Parts 1 and 2 of this series (*Pumps & Systems*, September and October 2015) discussed the engineering principles that dictate the operation of various elements of a piping system. Using those principles, we developed a mathematical model of an example piping system, used the model to simulate the operation of the physical system, and determined if the equipment is operating within the confines of the model. The model was compared with with the physical piping system to identify and isolate problems within the piping system to arrive at a course of corrective action. Part 3 will examine the results and model validation, exploring ways to evaluate the model.
Using the valve stem indicator on the control valve, we can determine the valve is approximately 75 percent open. Using this position, the manufacturers C_{v} table for valve position and the flow rate of 1,000 gpm through the flow meter, we can calculate the differential pressure across the control valve. If the calculated differential pressure across the control valve matches the differential pressure calculated above, we can validate the control valves inlet and outlet pressures. Using the ANSI/ISA – 75.01.01 Flow Equations for Sizing Control Valves standard, Equation 7 can determine the C_{v} value.

_{p}value. Table 1 displays the C

_{v}data for FCV-101.

_{v}and valve coefficient values as a function of the valve position. This can be used to simulate the operation of the specific control valve under various operating conditions. (Courtesy of the author)

_{v}value falls between the 70 and 80 percent valve open position. Performing a linear interpolation between the 70 and 80 percent open results in a calculated valve position of 74 percent for FCV-101 using the valve sizing equation. The calculated results correlates with the observed valve position. Because we have an independent method of calculation using the model with the actual observed values, we can validate the results of the control valve. The total energy values at the inlet and outlet of the head exchanger and the inlet and outlet of the flow meter have not been validated. Because the total energy calculated by the model at PI-101 and the inlet of FCV-101 have been validated, one could assume that the total energy calculated accurately reflects the physical piping system even without the validation of installed instrumentation. Based on the correlation between the calculated energy of the model and the observed values provided by the installed plant instrumentation, one could assume that the model accurately represents the operation of the system under this condition. Imagine two week after the system has been validated the operating tank level in TK-101 has increased from 10 to 15 feet of level. How will that effect the system? Again, the boundary parameters drive the system operation; in this example system, the boundary parameters consist of the supply tank, the destination tank and the flow control loop FCV-101 that regulates the flow rate to a set value. Changing any of these boundary values will change the operation of every item in the system. With a change of operating parameters, the plant operates at 30 psig and a 20 foot level in destination tank PV-102. Figure 5 shows the values of the installed instrumentation. We will use the existing model to determine if it still accurately reflects the system operation. The flow rate through the system is still maintained at 1,000 gpm by the flow control loop. We can see that the position of FCV-101 is now 82.6 percent open. We will evaluate the existing system to see if the model accurately reflects what the system is showing.

- The model accurately reflects the operation of the physical piping system.
- Any deviation between the model and the operation of the physical system can be traced to equipment not operating according to the manufacturer's supplied data or standard engineering calculations.