Salt cavern gas storage sealing performance evaluation method based on gas-water two-phase seepage

Abstract

The invention discloses a salt-cavern gas storage sealing performance evaluation method based on gas-water two-phase seepage, and belongs to the technical field of salt-cavern gas storages, the method comprises the following steps: embedding a formula in a fluid-solid-gas coupling theoretical model under a saturated water surrounding rock gas injection and production condition into finite element software, inputting mechanical parameters and pore permeability parameters of rock, and calculating the sealing performance of the salt-cavern gas storage according to the mechanical parameters and the pore permeability parameters; the correction coefficient of the slippage effect on the gas permeability, the gas relative permeability and the pore water relative permeability are obtained; based on the initial stress of surrounding rock, corresponding stratum stress values and hydrostatic pressure values are applied to the top, the bottom and the side faces of a rock stratum respectively, an injection-production air pressure boundary is applied to the surface of a salt cavern cavity, numerical simulation is carried out through a fluid-solid-gas coupling theoretical model and parameters, and the gas seepage velocity is obtained through solving. And evaluating the cumulative gas leakage rate in combination with the cumulative gas leakage rate model. According to the method, the gas seepage behavior under the real working condition is simulated, the slippage effect of the small molecule gas and the gas-water displacement process of the water-saturated rock stratum are considered, and the gas leakage amount evaluation is more accurate.

Description

Technical Field

[0001] This invention belongs to the technical field of salt cavern gas storage, and relates to a method for evaluating the sealing performance of salt cavern gas storage, specifically a method for evaluating the sealing performance of salt cavern gas storage based on gas-water two-phase permeation. Background Technology

[0002] Salt rock is formed from salt deposits dissolved in seawater or lake water under the influence of crustal movement and geological changes. It is characterized by its high solubility and fragility. Salt caverns are cavities formed after the salt in underground salt rock layers has been dissolved and extracted. Due to their excellent sealing properties, good creep behavior, and self-healing ability, salt caverns are considered good media for storing small molecule gases such as helium ("Research Progress on Mechanical Properties of Layered Salt Rock", Progress in Mechanics, 2008, No. 04, pp. 484-494).

[0003] Due to technological limitations, my country has not yet achieved helium storage in salt caverns. This is primarily because the layered salt rocks have thin salt layers, high impurity content, inconsistent interlayer deformation, and high permeability, posing significant challenges to helium storage. Furthermore, the helium molecule diameter of 0.26 nm is about 30% smaller than the methane molecule diameter of 0.38 nm. Under the same operating pressure, helium exhibits stronger permeation and diffusion, placing higher demands on the sealing performance of salt cavern gas storage facilities.

[0004] Helium molecules have extremely small diameters, with their molecular path of freedom on the same order of magnitude as the pore size of salt rocks. In dense rocks, the gas slippage effect is significant ("Identifying the Dominant Transport Mechanisms in Single-Nanopore and Three-Dimensional Nanoporous Media," *Basic Research*, 2023, Vol. 3, No. 3, pp. 409-421). Since salt caverns are often created using water-soluble cavity-building techniques, layered salt rocks are typically saturated with brine ("Experimental Study on Acoustic Emission Characteristics of Salt Rock after Brine Immersion," *Rock and Soil Mechanics*, 2013, Vol. 34, No. 7, pp. 1937-1942). Coupled with the influence of hydrostatic pressure, periodic gas injection and production displace pore water in the rock strata, causing gas-water two-phase flow. Furthermore, gas injection and production induce mechanical deformation in saturated rocks, leading to complex fluid-solid-gas coupling effects that influence gas flow behavior. Therefore, conducting fluid-solid-gas coupling behavior analysis of salt cavern gas storage, developing a helium seepage model applicable to layered salt rocks, and an effective method for evaluating sealing performance are of great significance for realizing large-scale helium storage.

[0005] However, existing methods for evaluating the gas tightness of salt cavern gas storage facilities are mostly based on single-phase gas seepage models, typically using modified Darcy's law to solve the seepage field, without fully considering the helium slippage effect, gas-water displacement effect, and fluid-solid-gas coupling effect. For example, the article "Tightness evaluation and countermeasures for hydrogen storage salt cavern contains various lithological interlayers" (published in *J Energy Storage*) ， (2022, Issue 50) The classical Darcy law is used to describe the seepage of helium in salt rock. The seepage field is solved based on the gas mass conservation equation, and then the sealing performance of the salt cavern cavity is evaluated. The disadvantages of this method are: (1) It does not consider the slippage effect caused by helium as a small molecule gas, which leads to a lack of accuracy in the gas leakage rate of constant permeability assessment; (2) It does not consider the engineering characteristics of saturated brine in the rock formation, and cannot describe the mechanism of gas injection and production displacing pore water, which leads to an overestimation of gas permeability.

[0006] In addition, Chen Xiangsheng et al. ("Evaluation Method of Gas Leakage in Underground Gas Storage of Multi-Layer Salt Mine", Rock and Soil Mechanics, 2018, Vol. 39, No. 1, pp. 11-20) used mathematical analysis to evaluate the gas leakage of multi-layer salt mine. The disadvantages of this method are: (1) Since it is a theoretical analysis method, it fails to consider the characteristics of the rock strata saturated with brine; (2) The mechanical deformation caused by gas injection and production is not reflected, so it cannot reveal the fluid-solid-gas coupling mechanism, which affects the accurate evaluation of the gas storage's sealing performance.

