Summary

This paper describes a gas network state estimator using field measurements. A gas network consist of pipes, supply and offtake points, compressors and reducers. The state of the network is defined by the pressures and flows prevailing in it. In order to do a predictive simulation, predictive setpoints of the supplies, offtakes, compressors and reducers are required. These setpoints may be time varying quantities. Furthermore a starting situation, initial state, is needed. In a real time environment this initial state depends on field measurements. However direct use of (part of) the measurements will give poor results, due to measurement errors and model inaccuracy. This holds especially if pressure measurement errors are of the same order of magnitude than the pressure drop in the network. With the Equal Error Fraction method the initial state can be estimated using all measurements. For each measurement the difference between the measured and calculated value will be of the same order of magnityde than the metering instrument accuracy. The Equal Error Fraction method and its generalisation represent a simple, stable state-estimator. Introduction Gas transport in a pipeline is described by two partial differential equations and the equation of state. Integrated over the length of the pipeline and simplified one obtains the pressure drop and line pack formula. So the pressure drop in a pipeline is proportional to the square of the flow. The meaning of the line pack formula is that pressure rise is proportional to the flow difference at the beginning and the end of a pipeline. The equations mentioned (and more equations in the sequel) are not intended to be precise, but are intended to highlight the physical characteristics valid in gas transport. Consider the case that we have a single pipeline with a supply and an offtake. Suppose we can measure pressure and flows at both ends of the pipeline. A state--estimator must calculate pressures and flows that are:

• consistent: obey physical laws;

• close to measured values at points of measurement.

The word close represents a relative conception. The difference between a calculated and measured value can best be related to the accuracy of the metering instrument. So let us define the error fraction as the difference between the measured and calculated value divided by the metering instrument accuracy. The average error is defined as the root mean square of the error fractions. So in the stationary case we require the calculated values to obey the pressure drop formula and the average error to be minimal. State estimation can be done by direct simulation.

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