A salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage

Abstract

The application discloses a salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage, and belongs to the technical field of salt cavern gas storage, and the method comprises the following steps: embedding a formula in a fluid-solid-gas coupling theory model under water-saturated surrounding rock injection and production conditions into finite element software, inputting mechanical parameters and porosity and permeability parameters of rock, and a correction coefficient of gas permeability, gas relative permeability and pore water relative permeability of a slippage effect; based on the initial stress of the surrounding rock, corresponding stratum stress values and hydrostatic pressure values are respectively applied to the top, bottom and side of the rock stratum, an injection and production pressure boundary is applied to the surface of the salt cavern cavity, numerical simulation is carried out by using the fluid-solid-gas coupling theory model and parameters, gas seepage velocity is obtained by solving, and gas cumulative leakage is evaluated in combination with a gas cumulative leakage model. The method simulates the gas seepage behavior under real working conditions, considers the slippage effect of small molecule gas and the gas-water displacement process of water-saturated rock stratum, and is more accurate in gas leakage evaluation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of salt cavern gas storage, and relates to a salt cavern gas storage sealing evaluation method, in particular to a salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage. BACKGROUND

[0002] Salt rock is a salt deposit dissolved in seawater or lake water and formed under the action of crustal movement and geological changes, and has the characteristics of good solubility and fragility. A salt cavern is a cavity formed after the salt in the underground salt rock layer is dissolved and mined out. Salt caverns are considered to be good media for storing small-molecule gases such as helium due to their excellent sealing performance, good creep behavior and self-healing ability (Research Progress on Mechanical Properties of Bedded Salt Rock, Advances in Mechanics, 2008, No. 04, pp. 484-494).

[0003] Due to the constraints of technological development, China has not yet realized the salt cavern storage of helium, mainly because the bedded salt rock salt layer is thin, the impurity content is high, the interlayer deformation is not coordinated, and the permeability is high, which makes the storage of helium face more challenges. Moreover, the diameter of a helium molecule is 0.26 nm, which is about 30% smaller than the diameter of a methane molecule (0.38 nm), and under the same operating pressure, the permeation and diffusion of helium are stronger, which also puts higher requirements on the sealing performance of the salt cavern gas storage.

[0004] The diameter of a helium molecule is extremely small, and its molecular free path is on the same order of magnitude as the pore diameter of salt rock. In dense rocks, gas slip effects are obvious (Identifying 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 usually formed using water-soluble technology, under normal circumstances, the bedded salt rock is in a brine-saturated state (Experimental Study on Acoustic Emission Characteristics of Salt Rock After Brine Immersion, Rock and Soil Mechanics, 2013, Vol. 34, No. 07, pp. 1937-1942), and combined with the influence of formation hydrostatic pressure, periodic gas injection and production will displace the pore water in the rock formation, causing gas-water two-phase seepage. In addition, gas injection and production will cause mechanical deformation of the saturated rock, and then complex fluid-solid-gas coupling effects will occur, affecting the seepage behavior of the gas. Therefore, it is of great significance to realize large-scale storage of helium to carry out analysis of the fluid-solid-gas coupling behavior of salt cavern gas storage, develop a helium seepage model suitable for bedded salt rock, and develop an effective sealing evaluation method.

[0005] However, the existing evaluation methods of the gas tightness of salt cavern gas storage are mostly based on the single-phase gas seepage model, usually use the modified Darcy's law to solve the seepage field, and do not fully consider the slip effect of helium, the gas-water displacement effect and the flow-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 ， In 2022, No. 50) uses the classical Darcy's law to describe the seepage of helium in salt rock, solves the seepage field based on the gas mass conservation equation, and then evaluates the tightness of the salt cavern cavity. The disadvantages of this method are: (1) the slip effect of helium as a small molecule diameter gas is not considered, resulting in the lack of accuracy of the constant permeability evaluation of the gas leakage amount; (2) the engineering properties of the brine-saturated rock formation are not considered, and the mechanism of displacing pore water by injecting gas is not described, resulting in a high gas permeability.

