Computing method for leakage rate of lining of pressure hydrogen energy storage cavern

Abstract

The invention discloses a method for calculating the leakage rate of a lining of a pressure hydrogen energy storage cavern. The method comprises the steps that a cavern heat-solid-permeability coupling model is established; stress, temperature and hydrogen concentration distribution are obtained through numerical simulation; deducing a simplified hydrogen leakage formula of the lining of the pressure hydrogen energy storage cavern on the basis of a hydrogen concentration distribution rule obtained by numerical analysis; coupling the simplified formula of the hydrogen leakage of the lining of the pressure hydrogen energy storage cavern into the heat-solid-seepage mathematical model and the numerical model, and calculating the long-term accumulated leakage rate based on the analytical formula of the hydrogen leakage of the lining of the pressure hydrogen energy storage cavern. According to the calculation method, the coupling driving effect of various physical gradients on hydrogen permeation and the two-way effect of'chamber leakage-in-hole gas storage 'are considered, the unstable hydrogen permeation behavior of the steel lining under the periodic heat-solid-permeation coupling effect is accurately represented, and the long-term accumulated leakage rate can be calculated; and a more accurate reference is provided for leakage risk assessment of the underground hydrogen storage.

Description

Technical Field

[0001] The present invention relates to the technical field of air tightness assessment of underground hydrogen storage caverns, and in particular to a method for calculating leakage of a lining of a compressed hydrogen energy storage cavern. Background Art

[0002] Compressed hydrogen energy storage (CHS) has become a key solution for supporting renewable energy consumption due to its large storage capacity, long discharge duration, and minimal environmental impact. This technology utilizes surplus electricity during off-peak hours to compress and store hydrogen in a gas storage facility. During peak electricity demand, the hydrogen is released to drive turbines for power generation, ensuring a stable power supply and the conversion of renewable energy.

[0003] Lined cavern structures consist of a steel liner, concrete lining, and surrounding rock. The steel liner seals the gas, while the lining transfers the load to the surrounding rock, which then bears the load. This structure offers advantages such as high gas purity, high turnover rate, and strong transport capacity, making it an ideal carrier for underground hydrogen storage. However, hydrogen, an active gas with the smallest molecular size and extremely high diffusivity and permeability, can cause leakage through the steel liner, posing a significant technical challenge to the airtightness of underground hydrogen storage caverns.

[0004] The current assessment of hydrogen storage facility air tightness mainly relies on two types of models: (1) Macro defect model: adopts porous media seepage theory (for hydrogen leakage in surrounding rock / concrete) or small hole outflow model (for leakage from structural cracks), ignoring hydrogen leakage caused by hydrogen permeation effect of steel lining under crack-free conditions; (2) Microscopic hydrogen permeation model: Based on Fick's diffusion law, only the driving force of concentration gradient is considered, and the synergistic driving effect of temperature gradient and stress gradient on hydrogen permeation in steel lining is not integrated.

[0005] Under the complex operating conditions of compressed hydrogen energy storage steel-lined caverns with high pressure, high temperature, long life, and multiple cycles, the existing hydrogen storage facility airtightness assessment model has fundamental flaws: a) Misunderstanding of leakage mechanism: Leakage is attributed to macroscopic defects, ignoring the penetration mechanism of hydrogen atoms through the metal lattice. This leads to an underestimation of the actual hydrogen leakage under crack-free conditions. b) Lack of driving factors: The hydrogen permeation equation driven by the coupling of multiple physical gradients has not been established, making it impossible to characterize the unsteady-state hydrogen permeation behavior under the coupling of periodic changes in stress, temperature, and concentration in the compressed hydrogen storage cavern; c) Failure under dynamic operating conditions: The time-varying characteristics of stress, temperature and concentration inside and outside the cavern during nearly 10,000 charging and discharging cycles were not taken into account, as well as the impact of hydrogen leakage in the cavern on the gas in the cavern under long-term operation (i.e. the two-way effect of "cavern leakage-cavern gas storage"). Summary of the Invention

[0006] The present invention aims to propose a calculation method for hydrogen leakage in compressed hydrogen energy storage caverns, taking into account the coupled driving effect of multiple physical gradients on hydrogen permeation and the bidirectional effect of "cave leakage-gas storage in the cavern", accurately characterizing the non-steady-state hydrogen permeation behavior of the steel lining under the periodic thermal-solid-permeation coupling effect, and thus calculating the long-term cumulative leakage rate, providing a more accurate reference for the leakage risk assessment of underground hydrogen storage reservoirs.

