Semi-theoretical estimation method and system for storage capacity and inflation and deflation rate of compressed air energy and gas storage

Abstract

The invention belongs to the crossing field of the compressed air energy storage (CAES) technology and underground gas storage engineering, and discloses a semi-theoretical estimation method and system for the storage capacity and the inflation and deflation rate of a compressed air energy storage and gas storage storage.The method comprises the steps that the thermodynamic theory serves as the core, and the mass conservation law and the energy conservation law are combined; constructing a unified calculation framework covering three types of scenes of a heat insulation cavern, an isothermal cavern and a heat transfer cavern; based on the unified calculation framework, through deriving explicit analytical expressions of the volume density and the mass density under different working conditions, the quantitative relation of the pressure, the temperature, the air mass and the density of the gas storage is determined, and a direct calculation model of the storage capacity and the inflation and deflation rate is established; and based on the direct calculation model, calculating the storage capacity and the inflation and deflation rate of the gas storage. Reliable technical support is provided for accurate design and efficient optimization of compressed air energy storage underground gas storage engineering, and the method has important engineering application value and popularization prospects.

Description

A semi-theoretical estimation method and system for compressed air energy storage gas storage capacity and filling / discharging rate Technical Field

[0001] This invention belongs to the interdisciplinary field of compressed air energy storage (CAES) technology and underground gas storage engineering, specifically involving a semi-theoretical estimation method and system for the storage capacity and filling / discharging rate of a compressed air energy storage gas tank. Background Technology

[0002] As the global energy structure transitions towards a low-carbon model, the penetration rate of intermittent renewable energy sources such as wind and solar power continues to increase, making the demand for large-scale energy storage technology in the power grid increasingly urgent. Compressed air energy storage (CAES), as a mature, large-capacity, long-life, and environmentally friendly energy storage method, has become one of the key technologies for solving the problem of renewable energy consumption and ensuring the safe and stable operation of the power grid, thanks to its advantage of being able to utilize underground space to store high-pressure air.

[0003] As the core energy storage unit of a CAES (Computational Energy Storage System), the gas storage facility's capacity directly determines the system's energy storage capacity, and its charging and discharging rate affects the power plant's rated power output. These two parameters are core parameters in the CAES power plant design phase, and their estimation accuracy directly affects the project's investment cost, operational efficiency, and safety and stability. However, existing methods for calculating gas storage facility capacity and charging / discharging rates have significant bottlenecks and are difficult to meet actual engineering needs: numerical simulation methods (such as computational fluid dynamics and thermodynamic coupling simulation) can achieve high-precision calculations, but they rely on specialized simulation software and high-performance computing power, making the calculation process time-consuming (often requiring several hours to several days for a single calculation), and demanding extremely high levels of professional knowledge from operators, making them unsuitable for scenarios requiring rapid decision-making, such as early-stage project scheme comparison and multi-parameter sensitivity analysis.

[0004] Furthermore, existing technologies lack a unified calculation framework covering different thermal conditions. In actual engineering projects, the thermal characteristics of gas storage facilities vary significantly due to factors such as burial depth, rock properties, and lining structure: deeply buried sealed storage facilities, due to their long heat exchange paths and good sealing performance, operate approximately under adiabatic conditions; near-surface storage facilities, due to sufficient heat exchange with the surrounding rock mass and environment, operate approximately under isothermal conditions; while most actual engineering storage facilities fall between these two categories, operating under heat transfer conditions (non-adiabatic). Existing methods require the establishment of separate calculation models for different conditions, which is cumbersome and has poor compatibility, greatly limiting their engineering application scope. Summary of the Invention

[0005] To address the technical pain points of existing numerical simulation methods, such as computational complexity, low efficiency, and difficulty in uniformly adapting to different thermal conditions, this invention provides a semi-theoretical estimation method and system for the capacity and inflation / deflation rate of compressed air energy storage tanks. Based on thermodynamic theory, it deeply integrates the laws of conservation of mass and energy to construct a unified calculation framework covering adiabatic tanks, isothermal tanks, and heat transfer tanks (non-adiabatic conditions).

