A method for measuring the internal diffusion coefficient and the surface interfacial permeability of a porous material

Abstract

The application discloses a method for measuring internal diffusion coefficient and surface interfacial permeability of porous materials, which comprises the following steps: measuring the change of desorption amount of the porous materials under the condition of being swept by a carrier gas after adsorption equilibrium by using a zero-length column method; determining the initial time of desorption of the porous materials according to the change data of adsorbate concentration signal of the empty tube experiment under the same test condition; processing the obtained change data of desorption amount, integrating the desorption concentration with respect to time, so as to obtain the change data of the desorption mass fraction; determining the limiting mechanism of the mass transfer process of the porous materials, establishing a mass conservation equation for describing the test system of the porous materials, and obtaining a control equation for describing the change process of the desorption amount through mathematical derivation; and directly and simultaneously obtaining the internal diffusion coefficient and the surface interfacial permeability of the porous materials through calculation and fitting of the control equation obtained through derivation and the change data of the desorption amount of the porous materials measured through experiments.

Description

TECHNICAL FIELD

[0001] The application relates to a method for measuring internal diffusion coefficient and surface interfacial permeability of a porous material, and belongs to the field of material testing. BACKGROUND

[0002] The mass transfer property of a porous material is crucial to its industrial practical application in catalytic reaction process and adsorption separation. Quantitative characterization of the mass transfer property of a porous material helps to reveal the reaction mechanism of a catalyst and guide the rational design and efficient utilization of the material. Development of a solving method suitable for experimental measurement of the mass transfer coefficient of a porous material is a prerequisite for characterization of the mass transfer property of the porous material, and is of great significance.

[0003] Compared with other methods for measuring the mass transfer coefficient of a porous material, the zero-length column method has the advantages of simple operation, wide test conditions, and easy exclusion of external diffusion and adsorption heat effects of the porous material, and has been widely used as a tool method for characterization and measurement of the mass transfer property of a porous material. The measurement principle of the zero-length column method is based on Fick's first law, and the concentration gradient is the driving force, that is, first, adsorption equilibrium is achieved at a very low adsorbate partial pressure, and then pure carrier gas is blown to record the change curve of the desorption concentration signal of the porous material at the outlet of the system with time.

[0004] The traditional solving model can obtain the apparent diffusion coefficient of the porous material, but according to the existing theory and experimental research, the mass transfer process of the porous material is jointly limited by the internal diffusion of the material and the mass transfer at the surface interface of the material. Therefore, decoupling the apparent diffusion coefficient, distinguishing and quantitatively describing the above two parts of the limiting effect can help researchers better understand and master the mass transfer process.

[0005] At present, the existing solving formula of the zero-length column method does not consider the mass transfer effect at the surface interface of the porous material. Many scholars at home and abroad are studying how to establish a method suitable for simultaneous measurement of the internal diffusion coefficient and the surface interfacial permeability of a porous material by the zero-length column method, but so far, there is still a lack of a test method which is convenient to operate, simple in form and has clear physical meaning. SUMMARY

[0006] The purpose of the present application is to provide a method suitable for simultaneous measurement of the internal diffusion coefficient and the surface interfacial permeability of a porous material by the zero-length column method. This method is simple to operate, the solving formula is based on Fick's law, has clear physical meaning, and can solve the problems of general description of the apparent diffusion coefficient, poor fitting of experimental data and large error of the existing zero-length column measurement method.

[0007] The existing zero-length column measurement method is based on the assumption that the diffusion properties of the porous material are the same everywhere, that is, it is believed that the diffusion of guest molecules inside the porous material is the dominant mechanism that limits the mass transfer process, and the mass transfer resistance of the surface interface of the porous material is ignored. When using the existing method to process experimental data, different data intervals selected by the long-time method will cause deviations in the processing results, and the full-time method will have poor fitting experimental data. Based on the existing understanding of the mass transfer theory of porous materials, that is, the mass transfer of guest molecules in porous materials is jointly limited by internal diffusion and surface interface mass transfer, the present application proposes that for the measurement of the mass transfer properties of porous materials by the zero-length column method, the apparent diffusion coefficient should be decoupled, and the internal diffusion coefficient and the surface interface permeability of the porous material are obtained, which corresponds to the real mass transfer physical process, so that the obtained quantities have clear physical meaning, and the internal diffusion and surface interface mass transfer processes of the porous material can be quantitatively described respectively.

