Compressed Air Energy Storage Cavern Research Articles

Cavern spacing of CAES cavern group in hard rock based on plastic zone and deformation analysis

Existing research on layout parameters of compressed air energy storage (CAES) cavern groups in hard rock has indicated that the key influential factors for group stability include buried depth, diameter, and cavern spacing. Among these, in contrasting to other factors, the research on cavern spacing is limited. This paper focuses on the issue of safe spacing and proposes a numerical method to determine it. By establishing a series of finite element models, the stress state of surrounding rock, changes in shape, equivalent plastic strain of plastic zone, and cavern wall deformation under different spacing have been studied. When a group of air storage caverns in rows is subjected to high internal pressure, for a small spacing, the plastic zone of the surrounding rock between two caverns is connected. Here, the size of the plastic zone, equivalent plastic strain value, and deformation of the cavern wall are relatively large, making the surrounding rock highly susceptible to damage. As the spacing increases, the horizontal width of the plastic zone, the maximum equivalent plastic strain value, the displacement changes of the cavern wall remain stable. This spacing is virtually the same as that when the plastic zone of the surrounding rock is no longer connected and can be selected as a safe spacing. This study explores the design of cavern safe spacing of underground CAES cavern groups and discusses several influencing factors, which can provide references for follow-up energy storage engineering and research.

Coupled thermal-gas-mechanical phase-field modeling for fracture initiation and propagation in the underground caverns for compressed air energy storage

With the aim of addressing the large-scale engineering fracture problems in an underground cavern for compressed air energy storage (CAES), in this study, a coupled thermal-gas-mechanical (TGM) phase-field modeling for simulating fracture initiation and propagation in the CAES caverns is proposed. This study also focuses on COMSOL Multiphysics strategy of the TGM phase-field fracture modeling. The temperature field, air seepage field, displacement field, initial geostress field, and phase field are fully coupled and solved in COMSOL. A circular preexisting fracture zone is generated and used to initialize the fracture propagation according to the newly specified history strain field. The results indicate that the proposed TGM phase-field modeling and the corresponding COMSOL implementation strategy can simulate the thermodynamic responses and fracture initiation and propagation well. The lateral pressure coefficient and gravitational stress field have a strong impact on the fracture patterns and critical pressure, inducing fractures.

Influence of spatial variability in surrounding rock on fracture propagation in compressed air energy storage caverns

The expansion of fractures around underground caverns for compressed air energy storage (CAES) has a significant impact on engineering stability. We established a thermo-mechanical coupled random phase field model to investigate the trajectory of fractures in the heterogeneous surrounding rock of underground gas storage caverns. By simulating the different mechanical parameters under different coefficients of variation and autocorrelation distances, we explored the impact of spatial variability of rock mass on the fracture mode of surrounding rock in underground gas storage caverns. The results indicate that when only the spatial variability of elastic modulus is considered, the coefficient of variation primarily affects the inclination and curvature degree of fractures while the autocorrelation distance has a slight impact on the bending shape of fractures. When only the spatial variability of fracture energy release rate is considered, both the coefficient of variation and the autocorrelation distance have a negligible effect on fracture propagation. Compared with the elastic modulus of the rock mass, the fracture energy release rate has a more significant impact on the path of the cavern fractures.

Projected effective energy stored of Zhangshu salt cavern per day in CAES in 2060

As a large-scale energy storage technology, compressed air energy storage (CAES) has the advantages of high efficiency and high reliability. This paper analyzed the feasibility of CAES cavern constructed in salt mine with multi-interlayer in Zhangshu, Jiangxi Province. Salt mine in Zhangshu is a typical bedded rock salt, and a method for calculating the cavern volume in Zhangshu was proposed. Using the proposed volume calculation method, it is expected that the volume of Zhangshu salt caverns can reach 27,840,000 m3 by 2060. By modelling the geomechanics used to calculate its stability. Based on the results of the simulation, the recommended operating pressure is 8.5–11.5 MPa. Finally, If this volume is used for CAES, the cycle pressure is assumed to be 8.5–11.5 MPa, energy storage efficiency of 50 %, the daily effective energy storage is 8.062 × 1014 J. This study will guide the development of the Zhangshu Salt Mine, provide lessons for similar areas and have a positive impact on the energy transition in Jiangxi.