[0006] To achieve the above objectives, the present invention provides the following solution: a semi-theoretical estimation method for the storage capacity and inflation / deflation rate of a compressed air energy storage tank, the method comprising: constructing a unified calculation framework covering three scenarios—insulated tanks, isothermal tanks, and heat transfer tanks—based on thermodynamic nitric acid theory and combined with the laws of conservation of mass and energy; based on the unified calculation framework, determining the quantitative relationship between storage tank pressure, temperature, air mass, and nitric acid density by deriving explicit analytical expressions for volumetric nitric acid density and mass nitric acid density under different operating conditions, and establishing a direct calculation model for storage capacity and inflation / deflation rate; and calculating the storage tank capacity and inflation / deflation rate based on the direct calculation model.

[0007] Preferably, the direct calculation models for storage capacity and gas filling / drainage rate include: calculation models for the storage capacity and gas filling / drainage rate of adiabatic storage chambers, calculation models for the storage capacity and gas filling / drainage rate of isothermal storage chambers, and calculation models for the storage capacity and gas filling / drainage rate of heat transfer storage chambers.

[0008] Preferably, the method for calculating the capacity and inflation / deflation rate of an insulated chamber, based on a calculation model for the chamber's capacity and inflation / deflation rate, includes the following: the relationship between the inflation ratio and pressure in the insulated chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass. The initial pressure inside the chamber. The initial temperature, The specific heat ratio of air. The temperature of the injected air, The maximum internal pressure of the gas storage chamber; the required volume of the insulated chamber is: ;in, For maximum storage, The volumetric density of the insulated chamber is given by the subscript. This refers to an adiabatic chamber; the mass density of the air injected into the adiabatic chamber is: ;in, air is the gas constant. The mass density of the air injected into the adiabatic chamber. This refers to the mass of the injected air; the formula for calculating the inflation / deflation rate during the inflation phase is: ;in, Inflation time, The inflow mass flow rate is the mass flow rate of the air. This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

[0009] Preferably, based on the calculation model of isothermal chamber capacity and inflation / deflation rate, the method for calculating the isothermal chamber capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the isothermal chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass; the formula for calculating the volume of the isothermal chamber is: ;in, The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber; the formula for calculating the mass density of the air injected into the isothermal chamber is: The formula for estimating the air mass flow rate during the inflation phase can then be obtained: .

[0010] Preferably, the method for calculating the storage capacity and filling / discharging rate of the heat transfer chamber based on the calculation model of the heat transfer chamber capacity includes: storage capacity: ;in, The mass density of the heat transfer chamber, subscript Indicates heat transfer chamber. The volume of the heat transfer chamber; the charge / discharge rate: ;in, This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

[0011] This invention also provides a semi-theoretical estimation system for the storage capacity and inflation / deflation rate of compressed air energy storage tanks. The system is used to implement the aforementioned method and includes: a framework construction module, a model construction module, and a calculation module. The framework construction module is used to construct a unified calculation framework covering three scenarios: adiabatic tanks, isothermal tanks, and heat transfer tanks, based on thermodynamic stoichiometry and incorporating the laws of conservation of mass and energy. The model construction module is used to, based on the unified calculation framework, derive explicit analytical expressions for volumetric stoichiometry and mass stoichiometry under different operating conditions, determine the quantitative relationship between storage tank pressure, temperature, air mass, and stoichiometry, and establish a direct calculation model for storage capacity and inflation / deflation rate. The calculation module is used to calculate the storage tank capacity and inflation / deflation rate based on the direct calculation model.

[0012] Preferably, the direct calculation models for storage capacity and gas filling / drainage rate include: calculation models for the storage capacity and gas filling / drainage rate of adiabatic storage chambers, calculation models for the storage capacity and gas filling / drainage rate of isothermal storage chambers, and calculation models for the storage capacity and gas filling / drainage rate of heat transfer storage chambers.

[0013] Preferably, based on the calculation model of the insulated chamber's capacity and inflation / deflation rate, the process of calculating the insulated chamber's capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the insulated chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass. The initial pressure inside the chamber. The initial temperature, The specific heat ratio of air. The temperature of the injected air, The maximum internal pressure of the gas storage chamber; the required volume of the insulated chamber is: ;in, For maximum storage, The volumetric density of the insulated chamber is given by the subscript. This refers to an adiabatic chamber; the mass density of the air injected into the adiabatic chamber is: ;in, air is the gas constant. The mass density of the air injected into the adiabatic chamber. This refers to the mass of the injected air; the formula for calculating the inflation / deflation rate during the inflation phase is: ;in, Inflation time, The inflow mass flow rate is the mass flow rate of the air. This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

[0014] Preferably, based on the calculation model for the isothermal chamber capacity and inflation / deflation rate, the process of calculating the isothermal chamber capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the isothermal chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass; the formula for calculating the volume of the isothermal chamber is: ;in, The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber; the formula for calculating the mass density of the air injected into the isothermal chamber is: The formula for estimating the air mass flow rate during the inflation phase can then be obtained: .

