The hydrogenation of organic substrates in a fixed-bed catalytic reactor is considered, using supercritical CO2 as a solvent to increase the solubility of hydrogen in the liquid reactants. Reaction rates can be adjusted by changing operating conditions, allowing the reaction volume to be much smaller than in conventional processes. Although it is possible to perform the reaction in a homogeneous phase, to avoid interphase mass-transfer limitations, extremely high temperature and pressure may be needed to reach such a condition; therefore, the reaction is carried out at conditions where both a gas and a liquid phase are present. Taking into account the solid catalyst, a three-phase reaction system has to be dealt with. A trickle-bed high-pressure reactor was simulated using a pseudo-homogeneous two-dimensional model, where both mass and energy balance are considered, The PDE system was solved using an orthogonal collocation method. The model does not include any adjustable parameters, and was developed as an user-written subroutine to be linked with a widely used process simulator (Aspen Plus), thus allowing accurate and flexible thermophysical and VLE calculations. Experiments were carried out in a pilot-scale unit running at Hoffmann-La Roche facilities, so that simulated and experimental values could be compared to state the accuracy of the model.