For chemical reactors with non-linear fluid dynamics, a linear model realisation is proposed. The inputs are the ingoing concentration of a certain component in the fluid, and the reaction rate. The output is the outgoing concentration. The realisation makes use of a first-order reaction equation, and the residence time distribution of the fluid particles inside the reactor. Also dead time is incorporated in the modelling. The method is tested on two non-linear models for which the residence time distributions are known analytically. The first model is a series of mixed tanks, and it is shown by simulation that the method gives an accurate approximation of the original model. The second model is a UV disinfection reactor, which has a dead time. For this model, the residence time distribution is first fitted by a form that is suitable for our realisation method. Simulations show that for realistic disturbances a high-performance linear controller can be designed. After that, the residence time distribution of a real life UV reactor (for which we have no model) is fitted by a suitable form. The fit is of the same quality as for the UV reactor model. This indicates that also for the real life UV reactor a high-performance controller can be designed.