical reactors, and even the suitability of human organ prostheses. Therefore, measuring the pore size distribution of porous materials is of great significance for various production practices.

[0003] Currently, commonly used methods for determining pore size distribution include mercury intrusion porosimetry, gas adsorption, and thermal porosimetry. These methods are based on the principles of mercury injection pressure, adsorbate liquid volume, and liquid phase transition threshold, respectively, to determine pore size. However, they all have drawbacks to varying degrees, such as excessively long measurement time, risk of sample damage, high instrument costs, and environmental pollution. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a safe, efficient, and accurate device and method for measuring the pore size distribution of porous media.

[0005] The objective of this invention is achieved through the following technical solution: An apparatus for measuring the pore size distribution of porous media by harmonic analysis includes a sample and a fluid storage container. The sample and fluid storage container include an upstream chamber 1 and a downstream chamber 4. A test sample 5 is placed between the upstream chamber 1 and the downstream chamber 4. The upstream chamber 1 and the downstream chamber 4 are respectively connected to the two detection ends of a pressure sensor 34. A valve 28 is also provided between the upstream chamber 1 and the downstream chamber 4 in parallel with the pressure sensor 34. The apparatus also includes a harmonic analysis component 9 connected to the upstream chamber 1. The harmonic analysis component 9 includes a signal application system and a displacement sensor. The displacement sensor and the pressure sensor are respectively connected to two independent transfer function analyzers 44.

[0006] Newtonian fluids are stored in the upstream chamber 1 and the downstream chamber 4.

[0007] The harmonic analysis component 9 includes a low-frequency harmonic analysis component for measuring the pore size distribution of apertures greater than 500 and / or a high-frequency harmonic analysis component for measuring the pore size distribution of apertures greater than 30.

[0008] The harmonic analysis component 9 uses an LVDT29 or a photodiode 42 as a displacement sensor. The LVDT29 or photodiode 42 and the pressure sensor 34 are respectively connected to two identical but independent transfer function analyzers 44.

[0009] The low-frequency harmonic analysis component includes a cam mechanism 25 fixed on a fixed base, a connecting rod support 16, a connecting rod shaft 18, a connecting rod 17, a piston 6, a piston guide plate 11, a spring 14, and an adapter 7. The connecting rod 17 is swayably fixed to the connecting rod support 16 via the connecting rod shaft 18 located at the top. The cam mechanism 25 is in contact with the bottom of the connecting rod 17 for transmission. The connecting rod 17 is fixed to the connecting rod support 16 via the connecting rod shaft 18. One side of the middle part of the connecting rod 17 is connected to the piston 6, and the other side is connected to the LVDT 29. The piston 6 is connected to the spring 14 via the piston guide plate 11. The spring 14 is connected to the upstream chamber 1 via the adapter 7.

[0010] The high-frequency harmonic analysis component includes a vibrating pot 35 fixed on a fixed base, a square bracket 2, a piston 37, a lighting lamp 43, a photodiode 42, and an adapter 7. One or more of the piston 37, lighting lamp 43, photodiode 42, and adapter 7 are fixed on the square bracket 2. The upstream chamber and harmonic analysis component are respectively fixed on both sides of the square bracket. The vibrating pot 35 can drive the piston 37 to move. The piston 37 is connected to the upstream chamber 1 through the adapter 7. The lighting lamp 43 and photodiode 42 are also provided as displacement sensors to detect the displacement of the piston 37.

[0011] A method for measuring the pore size distribution of porous media by harmonic analysis includes the following steps: Step A: Select appropriate device components, connect the sample, saturate the sample and check for air bubbles, then turn on the instrument; Step B: Connect two capillary tubes of different diameters in sequence according to the method in Step A, adjust the instrument, use a transfer function analyzer to collect the pressure and displacement signals and perform FFT analysis, and combine the theoretical admittance to calculate the transfer function required for measurement admittance; Step C: Connect the porous medium sample according to the method in Step A, collect and process the pressure and displacement signals during the test according to the method in Step B, calculate the porous medium admittance, and thus obtain the pore size distribution.