[0007] To achieve the above object, the present invention proposes a method for calculating the leakage of the lining of a compressed hydrogen energy storage cavern, the method comprising: S1, build a mathematical model. Based on the non-ideal hydrogen thermodynamic equations in the cave, the solid thermoelastic mechanics equations and the multi-physics gradient driven steel lining hydrogen permeation equation, a heat-solid-permeation coupled mathematical model of the compressed hydrogen energy storage cavern is constructed. The mutual coupling relationship of each physical field is shown in Figure 4 .

[0008] The expression of the non-ideal hydrogen thermodynamic equation in the hole is: Where, V is the volume of the cavern, in m 3 ; ρ is the gas density in the cave at any time, in kg / m 3 ; Indicates the mass flow rate of filling and discharging, in kg / s; is the hydrogen leakage rate during the operation cycle, in kg / s; C v is the specific heat of gas at constant volume, C p is the specific heat of gas at constant pressure, in J / (kg·K); Z is the compressibility coefficient of high-pressure hydrogen; p is the gas pressure, in Pa; T is the gas temperature in the cave, T i is the charging gas temperature, in K; R is the gas constant, unit is J / (kg·K); is the heat exchange rate between the gas in the cave and the cave wall, in W; F i (t) is the dimensionless compressed gas storage chamber inflation state function, F e (t) is the dimensionless compressed gas storage chamber degassing state function, such as Figure 5 shown.

[0009] The solid thermoelastic mechanics equation of the cave is: Considering the thermal expansion effect of the cavern, the thermal strain is expressed as: Where σ is the stress tensor, σ0 is the initial stress, in Pa; ε is the strain tensor; ε0 is the initial strain; ε T is thermal strain; T 0 is the initial temperature of the cave; F v is the body force vector, in N; u is the displacement vector, in m; α is the thermal expansion coefficient, in 1 / K; C is the fourth-order elastic tensor; “:” is the tensor double dot product; is the gradient operator.

[0010] The heat transfer equation is: Where, is the convective heat transfer rate between the hydrogen in the cave and the cave wall, in W; h c is the convection heat transfer coefficient of the cave wall, in W / m 2 K; A c is the heat exchange area of ​​the tunnel wall, in m 2 ; T RW is the wall temperature, in K; is the density of each layer structure; is the constant pressure specific heat of each layer structure; is the temperature of each layer structure; is the thermal conductivity of each layer structure; m =1, 2, 3 represent the sealing layer, concrete lining and surrounding rock respectively.

[0011] The multi-physics gradient driven steel liner hydrogen permeation equation is: Where, s is the hydrogen solubility in the steel lining, in ppm; is the hydrogen activity, dimensionless, , where c is the hydrogen concentration; D is the hydrogen diffusion coefficient, in cm 2 / s; k TTo reflect the coefficient of the driving effect of temperature gradient on hydrogen diffusion, ; k p To reflect the coefficient of the driving effect of stress gradient on hydrogen diffusion, ; , T is the thermodynamic temperature, T z is absolute zero, unit is K; σ h is the hydrostatic stress, in MPa.

[0012] S2, based on the thermal-solid-permeability coupling mathematical model and engineering data such as the cavern geometry parameters and material parameters, a thermal-solid-permeability coupling numerical model of the compressed hydrogen energy storage cavern was established; S3, conduct numerical simulation and calculate the state parameters of each cycle, including: S31, numerical simulation is performed through the thermal-solid-permeation coupling numerical model to obtain the temperature and stress of the steel lining in this cycle; S32, substituting the steel lining temperature and stress obtained in S31 into the steel lining hydrogen permeation formula driven by multiple physical gradients to obtain the hydrogen concentration distribution of the steel lining in this period; S33, substituting the steel lining temperature, stress and hydrogen concentration obtained in steps S31 and S32 into the analytical formula for hydrogen leakage of the compressed hydrogen storage cavern lining to obtain the cumulative hydrogen leakage rate of the cavern steel lining during this cycle.

[0013] The analytical formula for hydrogen leakage in the compressed hydrogen storage cavern lining is: Where, is the hydrogen leakage rate of the compressed hydrogen storage cavern, in kg / s; L is the length of the cave, , r 0 is the radius of the cavern section; J is the hydrogen diffusion flux; J x and J y They are x Direction and y The hydrogen diffusion flux in the direction; dS is the permeable surface, that is, the area element of the inner surface of the steel lining.