[0007] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this invention is to provide a method for evaluating the sealing performance of salt cavern gas storage based on gas-water two-phase flow. This method solves the problem that existing methods do not consider the slippage effect of small molecule gases. It also considers the slippage effect of small molecule gases and the gas-water displacement process of water-saturated rock layers. Moreover, the method of this invention provides a more accurate assessment of gas leakage.

[0009] To achieve the above objectives, this invention provides a method for evaluating the sealing performance of salt cavern gas storage facilities based on gas-water two-phase flow, the method comprising: The formulas in the fluid-solid-gas coupling theoretical model under gas injection and production conditions in saturated surrounding rock are embedded into the finite element software. The mechanical parameters and porosity parameters of the rock required for evaluating the gas-water two-phase seepage sealing are input into the finite element software, as well as the correction coefficient of the slippage effect on the gas permeability obtained by formula (9) based on the pore throat diameter of the reservoir surrounding rock. The relative permeability of the gas obtained by formulas (23) to (24) and relative permeability of pore water The mechanical parameters of the rock include: Young's modulus. Poisson's ratio Biot effective stress coefficient Solid density The porosity and permeability parameters of the rock include: the inherent permeability of the rock. Porosity aperture Breakthrough pressure value of gas intrusion into rock Displacement parameters Gas residual saturation Water residual saturation ; Based on the burial depth of the salt cavern Rock strata self-weight coefficient and hydrostatic pressure coefficient Calculate the initial formation stress hydrostatic pressure Combined with the initial pressure of the gas inside the rock Using the effective stress formula, the initial stress of the surrounding rock is obtained as follows: ; In the formula, It is the density of water. g It is gravitational acceleration. It is the initial gas saturation. It is the initial pore water saturation; Based on the initial stress of the surrounding rock, corresponding formation stress and hydrostatic pressure values ​​are applied to the top, bottom, and sides of the rock strata, respectively. Injection and production gas pressure boundaries are applied to the surface of the salt cavern cavity. Numerical simulations are then performed in the finite element software using an embedded fluid-solid-gas coupling theoretical model under injection and production conditions of saturated surrounding rock and the input parameters. The fluid-solid-gas coupling response law under injection and production conditions of the salt cavern gas storage is solved, and the gas seepage velocity at the interlayer on the cavity surface is obtained. Based on the gas permeation velocity at the interlayer on the cavity surface The cumulative gas leakage is assessed using the gas cumulative leakage model in formula (35) to verify whether the requirements for salt cavern sealing are met.

[0010] The fluid-solid-gas coupling theoretical model, which simultaneously considers helium slippage and gas-water displacement effects, includes: 1) The relationship between Knudsen number and gas pressure is: (4); In equation (4), It is a Knudsen number; It is the average path of molecule-wall collisions, defined as the pore throat diameter; It is a universal constant for ideal gases; It is the molar mass of an ideal gas; It is the temperature of the gas; It is the dynamic viscosity of the gas; It is the gas pressure inside the rock; 2) The correction for gas permeability due to the slippage effect is as follows: (9); In equation (9), It is the correction coefficient for the gas permeability due to the slippage effect; 3) The modified Darcy's law for gas seepage in saturated salt rock is: (11); In equation (11), This refers to the gas seepage velocity; It is the inherent permeability of the rock; This is due to the relative gas permeability caused by gas-water displacement; 4) The generalized Darcy's law considering gas-water displacement is: (16); In equation (16), It is the Darcy velocity of pore water; This is due to the relative permeability of pore water caused by gas-water displacement; It is the dynamic viscosity of water; It is pore water pressure; It is the density of water; g It is gravitational acceleration; 5) Establish a gas-water displacement model to describe the relationship between pressure, saturation, and seepage velocity, as follows: (17); (18); In equations (17) and (18), It is the effective saturation, which represents the effective proportion of water or gas in the pore space and reflects the change in the distribution of the two phases during the displacement process; It is capillary pressure; It is the breakthrough pressure value for gas to invade rock, that is, the minimum pressure required for gas to begin entering the pores; These are the empirical coefficients of the gas-water displacement model; 6) In gas-water two-phase flow analysis, gas saturation is expressed as: (19); In equation (19), and These are the saturation levels of pore water and gas, respectively. It is the saturation of residual gas, that is, the percentage of pore volume that cannot be displaced. 7) Considering the impact of residual water, establish the effective water saturation level. With gas saturation pore water saturation The connection between them is: (20); In equation (20), Residual water saturation, which is the percentage of pore volume that cannot be displaced; 8) Consider the changes in gas saturation and pore water saturation over time. t Changes, Establishment , Time partial derivatives and The relationship between the two phases describes the response characteristics of the two-phase fluid during the displacement process, thereby predicting the gas leakage trend. The relationship is as follows: (twenty one); (twenty two); In equations (21) and (22), It is the water storage coefficient of the rock; t Indicates time; express right t The partial derivatives; express right The derivative; 9) In gas-water two-phase flow, the relative permeability of the gas is... and relative permeability of pore water This reflects the rock's ability to conduct gas and water, and its effective saturation of pore water. They are closely related, and the relationship between them is as follows: (twenty three); (twenty four); 10) The gas mass conservation equation is: (30); In equation (30), It is porosity; It is the density of a free gas. It is Biot's effective stress coefficient; It is the volumetric strain of the surrounding rock of the gas storage facility; It is the average pore pressure after taking into account air pressure and water pressure; It is the bulk modulus of solid rock particles; 11) The mass conservation equation for pore water is: (32); 12) The momentum conservation equation is: (34); In equation (34), It is the stiffness tensor of the rock, expressed as a function of the elastic modulus and Poisson's ratio. The mechanical parameters of the rock were determined by testing. It is the strain tensor of the rock; It is a unit tensor; The model for the cumulative gas leakage is as follows: (35); In equation (35), This is the cumulative amount of gas leakage; It is the normal vector perpendicular to the surface of the interlayer; It is the gas density at room temperature and atmospheric pressure; It is the side length of the interlayer; The double integral formula represents the length of the interlayer side and time. t The points.

