A method for determining the relative permeability of shale gas and water considering CO2 connectivity

Abstract

This invention relates to the field of carbon dioxide geological storage and utilization technology, specifically to a method for determining the relative permeability of shale gas and water considering CO2 connectivity. It includes: obtaining basic parameters of the shale; establishing the relationship between CO₂ connectivity (CI) and bound water saturation (S). wi The quantitative relationship; based on the theory of variable diameter capillary tubes, the shape coefficient F of the pore throat unit is introduced. i This invention couples CO₂ connectivity (CI) into the analytical expression of gas-water relative permeability, constructing a shale gas-water relative permeability calculation model that considers CO₂ connectivity. By incorporating this dynamic key parameter into the model construction and establishing an exponential quantitative relationship between CO₂ connectivity and bound water saturation, the influence of the proportion of effective flow paths of CO₂ in the pore-throat network on seepage is accurately quantified. This results in a correlation coefficient between the model's calculated values ​​and experimentally measured values ​​exceeding 0.95, significantly outperforming the traditional Brooks-Corey model and improving the accuracy of relative permeability prediction for low-permeability shale.

Description

Technical Field

[0001] This invention relates to the field of carbon dioxide geological storage and utilization technology, specifically to a method for determining the relative permeability of shale gas and water considering CO2 connectivity. Background Technology

[0002] With the increasing severity of global climate change, carbon dioxide capture, utilization, and storage (CCUS) technology has become one of the key technologies for achieving carbon neutrality. Its core lies in the long-term storage of CO2 emitted from industry by injecting it into deep geological structures (such as saline aquifers and depleted oil and gas fields). The shale caprock serves as a crucial barrier in the storage system, and its sealing performance directly determines the long-term safety of the storage project. The relative permeability of gas and water is a core parameter characterizing the two-phase flow characteristics of CO2 and water in the shale caprock. Accurate calculation of this parameter is fundamental to assessing CO2 migration patterns and leakage risks.

[0003] Traditional models (such as the Brooks-Corey model) often simplify the shale pore structure to a uniform diameter capillary bundle, ignoring the differences in pore and throat size and geometric heterogeneity (such as pore-throat ratio and shape differences), which seriously deviates from the actual shale pore structure. Furthermore, some models fail to consider the dynamic key parameter of CO2 connectivity. CO2 connectivity specifically refers to the proportion of effective flow paths of CO2 in the pore-throat network, which is affected by factors such as pore structure, flow resistance, and bound water saturation. However, traditional models rely only on pore geometry and topology, leading to significant biases in the prediction of CO2 seepage characteristics in low-permeability shale. Traditional models have also not established a quantitative correlation between CO2 connectivity and bound water saturation, failing to reflect the impact of dynamic connectivity on fluid occurrence during CO2 migration, thus overestimating or underestimating the relative permeability of CO2 and affecting the accuracy of sequestration safety assessment. The aforementioned problems lead to significant errors in the relative permeability calculation of low-permeability shale caprock layers using traditional methods, failing to provide reliable theoretical support for safety assessment and risk warning of CO2 geological storage, and limiting the engineering application of CCS technology. Therefore, developing a gas-water relative permeability calculation model that considers CO2 connectivity and conforms to the actual pore structure of shale has become an urgent technical problem to be solved in this field. Summary of the Invention

[0004] To address the issues of traditional models neglecting CO2 connectivity and shale pore-throat heterogeneity, resulting in large deviations in relative permeability predictions, this invention provides a method for determining the relative permeability of shale gas and water that considers CO2 connectivity. By coupling this parameter with bound water saturation and introducing a shape coefficient, the correlation coefficient between the model's calculated values ​​and measured values ​​exceeds 0.95, enabling accurate characterization of seepage characteristics and providing a reliable tool for CO2 geological sequestration safety assessment.

