Layered dynamic thermodynamic modeling method for salt cavern gas storage for compressed air energy storage

Abstract

The invention provides a layered dynamic thermodynamic modeling method for a salt cavern gas storage for compressed air energy storage, and belongs to the technical field of compressed air energy storage. The core idea of the method is spatial discretization and layered solution, N control bodies are divided in the vertical direction according to the geometric characteristics of the salt cavern, then a mass conservation equation, an energy conservation equation and a Redl ich-Kwong real gas state equation are established for each control body, and finally all the control body equations are coupled into a nonlinear differential equation set. After initial conditions and boundary conditions are given, a numerical method is adopted for solving. According to the method, the temperature and pressure layering characteristics in the salt cavern can be accurately described, the problems that a traditional single-tank model underestimates the energy storage capacity and energy loss calculation is inaccurate are solved, high-precision model support is provided for compressed air energy storage power station power dispatching and system optimization, and high practicability and popularization value are achieved.

Description

Technical Field

[0001] This invention belongs to the field of compressed air energy storage technology, and relates to salt cavern gas storage, particularly a layered dynamic thermodynamic modeling method for salt cavern gas storage for compressed air energy storage. Background Technology

[0002] Compressed air energy storage, as a large-scale, long-term physical energy storage technology, plays an increasingly important role in peak shaving and valley filling in power systems, enhancing grid stability, and promoting the consumption of renewable energy. During the operation of a compressed air energy storage power station, real-time and accurate monitoring of the energy stored in the storage device (such as underground salt caverns, abandoned mine shafts, or high-pressure tanks) is crucial for power station power dispatch, system efficiency assessment, and power generation planning.

[0003] In compressed air energy storage systems, underground salt caverns serve as gas storage tanks, and the dynamic changes in their internal thermodynamic state directly affect the performance of the entire system. Due to gravity, denser, colder air sinks to the bottom of the cavity, while less dense, hotter air accumulates at the top, resulting in significant temperature and pressure stratification along the depth direction within the cavity.

[0004] Existing technologies typically treat salt caverns as a homogeneous "single-tank" model, assuming that the gas inside the cavity is instantaneously and uniformly mixed, with a single pressure and temperature. This simplified model has significant drawbacks: it fails to reflect the true pressure distribution, especially towards the end of the discharge process, where the actual pressure at the bottom is much higher than the average pressure calculated by the single-tank model. This causes the single-tank model to prematurely determine that the gas storage pressure is insufficient, thus severely underestimating the actual usable energy storage capacity and discharge duration. Furthermore, the single-tank model cannot calculate the impact of thermal stratification on heat transfer in the surrounding rock, leading to inaccurate calculations of energy losses throughout the cycle.

[0005] Therefore, developing a gas storage model that can accurately simulate a salt cavern-type compressed air energy storage power station is of vital importance for improving the power station's operational level and enhancing its competitiveness in the electricity market. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing a layered dynamic thermodynamic modeling method for salt cavern gas storage for compressed air energy storage. The technical problem this invention aims to solve is that existing single-tank models cannot characterize the layered characteristics inside salt cavern gas storage.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A layered dynamic thermodynamic modeling method for salt cavern gas storage for compressed air energy storage is proposed. The core technology involves spatial discretization and layered solution. By discretizing the continuous, heterogeneous salt cavern cavity into a finite number of series control volumes, thermodynamic laws are applied to each control volume and the solutions are coupled to reconstruct the complex dynamic characteristics of the system. The specific technical solution includes the following steps:

[0009] Preferably, spatial discretization: based on the geometric characteristics of the salt cavern (such as the variation law of height and cross-sectional area), it is divided into N independent control volumes along the vertical direction. The control volumes can be divided with equal height or non-uniformly divided according to the geometry of the cavity to improve the approximation accuracy of the real cavity structure.