A thermo-hydro-mechanical damage model for lined rock cavern for compressed air energy storage

Large-scale compressed air energy storage (CAES) technology is regarded as an effective way to alleviate the instability of electricity generated from renewable sources such as wind and solar power, which involves the expensive construction of underground caverns to store highly pressurized and high-temperature compressed air. This study documents mechanical behavior and gas permeability of granite under temperature-pressure synchronous cyclic loading, and the response of the surrounding rock to Thermo-Hydro-Mechanical-Damage (THMD) evolution. Firstly, physical experiments were conducted to examine mechanical property and gas permeability evolutions of granite due to temperature-pressure synchronous cyclic loading. Based on these experiments, equations describing the damage evolution of granite were deduced. Subsequently, using these equations in combination with a thermo-hydro-mechanical coupled model of porous media with two-phase fluid flow, a sophisticated computational routine for the thermo-hydro-mechanical-damage analysis of underground gas storage caverns was developed. Lastly, numerical simulations were conducted to study heat transfer, two-phase seepage, and mechanical response of a CAES cavern under operating conditions. Under low to medium pressure and high-temperature synchronous cyclic loading, granite exhibited a significant variation in elastic modulus and compressive strength. Also, its permeability showed a substantial increase due to damage evolution. After two months of operation, prominent heat transfer was observed in the surrounding rock, particularly in the region extending to approximately 10 m from the inner surface of the cavern, exceeding the range of gas leakage diffusion within the cavern. The plastic zone of surrounding rock is distributed above the cavern's roof and below its bottom. Moreover, areas with higher damage are concentrated in the surrounding rock near the cavern's side walls. These findings contributed to our understanding of the behavior of granite in the context of CAES technology and provided valuable insights for the design and operation of gas storage caverns. The development of the THMD model offered a valuable tool for investigating stress and deformation characteristics of the lining and surrounding rock in CAES plants.

Gas-mechanical coupled crack initiation analysis for local air-leakage of compressed air energy storage (CAES) cavern with consideration of seepage effect

The gas-tightness and stability of compressed air energy storage (CAES) cavern (usually with three-layered struction of sealing layer, concrete lining and surrounding rock) plays an important role for ensuring the power-generation efficiency of CAES system. Since the action of the compressed air with high temperature and high pressure would possibly cause the local damage of the sealing layer and lead to the air-leakage from the sealing layer to the surrounding rock, it is necassary to study the gas-mechanical (GM) coupled crack initiation behavior of the surrounding rock in order to provide a scientific basis for anti-cracking design and stability evaluation of CAES cavern. Currently, the GM coupled crack initiation are studied mainly by experimental and numerical methods but little by theoretical method, in which the gas pressure is taken as a static pressure regardless of the seepage effect. In this paper, the calculation formulea of GM coupled Mode I and Mode II SIFs are derived by the superposition principle with the consideration of seepage effect firstly. And then the criterion of GM coupled crack initiation is established based on our K-ratio criterion in order to analyze its mechanism for local air-leakage of CAES cavern. Finally, a gas seepage device is designed to conduct the tri-axial GM coupled compression tests of pre-cracked sandstone specimens on MTS815 hydraulic servo testing machine combined with PCI-II AE instrument to measure the crack initiation stress σi and initiation angle θC. Research results show both σi and θC are decreased with the increasing of gas pressure PG, while increased with the increasing of crack inclination angle β. All of these pre-cracked sandstone specimens have initiation mechanisms of Mode II. The prediction results of initiation angle with consideration of seepage effect is more closer to the test results than those of initiation angle without consideration of seepage effect, which can prove the validity of both our SIFs calculation formulea and the GM coupled criterion with consideration of seepage effect.

A new theoretical model of thermo-gas-mechanical (TGM) coupling field for underground multi-layered cavern of compressed air energy storage

Compressed air energy storage (CAES) is a promising method of large-scale energy storage. As the key components of the CAES, the underground cavern filled with compared air of the high-temperature and high-pressure would generate larger temperature, air seepage and stress fields to influence the safety of the CAES. Currently, coupling fields of CAES cavern are studied mainly by numerical method and little by theoretical method. The theoretical calculations of CAES cavern are almost by thermo-mechanical coupling model, where the air pressure is taken as a static pressure regardless of the gas seepage field. In this paper, a new theoretical model of thermo-gas-mechanical (TGM) coupling field with consideration of the gas seepage is established. Research results show the analytic solutions of the temperature, gas seepage and stress fields for single-, double- and three-layered caverns have almost the same changing trends with time but different with radius. The three-layered cavern has smaller heat/gas loss and better stability than the single- and double-layered cavern and therefore becomes a promising structure form. The new TGM coupling model is verified by the good agreement of our analytical solutions with available numerical results, and can provide theoretical basis for the safety assessment of the CAES multi-layered cavern.

