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Further development on globally convergent algorithms for solution of stationary network problems is presented. The algorithms make use of global non-degeneracy of Jacobi matrix of the system, composed of Kirchhoff's flow conservation conditions and transport element equations. This property is achieved under certain monotonicity conditions on element equations and guarantees an existence of a unique solution of the problem as well as convergence to this solution from an arbitrary starting point. In application to gas transport networks, these algorithms are supported by a proper modeling of gas compressors, based on individually calibrated physical characteristics. This paper extends the modeling of compressors by hierarchical methods of topological reduction, combining the working diagrams for parallel and sequential connections of compressors. Estimations are also made for application of topological reduction methods beyond the compressor stations in generic network problems. Efficiency of the methods is tested by numerical experiments on realistic networks.

The formulation of transport network problems is represented as a translation between two domain specific languages: from a network description language, used by network simulation community, to a problem description language, understood by generic non-linear solvers. A universal algorithm for this translation is developed, an estimation of its computational complexity given, and an efficient application of the algorithm demonstrated on a number of realistic examples. Typically, for a large gas transport network with about 10K elements the translation and solution of non-linear system together require less than 1 sec on the common hardware. The translation procedure incorporates several preprocessing filters, in particular, topological cleaning filters, which accelerate the solution procedure by factor 8.

Solving transport network problems can be complicated by non-linear effects. In the particular case of gas transport networks, the most complex non-linear elements are compressors and their drives. They are described by a system of equations, composed of a piecewise linear ‘free’ model for the control logic and a non-linear ‘advanced’ model for calibrated characteristics of the compressor. For all element equations, certain stability criteria must be fulfilled, providing the absence of folds in associated system mapping. In this paper, we consider a transformation (warping) of a system from the space of calibration parameters to the space of transport variables, satisfying these criteria. The algorithm drastically improves stability of the network solver. Numerous tests on realistic networks show that nearly 100% convergence rate of the solver is achieved with this approach.

The general method of topological reduction for the network problems is presented on example of gas transport networks. The method is based on a contraction of series, parallel and tree-like subgraphs for the element equations of quadratic, power law and general monotone dependencies. The method allows to reduce significantly the complexity of the graph and to accelerate the solution procedure for stationary network problems. The method has been tested on a large set of realistic network scenarios. Possible extensions of the method have been described, including triangulated element equations, continuation of the equations at infinity, providing uniqueness of solution, a choice of Newtonian stabilizer for nearly degenerated systems. The method is applicable for various sectors in the field of energetics, including gas networks, water networks, electric networks, as well as for coupling of different sectors.

Alkaline methanol oxidation is an important electrochemical process in the design of efficient fuel cells. Typically, a system of ordinary differential equations is used to model the kinetics of this process. The fitting of the parameters of the underlying mathematical model is performed on the basis of different types of experiments, characterizing the fuel cell. In this paper, we describe generic methods for creation of a mathematical model of electrochemical kinetics from a given reaction network, as well as for identification of parameters of this model. We also describe methods for model reduction, based on a combination of steady-state and dynamical descriptions of the process. The methods are tested on a range of experiments, including different concentrations of the reagents and different voltage range.

The paper presents the topological reduction method applied to gas transport networks, using contraction of series, parallel and tree-like subgraphs. The contraction operations are implemented for pipe elements, described by quadratic friction law. This allows significant reduction of the graphs and acceleration of solution procedure for stationary network problems. The algorithm has been tested on several realistic network examples. The possible extensions of the method to different friction laws and other elements are discussed.

It is shown that the electrochemical kinetics of alkaline methanol oxidation can be reduced by setting certain fast reactions contained in it to a steady state. As a result, the underlying system of Ordinary Differential Equations (ODE) is transformed to a system of Differential-Algebraic Equations (DAE). We measure the precision characteristics of such transformation and discuss the consequences of the obtained model reduction.

In this paper, an analysis of the error ellipsoid in the space of solutions of stationary gas transport problems is carried out. For this purpose, a Principal Component Analysis of the solution set has been performed. The presence of unstable directions is shown associated with the marginal fulfillment of the resistivity conditions for the equations of compressors and other control elements in gas networks. Practically, the instabilities occur when multiple compressors or regulators try to control pressures or flows in the same part of the network. Such problems can occur, in particular, when the compressors or regulators reach their working limits. Possible ways of resolving instabilities are considered.

In this paper, the electrochemical alkaline methanol oxidation process, which is relevant for the design of efficient fuel cells, is considered. An algorithm for reconstructing the reaction constants for this process from the experimentally measured polarization curve is presented. The approach combines statistical and principal component analysis and determination of the trust region for a linearized model. It is shown that this experiment does not allow one to determine accurately the reaction constants, but only some of their linear combinations. The possibilities of extending the method to additional experiments, including dynamic cyclic voltammetry and variations in the concentration of the main reagents, are discussed.

In this paper, modeling of piston and generic type gas compressors for a globally convergent algorithm for solving stationary gas transport problems is carried out. A theoretical analysis of the simulation stability, its practical implementation and verification of convergence on a realistic gas network have been carried out. The relevance of the paper for the topics of the conference is defined by a significance of gas transport networks as an advanced application of simulation and modeling, including the development of novel mathematical and numerical algorithms and methods.

The transport of carbon dioxide through pipelines is one of the important components of Carbon dioxide Capture and Storage (CCS) systems that are currently being developed. If high flow rates are desired a transportation in the liquid or supercritical phase is to be preferred. For technical reasons, the transport must stay in that phase, without transitioning to the gaseous state. In this paper, a numerical simulation of the stationary process of carbon dioxide transport with impurities and phase transitions is considered. We use the Homogeneous Equilibrium Model (HEM) and the GERG-2008 thermodynamic equation of state to describe the transport parameters. The algorithms used allow to solve scenarios of carbon dioxide transport in the liquid or supercritical phase, with the detection of approaching the phase transition region. Convergence of the solution algorithms is analyzed in connection with fast and abrupt changes of the equation of state and the enthalpy function in the region of phase transitions.