[0011] Preferably, the distribution range of pore throat diameter and the range of injection and production gas pressure of the rock sample are obtained, and the range of Knudsen number intervals for different pore sizes is evaluated using formula (4) to determine the gas flow regime. For flow regimes outside the continuous flow range, the gas permeability needs to be corrected. For gas flow regimes within the continuous flow range, the correction of gas permeability due to slippage effect does not need to be considered, i.e., the correction coefficient of gas permeability due to slippage effect. .

[0012] Preferably, the gas pressure inside different rocks is evaluated using formula (9) based on the distribution range of pore throat diameters in the rock samples. The correction of gas permeability by slippage effect is determined based on the injection and production gas pressure range, and the influence of slippage effect is analyzed.

[0013] Preferably, based on the pore throat diameter distribution range of the rock sample, a correction coefficient that simultaneously considers gas slippage and gas-water displacement effects is obtained according to the modified Darcy's law (11) for gas seepage in the saturated salt rock. Injection gas pressure The variation pattern was analyzed, and the effects of gas slippage and gas-water displacement on permeability under the field injection and production gas pressure were examined.

[0014] The method for evaluating the sealing performance of salt cavern gas storage facilities based on gas-water two-phase flow of the present invention solves the problem that existing methods do not consider the slippage effect caused by small molecule gases, and has the following advantages: (1) The method for evaluating the airtightness of salt cavern gas storage proposed in this invention can simulate gas seepage behavior under real working conditions, while considering the slippage effect of small molecule gases and the gas-water displacement process of saturated rock layers. Moreover, the method of this invention has the advantages of high computational efficiency, convenient parameter calibration, and accurate assessment of gas leakage. This invention can reasonably evaluate the gas airtightness of salt cavern helium storage, which has important theoretical and practical significance for promoting the development of large-scale helium storage technology.

[0015] (2) In the method of the present invention, the gas slip flow discrimination method is based on the rock pore size distribution range and Knudsen number calculation formula to determine the gas flow region (transition flow, slip flow, continuous flow) under the gas injection and production conditions.

[0016] (3) The model construction method of the present invention takes into account the gas slippage effect, the gas-water displacement process, and the mechanical deformation of the surrounding rock caused by gas injection and production on the basis of fluid-solid-gas coupling, and then establishes a fluid-solid-gas coupling theoretical model, which is used for the evaluation of the helium sealing performance of actual salt cavern gas storage. Attached Figure Description

[0017] Figure 1 This is a distribution diagram of the pore throat diameter range of the test rock sample in Application Example 1 of the present invention.

[0018] Figure 2 This is a graph showing the relationship between injection and extraction gas pressure and Knudsen number in application example 1 of the present invention.

[0019] Figure 3 This is a graph showing the relationship between the correction coefficient of the slippage effect on gas permeability and the injection and production gas pressure in Application Example 1 of the present invention.

[0020] Figure 4 This is a graph showing the relative permeability changes of gas and pore water in application example 1 of the present invention.

[0021] Figure 5 This is a graph showing the relationship between the correction coefficients for gas seepage caused by slippage and gas-water displacement and the injection and production gas pressures in Application Example 1 of this invention.

[0022] Figure 6 This is a graph showing the daily helium leakage rate under normal temperature and atmospheric pressure conditions in Application Example 1 of this invention.

[0023] Figure 7This is a graph showing the cumulative helium leakage under normal temperature and atmospheric pressure conditions in Application Example 1 of the present invention. Detailed Implementation

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] It should be noted that: Unless otherwise specified in the examples, conditions should be followed according to standard conditions or the manufacturer's recommendations. Instruments used without a specified manufacturer are all commercially available standard products.

[0026] The features mentioned in this invention can be combined arbitrarily, and all possible combinations should be considered within the scope of this specification, provided that there is no contradiction in the combination of these features. Each feature disclosed in the specification can be replaced by any alternative feature that provides the same, equivalent, or similar purpose. Therefore, unless otherwise specified, the disclosed features are merely general examples of equivalent or similar features.

[0027] This invention proposes a method for evaluating the sealing performance of salt cavern gas storage facilities based on gas-water two-phase flow. This method reflects the actual operating conditions of the salt cavern gas storage facility and calculates gas sealing performance. It also simultaneously considers the slippage of small molecule gases (including helium and hydrogen) and the gas-water displacement effect, thus providing a more accurate assessment of the storage facility's sealing performance. This invention establishes a fluid-solid-gas coupling theoretical model under water-saturated surrounding rock gas injection and production conditions. The specific construction process is as follows:

[0028] Darcy's law applies to flow in porous media (such as rock) under low-velocity seepage conditions (i.e., laminar flow). It effectively describes the relationship between gas velocity and pressure gradient. The application of Darcy's law to gas seepage is as follows: (1); In equation (1), It is the gas seepage velocity; It is the inherent permeability of the rock; It is the dynamic viscosity of the gas; It is the gas pressure inside the rock.

