## 1 Introduction  
Scenarios considered by international entities such as the International Agency (IEA) point out the complexity of actions needed to achieve goals established for reducing emissions of greenhouse gases in the coming decades, simultaneously with the desired transformation in energy generation sources. The report \"World Energy Outlook 2022\" [1] emphasizes that multiple technologies and energy sources will play an essential joint role in providing energy resources for the planet in a more sustainable scenario. Among the various options for reducing CO\({}_{2}\) emissions, Carbon Capture and Storage (CCS) presents itself as a technology with significant potential to reduce CO\({}_{2}\) emissions in a (probable) scenario of continued use of fossil fuels in the coming decades. A CCS project involves CO\({}_{2}\) capture from high-emission industries and injecting it into geological formations such as aquifers and depleted hydrocarbon reservoirs. One of the most critical barriers to long-term and large-volume CO\({}_{2}\) storage in geological formations is the proof of safe and reliable storage. For that, CO\({}_{2}\) can take advantage of different trapping mechanisms in porous media [2; 3; 4; 5]; for example, free CO\({}_{2}\) migration is controlled by the structural and stratigraphic trapping exerted by the caprock during the short term encompassing the injection time, known as a primary mechanism. During this stage, the caprock plays an essential role in the security of the CCS operation due to CO\({}_{2}\) buoyancy which can move it up to the surface or the seafloor in the case of offshore storage sites. In the Frio CO\({}_{2}\) field demonstration project conducted in the U.S. [6], CO\({}_{2}\) was injected in a deeper zone below several well-known shale seals. However, some authors [7] are currently reviewing the need for a caprock to control the plume rise because of the following reasons: (i) there is no prescriptive regulation concerning geologic seals; and (ii) the concept of the composite confining system is introduced, as a set of discontinuous barriers which create long and tortuous paths that attenuate mobile CO\({}_{2}\) rise. During the mid- and long term, part of mobile CO\({}_{2}\) will be dissolved in water (solubility trapping), as time passes, especially in low-salinity brine under high-pressure and low-temperature conditions [8; 9]. Saturation changes caused by the rising plume can lead to more CO\({}_{2}\) being trapped as a residual phase due to relative permeability and capillary hysteresis [10; 11; 12]. Beyond that, in few cases, some CO\({}_{2}\) can be trapped as minerals because of the resulting pH of the brine and the mineralogy of the rock [13; 14]. Therefore, those additional mechanisms increase storage security, when the buoyant CO\({}_{2}\) is immobile in the pore space or no longer exists as a free phase (generally as super-critical CO\({}_{2}\)). Modeling CO\({}_{2}\) retention in porous media depends on the rock properties, such as porosity and permeability, and intrinsic parameters related to each trapping mechanism mentioned beforehand [15]. In this study, the entrapment of CO\({}_{2}\) in porous media will be rigorously modeled to allow a fair evaluation between two well geometries to inject CO\({}_{2}\): vertical and horizontal wells. The hypothesis to be investigated is related to CO\({}_{2}\) spreading around the well. With vertical wells, CO\({}_{2}\) is concentrated nearby with a limited spread due to the dominance of gravitational forces. However, with horizontal wells, CO\({}_{2}\) is broadly spread in porous media, developing a larger swept area, and it is thus likely to become trapped in that area due to hysteresis as a residual phase. Besides that, there is a possibility of contacting poor CO\({}_{2}\)-saturated brine, enhancing the solubility and ionic entrapment.