[0012] In step A, the experimental apparatus is required to be filled with fluid from the connection between the piston and the upstream chamber to the outlet hole before the test, and different harmonic analysis components are used to measure the pore size distribution of different apertures.

[0013] Step B specifically includes the following steps: (1) Connect two capillary tubes of different diameters in succession for testing, turn on the instrument, and use the actuator to generate a signal to apply an oscillating flow; (2) Calibrate the sensor; (3) Pressure and displacement signals were collected from two capillaries with different diameters, and harmonic analysis was performed on the signals; (4) Substitute the analysis results of the two sets of pressure and displacement signals and the theoretical admittance of the two capillaries under test into the admittance calculation formula to calculate the transfer function required to measure the admittance of the porous medium. The transfer function measured by the two capillaries should be the same.

[0014] Step C specifically includes the following steps: (1) Connect the porous medium, turn on the instrument, and use the actuator to generate a signal to apply an oscillating flow; (2) Acquire pressure and displacement signals for porous media and perform harmonic analysis on the signals; (3) Substitute the analysis results of the pressure and displacement signals of the porous medium and the transfer function measured in step B into the admittance calculation formula to obtain the total admittance of the porous medium. Based on the total admittance and the basic capillary theoretical admittance, the pore size distribution of the porous medium is obtained.

[0015] When the harmonic analysis component is a low-frequency harmonic analysis component, it is used to measure apertures greater than 500. The pore size distribution, the low frequency harmonic analysis component adopts a cam mechanism to form an actuator, the cam mechanism is in contact with the connecting rod, the connecting rod is fixed on the connecting rod support through the connecting rod shaft, the upper right side of the connecting rod is connected to the piston, the left side is connected to the LVDT displacement sensor, the piston is connected to the spring through the piston guide plate, and the spring is connected to the upstream chamber through the adapter.

[0016] When the harmonic analysis component is a high-frequency harmonic analysis component, it can measure harmonics greater than 30. The small aperture pore size distribution, the high frequency harmonic analysis component adopts a vibrating pot as the actuator, the vibrating pot and the square bracket are connected to a piston, a lighting lamp is provided on one side of the gap where the piston is located, and a photodiode is provided on the other side as a displacement sensor, and the piston is connected to the upstream chamber through an adapter.

[0017] The beneficial effects of this invention are: This method overcomes the shortcomings of current common pore size distribution measurement methods, such as high instrument cost, long measurement time, sample damage during measurement, and generation of toxic substances. It uses an oscillating flow applied to porous media and harmonic analysis of the signal to determine its pore size distribution. This method is safe, efficient, and can accurately reflect the size distribution of most pores. It has important practical significance for a deeper understanding of the pore structure of porous media and the evaluation of the permeability of porous media. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the overall invention; Figure 2 This is a front view of the low-frequency harmonic analysis device of the present invention; Figure 3 for Figure 2 Enlarged schematic diagram of the middle harmonic analysis component; Figure 4 This is a schematic diagram of the top surface of the low-frequency harmonic analysis device of the present invention; Figure 5 This is a schematic diagram of the top surface of the high-frequency harmonic analysis device of the present invention; Figure 6 for Figure 5 Enlarged schematic diagram of the middle harmonic analysis component.

[0020] In the diagram: 1. Upstream chamber; 4. Downstream chamber; 5. Test sample; 9. Harmonic analysis component; 28. Valve; 45. Sensor housing; 34. Inductive thin-film sensor; 2. Square bracket; 3. Upstream cap; 6. Piston; 7. Adapter; 8. Bolt; 10. Nut; 11. Piston guide plate; 12. Sealing material; 13. Sealing material; 14. Cylindrical helical spring; 16. Connecting rod shaft support; 17. Connecting rod; 18. Connecting rod shaft; 19. Worm gear; 20. Eccentric shaft support; 21. Rolling bearing; 22. Rotating shaft; 23. Spur gear; 24. Eccentric wheel; 25. Cam mechanism; 26. Cam connecting rod contact hammer; 27. Support rod; 29. ​​LVDT; 30. Flange; 31. Tie rod; 32. Base; 33. Screw; 35. Vibrating cooker; 37. Piston; 38. Cylinder liner; 40. Photodiode bracket; 42. Photodiode; 43. Lighting lamp; 44. Transfer function analyzer. Detailed Implementation

