Reduced order models, commonly referred to as ROMs, have been used in many areas of engineering and physics due to their reduced complexity and corresponding speed of computation of solutions. In gas pipeline transient simulation, transfer function-based ROMs have experienced widespread adoption spanning multiple decades due to their efficiency compared with higher order methods of computational fluid dynamics. Many examples can be traced back to the 1980s Králik et. al. paper that considers simplified transfer functions. Different variations of these transfer functions have appeared in the literature over the years, but each variation tends to be a minor change in the Maclaurin series expansion of Králik et. al.’s original model.
In this paper we start by reviewing Králik et. al.’s model and many of the variations found in the literature while remarking on some typos that have crept into previous papers. In the Appendix we include a derivation of one of the previous models and then show how it can be improved. Next, we present a novel approach to the transfer function approximations using Padé approximants. We then draw conclusions about each model by examining the approximations in the Frequency Domain. Further comparisons are made by utilizing common examples found in the literature as well as real field data, with solutions in the Time Domain. The paper ends with a discussion of the results, additional comparisons with commercially available software and conclusions drawn regarding the novel application of the Padé approximation method.