[0014] Furthermore, the hydrogen leakage rate of the subsequent cycles (referring to the non-first cycle, i.e. the second cycle and subsequent cycles) described in the above thermal-solid-permeation coupling model is , calculated by the simplified formula of hydrogen leakage in the compressed hydrogen storage cavern lining: Where, C int Indicates the hydrogen concentration on the inner wall of the steel lining;C out Indicates the hydrogen concentration of the outer wall of the steel lining. Since hydrogen penetrates the steel lining in atomic form, it will recombine into hydrogen molecules once it comes into contact with air. C out =0; d is the thickness of the steel lining; A c is the surface area of ​​the outer wall of the steel lining, which is approximately the surface area of ​​the inner wall of the steel lining.

[0015] Furthermore, the hydrogen storage cavern is a horizontal tunnel-type compressed hydrogen energy storage cavern with a circular cross-section.

[0016] Compared with the prior art, the present invention has the following advantages: (1) Accurately predict long-term leakage. This model breaks through the limitations of traditional hydrogen leakage calculation models that ignore hydrogen permeation effects. It considers the multi-physics field coupling driving effect, integrates the thermal-solid-permeation multi-field coupling and periodic time-varying dynamic conditions, and overcomes the difficulty of accurately quantifying leakage under long-term charging and discharging cycles, providing a reliable tool for the design, operation and maintenance of hydrogen storage facilities.

[0017] (2) Significant cost reduction and efficiency improvement. Based on the accurate prediction of hydrogen leakage, the seal selection and operation and maintenance strategy are optimized, effectively reducing the initial construction cost, reducing the long-term hydrogen leakage loss, and improving the system operation efficiency.

[0018] (3) Supporting safety assessment of hydrogen storage facilities: By calculating the cumulative leakage over a long period of time (e.g., 30 years of service), a calculation tool is provided for leakage quantification, seal selection, and operation and maintenance strategy formulation of lined hydrogen storage caverns, thereby ensuring the long-term operational safety and reliability of large-scale compressed hydrogen energy storage systems and effectively supporting the large-scale and safe development of the hydrogen energy industry.

[0019] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flow chart of a method for calculating leakage of a compressed hydrogen energy storage cavern lining according to an embodiment of the present invention; Figure 2 A schematic cross-sectional view of a circular-section tunnel-type compressed hydrogen energy storage cavern according to one embodiment of the present invention; Figure 3 Schematic diagram of hydrogen permeation process in steel lining; Figure 4 This is the multi-physics coupling diagram of the constructed thermal-solid-permeation coupling model; Figure 5 Schematic diagram of the hydrogen mass rate in the compressed hydrogen storage cave during a typical operation cycle; Figure 6 A thermal-solid-permeability coupling numerical model established based on a compressed air energy storage cavern in Hanwula Wind Field, Inner Mongolia, according to one embodiment of the present invention; Figure 7 The daily hydrogen leakage rate curve of the 4130X steel-lined cavern is calculated using the analytical formula for hydrogen leakage in the compressed hydrogen storage cavern lining; Figure 8 The hydrogen leakage rate variation curve of the cavern steel lining is based on the consideration of only the concentration gradient on the driving force of hydrogen penetration into the steel lining. Figure 9 The hydrogen leakage rate variation curve of the cavern steel lining is based on the consideration of only the stress gradient driving force for hydrogen penetration into the steel lining. Figure 10 The hydrogen leakage rate variation curve of the cavern steel lining is based on the consideration of only the temperature gradient driving force for hydrogen penetration into the steel lining. Figure 11 The proportion of hydrogen leakage contributed by concentration gradient, stress gradient and temperature gradient; Figure 12 The cloud map of hydrogen concentration distribution in the steel lining and the local magnified map at the same time; Figure 13 To compare the cavern pressure curves with those without considering the bidirectional effects of "cavern leakage-cavern gas storage"; Figure 14 To compare the temperature curves in the cavern with those without considering the bidirectional effects of "cavern leakage-cavern gas storage"; Figure 15 To compare the daily hydrogen leakage rate curve of the cavern with and without considering the bidirectional influence of "cavern leakage-in-cave gas storage". DETAILED DESCRIPTION

[0021] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0022] The following describes a method for calculating the leakage of the lining of a compressed hydrogen energy storage cavern proposed in an embodiment of the present invention with reference to the accompanying drawings.