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description. Any feature disclosed in this specification (including any appended claims, abstract, and drawings) may be replaced by other equivalent or similar features unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Before describing the embodiments, some necessary terms need to be explained. For example: If terms such as "first" and "second" are used to describe various elements in this application, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. Therefore, the "first" element discussed below may also be referred to as the "second" element without departing from the teachings of this invention. It should be understood that when an element is referred to as "connected" or "linked" to another element, it may be directly connected or directly linked to the other element, or there may be an intermediate element. Conversely, when an element is referred to as "directly connected" or "directly linked" to another element, there is no intermediate element. The terms "mounted," "connected," and "linked" should be interpreted broadly. For example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection, an electrical connection, or the ability to communicate with each other; they may refer to a direct connection or an indirect connection through an intermediate medium; they may refer to the internal communication of two elements or the interaction between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0024] The various terms appearing in this application are used merely for the purpose of describing specific embodiments and are not intended to limit the invention. Unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. Terms such as "upper," "lower," "side," "inner," "outer," "top," "bottom," "left," and "right" indicate orientations or positional relationships based on installation orientations or positional relationships, and are used only for the convenience of describing the invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0025] When the terms “comprising” and / or “including” are used in this specification, these terms indicate the presence of the said feature, integral, step, operation, element and / or component, but do not exclude the presence and / or addition of more than one other feature, integral, step, operation, element, component and / or group thereof.

[0026] Please refer to the attached diagram. An apparatus for measuring the pore size distribution of porous media using harmonic analysis includes an upstream chamber 1, connected to a harmonic analysis component 9 on its left side. A porous media test sample 5 is placed between the upstream chamber 1 and a downstream chamber 4. An inductive thin-film sensor 34 is externally connected to both the upstream and downstream chambers 1 and 4. The inductive thin-film sensor 34 is encased in a sensor housing 45. Valves 28 are also connected to both ends of the inductive thin-film sensor 34. Specifically, a zeroing valve 28, connected in parallel with the pressure sensor 34, is also provided between the upstream and downstream chambers 1 and 4 to facilitate zeroing the value at the initial detection state. The inductive thin-film sensor 34 is connected to a transfer function analyzer 44 via a displacement sensor LVDT 29 or a photodiode 42. The transfer function analyzer 44 is a device for acquiring pressure and displacement signals and performing FFT analysis, i.e., harmonic analysis, which can generate FFT images. In this embodiment, the inductive thin-film sensor 34 is model dp103; the piston is model D6_v2; the adapter is model 1-4G D10; the sealing material 12 is model METC6-10-16; the sealing material 13 is model METC10-16-8; the cylindrical helical spring is model R203104; the worm gear is model W1-1; the rolling bearing is model d8D22b7; the shaft is model D8; the flange is model DCTH300; the tie rod is model DCTH300; the base is model DCTH300; the screw is model CHC M6L12; and the transfer function analyzer is model SOLARTON 1250A.