[0010] Preferably, mass conservation, energy conservation, and gas law are established for each control volume, forming the core calculation system of the model:

[0011] Furthermore, the mass conservation equation states that the accumulation rate of gas mass within the control body is equal to the difference between the mass flow rate flowing into and out of the control body, ensuring mass continuity. The mathematical expression is: dm_i / dt=m_in,i-m_out,i;

[0012] Where m_i = ρ_i * V_i is the gas mass in control volume i;

[0013] m_in,i and m_out,i are the mass flow rates flowing into and out of control volume i.

[0014] The flow direction is set according to the inflation / deflation process:

[0015] Inflation process (from top to bottom): m_in,1 = wellhead injection flow rate, m_in,i = m_out,i-1 (i = 2to6);

[0016] Gas release process (from bottom to top): m_out,6 = wellhead production flow rate, m_out,i = m_in,i+1 (i = 1 to 5) dm / dt = mm, where m is the gas mass in control volume i, m and m are the mass flow rates flowing into and out of control volume i respectively, and t is time.

[0017] Furthermore, the energy conservation equation states that the rate of change of the internal energy of the gas within the body is equal to the difference between the enthalpy carried by the inflowing gas and the enthalpy carried by the outflowing gas, plus the heat exchange with the surrounding rock. This comprehensively reflects the energy transport and exchange process, and the mathematical expression is: d(m_i*u_i) / dt=m_in,i*h_in,i-m_out,i*h_out,i+Q_rock,i-P_i*dV_i / dt;

[0018] u_i is the specific internal energy of the gas in control volume i, and h_in,i and h_out,i are the specific enthalpy of the gas entering and exiting.

[0019] Q_rock,i represents the heat exchange between control volume i and the surrounding salt rock, calculated using a coupled unsteady heat conduction model;

[0020] -P_i*dV_i / dt is a key term in high-pressure closed systems. Since the total volume of the salt cavern, V_total, is constant, for incompressible salt rock, dV_i / dt = 0. This term macroscopically manifests as the pressure of all control volumes rising synchronously (being compressed) when net flow flows in, leading to an increase in temperature; and vice versa.

[0021] Furthermore, the gas law: A real gas law suitable for high-pressure scenarios is adopted to establish the relationship between pressure, density, and temperature. This invention uses the Redlich-Kwong equation:

[0022] P=R*T / (vb)-a / [√T*v*(v+b)];

[0023] Where v is the specific volume, and a and b are the physical properties of air. Through this equation, the pressure P_i can be solved from the density ρ_i (or specific volume v_i) and temperature T_i, or the reverse calculation can be performed.

[0024] Preferably, coupling and solution: the core equations of all control volumes together constitute a closed nonlinear differential equation system. Given the initial state (initial pressure, temperature distribution) and boundary conditions (gas filling / discharging flow rate, temperature), the system is solved in a simulation platform (such as MATLAB / Simulink or Python) using numerical integration methods (such as the fourth-order Runge-Kutta method) to obtain the state parameters such as pressure, temperature, and density of each control volume at each time step.

[0025] Compared with existing technologies, the layered dynamic thermodynamic modeling method for salt cavern gas storage for compressed air energy storage of the present invention has the following advantages:

[0026] 1. Significantly improved prediction accuracy: By considering thermal stratification, the model can accurately calculate the real-time pressure at the gas storage tank outlet, thereby more accurately assessing the power plant's discharge capacity and available energy storage duration.

[0027] 2. Realistically reflects the physical process: The model naturally captures the natural convection and temperature stratification phenomena caused by the density difference of the gas during the inflation and deflation process, and the calculation results are more consistent with the physical reality.

[0028] 3. Provides more reliable input for system optimization: Accurate outlet parameters (pressure, temperature) are key inputs for calculating downstream turbine generator units under varying operating conditions. The precise boundary conditions provided by this model fundamentally improve the simulation accuracy of the entire power plant system.