[0008] A method for measuring the internal diffusion coefficient and the surface interface permeability of a porous material, comprising the following steps:

[0009] (S1) introducing an adsorbate gas flow into the porous material to be measured, so that the porous material to be measured is saturated with adsorption;

[0010] (S2) switching to a carrier gas to purge the porous material to be measured, and recording the change of the adsorbate concentration on the outlet side, the process measurement parameters including:

[0011] the desorption concentration signal I of the outlet side of the porous material to be measured at each time t ;

[0012] the signal I0 of the outlet side of the porous material to be measured at the termination time;

[0013] (S3) taking out the porous material to be measured, and performing empty tube measurement under the same conditions to obtain the change of the adsorbate concentration on the outlet side under the empty tube condition, the process measurement parameters including:

[0014] the desorption concentration signal I of the outlet side of the empty tube at the initial time 空max ;

[0015] the desorption concentration signal I of the outlet side of the empty tube at each time 空t ;

[0016] the signal I of the outlet side of the empty tube at the termination time 空0 ;

[0017] (S4) using formula (1) to process the measured desorption concentration signal under the empty tube condition, to obtain the normalized desorption concentration-time curve under the empty tube condition;

[0018]

[0019] (S5) According to the normalized desorption concentration-time curve under the air traffic condition, the desorption initial time t0 after excluding the influence of the dead volume of the device when measuring the desorption concentration signal of the porous material to be tested in step (S2) is determined, and the concentration signal at this time is determined as Imax, and the desorption concentration signal of the outlet side of the porous material to be tested is processed by using formula (2) to obtain the desorption concentration-time curve of the porous material to be tested;

[0020]

[0021] (S6) The desorption concentration C t is time-integrated to obtain the normalized desorption mass m t , and the control equation containing the surface permeability a of the porous material describing the outflow mass fraction at the initial stage of desorption is shown in formula (3):

[0022]

[0023] In formula (3), m ∞ is the total desorption mass, k f is the ratio of the carrier gas volume flow rate to the bed volume, f is the Henry coefficient of the porous material, l is the characteristic length of the porous material, t is the desorption time, and h is obtained by formula (4);

[0024]

[0025] In formula (4), S is the surface area of the porous material, V is the volume of the porous material, and ε is the bed voidage.

[0026] The surface permeability a of the porous material to be tested is obtained by formula (3).

[0027] Optionally, the internal diffusion coefficient D of the porous material is calculated according to formula (5);

[0028]

[0029] In formula (5), L = a l / D, L is the ratio of the characteristic time of internal diffusion of the porous material to the characteristic time of surface interface mass transfer, k n is a parameter in the equation.

[0030] Optionally, the fitting curve of the control equation (3) and the experimental value are judged according to the calculation formula (6) of the root mean square error and the determination coefficient to determine the accuracy of the fitting of the control equation:

[0031]

[0032] Wherein, RMSE is the root mean square error between the fitting value of the control equation and the measured desorption concentration, R 2 is the determination coefficient thereof. is the normalized desorption concentration of the porous material at each time calculated by the control equation (3), is the average value of the normalized desorption concentration of the porous material at each time in the experimental test.

[0033] Optionally, in step (S3), the experimental conditions for the blank test and the actual measurement of the mass transfer coefficient of the porous material are consistent, including temperature, flow rate of the adsorbate gas, flow rate of the carrier gas, and signal acquisition time of the detector.

[0034] Optionally, in step (S1), the low-concentration adsorbate gas is introduced into the test system for a sufficient time to achieve adsorption equilibrium of the porous material.

[0035] Optionally, in step (S2), the adsorbate side gas path is closed, and the test system is purged with pure carrier gas, the carrier gas flow rate Vs is recorded, and the change of the system outlet concentration signal It with time is detected, i.e., the desorption concentration signal of the porous material changes with time.

[0036] Optionally, the criterion for determining the initial desorption time is the time when the normalized concentration of the empty pipe condition test decreases to 0.001.

[0037] Optionally, the criterion for determining the initial desorption time of the test system excluding the effect of dead volume is the time when the normalized concentration of the system outlet decreases from 1 to 0.01 in the blank test.