Temperature Regulation Model and Experimental Study of Compressed Air Energy Storage Cavern Heat Exchange System

The first hard rock shallow-lined underground CAES cavern in China has been excavated to conduct a thermodynamic process and heat exchange system for practice. The thermodynamic equations for the solid and air region are compiled into the fluent two-dimensional axisymmetric model through user-defined functions. The temperature regulation model and experimental study results show that the charging time determines the air temperature and fluctuates dramatically under different charging flow rates. The average air temperature increases with increasing charging flow and decreasing charging time, fluctuating between 62.5 °C and −40.4 °C during the charging and discharging processes. The temperature would reach above 40 °C within the first 40 min of the initial pressurization stage, and the humidity decreases rapidly within a short time. The use of the heat exchange system can effectively control the cavern temperature within a small range (20–40 °C). The temperature rises and regularly falls with the control system’s switch. An inverse relationship between the temperature and humidity and water vapor can be seen in the first hour of the initial discharging. The maximum noise is 92 and 87 decibels in the deflation process.

Temperature and pressure variations in salt compressed air energy storage (CAES) caverns considering the air flow in the underground wellbore

The flow of compressed air in the wellbore affects the thermodynamic performance in the salt compressed air energy storage (CAES) cavern and this effect is still uncharted. In this study, a coupled explicit finite difference model considering the wellbore flow is proposed to obtain thermodynamic performance of the compressed air in the cavern. It is found that the thermodynamic performance is directly determined by the air temperature and pressure at the wellbore outlet, which are changed by the flow in the wellbore. A sensitivity study shows that the injection mass rate is the key parameter and significantly increases the air temperature and pressure in the cavern. The injection temperature and wellbore length are secondary factors. A high injection pressure is beneficial for energy storage. The inner diameter, roughness and thermal conductivity of the wellbore influence the performance slightly. The developed combined model is a more accurate tool for predicting the thermodynamic performance of a deep CAES cavern.

A new theoretical model of local air-leakage seepage field for the compressed air energy storage lined cavern

Current study on air-leakage of compressed air energy storage (CAES) cavern is focused on the global air-leakage seepage field without consideration of the thermo-gas-mechanical (TGM) coupling theory. In this study, a new theoretical model of local air-leakage seepage field for the lined CAES cavern is established based on the thermo-gas-mechanical (TGM) coupling theory and boundary conditions of the non-continuous and non-axisymmetric seepage. Calculation results show that with the increasing of the air-leakage distance, the local air-leakage seepage field p(r,θ,t) is decreased fast at first and then tends to the stable value p(r,θ,t)= 0.1 MPa (atmospheric pressure) at the maximum leakage distance RAA'm (when the air-leakage is stopping). The distribution area of the local air-leakage seepage field (related to the radius r and polar angle θ) is increased gradually from the non-axisymmetric about the center of cavern fan-shape and peach-shape to the axisymmetric circle, which is different from that of the global air-leakage seepage field (circle, independent of θ ). The new theoretical model of local air-leakage seepage field is proved to be valid by numerical simulation results and provides a scientific basis for the safety assessment of the underground geotechnical engineering with local fluid-leakage.

Stability analysis for compressed air energy storage cavern with initial excavation damage zone in an abandoned mining tunnel

Compressed air energy storage (CAES) is a buffer bank for unstable new energy sources and traditional power grids. The stability of a CAES cavern is a key issue to cavern safety. However, the stability of a cavern from an abandoned mining tunnel has not been well studied. This paper investigates the stability of the CAES cavern from an abandoned mining tunnel. Firstly, an initial heterogeneous excavation damage zone (EDZ) in the surrounding rock mass is partitioned based on mining and operation processes. Then, a thermal-hydraulic-mechanical coupling model is formulated for the CAES cavern with a sealing layer and implemented within COMSOL Multiphysics. After verification with available data in literature, this coupling model is used to investigate the influence of partitioned EDZ heterogeneity on the displacement and stability of cavern. It is found that the displacement at the cavern wall increases with operation cycle. The principal stress decreases with operation cycle in the high-damage zone but remains stable in the low-damage zone. The principal stress difference changes first and then becomes stable in the disturbance zone. Larger cavern radius, heat transfer coefficient, initial pressure of cavern, temperature of injected air, and faster gas injection rate induce bigger displacement. These results on the stability of a CAES cavern can be a basis for the repair of an existing cavern.