[0029] Tight salt reservoirs are dominated by micron- and nanopores. The transport mechanism and flow patterns of gas in the micro- and nano-scale pore throats are influenced by both pore size and mean molecular free path. To describe the transport characteristics of gas at the microscale, the Knudsen number (KKN) is used. ) is introduced to characterize different flow regimes of gas flow: (2); In equation (2), It is a Knudsen number; It is the average path of molecule-wall collisions, defined as the pore throat diameter; It is the mean free path of a gas molecule, which is the average distance a molecule travels between successive molecule-molecule collisions.

[0030] In order to obtain the expression for the Knudsen number (2) to analyze the microscopic motion characteristics of gas in porous media, according to the dynamics theory of ideal gases, the mean free path of gas molecules can be expressed as: (3); In equation (3), It is the gas pressure inside the rock; It is the dynamic viscosity of the gas; It is the universal constant for ideal gases, which is 8.314 J / mol / K; It is the molar mass of an ideal gas; It refers to the temperature of the gas.

[0031] Substituting equation (3) into equation (2), we can obtain the relationship between the Knudsen number and the gas pressure, as follows: (4); Because Darcy's law for gas flow does not account for slippage and molecular-pore wall collisions, gas flow in tight salt reservoirs undergoes transitions from continuous flow (Darcy flow) to slip flow, transitional flow, and even free molecular flow. In these flow states, molecular-pore wall collisions significantly affect gas transport, thus requiring corrections to traditional permeability calculations. For continuous flow, slippage is not a concern. Beskok and Karniadakis's formula corrects gas flow in micro- and nano-pores, with the following permeability correction coefficients: (5); In equation (5), It is the permeability of the rock after considering the gas slippage effect; It is the correction coefficient for the gas permeability due to the slippage effect; The thinning coefficient reflects the influence of pore structure or fluid; it can adjust the degree of correction for gas seepage. It decreases as the Knudsen number increases.

[0032] when When the dilution coefficient is small, it approaches 1, and gas flow mainly follows Darcy's law, with the slippage effect having a relatively small impact on gas permeability; as the dilution coefficient decreases, the gas flow becomes more efficient. As the concentration increases, the thinning coefficient gradually decreases, and the collision between gas and pore walls significantly affects the flow, leading to an increased degree of permeability correction. In the slip flow region (i.e., 0.01...), the thinning coefficient gradually decreases. When the coefficient is 0.1, the thinning coefficient reflects the influence of pore structure on gas permeation behavior by correcting for gas flow. The degree of correction is inversely proportional to the Knudsen number, and is usually approximated by the following relationship: (6); (7); Substitute equations (6) to (7) into equation (5) and ignore... The first-order and higher terms yield the correction coefficient for the slippage effect on gas permeability as follows: (8); Based on equation (8), we introduce the expression (4) for the Knudsen number, and obtain: (9); In brine-saturated salt rock reservoirs, gas-water displacement is a common phenomenon during gas seepage. It alters the sealing capacity of salt cavern gas storage by affecting the relative permeability of the gas. Due to the fluid interaction in the gas-water two-phase flow, the relative permeability between the water and gas phases varies under different pore structures and flow conditions. Therefore, considering the impact of gas-water displacement on gas flow, the gas permeability must be corrected, as follows: (10); In equation (10), It is the permeability of the rock after considering the gas-water displacement effect; This is due to the relative permeability of gas caused by gas-water displacement.

[0033] By comparing equation (1) with equations (9) to (10), and considering the gas slippage effect and gas-water displacement, the gas permeability is corrected, and the corrected Darcy's law describing gas seepage in saturated salt rocks is obtained as follows: (11); During gas injection and production in salt rock reservoirs, changes in pore water pressure are primarily driven by gas pressure, resulting in two-phase gas-water flow. Because the rock formation is saturated and the water phase is relatively continuous, the gas-water displacement does not cause drastic disturbances in the water phase. Therefore, pore water flow still conforms to laminar flow characteristics and does not enter a turbulent flow state. Under these conditions, pore water flow is controlled by the hydraulic gradient and has a linear relationship with the volumetric flow rate. Darcy's law can be used to describe the seepage behavior of pore water, as shown in the following equation: (12); In equation (12), It is the volumetric flow rate of pore water through rock; It is the cross-sectional area of ​​the pore water outlet; It is the pressure head; It is pore water pressure; It is the permeability coefficient of the rock (unit: m / s); It is the density of water; g It is gravitational acceleration.

[0034] rock permeability coefficient Its inherent penetration rate The following relationship exists: (13); In equation (13), The inherent permeability of the rock (unit: m) 2 ), It is the dynamic viscosity of water.

[0035] Since the gas-water displacement effect affects the relative permeability of pore water, and thus its effective permeability, the volumetric flow rate of pore water needs to take into account the influence of relative permeability. Therefore, Darcy's law in formula (12) is modified as follows: (14); In equation (14), This is due to the relative permeability of pore water caused by gas-water displacement.

[0036] The volumetric flow rate of pore water is related to Darcy velocity as follows: (15); In equation (15), It is the Darcy velocity of pore water.

