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Calibrating Your Hydraulic Model with Multiple Data Sets

When evaluating the hydraulic behavior of aged pipelines and/or pipelines that are exposed to particularly corrosive or dirty fluids, building and running a hydraulic model is a great first step, but more engineering may be required. This is because, over time, residue in the pipeline fluid can buildup in the pipeline and essentially decrease the pipe inner diameter while increasing the roughness of the pipe’s inner surface. Corrosion can also change the roughness of the pipe’s inner surface. Engineers know that these changes due to buildup and corrosion in the pipes can significantly affect the hydraulics of the system, so while building a hydraulic model of the system is essential to evaluate its behavior, calibrating the model to account for these changes can be just as important in getting an accurate representation of your system. AFT Fathom and AFT Arrow offer a goal seeking module to assist with this calibration process with one data set of flow data. To understand how this can be done, visit Dylan’s blog. My blog here will take Dylan’s discussion one step further and discuss how AFT Fathom and AFT Arrow can be used to calibrate a hydraulic model with not just one but with multiple data sets using the GSC (Goal Seek and Control) module.

 There are several advantages to calibrating a model to multiple data sets. The primary advantage is of course the increased level of confidence you can have in your model calibration, especially if you use pressure and flow data from the system while it is operating in different configurations (i.e, with different valve positions, different equipment in service and out of service, etc.) to calibrate your model. A popular phrase at AFT is that the results of a model can only be as accurate as the data used as model input in the first place (actually, we are slightly more abrupt in stating that garbage in=garbage out, but you get the point!). In the case of model calibrations, there is nearly an infinite amount of possible ways to calibrate a model that will still fit the recorded flow and pressure data. The more data you have means you are applying more rigid criteria for the calibration, leading to a more accurate model calibration. 

For example, if you have a pressure of 30 psig recorded at one location in your system, the pressure drop in the system required to achieve this measured pressure can be applied all in one location in the hydraulic model, or it can be spread out over several components in the model. In both cases, the hydraulic model’s predicted pressure of 30 psig at this location will match the measured pressure, but there can only be one actual configuration in the system itself that is making your system produce these specific hydraulic results. The only way to distinguish between a plausible hydraulic model of your system and a hydraulic model that actually represents your system is to calibrate the model using as much pressure and flow data as possible, ideally with pressure and flow data from different operating configurations. When it comes to model calibration, more is better!

 The following example details how to use AFT Fathom to simultaneously calibrate two data sets of a simple hydraulic model. Note that this procedure can be replicated in AFT Arrow, as well.

Let’s say you have the following pipeline shown in Figure 1 with two operating configurations that include 1) both Valve A and Valve B open at 100% of their full open Cv (500) in the first operating configuration, and 2) the position of Valve B is decreased to 30% of its full open Cv (150) in the second operating configuration. Figure 1 shows the system in these two operating configurations.

Figure 1: AFT Fathom model showing both operating configurations

Now let’s say the following data was recorded in the field for both operating configurations:

Figure 2: Pressure and Flow Field data for System in both Operating Configurations

The model is built and the field data is collected. We now need to calibrate the hydraulic model so that it will predict the pressures and flows recorded when the system was in Operating Configuration 1. This needs to be performed when the hydraulic model is in Operating Configuration 1 with both valves in their full open positions. 

Similarly, we need to calibrate the hydraulic model so that it will predict the pressures and flows recorded when the system was in Operating Configuration 2. This needs to be performed when the hydraulic model is in Operating Configuration 2 with Valve A at full open and Valve B at 30% of its full open Cv.

To calibrate the model, we will add ID reduction (also called Scaling) to represent fouling in the pipes, as well as increase pipe roughness values to represent the increasingly rough flow surface as buildup and corrosion occur in the pipes. We first make a copy of the original, uncalibrated hydraulic model and use one copy to represent the system in Operating Configuration 1 and another to represent the system in Operating Configuration 2. Note that AFT Fathom and AFT Arrow allow both models to be run in the same hydraulic calculation, so there is no need to make separate model files (very nice!). While we are calibrating each model according to its field-recorded data, keep in mind that this is the same system. Therefore, any scaling or increased pipe roughness value applied to a pipe in the first model (Pipe 2, for example) must be applied identically to the corresponding pipe in the second model (Pipe 11). Ultimately, then, the final goal is to develop one hydraulic model that, when placed in a certain operating configuration, will predict the pressures and flows measured in the system when it was operating in that configuration. Switching the same hydraulic model’s configuration should then yield pressure and flow results that were recorded in the field when the system was operating in that configuration.

GSC automatically adjusts the pipe roughness or scaling values (it can only change one parameter per variable at a time) to achieve the pressure and flow goals we are looking to achieve, so it needs to be configured. To set up the GSC Manager, first globally add some scaling to all pipes so that this is an applicable pipe parameter to vary within GSC. Then open the GSC Manager. We will input all the pipes as variables first. Add a variable for each pipe and make each pipe variable the ID Reduction. Note that GSC allows you to link pipes, meaning that they will be varied identically. This is very handy because it means that we can link the corresponding pipes in each model to each other. This has been completed in Figure 3. Note that Pipe 1 is linked to Pipe 10 under the “Link To” column because these represent identical pipes in the physical system. All other pipes are linked to their respective pipes, as well.

Figure 3: The GSC Manager’s Variables tab is shown here to demonstrate how the pipe ID reduction values are specified as variables with linked pipes

The Goals tab in the GSC Manager is then completed to specify the flow and pressure goals we want to achieve in each model by varying the specified variables.

Figure 4: The GSC Manager’s Goals tab is shown here to demonstrate how the pressure and flow goals are specified for both data sets

After entering the goals into the GSC Manager, we run the model. The output shows the values of the variables and the resulting goals that were achieved. See Figures 5 and 6 for the resulting goals and variables.

Figure 5: The resulting pipe ID reduction values calculated by GSC from the Output

Figure 6: The resulting volumetric flow rates and pressures achieved by GSC with the Variables in Figure 5 applied to the model

After GSC has generated this Output, we can refine the process by changing initial guesses of ID reduction if necessary, as well as applying these scaling values to the pipes and then varying the pipe roughnesses using the GSC Manager. This process can be repeated until we are satisfied that the results are sufficiently close to the measured field values.

Calibrating a hydraulic model using multiple data sets improves the accuracy of your hydraulic model and will predict hydraulic behavior more in-line with the actual system’s behavior. Because a more accurately calibrated hydraulic model using more data requires more time to both record the data as well as calibrate the model, the engineer must determine what level of accuracy is required when calibrating the model. However, because AFT Fathom and AFT Arrow can significantly decrease the amount of time necessary to perform this calibration, this trade-off becomes less dramatic and a more accurately calibrated model is more easily and quickly achieved. Once your hydraulic model has been successfully calibrated, you can gain valuable insight into how changes in your piping system would affect the system hydraulics, as well as what areas of the system could be causing the most problematic pressure drops.


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Wednesday, 22 March 2023
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