[0006] In addition, Chen Xiangsheng et al. (Multi-interlayer salt mine underground gas storage gas leakage evaluation method, Rock and Soil Mechanics, 2018, Vol. 39, No. 01, 11-20) use a mathematical analysis method to evaluate the gas leakage of multi-interlayer salt mines. The disadvantages of this method are: (1) since it is a theoretical analysis method, the properties of the brine-saturated rock formation are not considered; (2) the mechanical deformation caused by gas injection is not reflected, so the flow-solid-gas coupling mechanism cannot be revealed, affecting the accurate evaluation of the tightness of the gas storage.

[0007] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0008] The purpose of the present application is to provide a salt cavern gas storage tightness evaluation method based on gas-water two-phase seepage, which solves the problem that the existing method does not consider the slip effect of small molecule gas, and at the same time considers the slip effect of small molecule gas and the gas-water displacement process of saturated rock formation, and the gas leakage amount evaluation of the present application is more accurate.

[0009] In order to achieve the above purpose, the present application provides a salt cavern gas storage tightness evaluation method based on gas-water two-phase seepage, which comprises:

[0010] Embedding the formula in the finite element software under the condition of water-saturated surrounding rock gas injection and production, inputting the mechanical parameters and porosity and permeability parameters of the rock required for gas-water two-phase seepage sealing evaluation in the finite element software, and the correction coefficient of the slippage effect on gas permeability obtained by formula (9) based on the pore throat diameter of the surrounding rock of the reservoir , the gas relative permeability obtained by formula (23)~(24) , and the pore water relative permeability ; wherein 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: intrinsic permeability of the rock , porosity , pore size , breakthrough pressure value of gas invading the rock , displacement parameter , gas residual saturation , water residual saturation ;

[0011] Based on the depth of the salt cavern cavity , the rock self-weight coefficient and the hydrostatic pressure coefficient , the initial formation stress , the hydrostatic pressure are calculated, combined with the initial gas pressure inside the rock and the effective stress formula, the initial stress of the surrounding rock is obtained as: ;

[0012] In the formula, is the density of water, g is the acceleration of gravity, is the initial gas saturation, is the initial pore water saturation;

[0013] Based on the initial stress of the surrounding rock, the corresponding formation stress value and hydrostatic pressure value are applied to the top, bottom and side of the rock respectively, and the gas injection and production pressure boundary is applied to the surface of the salt cavern cavity. Using the embedded flow-solid-gas coupling theory model under the condition of water-saturated surrounding rock gas injection and production and the input parameters, numerical simulation is carried out in the finite element software to solve the flow-solid-gas coupling response law under the condition of salt cavern gas storage injection and production, and the gas seepage velocity at the interlayer of the cavity surface is obtained The gas cumulative leakage amount is evaluated by the gas cumulative leakage amount model of formula (35), and it is verified whether the salt cavern sealing requirement is met.

[0014] The flow-solid-gas coupling theory model simultaneously considers helium slip and gas-water displacement effects, and includes:

[0015] 1) The relationship between Knudsen number and gas pressure is: (4);

[0016] In formula (4), Kn is the Knudsen number; is the average path of molecule-wall collision, defined as the pore throat diameter; R is the universal constant of ideal gas; M is the molar mass of ideal gas; T is the gas temperature; is the dynamic viscosity of the gas; P is the gas pressure inside the rock;

[0017] 2) The correction of gas permeability due to slip effect is: (9);

[0018] In formula (9), is the correction coefficient of gas permeability due to slip effect;

[0019] 3) The modified Darcy law of gas seepage in saturated salt rock is: (11);

[0020] In formula (11), is the gas seepage velocity; is the inherent permeability of the rock; is the relative permeability of the gas due to gas-water displacement;

[0021] 4) The generalized Darcy law considering gas-water displacement effect is: (16);

[0022] In formula (16), is the Darcy velocity of pore water; is the relative permeability of pore water due to gas-water displacement; is the dynamic viscosity of water; is the pore water pressure; is the density of water; g is the acceleration of gravity;

[0023] 5) Establish a gas-water displacement model to describe the relationship between pressure, saturation and seepage velocity, for: (17);

[0024] (18);

[0025] In formula (17), (18), is the effective saturation, which represents the effective proportion of water or gas in the pore space, reflecting the change of two-phase distribution in the displacement process; is the capillary pressure; is the breakthrough pressure value of gas invading rock, that is, the minimum pressure required for gas to enter the pore; is the empirical coefficient of gas-water displacement model;

[0026] 6) In the analysis of gas-water two-phase seepage, the gas saturation is expressed as: (19);