[0029] 4. Modularity and flexibility: The layered model itself is an independent and fully functional module that can be easily integrated with other device models and can also be adapted to salt caves with different geometries. Attached Figure Description

[0030] Figure 1 This invention provides a method for stratified dynamic thermodynamic modeling of salt cavern gas storage for compressed air energy storage, including the flow pattern and thermal stratification of a high-pressure sealed salt cavern during the inflation and deflation process.

[0031] Figure 2 This is a graph showing the temperature and pressure changes in a high-pressure sealed salt cavern during the inflation and deflation processes, based on a layered dynamic thermodynamic modeling method for compressed air energy storage salt caverns in this invention. Detailed Implementation

[0032] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0033] Example Parameter Settings:

[0034] Taking a cylindrical salt cavern gas storage facility as the research object, the specific parameters are set as follows:

[0035] Geometric parameters: Assume the total height of the cylindrical salt cave is H = 300 meters, the cross-sectional area A is constant, and it is divided into 6 control volumes along the depth direction, i.e. N = 6, and the height of each control volume is Δh = H / 6 = 50 meters.

[0036] The volume of each control body is V_i = A*Δh (i = 1, 2, ..., 6), with control body 1 being the top control body and control body 6 being the bottom control body.

[0037] Initial conditions: Initial uniform pressure P = 6.0 MPa; temperature set according to geothermal gradient (surface temperature 25℃, geothermal gradient 0.03℃ / m).

[0038] Control body 1 (top, depth 0-50 meters): average depth 25 meters, temperature T1_init=25+0.03*25≈25.8℃ (298.8K);

[0039] Control body 2 (depth 50-100 meters): average depth 75 meters, temperature T2_init=25+0.03*75=27.3℃ (300.3K);

[0040] Control body 3 (depth 100-150 meters): average depth 125 meters, temperature T3_init = 28.8℃ (301.8K);

[0041] Control body 4 (depth 150-200 meters): average depth 175 meters, temperature T4_init = 30.3℃ (303.3K);

[0042] Control body 5 (depth 200-250 meters): average depth 225 meters, temperature T5_init = 31.8℃ (304.8K);

[0043] Control body 6 (bottom, depth 250-300 meters): average depth 275 meters, temperature T6_init = 33.3℃ (306.3K).

[0044] Boundary conditions:

[0045] Inflation process: Set boundary conditions at the top wellhead (inlet of control body 1): mass flow rate m_in_well (e.g., 100 kg / s) and temperature T_in_well (e.g., 45°C / 318.15 K).

[0046] Gas venting process: Set boundary conditions at the top wellhead (outlet of control body 1): mass flow rate m_out_well (e.g., 80 kg / s). At this time, the outlet state (P1, T1) of control body 1 is the inlet state of the turbine unit.

[0047] Implementation steps:

[0048] Step 1: Model Initialization and Spatial Discretization

[0049] Based on the above geometric parameters, a three-dimensional model of the salt cave is constructed. The cavity is discretized into 6 control volumes along the vertical direction. The basic parameters such as initial pressure, temperature, and volume of each control volume are defined, and the airflow connection relationship between the control volumes is clarified.

[0050] Step 2: Construction of Control Volume Equations

[0051] For each control volume, the following equations are established:

[0052] Mass conservation equation: dm / dt=mm, where the gas filling process (from top to bottom): m_in,1=wellhead injection flow rate, m_in,i=m_out,i-1 (i=2to6); the gas release process (from bottom to top): m_out,6=wellhead production flow rate, m_out,i=m_in,i+1 (i=1to5) dm / dt=mm;

[0053] Energy conservation equation: d(m·u) / dt=m·hm·h+QP·dV / dt, where the salt rock is incompressible and the total volume of the cavity is constant, so dV / dt=0, and Q is calculated through an unsteady heat conduction model;

[0054] The gas law is based on the Redlich-Kwong equation: P = R·T / (vb) - a / [√T·v·(v+b)], relating pressure, temperature and specific volume.

