## 1 Introduction
### Introduction to Impurities in CO\({}_{2}\)  
In the chain of CCUS, the requirements of gas composition are different depending on the quality and standards of CO\({}_{2}\) pipelines. While the transportation comprises mainly CO\({}_{2}\), the presence of impurities in the gas cannot be ignored. The lack of a defined standard for the maximum allowable concentration of impurities in CO\({}_{2}\) is a cause for concern for safe transportation in pipelines [4]. Based on pre-combustion and post-combustion processes, the composition of impurities can vary. Some of the issues that impurities can present include alterations to the compression process in pumps, toxicity limitations, hydrate formation, corrosion and the formation of free water, including the cross effect of the presence of certain reactive species such as H\({}_{2}\)S + H\({}_{2}\)O or H\({}_{2}\)O + CH\({}_{4}\)[5]. Flue gases from coal combustion (mainly power plants) contain CO\({}_{2}\), N\({}_{2}\), O\({}_{2}\) and water, but also consist of air pollutants such as sulfur oxides (SO\({}_{\rm x}\)), nitrogen oxides (NO\({}_{\rm x}\)) and traces of HCl, HF along with other particulates. The pre-combustion capture of CO\({}_{2}\) has been shown to carry N\({}_{2}\), H\({}_{2}\), CH\({}_{4}\), CO and H\({}_{2}\)S as major impurities. Water, as an impurity in the CO\({}_{2}\)-rich mixture, can cause corrosion, uneven phase changes, ice formation, hydrate formation, etc. Therefore, the CCUS process requires dehydration to remove the water content from the mixture [6]. An experimental study on a commercially purchased CO\({}_{2}\)-rich mixture, by [PERSON] et al. [3], provides details of the impurities in CO\({}_{2}\) captured from flue gases and their effect on density, viscosity and other thermodynamic properties. The effect of water presence was also studied, along with the best approaches to adopt in similar studies. The authors suggested the use of cubic plus association equation of state (CPA-EoS) or Soave-Redlich-Kwong equation of state (SRK-EoS) when no water is present in the mixture. The presence of impurities has also been shown to significantly change the phase envelope shape and particularly the critical point coordinates [7]. These studies clearly show the need to consider the impurities while designing pumps for CCS systems. To avoid the two-phase flow problems, the CCS streams are designed to be transported in a liquid or supercritical state. Therefore, a thorough understanding of the phase envelope for the (CO\({}_{2}\) + impurities) system is pivotal for the CCS process. Designing and establishing a working methodology for CO\({}_{2}\) compressors is a crucial step in the industrial scaling of the CO\({}_{2}\) compression process. The works of [PERSON] [8], [PERSON] [9] and [PERSON] [10; 11] provide insight into these challenges. The work of [PERSON] et al. [12] highlights the efficiency of power-cycles in pumps/compressors and the effect phase change has on them. The work also presents the validation of the phase change of CO\({}_{2}\) using nozzle studies by [PERSON] [13] and [PERSON] [10; 11]. These studies provide a distinction between the various models available to tackle the phase change close to the supercritical state of the mixture, namely the homogeneous equilibrium model (HEM), non-homogeneous equilibrium model (NEM), homogeneous frozen model (HFM) and delayed equilibrium model (DEM). However, previous studies have overlooked the existence of impurities in CO\({}_{2}\) while studying compression, thus inspiring the current study. The thermodynamic properties of the captured CO\({}_{2}\)-rich stream may differ significantly from those of pure CO\({}_{2}\). No experimental data on CO\({}_{2}\)-rich fluid mixtures are currently available in the open source domain to validate the existing models [3; 5].