[0027] In formula (19), and are the saturations of pore water and gas, respectively; is the residual gas saturation, that is, the percentage of residual gas occupying the pore volume that cannot be displaced;

[0028] 7) Considering the influence of residual water, the effective saturation of water is established, and the relationship between , the gas saturation, , the pore water saturation, is as follows: (20);

[0029] In formula (20), is the residual water saturation, that is, the percentage of residual water occupying the pore volume that cannot be displaced;

[0030] 8) Considering the changes of gas saturation and pore water saturation with time t , the relationship between the time partial derivative of , and is established to describe the response characteristics of two-phase fluid in the displacement process, so as to predict the gas leakage trend, which is as follows: (21);

[0031] (22);

[0032] In formula (21), (22), is the water storage coefficient of rock; t represents time; denotes the partial derivative of t ; denotes the derivative of ;

[0033] 9) In gas-water two-phase seepage, the gas relative permeability and the relative permeability of pore water reflect the flow conductivity of the rock to gas and water, and are closely related to the effective saturation of pore water , and the relationship between them is: (23);

[0034] (24);

[0035] 10) The gas mass conservation equation is: (30);

[0036] In equation (30), is the porosity; is the density of free gas; is the coefficient of Biot effective stress; is the volumetric strain of the surrounding rock of the gas storage; is the average pore pressure considering gas pressure and water pressure; is the bulk modulus of rock solid particles;

[0037] 11) The pore water mass conservation equation is: (32);

[0038] 12) The momentum conservation equation is: (34);

[0039] In equation (34), is the stiffness tensor of the rock, which is determined by the mechanical parameters test of the rock such as elastic modulus and Poisson's ratio; is the strain tensor of the rock; is the unit tensor;

[0040] The cumulative gas leakage model is: (35);

[0041] In equation (35), is the cumulative gas leakage; is the normal vector of the vertical interlayer surface; is the gas density at normal temperature and atmospheric pressure;​ is the length of the interlayer edge; represents the double integral formula along the interlayer edge and time t .

[0042] Preferably, the pore throat diameter distribution range of the rock sample and the on-site injection and production gas pressure interval are obtained, the Knudsen number interval range of different pore diameters is evaluated by formula (4), so as to judge the gas flow state, and the gas permeability needs to be modified for the flow state not in the continuous flow range; for the case that the gas flow state is in the continuous flow range, the modification of the gas permeability by the slippage effect does not need to be considered, that is, the modification coefficient of the gas permeability by the slippage effect .

[0043] Preferably, for the pore throat diameter distribution range of the rock sample, the modification of the gas permeability by the slippage effect under different gas pressures inside the rock is evaluated by formula (9), and the modification coefficient interval of the gas permeability by the slippage effect is obtained according to the injection and production gas pressure interval, so as to analyze the influence of the slippage effect.

[0044] Preferably, for the pore throat diameter distribution range of the rock sample, the modified Darcy law formula (11) of the saturated salt rock gas seepage is used to obtain the modified coefficient considering the gas slippage and gas-water displacement effect with the change rule of the injection and production gas pressure , so as to analyze the influence of the gas slippage and gas-water displacement effect on the permeability under the on-site injection and production gas pressure.

[0045] The salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage of the application solves the problem that the existing method does not consider the slippage effect caused by small molecule gas and has the following advantages:

[0046] (1) The salt cavern gas storage sealing evaluation method provided by the application can simulate the gas seepage behavior under real working conditions, simultaneously consider the slippage effect of small molecule gas and the gas-water displacement process of saturated rock layer, and has the advantages of high calculation efficiency, convenient parameter calibration and accurate evaluation of gas leakage amount. The application can reasonably evaluate the gas sealing property of the salt cavern stratum helium storage, and has important theoretical and practical significance for promoting the development of large-scale helium storage technology;

[0047] (2) In the method of the application, the gas slippage flow discrimination method discriminates the gas flow region (transition flow, slippage flow, continuous flow) under the injection and production gas condition according to the rock pore size distribution range and the Knudsen number calculation formula.

[0048] ​(3) The model construction method of the present application considers the gas slippage effect, gas-water displacement process and mechanical deformation of surrounding rock caused by gas injection and production on the basis of fluid-solid-gas coupling, and further establishes a fluid-solid-gas coupling theoretical model, and is used for helium gas sealing evaluation of an actual salt cavern gas storage. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 A pore throat diameter range distribution graph of the rock sample tested in application example 1 of the present application.

