Method for measuring gas-liquid diffusion coefficient in micro-nano confined space

Abstract

The application provides a kind of determination method of gas-liquid diffusion coefficient in micro-nano confined space, belongs to the technical field of unconventional oil and gas reservoir micro seepage and rock physics experiment.The method in the application does not need to rely on expensive and complex analysis equipment, but continuously collects the time-space evolution image of liquid fluorescence intensity in confined pore in micro-nano flow control visualization experiment, calculates local experimental swelling factor through fluorescence signal change, and establishes the corresponding relationship between experimental swelling factor and theoretical swelling factor by combining confined space correction PR state equation, so as to invert the real gas concentration distribution in liquid phase in high-pressure gas diffusion process.The concentration data obtained is substituted into the mass transfer mathematical model for fitting, and the gas-liquid diffusion coefficient in nano to micron confined pore considering swelling effect is obtained.The method can include the liquid phase swelling effect induced by gas dissolution into the concentration inversion and diffusion coefficient calculation process, and improve the characterization accuracy of gas-liquid mass transfer process in micro-nano confined space.

Description

Technical Field

[0001] This invention belongs to the field of microscopic seepage and rock physics experimental technology of unconventional oil and gas reservoirs, and particularly relates to a method for determining the gas-liquid diffusion coefficient in a micro-nano confined space. Background Technology

[0002] With the continued deepening of unconventional oil and gas resource exploration and development, shale oil and tight oil reservoirs have become important replacement areas for increasing crude oil reserves and production. Due to the small pore size, low permeability, and difficulty in fluid mobilization in these reservoirs, gas injection displacement and gas injection huff and puff technologies have gradually become important development methods to improve fluid flowability and enhance crude oil recovery. During gas injection development, the diffusion, dissolution, and miscibility processes between the injected gas and the formation crude oil directly affect the interphase mass transfer efficiency, the miscibility front advancement characteristics, and the degree of microscopic mobilization of crude oil within the matrix pores. Therefore, the gas-liquid diffusion coefficient, as a key physical property parameter characterizing the mass transfer rate of gas in a liquid, is of great significance for revealing the gas injection enhancement mechanism, evaluating reservoir potential, and optimizing gas injection development schemes.

[0003] Under actual reservoir conditions, the matrix pores of shale oil and tight oil reservoirs typically exhibit a multi-scale confined characteristic consisting of nanoscale to microscale pores. The mass transfer behavior of fluids in such micro-nano confined spaces is not only affected by temperature, pressure, and fluid composition, but also jointly controlled by confinement effects such as pore size and solid-liquid interface interactions, and its diffusion law differs significantly from that of conventional bulk fluids.

[0004] Currently, the determination of gas-liquid diffusion coefficients mainly relies on macroscopic physical experiments and molecular dynamics simulations. Macroscopic experimental methods, including the PVT tube method and pressure decay method, have the advantage of mature experimental systems and controllable test conditions. However, these methods are usually conducted on bulk fluids and are difficult to reproduce the confined environment in nano- to micro-sized pores. They also fail to reflect the influence of pore size and solid-liquid interface interactions on the mass transfer process, and the diffusion coefficients obtained are more representative of macroscopic bulk or apparent diffusion characteristics. Molecular dynamics simulations can reveal diffusion mechanisms in nanopores at the molecular scale, but their results are highly dependent on model construction, force field parameters, and boundary condition settings. Furthermore, the simulation scale and time scale are limited, and in-situ experimental results at the same scale are still needed for verification.

[0005] On the other hand, to obtain more direct information on component concentration within micro- and nano-pores, some existing technologies attempt to introduce online detection methods such as Raman spectroscopy. However, such equipment is costly and has strict requirements for optical path stability, testing environment, and operating conditions, which is not conducive to the widespread application of conventional experimental platforms. Especially in confined flow channels at the nanometer to micrometer scale, the liquid sample volume is extremely small, the spectral signal intensity is limited, and the identification of characteristic peaks and concentration quantification are quite difficult. At the same time, high-energy lasers may cause local thermal effects in narrow channels, thereby changing the true phase state and mass transfer behavior of high-pressure fluids and affecting the reliability of test results. Therefore, detection methods relying on complex spectroscopic equipment still have insufficient applicability in the determination of gas-liquid diffusion coefficients in micro- and nano-confined spaces. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the gas-liquid diffusion coefficient in micro-nano confined spaces. The method of this invention does not rely on expensive and complex external component analysis equipment such as Raman spectroscopy, and can incorporate the liquid-phase swelling effect induced by gas dissolution into the concentration inversion and diffusion coefficient calculation process, thereby improving the characterization accuracy of gas-liquid mass transfer processes in micro-nano confined spaces. This provides experimental basis for evaluating interphase mass transfer and optimizing enhanced oil recovery schemes during gas injection displacement and gas injection huff and puff processes in unconventional oil and gas reservoirs such as shale oil and tight oil.

[0007] This invention provides a method for determining the gas-liquid diffusion coefficient in a micro / nano confined space, comprising the following steps: First, a micro / nanofluidic experimental system for measuring the gas-liquid diffusion coefficient needs to be built. This system mainly includes: a micro / nanofluidic chip, a microscope and fluorescence image acquisition system, a high-pressure constant-speed / constant-pressure pump assembly, an intermediate container containing the gas and liquid to be tested, and a temperature control system. The microfluidic chip is installed and fixed on the microscope stage, the fluid lines and injection / sampling components are connected, and the airtightness of the entire system is tested.