[0015] Preferably, based on the calculation model of the heat transfer chamber capacity and filling / discharging rate, the process of calculating the heat transfer chamber capacity and filling / discharging rate includes: Capacity: ;in, The mass density of the heat transfer chamber, subscript Indicates heat transfer chamber. The volume of the heat transfer chamber; the charge / discharge rate: ;in, This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

[0016] Compared with existing technologies, the beneficial effects of this invention are as follows: Based on thermodynamic stoichiometry theory and combined with the laws of conservation of mass and energy, this invention constructs a unified calculation framework covering three typical scenarios: adiabatic storage tanks, isothermal storage tanks, and heat transfer storage tanks (non-adiabatic conditions). By deriving explicit analytical expressions for volumetric stoichiometry (storage stoichiometry per unit volume) and mass stoichiometry (storage stoichiometry per unit mass) under different operating conditions, the quantitative relationship between key parameters such as pressure, temperature, and air quality of the gas storage tank and stoichiometry is clarified, thereby establishing a direct calculation model for storage capacity and gas filling / discharging rates. Among them, the adiabatic chamber model considers the characteristics of no heat exchange, the isothermal chamber model is based on the assumption of constant temperature with sufficient heat exchange, and the heat transfer chamber model represents the intermediate thermodynamic state between the adiabatic and isothermal chambers. Its volumetric density and air mass density are also limited by these two extreme cases. This invention balances accuracy and practicality through a weighted coefficient fusion method (the default weighted coefficient is 0.5, which can be adjusted according to actual heat exchange conditions). The invention has a solid theoretical foundation. Through a power plant example, the storage capacity estimation error is ≤10%, and the gas filling and discharging rate estimation error is ≤3%, which is significantly better than traditional empirical methods. At the same time, it does not require complex numerical iterations, and the calculation process is simple and efficient. It can be solved quickly directly using design parameters such as the power plant's rated power, charging and discharging time, and initial pressure. It provides reliable technical support for the accurate design and efficient optimization of compressed air energy storage underground gas storage projects, and has important engineering application value and promotion prospects. Attached Figure Description

[0017] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 is a schematic diagram of the estimation process for an adiabatic storage tank according to an embodiment of the present invention; Figure 2 is a schematic diagram of the estimation process for an isothermal storage tank according to an embodiment of the present invention; Figure 3 is a schematic diagram of the estimation process for a heat transfer storage tank using a semi-analytical method according to an embodiment of the present invention; Figure 4 is a thermographic diagram of the volumetric density of a heat transfer storage tank according to an embodiment of the present invention; Figure 5 is a thermographic diagram of the mass density of a heat transfer storage tank according to an embodiment of the present invention; Figure 6 is an error comparison diagram of an embodiment of the present invention, wherein (a) is an error comparison diagram of the adiabatic storage tank, isothermal storage tank, heat transfer storage tank and actual value in terms of storage capacity, and (b) is an error comparison diagram of the adiabatic storage tank, isothermal storage tank, heat transfer storage tank and actual value in terms of gas filling and discharging rate; Figure 7 is a schematic diagram of a semi-theoretical estimation method for the storage capacity and gas filling and discharging rate of a compressed air energy storage tank according to an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Example 1 addresses the core pain points of existing technologies in estimating gas storage capacity and filling / discharging rates, such as "lack of physical basis, insufficient accuracy, low efficiency, and poor adaptability." This invention provides a semi-theoretical estimation method for compressed air energy storage gas storage capacity and filling / discharging rates. Specifically, it belongs to the early design direction of gas storage, and is particularly suitable for underground gas storage facilities in heat transfer chambers (non-insulated conditions), providing core technical support for the precise and efficient design of underground gas storage projects. As shown in Figure 7, the method includes: constructing a unified calculation framework covering three scenarios—insulated storage tanks, isothermal storage tanks, and heat transfer storage tanks—based on thermodynamic stoichiometry theory and combined with the laws of conservation of mass and energy; based on the unified calculation framework, determining the quantitative relationship between gas storage tank pressure, temperature, air mass, and stoichiometry by deriving explicit analytical expressions for volumetric stoichiometry and mass stoichiometry under different operating conditions, and establishing direct calculation models for storage tank capacity and gas filling / discharging rates; wherein, the direct calculation models for storage tank capacity and gas filling / discharging rates include: calculation models for insulated storage tank capacity and gas filling / discharging rates, calculation models for isothermal storage tank capacity and gas filling / discharging rates, and calculation models for heat transfer storage tank capacity and gas filling / discharging rates; and calculating the storage tank capacity and gas filling / discharging rate based on the direct calculation models.