[0050] Figure 2 A graph of the relationship between injection and production gas pressure and Knudsen number in application example 1 of the present application.

[0051] Figure 3 A graph of the relationship between the correction coefficient of gas permeability of the slippage effect and injection and production gas pressure in application example 1 of the present application.

[0052] Figure 4 A graph of the change of relative permeability of gas and pore water in application example 1 of the present application.

[0053] Figure 5 A graph of the relationship between the correction coefficient of gas seepage of slippage and gas-water displacement and injection and production gas pressure in application example 1 of the present application.

[0054] Figure 6 A graph of the helium gas daily leakage rate under normal temperature and atmospheric pressure conditions in application example 1 of the present application.

[0055] Figure 7 A graph of the cumulative helium gas leakage amount under normal temperature and atmospheric pressure conditions in application example 1 of the present application. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the present application will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0057] It should be noted that, in the embodiments, the specific conditions not specified are carried out according to the conventional conditions or the conditions recommended by the manufacturer. The instruments used are all conventional products that can be obtained by market purchase.

[0058] The features mentioned in the present application can be combined arbitrarily, as long as the combination of these features does not exist contradictions, and all possible combinations should be considered as the scope disclosed in the present specification. Each feature disclosed in the specification can be replaced by any alternative feature that provides the same, equivalent or similar purpose. Therefore, unless specifically stated, the disclosed features are only general examples of equivalent or similar features.

[0059] The application provides a salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage, which can reflect the real working condition of the salt cavern gas storage, calculate the gas sealing, simultaneously consider the slip of small molecule gas (including helium, hydrogen and the like) and gas-water displacement effect, and more accurately evaluate the sealing of the gas storage.

[0060] Darcy's law is applicable to the flow of porous medium (such as rock) under low-speed seepage condition (i.e., the flow of fluid is laminar flow), can effectively depict the relationship between the flow rate of gas and the pressure gradient, and the Darcy flow law is applied to the gas seepage as follows: (1);

[0061] In formula (1), is the gas seepage velocity; is the inherent permeability of rock; is the dynamic viscosity of gas; is the gas pressure in the rock.

[0062] The dense salt rock reservoir is mainly micron and nanometer pores, and the migration mechanism and flow rule of gas in the micron and nanometer pore throat are jointly affected by the pore diameter and the average molecular free path. To describe the migration characteristics of gas at the microscale, Knudsen number (Knudsen Number, (2);

[0063] In formula (2), is the Knudsen number; is the average path of molecule-wall collision, defined as the pore throat diameter; is the average free path of gas molecules, that is, the average distance of a molecule to migrate between continuous molecule-molecule collisions.

[0064] In order to obtain the expression (2) of the Knudsen number to analyze the micro motion characteristics of gas in the pore medium, according to the kinetic theory of ideal gas, the average free path of gas molecules can be expressed as: (3);

[0065] In formula (3), is the gas pressure in the rock; is the dynamic viscosity of gas; is the universal constant of ideal gas, 8.314 J / mol / K; is the molar mass of ideal gas; is the gas temperature.

[0066] Substituting equation (3) into equation (2), the relationship between Knudsen number and gas pressure can be obtained as follows: (4);

[0067] Since the Darcy's law for gas seepage does not consider the slip effect and the collision between molecules and pore walls, for the dense salt rock reservoir, the gas flow will experience a transition from continuous flow (Darcy flow) to slip flow, transition flow or even free molecular flow, in which the collision between molecules and pore walls has a significant impact on gas transmission, thus the traditional permeability calculation needs to be corrected, and the slip effect does not need to be considered for continuous flow. The formula proposed by Beskok and Karniadakis corrects the gas seepage in micro-nano pores, and the permeability correction coefficient is as follows: (5);

[0068] In equation (5), is the permeability of the rock considering the gas slip effect; is the correction coefficient of the gas permeability by the slip effect; is the rarefaction coefficient, which reflects the influence of pore structure or fluid, and it can adjust the correction degree of gas seepage. The rarefaction coefficient decreases with the increase of Knudsen number.

