Analysis of usefluness of some algorithms for steady state simulation in the loop gas networks

Authors: S. Nagy, A. Olajossy, J. Siemek

This paper is devoted to the analysis of classical methods in the steady-state gas flow in a network and to the linear version of a system of equations based on known [Pi] and Q algorithms with the reduction of rank of matrices and with random initial parameters. The presented algorithms may be alternative for the classical gradient type numerical scheme, when any convergence problems may occur. Classes of problems in the steady state gas network simulation have been presented.

The stability, robustness and simplicity are analyzed as well as numerical implementation. The Netwon-Raphson (NR) methods (algorithm 1 and 2) have better convergence, and number of iteration is a rather weak function of the desired accuracy of solution, the proposed algorithms have much stronger relation between the num­ber of iterations and accuracy of solution. The error of initial approximation of the solution is the main disadvantage of NR methods (Zhou Adewumi 1998; Stoner 1969; Szilas 1986; Osiadacz 2001). The authors propose a hybrid algorithm: start using algorithm 3 and 4; after achieving of good approximation of final solution to switch to the NR method. Three simulations of gas network are shown in the paper (low-pressure (Szilas 1986) medium- and high-pressure variants (Stoner 1969)).

The real gas network (Stoner 1969) - geometry shown in the Fig. 4 - a solution given by proposed hybrid algorithm 7 which takes into consideration the real natural gas properties employing Dranchuk-Purvis-Robinson EOS and by linear resistance of each branch of the net in each iteration step is shown in table 8. The average error of computation of pressure in the nodes of network is below 1.3%, which is equivalent to 1 bar and may be sufficient for industry requirements. The results of computation confirm the usefulness of the proposed computation schemes with iterative calculation of properties of gas and friction coefficients. Other results of computation of medium and low case are shown in tables 6 and 10.

The proposed robust algorithm 7, which is a hybrid of algorithm 3 (or 4) with algorithm 1 makes it possible to combine the advantage of algorithm 3 (or 4) - low sensitivity for initial start solution - with the main advantages of NR schemes - high convergence and speed.