[0022] The specific implementation process is as follows: During the air filling and degassing stages, the mass conservation and energy conservation within the chamber are expressed by equations (1) and (2), respectively: (1) (2) Among them, For the quality of air inside the tunnel, and These are the inflow and outflow mass flow rates of air, respectively. The specific internal energy of air. The heat transfer rate of the chamber wall is denoted as . Enthalpy of air.

[0023] heat transfer rate It can be represented as: (3) (4) Among them, The average heat transfer coefficient, The area of ​​the chamber wall is denoted as . The temperature of the chamber wall. The temperature inside the tunnel. For the pressure inside the chamber, Let V be the volume of the chamber.

[0024] The equation of state for air is: (5) Among them, air-to-gas constant , Let be the temperature inside the tunnel. Combining equations (1), (3), and (4), the differential forms of equations (2) and (5) can be expressed as: (6) Among them, The specific enthalpy of the incoming air.

[0025] For isochoric air storage, the chamber volume remains constant. Based on equation (6), if the specific heat capacity of air is constant, the changes in temperature and pressure within the chamber can be expressed as: (7) Among them, The specific heat ratio of air. , The temperature of the injected air, It is the temperature of the chamber wall.

[0026] The temperature change caused by heat conduction in the rock mass is represented by equation (8): (8) Among them, For rock density, For the specific heat capacity of the rock, The thermal conductivity of the rock, For rock temperature, Where is the radius of the chamber. For ambient temperature, This represents the radial distance.

[0027] As the temperature and pressure inside the chamber change, the stored energy is expressed by formula (9): (9) Among them, The specific heat capacity at constant volume of air. Due to environmental pressures, .

[0028] The formula for calculating the initial air quality inside the chamber is: (10) of which The initial pressure inside the chamber. The initial temperature, The initial air quality inside the chamber.

[0029] Equations (1)-(10) are based on existing theories and provide incremental solutions for temperature, pressure, and nitrogen in gas storage tanks. However, they do not provide explicit expressions for temperature, pressure, and nitrogen, and therefore cannot be used for rapid estimation of gas storage tank capacity and filling / discharging rates. This invention further addresses the thermodynamic differences between adiabatic, isothermal, and heat transfer conditions by deriving analytical / semi-analytical expressions for nitrogen density for different scenarios, as shown in equations (11)-(35). These expressions can efficiently estimate gas storage tank capacity and filling / discharging rates.

[0030] 1. Insulated Chamber: The core characteristic of an insulated chamber is that there is no heat exchange between the chamber walls and the outside environment; the heat transfer rate of the chamber walls is zero, that is: (11) During the inflation phase, the air mass flow rate is defined as: (12) Considering that most gas storage facilities in the project are designed for constant volume energy storage, that is, the volume of the storage chamber is constant, and the change of air specific heat capacity with temperature is ignored (to simplify engineering calculations while ensuring accuracy), the dynamic relationship between temperature and pressure in the storage chamber can be derived, as shown in equations (13) and (14): (13) of which For time.

[0031] (14) Subsequently, by integrating equation (9) using the temperature and pressure in equations (13) and (14), the formula for calculating the volumetric density of the adiabatic chamber can be obtained: (15) (16) (17) of which The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the insulated chamber is given by the subscript. It indicates an adiabatic chamber. For maximum storage, , and It is a parameter related to the properties of compressed air. It is the ratio of the injected air mass to the initial air mass, referred to as the inflation ratio in this invention. This refers to the inflation time.