[0008] The micro / nanofluidic chip includes a main fluid channel and a gas-liquid diffusion channel connected to the main fluid channel. One end of the main fluid channel has a gas injection port, and the other end has a liquid injection port. The microchannels in the microfluidic chip adopt an S-shaped coil structure design. This structure can extend the effective channel length for gas-to-liquid diffusion within the same observation field, thereby increasing the observable diffusion area and improving the continuity and accuracy of fluorescence signal acquisition. The micro / nanofluidic chip has multiple gas-liquid diffusion channels with a depth of 10 nm to 1000 μm.

[0009] A) The test liquid containing different concentrations of fluorescent dye was saturated into the micro-nano fluid control chip, fluorescence images were acquired, and the average fluorescence signal gray value of the liquid region in the fluorescence image was extracted to obtain the relationship curve between the concentration of fluorescent dye and the fluorescence signal gray value. Under normal circumstances, with constant light source intensity, optical path length, and imaging parameters, a higher concentration of fluorescent dye in a liquid results in a stronger grayscale value of the acquired fluorescence signal. Therefore, changes in the fluorescence signal can reflect changes in dye concentration. However, within micro- and nano-porous spaces, due to factors such as small channel size, limited optical path, wall reflection, and differences in local light intensity distribution, the grayscale value of the fluorescence signal does not necessarily maintain a strictly linear relationship with the dye concentration (i.e., the Beer-Lambert law does not necessarily strictly satisfy a linear relationship within micro- and nano-porous spaces). Furthermore, at higher concentrations, fluorescent dyes may exhibit internal filtration effects or fluorescence quenching, further deviating the relationship between grayscale value and concentration. Therefore, before conducting formal diffusion experiments, it is necessary to pre-calibrate the correspondence between the grayscale value of the fluorescence signal and the concentration of the fluorescent dye.

[0010] The specific operation involves saturating the test liquid with different known concentrations of fluorescent dye into a micro / nanofluidic chip, and acquiring fluorescence images of samples with different concentrations under strictly fixed conditions of light source intensity, exposure time, objective lens magnification, camera gain, and other imaging parameters. Subsequently, the average fluorescence signal grayscale value of the liquid region in the image is extracted and normalized. This normalization process uses the grayscale value of the background region as a background benchmark and the grayscale value of the initial standard sample or the highest concentration sample as a reference benchmark, converting the original grayscale value into a dimensionless relative fluorescence signal value. This reduces the influence of background noise, minor fluctuations in the light source, chip fabrication differences, and subtle changes in imaging conditions on the calibration results. Finally, regression analysis is performed based on the normalized fluorescence signal grayscale value and the known fluorescent dye concentration to obtain a quantitative mapping relationship curve between the two, providing a calibration basis for subsequent inversion of the local liquid-phase swelling factor and gas concentration based on the fluorescence image grayscale value.

[0011] B) Saturate the microfluidic chip with the test liquid containing the initial concentration of fluorescent dye, heat the chip to the target temperature, and keep the temperature constant until the system reaches a thermodynamically stable state. Then inject the test gas and pressurize it to the target pressure to allow the test gas to dissolve and diffuse into the test liquid. Clean and resaturate the test liquid with the initial concentration of fluorescent dye into the nano- to micro-scale confined flow channel network of the quartz micro-nano fluidic chip; turn on the temperature control system, heat the chip to the target test temperature, and let it stand at a constant temperature until the system reaches a thermodynamically stable state.

[0012] Start the pump set to inject the gas to be tested. After the gas fills the main channel of the micro-nano fluid control chip, close the back pressure valve at the outlet end. Quickly pressurize to increase the injection pressure and maintain it at the target test pressure. Driven by the local pressure difference and concentration difference, the gas spontaneously dissolves and diffuses into the liquid in the confined micro-nano pores.

[0013] C) Acquire liquid fluorescence images at different diffusion times, and perform fluorescence image data processing, concentration inversion, and diffusion coefficient calculation.

[0014] By strictly fixing the field of view of the microscope and focusing on the confined micro-nano pore region, liquid fluorescence images at different diffusion times are continuously captured at set time intervals to fully record the attenuation process of fluorescence signal during the volume swelling of the liquid caused by gas diffusion.

[0015] Multiple local regions in the fluorescence image were selected as sampling points using ImageJ software. The distance between each sampling point and the gas-liquid interface, as well as the normalized average gray value at each time step, were statistically analyzed. Subsequently, based on the fluorescent dye concentration calibration relationship, the swelling factor calculation method, and the confined space modified PR equation of state, the local gas molar concentration at each sampling point at different time steps was retrieved. Each sampling point served as an independent diffusion coefficient calculation unit, and the corresponding diffusion coefficient was obtained by fitting the gas molar concentration changes at that sampling point over multiple time steps. The calculation results from multiple sampling points were used for cross-validation, outlier removal, and statistical averaging to reduce the impact of local image noise, sampling position errors, and gray-level fluctuations on the final diffusion coefficient result.

[0016] Specifically, the following steps are included: Fluorescence images acquired continuously at different times are processed.

[0017] In ImageJ software, several local areas were selected as sampling points along the 104 gas-liquid diffusion channel. Sampling points should be located within the liquid region of the channel, avoiding channel edges, areas of severe gas-liquid interface curvature, and areas of local image noise. For each sampling point, the distance between it and the gas-liquid interface was recorded, and the normalized average gray value of the sampling point in the fluorescence image at different times was calculated, forming a data table of "Sampling Point Number—Distance between Gas-Liquid Interface and Sampling Point—Diffusion Time—Normalized Average Gray Value". This data table is used for subsequent conversion of fluorescent dye concentration, calculation of local swelling factor, gas concentration inversion, and diffusion coefficient fitting.

[0018] Calculation of experimental swelling factor based on fluorescence intensity.