[0038] Optionally, in step (S4), the surface permeability for describing the mass transfer of guest molecules on the surface of the porous material is determined, and the desorption concentration Ct is time-integrated to obtain the relationship between the desorption mass fraction and time. When the desorption time is small enough, the control equation (3) is obtained, and the surface permeability α of the guest molecules in the porous material is determined according to the equation.

[0039] Optionally, the criterion for determining the initial desorption time of the test system excluding the effect of dead volume is the time when the normalized concentration of the system outlet decreases from 1 to 0.01 in the blank test.

[0040] Optionally, the time resolution for detecting the outlet concentration signal of the porous material is 0.02 seconds to 5 seconds.

[0041] Preferably, the time resolution for detecting the outlet concentration signal of the porous material is 0.1 seconds to 2 seconds.

[0042] Optionally, the loading mass of the porous material to be tested is 2 milligrams to 30 milligrams.

[0043] Optionally, the gas flow rate for purging the porous material with the carrier gas is 20 milliliters per minute to 100 milliliters per minute.

[0044] Optionally, the bed porosity of the porous material to be measured is 0-0.2.

[0045] Optionally, in the control equation (3), the corresponding time interval at the initial moment is 0-8 seconds.

[0046] Optionally, the control equation (3) is used to describe the variation process of the macroscopic desorption concentration of the porous material at the initial moment of desorption, and the corresponding time interval at the initial moment should be 0-8 seconds.

[0047] Optionally, the calculated curve is consistent with the experimental measurement of the desorption amount of the porous material with time, the mean square error is 0-0.01, and the determination coefficient is 0.95-1.

[0048] Optionally, the internal diffusion coefficient and surface interface permeability of the porous material obtained by fitting and solving are substituted into the theoretical control equation, and the calculated curve is consistent with the experimental measurement of the desorption amount of the porous material with time, the mean square error is 0-0.01, and the determination coefficient is 0.95-1.

[0049] Optionally, the method measures guest molecules including at least one of methane, ethane, ethylene, propane, propylene, and n-butane.

[0050] The application can produce beneficial effects, including:

[0051] 1) The method for measuring the internal diffusion coefficient and surface interface permeability of the porous material provided by the application can simply and conveniently obtain the internal diffusion coefficient and surface interface permeability of the porous material, and quantitatively describe the surface mass transfer resistance and internal diffusion of the porous material.

[0052] 2) The method for measuring the internal diffusion coefficient and surface interface permeability of the porous material provided by the application, according to the existing mass transfer theory, the method for measuring the internal diffusion coefficient and surface interface permeability of the porous material suitable for the zero-length column decouples the apparent diffusion coefficient, and obtains mass transfer parameters with clear physical meaning, so as to accurately measure the mass transfer limitation process of the guest molecules in the porous material. Researchers in the field of material design can use this method to measure and evaluate the mass transfer performance of the modified or synthesized porous material, optimize the material design, and have a deeper understanding of the surface interface mass transfer resistance mechanism and internal diffusion mechanism of the porous material. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The flowchart of the embodiment of the application for measuring the internal diffusion coefficient and surface interface permeability of the guest molecules in the porous material.

[0054] Figure 2The experimental data of the change of the desorption mass fraction with time and the curve fitting results of the change of the mass fraction with time of the control equation in the initial stage of desorption in the experiment of measuring the internal diffusion coefficient and the surface interfacial permeability of the porous material in Example 1 of the present application.

[0055] Figure 3 The experimental data of the change of the desorption concentration with time and the curve fitting results of the change of the concentration with time of the control equation in the experiment of measuring the internal diffusion coefficient and the surface interfacial permeability of the porous material in Example 1 of the present application.

[0056] Figure 4 The experimental data of the change of the desorption mass fraction with time and the curve fitting results of the change of the mass fraction with time of the control equation in the initial stage of desorption in the experiment of measuring the internal diffusion coefficient and the surface interfacial permeability of the porous material in Example 2 of the present application.

[0057] Figure 5 The experimental data of the change of the desorption concentration with time and the curve fitting results of the change of the concentration with time of the control equation in the experiment of measuring the internal diffusion coefficient and the surface interfacial permeability of the porous material in Example 2 of the present application. DETAILED DESCRIPTION

[0058] The present application will be described in detail below in combination with examples, but the present application is not limited to these examples.