[0037] By introducing the relationship between permeability coefficient and intrinsic permeability (13) and (15) into formula (14), we can obtain the generalized Darcy's law considering gas-water displacement, as follows: (16); Due to their tightness and complex pore-throat structure, salt rock reservoirs suffer from difficulty in completely expelling fluids from the pore-throat channels, resulting in the persistent presence of small amounts of water or gas within the rock. This characteristic influences gas-water two-phase flow behavior and forms the basis for evaluating gas tightness. As gas pressure within the storage facility increases, the gas-water displacement process becomes significant, altering the saturation distribution. To quantify this phenomenon, a gas-water displacement model needs to be established to describe the relationship between pressure, saturation, and flow velocity, as follows: (17); (18); In equations (17) to (18), It is the effective saturation, which represents the effective proportion of water or gas in the pore space and reflects the change in the distribution of the two phases during the displacement process; It is capillary pressure; It is the breakthrough pressure value for gas to invade rock, that is, the minimum pressure required for gas to begin entering the pores, which is related to the density of the rock; These are empirical coefficients of the gas-water displacement model, characterizing the nonlinear features of the displacement process. They depend on the pore-throat characteristics of the rock and can be obtained in the laboratory by testing the relative permeability curves of the rock.

[0038] In gas-water two-phase flow analysis, gas saturation represents the proportion of pore space occupied by gas, expressed as: (19); In equation (19), and These are the saturation levels of pore water and gas, respectively. It is the saturation of residual gas, that is, the percentage of pore volume of retained gas that cannot be displaced.

[0039] Further considering the impact of residual water, the effective saturation of water is established. With gas saturation pore water saturation The connections between them are as follows: (20); In equation (20), Residual water saturation is the percentage of pore volume that cannot be displaced.

[0040] The above relationships (17) to (20) reflect the dynamic equilibrium of the two-phase fluids during the gas-water displacement process, providing a basis for quantifying gas-water distribution, evaluating seepage characteristics and sealing performance.

[0041] To further analyze the dynamic evolution during the displacement process, it is necessary to consider the changes in gas saturation and pore water saturation over time. t The change, that is , These changes are closely related to capillary pressure, establishing , Time partial derivatives and The relationship between the two phases can describe the response characteristics of the two-phase fluid during the displacement process, thereby predicting the gas leakage trend. The relationship is as follows: (twenty one); (twenty two); In equations (21) to (22), It is the water storage coefficient of the rock; t Indicates time; express right t The partial derivatives; express right The derivative of .

[0042] In gas-water two-phase flow, the relative permeability of the gas and relative permeability of pore water This reflects the rock's ability to conduct gas and water, and its effective saturation of pore water. They are closely related, and their relationship is as follows: (twenty three); (twenty four); Ignoring temperature changes caused by gas injection and production, the gas-water seepage process in the surrounding rock of a salt cavern gas storage facility leads to changes in pore pressure, which in turn causes deformation of the solid framework. This process can be described using the effective stress principle: (25); In equation (25), It is the total stress. It is the effective stress of the rock, reflecting the actual stress borne by the skeleton; It is Biot's effective stress coefficient. It is the bulk modulus of rock under drainage conditions. It is the bulk modulus of solid rock particles. It primarily measures the contribution of pore pressure to skeleton deformation; It is the average pore pressure after taking into account air pressure and water pressure; This is a unit tensor. This relationship reveals how changes in pore pressure affect the stability of the surrounding rock through effective stress, providing a theoretical basis for assessing the sealing performance and mechanical response of gas storage facilities.

[0043] The effective stress in a rock medium is closely related to its stiffness properties, as shown below: (26); In equation (26), It is the stiffness tensor of the rock, which is determined by testing the mechanical parameters of the rock such as Young's modulus and Poisson's ratio; It is the strain tensor, which represents the deformation of rock under the action of external forces and pore pressure.

[0044] Based on the gas contained within the rock pores, the initial form of the gas mass conservation equation is: (27); In equation (27), Porosity is the ratio of pore space volume to the total volume of rock. It is the density of a free gas.

[0045] Density of free gas The function that changes with time is: (28); Porosity The function that changes with time is: (29); Substituting equations (20)~(22) and (28)~(29) into equation (27), we obtain the final gas mass conservation equation, as follows: (30); Equation (30) integrates the dynamic changes in gas density, porosity and gas saturation to describe the mass balance in gas-water seepage, providing a dynamic model for assessing gas leakage and sealing performance of gas storage facilities.

[0046] Based on the water content within the rock pores, the initial form of the pore water mass conservation equation is: (31); Assuming that the mass of water is incompressible, substituting equations (22) and (29) into (31) yields the final equation for the conservation of pore water mass: (32); Equation (32) reflects the dynamic equilibrium of pore water under the assumption of incompressibility. Combined with the deformation and seepage characteristics of the surrounding rock, it provides theoretical support for evaluating the gas-water distribution and sealing performance of the gas storage tank.

[0047] Based on the mass ratios of solids, liquids, and gases in the salt rock, the initial form of the momentum conservation equation is: (33); In equation (33), the average density of the solid-liquid-gas three phases is: .

