There are two main analysis engines that solve for pressures and flows during transient events within incompressible fluids: These are the Wave Plan Method (WPM) and the Method of Characteristics (MOC). Tran-Surge uses the Wave Plan Method (WPM).
How Do These Analysis Engines Work?
WPM and MOC utilize different approaches to solving for pressures and flows in transient simulations. MOC divides all the pipes in the system into many smaller lengths, and performs a friction calculation at each of these small increments within the pipeline (including calculating the effects of wave reflection at devices and junctions). So even a very short pipeline may have hundreds of computations required within small, physically identical lengths of pipes at each time step, and the number of computations for all pipes can become extreme for medium-size and large-size systems. This discrete length at which calculations are required is referred to as the Length Accuracy.
WPM, on the other hand, approaches pipes based on higher Length Accuracy values, dispensing with the need to make extra calculations within portions of the system that are physically identical (i.e., WPM may make one friction-based calculation within a pipe as opposed to several, depending on the pipe length, given that the physical characteristics within that pipe did not change). That is to say, for a given Length Accuracy value, say 10 feet, or 50 feet, WPM only performs one calculation to account for friction for that entire length of pipe. The WPM analysis engine also makes a dedicated calculation for wave reflection at devices and junctions. However, in general, WPM tracks the movement of pressure waves and only makes a calculation where waves interact or where one of the above discrete friction points (or junctions or devices) is reached. MOC makes calculations at all discrete points within the system regardless of whether a pressure wave is passing a given point at that time or not. While the Length Accuracy of both WPM and MOC can be reduced to increase accuracy, the cost in extra analysis time for the MOC can quickly become extreme due to the higher number of calculations required, see more below.
Which is More Accurate, WPM or MOC?
As stated, both analysis engines require the user to specify the discrete distance within pipes at which a calculation of the system equations is made, known as the Length Accuracy. The smaller the Length Accuracy, the higher the output accuracy for parameters such as pressures and flows. For most real- world systems, the accuracies are the same, but for some systems, MOC can be made to be slightly more accurate by specifying decreased Length Accuracies. Although to do so, MOC requires orders of magnitude more time to arrive at a solution than WPM. And, for larger models, depending on the accuracy required, the analysis time for MOC can become unacceptable.
How Much More Accurate Is MOC Than WPM in Such Cases?
As stated, MOC can be made to be extremely accurate with increasing model analysis times, somewhat ahead of WPM. With WPM, while the trend of increasing analytical accuracy with decreasing Length Accuracy is similar, the trade-off in accuracy for analysis time is much less, and accuracy suffers very little. For example, Lingireddy (2021) examined the effect of WPM model accuracy of analyzing pipe lengths (as proxies for Length Accuracy) between 10 m, 50 m, 500 m, and 1000 m. Lingireddy found differences in the accuracy of model pressure predictions as pipe length increased; specifically, these differences could be seen within the second, third, or fourth decimal place of the pressure result value. Therefore, even at the maximum length used for Lingireddy’s calculations, the loss in accuracy was still <0.1%. However, Lingireddy went on to note that a pipe length of 1000 m (where the lowest accuracy was obtained) is normally too high a value to be used for Length Accuracy within any given model – this is because best modeling practices suggest the placement of nodes at locations of elevation inflection points in order to capture pressure changes at these locations. Therefore, Lingireddy recommends that Length Accuracy should not normally exceed 500 m, although practically speaking, Length Accuracy is usually set to smaller values than 500 m, more closely approximating the lengths of the smaller individual pipes within the model. In such cases, the accuracy loss for WPM can be expected to be <0.01%.
While average pipe lengths are often very high for long transmission mains modeled within Transurge, such systems also often involve pumping stations that have much shorter pipe lengths; so even for projects modeled in Transurge, the Length Accuracy values are normally smaller than 500 m. For pipelines without pumping stations, such as those that gravity flow from reservoir to reservoir, modelers can examine the trade-off between analysis times and accuracy for longer values of the Length Accuracy parameter. However as stated above, elevation inflection points should be accounted for, and 500 m is normally the maximum recommended.
Lingireddy also points out that pressure variations in the model results that can only be seen in the second, third, or fourth decimal place are almost always more than acceptable, for two reasons: First, such inaccuracies are lower than the inaccuracies of many of the input variables to the model (pipe length, pipe roughness, etc.). Second, since the magnitude of negative pressure waves of concern is in the vicinity of -14.7 psi or -10.1 m, and the magnitude of positive pressure waves of concern is much higher (usually well over 100 psi or 142.2 m) – in these situations, small variances will not affect the need for, or design of, surge protection devices for a given system. And, as stated, if more accuracy is needed, say for extreme systems such as nuclear reactors where very precise calculations are required, the Length Accuracy can always be shortened so the accuracy of WPM approaches or equals that of MOC, depending on the situation, while still resulting in shorter analytical run times than MOC.
What is the Difference in Number of Calculations Performed Between WPM and MOC? And What are the Difference in Analytical Run Times?
Lingireddy has found that, for most systems, the WPM approach requires vastly fewer calculations. For one example, which was a 2517-pipe potable water distribution system, MOC required 323,995 calculations per time step. On the other hand, WPM required 4267 calculations per time step while producing virtually identical solutions. This difference in computational time is extreme enough that sometimes the skeletonization of a portion of a system is required to even run MOC within a realistic timeframe.
Similarly, Ramalingam (2007) concluded that both WPM and MOC were able to obtain the same level of accuracy during his testing, but with a large difference in the number of calculations performed. Specifically, Ramalingam modeled a 1.1 km pipeline system: To produce accuracy values less than 0.1%, MOC required that the pipeline be divided into 100 segments, whereas WPM produced the same accuracy with the pipeline divided into 5 segments, with concomitant decreases in analysis time. For the types of systems studied by Ramalingam, the analysis time of WPM was several orders of magnitude faster than that of MOC to produce the same level of accuracy.
Conclusion
In sum, while the computational excess of MOC can result in slightly higher levels of accuracy in niche< situations, the trade-off in accuracy for computation time is vastly in favor of WPM when modeling most real-world systems.
- Lingireddy and Wood (2021). Surge analysis and the Wave Plan Method: a powerful, accurate and stable method for water hammer studies.
- Ramalingam (2007). Design aids for air vessels for transient protection of large pipeline networks – a framework based on parameterization of knowledge derived from optimized network models, a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Engineering at the University of Kentucky.