[0023] like Figure 2As shown, the underground compressed hydrogen energy storage cavern is a lined rock cavern structure, which is composed of a steel lining, a concrete lining and surrounding rock. The steel lining seals the gas, the lining transfers the load to the surrounding rock, and the surrounding rock bears the load. This structure has the advantages of high gas storage purity, high turnover rate and strong transportation capacity, making it an ideal carrier for underground hydrogen storage, especially suitable for the reuse of a large number of abandoned mines in my country during the energy transition period. However, as hydrogen is an active gas with the smallest molecular size, the strongest diffusivity and permeability, hydrogen leakage caused by hydrogen permeation in the steel lining poses a major technical challenge to the airtightness of underground compressed hydrogen energy storage caverns. The hydrogen permeation process in the steel lining is as follows: Figure 3 As shown in the figure, the hydrogen permeation process can be summarized as follows: hydrogen molecules are adsorbed on the surface of steel, then dissolve into hydrogen atoms, the dissolved hydrogen enters the interior of the steel, then permeates the steel, and finally leaves the outer wall of the steel and escapes into the atmosphere.

[0024] Figure 1 The present invention is a flowchart of a method for calculating the leakage of a compressed hydrogen energy storage cavern lining according to an embodiment of the present invention.

[0025] like Figure 1 As shown, the method for calculating the leakage of the compressed hydrogen energy storage cavern lining according to an embodiment of the present invention may include the following steps: S1, based on the non-ideal hydrogen thermodynamic equation, solid thermoelasticity equation, heat transfer equation and multi-physics gradient driven steel lining hydrogen permeation equation, a heat-solid-permeation coupled mathematical model of the compressed hydrogen storage cavern is constructed. The coupling relationship between the various physical fields is shown in Figure 4 .

[0026] According to one embodiment of the present invention, in step S1, the non-ideal gas thermodynamic equation includes the mass conservation equation of hydrogen in the cave, the energy conservation equation of hydrogen in the cave, and the gas state equation of hydrogen in the cave, wherein: The expression of the conservation equation of hydrogen mass in the cave is: (1) The expression of the conservation equation of hydrogen energy in the cave is: (2) The gas state equation of hydrogen in the cave is expressed as: (3) Where, V is the volume of the cavern, in m 3 ; ρ is the gas density in the cave at any time, in kg / m 3 ; Indicates the mass flow rate of filling and discharging, in kg / s; is the hydrogen leakage rate during the operation cycle, in kg / s; Cv is the specific heat of gas at constant volume, C p is the specific heat of gas at constant pressure, in J / (kg·K); Z is the hydrogen compression coefficient; p is the gas pressure, in Pa; T is the gas temperature in the cave, T i is the charging gas temperature, in K; R is the gas constant, unit is J / (kg·K); is the heat exchange rate between the gas in the cave and the cave wall, in W; F i (t) is the dimensionless compressed gas energy storage chamber inflation state function; F e (t) is the dimensionless compressed gas storage chamber degassing state function. Figure 5 As shown, CD is the ratio of the deflation mass flow rate to the inflation mass flow rate, t 1 is the end time of the inflation phase, t 2 is the end time of the first storage phase, t 3 is the end time of the deflation phase, t p The end time of an operation cycle. A typical compressed hydrogen energy storage operation cycle consists of the filling phase (0~ t 1) The first storage stage ( t 1~ t 2) Deflation stage ( t 2~ t 3) and the restoring phase ( t 3~ t p ) is composed of, and the temperature and pressure in the cave will return to their initial states at the end of each operation cycle.

[0027] In order to fully reflect the non-ideal gas characteristics of high-temperature and high-pressure hydrogen inside the compressed hydrogen storage cavern, the high-pressure hydrogen compressibility coefficient equation measured by NIST is used to describe the deviation of hydrogen under actual working conditions from the ideal gas assumption: (4).

[0028] According to one embodiment of the present invention, in step S1, the following formula is used to describe the thermoelastic mechanics equation of the cavern: (5) (6) (7) (8) Where σ is the stress tensor, σ0 is the initial stress, in Pa; ε is the strain tensor; ε0 is the initial strain; ε T is thermal strain; T 0 is the initial temperature of the cave; F v is the body force vector, in N; u is the displacement vector, in m; α is the thermal expansion coefficient, in 1 / K; C is the fourth-order elastic tensor; “:” is the tensor double dot product; is the gradient operator.

[0029] Specifically, considering the convection heat transfer between the hydrogen in the cave and the cave wall, the solid-liquid heat transfer equation between the hydrogen in the cave and the cave wall is expressed as: (9) Where, is the convective heat transfer rate between the hydrogen in the cave and the cave wall, in W; h c is the convection heat transfer coefficient of the cave wall, in W / m 2 K; A c is the heat exchange area of ​​the tunnel wall, in m 2 ; T RW is the wall temperature in K.

[0030] Assuming that the materials of each layer are in good contact and thermal resistance is ignored, the solid heat conduction equation between the steel lining, concrete lining and surrounding rock is: (10) In the formula, the subscript m =1, 2, 3 represent sealing layer, concrete lining and surrounding rock respectively, is the density of each layer structure, is the constant pressure specific heat of each layer structure, is the temperature of each layer structure, is the thermal conductivity of each layer structure.

