## 1 Introduction  
In recent years, the discourse surrounding climate change has intensified, with a growing consensus on the imperative need to transition the global economy towards achieving net-zero greenhouse gas emissions by mid-century. This ambitious goal, essential to averting dangerous anthropogenic interference with the climate system, requires rapid investment increase in near-zero emission technologies across all sectors [1]. Among these technologies, Carbon Capture and Storage (CCS), also referred to as CCUS, where \"U\" stands for utilization, shows to be a pivotal solution to reducing carbon emissions, addressing climate change, and facilitating the transition to a carbon-neutral future [2, 3]. Its significance lies in its potential to address emissions from various sources, including power-generating plants, hard-to-abate industries (such as cement and refineries), and hydrogen production. CCUS is the only technology capable of guiding industries to absolute net neutrality by capturing and treating emissions. Once CO\({}_{2}\) is captured, it undergoes compression and transport to be permanently stored in geological formations, acting as a \"sink\" through injection. These geological formations must possess certain key characteristics [4]. Essential conditions for a formation to be considered a suitable carbon storage site include the formation of a pore unit with sufficient capacity to store the intended CO\({}_{2}\) volume; pore interconnectivity allowing injection at the required rate; and the presence of an extensive cap rock or barrier at the top of the formation to retain the injected CO\({}_{2}\), prevent unwanted migration, and ensure long-term containment [5]. Saline water-bearing formations [6; 7; 8] are widely regarded as the most mature options for CO\({}_{2}\) storage, as demonstrated by numerous projects worldwide. Additionally, depleted oil and gas fields have recently emerged as potential storage sites, benefitting from operational experience gained through CO\({}_{2}\)-EOR operations [9; 10; 11]. Deploying CCUS technology on a large scale in saline aquifers or hydrocarbon fields necessitates accurate characterization of the storage site and reservoir, involving a complex process, from screening to deep geological and geophysical characterization [12]. Numerical simulation and modeling using computational fluid dynamics (CFD), possibly coupled with reactive transport simulations, are employed to address complex subsurface geology, simulating the flow behavior of the injected and the in situ fluids. The goal of such models is to estimate the field sequestration capacity of the injected CO\({}_{2}\) under different trapping mechanisms, such as structural, dissolution, residual, and mineral storage, during all project phases [13; 14]. Reservoir simulation is a crucial tool in the field of petroleum engineering that aids in modeling and predicting fluid flow behavior within subsurface reservoirs. The primary objective is to simulate the complex interactions among various components, such as rock, fluids, and wells. One of the fundamental principles underlying reservoir simulation is Darcy's law, which describes the flow of fluids through porous media. The Darcy equation (Equation (1)) relates fluid velocity to pressure gradient, permeability, and fluid viscosity [15]. The simulator employs numerical methods to solve the mass, momentum, and energy differential equations governing fluid flow (2) in the porous medium. The most widely used flow model in reservoir simulation is the black-oil one [16]. In the black-oil formulation [17], the model is considered to consist of three separate fluid phases or pseudocomponents (water, oil, and gas). Mixing among phases is allowed, and the amount of how much each phase is dissolved in the others and how it affects flow properties need to be kept tracked of.