[0069] When is small, the rarefaction coefficient is close to 1, the gas flow mainly follows Darcy's law, and the influence of the slip effect on the gas permeability is small; with the increase of , the rarefaction coefficient gradually decreases, the collision between gas and pore wall significantly affects the flow, leading to an increase in the correction degree of permeability. In the slip flow region (i.e. 0.01 0.1), the rarefaction coefficient reflects the influence of pore structure on the gas seepage behavior through the correction of gas flow, and the correction degree is inversely proportional to the Knudsen number, and there is usually an approximate relationship as follows: (6);

[0070] (7);

[0071] Substituting equations (6)-(7) into equation (5) and ignoring the first order and above of , the correction coefficient of the gas permeability by the slip effect is obtained as follows: (8);

[0072] Based on equation (8), the expression (4) of Knudsen number is introduced, and the following equation can be obtained: (9);

[0073] In the salt rock reservoir saturated with brine, gas-water displacement is a common phenomenon in gas seepage process, which will change the sealing capacity of salt cavern gas storage by affecting the relative permeability of gas. Due to the fluid interaction in gas-water two-phase flow, the relative permeability between water phase and gas phase will change under different pore structures and flow conditions. Therefore, considering the influence of gas-water displacement effect on gas flow, the gas permeability must be corrected as follows: (10);

[0074] In formula (10), is the permeability of rock considering gas-water displacement effect; is the relative permeability of gas due to gas-water displacement.

[0075] By comparing formula (1) with formula (9)~(10), the gas permeability is corrected on the basis of considering gas slippage effect and gas-water displacement effect, and the modified Darcy's law describing gas seepage in saturated salt rock can be obtained as follows: (11);

[0076] In the process of gas injection and production in salt rock reservoir, the change of pore water pressure is mainly driven by gas pressure to form gas-water two-phase seepage. Since the rock layer is in a saturated state, the water phase is relatively continuous, and the gas-water displacement effect will not cause severe disturbance to the water phase, so the pore water flow still conforms to the characteristics of laminar flow and will not enter the turbulent flow state. Under this condition, the flow of pore water is controlled by the hydraulic gradient and has a linear relationship with the volume flow rate. Darcy's law can be used to describe the seepage behavior of pore water, and the equation is as follows: (12);

[0077] In formula (12), is the volume flow rate of pore water through the rock; is the cross-sectional area of the pore water outlet; is the pressure head; is the pore water pressure; is the permeability coefficient of rock (unit: m / s); is the density of water; g is the acceleration of gravity.

[0078] Permeability coefficient of rock and its inherent permeability have the following relationship: (13);

[0079] In formula (13), is the intrinsic permeability of rock (unit: m 2 ), is the dynamic viscosity of water.

[0080] Since the gas-water displacement will affect the relative permeability of pore water, and then affect the effective permeability of pore water, the volumetric flow rate of pore water needs to consider the influence of relative permeability. Therefore, the Darcy law of formula (12) is modified as follows: (14);

[0081] In formula (14), is the relative permeability of pore water due to gas-water displacement.

[0082] The volumetric flow rate of pore water and Darcy velocity have the following relationship: (15);

[0083] In formula (15), is the Darcy velocity of pore water.

[0084] Introducing the permeability coefficient-intrinsic permeability relationship formula (13) and formula (15) in formula (14), the generalized Darcy law considering gas-water displacement is obtained, as follows: (16);

[0085] Due to the compactness and complex pore-throat structure of salt rock reservoir, it is difficult for the fluid in the pore-throat channel to be completely discharged, and a small amount of water or gas is always left inside the rock. This feature affects the gas-water two-phase seepage behavior and is the basis for gas sealing evaluation. With the increase of gas pressure in the gas storage, the gas-water displacement process becomes significant, changing the saturation distribution. To quantify this phenomenon, a gas-water displacement model needs to be established to describe the relationship between pressure, saturation and seepage velocity, as follows: (17);

[0086] (18);

[0087] In formulas (17)-(18), is the effective saturation, indicating the effective proportion of water or gas in the pore space, reflecting the change of two-phase distribution in the displacement process; is the capillary pressure; is the breakthrough pressure value of gas invading rock, that is, the minimum pressure required for gas to enter the pore, which is related to the compactness of the rock; is the empirical coefficient of the gas-water displacement model, representing the nonlinear characteristics of the displacement process, which depends on the pore-throat channel characteristics of the rock, and can be obtained by testing the relative permeability curve of the rock in the laboratory.