[0005] The solution adopted by this invention to solve its technical problem is: a method for determining the relative permeability of shale gas and water considering CO2 connectivity, which is obtained through the following steps: Step 1: Obtain the basic parameters of shale and fluid, including the pore radius r. p , throat radius r t , throat ratio D pt Porosity ϕ, absolute permeability k, CO2 connectivity CI, bound water saturation S wi Interfacial tension σ, contact angle θ, and gas-liquid viscosity μ g μ w ; Step 2: Establish the relationship between CO2 connectivity CI and bound water saturation S wi Quantitative relationship; Step 3: Based on the theory of variable diameter capillary tubes, introduce the shape factor F of the pore throat unit. i Establish the shape factor F of the pore throat element. i By coupling the CO2 connectivity CI to the analytical expression of gas-water relative permeability, a shale gas-water relative permeability calculation model considering CO2 connectivity is constructed. The analytical expression of the gas-water relative permeability calculation model is as follows: Relative permeability of water phase: (1) Relative permeability of the gas phase: (2).

[0006] Furthermore, in step one, the CO2 connectivity is calculated using the following method: (1) Based on the step-injection pressure displacement test combined with nuclear magnetic resonance technology, a T2-P structure was constructed. c Two-dimensional relaxation spectrum to obtain the intensity of movable water signal in different pore throat units; (2) Based on the variable diameter capillary model, calculate the viscous resistance P of a single pore throat element. v Capillary resistance P c and inlet resistance P ent The CO2 connectivity CI of the single-hole throat unit was obtained. jr ; (3) Using the strength of the movable water signal as the weight, calculate the CO2 connectivity CI for all pore throat units. jr The weighted average yields the overall CO2 connectivity of the shale.

[0007] Furthermore, in step two, the bound water saturation S wi The connectivity parameter CI with carbon dioxide satisfies S wi =e (c+d×CI), where c and d are correction coefficients.

[0008] Furthermore, the gas-water relative permeability calculation model is constructed through the following steps: (1) The pore structure of shale is simplified into a variable diameter pore throat capillary unit; (2) Based on Poiseuille's law and the conservation of flow rate in series, an analytical relationship between the flow rate q of a single-hole throat unit and the total pressure drop ΔP is established, and the flow rate of the single-hole throat capillary is obtained as follows: (3) Where, r t Where is the throat radius, and μ is the fluid viscosity; (3) By summing the weighted average of all pore throat units by volume fraction, the expression for the core permeability k is obtained: (4) Let F i The shape factor of the pore throat element: (5) In equation (4), the shape coefficient F of the pore throat element is introduced. i : (6) Rewriting equation (6) in integral form, and introducing the tortuosity parameter of the wetted and non-wetted phases, we obtain the formula for calculating the relative permeability of the aqueous phase: (7) Similarly, the relative permeability of the carbon dioxide phase is expressed as: (8) (4) Introducing CO2 connectivity CI and bound water saturation S wi Based on experience, S wi Substituting into the above equation, we obtain the phase permeation equation considering the interconnectivity of carbon dioxide: (9) (10) Where b, c, d, α, β, and γ are dimensionless correction coefficients, the values ​​of which are determined by experimental calibration.

[0009] Furthermore, in step three, the parameters of the variable diameter capillary theory are defined as follows: Throat-orifice ratio: D pt =r p / r t , where r p r is the pore radius. t The radius of the throat; Total length of the pore throat capillary: L e =L p +L t , where L p L is the total length of the pores. t This represents the total length of the larynx.

[0010] Furthermore, the shape factor F of the pore throat unit i Satisfy F i =F0+a×e (−Si / b) , where F0, a, and b are constants.

[0011] Furthermore, the correction coefficients b, c, and d are determined through a displacement test with gradually increasing injection pressure. The experimental steps include: (1) Under the conditions of 50℃ and confining pressure of 15MPa, the initial injection pressure is 8MPa, and the displacement pressure is gradually increased to 14MPa in increments of 1MPa. (2) Low-field nuclear magnetic resonance online monitoring was used to obtain the saturation distribution and pressure difference data of the gas and water phases; (3) The saturation of bound water has a negative exponential relationship with the connectivity of CO2. b, c, and d can be inverted by fitting the least squares formula.