[0059] The porous material selected for testing in the present application is a SAPO-34 molecular sieve catalyst, wherein the SAPO-34 molecular sieve in Example 1 is purchased from China Catalyst New Technology (Dalian) Co., Ltd., the crystal particle size is 2 microns, and the characteristic length is 0.49 microns; the SAPO-34 molecular sieve in Example 2 is synthesized by the laboratory itself, and the synthesis method is described in the literature Yang M, Tian P, Chan W et al. A top-down approach to prepare silicoaluminophosphate molecularsieve nanocrystals with improved catalytic activity [J]. Chemical Communications, 2014, 50(15): 1845-1847.

[0060] The zero-length column method testing device used in the present application is built by the laboratory itself, the SAPO-34 molecular sieve is filled into a φ6 straight-through column, and the concentration signal detector is a gas chromatograph FID detector.

[0061] wherein, Figure 1The embodiment flowchart for measuring the internal diffusion coefficient and the surface interfacial permeability of a guest molecule in a porous material of the present application. First, the zero-length column method is used to measure the change in the desorption amount of the porous material after adsorption equilibrium and the generation of a carrier gas purge; according to the adsorbate concentration signal change data of the empty tube experiment under the same test conditions, the initial time of desorption of the porous material is determined; according to the signal values at the beginning and end of desorption, the obtained desorption amount change data is processed, the desorption concentration is integrated with respect to time, and the change data of the desorption mass fraction is obtained; the limiting mechanism of the mass transfer process of the porous material is determined, the corresponding mass conservation equation describing the porous material test system is established, the control equation describing the desorption amount change process is obtained through mathematical derivation; the control equation obtained by derivation is calculated and fitted with the desorption amount change data of the porous material measured by experiment, and the internal diffusion coefficient and the surface interfacial permeability of the porous material can be directly and simultaneously obtained.

[0062] Example 1

[0063] The internal diffusion coefficient and surface interfacial permeability of propane molecules in SAPO-34 molecular sieve (crystal particle size of 2 microns) under low load were measured. The zero-length column test device was filled with a straight-through disassembled porous material catalyst, and the SAPO-34 molecular sieve catalyst synthesized in the laboratory was placed between the gaskets. The catalyst loading was 10 mg, and the bed voidage was 0.2. After the porous material was loaded, the straight-through was put back into the test device, and the device airtightness was checked. Before the test, the SAPO-34 molecular sieve catalyst sample was first pretreated, the column tank temperature was adjusted to 200°C, the carrier gas nitrogen flow rate was 100 ml / min, and the system outlet concentration signal measured by the chromatographic FID detector was reduced to the baseline and remained stable for 8 hours. Propane was selected as the adsorbate guest molecule, and nitrogen was used as the dilution gas to ensure that the adsorbate guest molecule concentration measured during the experiment met the linear region of the Henry's law. According to the isothermal saturation adsorption line of propane molecules in the SAPO-34 molecular sieve at 40°C measured by the Micromeritics Gemini 2390 physical adsorption instrument, the Henry coefficient was determined to be 443, and the propane-nitrogen mixed gas was selected to pass through the porous material at normal pressure, with a propane partial pressure of 2.5 mbar. The test system temperature was set to 40°C, the adsorption mixed gas flow rate was 40 ml / min, and the detector signal acquisition time resolution was 0.02 seconds. According to the recorded system outlet concentration signal, when the signal value remained basically unchanged for 30 min and the fluctuation was within 0.01%, it was judged that the porous material had reached adsorption equilibrium. The four-way valve was rotated to switch the adsorption gas to the carrier gas for purging, and the carrier gas flow rate was 60 ml / min. The porous material outlet concentration signal of the test system was recorded every 0.1 seconds. According to the blank test results under the same conditions, the initial time of the desorption of the porous material after the four-way valve was switched was determined. The recorded data was processed by formulas (1) and (2) to obtain the desorption concentration-time curve, and the desorption mass fraction-time relationship was obtained by integrating the desorption concentration with respect to time. The experimental data were curve-fitted using the control equation of formula (3), and the results are shown in Figure 2 . The surface interfacial permeability of propane molecules in the SAPO-34 molecular sieve catalyst at 40°C was finally obtained as α = 2.13 x 10 -9 m / s, and the determination coefficient between the curve fitted by the control equation and the experimental data was 0.999, indicating that the theoretical control equation was in good agreement with the experimental values. According to the obtained surface interfacial permeability, the experimental data were fitted using formula (5), and the results are shown in Figure 3, and the internal diffusion coefficient of propane molecule in SAPO-34 molecular sieve catalyst is D = 1.57 x 10 -16 The mean square error of fitting value of the control equation and experimental value is 0.0085, and the determination coefficient is 0.988, indicating that the control equation has high reliability and the result is accurate.