[0027] Please see the appendix Figure 3The harmonic analysis component 9 and the upstream chamber 1 are fixed on the left and right sides of the square bracket 2, respectively. An upstream cap 3 is provided on the upper part of the upstream chamber 1 near the square bracket 2. Upstream chamber 1 and harmonic analysis component 9 are connected via adapter 7. The left side of adapter 7 is connected to cylindrical helical spring 14. The two ends of cylindrical helical spring 14 are covered with sealing material METC6-10-16 and sealing material METC10-16-8. Sealing material 13 is connected to piston 6. Piston 6 is fixed on piston guide plate 11. Piston guide plate 11 is fixedly connected by four sets of bolts 8 and nuts 10. A connecting rod shaft support 16 is welded to the left side of piston guide plate 11. The connecting rod shaft support 16 is hollow inside and has a connecting rod shaft 18. A support rod 27 is sleeved on the connecting rod shaft 18. The connecting rod shaft 18 suspends the connecting rod 17, forming a free swing structure with the pivot at the top. The middle part of the connecting rod 17 is connected to piston 6. The lower end of the connecting rod 17 is fixed with cam connecting rod contact hammer 26. Cam connecting rod contact hammer 26 is in contact with cam mechanism 25 and swings under the drive of cam mechanism 25. The cam mechanism 25 includes a rolling bearing 21, on which an eccentric wheel 24 is placed. The eccentric wheel 24 contacts the cam connecting rod contact hammer 26. An eccentric shaft support 16 is fitted over the rolling bearing 21 and the eccentric wheel 24. The rolling bearing 21 and the eccentric wheel 24 are connected to a spur gear 23 by a rotating shaft 22. The spur gear 23 is connected to an externally supplied signal controller gear via a worm gear 19. A displacement sensor LVDT 29 is connected at the same horizontal level on the other side of the connecting rod 17, which is connected to the piston 6. The displacement sensor LVDT 29 includes a pull rod 31. The pull rod 31 and other internal components are inserted into a fixed component base 32. A flange 30 and a screw 33 are connected to the upper end of the fixed component base 32.

[0028] Please see Figure 6 A movable piston 37 is disposed between the vibrating pot 35 and the square support 2. The piston 37 is movably fixed on the square support 2 and reciprocates under the drive of the vibrating pot 35. The piston 37 is connected to the upstream chamber 1 through the adapter 7. A light 43 is installed in the gap between the square support 2 and the vibrating pot 35. A photodiode bracket 40 opposite to the light 43 is welded on the square support 2. The photodiode bracket 40 is provided with a photodiode circuit and a photodiode 42. A razor blade and bracket are provided on the vibrating pot 35 near the photodiode circuit. The movement is detected by this structure.

[0029] This test is based on the parallel capillary model theory, where an oscillating pressure gradient is applied between the inlet and outlet when a Newtonian fluid passes through a circular tube. According to Womersley's momentum diffusion formula for a circular cross-section tube, we have: (1) In the formula, r represents the capillary radius and r represents the hydrodynamic penetration depth (boundary layer thickness). The ratio, It is a first-order Bessel function of the first kind. The ratio of flow rate to pressure gradient is given by the capillary theory admittance: (2) By admittance and The relationship diagram shows that the modulus and phase of the admittance depend on the ratio of the capillary radius to the boundary layer thickness. Therefore, using the harmonic analysis results to calculate the modulus and phase of the admittance is sufficient to estimate the pore radius. The cutoff frequency corresponds to... ,at this time Therefore, the smaller the pore size of the porous medium to be tested, the more necessary it is to increase the frequency or decrease the viscosity for testing. In this embodiment, the method of increasing the frequency is adopted.

[0030] Its operation method includes the following steps: A: Select appropriate device components, connect the sample, saturate the sample and check for air bubbles, then turn on the instrument.

[0031] B: Connect two capillary tubes of different diameters sequentially as described in step A, adjust the instrument, collect and process the pressure and displacement signals from the two capillary tubes respectively, and calculate the transfer function required for the measurement admittance. .

[0032] C: Connect the porous sample according to the method in step A, collect and process the pressure and displacement signals of the porous medium during the test according to the method in step B, calculate the admittance of the porous medium, and thus obtain the pore size distribution.

[0033] Specifically, as a preferred embodiment, in step A, the entire experimental apparatus needs to be filled with fluid from the connection between the piston and the upstream chamber to the outlet hole before testing. The preferred fluid is pure water or water with 75% glycerol, as glycerol can enhance the pressure sensor signal. Air fluid can also be used. First, fluid is injected from the connection between the piston and the upstream chamber, and the air present in the pores is discharged through the outlet hole. Then, each chamber is filled and checked with a syringe to ensure that there are no air bubbles. Finally, the components are sealed and connected, and the device is turned on.