[0032] Further, from equation (13), the relationship between the air ratio and pressure in the adiabatic chamber can be obtained as follows: (18) of which This represents the maximum internal pressure of the gas storage chamber. Derived from equation (15), the required volume of the adiabatic chamber can be estimated as follows: (19) Furthermore, combining equations (10), (17), (18), and (19), the mass density of the air injected into the adiabatic chamber can be derived, given by equation (20): (20) of which The mass density of the air injected into the chamber. The mass density of the air injected into the adiabatic chamber. It refers to the mass of the injected air.

[0033] Furthermore, the formula for calculating the inflation and deflation rates during the inflation phase can be obtained, expressed by equation (21): (21) of which This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

[0034] 2. Isothermal Chamber: Unlike adiabatic chambers which have no heat exchange characteristics, the core assumption of isothermal chambers is that the chamber exchanges heat sufficiently with the surrounding environment, and the overall temperature remains constant. =constant). The pressure increment during the inflation stage can be derived from equation (7): (22) Further integration of equation (22) yields the formula for calculating the pressure change during the inflation stage, expressed by equation (23): (23) Combining with equation (9), the formula for calculating the volumetric density of an isothermal chamber can be derived as follows: (twenty four) (25) of which The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber. It is a parameter related to the characteristics of compressed air.

[0035] From equation (23), we can derive the relationship between the air ratio and pressure in the isothermal chamber as follows: (26) The volume calculation formula for the isothermal chamber can be derived from equation (24), as shown in equation (27): (27) Furthermore, combining equations (10), (17), and (26), the formula for calculating the mass density of the air injected into the isothermal chamber can be derived, expressed by equation (28): (28) The formula for estimating the air mass flow rate during the inflation stage can then be obtained: (29) of which This refers to the inflation and deflation rate during the inflation phase of the isothermal chamber.

[0036] Using equations (26) to (29), the volume of the isothermal chamber and the inflation / deflation rate can be estimated.

[0037] 3. Heat Transfer Chambers: In practical engineering, the heat transfer process of most heat transfer chambers is affected by multiple factors such as burial depth, rock properties, and lining structure, resulting in complex mechanisms that make it difficult to directly derive purely analytical solutions for volume and air mass flow rate. This invention proposes a semi-analytical method to estimate the volume and air mass flow rate of a heat transfer chamber. Since a heat transfer chamber represents an intermediate thermodynamic state between an adiabatic chamber and an isothermal chamber, its volumetric density and air mass density are also limited by these two limiting cases. The following semi-analytical expressions are introduced to estimate the volumetric density and air mass density of a heat transfer chamber.

[0038] To balance computational accuracy and engineering practicality, this invention introduces weighting coefficients. A semi-analytic expression is proposed, where Corresponding to the insulated chamber, Corresponding isothermal chamber.

[0039] (30) (31) of which The volumetric density of the heat transfer chamber. The mass density of the heat transfer chamber, subscript It indicates a heat transfer chamber (diabatic).

[0040] To simplify the analysis, this invention takes By integrating the density characteristics of adiabatic and isothermal tunnels, semi-analytical expressions for the volumetric density and mass density of heat transfer tunnels are derived through simplified derivation, as shown in equations (32) and (33), respectively: (32) (33) Furthermore, the volume of the heat transfer chamber and the air mass flow rate can be estimated semi-analytically using equations (34) and (35): Storage capacity: (34) of which This represents the volume of the heat transfer chamber.

[0041] Inflation and deflation rates during the inflation phase: (35) of which This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

[0042] In summary, this invention is based on thermodynamic stoichiometry theory, deeply integrating the laws of conservation of mass and energy to construct a unified calculation framework covering adiabatic, isothermal, and heat transfer (non-adiabatic) storage chambers. The following sections will derive explicit analytical or semi-analytical expressions for volumetric stoichiometry (storage stoichiometry per unit volume) and mass stoichiometry (storage stoichiometry per unit mass) according to the differences in characteristics of these three typical thermodynamic conditions. This provides a theoretical basis for establishing direct calculation models for storage capacity and gas filling / expansion rates, ensuring that the method possesses a solid thermodynamic foundation, broad adaptability to various operating conditions, and simple and efficient engineering operability.

