Methods for gas network simulation – loops method
REFERENCES:
A.E. Fincham and N.H. Goodwin, “Methods for gas network simulation”
There are many methods of analyzing the mathematical models of gas networks but they can be divided into
two types as the networks, the solvers for low pressure networks and solvers for high pressure networks.
The networks equations are non-linear and are generally solved by some of Newton iteration; rather then use full
set of variables it is possible to eliminate some of them. Based on the type of elimination we can get solution
techniques are termed either nodal or loop methods. In this article we will review basics of the loops method.
Before using loops method the fundamental set of loops need to be found. Basically the fundamental set of loops
can be found by constructing spanning tree for the network. The standard methods for producing spanning tree is
based on a breadth first search or on a deep first search which are not so efficient for large networks, because
the computing time of these methods is proportional to n
2, where n is the number of pipes in the network. More
efficient method for large networks is the “Forest method” and its computational time is proportional to n*logn
2n.
The loops that are produced from the spanning tree by adding in the co-tree pipes are not the best set that could
be produced. There is often significant overlap between loops with some pipes shared between several loops;
this slows down convergence in the Hardy Cross algorithm and wasteful on loops storage. We can reduce the overlap
by replacing the loops in the original fundamental set by smaller loops produced linear combination of the original
set.
The loops method has a number of disadvantages compared to nodal method:
- It requires extra computation to produce a set of loops.
- The dimension of the equations to be solved is smaller but they are much less sparse.
- The method is not suitable for networks containing non-pipe elements.
The main advantage is that the equation can be solved very efficiently with an iterative technique that avoids
the need of matrix factorization and consequently has a minimal requirement for storage; this makes it very
attractive for low pressure networks with a large number of pipes.