[0048] Substituting the mechanical equilibrium equation (25) into equation (33), the final momentum conservation equation can be derived: (34); Equation (34) describes the mechanical equilibrium of the solid-liquid-gas three-phase medium under stress and pore pressure. Equations (30), (32), and (34) constitute the final coupled control equations, where the gas permeation velocity is... The results can be obtained from equation (11) by combining the gas permeability test results. The results can be obtained from equation (16) by combining the test results of rock permeability and relative permeability.

[0049] Example 1 A method for evaluating the airtightness of a salt cavern gas storage facility based on gas-water two-phase flow, taking the assessment of helium leakage as an example, includes the following steps: (1) Establish a fluid-solid-gas coupling theoretical model under the gas injection and production conditions of saturated surrounding rock, namely formulas (4), (9), (11), (16) ~ (24), (30), (32) and (34); (2) Obtain the rock's mechanical parameters and porosity / permeability parameters required for evaluating the gas-water two-phase seepage sealing performance. The mechanical parameters include: Young's modulus. Poisson's ratio Biot effective stress coefficient Solid density Pore ​​permeability parameters include: the inherent permeability of the rock. Porosity aperture Breakthrough pressure value of gas intrusion into rock Displacement parameters Gas residual saturation Water residual saturation Among them, through Young's modulus Compared to Poisson Obtain the stiffness tensor of the rock ; (3) Obtain the distribution range of pore throat diameter and the injection-production gas pressure range of the rock sample. Use formula (4) in the theoretical model of step (1) to evaluate the range of Knudsen number for different pore sizes, thereby determining the main gas flow regime. Flow regimes outside the continuous flow range need to be corrected for gas permeability. For gas flow regimes within the continuous flow range, there is no need to consider the correction of gas permeability by the slip effect, i.e., the correction coefficient of gas permeability by the slip effect. ; Use formula (9) in the theoretical model of step (1) to obtain the correction coefficient of the slip effect on gas permeability, so as to evaluate the correction of the helium slip effect on gas permeability; (4) Use formulas (23) to (24) in the theoretical model of step (1) to solve the relative permeability change curves of gas and pore water, and combine formulas (9), (10), and (23) to solve the correction of gas permeability by gas slippage and gas-water displacement effect; (5) Based on the burial depth of the salt cavern Rock strata self-weight coefficient and hydrostatic pressure coefficient Calculate the initial formation stress hydrostatic pressure Combined with the initial pressure of the gas inside the rock Using the effective stress formula (25), the initial stress of the surrounding rock is calculated. ,Right now: ; In the formula, It is the density of water. g It is gravitational acceleration. It is the initial gas saturation. It is the initial pore water saturation; (6) Embed the formula in the theoretical model of step (1) into the finite element software COMSOL Multiphysics (other finite element software can also be used, but it is not limited to this one, mainly for solving the constructed equations), input the mechanical and porosity parameters of the rock in step (2), and input the correction coefficient of the gas permeability obtained in step (3) and the relative permeability of gas-water in step (4) in combination with the specific pore throat diameter of the reservoir surrounding rock, as well as the correction coefficient of permeability of gas slippage and gas-water displacement effect; (7) Excavate a salt cavern cavity in an elastic rock mass of a certain size. Based on the initial stress of the surrounding rock determined in step (5), apply the corresponding formation stress value and hydrostatic pressure value to the top, bottom and side of the rock layer respectively. Apply the injection and production gas pressure boundary to the surface of the salt cavern cavity. Use the software with embedded theoretical model and parameters in step (6) to carry out numerical simulation to solve the fluid-solid-gas coupling response law of the salt cavern gas storage under 30-year injection and production conditions. Based on the gas seepage velocity at the interlayer on the surface of the cavity, evaluate the sealing performance, i.e., formula (35), assess the daily leakage rate and cumulative leakage of helium, and verify whether the requirements for the sealing performance of the salt cavern are met.

[0050] (35) In equation (35), Q This is the cumulative amount of gas leakage. n It is the normal vector perpendicular to the surface of the interlayer. It is the gas density at room temperature and atmospheric pressure. It is the side length of the interlayer. t It's time.

[0051] Application Example 1 Taking a certain salt cavern gas storage as an example, the distribution range of pore throat diameter of rock samples was obtained by mercury intrusion porosimetry. The five complete rock samples were numbered #1-25, #3-5, #6-2, #7-12 and #12-8, as shown in Figure 1. The pore size distribution range of the complete rock samples is mainly concentrated between 20 nm and 80 nm.

[0052] In this example, the periodic injection and extraction gas pressure is represented by a trigonometric function as follows: (36); In equation (36), It refers to time, in units of years. It is the periodic injection and extraction gas pressure, in MPa.

[0053] Regarding the pore size distribution range of the rock sample ( Figure 1 As shown), the relationship between Knudsen number and air pressure is output using formula (4) of this invention, as shown in the figure. Figure 2 As shown, with the gas pressure inside the rock p g Increase, Knudsen number The gradual decrease indicates a shortening of the free path of gas molecules, and a gradual shift in the flow pattern from transitional flow to slip flow to continuous flow. The injection and production gas pressure variations under field conditions range from 9 MPa to 21 MPa, representing the gas pressure inside the rock. p g The gas pressure inside the rock caused by the applied injection and production gas pressure. p g The injection-production gas pressure is lower than the production gas pressure, therefore the production-production gas pressure is used at... Figure 2 The flow pattern can be determined from the data. The gas flow pattern is mainly slip flow, so the gas slip effect needs to be considered, and Darcy's law needs to be modified.