[0043] Example 2: To make the technical solution of the present invention clearer and more operable, the following example, using a power plant project as a case study, elaborates on the complete estimation process of gas storage capacity and gas filling and releasing rate, covering all aspects of parameter input, calculation under different operating conditions, result verification and adjustment, to ensure that engineering technicians can directly refer to and implement it.

[0044] The operating pressure range of a certain power station is 4.6~6.6 MPa, the rated output power is 290 MW, the inflation time is 8 hours, the deflation time is 2 hours, the actual total reservoir capacity is 300,000 m³, and the average inflation / deflation rate is 108 kg / s.

[0045] S1: Determine the estimation premises and input parameters: Premise: constant volume gas storage, air is an ideal gas, heat transfer chamber has default weighting coefficients. =0.5 (adjustable from 0 to 1).

[0046] Input parameters: Rated power of the power plant ( ), inflation / deflation time ( , ), initial / maximum pressure ( , ), environmental pressure ( ), initial / injected air temperature ( , ); air heat capacity ratio (γ=1.4), gas constant ( ).

[0047] S2: Calculate total storage .

[0048] S3: Calculation of air density under different working conditions: S3.1 Insulated chamber 1. Based on the parameters given by the chamber, the air filling ratio of the insulated chamber is calculated according to formula (18). 2. Calculate the parameters related to the properties of compressed air according to equation (16). , , Substitute into equation (15) to calculate the volumetric density. Substituting the volumetric density into equation (19) in reverse, the storage capacity of the cavern is derived. 3. Substitute the volume density into equation (20) to calculate the mass density. Then, substituting the obtained mass density into equation (21), the inflation / deflation rate is calculated. .

[0049] The calculation process for the capacity and inflation / deflation rate of the insulated storage chamber is shown in Figure 1.

[0050] S3.2 Isothermal Chamber 1. Based on the pre-input parameters, the air filling ratio of the isothermal chamber can be calculated using equation (26). Based on the inflation ratio and ambient pressure parameters obtained in the previous step, calculate the parameters related to compressed air characteristics using equation (25). 2. Calculate the volumetric density using equation (24). Substituting the obtained volumetric density and total storage capacity of the cavern into equation (27), the cavern capacity is derived. 3. Combining the volumetric density obtained in the previous step, substitute it into equation (28) to calculate the mass density of the cavern. Substituting into equation (29), the inflation rate of the chamber can be calculated. .

[0051] The calculation process for the isothermal chamber capacity and inflation / deflation rate is shown in Figure 2.

[0052] S3.3 Heat Transfer Chamber 1. As shown in equation (32), the average value of the volumetric density calculated from the adiabatic and isothermal chambers is taken to obtain the volumetric density of the heat transfer chamber. 2. Similarly, as shown in equation (33), the average mass density of the adiabatic and isothermal chambers is taken to obtain the mass density of the heat transfer chamber. The heat transfer chamber capacity is calculated using equations (34) and (35). With inflation and deflation rates .

[0053] The calculation process for the heat transfer chamber capacity and filling / discharging rate is shown in Figure 3.

[0054] S4: Result Verification: Based on the analytical model of the adiabatic reservoir: the estimated total reservoir capacity is 389,689 m³, and the gas filling and releasing rate is 208.4 kg / s; Based on the analytical model of the isothermal reservoir: the estimated reservoir capacity is 261,626 m³, and the gas filling and releasing rate is 104.4 kg / s; Based on the semi-analytical solution: the estimated reservoir capacity is 313,068 m³, and the gas filling and releasing rate is 104.3 kg / s.

[0055] By comparing the measured and estimated values, the relative errors of the semi-analytical solutions are all less than 10%, which is in good agreement with the actual values; the inflation and deflation rates predicted by the three models are highly similar. The error comparison chart is shown in Figure 6.

[0056] Based on this method, Figure 4 shows the volumetric density thermogram of the heat transfer chamber, and Figure 5 shows the mass density thermogram of the heat transfer chamber. Based on Figures 4 and 5, Table 1 lists the estimation results of the chamber capacity and gas filling / expanding rate under several other conditions.