[0012] The beneficial effects of this invention are: This invention incorporates the dynamic key parameter of CO2 connectivity into the model construction. By establishing an exponential quantitative relationship between CO2 connectivity and bound water saturation, it accurately quantifies the impact of the proportion of effective flow paths of CO2 in the pore-throat network on seepage. At the same time, it comprehensively considers the synergistic effect of viscous resistance, capillary resistance, and inlet resistance, so that the correlation coefficient between the model calculation value and the experimental measured value is higher than 0.95, which is significantly better than the traditional Brooks-Corey model (correlation coefficient ≤ 0.82), and greatly improves the accuracy of predicting the relative permeability of low-permeability shale. This model is based on the variable diameter capillary theory, simplifying shale pores into pore-throat units composed of pores and throats, and introducing a shape factor F. i The quantitative analysis of pore throat geometric heterogeneity breaks through the traditional model's assumption of pore throat uniformity and better reflects the multi-scale pore structure characteristics of shale large-pore reservoirs and throat-controlled flow. This model can accurately capture the gas-water seepage patterns of shale with different CO2 connectivity, and can be directly applied to CO2 geological storage projects. It provides a scientific tool for evaluating the sealing performance of shale caprock, predicting the depth of CO2 intrusion, and providing early warning of leakage risks, effectively ensuring the long-term safety of CCS projects. Attached Figure Description

[0013] Figure 1 This is a graph showing the T2 curve changes of shale samples during the CO2 water displacement process of this invention. Figure 2This is the evolution relationship of CO2 connectivity with residual water saturation in this invention; Figure 3 This invention provides CO2 connectivity for the pore throat unit. Figure 4 This invention relates the shape factor of the throat unit to the degree of saturation. Figure 5 This is a comparison chart of the relative permeability of different shale samples from this invention. Detailed Implementation

[0014] The following is in conjunction with the appendix Figure 1-5 The present invention will be further described in detail with specific embodiments. These embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention. Based on four groups of shale samples taken from Luzhou City (LZ), Yibin City (YB), Guiyang City (GY), and Changde City (CD), this embodiment systematically describes the complete construction and verification process of the shale gas-water relative permeability calculation model considering CO2 connectivity.

[0015] Example 1: This embodiment uses four groups of shale samples with different pore structure characteristics as the research object to construct and verify a method for determining the relative permeability of shale gas and water considering CO2 connectivity. The specific steps are as follows: I. Experimental Preparation and Acquisition of Basic Parameters (1) Sample pretreatment and test system setup Four sets of shale samples were processed into standard cylindrical cores with a diameter of φ25mm × 20mm. A unified pretreatment procedure was followed: drying at 105℃ for 24 hours until the mass was constant, degassing under vacuum (-0.1MPa) for 6 hours, and then saturating with distilled water at 15MPa for 24 hours to ensure complete pore saturation. An online analysis and imaging system for the seepage process using low-field nuclear magnetic resonance was employed. This system integrates a core holder, confining pressure / axial pressure control system, displacement pressure control system, gas-liquid separation system, and data acquisition module, enabling dynamic monitoring under seepage-stress coupling conditions.

[0016] The test conditions strictly simulated the in-situ environment of CO2 geological storage: the temperature was kept constant at 50℃, the confining pressure and axial pressure were both set at 15MPa, corresponding to the formation pressure at a storage depth of 800-1200m, the displacement pressure was gradually increased from 8MPa to 14MPa in increments of 1MPa, and each pressure was stabilized for 12 hours to achieve stress-seepage balance.

