Kavan Khaledi

Sensitivity analysis and parameter identification of a time dependent constitutive model for rock salt

The tendency to shift from fossil and nuclear energy sources to renewable energy carriers has increased during the past couple of decades. Subsequently, development of effective energy storage systems has become more attractive. Nowadays, caverns excavated in rock salt formations are recognized as the appropriate places for underground storage of energy in the form of compressed air or hydrogen. Accurate design of these underground cavities requires suitable numerical simulations employing appropriate constitutive models to describe the material behavior of rock salt under various geological conditions. It is obvious that to have a realistic numerical simulation, it is essential to have a comprehensive knowledge concerning the unknown material parameters and their influence on the calculation results. In this paper, a time dependent model is selected to describe the mechanical response of the rock salt around the cavern. This model is implemented in a finite element code and its application in numerical modeling of salt caverns is illustrated. In addition, global sensitivity analysis is used to investigate the influence of material parameters on the mechanical behavior of the salt cavern. Finally, inverse analysis of the synthetic data is performed to identify the material parameters of the selected model. The applied global sensitivity and inverse analysis algorithms employ metamodeling technique in order to reduce the time which is needed for these computationally expensive calculations.

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.

Concept for an integral approach to explore the behavior of rock salt caverns under thermo-mechanical cyclic loading in energy storage systems

The fluctuating nature of renewable energy sources can be managed by storing the surplus of electrical energy in an appropriate reservoir. The excess electricity available during off-peak periods of consumption may be used to compress air or electrolyze hydrogen. Afterward, the pressurized gas is stored in the rock salt cavities and discharged to compensate the shortage of energy when required. During this process, the rock salt surrounding the cavern undergoes thermo-mechanical cyclic loading. In order to achieve a reliable geotechnical design, the stress–strain response of rock salt under such loading condition has to be identified and predicted. In order to investigate the rock salt behavior under such loading, a comprehensive study using three concepts of geotechnical engineering, i.e., experimental investigation, constitutive modeling and numerical analysis, is conducted. A triaxial experimental setup is developed to supplement the knowledge of the cyclic thermo-mechanical behavior of rock salt. The imposed boundary conditions in the experimental setup are assumed to be similar to the stress state obtained from a full-scale numerical simulation. The computational model relies primarily on the governing constitutive model for predicting the behavior of rock salt cavity. Hence, a sophisticated elasto-viscoplastic creep constitutive model is developed to take into account the dilatancy and damage progress, as well as the temperature effects. The contributed input parameters in the constitutive model can be calibrated using the experimental measurements. In the following, the initial numerical simulation is modified based on the calibrated constitutive model. However, because of the significant levels of uncertainties involved in the design procedure of such structures, a reliable design can be achieved by employing probabilistic approaches. Therefore, the numerical calculation is extended by statistical tools such as sensitivity analysis, optimum experimental design, back analysis, probabilistic analysis and robust reliability-based design to get final design parameters of paramount need for practice.

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

This study focuses on the failure probability of storing renewable energy in the form of hydrogen or compressed air in rock salt caverns. The validation of the short- and long-term integrity and stability of rock salt cavern is a prerequisite in their design process. The present paper provides a reliability-based analysis of a typical renewable energy storage cavern in rock salt. An elasto-viscoplastic creep constitutive model is implemented into a numerical model of rock salt cavern to assess its behavior under different operation conditions. Sensitivity measures of different variables involved in the mechanical response of cavern are computed by elementary effect global sensitivity method. Subset simulation methodology is conducted to measure the failure probability of the system with a low computational cost. This methodology is further validated by a comparison with a Monte Carlo-based probabilistic analysis. The propagation of parameter uncertainties and the failure probability against different failure criteria are evaluated by utilizing a Monte Carlo-based analysis. In this stage, the original finite element model is substituted by a surrogate model to further reduce the computational effort. Finally, a reliability analysis approach is employed to obtain the minimum admissible internal pressure in a cavern.

APPLICATION OF METAMODELLING TECHNIQUES FOR MECHANIZED TUNNEL SIMULATION

Abstract Complex engineering problems require using computation- ally expensive simulations which take relatively long time. In such cases, routine tasks such as design optimization, parameter identification, or sensitivity analysis become impractical since they require thousands or even millions of simulations. A common practice for engineers to solve this problem is to use metamodels in place of actual simulation models. In this paper, we investigate the performance of four metamodelling approaches, namely, Response Surface Methodology, Moving Least Squares, POD-RBF, and Neighborhood Approximation considering the effect of sample size and sampling methods. Our main goal in this work is to find a reliable and robust metamodel technique in order to construct an approximated function for mechanized tunnel simulation. For this reason, a numerical study is carried out on a 3D tunnel modeled in Plaxis3D and the accuracy and robustness of the aforementioned metamodelling techniques are discussed

Numerical simulation of deep and shallow energy storage systems in rock salt

The design and safe operation of caverns in rock salt need an accurate stability analysis. This paper provides the results of a geomechanical survey on the stability of a typical hydrogen underground storage. To accompolish this, first the behaviour of the cavern is analysed by a numerical model, taking into account the nonlinear creep behaviour of the rock salt. Then, the safety of the cavern is evaluated by comparing stress states for different regions around the cavern with a compression/dilatancy (C/D) boundary. Different depth of cavern’s roof location and various internal loads are considered. Results show minimum values for internal cavern pressure to guarantee the stability of the cavern for different depth of cavern location.

Parameter Identification of a Rate Dependent Constitutive Model for Rock Salt

The tendency to shift from fossil and nuclear energy sources to renewable energy carriers in Germany leads to the necessity to develop effective energy storage systems. Nowadays, caverns excavated in rock salt formations are recognized as the appropriate places for underground storage of energy in the form of compressed air, hydrogen and natural gas. Accurate design of these underground cavities requires suitable numerical simulations employing proper constitutive models to describe the material behavior of rock salt under various geological conditions. In this paper, a rate dependent model is selected to describe the mechanical response of the rock salt around the cavern. This model is implemented in the finite element code CODE-BRIGHT, then its application in numerical modeling of salt caverns is illustrated. Finally, inverse analysis of the synthetic data is performed to identify the material parameters of the selected model. The applied inverse analysis algorithm employs metamodeling technique in order to reduce the computation time of the parameter identification procedure.