In this PhD-study the different areas of chemical engineering, heterogeneous catalysis, supercritical fluids, and phase equilibrium thermodynamics have been brought together for selected reactions. To exploit the beneficial properties of supercritical fluids in heterogeneous catalysis, experimental studies of catalytic chemical reactions in dense and supercritical carbon dioxide have been complemented by the theoretical calculations of phase equilibria using advanced thermodynamic models. In the recent years, the use of compressed carbon dioxide as innovative, non-toxic and non-flammable, cheap, and widely available reaction medium for many practical and industrial applications has drastically increased. Particularly attractive are heterogeneously catalysed chemical reactions. The beneficial use of CO2 is attributed to its unique properties at dense and supercritical states (at temperatures and pressuresabove the critical ones), i.e. when it combines both gas-like and liquid-like properties. In terms of practical use it means that CO2 can be used as an effective solvent for reactants, while the viscosity and diffusion coefficients are close to those for gases, which minimises heat and mass transport limitations in case of heterogeneous catalysis. Previous reports and the studies in the present thesis have shown that phase behaviour can play a crucial role in chemical reactions, especially when they are performed near the supercritical region of the reaction mixture. Experimental monitoring and determination of phase equilibria is very time consuming, expensive, and very often reveals very little information. However, these problems can be overcome when thermodynamic modelling is applied. The Cubic-Plus-Association Equation of State (CPA) was used throughout this study; therefore this model is discussed more extensively. Heterogeneously catalysed hydrogenation reactions are considered to be quite well studied and established. However, the catalyst performance can alter significantly when the reaction is performed in carbon dioxide medium. This effect was studied with the example of the selective hydrogenation of 2-butenal over palladium catalyst. It was found that the maximum conversion of 2-butenal is achieved when the reaction mixture exists in the near-critical region, or the so-called “expanded-liquid” phase. Some possible reasons for that have been proposed. Aldol reactions are the complex processes that are very important for the chemical industry. Furthermore, multistep reactions performed in “one-pot” using multifunctional catalysts attract a lot of interest. Thus, a part of this thesis was devoted to performing the aldol reaction and the “one-pot” synthesis of aldol products starting from the selective hydrogenation of unsaturated aldehydes in carbon dioxide medium. It was found that supported tungstosilicic acid catalysts and acidic resin Amberlyst-15 are very effective for performing aldol reactions. The positive influence of temperature and CO2-content on catalyst activity was studied. Furthermore, the “one-pot” synthesis with 2-butenal was performed using bifunctional and mixed catalysts. The reactions were studied in different reactor types and reaction conditions were optimised using CPA calculations. Extensive catalyst characterisation was carried out in order to understand the catalyst structure. Carbon dioxide can play a dual role in some chemical reactions, i.e. as reaction medium and as one of the reactants. An example of this reaction is the synthesis of propylene carbonate from propylene oxide and CO2. The study of the phase equilibrium in this case is more complex not only because the composition changes due to the chemical reaction, but also due to the constantly decreasing amount of solvent. Furthermore, organic carbonates have significantly lower solubility in CO2 than reacting epoxides. In this part of the study, the influence of CO2-content on the performance of the immobilized 1-hydroxyethyl-9-propyl-cyclicguanidinium bromide on SBA-15 (HEPCGBr/SBA-15) catalyst was investigated. The maximum conversion was observed in the transition region from the two- to one-phase state. This finding was supported by previous experimental studies. Thermodynamic calculations were shown to be extremely useful for the phase behaviour investigations. The direct synthesis of dimethyl carbonate from methanol and CO2 has been investigated for quite a long time, however hardly any sufficiently active catalysts have been found so far. Nevertheless, optimisation of the phase equilibria of the reaction mixture can make the process economically more feasible. Many different thermodynamic models of different capability and applicability have been applied for this task. The CPA model is an advanced model that accounts for complex interactions between associating molecules like water and methanol. It has been shown that CPA can satisfactorily describe any type of phase equilibria for the quaternary reaction mixture as well as ternaries and binaries that comprise it. This makes CPA a universal and very useful model for many practical applications. All aforementioned studies have shown that supercritical fluids in heterogeneous catalysis complemented by thermodynamic modelling have an immense potential for further investigations.