[0054] For the pore size distribution range of the rock sample (e.g.) Figure 1 As shown), the correction coefficient for the slippage effect on gas permeability and the gas pressure inside the rock are obtained using formula (9). p g Relationships (such as) Figure 3 As shown, the correction range of the slippage effect on gas permeability can be viewed based on the injection and production gas pressure. The slippage effect is more significant at low pressure and smaller pore throat diameter scales. As the pressure increases or the pore throat diameter increases, the influence of the slippage effect gradually weakens and eventually tends to a non-slippage state.

[0055] Since the layered salt rock contains mudstone interlayers, the actual parameters of the surrounding rock of the salt cavern gas storage were obtained during the test, as shown in Table 1 and Table 2.

[0056] Table 1 Mechanical parameters of rocks

[0057] Table 2. Porosity and permeability parameters of rocks

[0058] The effective saturation is calculated using formula (18). Then, the pore water saturation is calculated using formula (20). The relative gas permeability due to gas-water displacement is obtained by using formulas (23) to (24). and relative permeability of pore water Plot the relative permeability of the output gas and relative permeability of pore water With pore water saturation Relationship curves (such as) Figure 4 (As shown), gas relative permeability It can match the experimental data well. In addition, according to the gas-water displacement formula (18) and the range of injection and production gas pressure changes, the saturation range of pore water is very small, and the resulting change in gas relative permeability is also very small, basically only increasing from 0 to 0.0001. Therefore, not considering the gas-water displacement effect will directly lead to an increase in gas permeability, affecting the accurate assessment of leakage.

[0059] Based on the gas flow equation (11) describing saturated salt rocks, i.e. Plot the correction coefficients for gas slip and gas-water displacement effects. The variation pattern of injection and production gas pressure is as follows: Figure 5 As shown, the correction factor is calculated when the injection and production gas pressure varies from 9 to 21 MPa. The change only increased from 0 to approximately 0.03. Therefore, the injection and production gas pressure did not reach the breakthrough pressure value for gas intrusion into the rock. In such cases, saturated rock formations have excellent sealing properties, which is reflected in their extremely low permeability.

[0060] Based on the geological conditions and on-site working conditions of a salt cavern gas storage facility, the depth of the cavern ranges from 1217 to 1273 m, the volume is approximately 200,000 cubic meters, and the periodic injection and production gas pressure is 9 to 21 MPa. Numerical simulations were conducted using software embedding theoretical models and parameters to determine the gas seepage velocity within the rock. The helium leakage rate of the salt cavern interlayer at the boundary of the gas storage cavity was assessed and converted into the leakage formula (35) under normal temperature and atmospheric pressure conditions, and the daily leakage rate was obtained as follows: Figure 6 As shown, the cumulative leakage amount is as follows Figure 7 As shown in the figure, it can be seen that when the injected gas pressure is less than the breakthrough pressure value for gas intrusion into the rock... At this time, the slip flow caused by the gas slip effect is the dominant flow pattern, the gas-water displacement process basically does not occur, and the leakage rate is very small, such as Figure 6 The reproduced trend; when the injection and production gas pressure exceeds the breakthrough pressure value of gas intrusion into the rock. At 7 MPa, the slippage effect has little impact on gas flow in saturated salt rocks. Capillary pressure-controlled gas-water two-phase flow is the dominant flow pattern. Helium preferentially displaces pore water through large-diameter pore throats, eventually leaking into the surrounding rock. Furthermore, once helium leaks, the cumulative leakage rate shows a continuously increasing trend. Figure 7The trend shown indicates that the cumulative helium leakage over 30 years is approximately 3%, which meets the gas sealing requirements of salt cavern gas storage facilities.