[0019] For a single sampling point, the normalized average gray value before gas injection (initial state). I 0 Normalized average gray value at time t after gas injection I t Based on the mapping relationship between the fluorescence signal grayscale value and the fluorescent staining agent concentration established above, the staining agent concentration under the corresponding state can be obtained. C 0 and C tAccording to the law of conservation of mass of fluorescent staining agents, volume expansion will lead to a proportional dilution of the staining agent concentration. Therefore, the experimental swelling factor of this spatial node at time t can be calculated. SF exp The calculation formula is as follows: Formula 1; In Equation 1, V 0 This is the reference volume of the liquid at this sampling point in its initial state; V t Let t be the volume of liquid in the sampling area after the gas dissolves and expands. C 0 This represents the initial concentration of the fluorescent dye in the liquid phase. C t The real-time concentration of the fluorescent dye in the liquid phase of the sampling point region after the gas dissolution and expansion occurs at time t; Gas concentration in the sampling area is calculated based on the modified PR equation of state in a confined space.

[0020] To address the confinement effect in micro- and nano-pores, traditional equations of state are insufficient to accurately describe fluid phase behavior. Therefore, a modified PR equation of state (Equation 2) that comprehensively considers capillary forces, wall-selective adsorption, and critical property shifts needs to be introduced. Formula 2; In Equation 2, P is the experimental pressure, T is the experimental temperature, and R is the universal gas constant. v mix The molar volume of the gas-liquid mixture. This represents the proportion of molecules in the adsorption region of a fluid mixture within a confined pore. a mix The parameters of the gravitational term after correction for the mixture. b mix For parameters of the repulsion term of the mixture, α(T) It is a function of temperature; The detailed calculation formulas for the above-mentioned parameters are as follows: Formula 3; Equation 4; Formula 5; Formula 6; Formula 7; In equations 3 to 7, ΔT c This is a dimensionless change in critical temperature. r e To account for the effective pore radius of the adsorption thickness, σLJ For Lennard Jones's dimensional parameters, x i Pure components i mole fraction, x j pure components j The mole fraction, where N represents the total number of components in the gas and liquid mixture (2≤N≤70). a ij For the interaction term between components i and j, b i Pure components i The repulsive force parameters, k ij For binary interaction coefficients, a i pure components i gravitational parameters, a j pure components j gravitational parameters, m i for i Temperature correction parameters of the components T r For temperature comparison.

[0021] Given the experimental pressure P, experimental temperature T, and characteristic pore size r (if measuring the diffusion coefficient of a multi-component gas in a multi-component liquid, the composition ratios of each component in the gas mixture and the liquid mixture are also required), the molar volume of the gas-liquid mixture after gas diffusion can be obtained. v mix Total mole fraction of gas x gas relational formula v mix ( x gas P, T For the specific calculation process, please refer to the literature "Zhong Junjie, Xu Lilong, Liu Tengyu, et al. Prediction of fluid phase equilibrium and experimental study of micro-nano fluid control in shale reservoirs [J]. Oil and Gas Reservoir Evaluation and Development, 2026, 16(4)". The swelling factor is equal to the ratio of the volume of the gas-liquid mixture after gas diffusion to the volume of the original undiffused pure liquid. Therefore, the theoretical swelling factor is... SF cal It can also be written as formula 8: Formula 8; In Equation 8, v liquid ( P, T) is the theoretical molar volume of a pure liquid under the same test temperature, pressure, and micro-nano confinement conditions, which can be calculated based on the modified PR equation of state when the molar fraction of the gas phase is 0.

[0022] By adjusting the experimental swelling factor SF exp Compared with theoretical swelling factor SF cal Equal to obtain the molar volume of the gas-liquid mixture in the sampling point region. v mix and total mole fraction of gases x gas ; Then, at time t, the molar concentration of the gas in the sampling area is... C g This can be expressed as Formula 9: Equation 9; Calculation of gas-liquid diffusion coefficient in a confined space considering swelling effect.

[0023] Gas molar concentrations at different times t C g Substituting into the one-dimensional unsteady mass transfer physical model based on Fick's second law, and combining the physical boundary conditions of constant pressure gas injection at one end of the microfluidic channel and closure at the other end, after setting the initial and boundary conditions, its analytical solution form is Equation 10: Formula 10; In Equation 10, C s This represents the equilibrium molar concentration at the gas-liquid interface. l n Let be the distance from the nth sampling point to the gas-liquid interface, and t be the diffusion time. D n Let be the confined space diffusion coefficient of the gas component in the liquid component at the nth sampling point. erfc The remainder error function; For other sampling points, the gas molar concentration obtained from inversion at different times is nonlinearly least squared fitted with the concentration calculated by the one-dimensional unsteady diffusion model, and Equation 10 is transformed to obtain the diffusion coefficient corresponding to that sampling point. D n ), Equation 12; In Equation 12, The molar concentration of the gas component obtained by inversion of the swelling factor at the nth sampling point at the kth time; N t This represents the number of time points. D n The diffusion coefficient is calculated for the nth sampling point.

[0024] To reduce the impact of local grayscale fluctuations, sampling position errors, and image noise on the calculation results, outliers were removed from the calculation results of multiple sampling points, and the diffusion coefficients of the retained effective sampling points were statistically averaged to obtain the final gas-liquid diffusion coefficient D in the micro-nano confined space considering the swelling effect, as shown in Equation 11: Formula 11; In Equation 11, Ω represents the set of valid sampling points after removing outliers. N v This represents the number of valid sampling points.

