Use of combined physical and statistical models for online applications in the pulp and paper industry

This paper discusses the accuracy of different types of models. Statistical models are based on process data and/or observations from lab measurements. This class of models are called black box models. Physical models use physical relationships to describe a process. These are called white box models or first principle models. The third group is sometimes called grey box models, being a combination of black box and white box models. Here we discuss two examples of model types. One is a statistical model where an artificial neural network is used to predict NO x in the exhaust gases from a boiler at Mälarenergi AB in Västerås, Sweden. The second example is a grey box model of a continuous digester. The digester model includes mass balances, energy balances, chemical reactions and physical geometrical constraints to simulate the real digester. We also propose that a more sophisticated model is not required to increase the accuracy of the predicted measurements.