[0064] Example 2

[0065] The internal diffusion coefficient and surface interfacial permeability of ethane molecule in SAPO-34 molecular sieve (crystal particle size is 7 microns) under low load are measured. The zero-length column test device is filled with a straight-through catalyst of porous material, and the SAPO-34 molecular sieve catalyst synthesized by the laboratory is placed between the gaskets. The catalyst loading is 10 milligrams, and the bed voidage is 0.2. After the porous material is loaded, the straight-through is put back into the test device, and the gas tightness of the device is checked. Before the test, the SAPO-34 molecular sieve catalyst sample is first pretreated, the column tank temperature is adjusted to 200°C, the flow rate of the carrier gas nitrogen is 100 ml / min, and the system outlet concentration signal measured by the chromatographic FID detector is reduced to the baseline and kept stable after purging for 8 hours. Ethane is selected as the adsorbate guest molecule, and nitrogen is selected as the dilution gas, so that the concentration of the adsorbate guest molecule measured during the experiment satisfies the linear region of Henry's law. According to the isothermal saturation adsorption line of propane molecule in the SAPO-34 molecular sieve at 25°C measured by the Gemini 2390 physical adsorption instrument of Micromeritics Company, the Henry coefficient is determined to be 334, and the propane-nitrogen normal pressure mixed gas is selected to pass into the porous material, in which the ethane partial pressure is 2.5 mbar. The test system temperature is given as 25°C, the adsorption mixed gas flow rate is 40 ml / min, and the detector signal acquisition time resolution is 0.02 seconds. According to the recorded system outlet concentration signal, when the signal value is basically unchanged for 30 min and the fluctuation is within 0.01%, it is judged that the porous material has reached adsorption equilibrium. The four-way valve is rotated to switch the adsorption gas to the carrier gas purge, the carrier gas flow rate is 60 ml / min, and the porous material outlet concentration signal of the test system is recorded every 0.1 seconds. According to the blank test results under the same conditions, the initial time of desorption of the porous material after switching the four-way valve is judged. The recorded data is processed by formulas (1), (2) to obtain the desorption concentration-time curve, the desorption concentration-time integral is obtained, the desorption mass fraction-time relationship is obtained, the experimental data is curve-fitted by using the control equation of formula (3), and the experimental desorption mass fraction-time change data and the mass fraction-time change control equation curve-fitting results of the initial stage of desorption are shown in Figure 4 The surface interfacial permeability of ethane molecule in SAPO-34 molecular sieve catalyst at 25°C is α = 1.88 x 10 -7m / s, the determination coefficient between the curve fitted according to the control equation and the experimental data is 0.999, which can show that the theoretical control equation is in good agreement with the experimental value. According to the obtained interfacial permeability, the experimental desorption concentration and the interfacial permeability of the porous material are measured by using formula 5) to fit the experimental data. The experimental data of the desorption concentration change with time and the curve fitting results of the concentration change control equation with time are shown in Figure 5 Finally, the internal diffusion coefficient D of ethane molecules in the SAPO-34 molecular sieve catalyst is obtained as D=4.43×10 -13 m / s, the determination coefficient between the curve fitted according to the control equation and the experimental data is 0.999, which can show that the theoretical control equation is in good agreement with the experimental value. According to the obtained interfacial permeability, the experimental desorption concentration and the interfacial permeability of the porous material are measured by using formula 5) to fit the experimental data. The experimental data of the desorption concentration change with time and the curve fitting results of the concentration change control equation with time are shown in

[0066] The above is only a few embodiments of the present application, and does not limit the present application in any form. Although the preferred embodiments are disclosed above, the present application is not limited thereto. Any person skilled in the art can make some changes or modifications to the above disclosed technical contents without departing from the scope of the present application, and such changes or modifications are equivalent to equivalent embodiments, and are within the scope of the technical solution.