[0025] This invention provides a method for determining the gas-liquid diffusion coefficient in micro-nano confined spaces. This method eliminates the need for expensive and complex external component analysis equipment such as Raman spectroscopy. Instead, it continuously acquires spatiotemporal evolution images of liquid fluorescence intensity within confined pores in a micro-nano fluidic visualization experiment. Local experimental swelling factors are calculated based on fluorescence signal changes, and a correspondence between the experimental and theoretical swelling factors is established using the confined space modified PR equation of state. This allows for the inversion of the actual gas concentration distribution within the liquid phase during high-pressure gas dissolution. Based on this, the inverted concentration data is fitted into a mass transfer mathematical model to quantitatively determine the gas-liquid diffusion coefficient considering the swelling effect in nano- to micro-scale confined pores. This method incorporates the liquid-phase swelling effect induced by gas dissolution into the concentration inversion and diffusion coefficient calculation process, improving the characterization accuracy of gas-liquid mass transfer processes in micro-nano confined spaces. It provides experimental evidence for evaluating interphase mass transfer and optimizing enhanced oil recovery schemes during gas injection displacement and huff-and-puff processes in unconventional oil and gas reservoirs such as shale oil and tight oil.

[0026] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention constructs a gas-liquid diffusion measurement environment in nanometer to micrometer-scale confined pores based on a micro-nano fluidic visualization experimental system. It can record in situ the dynamic processes of high-pressure gas diffusion into liquid, dissolution, and induced liquid-phase swelling at spatial scales approaching the micro-nano pore characteristics of unconventional reservoirs. Compared to traditional macroscopic PVT tube methods and pressure decay methods, this invention can more realistically reflect the influence of pore size, interfacial interactions, and confinement effects on gas-liquid mass transfer behavior in micro-nano confined spaces, improving the applicability of gas-liquid diffusion coefficient measurement results to actual development conditions of unconventional reservoirs such as shale oil and tight oil.

[0027] 2. This invention calculates the local experimental swelling factor using in-situ fluorescence image signals and, combined with the modified PR equation of state for confined spaces, inverts the actual gas concentration within micro / nano pores, establishing a quantitative correlation between fluorescence signals, liquid-phase swelling behavior, thermodynamic properties, and gas concentration. This method no longer simply equates fluorescence intensity decay with gas concentration changes; instead, it incorporates the liquid-phase swelling effect into the fluorescence signal interpretation and concentration inversion process, thereby improving the accuracy and reliability of obtaining the gas concentration field in micro / nano confined spaces.

[0028] 3. This invention incorporates the liquid-phase swelling effect induced by gas dissolution into the diffusion coefficient calculation process, avoiding the simplistic attribution of staining agent dilution, interface advancement, or local fluid displacement caused by swelling to the gas diffusion process. Compared to existing methods that directly apply Fick's law to fit image responses or changes in the diffusion front, this invention reduces the calculation deviation of the diffusion coefficient caused by neglecting the swelling effect, and obtains a micro / nano confined space gas-liquid diffusion coefficient that can characterize the mass transfer characteristics under gas dissolution-diffusion-swelling coupling conditions.

[0029] 4. This invention utilizes only micro / nano fluidic chips, fluorescence microscopy imaging systems, and thermodynamic model inversion methods to quantitatively determine the gas-liquid diffusion coefficient. This reduces reliance on expensive and complex component analysis equipment such as Raman spectroscopy, offering advantages such as relatively simplified experimental setup, controllable operation, clear data processing flow, and strong repeatability. This method can be used to evaluate the mass transfer capacity of injected gases such as carbon dioxide and hydrocarbon gases in crude oil or other liquids, providing key experimental parameters and microscopic theoretical basis for assessing interphase mass transfer efficiency, determining miscibility, and optimizing enhanced oil recovery schemes during gas injection displacement and huff-and-puff processes in unconventional oil and gas reservoirs. Attached Figure Description

[0030] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0031] Figure 1 A flowchart illustrating the implementation of a method for determining the gas-liquid diffusion coefficient in a micro / nano confined space considering the swelling effect, as provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the "S"-shaped single-ended blind-end coil-type micro / nano fluid control chip structure provided in an embodiment of the present invention; Figure 3 A schematic diagram of an experimental system for measuring the gas-liquid diffusion coefficient considering the swelling effect, provided in an embodiment of the present invention; Figure 4These are fluorescence images of n-heptane samples with different concentrations of fluorescent agent in the embodiments of the present invention; Figure 5 This is a schematic diagram illustrating the fitting relationship between the normalized fluorescence signal gray value and the fluorescent agent concentration in an embodiment of the present invention; Figure 6 This is a schematic diagram showing fluorescence images and sampling point area markings at different times during the diffusion of CO2 into n-heptane at a scale of 50 μm in an embodiment of the present invention. Figure 6 In the diagram, 1 represents sampling point 1, 2 represents sampling point 2, 3 represents sampling point 3, and 4 represents sampling point 4. Figure 7 This is a graph showing the diffusion coefficient of CO2 in heptane as a function of pressure under different micro / nano-scale spaces at 298 K in this embodiment of the invention. Figure 8 The graph shows the variation of the diffusion coefficient of CO2 in heptane with temperature under different micro-nano scale spaces under a pressure of 10 MPa in this embodiment of the invention. Detailed Implementation

[0032] To further illustrate the present invention, the following detailed description of a method for determining the gas-liquid diffusion coefficient in a micro-nano confined space provided by the present invention is provided in conjunction with embodiments, but it should not be construed as limiting the scope of protection of the present invention.

[0033] Example 1

[0034] In this embodiment, the diffusion coefficient of CO2 in n-heptane, considering the swelling effect, was determined in a 50 μm space under the conditions of 298 K, 10 MPa pressure.

