  To operate process engineering systems in a safe and reliable manner,
predictive models are often used in decision making. In many cases, these are
mechanistic first principles models which aim to accurately describe the
process. In practice, the parameters of these models need to be tuned to the
process conditions at hand. If the conditions change, which is common in
practice, the model becomes inaccurate and needs to be re-tuned. In this paper,
we propose a hybrid modeling machine learning framework that allows tuning
first principles models to process conditions using two different types of
Bayesian Neural Networks. Our approach not only estimates the expected values
of the first principles model parameters but also quantifies the uncertainty of
these estimates. Such an approach of hybrid machine learning modeling is not
yet well described in the literature, so we believe this paper will provide an
additional angle at which hybrid machine learning modeling of physical systems
can be considered. As an example, we choose a multiphase pipe flow process for
which we constructed a three-phase steady state model based on the drift-flux
approach which can be used for modeling of pipe and well flow behavior in oil
and gas production systems with or without the neural network tuning. In the
simulation results, we show how uncertainty estimates of the resulting hybrid
models can be used to make better operation decisions.
