Hydrogenation of vegetable fats is an important biomolecule modification process, traditionally carried out in a slurry reactor at low pressure (2–6 bar). Here, the hydrogenation of sunflower oil in supercritical propane and dimethyl ether catalysed by Pd (supported on activated carbon or alumina) is studied. One-dimensional simulation models for plug flow and mixed flow reactors, as well as two-dimensional dispersed plug flow reactor models, were developed for the case of isothermal and adiabatic operation. The hydrogenation of sunflower oil is considered as a reaction network based on linoleate, oleate (cis C18:1), elaidate (trans C18:1) and stearate triesters. Since trans fatty C18:1 ester and stearate formation is not desired, the question arises as to which reactor type is best to achieve a low elaidate content. Depending on the final allowed stearate content, different mixed and plug flow reactor models can be applied. However, for a fixed stearate formation rate, the mixed reactor gives a lower trans content than the plug flow reactor in most cases. Also, low temperature operation results in better oleate/stearate selectivity. Two-dimensional tubular reactor dispersed simulation does not give further insight into the problem. The use of Multiphysics (finite element method) for solving the dispersed plug flow model provides a way to simulate CSTR reactor behaviour. In our case, both heat and mass Péclet numbers of 10−4 or less are sufficient to describe well-mixed reactor behaviour using the 2D mass and heat transfer pseudo-homogeneous model with radial and axial effects, with parameter values available for SCF. The models can be used for planning reaction operations in SCF as solvents intended for low trans fatty acid.