**2. Methodology**

#### *2.1. Hydraulic Model*

The flow simulation accounts for multiphase fluid flow in porous media. A hydraulic model is usually conducted by reservoir simulation, i.e., a form of numerical modelling in which physical phenomena are quantified and interpreted throughout the history of a reservoir and beyond, with the ability to extend this model to future performances. Reservoir simulation is a proven and effective method for dealing with uncertainties during exploration and production [13]. It is also helpful to determine the amount of gas that can be stored in each underground gas (CO2, hydrogen, or methane) storage reservoir [13]. The physical phenomenon behind (fluid flow) reservoir simulations are based mainly Darcy's law and mass material balance [10].

The composition of the fluid can be treated in different ways in reservoir simulations. Black oil simulators assume oil and gas phases to be one component through space and time. The properties of this component can change with pressure and temperature, while the composition does not change [13]. Thereby, the behaviour of the multiphase system can be described by complex PVT (pressure, volume, temperature) and SCAL (special core analysis) relations [13].

As a general solution method, the reservoir is divided into several cells with provided petrophysical properties, such as porosity and permeability. Then, the wells are placed within cells, and production rates are provided with different time steps. Last, the equations are solved to determine the pressure, temperature, and saturation for each cell. Each cell is solved simultaneously; therefore, the number of cells in the reservoir simulation is directly related to the time required to solve a time step [13].

### *2.2. Thermal Model*

The thermal-flow-stress simulation model considers the proportional heat transfer in porous media when considering the multi-fluid flow concept in a THM simulation. The thermal flow model is usually performed by numerical modelling, in which the thermal hydraulic aspects are quantified together with the geomechanical simulation and interpreted throughout the history of a reservoir and storage operations in underground gas storage facilities. The main governing law in the thermal modelling is Fourier's law, also known as the law of heat conduction. The law states that the rate of heat transfer through a material is proportional to the negative temperature gradient and to the area at right angles to that gradient through which the heat flows. The governing equation of Fourier's law describes that the local heat flux density (*qh*) is equal to the product of the thermal conductivity (*kt*) and the negative local temperature gradient (−∇*T*) [14]:

$$q\_h = -k\_t \nabla T\_\prime \tag{1}$$

where *qh* is in (W/m2), *kt* is in (W/m. K), and ∇*<sup>T</sup>* is in (K/m). Fourier's law can also be used in uni-dimensional form in any direction, *i*, *j*, *k*; for that reason, the equation becomes:

$$q\_h = -k\_t \frac{dT}{d(i, j, k)}\,'\,\tag{2}$$