[0031] The boundary conditions of formula (10) can be expressed as: (11) Where, T 0 is the initial temperature of the cave, in K; S i Represents the inner wall of the cave; S0 represents the outer boundary of the surrounding rock.

[0032] At the initial moment, the temperature of each layer of the cave structure is T 0, that is, the initial condition can be expressed as: (12).

[0033] Specifically, the stress and temperature distribution inside and outside the periodic tunnel can be calculated by combining formulas (1) to (12), which prepares for the subsequent calculation of the stress, temperature, and concentration distribution inside and outside the steel lining.

[0034] According to one embodiment of the present invention, in step S1, a multi-physical gradient driven steel liner hydrogen permeation equation is used, which considers the driving force of the temperature gradient, stress gradient and concentration gradient inside and outside the cavern on the hydrogen permeation of the steel liner. The multi-physical gradient driven steel liner hydrogen permeation equation is expressed as: (13) Where, s is the hydrogen solubility in the steel lining, in ppm; is the hydrogen activity, dimensionless, ,in, c is the hydrogen concentration; D is the hydrogen diffusion coefficient, in cm 2 / s; k T To reflect the coefficient of the driving effect of temperature gradient on hydrogen diffusion, ; k p To reflect the coefficient of the driving effect of stress gradient on hydrogen diffusion, ; , T is the thermodynamic temperature, T z is absolute zero, unit is K; σ h is the hydrostatic stress, in MPa.

[0035] Specifically, the penetration of hydrogen atoms in the steel lining satisfies the law of conservation of mass, that is, the change in concentration within the control volume is equal to the hydrogen diffusion flux passing through J The vector sum of : (14) Where, c is the hydrogen concentration in ppm; t is the penetration time, in s; is the gradient operator.

[0036] There is a certain difference between the permeation of non-ideal hydrogen and the permeation of ideal gas. Under non-ideal conditions, only hydrogen atoms that enter the interior of the steel will undergo hydrogen permeation, while the remaining hydrogen atoms are adsorbed on the surface of the steel and do not participate in the permeation. In order to accurately describe the permeation behavior of non-ideal hydrogen in the compressed hydrogen storage cavern, the hydrogen activity is introduced. This dimensionless variable is used to describe the hydrogen concentration under actual working conditions. Hydrogen activity is the ratio of hydrogen concentration to hydrogen solubility, that is, ,in s is the hydrogen solubility, and the unit is ppm.

[0037] Traditional metal mass transfer theory uses Fick's law to describe hydrogen permeation in steel, which assumes that the concentration gradient is the only driving force for hydrogen permeation: (15) Where, D is the hydrogen diffusion coefficient, in cm 2 / s; is the Laplace operator, .

[0038] However, the steel lining of the compressed hydrogen storage cavern is not only subjected to the high temperature, high pressure and high concentration of hydrogen in the cavern, but is also affected by the geothermal field and geostress field of the rock surrounding the cavern. Hydrogen atoms in the steel may permeate hydrogen under concentration gradient, stress gradient and temperature gradient. In order to fully consider the above factors, the temperature gradient term and stress gradient term are introduced into the traditional Fick law that only considers the driving force of concentration gradient to consider the joint driving effect of concentration gradient, temperature gradient and stress gradient on hydrogen diffusion, so as to more accurately predict the hydrogen permeation behavior of the compressed hydrogen storage cavern. Comprehensively consider the diffusion flux of various physical gradients J It can be expressed as: (16) Where, D is the hydrogen diffusion coefficient, in cm 2 / s;k T To reflect the coefficient of the driving effect of temperature gradient on hydrogen diffusion, ;k p To reflect the coefficient of the driving effect of stress gradient on hydrogen diffusion, ; , T is the thermodynamic temperature, T z is absolute zero, unit is K; σ h is the hydrostatic stress, in MPa.

[0039] Diffusion fluxes of various physical gradients will be considered J Substituting the hydrogen atomic mass conservation equation into the steel lining hydrogen permeation equation considering multiple physical gradients is obtained: (17).

[0040] S2, based on the thermal-solid-permeability coupling mathematical model, establish a thermal-solid-permeability coupling numerical model of the compressed hydrogen energy storage cavern.