[0034] The minimum aperture determines the maximum frequency required for measurement. Cam mechanisms can only generate low-frequency sinusoidal signals below 2Hz, but this can be increased to 4Hz by using a stiffer spring, making them suitable for measuring apertures larger than 500mm. The pore size is small; the vibrating cooker generates a high-frequency sinusoidal signal, which is suitable for pores with small diameters, but due to the limitation of the pressure sensor's measurement frequency range, it can only detect pores larger than 30. pores.

[0035] Based on our sensor linearity tests, LVDT is suitable as a displacement sensor for low-frequency signals, while photodiode is more suitable as a displacement sensor for high-frequency signals.

[0036] In this embodiment, all devices, whether for calibration or measurement, must be turned on two hours before use to ensure that the temperature of electronic components remains stable.

[0037] In a preferred embodiment, in step B, the displacement sensor and pressure sensor need to be calibrated before the formal test.

[0038] This step only selects samples with a diameter of 289. and 1895 Two capillaries were used to measure pressure and displacement sequentially. The transfer function was... The displacement sensor LVDT measures the amplitude as follows: The applied displacement produces a phase shift of Traffic The transfer function is The pressure sensor measures the flow rate. The pressure difference generated by the fluid passing through the porous medium .

[0039] Two transfer function analyzers were used to simultaneously acquire pressure and displacement signals, collecting 200 consecutive frequency signal points from 1 to 500 Hz. The acquisition of each point was delayed for 2 seconds, and then the signal was recorded and integrated for 5 seconds. Here, the displacement and pressure difference signals were analyzed for harmonics using Fast Fourier Transform (FFT).

[0040] We have the formula for admittance calculation: (3) in The transfer function for calculating the admittance based on the measured signal is denoted as: The combined diameter is 289. and 1895 Based on the theoretical admittances of the two capillaries and the processing results of the two sets of pressure and displacement signals, the transfer function is calculated using formula (3). The frequency response can reveal the different capillaries. The coincidence of modulus and phase proves that the transfer function is completely independent of the selected capillary and depends on the system parameters. Therefore, this method can be used to obtain the required measurement parameters before each measurement of porous media admittance. .

[0041] In a preferred embodiment, in step C, the signal generation and acquisition device and the signal processing method are the same as in step B, and the porous media sample is measured. , FFT and previously obtained Substituting into formula (3), the total admittance is obtained. The modulus and phase diagram. The admittance of porous media is the sum of the fundamental admittances, written in matrix form: (4) By transforming formula (4), the pore size distribution of the porous medium can be obtained: (5) in The matrix is ​​the admittance matrix of basic capillary theory.

[0042] If the admittance calculation results are noisy, a low-order polynomial can be used for fitting, and a horizontal tangent with a modulus of 1 and a phase of 0 can be forcibly fitted near the minimum frequency. If the results are severely deviated at high frequencies, the points with large deviations can be discarded to avoid introducing distortion.

[0043] The remaining technical features in this embodiment can be flexibly selected by those skilled in the art to meet different specific practical needs. However, it is obvious to those skilled in the art that these specific details are not necessary to implement the present invention. In other instances, to avoid obscuring the present invention, well-known components, structures, or parts are not specifically described, and all are within the scope of technical protection defined by the claims of the present invention.

