We present a method for synthesizing chemical process models that combines prior knowledge and artificial neural networks. The inclusion of prior knowledge is investigated as a means of improving the neural network predictions when trained on sparse and noisy process data. Prior knowledge enters the hybrid model as a simple process model and first principle equations. The simple model controls the extrapolation of the hybrid in the regions of input space that lack training data. The first principle equations, such as mass and component balances, enforce equality constraints. The neural network compensates for inaccuracy in the prior model. In addition, inequality constraints are imposed during parameter estimation. For illustration, the approach is applied in predicting cell biomass and secondary metabolite in a fed-batch penicillin fermentation. Our results show that prior knowledge enhances the generalization capabilities of a pure neural network model. The approach is shown to require less data for parameter estimation, produce more accurate and consistent predictions, and provide more reliable extrapolation.