[0057] Table 1 Example 3: This invention also provides a semi-theoretical estimation system for the storage capacity and inflation / deflation rate of compressed air energy storage tanks. The system is used to implement the method described in Example 1. The system includes: a framework construction module, a model construction module, and a calculation module. The framework construction module is used to construct a unified calculation framework covering three scenarios—insulated tanks, isothermal tanks, and heat transfer tanks—based on thermodynamic nitric acid theory and combined with the laws of conservation of mass and energy. The model construction module is used to, based on the unified calculation framework, derive explicit analytical expressions for volumetric nitric acid and mass nitric acid under different operating conditions, determine the quantitative relationship between storage tank pressure, temperature, air mass, and nitric acid, and establish a direct calculation model for storage capacity and inflation / deflation rate. The calculation module is used to calculate the storage tank capacity and inflation / deflation rate based on the direct calculation model.

[0058] In this embodiment, the direct calculation models for storage capacity and gas filling / drainage rate include: a calculation model for the storage capacity and gas filling / drainage rate of an adiabatic storage chamber, a calculation model for the storage capacity and gas filling / drainage rate of an isothermal storage chamber, and a calculation model for the storage capacity and gas filling / drainage rate of a heat transfer storage chamber.

[0059] In this embodiment, the process of calculating the capacity and inflation / deflation rate of the insulated chamber based on the calculation model includes: the relationship between the inflation ratio and pressure in the insulated chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass. The initial pressure inside the chamber. The initial temperature, The specific heat ratio of air. The temperature of the injected air, The maximum internal pressure of the gas storage chamber; the required volume of the insulated chamber is: ;in, For maximum storage, The volumetric density of the insulated chamber is given by the subscript. This refers to an adiabatic chamber; the mass density of the air injected into the adiabatic chamber is: ;in, air is the gas constant. The mass density of the air injected into the adiabatic chamber. This refers to the mass of the injected air; the formula for calculating the inflation / deflation rate during the inflation phase is: ;in, Inflation time, The inflow mass flow rate is the mass flow rate of the air. This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

[0060] In this embodiment, the process of calculating the isothermal chamber capacity and inflation / deflation rate based on the isothermal chamber capacity and inflation / deflation rate calculation model includes: the relationship between the inflation ratio and pressure in the isothermal chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass; the formula for calculating the volume of the isothermal chamber is: ;in, The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber; the formula for calculating the mass density of the air injected into the isothermal chamber is: The formula for estimating the air mass flow rate during the inflation phase can then be obtained: .

[0061] In this embodiment, the process of calculating the heat transfer chamber capacity and filling / discharging rate based on the heat transfer chamber capacity and filling / discharging rate calculation model includes: Capacity: ;in, The mass density of the heat transfer chamber, subscript Indicates heat transfer chamber. The volume of the heat transfer chamber; the charge / discharge rate: ;in, This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

[0062] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A semi-theoretical estimation method for the storage capacity and filling / discharging rate of a compressed air energy storage tank, characterized in that, The method includes: using thermodynamic sludge theory as the core, and combining the laws of conservation of mass and energy, constructing a unified calculation framework covering three scenarios: adiabatic storage tanks, isothermal storage tanks, and heat transfer storage tanks; based on the unified calculation framework, by deriving explicit analytical expressions for volumetric sludge density and mass sludge density under different operating conditions, determining the quantitative relationship between pressure, temperature, air mass, and sludge density of the gas storage tank, and establishing a direct calculation model for storage capacity and gas filling / discharging rate; and based on the direct calculation model, calculating the storage capacity and gas filling / discharging rate of the gas storage tank.

2. The method according to claim 1, characterized in that, The direct calculation models for storage capacity and filling / drainage rates include: calculation models for adiabatic storage capacity and filling / drainage rates, calculation models for isothermal storage capacity and filling / drainage rates, and calculation models for heat transfer storage capacity and filling / drainage rates.

