  Model identifiability concerns the uniqueness of uncertain model parameters
to be estimated from available process data and is often thought of as a
prerequisite for the physical interpretability of a model. Nevertheless, model
identifiability may be challenging to obtain in practice due to both stochastic
and deterministic uncertainties, e.g. low data variability, noisy measurements,
erroneous model structure, and stochasticity and locality of the optimization
algorithm. For gray-box, hybrid models, model identifiability is rarely
obtainable due to a high number of parameters. We illustrate through an
industrial case study - modeling of a production choke valve in a petroleum
well - that physical interpretability may be preserved even for
non-identifiable models with adequate parameter regularization in the
estimation problem. To this end, in a real industrial scenario, it may be
beneficial for the model's predictive performance to develop hybrid over
mechanistic models, as the model flexibility is higher. Modeling of six
petroleum wells on the asset Edvard Grieg using historical production data show
a 35\% reduction in the median prediction error across the wells comparing a
hybrid to a mechanistic model. On the other hand, both the predictive
performance and physical interpretability of the developed models are
influenced by the available data. The findings encourage research into online
learning and other hybrid model variants to improve the results.