Seepage and Heat Transfer Characteristics of Gas Leakage under the Condition of CAES Air Reservoir Cracking

The contradiction between supply and demand of energy leads to more and more attention on the large-scale energy storage technology; Compressed Air Energy Storage (CAES) technology is a new energy storage technology that is widely concerned in the world. The research of coupled heat transfer and seepage in fractured surrounding rocks is the necessary basis to evaluate the operation safety and effectiveness of CAES. Current studies point to the possibility of cracking in concrete liner seals, but the thermodynamic processes and leakage characteristics of compressed air in the presence of cracking and the heat transfer characteristics of seepage have not been addressed and reported. In order to investigate the leakage, the gas seepage and heat transfer law in fractured rock when the hard rock CAES gas reservoir seal cracks, the COMSOL fracture Darcy module, and the non-Darcy Forchheimer model are used as the constitutive seepage. The global ODE is used to calculate the thermodynamic process of compressed air in gas storage with coupled seepage and heat transfer process. The pressure and temperature of compressed air are obtained as the unsteady boundary of the seepage heat transfer model. A program for calculating the seepage and heat transfer characteristics of fractured surrounding rock in the CAES gas reservoir is established. On this basis, with the proposed Suichang CAES cavern as the background, the seepage and heat transfer characteristics of the fractured surrounding rock of the gas storage are studied. The results showed that when there are fewer cracks in the lining and surrounding rock of the air reservoir, the air pressure decreases due to a small amount of air leakage after 30 operation cycles, and the leakage rate of each cycle is 0.7% of the gas storage capacity, but it still meets the engineering requirements. If the plant is operating under these conditions, the charging rate will need to be increased by 1.2 kg/s per cycle charging stage. In the discharging and power generation phase, the high-pressure air that previously percolated into the rock mass cracks could flow back into the air storage through the lining cracks. Therefore, it is incorrect and unreliable to consider the gas which flows out from the inner surface of the lining as unusable. When the lining crack width is less than 0.3 mm, the seepage flow is Darcy flow and the non-Darcy effect can be ignored; when the lining crack width is greater than 0.5 mm, the non-Darcy effect of seepage cannot be ignored. The gas velocity in the surrounding rock fracture medium is on the order of 0.01 m/s with an influence range of over 100 m, and the gas velocity in the pore medium is on the order of 10-6 m/s with an influence range of 50 m. The findings of this study contribute to a better understanding of the interaction between the thermodynamic properties of compressed air and the seepage heat transfer process in compressed air storage underground reservoirs, as well as the gas leakage process in the event of liner seal cracking.

A Modified Creep Model for Cyclic Characterization of Rock Salt Considering the Effects of the Mean Stress, Half-Amplitude and Cycle Period

The fluctuation of the operation pressure during injection and withdrawal is a key factor affecting the long-term stability of surrounding rock in a compressed air energy storage (CAES) cavern. To assess the mechanical behavior of rock salt under different pressure fluctuations and to optimize the operating parameters of CAES caverns, uniaxial cyclic loading tests under the sine condition were carried out by changing three cycle parameters, namely the mean stress, half-amplitude and cycle period. The test results show that the deformation behavior during cyclic loading tests can be divided into transient, steady, and accelerated stages, which is similar to that of creep tests. The strain and steady strain rates increase with increasing cycle parameters, showing a nonlinear deformation property of rock salt under cyclic loading. To describe the nonlinear response that cannot be captured by the Burgers model, a stiffness scaling factor is proposed based on the test results. A modified cyclic creep model of rock salt is established by introducing this stiffness scaling factor into the conventional Burgers creep model. The agreement with the experimental data indicates that the modified cyclic creep model can accurately reflect the influence of the three cyclic parameters on the deformation properties of rock salt.