Claims

1. A method for measuring the internal diffusion coefficient and surface permeability of a porous material, characterized in that, Includes the following steps: (S1) Introduce an adsorbate gas stream into the porous material to be tested to saturate the porous material with adsorption. (S2) Switch to carrier gas to purge the porous material under test, record the change in adsorbate concentration on the outlet side, and measure the following parameters: Desorption concentration signal I of the porous material at the outlet side at various times t ; The termination time is measured at the outlet side signal I0 of the porous material under test. (S3) Remove the porous material to be tested and perform empty tube measurements under the same conditions to obtain the change in adsorbate concentration on the outlet side under empty tube conditions. The process measurement parameters include: Initial time desorption concentration signal I at the outlet side of the air tube 空max ; Desorption concentration signal I at the air tube outlet side at various times 空t ; Termination time air pipe outlet side signal I 空0 ; (S4) The desorption concentration signal measured under empty tube conditions is processed using formula (1) to obtain the normalized desorption concentration versus time curve under empty tube conditions. （1） (S5) Based on the normalized desorption concentration versus time curve under empty tube conditions, determine the initial desorption time t0 after eliminating the influence of the dead volume of the device when measuring the desorption concentration signal of the porous material to be tested in step (S2), and determine the concentration signal at this time as Imax. Use formula (2) to process the desorption concentration signal of the porous material to be tested on the outlet side to obtain the desorption concentration versus time curve of the porous material to be tested. （2） (S6) Regarding the desorption concentration C t By performing time integration, the normalized desorption mass m is obtained. t Equation (3) shows the governing equation for the surface permeability α of the porous material, which describes the effluent mass fraction during the initial stage of desorption: （3） In equation (3), For the total desorption mass, k f denoted as the ratio of carrier gas volumetric flow rate to bed volume, where f is the Henry's law coefficient for porous materials. l The characteristic length of the porous material is given by t, the desorption time is given by h, which is obtained by equation (4). （4） In equation (4), S is the surface area of ​​the porous material, V is the volume of the porous material, and ε is the porosity of the bed. The surface permeability α of the porous material to be tested is obtained by formula (3); The diffusion coefficient D inside the porous material is calculated according to formula (5); （5） In equation (5), L=αl / D L is the ratio of the characteristic time of diffusion inside the porous material to the characteristic time of mass transfer at the surface and interface, and kn is the parameter in the equation.

2. The method according to claim 1, characterized in that, The accuracy of the fit between the control equation (3) and the experimental values ​​is determined by using the formula (6) for calculating the root mean square error and coefficient of determination. （6） Where RMSE is the root mean square error between the fitted value of the governing equation and the experimentally measured desorption concentration, R0 2 The coefficient of determination for both. The normalized desorption concentration of the porous material at each time point is calculated using the governing equation (3). This represents the average normalized desorption concentration of the porous material at various time points during the experimental test.

3. The method according to claim 1, characterized in that, The standard for determining the initial moment of desorption is the time when the concentration under empty tube conditions drops to 0.001 after normalization.

4. The method according to claim 1, characterized in that, The time resolution for detecting the outlet concentration signal of porous materials is 0.02 seconds to 5 seconds.

5. The method according to claim 1, characterized in that, The time resolution for detecting the outlet concentration signal of porous materials is 0.1 seconds to 2 seconds.

6. The method according to claim 1, characterized in that, The loading mass of the porous material to be tested is 2 mg to 30 mg.

7. The method according to claim 1, characterized in that, The gas flow rate for purging the porous material with carrier gas is 20 ml / min to 100 ml / min.

8. The method according to claim 1, characterized in that, The porosity of the bed of the porous material to be tested is 0~0.

2.

9. The method according to claim 1, characterized in that, In the control equation (3), the time interval corresponding to the initial moment is 0 seconds to 8 seconds.

10. The method according to claim 2, characterized in that, The calculated curve matches the experimentally measured data points of the desorption amount of porous material over time, with a mean square error of 0 to 0.01 and a coefficient of determination of 0.95 to 1.

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