3. The method according to claim 2, characterized in that, Based on the calculation model of the insulated chamber's capacity and inflation / deflation rate, the method for calculating the insulated chamber's capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the insulated chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass. The initial pressure inside the chamber. The initial temperature, The specific heat ratio of air. The temperature of the injected air, The maximum internal pressure of the gas storage chamber; the required volume of the insulated chamber is: ;in, For maximum storage, The volumetric density of the insulated chamber is given by the subscript. This refers to an adiabatic chamber; the mass density of the air injected into the adiabatic chamber is: ;in, air is the gas constant. The mass density of the air injected into the adiabatic chamber. This refers to the mass of the injected air; the formula for calculating the inflation / deflation rate during the inflation phase is: ;in, Inflation time, The inflow mass flow rate is the mass flow rate of the air. This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

4. The method according to claim 3, characterized in that, Based on the calculation model of isothermal chamber capacity and inflation / deflation rate, the method for calculating the isothermal chamber capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the isothermal chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass; the formula for calculating the volume of the isothermal chamber is: ;in, The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber; the formula for calculating the mass density of the air injected into the isothermal chamber is: The formula for estimating the air mass flow rate during the inflation phase can then be obtained: 。 5. The method according to claim 4, characterized in that, Based on the calculation model of heat transfer chamber capacity and filling / discharging rate, the method for calculating the heat transfer chamber capacity and filling / discharging rate includes: Capacity: ;in, The mass density of the heat transfer chamber, subscript Indicates heat transfer chamber. The volume of the heat transfer chamber; the charge / discharge rate: ;in, This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

6. A semi-theoretical estimation system for the storage capacity and inflation / deflation rate of a compressed air energy storage tank, said system being used to implement the method described in any one of claims 1-5, characterized in that, The system comprises: a framework construction module, a model construction module, and a calculation module. The framework construction module, based on thermodynamic stoichiometry and incorporating the laws of conservation of mass and energy, constructs a unified calculation framework covering three scenarios: adiabatic, isothermal, and heat transfer storage tanks. The model construction module, based on the unified calculation framework, derives explicit analytical expressions for volumetric stoichiometry and mass stoichiometry under different operating conditions, determines the quantitative relationship between pressure, temperature, air mass, and stoichiometry in the gas storage tank, and establishes a direct calculation model for storage capacity and gas filling / discharging rates. The calculation module, based on the direct calculation model, calculates the storage capacity and gas filling / discharging rates of the gas storage tank.

7. The system according to claim 6, characterized in that, The direct calculation models for storage capacity and filling / drainage rates include: calculation models for adiabatic storage capacity and filling / drainage rates, calculation models for isothermal storage capacity and filling / drainage rates, and calculation models for heat transfer storage capacity and filling / drainage rates.

8. The system according to claim 7, characterized in that, Based on the calculation model for the capacity and inflation / deflation rate of an adiabatic chamber, the process of calculating the capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the adiabatic chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass. The initial pressure inside the chamber. The initial temperature, The specific heat ratio of air. The temperature of the injected air, The maximum internal pressure of the gas storage chamber; the required volume of the insulated chamber is: ;in, For maximum storage, The volumetric density of the insulated chamber is given by the subscript. This refers to an adiabatic chamber; the mass density of the air injected into the adiabatic chamber is: ;in, air is the gas constant. The mass density of the air injected into the adiabatic chamber. This refers to the mass of the injected air; the formula for calculating the inflation / deflation rate during the inflation phase is: ;in, Inflation time, The inflow mass flow rate is the mass flow rate of the air. This refers to the inflation and deflation rate during the inflation phase of the adiabatic chamber.

9. The system according to claim 8, characterized in that, Based on the calculation model for isothermal chamber capacity and inflation / deflation rate, the process of calculating the isothermal chamber capacity and inflation / deflation rate includes: the relationship between the inflation ratio and pressure in the isothermal chamber is as follows: ;in, It is the ratio of the injected air mass to the initial air mass; the formula for calculating the volume of the isothermal chamber is: ;in, The volumetric density of the chamber is given by [the density of the chamber]. The volumetric density of the isothermal chamber is given by the subscript. This indicates an isothermal chamber; the formula for calculating the mass density of the air injected into the isothermal chamber is: The formula for estimating the air mass flow rate during the inflation phase can then be obtained: 。 10. The system according to claim 9, characterized in that, Based on the calculation model of heat transfer chamber capacity and filling / discharging rate, the process of calculating the heat transfer chamber capacity and filling / discharging rate includes: Capacity: ;in, The mass density of the heat transfer chamber, subscript Indicates heat transfer chamber. The volume of the heat transfer chamber; the charge / discharge rate: ;in, This refers to the gas filling and venting rate during the gas filling phase of the heat transfer chamber.

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