[0017] (2) Basic parameter testing and acquisition Through indoor testing and data analysis, the core basic parameters of the four groups of samples were obtained. All parameters were determined using standardized testing methods, as detailed below: Pore ​​structure parameters: The average pore radius r was determined by a combination of nuclear magnetic resonance (NMR) and high-pressure mercury intrusion (MIP) measurements. p Average throat radius r t Calculate the pore-throat ratio D pt =r p / r t The porosity ϕ was verified by a combination of saturated weighing and NMR methods to ensure that the test error was ≤0.05%; the absolute permeability k was determined by steady-state seepage test.

[0018] Fluid and interface parameters: The contact angle θ of the CO2-water-shale system was measured using an optical contact angle meter; the viscosity μ of CO2 and water was corrected according to the experimental temperature and pressure conditions. g μ w The viscosity of CO2 is corrected using the real gas equation of state, and the interfacial tension is calculated using empirical formulas.

[0019] CO2 connectivity CI: determined by a combination of stepped injection pressure displacement test (SIPD) and NMR technology, as follows: 1) After each displacement pressure stabilizes, NMRT2 spectra of the core are collected. Matric signal interference is eliminated through subtraction to obtain the T2 distribution of mobile water. This is then combined with the capillary pressure P corresponding to different displacement pressures. c Construct T2-P c Two-dimensional relaxation spectroscopy was used to extract the mobile water signal intensity of different pore throat units. As the displacement pressure increased, the T2 signal intensity corresponding to mesopores and macropores gradually decreased, indicating that pore water was gradually displaced by CO2. Figure 1 As shown. The specific calculation method is as follows: The T2 spectra collected under different injection pressures were processed, and the T2 relaxation time was converted into pore radius based on the following formula: (1) In the formula, T2 is the transverse relaxation time (ms), S / V is the pore specific surface area (μm-1), and F s is the pore shape factor, and r is the pore radius (μm). The Butler-Reeds-Dawson algorithm was used to perform multi-exponential inversion calculations within the range of 0.01ms to 10000ms, with 200 inversion data points.

[0020] By combining the relationship between injection pressure and pore throat radius, a nuclear magnetic resonance T2-P structure was constructed. c Two-dimensional relaxation spectrum: (2) The movable water signal intensity M of different pore throat units is obtained by inversion using the following formula. is : (3) In the formula, M is f is the intensity of the i-th echo under the s-th displacement pressure. jr (P cr ,T 2j ) indicates that the lateral relaxation time is T. 2j The capillary pressure is P cr The signal strength of the movable fluid, kernel function exp(-t) i / T 2j H(P) represents the attenuation term of the echo intensity, and the kernel function is H(P). cr -P s ) is a step function, m is the number of transverse relaxation times, which is logarithmically distributed over 200 intervals, ranging from 0.01 to 1000 ms, and p is 7 injection pressures: 8, 9, 10, 11, 12, 13, and 14 MPa.

[0021] 2) Based on the variable diameter capillary model, considering the heterogeneity of shale pores, calculate the three types of resistance in a single pore throat element: viscous resistance P v Capillary resistance P c Inlet resistance P ent This leads to the CO2 connectivity CI of the single-pore throat unit. jr The calculation method is as follows: Viscous resistance P v : (4) Where v is the flow velocity of the fluid in the capillary, and r g It is the gas flow radius, μ g δ is the gas phase viscosity, δ is the thickness of the bound water film, and Q is the gas phase viscosity. vd This is the flow rate of a capillary model with equal radius. Capillary resistance P c Based on the Young-Laplace equation, the expression is: (5) Where σ is the gas-liquid interfacial tension, θ is the contact angle, and r t The radius of the throat; Inlet resistance P ent The streamline direction is determined by the angle α, and the expression is: (6) Carbon dioxide connectivity CI of a single pore throat unit jr Calculate using the following formula: (7) Where C=3 (numerical factor), rpj Let r be the radius of the j-th pore. tr Let r represent the radius of the throat of the r-th pore, μ be the fluid viscosity, L be the sample length, and α be the angle of change of the streamline direction.

