The modeling equations for transient gas and liquid pipeline behavior are well established as well as certain standard methods for their solution. The focus here is the solution to the transport equation which describes the movement of gas qualities (composition, specific gravity, heating value, etc.). The different sections of the paper correspond to the definition of the problem, the needs and applications of quality tracking, a technical description of the two solution techniques, an outline of the analysis performed, and a summary of the conclusions drawn from the studies. The solution of the transport equation must be accurate enough in time and space without being computationally intensive. The accuracy, a function of the time and grid discretization, behaves differently depending on the solution technique employed. Since all of the equations are coupled, that is they depend on each other, it is also important to study the affect of the quality solution to the solution of the other hydraulic equations. This coupling, influenced by a number of factors including the choice of time and distance steps, is different for the two methods under study. The analysis performed is broken down into two levels: one using simple configurations and one using complex configurations. In the simple runs, where detailed analysis is tractable, the emphasis is on the quality profile solution change with time and the transient behavior of the packing rate. In the complex configurations, the affects of the two solutions is reported in terms of aggregate results like fuel and power usage and system packing rate. This configuration is also used to show how automatic time step selection affects these aggregate numbers.
The pipeline modeling equations consist of a set of balance equations: the Mass Balance, the Momentum Balance and the Thermal Balance. The detailed equations are given in the methods section in Part 3. These nonlinear equations are coupled together through the dependence of many variables including density. The density is computed using an assumed equation of state which is a function of pressure, temperature, and gas composition. Hence, the accounting and tracking of gas composition is important in the accuracy of the solution to the balance equations. Also, the accounting of impurity compositions like water or hydrogen sulfide is critical in certain applications. Additionally, the tracking of other qualities, which like gas composition obey the transport equation and travel at local fluid velocity, specifically specific gravity and heating value is important in many applications. The cost of gas may also be tracked. In summary, any property that moves at local fluid velocity such as batches of gas or liquid or even a pig traveling through the pipeline may be refered to and treated as a quality. A predictive model may be used by a dispatcher, operator or pipeline engineer to study the design and/or operation of a pipeline network. The types of studies typically fall under two areas: normal system operation, and transient system response.