A coupled thermo-hydro-mechanical model for evaluating air leakage from an unlined compressed air energy storage cavern

Compressed air energy storage (CAES), a large-scale energy storage technology, is a link between unstable renewable energy and conventional power grids. Air leakage may significantly impact the CAES efficiency. This paper presented a coupled thermo-hydro-mechanical model to evaluate the air leakage from an unlined CAES cavern. This model was validated with field tests, numerical simulations, and an analytical solution. The impacts of air leakage on the variations of temperature and pressure within a CAES cavern and the air seepage in surrounding rock were numerically analyzed. Finally, the effects of rock permeability, mass flow rate of air injection, and cavern radius on air leakage were investigated. It is found that rock permeability is a key parameter to air leakage. For the first cycle and under operational pressure of 5 and 8 MPa, rock permeability should be smaller than 3 × 10−19 m2 to satisfy the tightness requirement for an unlined CAES cavern. That is less than 1% daily air leakage percentage. Larger cavern radius and higher mass flow rate of air injection are helpful to reducing the daily air leakage percentage. These results can provide guidelines for tightness requirements for existing cavern repair or new CAES cavern construction design.

An Analytical Solution for Analyzing the Sealing-efficiency of Compressed Air Energy Storage Caverns

Compressed Air Energy Storage (CAES) is a commercial, utility-scale technology that is suitable for providing long-duration energy storage. Underground air storage caverns are an important part of CAES. In this paper, an analytical solution for calculating air leakage and energy loss within underground caverns were proposed. Using the proposed solution, the air leakage and energy loss under a typical CAES operation pressure were analyzed, and the influences of the permeability of the concrete lining and the lining thickness on the sealing efficiency of underground caverns were investigated. The results showed that under a typical CAES operation pressure, a concrete lining with a permeability of less than 6.36 × 10−18 m2 would result in an acceptable air leakage rate of less than 1%. Air leakage will increase linearly with increasing lining permeability. Increasing the thickness of the concrete lining could enhance the sealing efficiency of the storage cavern.

Debrining prediction of a salt cavern used for compressed air energy storage

Using salt caverns for compressed air energy storage (CAES) is a main development direction in China to provide a continuous power supply produced by renewable energy (e.g., solar, wind, tidal energy). A mathematical model used to predict the debrining parameters for a salt cavern used for CAES is built based on the pressure equilibrium principle. Combined with the sonar survey data of a salt cavern, the equations are deduced for calculating the debrining parameters. A mathematical model is proposed for the calculation of the critical safe distance between the air and brine interface (AB interface) and debrining tubing inlet. Based on above mathematical models, a program is developed using Visual Basic computer language. A salt cavern of Jintan salt district, Changzhou city, Jiangsu province, China, is simulated as an example. Results show the tubing size is the most important parameter for improving debrining efficiency. The tubing with diameter and wall thickness of 139.7 mm × 6.98 mm is proposed in the CAES cavern debrining to replace the one with size of 114.3 mm × 6.88 mm used in the traditional debrining for the salt cavern gas storage of Jintan. This can decrease the total debrining time by 43%, and only increases energy consumption by about 10%. This study can provide a theoretical foundation and a technological reference for the debrining of Jintan salt cavern used for CAES.

An iterative method for evaluating air leakage from unlined compressed air energy storage (CAES) caverns

Abstract Evaluating sealing capacity against the air leakage from unlined underground caverns for compressed air energy storage (CAES), a large-scale energy storage technology, is usually costly and time consuming. This paper presents an iterative method that can quickly estimate the air leakage rate of an unlined CAES cavern with adequate accuracy and requires fewer parameters than numerical simulations. The field tests of a pilot cavern in Japan and the NK1 cavern of the Huntorf plant as well as some numerical simulations were used as case studies to verify the proposed method. In these verifications, the proposed method achieved satisfactory results in terms of air leakage and cavern pressure. A sensitivity analysis was also conducted to examine the dependence of the air leakage from an unlined CAES cavern on the cavern characteristics and operating conditions. The most influential parameters were rock permeability, cavern radius, and the mass rate of injected air. Rock permeability should be smaller than 2.5 × 10−19 m2 to achieve a daily leakage percentage of less than 1% for a dry CAES cavern under pressure between 5 and 8 MPa. Moreover, a large cavern radius and a large mass rate of injected air could decrease a daily leakage percentage.