[0088] In the analysis of gas-water two-phase flow, gas saturation represents the proportion of gas occupying the pore space, expressed as: (19);

[0089] In formula (19), and are the saturations of pore water and gas, respectively; is the residual gas saturation, i.e., the percentage of pore volume occupied by trapped gas that cannot be displaced.

[0090] Further considering the effect of residual water, the effective saturation of water is established, and the relationship between gas saturation , pore water saturation is as follows: (20);

[0091] In formula (20), is the residual water saturation, i.e., the percentage of pore volume occupied by trapped water that cannot be displaced.

[0092] The above relationships (17)~(20) reflect the dynamic balance of two-phase fluids during gas-water displacement, providing a basis for quantifying gas-water distribution, evaluating seepage characteristics, and assessing sealing properties.

[0093] To further analyze the dynamic evolution during displacement, the changes of gas saturation and pore water saturation with time t need to be considered, i.e., , These changes are closely related to capillary pressure, and the relationship between the time partial derivatives of , and can describe the response characteristics of two-phase fluids during displacement, thereby predicting the gas leakage trend, which is as follows: (21);

[0094] (22);

[0095] In formulas (21)~(22), is the water storage coefficient of the rock; t represents time; represents the partial derivative of with respect to t ; represents the derivative of with respect to .

[0096] In gas-water two-phase seepage, gas relative permeability and pore water relative permeability reflect the flow conductivity of rock to gas and water, and are closely related to the effective saturation of pore water , and their relationship is as follows: (23);

[0097] (24);

[0098] Ignoring the temperature change caused by gas injection and production, the gas-water seepage process in the surrounding rock of the salt cavern gas storage will lead to changes in pore pressure, which in turn will cause deformation of the solid skeleton. This process can be described by the effective stress principle: (25);

[0099] In equation (25), is the total stress, is the effective stress of the rock, reflecting the actual stress borne by the skeleton; is the Biot effective stress coefficient, is the bulk modulus of the rock under drainage conditions, is the bulk modulus of the solid particles of the rock, mainly measures the contribution of pore pressure to skeleton deformation; is the average pore pressure considering gas pressure and water pressure; is the 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 evaluating the sealing performance of the gas storage and the mechanical response of the surrounding rock.

[0100] The effective stress of rock media is closely related to its stiffness properties, which can be expressed as: (26);

[0101] In equation (26), is the stiffness tensor of the rock, which is determined by the mechanical parameters of the rock such as Young's modulus and Poisson's ratio; is the strain tensor, representing the deformation of the rock under the action of external force and pore pressure.

[0102] According to the gas contained in the pores of the rock, the initial form of the gas mass conservation equation is: (27);

[0103] In equation (27), is the porosity, representing the ratio of pore space volume to total rock volume; is the density of free gas.

[0104] The density of free gas The function of time is: (28);

[0105] Porosity The function of time is: (29);

[0106] Substitute equations (20)-(22), (28)-(29) into equation (27), the final gas mass conservation equation can be obtained as follows: (30);

[0107] Equation (30) integrates the dynamic changes of gas density, porosity and gas saturation, and describes the mass balance in gas-water seepage, which provides a dynamic model for evaluating gas seepage and sealing performance of gas storage.

[0108] According to the water contained in the rock pores, the initial form of the pore water mass conservation equation is: (31);

[0109] Substitute equations (22) and (29) into equation (31) under the assumption that the mass of water is incompressible, the final pore water mass conservation equation can be derived as follows: (32);

[0110] Equation (32) reflects the dynamic balance of pore water under the assumption of incompressibility, and combines the deformation and seepage characteristics of surrounding rock, which provides theoretical support for evaluating gas-water distribution and sealing performance of gas storage.

[0111] According to the mass proportion of solid, liquid and gas in salt rock, the initial form of the momentum conservation equation is: (33);

[0112] In equation (33), the average density of solid-liquid-gas three-phase is .

[0113] Substitute the mechanical equilibrium equation (25) into equation (33), the final momentum conservation equation can be derived as follows: (34);

[0114] Equation (34) describes the mechanical equilibrium of solid-liquid-gas three-phase medium under the action of stress and pore pressure. Equations (30), (32) and (34) constitute the final coupling control equation, in which the gas seepage velocity can be obtained from equation (11) combined with the gas permeability test results, The permeability and relative permeability test results of the rock can be obtained from equation (16).

