A transition towards more renewable energy sources such as wind- and solar energy is underway. These sources can be unpredictable with regard to energy production and therefore energy storage has become a major concern. A promising technique, Underground Hydrogen Storage (UHS), converts excess energy into hydrogen and stores it underground, after which, by reversing the process, the stored energy can be used when the imbalance between supply and demand is great. Hydrogen storage in salt caverns is particularly attractive because of their high sealing capacity, low amount of cushion required, the inert nature of rock salt and high possible injection and withdrawal rates. For energy storage purposes, these salt caverns are exposed to different cyclic loading conditions during operation, resulting in variations in stress in and around the cavern. Investigation of the mechanical response of rock salt under cyclic loading conditions is essential for the safety assessment and usability of the cavern. The response of the system to varying loading conditions can be mainly divided into two groups, either time-dependent or stress-dependent. The main focus of this thesis is to record the stress-dependent behaviour of rock salt under varying loading conditions. More specifically, it focuses on nonlinearity that occurs due to viscoplasticity. This phenomenon can be described as the rate dependent
behaviour of a material that occurs when a material exceeds a certain stress level, after which irreversible deformation occurs. This thesis describes the development of a 2D FEM (finite element method) simulator on an unstructured grid that captures the mechanical response. To model the stress-dependent behaviour, the viscoplastic model proposed by Desai is used. This model is
based on the non-associated flow rule and takes into account material dilatancy and compressibility. In addition, the model allows for hardening, the tensile strength of rock salt and variation in yield behaviour with pressure variation. Sonar data from cavern EPE S43 is utilised to test the simulator. This case showed that irreversible deformation occurs as a result of the stress-dependent behaviour of rock salt. For this specific cavern, the total working volume of the cavern decreased roughly by 0.0003% over three operating cycles, indicating that viscoplastic deformation itself does not pose significant risks to the cyclic storage of hydrogen in salt caverns.

The demand for accurate and efficient simulations in order to test the geomechanical effects is a reality for the entire geoscience community. The motivation that arises from that need is the development and the evolution of modelling methods to study these effects. Deep understanding of any problem in fine scale is crucial, especially when it extends to much coarser scales.
In this work the finite volume method (FVM) is used for mechanical modelling of deformation in elastic media. The momentum balance equation is solved as the governing equation for mechanics, assuming linear elasticity for the stress tensor. Here, displacement is mapped onto a vertex-centred grid in three dimensions (3D). A set of eight trilinear basis functions are used to locally interpolate the value of displacement within each grid cube. In the finite volume method, the discretized form of the equations are obtained by integrating the governing equation over control volume surfaces, since in 3D the control volume is a cube. Hence, discretized forms are obtained by considering 24 surfaces, which form between a displacement node and its neighbouring displacement cells. This required extensive derivation. The implementation of the numerical model was carried out by writing a code in MATLAB. Several numerical test cases are presented to demonstrate the capability of this model. In the first place, the consistency of the model is checked through comparison with synthetic analytical solutions, which are compared to the numerical solutions. Furthermore, the simple test case of uniaxial compression, has been carried out with this model, but also compared to the results with a 2D FVM model and a 3D finite element (3D FEM) one. In another test case, ground plain strain subsidence is studied in a real hydrocarbon field with a heterogeneous map for elasticity parameters. It is shown that 3D FVM is in close agreement with 3D FEM in predicting the subsidence due to field depletion. Last but not least, displacement and stresses, in a faulted reservoir in which fluids are injected, are modelled and the results are shown to coincide with a robust analytical solutions for the system. Finally, the aim of this work is to shed some more light on the finite volume method for mechanics and bring it closer to the audience of science.