There is a need for efficient modeling strategies that quickly lead to reliable models. In the serial gray-box modeling strategy the inaccurately known terms in the macroscopic balance are modeled with a black-box model structure such as a neural network. This way one efficiently obtains an accurate model with good extrapolation properties without the need to develop a rigorous white-box model in which much more knowledge would be involved and without the need to do many identification experiments. Different types of extrapolation are specified and analyzed and they are related to the different parts of the serial gray-box model structure. The strategy is demonstrated for modeling pH effects on the enzymatic conversion of penicillin G using real-life data. The resulting serial gray-box model is compared with a model from a more knowledge-driven white-box strategy and with a model from a more data-driven black-box strategy. The serial gray-box modeling strategy is especially advantageous of the medium level of process operation, which is mainly concerned with the calculation of optimal condition for (bio)chemical processes.