[0035] Micro / nanofluidic chip channel design such as Figure 2 As shown, 101 is the gas injection port, 102 is the liquid injection port, 103 is the main fluid channel, and 104-106 are gas-liquid diffusion channels. The gas-liquid diffusion channels are designed as an "S"-shaped single-end blind-end coil structure. This structure extends the effective flow path length for gas-to-liquid diffusion within the same observation field, thereby increasing the observable diffusion area and improving the continuity and accuracy of fluorescence signal acquisition. Gas-liquid diffusion channels of different depths can be etched simultaneously on the same chip, facilitating multi-scale diffusion coefficient measurements. Specifically, the depth of gas-liquid diffusion channel 104 is 50 μm; the depth of gas-liquid diffusion channel 105 is 3 μm; and the depth of gas-liquid diffusion channel 106 is 10 nm.

[0036] The gas-liquid diffusion coefficient determination experimental system considering the swelling effect provided in the embodiments is as follows: Figure 3As shown, it mainly includes: 1-micro-nano fluidic chip; 2-micro-nano fluidic chip holder; 3-electric heating temperature control system; 4-image acquisition system; 5-CMOS camera and fluorescence microscope; 6-vacuum pump; 701-gas intermediate container; 702-liquid intermediate container; 801-gas injection pump; 802-liquid injection pump; 9-pressure gauge; 1201-vacuum valve; 1202-gas injection valve; 1203-liquid injection valve; 1204-vent valve.

[0037] S1: Build as follows Figure 3 The micro / nanofluidic experimental setup shown consists of two containers: 701 (gas intermediate container) filled with CO2, and 702 (liquid intermediate container) filled with n-heptane of known dye concentration. A brand-new, clean 1-micro / nanofluidic chip is installed into the 2-micro / nanofluidic chip holder, and all tubing is connected. The entire experimental setup is checked for airtightness. After ensuring good airtightness, the 6-vacuum pump is turned on to evacuate for 1 hour, maintaining a vacuum level inside the chip below 10 Pa to eliminate air interference with the experimental results.

[0038] S2: Calibrate the relationship between fluorescent dye concentration and fluorescence signal grayscale value. Adjust the 4-image acquisition system and 5-CMOS camera and fluorescence microscope (including: field flattening correction to ensure uniform image light source, fixed light source intensity, exposure time, objective magnification, and camera parameters). Saturate the chip with n-heptane of different fluorescent dye concentrations. The specific steps are as follows: keep the 1201-vacuum valve, 1202-gas injection valve, and 1204-vent valve closed, open the 1203-liquid injection valve and 702-liquid intermediate container, and inject n-heptane of known fluorescent dye concentration into the chip at a pressure of 1 MPa. After the 104-106 gas-liquid diffusion channels are filled with fluorescence signal, capture the fluorescence signal image. After measuring the signal of one fluorescent dye concentration, clean the 702-liquid intermediate container and pipeline, fill with the liquid of the next fluorescent dye concentration to be tested, replace the micro / nanofluidic chip, and repeat the above steps to capture the fluorescence signal image. This embodiment captured fluorescence signal images at six different fluorophore concentrations (3.40 g / L, 2.83 g / L, 2.27 g / L, 1.70 g / L, 1.14 g / L, and 0.57 g / L), as shown below. Figure 4 As shown.

[0039] The average fluorescence grayscale value of the liquid region was extracted using ImageJ image processing software, and then normalized. This normalization process involves using the grayscale value of the image background region or blank sample as the background grayscale value, and the grayscale value of the sample with the highest phosphor concentration or the initial standard sample as the reference grayscale value. This converts the original grayscale values ​​extracted from different images into dimensionless relative fluorescence signal values ​​within the range of 0 to 1. This processing can reduce the influence of background noise, minor fluctuations in the light source, chip differences, and subtle changes in imaging conditions on the grayscale values, making the fluorescence responses of samples with different phosphor concentrations comparable and improving the stability and repeatability of subsequent fitting relationships. Based on the normalized fluorescence signal grayscale value and the known phosphor concentration, regression fitting is performed to establish a quantitative mapping relationship between the two, such as... Figure 5 As shown.

[0040] S3: After calibrating the relationship between fluorescent dye concentration and fluorescence signal grayscale value, clean the experimental tubing and intermediate container, and replace with a brand new, clean micro / nanofluidic chip. Then, resaturate the micro / nanofluidic chip with n-heptane containing 2.27 g / L of fluorescent dye (the smaller the pore size, the higher the required fluorescent dye concentration), ensuring that the 10⁴–10⁶ gas-liquid diffusion channels are completely filled with liquid and that the fluorescence signal is uniformly distributed. After the chip is saturated, activate the 3-electric heating temperature control system to heat the chip to the target test temperature of 298 K. During the experiment, monitor the chip and the internal fluid temperature in real time through the temperature measuring port in the 2-micro / nanofluidic chip holder until the system temperature stabilizes, then proceed to the subsequent gas injection diffusion experiment.

[0041] S4: After the chip temperature stabilizes at 298 K, CO2 injection begins. First, the pressure in the 701-gas intermediate container is increased to 1 MPa. Then, the 1203-liquid injection valve is closed, and the 1204-vent valve and 1202-gas injection valve are opened sequentially to allow CO2 to enter the micro / nanofluidic chip. Since the 1204-vent valve is open, CO2 can quickly displace the n-heptane in the 103-fluid mainstream channel. The fluorescence signal changes in the mainstream channel are observed under a microscope. When the liquid fluorescence signal in the 103-fluid mainstream channel completely disappears and stable gas is observed to be discharged from the vent end, the 1204-vent valve is closed. Subsequently, the CO2 injection pressure is rapidly increased to the test target pressure of 10 MPa and kept constant, allowing CO2 to dissolve and diffuse into the n-heptane in the 104-106 gas-liquid diffusion channel under the drive of pressure and concentration difference.