[0022] With T2-P c The movable water signal intensity of each pore throat element in the spectrum is used as a weight for the CI of all pore throat elements. jr A weighted average was performed to obtain the overall CO2 connectivity CI of the four groups of samples, calculated as follows: (8) (9) Wherein, CI represents the carbon dioxide connectivity of the shale sample, as shown in Table 1. jr Two-dimensional T2-P c Each coordinate point (T2, P) in the distribution map c The corresponding signal strength represents the number or volume weight of aperture throat units of a specific size, D. jr Indicates T2-P c Figure 2 The product of carbon oxide phase connectivity and signal strength matrix data.

[0023] In summary, the results of the basic parameter measurements for the four groups of samples are shown in Table 1 below: Table 1. Results of basic parameter determination for shale samples. Sample LZ YB GY CD Porosity ϕ (%) 2.92 2.01 1.76 1.44 Gas-liquid interfacial tension (mN / m) 32.9 27.5 41.3 35.1 Contact angle (°) 40.9 73.4 17.9 46.0 <![CDATA[CO2 viscosity μ g (Pa・s)]]> <![CDATA[5.2×10 -5 ]]> <![CDATA[5.2×10 -5 ]]> <![CDATA[5.2×10 -5 ]]> <![CDATA[5.2×10 -5 ]]> <![CDATA[Viscosity of water μ w (Pa・s)]]> <![CDATA[3.6×10 -4 ]]> <![CDATA[3.6×10 -4 ]]> <![CDATA[3.6×10 -4 ]]> <![CDATA[3.6×10 -4 ]]> <![CDATA[CO2 connectivity CI]]> 0.111 0.103 0.089 0.056 II. CO2 connectivity (CI) and bound water saturation (S) wi Establishment of quantitative relationships Unsteady-state CO2 displacement of water was conducted using an online NMR monitoring test. The bound water signal intensity of four groups of samples after displacement stabilization was obtained. Combined with the initial saturation signal intensity, the bound water saturation S of each group of samples was calculated. wi Experiments have shown that CO2 connectivity (CI) is related to bound water saturation (S). wi A significant exponential correlation is observed because a higher CI indicates a larger proportion of effective flow paths for CO2 in the pore-throat network, enabling more complete displacement of the water phase in the pores and resulting in lower bound water saturation. The experimental data were fitted using the least squares method, as shown below. Figure 2 As shown, the quantitative relationship between the two is: S wi =e^ (c+d×CI) , where c and d are dimensionless correction coefficients, which are determined by the pore structure and fluid properties of the sample.

[0024] III. Construction of a Gas-Water Relative Permeability Model Based on CO2 Connectivity Shale has a complex pore structure, and traditional uniform-diameter capillary bundle models are insufficient to accurately characterize its seepage properties. This invention simplifies the complex core pore structure into a pore-throat capillary model, where the total pore length of each capillary is L. p The total length of the larynx is L t The total length is L e =L p +L t When fluid flows through pores, since the throat and pores are connected in series, the flow rates in the throat and pore portions are exactly equal, according to Poiseuille's law: (10) In the formula, ∆P t It is the flow pressure of the fluid passing through the throat section, ∆P p This is the flow pressure of the fluid passing through the pore portion. The total pressure difference across the pore is the sum of the pressure differences in the throat and the pore portion, i.e.: (11) Combining equations (10) and (11), we get: (12) Substituting equation (12) into equation (11) and combining it with equation (10), the flow rate of a single-hole throat capillary is: (13) If the sample contains n such pore-throat units, then the flow rate of the rock sample is: (14) Based on Darcy's law, the permeability of the core is expressed as: (15) The fraction of the pore-throat capillary volume i to the core pore volume is expressed as: (16) Substituting equation (16) into equation (15), and summing the values ​​of all pore throat elements in the core by volume fraction, we obtain the expression for the core permeability k: (17) Let F i The shape factor of the pore throat element: , (18) To further characterize the influence of geometric differences in different pore throat elements on seepage, a pore throat element shape factor F is introduced. i :F i =F0+a×e^ (-Si / b)Where F0, a, and b are constants obtained by fitting the pore throat geometry of the sample. For example... Figure 4 As shown, S i F represents the saturation of the pore throat element. As the saturation increases, F... i The shape factor of different pore throat units decreases exponentially, and the relationship between saturation and saturation is as follows: Figure 4 As shown. Then equation (17) becomes: (19) Rewriting equation (19) in integral form and introducing the tortuosity parameters of the wetted and non-wetted phases, we obtain the formula for calculating the relative permeability of the aqueous phase: (20) Similarly, the relative permeability of the carbon dioxide phase is expressed as: (twenty one) Connecting CO2 connectivity CI with bound water saturation S wi Quantitative relationship (S) wi =e (c+d×CI) Substituting the analytical expression for the relative permeability of air and water, and combining it with the shape factor F... i A gas-water relative permeability calculation model considering CO2 connectivity was constructed: (twenty two) (twenty three) Among them, the correction coefficients b, c, and d are dimensionless correction coefficients, calibrated through displacement tests with gradually increasing injection pressure: 1) Under the conditions of 50℃ and confining pressure of 15MPa, the initial injection pressure is 8MPa, and the displacement pressure is gradually increased to 14MPa in increments of 1MPa. 2) Low-field nuclear magnetic resonance was used for online monitoring of the gas-water two-phase saturation distribution and upstream-downstream pressure difference data; 3) The correction coefficients b, c, and d are obtained by fitting and inverting using the least squares method.