[0061] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for evaluating the sealing performance of a salt cavern gas storage facility based on gas-water two-phase flow, characterized in that, The method includes: The formulas in the fluid-solid-gas coupling theoretical model under gas injection and production conditions in saturated surrounding rock are embedded into the finite element software. The mechanical parameters and porosity parameters of the rock required for evaluating the gas-water two-phase seepage sealing are input into the finite element software, as well as the correction coefficient of the slippage effect on the gas permeability obtained by formula (9) based on the pore throat diameter of the reservoir surrounding rock. The relative permeability of the gas obtained by formulas (23) to (24) and relative permeability of pore water The mechanical parameters of the rock include: Young's modulus. Poisson's ratio Biot effective stress coefficient Solid density The porosity and permeability parameters of the rock include: the inherent permeability of the rock. Porosity Aperture Breakthrough pressure value of gas intrusion into rock Displacement parameters Gas residual saturation Water residual saturation ; Based on the burial depth of the salt cavern Rock strata self-weight coefficient and hydrostatic pressure coefficient Calculate the initial formation stress hydrostatic pressure The initial pressure of the gas inside the rock Using the effective stress formula, the initial stress of the surrounding rock is obtained as follows: ； In the formula, It is the density of water. g It is gravitational acceleration. It is the initial gas saturation. It is the initial pore water saturation; Based on the initial stress of the surrounding rock, corresponding formation stress and hydrostatic pressure values ​​are applied to the top, bottom, and sides of the rock strata, respectively. Injection and production gas pressure boundaries are applied to the surface of the salt cavern cavity. Numerical simulations are then performed in the finite element software using an embedded fluid-solid-gas coupling theoretical model under injection and production conditions of saturated surrounding rock and the input parameters. The fluid-solid-gas coupling response law under injection and production conditions of the salt cavern gas storage is solved, and the gas seepage velocity at the interlayer on the cavity surface is obtained. Based on the gas permeation velocity at the interlayer on the cavity surface The cumulative gas leakage rate is evaluated using the gas cumulative leakage rate model of formula (35) to verify whether the requirements for salt cavern sealing are met. The fluid-solid-gas coupling theoretical model, which simultaneously considers helium slippage and gas-water displacement effects, includes: 1) The relationship between Knudsen number and gas pressure is: (4); In equation (4), It is a Knudsen number; It is the average path of molecule-wall collisions, defined as the pore throat diameter; It is a universal constant for ideal gases; It is the molar mass of an ideal gas; It is the temperature of the gas; It is the dynamic viscosity of the gas; It is the gas pressure inside the rock; 2) The correction for gas permeability due to the slippage effect is as follows: (9); In equation (9), It is the correction factor for the gas permeability due to the slippage effect; 3) The modified Darcy's law for gas seepage in saturated salt rock is: (11); In equation (11), This refers to the gas seepage velocity; It is the inherent permeability of the rock; This is due to the relative gas permeability caused by gas-water displacement; 4) The generalized Darcy's law considering gas-water displacement is: (16); In equation (16), It is the Darcy velocity of pore water; This is due to the relative permeability of pore water caused by gas-water displacement; It is the dynamic viscosity of water; It is pore water pressure; It is the density of water; g It is gravitational acceleration; 5) Establish a gas-water displacement model to describe the relationship between pressure, saturation, and seepage velocity, as follows: (17); （18）； In equations (17) and (18), It is the effective saturation, which represents the effective proportion of water or gas in the pore space and reflects the change in the distribution of the two phases during the displacement process; It is capillary pressure; It is the breakthrough pressure value for gas intrusion into rock, that is, the minimum pressure required for gas to begin entering the pores; These are the empirical coefficients of the gas-water displacement model; 6) In gas-water two-phase flow analysis, gas saturation is expressed as: (19); In equation (19), and These are the saturation levels of pore water and gas, respectively. It is the saturation of residual gas, that is, the percentage of pore volume that cannot be displaced. 7) Considering the impact of residual water, establish the effective water saturation level. With gas saturation pore water saturation The connection between them is: (20); In equation (20), Residual water saturation, which is the percentage of pore volume that cannot be displaced; 8) Consider the changes in gas saturation and pore water saturation over time. t Changes, Establishment , Time partial derivatives and The relationship between the two phases describes the response characteristics of the two-phase fluid during the displacement process, thereby predicting the gas leakage trend. The relationship is as follows: （21）； （22）； In equations (21) and (22), It is the water storage coefficient of the rock; t Indicates time; express right t The partial derivatives; express right The derivative; 9) In gas-water two-phase flow, the relative permeability of the gas is... and relative permeability of pore water This reflects the rock's ability to conduct gas and water, and its effective saturation of pore water. They are closely related, and the relationship between them is as follows: （23）； （24）； 10) The gas mass conservation equation is: （30）； In equation (30), It is porosity; It is the density of a free gas. It is Biot's effective stress coefficient; It is the volumetric strain of the surrounding rock of the gas storage facility; It is the average pore pressure after taking into account air pressure and water pressure; It is the bulk modulus of solid rock particles; 11) The mass conservation equation for pore water is: （32）； 12) The momentum conservation equation is: （34）； In equation (34), It is the stiffness tensor of the rock, expressed as a function of the elastic modulus and Poisson's ratio. The mechanical parameters of the rock were determined by testing. It is the strain tensor of the rock; It is a unit tensor; The model for the cumulative gas leakage is as follows: (35); In equation (35), This is the cumulative amount of gas leakage; It is the normal vector perpendicular to the surface of the interlayer; It is the gas density at room temperature and atmospheric pressure; It is the side length of the interlayer; The double integral formula represents the length of the interlayer side and time. t The points.

2. The method for evaluating the sealing performance of salt cavern gas storage based on gas-water two-phase flow according to claim 1, characterized in that, Obtain the pore throat diameter distribution range and the injection and production gas pressure range of the rock sample. Use formula (4) to evaluate the Knudsen number range of different pore sizes to determine the gas flow regime. For flow regimes outside the continuous flow range, the gas permeability needs to be corrected. For gas flow regimes within the continuous flow range, there is no need to consider the correction of gas permeability by the slip effect, i.e., the correction coefficient of gas permeability by the slip effect. .

3. The method for evaluating the sealing performance of salt cavern gas storage based on gas-water two-phase flow according to claim 1, characterized in that, Based on the distribution range of pore throat diameters in the rock samples, the gas pressure inside different rocks is evaluated using formula (9). The correction of gas permeability by slippage effect is determined based on the injection and production gas pressure range, and the influence of slippage effect is analyzed.

4. The method for evaluating the sealing performance of salt cavern gas storage based on gas-water two-phase flow according to claim 1, characterized in that, Based on the pore throat diameter distribution range of the rock sample, and according to the modified Darcy's law (11) for gas seepage in the saturated salt rock, a correction coefficient that simultaneously considers gas slippage and gas-water displacement effects is obtained. Injection gas pressure The variation pattern was analyzed, and the effects of gas slippage and gas-water displacement on permeability under the field injection and production gas pressure were examined.

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