[0041] Specifically, considering that the length of the cavern is much larger than the cross-sectional size, the mechanical response of the cavern is simplified to a plane strain problem, and a two-dimensional model of the cavern cross section is established. In combination with the symmetry of the cavern, only 1 / 2 of the structure is taken for calculation. The established two-dimensional numerical model is as follows: Figure 6As shown. Taking a compressed gas energy storage steel-lined cavern in Hanwula Wind Farm in Inner Mongolia, which was transformed from an abandoned coal mine, as the prototype, the main body of the cavern is the radius r 0 = 8m horizontal circular tunnel chamber, design volume V =3×10 5 m 3 The cavern is excavated to a depth of 100m. After excavation, a 0.5m thick concrete lining is applied, and a 0.1mm thick 4130X steel plate is installed as a sealing layer. 4130X steel is a commonly used steel grade for hydrogen storage systems as specified in the current Chinese hydrogen system specification (GB / T297292022). It has excellent anti-permeability and mechanical properties. Therefore, this embodiment uses a 0.1m thick 4130X steel lining as a sealing layer. Its hydrogen permeability coefficient is D 4130X =1.03×10 6 cm 2 / s, hydrogen solubility s =1 ppm. The initial pressure of the compressed gas energy storage liner cavern is p 0=4.5MPa, initial temperature T 0=310K, specific operating parameters and material parameters are shown in Table 1.

[0042] Table 1 Parameters used in numerical simulation S3, conduct numerical simulation and calculate the state parameters of each cycle, including: S31, numerical simulation is performed through the thermal-solid-permeation coupling numerical model (the hydrogen leakage rate in the first cycle is 0, and the hydrogen leakage rate in subsequent cycles is calculated by the simplified formula for hydrogen leakage of the compressed hydrogen storage cavern lining) to obtain the temperature, stress and hydrogen concentration distribution of the steel lining in this cycle.

[0043] S32, substituting the result obtained in step S31 into the steel liner hydrogen permeation equation driven by multi-physics gradient to obtain the hydrogen concentration distribution of the steel liner in this period.

[0044] S33, substituting the steel lining temperature, stress and hydrogen concentration obtained in steps S31 and S32 into the analytical formula for hydrogen leakage of the compressed hydrogen storage cavern lining to obtain the cumulative hydrogen leakage rate of the cavern steel lining during this cycle.

[0045] The analytical formula for hydrogen leakage in the compressed hydrogen storage cavern lining is: (18) Where, is the hydrogen leakage rate of the compressed hydrogen storage cavern, in kg / s; L is the length of the cave, , r 0 is the radius of the cavern section; J is the hydrogen diffusion flux;J x and J y They are x Direction and y The hydrogen diffusion flux in the direction; dS is the permeable surface, that is, the area element of the inner surface of the steel lining.

[0046] Specifically, to evaluate the sealing performance of compressed hydrogen storage caverns, the daily gas leakage rate is defined as ξ Leakage rate and inflation rate The ratio of: (19) The daily leakage rate curve of 4130X steel lining drawn based on formula (19) is as follows: Figure 7 As shown in the figure, the peak value of daily hydrogen leakage rate of 4130X steel lining is 8.83×10 -4 %, which is the leakage rate obtained by fully considering the driving force of the three physical gradients on hydrogen penetration of the steel lining. In order to further analyze the influence of each gradient on hydrogen leakage, the hydrogen leakage rate under a single gradient was calculated, such as Figures 8 to 10 The contribution of different dynamic gradients to the total leakage rate is shown in Figure 11 As shown in the figure, the concentration gradient contributes 99.5% of the hydrogen leakage, while the temperature gradient and stress gradient contribute 0.3% and 0.2% of the hydrogen leakage, respectively, which indicates that the hydrogen concentration gradient is the key factor dominating the hydrogen leakage of the steel lining.

[0047] The analytical formula for hydrogen leakage in the lining of the compressed hydrogen energy storage cavern proposed in this invention comprehensively considers the driving forces of various physical gradients on hydrogen penetration, improves the calculation accuracy of the cavern leakage, and thus improves the leakage calculation theory of underground hydrogen storage reservoirs. However, although the analytical formula for hydrogen leakage in the steel lining of the compressed hydrogen energy storage cavern accurately and comprehensively considers all hydrogen penetration driving forces, it contains complex integrals and partial differentials, which is computationally intensive and also introduces x and y Directly substituting the two geometric variables into the hydrogen mass conservation equation and energy conservation equation in the cave for numerical calculation cannot converge. The only way is to solve the temperature, stress and hydrogen concentration inside and outside the cave as a post-processing step to solve the hydrogen leakage amount at a certain moment.

[0048] In order to improve convergence, simplify calculation amount and reduce dependence on geometric structure, the present invention proposes a simplified formula for hydrogen leakage of compressed hydrogen storage cavern lining, so as to substitute it into the thermal-solid-permeability coupling model to solve the long-term cumulative hydrogen leakage rate of compressed hydrogen storage cavern lining.

