An Improved Gas Transmission System Simulator
Authors: Berard G.P. , Eliason B.G. 
Published: December 2007

Abstract
CASPR (acronym for Capability And Simulation Program) is a new computer program that simulates Program) is a new computer program that simulates steady-state gas transmission networks based on the Newton-Raphson balance of nodes method. The program contains several refinements, such as an program contains several refinements, such as an optimal node-numbering scheme to eliminate pivoting of the coefficient matrix and to reduce matrix an implicit compressor-fuel gas calculation, the ability to prorate equally gas volumes entering the network system, and the optional calculation of a flowing-gas temperature profile.

Introduction
The simulation of gas transmission systems requires increasingly sophisticated computer software as these systems grow in size and complexity. The major complication of system modeling is the need to accommodate systems with closed loops. Other factors also contribute to the need for improved system modeling, such asaccurate accountability of more expensive compressor-station fuel gas consumption,proper proration of gas supply from many collection points proration of gas supply from many collection points to assure adequate transmission-system capacity for a given demand, anda detailed knowledge of the gas-flowing temperature through accurate simulation of heat-transfer effects.
CASPR was developed to meet these requirements with improved computational efficiency through the use of optimal node numbering.

THE DEVELOPMENT OF CLOSED-LOOP MODELS
The need to simulate closed-loop systems has resulted in implementation of techniques evolving from the original work of Cross, to that of Epp and Fowler, Shamir and Howard, and the adaption of the last study to the gas-distribution industry by Stoner.
These closed-loop models all satisfy one or more of Kirchoff's laws; (1) the sum of the potentials around a closed loop is zero, and (2) the flow into a point equals the flow out of that point. Methods satisfying one or both of these laws can be broadly classified as either explicit or implicit. Explicit models were formulated by several authors, however, the lack of mathematical rigor prevents the modeling of sensitive systems or systems with many closed loops.
Implicit methods involve writing a series of nonlinear algebraic equations and solving them, using a technique such as the n-dimensional Newton-Raphson method. This method requires solving for an n x n coefficient matrix, which for large n can require large amounts of computer time and storage. Several workers have taken advantage of the usually sparse structure of the coefficient matrix to minimize this problem, although the sparse matrix formulation can be cumbersome to set up and update, especially if pivoting is required to ensure diagonal fill-in and reduce round-off error.

FORMULATION OF THE NODAL PROGRAM
In the well known nodal formulation, a pipeline system (Fig. 1) is represented by a network of nodes and node connecting elements (NCE's)
q1? (prorate) q2? (prorate)
Node Node Node1 2 1 3
P1 P2? Pc? Pc
qf1? q3
q1 . unknown prorated receipt point volume at node 1
p1 . fixed pressure at node 1
q2 . unknown prorated receipt point volume at node 2
P2 . unknown pressure at node 2 (compressor station suction)
qf1 . compressor station 1 fuel gas (function of horsepower)
PC . unknown horsepower at compressor station 1
. compressor station 1
P3 . fixed pressure at node 3 (compressor station discharge)
q3 . fixed delivery point volume at node 3
FIG. 1 - SCHEMATIC OF NODES AND NCE'S.
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