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A non-linear first principle model of an industrial methane rich gas (MRG) network for a large petrochemical plant is developed in this paper. The model is validated against industrial plant data. The non-linearity of gas compressibility, which is sensitive to changes in pressure, composition and temperature, is a challenge for the control of such a network. This model addresses these non-linearities, and is validated with industrial plant data. Each subsystem in the network is modelled separately, and includes models for the pipe segments, gas compressibility, pipe friction factor and gas viscosity. A first principle non-linear model of the system will assist the design of supervisory and optimisation controllers which remain relevant over a large operating region.

A nonlinear phenomenological model of a grinding mill is used to determine five run-of-mine (ROM) grinding milling circuit parameters. The five parameters are fraction of fines and fraction of rocks in the ore fed to the mill, rock and steel abrasion factor and power needed for a ton of fines produced. The model is analyzed according to an identifiability procedure to identify the system data needed to calculate the parameter values. It is shown that a minimum of 18 measurements for a single-stage closed circuit and a minimum of 16 measurements for a single-stage open circuit are needed to determine the five milling circuit parameters. For the closed circuit, the time signals of 8 quantities in the mill will be sufficient to determine all five parameters since the other 10 measurements are time derivatives of these signals. The measurements require the holdup quantities of states within the mill. Since these measurements are not readily available in real-time at plants, it may be difficult to estimate the parameters on-line.