[0049] By analyzing the numerical simulation results, we can obtain the hydrogen permeation laws of the steel lining of two circular cross-section tunnel caverns: (1) The hydrogen leakage caused by the concentration gradient is dominant, and the hydrogen leakage caused by the stress gradient and temperature gradient can be ignored. Figure 11 As shown in the figure; (2) The hydrogen permeation of the steel lining is dominated by radial diffusion, and the radial hydrogen concentration presents an isotropic linear distribution, as shown in the figure. Figure 12 shown.

[0050] According to rule (1), hydrogen leakage caused by concentration gradient is dominant, so hydrogen leakage caused by stress gradient and temperature gradient can be ignored. Then formula (18) can be simplified to: (20) According to law (2), radial diffusion in the steel lining of a circular tunnel chamber ( r The annular hydrogen diffusion in the circular tunnel chamber can be ignored because the hydrogen concentration at each point on the steel lining is isotropic and linearly distributed. Therefore, it can be assumed that the concentration at points on the steel lining at the same distance from the inner wall is the same. The integral of formula (18) can be simplified to: (twenty one) Where, C int Indicates the hydrogen concentration on the inner wall of the steel lining; C out Indicates the hydrogen concentration of the outer wall of the steel lining. Since hydrogen penetrates the steel lining in atomic form, it will recombine into hydrogen molecules once it comes into contact with air. C out =0; d is the thickness of the steel lining; A c is the surface area of ​​the outer wall of the steel lining. Since the thickness of the steel lining is much smaller than the surface area, the surface area of ​​the inner wall can be approximated.

[0051] In order to consider the influence of the cavern leakage in the previous cycle on the pressure, temperature and hydrogen concentration of the cavern gas storage in the next cycle under long-term operation conditions (i.e., the two-way effect of "cavern leakage-cavern gas storage"), the simplified formula for hydrogen leakage in the compressed hydrogen storage cavern lining, i.e., formula (21), is substituted into the cavern hydrogen mass conservation equation and energy conservation equation in the thermal-solid-permeation coupling mathematical model constructed in step S1, so as to correct the cavern stress, temperature and hydrogen concentration in subsequent cycles (i.e., the second cycle and subsequent cycles), thereby accurately calculating the cumulative hydrogen leakage rate under long-term operation conditions.

[0052] The cavern pressure, cavern temperature and cavern leakage rate after considering the dual effect of "cave leakage-cave gas storage" are compared with the results without considering this effect (such as Figures 13 to 15(as shown in Figure 2 ), it was found that after considering the dual effect of "cavern leakage and in-cave gas storage," the recalculated air pressure decreased by 3%, the air temperature decreased by 1%, and the leakage rate decreased by 5%. This indicates that accounting for the impact of leakage on gas storage can, to a certain extent, reduce the thermodynamic fluctuations of hydrogen in the cave and cavern leakage. This finding proves that not only does the concentration, temperature, and pressure of hydrogen in the cave drive hydrogen permeation, but hydrogen leakage itself also has a significant impact on the gas state in the cave. Therefore, it is necessary to consider the dual effect of "cavern leakage and in-cave gas storage" in the numerical model to accurately calculate the long-term cumulative hydrogen leakage rate.

[0053] The simplified formula for hydrogen leakage in the compressed hydrogen storage cavern lining proposed in this invention is similar in form to the "constant concentration" hydrogen diffusion formula used in traditional metal mass transfer studies, which assumes that the concentration on both sides of the steel specimen is constant and the hydrogen permeation in the steel is considered as a one-dimensional steady-state permeation. However, the difference is that the simplified formula proposed in this invention introduces the hydrogen concentration of the inner wall of the steel lining. C int (This variable changes dynamically with time, temperature, and pressure) to describe the non-steady-state permeation in the steel lining, more accurately reflecting the actual hydrogen permeation process in the steel lining under dynamic conditions of cyclic hydrogen charging and discharging. Furthermore, the simplified formula proposed in this paper fully considers the dual interaction of "cavern leakage and in-cavern gas storage," effectively improving the accuracy of calculating the cumulative hydrogen leakage rate of the cavern under long-term operating conditions, helping to reduce the additional costs caused by cavern leakage.

[0054] According to one embodiment of the present invention, the compressed hydrogen energy storage cavern is a horizontal tunnel-type compressed hydrogen energy storage cavern with a circular cross-section.