[0115] Embodiment 1

[0116] A salt cavern gas storage sealing evaluation method based on gas-water two-phase seepage, taking the evaluation of helium leakage as an example, the method comprises the following steps:

[0117] (1) Establish a fluid-solid-gas coupling theoretical model under the conditions of saturated surrounding rock gas injection and production, namely equations (4), (9), (11), (16)-(24), (30), (32) and (34);

[0118] (2) Obtain the mechanical parameters and porosity and permeability parameters of the rock required for gas-water two-phase seepage sealing evaluation, the mechanical parameters include: Young's modulus , Poisson's ratio , Biot effective stress coefficient , solid density , the porosity and permeability parameters include: intrinsic permeability of the rock, porosity , pore size , breakthrough pressure value of gas invading rock , displacement parameter , gas residual saturation , water residual saturation ; wherein, the stiffness tensor of the rock is obtained by Young's modulus and Poisson's ratio ;

[0119] (3) Obtain the pore throat diameter distribution range of the rock sample and the on-site injection and production pressure interval, use equation (4) in the theoretical model of step (1) to evaluate the Knudsen number interval range of different pore sizes, to judge the main gas flow state, the flow state not in the continuous flow range needs to be modified for the gas permeability, for the case that the gas flow state is in the continuous flow range, the modification coefficient of the gas permeability by the slip effect does not need to be considered; use equation (9) in the theoretical model of step (1) to obtain the modification coefficient of the gas permeability by the slip effect, to evaluate the modification of the gas permeability by the helium slip effect;

[0120] (4) Use equations (23)-(24) in the theoretical model of step (1) to solve the relative permeability change curves of the gas and the pore water, combine equations (9), (10), (23) to solve the modification of the gas permeability by the gas slip and gas-water displacement effect;

[0121] (5) Based on the depth of the salt cavern cavity , the rock self-weight coefficient and hydrostatic pressure coefficient , calculate initial formation stress , hydrostatic pressure , combined with the initial pressure of the gas inside the rock and effective stress formula (25), calculate the initial stress of the surrounding rock , that is: ;

[0122] In the formula, is the density of water, g is the acceleration of gravity, is the initial gas saturation, is the initial pore water saturation;

[0123] (6) Embed the formula in the theoretical model in step (1) into the finite element software COMSOL Multiphysics (other finite element software can also be used, and is not limited to this, mainly for solving the constructed equation), input the mechanical and porosity parameters of the rock in step (2), combined with the specific pore throat diameter of the reservoir surrounding rock, input the correction coefficient of the slippage effect on gas permeability obtained in step (3) and the gas-water relative permeability in step (4), as well as the correction coefficient of the permeability of the gas slippage and gas-water displacement effect;

[0124] (7) Excavate a salt cavern in an elastic rock mass of a certain size, based on the initial stress of the surrounding rock calculated and determined in step (5), apply the corresponding formation stress value and hydrostatic pressure value on the top, bottom and side of the rock layer, and apply the injection and production gas pressure boundary on the surface of the salt cavern. Use the software embedded with the theoretical model and parameters in step (6) to carry out numerical simulation, solve the fluid-solid-gas coupling response law under the conditions of 30 years of injection and production of gas in the salt cavern gas storage, evaluate the sealing performance based on the gas seepage velocity at the interlayer on the surface of the cavity, that is, formula (35), evaluate the daily leakage rate and cumulative leakage of helium, and verify whether it meets the requirements of salt cavern sealing.

[0125] (35)

[0126] In formula (35), Q is the cumulative leakage of gas, n is the normal vector perpendicular to the surface of the interlayer, is the gas density at normal temperature and atmospheric pressure, is the side length of the interlayer, t is time.

[0127] Application Example 1

[0128] 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.

[0129] In this example, the periodic injection and extraction gas pressure is represented by a trigonometric function as follows: (36);

[0130] In equation (36), It refers to time, in units of years. It is the periodic injection and extraction gas pressure, in MPa.

[0131] 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.

[0132] 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.

[0133] 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.

[0134] Table 1 Mechanical parameters of rocks

[0135]

[0136] Table 2. Porosity and permeability parameters of rocks

[0137]

[0138] 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.

[0139] 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.

[0140] 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 7 The 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.

[0141] 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 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 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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