Claims

1. An apparatus for measuring the pore size distribution of porous media by harmonic analysis, comprising a sample and a fluid storage container, characterized in that: The sample and fluid storage container includes an upstream chamber (1) and a downstream chamber (4). The test sample (5) is placed between the upstream chamber (1) and the downstream chamber (4). Newtonian fluid is stored in the upstream chamber (1) and the downstream chamber (4). The upstream chamber (1) and the downstream chamber (4) are respectively connected to the two detection ends of the pressure sensor (34). The container also includes a harmonic analysis component (9) connected to the upstream chamber (1). The harmonic analysis component (9) includes a signal application system and a displacement sensor. The displacement sensor and the pressure sensor are respectively connected to two independent transfer function analyzers (44). The harmonic analysis component (9) includes a measurement aperture greater than 500 μm. Low-frequency harmonic analysis components for pore size distribution and for measuring greater than 30 High-frequency harmonic analysis of components with small-aperture pore size distribution; The low-frequency harmonic analysis component includes a cam mechanism (25) fixed on a fixed base, a connecting rod support (16), a connecting rod shaft (18), a connecting rod (17), a piston (6), a piston guide plate (11), a spring (14), and an adapter (7). The connecting rod (17) is sway-fixed on the connecting rod support (16) via the connecting rod shaft (18) set at the top. The cam mechanism (25) is in contact with the bottom of the connecting rod (17) for transmission. One side of the middle part of the connecting rod (17) is connected to the piston (6), and the other side is connected to the LVDT (29). The piston (6) is connected to the spring (14) via the piston guide plate (11), and the spring (14) is connected to the upstream chamber (1) via the adapter (7). The high-frequency harmonic analysis component includes a vibrating pot (35) fixed on a fixed base, a square bracket (2), a piston (37), a lighting lamp (43), a photodiode (42), and an adapter (7). One or more of the piston (37), lighting lamp (43), photodiode (42), and adapter (7) are fixed on the square bracket (2). The vibrating pot (35) can drive the piston (37) to move. The piston (37) is connected to the upstream chamber (1) through the adapter (7). The lighting lamp (43) and photodiode (42) are also provided to detect the displacement of the piston (37).

2. The device for measuring the pore size distribution of porous media by harmonic analysis according to claim 1, characterized in that: The harmonic analysis component (9) uses an LVDT (29) or a photodiode (42) as a displacement sensor. The LVDT (29) or photodiode (42) and the pressure sensor (34) are respectively connected to two identical but independent transfer function analyzers (44).

3. A method for measuring the pore size distribution of a porous medium using the apparatus described in any one of claims 1-2, characterized in that: Includes the following steps: Step A: Select appropriate device components, connect the sample, saturate the sample and check for air bubbles, then turn on the instrument; Step B: Connect two capillary tubes of different diameters sequentially as in Step A, adjust the instrument, and use a transfer function analyzer to perform FFT analysis on the acquired pressure and displacement signals. Combine this with theoretical admittance calculation to obtain the transfer function required for measurement admittance. ; Step C: Connect the porous medium sample according to the method in Step A, collect and process the pressure and displacement signals during the test according to the method in Step B, calculate the porous medium admittance, and thus obtain the pore size distribution; Step B specifically includes the following steps: (1) Connect two capillary tubes of different diameters in succession for testing, turn on the instrument, and use the actuator to generate a signal to apply an oscillating flow; (2) Calibrate the sensor; (3) Pressure and displacement signals were collected from two capillaries with different diameters, and harmonic analysis was performed on the signals; (4) Substitute the analysis results of the two sets of pressure and displacement signals and the theoretical admittance of the two measured capillaries into the admittance calculation formula. The transfer function required to measure the admittance of porous media is calculated in reverse. ,Right now Measured by two capillaries They should be the same; Step C specifically includes the following steps: (1) Connect the porous medium, turn on the instrument, and use the actuator to generate a signal to apply an oscillating flow; (2) Acquire pressure and displacement signals for porous media and perform harmonic analysis on the signals; (3) Compare the analysis results of the pressure and displacement signals of the porous medium with the transfer function measured in step B. Substituting the values ​​into the admittance calculation formula, the total admittance of the porous medium is obtained. Based on the total admittance and the basic capillary theoretical admittance, the pore size distribution of the porous medium is then determined. The admittance of porous media is the sum of the basic admittances, and can be written in matrix form as follows: ， By transforming the above formula, we can obtain the pore size distribution of porous media: 。 4. A method for measuring the pore size distribution of a porous medium using the apparatus described in any one of claims 1-2, as claimed in claim 3, characterized in that: In step A, the experimental setup is required to be filled with fluid from the connection between the piston and the upstream chamber to the outlet orifice before the test, and different harmonic analysis components are used to measure the pore size distribution of different orifice diameters.

Images