[0055] According to one embodiment of the present invention, the method of the above embodiment is used to evaluate the dynamic hydrogen leakage risk of the steel lining under nearly 10,000 hydrogen charging and discharging cycles during its service life (eg, 30 years).

[0056] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0057] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0058] In the present invention, unless otherwise specified or limited, the terms "installed," "connected," "connect," "fixed," etc. should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integration; mechanical connection, electrical connection; direct connection, or indirect connection through an intermediate medium; internal communication between two components, or interaction between two components, unless otherwise specified. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0059] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the leakage of the lining of a compressed hydrogen energy storage cavern, characterized in that: The following steps are involved: S1, based on the non-ideal hydrogen thermodynamic equation, solid thermoelasticity equation, heat transfer equation and multi-physics gradient driven steel lining hydrogen permeation equation, a thermal-solid-permeation coupled mathematical model of the compressed hydrogen storage cavern is constructed; S2, based on the thermal-solid-permeability coupling mathematical model, establish a thermal-solid-permeability coupling numerical model of the compressed hydrogen energy storage cavern; S3, conduct numerical simulation and calculate the state parameters of each cycle, including: S31, numerical simulation is performed through the thermal-solid-permeation coupling numerical model to obtain the temperature and stress of the steel lining in this cycle; S32, substituting the steel lining temperature and stress obtained in step S31 into the steel lining hydrogen permeation formula driven by multi-physics gradient to obtain the hydrogen concentration distribution of the steel lining in this period; S33, substituting the steel lining temperature, stress and hydrogen concentration obtained in steps S31 and S32 into the analytical formula for hydrogen leakage of the compressed hydrogen storage cavern lining to obtain the cumulative hydrogen leakage rate of the cavern steel lining during this cycle.

2. The method for calculating the leakage of the compressed hydrogen energy storage cavern lining according to claim 1 is characterized in that: In step S1, a multi-physical gradient driven steel lining hydrogen permeation equation is used, which considers the driving force of the temperature gradient, stress gradient and concentration gradient inside and outside the cavern on the hydrogen permeation of the steel lining. The multi-physical gradient driven steel lining hydrogen permeation equation is expressed as: Where, s is the hydrogen solubility in the steel lining, in ppm; is the hydrogen activity, dimensionless, , where c is the hydrogen concentration; D is the hydrogen diffusion coefficient, in cm 2 / s; k T To reflect the coefficient of the driving effect of temperature gradient on hydrogen diffusion, ; k p To reflect the coefficient of the driving effect of stress gradient on hydrogen diffusion, ; ,in T and T z are thermodynamic temperature and absolute zero, respectively, in K; σ h is the hydrostatic stress, in MPa.

3. The method for calculating the leakage of the compressed hydrogen energy storage cavern lining according to claim 1 is characterized in that: In step S3, the analytical formula for hydrogen leakage in the compressed hydrogen energy storage cavern lining is: Where, is the hydrogen leakage rate of the compressed hydrogen energy storage cavern, in kg / s; L is the length of the cave, , where r0 is the inner diameter of the cavern, in m; J is the hydrogen diffusion flux; J x and J y The x direction and y Directional hydrogen diffusion flux; s is the hydrogen solubility in the steel lining, in ppm; is the hydrogen activity, ,in c is the hydrogen concentration in ppm; D is the hydrogen diffusion coefficient, in cm 2 / s; k T To reflect the coefficient of the driving effect of temperature gradient on hydrogen diffusion, ; k p To reflect the coefficient of the driving effect of stress gradient on hydrogen diffusion, ; ,in T and T z are thermodynamic temperature and absolute zero, respectively, in K; σ h is the hydrostatic stress, in MPa; dS is the penetration surface, that is, the area of ​​the inner surface of the steel lining.

4. The method for calculating the leakage of the compressed hydrogen energy storage cavern lining according to claim 1 is characterized in that: In step S3, the simplified formula for hydrogen leakage in the compressed hydrogen energy storage cavern lining is expressed as: Where, C int Indicates the hydrogen concentration on the inner wall of the steel lining; C out Indicates the hydrogen concentration of the outer wall of the steel lining. Since hydrogen penetrates the steel lining in atomic form, it will recombine into hydrogen molecules once it comes into contact with air. C out =0; d is the thickness of the steel lining; A c is the surface area of ​​the outer wall of the steel lining, which is approximately the surface area of ​​the inner wall of the steel lining.

5. The method for calculating the leakage of the compressed hydrogen energy storage cavern lining according to any one of claims 1 to 4, characterized in that: The compressed hydrogen energy storage cavern is a horizontal tunnel-type compressed hydrogen energy storage cavern with a circular cross-section.

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