(184t) Dynamic Optimization of Natural Gas Network with Rigorous Thermodynamics

Pipelines are widely used in the transportation of natural gas, and their optimal operation requires accurate models. In particular, accurate thermodynamic properties are important for the dynamic models, as the gas goes through significant changes of thermodynamic properties across time and space.

Gas thermodynamic properties, like gas compressibility factor (Z-factor), are influenced by internal properties like gas composition, and environmental conditions like temperature and pressure. Previous work has applied experiment results in the form of charts for reference. The major drawback of these reference charts is that they only provide rough estimations and cannot be used directly in the mathematical optimization models. In the last few decades, several methods for gas thermodynamic properties have been proposed and accurate approximations can be obtained. These methods solve implicit nonlinear equations, and their direct implementation would make the dynamic model prohibitively expensive to solve. As a result, many researchers have simplified the natural gas model by assuming the natural gas to be an ideal gas, which inevitably introduces errors to the models.

In this study, we develop and compare different thermodynamic property methods for the Z-factor to find the most accurate approximation for the existing dynamic transmission model. Since the direct implementation of the existing thermodynamic calculating methods are difficult to solve, reduced order models(ROM) are used to replace the complex thermodynamic equations. Here, the ROM method can help accelerate the computation but may lead to inaccurate approximations to the original model. To guarantee convergence to an optimum, a trust-region based optimization framework is required. However, ROMs are computational tractable for problems with less than a few dozen variables. While in the dynamic pipeline network, we need to calculate Z-factors at every spatial and temporal discretization point, and the number of variables grows rapidly as the resolution of the model increases. Therefore, the ROM-based trust-region method is overwhelmed by the dynamic model. To address this challenge, we propose a distributed trust region method, which builds separate trust regions at every discretization point. In this way, each trust region only needs to handle a small number of ROM variables. When the resolution discretization increases, only the number of trust regions increases, while the size of the ROMS remains the same for every trust region.

This approach is incorporated within Pyomo, an optimization modeling platform and solver interface. This platform works as well as any other algebraic modeling languages such as GAMS and AMPL in terms of model formulation and analysis. Moreover, it contains a rich set of meta-solvers developed by Process Systems Engineering community. Finally, Pyomo’s modeling objects are embedded within Python, which makes it flexible to implement user-defined optimization framework.

To demonstrate this ROM-based trust region approach, we consider a dynamic natural gas pipeline network with multiple compressors and present significant improvements in the efficiency of the optimization strategy and the quality of solutions.