[0025] This model incorporates the dynamic parameter of CO2 connectivity through S... wi Coupled to the phase permeability equation, while considering the geometric heterogeneity of the pore throat (shape factor F) i This model breaks through the limitations of traditional models that rely solely on pore geometry and topology. It quantifies the synergistic effect of flow resistance and pore connectivity through CI, which is more consistent with the actual seepage mechanism.

[0026] IV. Model Validation and Result Analysis Substituting the basic parameters and correction coefficients of the four groups of samples into the constructed model, the relative air-water permeability curves of each group of samples were calculated and compared with the experimentally measured values ​​and the values ​​calculated by the traditional Brooks-Corey (BC) model. Figure 5 As shown, the reliability and superiority of the model are verified.

[0027] LZ sample: The correlation coefficient between the model calculated value and the measured value is R²=0.98, and the calculated value of the BC model is R²=0.82; YB sample: The correlation coefficient between the model calculated value and the measured value is R²=0.97, and the calculated value of the BC model is R²=0.80; For the GY sample: the correlation coefficient between the model-calculated value and the measured value is R²=0.96, and the calculated value of the BC model is R²=0.78; For CD sample: the correlation coefficient between the model calculated value and the measured value is R²=0.95, and the calculated value of BC model is R²=0.75.

[0028] The verification results of the above four sets of samples all show that the model constructed in this invention can accurately capture the gas-water seepage characteristics of shale with different CO2 interconnectivity, and the calculation accuracy is significantly higher than that of the traditional BC model. This embodiment, through a complete experimental process and model verification, fully demonstrates that the model of this invention can accurately characterize the gas-water seepage characteristics of shale with different CO2 interconnectivity, providing a scientific and reliable theoretical tool for evaluating the sealing performance of shale caprock in CO2 geological storage. It can be directly applied to the safety assessment and risk warning of geological storage projects. By calculating the relative permeability under different CI levels through the model, combined with numerical simulation (such as COMSOL Multiphysics), the depth of CO2 intrusion can be predicted, providing a basis for the selection of storage sites and optimization of engineering parameters.