[0055] Step 3: Model Solving and Result Analysis

[0056] The equations established for the six control volumes (a total of six mass and energy equations, supplemented by state equations and heat transfer models) are coupled into a closed nonlinear differential equation system.

[0057] Numerical integration is performed using the fourth-order Runge-Kutta method in a simulation platform (such as MATLAB / Simulink or Python).

[0058] Set a time step (e.g., 1 second), start from the initial state, and gradually advance the solution to simulate the complete cycle of "inflation-resting-deflating". The results are as follows:

[0059] Inflate for 4 hours: from the initial 6.0MPa to 8.0MPa.

[0060] Results: The model clearly shows temperature stratification. Control volume 1 has the highest temperature, reaching about 75°C, because it continuously receives and compresses the subsequent gas. Control volume 6 has the lowest temperature, stabilizing at about 50°C, because it receives low-temperature air that has flowed through the entire cavity and has fully exchanged heat with the surrounding rock. A static pressure difference of about 0.25 MPa is formed in the cavity (bottom ~ 8.25 MPa, top ~ 8.0 MPa).

[0061] Release gas for 4 hours: from 8.0 MPa to 5.0 MPa.

[0062] Key Result 1 (Capacity Assessment): Simulations show that when the pressure at the top wellhead (control body 1) drops to 5.0 MPa (turbine cutoff pressure), the pressure at the bottom control body 6 remains at 5.45 MPa. This indicates that conventional homogeneous models would incorrectly determine at this point that the gas storage is unusable, while the model of this invention reveals that approximately 8% of the usable high-pressure gas is still sealed at the bottom, accurately assessing the true usable capacity.

[0063] Key Result 2 (Performance Prediction): The temperature change curve of the outlet gas (from control unit 1) is shown in Figure 1. Figure 2 As shown, the temperature is high (about 70°C) at the beginning of venting. As venting proceeds, the temperature begins to drop significantly and continuously after about 2.5 hours, eventually dropping to about 38°C. This accurate prediction is crucial for assessing the efficiency changes of turbine units during operation, a phenomenon that traditional homogeneous models cannot capture at all.

[0064] Inflation process of this invention:

[0065] like Figure 1As shown: High-pressure room-temperature air (gray) is injected at the top. Due to its high density, it sinks and compresses the gas in the cavity, causing the temperature of the gas in the top area to rise due to compression (black). The arrow indicates the flow direction from top to bottom.

[0066] Gas release process: Gas is drawn from the top, causing the high-pressure, low-temperature air (dark gray) accumulated at the bottom to flow back upwards to replenish it. The arrows indicate the upward flow direction. The key term in the energy equation, P·dV, is highlighted in the figure, emphasizing its importance in high-pressure sealed cavities.

[0067] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for stratified dynamic thermodynamic modeling of salt cavern gas storage for compressed air energy storage, characterized in that, The core idea is spatial discretization and layered solution, including the following steps: S1 spatial discretization: Divide the salt cavern geometry into N serial control volumes along the vertical direction; S2 establishes the control volume equations, including the mass conservation equation, energy conservation equation, and gas state equation; S3 Coupled Solution: All control volume equations are formed into a nonlinear differential equation system. Given the initial state and boundary conditions, numerical methods are used to solve the system and obtain the dynamic state parameters of each control volume.

2. The method according to claim 1, characterized in that, In step S1, the control volume is divided into equal height or non-uniform sections, with the non-uniform section adapting to the changing characteristics of the salt cave cross-sectional area.

3. The method according to claim 1, characterized in that, In step S2, the energy conservation equation takes into account the enthalpy difference between the inflow and outflow gases and the heat exchange with the surrounding rock, and the gas state equation adopts the Redlich-Kwong real gas equation.

4. The method according to claim 1, characterized in that, Step S3 is solved in the simulation platform using the fourth-order Runge-Kutta method, with a time step of 1 second.

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