[0042] S5: After establishing a constant pressure diffusion boundary of 10 MPa, adjust the observation field of the fluorescence microscope to the area in the 104 gas-liquid diffusion channel where CO2 has not yet diffused, i.e., the fluorescence signal remains stable in this area and can be used as an initial reference area for subsequent grayscale change comparison. Subsequently, fix the microscope field of view, light source intensity, exposure time, objective magnification, and camera parameters, and use the timed capture function of the 4-image acquisition system to acquire a fluorescence signal image every 30 seconds, continuously recording the entire process of CO2 diffusion into n-heptane in the 50 μm scale channel and the resulting change in fluorescence signal. Figure 6 The fluorescence image shows the process of CO2 gradually diffusing from an unaffected state to the target area in an "S"-shaped micro / nano channel.

[0043] S6: Fluorescence image data processing, gas concentration inversion and diffusion coefficient calculation.

[0044] In steps S601-S603, the following are used: Figure 6 The calculation of CO2 concentration at sampling point 1 at time t = 750 s is taken as an example.

[0045] S601, Extraction of fluorescence image sampling point information. Fluorescence images acquired continuously at different times in S5 are processed. Four local regions are selected as sampling points along the 104 gas-liquid diffusion channel in ImageJ software. Figure 6 As shown. Sampling points should be located in the liquid region inside the channel, avoiding the channel edges, areas of severe bending at the gas-liquid interface, and areas of local image noise. For each sampling point, record its distance from the gas-liquid interface and calculate the normalized average gray value of the sampling point in the fluorescence image at different times, forming a data table of "Sampling Point Number - Distance between Gas-Liquid Interface and Sampling Point - Diffusion Time - Normalized Average Gray Value". This data table is used for subsequent conversion of fluorescent dye concentration, calculation of local swelling factor, gas concentration inversion, and diffusion coefficient fitting. For example, at diffusion time t = 750 s, sampling point 1 has a distance of 2.00 mm between the gas-liquid interface and the sampling point. The normalized average gray value of this sampling point at t = 750 s is extracted using ImageJ software and is 0.473. Based on the fitting relationship between the normalized fluorescence signal gray value and the fluorescent dye concentration established in S2, this normalized average gray value can be converted into the fluorescent dye concentration, that is, the fluorescent dye concentration of this sampling point at t = 750 s is 0.467 g / L.

[0046] S602, calculate the swelling factor SF according to Formula 1:

[0047] The results indicate that at t = 750 s, the local volume of n-heptane at sampling point 1 due to CO2 dissolution is approximately 4.86 times that of the initial state.

[0048] S603, CO2 concentration inversion based on confined space modified PR equation of state. In this embodiment, the experimental pressure is 10 MPa, the experimental temperature is 298 K, the microfluidic channel characteristic scale is 50 μm, and the system to be tested is a CO2-n-heptane system. The above temperature, pressure, channel scale, and physical properties of CO2 and n-heptane are input into the confined space modified PR equation of state (Equation 2-7) to calculate the molar volume of the CO2-n-heptane mixture under different CO2 molar fractions, and compare it with the molar volume of pure n-heptane under the same temperature, pressure, and scale conditions to obtain the theoretical swelling factor corresponding to different CO2 molar fractions.

[0049] In this embodiment, the theoretical molar volume of pure n-heptane under conditions of 10 MPa, 298 K, and 50 μm scale is 1.465 × 10⁻⁶. -4 m 3 / mol. When the CO2 mole fraction is 0.800, the molar volume of the CO2-n-heptane mixture calculated using the confined space modified PR equation of state is 1.424 × 10⁻⁶. -4 m 3 / mol. The theoretical swelling factor at this point is (Formula 8):

[0050] The theoretical swelling factor is consistent with the experimental swelling factor calculated in S602, therefore the CO2 mole fraction at sampling point 1 at t = 750 s can be determined to be 0.800. Further calculation of the CO2 molar concentration based on the CO2 mole fraction and the molar volume of the mixed system (Formula 9) is then performed:

[0051] Therefore, the CO2 molar concentration obtained from sampling point 1 at t=750s is 5.62×10⁻⁶. 3 mol / m 3 .

[0052] S604, Calculation of gas-liquid diffusion coefficient considering swelling effect. Following the methods in S601 to S603, batch processing of fluorescence image data from different sampling points and at different times was performed to obtain concentration field evolution data of CO2 diffusion into n-heptane within a 50 μm confined channel. Subsequently, for each sampling point, the CO2 molar concentration obtained at different times was substituted into a one-dimensional unsteady-state diffusion model. The deviation between the experimentally retrieved concentration and the model-calculated concentration was fitted using the nonlinear least squares method to obtain the diffusion coefficient corresponding to that sampling point (Equation 10). The diffusion coefficients corresponding to multiple sampling points were calculated using the same method, and statistical analysis and outlier removal were performed on the calculation results for each sampling point. Finally, the average value of the diffusion coefficients of the retained valid sampling points was taken (Equation 11). Thus, the diffusion coefficient of CO2 in n-heptane under the conditions of 10 MPa, 298 K, and 50 μm scale was obtained as 5.49 × 10⁻⁶. -9 m 2 / s. This diffusion coefficient is used to characterize the gas-liquid mass transfer capacity of CO2 under conditions of diffusion, dissolution, and induced liquid-phase swelling into n-heptane within a 50 μm confined channel.

[0053] Examples 2-4: The method for determining the gas-liquid diffusion coefficient in micro-nano confined spaces considering the swelling effect provided by the present invention can explore the influence of pore size, pressure and temperature on the diffusion coefficient. Examples 2-4 only change the pore size, pressure and temperature conditions in Example 1.