[0029] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the relative permeability of shale gas and water considering CO2 connectivity, characterized in that, It is obtained through the following steps: Step 1: Obtain the basic parameters of shale and fluid, including the pore radius r. p , throat radius r t , throat ratio D pt Porosity ϕ, absolute permeability k, CO2 connectivity CI, bound water saturation S wi Interfacial tension σ, contact angle θ, and gas-liquid viscosity μ g μ w ; Step 2: Establish the relationship between CO2 connectivity CI and bound water saturation S wi Quantitative relationship; Step 3: Based on the theory of variable diameter capillary tubes, introduce the shape factor F of the pore throat unit. i Establish the shape factor F of the pore throat element. i By coupling the CO2 connectivity CI to the analytical expression of gas-water relative permeability, a shale gas-water relative permeability calculation model considering CO2 connectivity is constructed. The analytical expression of the gas-water relative permeability calculation model is as follows: Relative permeability of water phase: （1） Relative permeability of the gas phase: （2）。 2. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 1, characterized in that, In step one, the CO2 connectivity is calculated using the following method: (1) Based on the step-injection pressure displacement test combined with nuclear magnetic resonance technology, a T2-P structure was constructed. c Two-dimensional relaxation spectrum to obtain the intensity of movable water signal in different pore throat units; (2) Based on the variable diameter capillary model, calculate the viscous resistance P of a single pore throat element. v Capillary resistance P c and inlet resistance P ent The CO2 connectivity CI of the single-hole throat unit was obtained. jr ; (3) Using the strength of the movable water signal as the weight, calculate the CO2 connectivity CI for all pore throat units. jr The weighted average yields the overall CO2 connectivity of the shale.

3. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 1, characterized in that, In step two, the bound water saturation S wi The connectivity parameter CI with carbon dioxide satisfies S wi =e (c+d×CI) , where c and d are correction coefficients.

4. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 3, characterized in that, The air-water relative permeability calculation model is constructed through the following steps: (1) The pore structure of shale is simplified into a variable diameter pore throat capillary unit; (2) Based on Poiseuille's law and the conservation of flow rate in series, an analytical relationship between the flow rate q of a single-hole throat unit and the total pressure drop ΔP is established, and the flow rate of the single-hole throat capillary is obtained as follows: （3） Where, r t Where is the throat radius, and μ is the fluid viscosity; (3) By summing the weighted average of all pore throat units by volume fraction, the expression for the core permeability k is obtained: （4） Let F i The shape factor of the pore throat element: （5） In equation (4), the shape coefficient F of the pore throat element is introduced. i : （6） Rewriting equation (6) in integral form, and introducing the tortuosity parameter of the wetted and non-wetted phases, we obtain the formula for calculating the relative permeability of the aqueous phase: （7） Similarly, the relative permeability of the carbon dioxide phase is expressed as: （8） (4) Introducing CO2 connectivity CI and bound water saturation S wi Based on experience, S wi Substituting into the above equation, we obtain the phase permeation equation considering the interconnectivity of carbon dioxide: （9） （10） Where b, c, d, α, β, and γ are dimensionless correction coefficients, the values ​​of which are determined by experimental calibration.

5. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 4, characterized in that, In step three, the parameters of the variable diameter capillary theory are defined as follows: Throat-orifice ratio: D pt =r p / r t , where r p r is the pore radius. t The radius of the throat; Total length of the pore throat capillary: L e =L p +L t , where L p L is the total length of the pores. t This represents the total length of the larynx.

6. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 4, characterized in that, The shape factor F of the orifice throat unit i Satisfy F i =F0+a×e (−Si / b) , where F0, a, and b are constants.

7. The method for determining the relative permeability of shale gas and water considering CO2 connectivity according to claim 1, characterized in that, The correction coefficients b, c, and d were determined through a displacement test with gradually increasing injection pressure. The experimental steps included: (1) Under the conditions of 50℃ and confining pressure of 15MPa, the initial injection pressure is 8MPa, and the displacement pressure is gradually increased to 14MPa in increments of 1MPa. (2) Low-field nuclear magnetic resonance online monitoring was used to obtain the saturation distribution and pressure difference data of the gas and water phases; (3) The saturation of bound water has a negative exponential relationship with the connectivity of CO2. b, c, and d can be inverted by fitting the least squares formula.

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