Exergy storage of compressed air in cavern and cavern volume estimation of the large-scale compressed air energy storage system

Accurate estimation of the energy storage capacity of a cavern with a defined storage volume and type is the very first step in planning and engineering a Compressed Air Energy Storage (CAES) plant. The challenges in obtaining a reliable estimation arise in the complexity associated with the thermodynamics of the internal air compression and expansion processes and the coupled heat transfer with surroundings. This study developed the methodology for estimating the exergy storage capacity with a known cavern volume, as well as the cavern volume required for a defined exergy storage capacity with different operation and heat transfer conditions.The work started by developing the mathematical models of the thermodynamic responses of air in a cavern subject to cavern operation in isochoric uncompensated or isobaric compensated modes, and heat transfer conditions including isothermal, convective heat transfer (CHT) and adiabatic wall conditions. The simulated transient air pressure and temperature were verified with the operational data of the Huntorf CAES plant. The study of the Huntorf CAES cavern confirmed the importance of the heat transfer influence on the energy conversion performance. The increase of mass storage due to the reduced temperature variation leads to an enhanced total exergy storage of the cavern. According to our simulations, within the operating range of the Huntorf plant, 34.77% more exergy after the charging and 37.98% more exergy after throttling can be stored in the cavern with isothermal wall condition than those in the cavern with adiabatic wall condition. Also, the nearly isothermal behaviour and high operating pressure in the compensated isobaric cavern resulted in the high effectiveness of exergy storage per unit cavern volume. The required cavern volume of the assumed isobaric cavern operation can be reduced to only 35% of the current cavern volume at the Huntorf plant. Finally, cavern volumes for an operational gas storage facility were used to demonstrate the methodology in estimating the exergy storage capacity, which provided an initial assessment of the storage capacity in the UK.

Analysis of compressed air storage caverns in rock salt considering thermo-mechanical cyclic loading

Exploring the material response of rock salt subjected to the variable thermo-mechanical loading is essential for engineering design of compressed air energy storage (CAES) caverns. Accurate design of salt caverns requires adequate numerical simulations which take into account the most important processes affecting the development of stresses and strains. To fulfill this objective, this paper presents a two-step simulation to analyze the thermo-mechanical behavior of rock salt in the vicinity of CAES caverns. In the first step, the changes in air temperature and pressure resulted from injection and withdrawal processes are estimated using an analytical thermodynamic model. Then, in the second step, the temperature and pressure variations obtained from the analytical model are utilized as the boundary condition for a finite element model of CAES cavern. An elasto-viscoplastic creep model is employed to describe the material behavior of rock salt. In the numerical section, a computational model to simulate the thermo-mechanical behavior of rock salt around the cavern is presented. Finally, the stability and long-term serviceability of the simulated cavern are evaluated considering two extreme loading scenarios: (1) low-pressure working condition and (2) high-temperature operation. Obtained results show that both stability and serviceability of the cavern are highly affected by the internal operating pressure. Dilatancy, damage propagation, tensile failure and increasing the rate of cavern closure are the unfavorable consequences of low-pressure working condition. Similarly, the increased creep rate due to the elevated temperature accelerates the volume convergence and subsequently endangers the serviceability of the system.

A simplified and unified analytical solution for temperature and pressure variations in compressed air energy storage caverns

Temperature and pressure variations in compressed air energy storage (CAES) caverns are important factors that affect the overall performance of CAES systems. However, current air storage cavern models used in the thermodynamic analysis of CAES systems usually ignore the effect of heat exchange between cavern air and the surrounding environment and thus cannot accurately predict temperature and pressure variations. In this study, a diabatic analytical solution in a simple and unified form and that considers heat exchange is proposed for temperature and pressure variations in CAES caverns. The solution is derived on the basis of assumptions that the air density in the cavern can be represented by a constant average value and that the cavern wall temperature remains constant. The proposed solution is validated with the test data of the Huntorf plant trial test and the results calculated with other solutions. Moreover, the errors of the proposed solution caused by the assumptions are analyzed. Results show that in representative ranges, the errors have a significant positive correlation with the ratio of the injected to the initial cavern air mass and the difference between the injected air temperature and the initial air temperature. The errors also have an insignificant negative correlation with the rock thermal effusivity and the heat transfer coefficient. Finally, the condition under which the proposed solution is applicable with an error less than 20% is defined on the basis of the combination of the ratio of the injected to the initial cavern air mass and the difference between the injected air temperature and the initial air temperature. This simplified and unified solution can be a simple yet adequately accurate tool to be used in the thermodynamic analysis of CAES systems.