[0054] Example 2: This example only changes the channel depth from 3 μm to 10 nm in Example 1.

[0055] Example 3: This example only changes the pressure conditions in Example 1 to 14 MPa, 18 MPa, 22 MPa, 26 MPa, and 30 MPa.

[0056] Example 4: This example only changes the temperature conditions in Example 1 to 308 K, 318 K, 328 K, 338 K, and 348 K.

[0057] The effects of different pore sizes, pressures, and temperatures on the diffusion coefficient of CO2-n-heptane in a confined space are as follows: Figure 7 and Figure 8 As shown, Example 1 was set as the control group, and the following patterns were observed in the comparison: (1) Pore size has a significant impact on the diffusion coefficient. Under the same temperature and pressure conditions, the diffusion coefficient of CO2 in n-heptane increases with the increase of the confined space size. Taking 298 K and 10 MPa as an example, the diffusion coefficients at the scales of 10 nm, 3 μm and 50 μm are 2.57 × 10⁻⁶. -9 m 2 / s, 5.09×10-9 m 2 / s and 5.49×10 -9 m 2 / s. Compared to the 10 nm confined space, the diffusion coefficients at the 3 μm and 50 μm scales are significantly increased, indicating that the nanoscale confinement effect significantly inhibits the diffusion and mass transfer of CO2 in n-heptane. When the scale increases to the micrometer scale, the diffusion coefficient further increases, but the difference between 3 μm and 50 μm is relatively smaller than the difference between 10 nm and micrometer scales, indicating that the strong confinement effect is mainly concentrated in the nanoscale range.

[0058] (2) Increased pressure reduces the diffusion coefficient of CO2 in n-heptane. At 298 K, as the pressure increases from 10 MPa to 30 MPa, the diffusion coefficient at the 10 nm scale decreases from 2.57 × 10⁻⁶. -9 m 2 / s decreased to 2.06×10 -9 m 2 / s, at a scale of 3 μm, it is 5.09 × 10 -9 m 2 / s decreased to 3.94×10 -9 m 2 / s, at a scale of 50 μm, it is 5.49 × 10 -9 m 2 / s decreased to 4.43×10 -9 m 2 / s. This result indicates that within the test range of this embodiment, increased pressure causes stronger compression of the gas-liquid system, resulting in a more compact arrangement of liquid phase molecules and increased resistance to CO2 migration in n-heptane, thus leading to an overall decrease in the diffusion coefficient. Furthermore, pressure has a greater impact on the CO2 diffusion coefficient in n-heptane than on nanopore spaces within micron-sized pore spaces.

[0059] (3) Increased temperature significantly increases the diffusion coefficient of CO2 in n-heptane. Under 10 MPa conditions, as the temperature increases from 298 K to 348 K, the diffusion coefficient at the 10 nm scale increases from 2.57 × 10⁻⁶. -9 m 2 / s increased to 5.16×10 -9 m 2 / s, at a 3μm scale, it is 5.09×10 -9 m 2 / s increased to 11.05×10 -9 m 2 / s, at a scale of 50 μm, it is 5.49 × 10 -9 m 2 / s increased to 11.78×10 -9m 2 / s. This result indicates that increased temperature enhances molecular thermal motion and reduces liquid-phase mass transfer resistance, thereby promoting CO2 diffusion in n-heptane. Considering the three factors of pore size, pressure, and temperature, it is evident that larger pore size, lower pressure, and higher temperature are more conducive to CO2 diffusion and mass transfer in n-heptane, while nanoscale confined spaces and high-pressure conditions significantly inhibit the diffusion process.

[0060] (4) According to Figure 5 The response relationship between the gray value of the fluorescence signal and the concentration of the fluorescent dye differs significantly at different pore scales, indicating the necessity of the concentration calibration step in S2. The calibration results show that at the 10 nm scale, the normalized gray value of the fluorescence signal changes approximately linearly with increasing fluorescent dye concentration; however, at the 3 μm and 50 μm scales, the fluorescence signal exhibits a significant non-linear growth characteristic with increasing concentration. This indicates that at different pore scales, due to differences in optical path length, channel size, local light intensity distribution, and fluorescence signal response characteristics, a simple linear relationship cannot be used to convert the gray value of the fluorescence signal to the dye concentration. Directly equating the change in fluorescence signal linearly to the change in dye concentration will affect the accuracy of subsequent swelling factor calculations and CO2 concentration inversion results. Therefore, this invention establishes a calibration relationship between the normalized gray value of the fluorescence signal and the concentration of the fluorescent dye at different pore scales before the formal diffusion experiment, which can effectively improve the reliability of liquid-phase swelling factor calculations, local gas concentration inversion, and final diffusion coefficient determination results.

[0061] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the gas-liquid diffusion coefficient in a micro / nano confined space, characterized in that, Includes the following steps: A) The test liquid containing different concentrations of fluorescent dye was saturated into the micro-nano fluid control chip, fluorescence images were acquired, and the average fluorescence signal gray value of the liquid region in the fluorescence image was extracted to obtain the relationship curve between the concentration of fluorescent dye and the fluorescence signal gray value. B) Saturate the microfluidic chip with the test liquid containing the initial concentration of fluorescent dye, heat the chip to the target temperature, then inject the test gas, pressurize to the target pressure, so that the test gas dissolves and diffuses into the test liquid; C) Acquire liquid fluorescence images at different diffusion times, select multiple sampling points for the liquid fluorescence images, and obtain the distance between each sampling point and the gas-liquid interface. l n And the normalized average gray value of each sampling point before the gas to be tested is injected. I 0 Normalized average gray values ​​at different diffusion times t I t Based on the relationship curve between the concentration of the fluorescent dye and the gray value of the fluorescence signal obtained in step A), the concentration of the fluorescent dye in the liquid phase in the initial state is obtained. C 0 The real-time concentration of fluorescent dye in the liquid phase of the sampling point region after gas dissolution and expansion at time t. C t ; The experimental swelling factor at time t of the sampling point was calculated according to Equation 1. SF exp : Formula 1; In Equation 1, V 0 This is the reference volume of the liquid at this sampling point in its initial state; V t Let t be the volume of liquid in the sampling area after the gas dissolves and expands. C 0 This represents the initial concentration of the fluorescent dye in the liquid phase. C t The real-time concentration of the fluorescent dye in the liquid phase of the sampling point region after the gas dissolution and expansion occurs at time t; The molar volume of the gas-liquid mixture after gas diffusion is obtained according to the PR equation of state based on confined space correction, as shown in Equations 2 to 7. v mix Total mole fraction of gas x gas relational formula v mix ( x gas P, T ), Formula 2; In Equation 2, P is the experimental pressure, T is the experimental temperature, and R is the universal gas constant. v mix The molar volume of the gas-liquid mixture. This represents the proportion of molecules in the adsorption region of a fluid mixture within a confined pore. a mix The parameters of the gravitational term after correction for the mixture. b mix For parameters of the repulsion term of the mixture, α(T) It is a function of temperature; Formula 3; Equation 4; Formula 5; Formula 6; Formula 7; In equations 3 to 7, ΔT c This is a dimensionless change in critical temperature. r e To account for the effective pore radius of the adsorption thickness, σ LJ For Lennard Jones's dimensional parameters, x i Pure components i mole fraction, x j Pure components j The mole fraction, where N represents the total number of components in the diffusing gas and the diffused liquid, 2 ≤ N ≤ 70. a ij For the interaction term between components i and j, b i Pure components i The repulsive force parameters, k ij For binary interaction coefficients, a i Pure components i gravitational parameters, a j Pure components j gravitational parameters, m i for i Temperature correction parameters of the components T r For comparison temperature; Then, the theoretical swelling factor is calculated according to Equation 8. SF cal , Formula 8; In Equation 8, v liquid ( P, T ( ) represents the theoretical molar volume of a pure liquid under the same test temperature, pressure, and micro / nano confinement conditions; By adjusting the experimental swelling factor SF exp Compared with theoretical swelling factor SF cal Equal to obtain the molar volume of the gas-liquid mixture in the sampling point region. v mix and total mole fraction of gases x gas ; The gas molar concentration of the nth sampling point region was calculated according to Equation 9. C g Furthermore, the gas molar concentration at the nth sampling point at different times t was obtained. C g ( n, t ): Equation 9; The diffusion coefficient D corresponding to the nth sampling point is calculated according to formula 10. n Formula 10; In Equation 10, C s This represents the equilibrium molar concentration at the gas-liquid interface. l n D is the distance from the nth sampling point to the gas-liquid interface, t is the diffusion time, and D is the distance from the nth sampling point to the gas-liquid interface. n Let be the confined space diffusion coefficient of the gas component in the liquid component at the nth sampling point. erfc The remainder error function; Further calculations yielded the diffusion coefficient D corresponding to multiple sampling points. n For multiple sampling points, the diffusion coefficient D n Statistical averaging yields the gas-liquid diffusion coefficient D in the micro-nano confined space.

2. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, In step A), the average fluorescence signal gray value is normalized to obtain a normalized fluorescence signal gray value.

3. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 2, characterized in that, Regression analysis was performed on the normalized fluorescence signal gray value and the corresponding fluorescent dye concentration to obtain the relationship curve between the fluorescent dye concentration and the fluorescence signal gray value.

4. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, The micro / nano fluid control chip includes a main fluid channel and a gas-liquid diffusion channel connected to the main fluid channel. One end of the main channel is provided with a gas injection port, and the other end is provided with a liquid injection port; The gas-liquid diffusion channel has an S-shaped single-end blind-end coil structure.

5. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 4, characterized in that, The micro / nano fluid control chip has multiple gas-liquid diffusion channels with a depth of 10nm~1000μm.

6. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 4, characterized in that, In step B), the gas to be tested is injected through the gas injection port. After the gas fills the main fluid channel, the back pressure valve is closed, and the injection pressure is increased and maintained at the target pressure, so that the gas to be tested spontaneously dissolves and diffuses into the liquid to be tested in the gas-liquid diffusion channel of the confined micro-nano pores.

7. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, In step C), the sampling point is located in the liquid region inside the microchannel, and avoids the channel edge, the area of ​​severe bending at the gas-liquid interface, and the area of ​​local image noise.

8. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, In step C), the diffusion coefficient D corresponding to multiple sampling points is obtained by performing nonlinear least squares fitting between the gas molar concentration obtained from other sampling points at different times and the concentration calculated by the one-dimensional unsteady diffusion model. n .

9. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, The gas-liquid diffusion coefficient in a micro-nano confined space was determined using a micro-nano fluid control experimental system, which includes a micro-nano fluid control chip, a fluorescence image acquisition system, a high-pressure constant-speed and constant-pressure pump group, a gas container, a liquid container, and a temperature control system.

10. The method for determining the gas-liquid diffusion coefficient in a micro / nano confined space according to claim 1, characterized in that, The diffusion coefficient D corresponding to multiple sampling points was obtained. n Then, outliers were removed, and the diffusion coefficient of the retained valid sampling points was calculated according to Equation 11 to obtain the gas-liquid diffusion coefficient D in the micro-nano confined space: Formula 11; In Equation 11, Ω represents the set of valid sampling points after removing outliers. N v This represents the number of valid sampling points.

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