Part 1 of this series (Pumps & Systems, September 2015, online here) discussed the engineering principles that dictate the operation of various elements of a piping system. Using those principles, we built a mathematical model of the example piping system based on information supplied by the equipment manufacturers and design data about the tanks and pipelines. This model can be used to simulate the operation of the physical piping system under any expected operating condition. Once the model is available, the next step is to gather the plant's operating data, which is broken down into system boundary parameters and operating results, to compare it with results of the system model. Figure 1 depicts the model piping system with plant operating data listed next to the installed instrumentation. The installed instrumentation consists of the supply tank level, the destination tank level and pressure, the pump suction PI-100 and discharge PI-101 pressures, the position of the control valve, and the flow meter FT-101, which is part of the flow control loop.
Second of Three Parts
10/14/2015
Figure 1. Piping system with plant operating data (Courtesy of the author)
Using this data, the actual operation of the system can be compared with the model. These calculations were demonstrated in past Pumps & Systems articles and will be referenced in the following discussion.
Figure 2. Manufacturer's pump curve for the centrifugal pump
The pump curve indicates that the head developed by the pump at a flow rate of 1,000 gpm is 192 feet of fluid. The total energy at the pump suction as calculated is 14.65 feet of fluid. Adding the total head developed by PU-101 results in a total head of 206.65 feet.
Using the Bernoulli equation, we will calculate the pressure at PI-101, which is 2 feet above the datum elevation. Pressure gauge PI-101 is connected to an 8-inch schedule 40 steel pipe, and, with a flow rate of 1,000 gpm through the pipe, the fluid velocity is 6.4 feet per second. Equation 5 shows the calculation for pressure using the Bernoulli equation.
The calculated pressure of PI-101 is 87.84 psig, and the observed value at pressure gauge PI-101 is 87.8 psig. The observed pressure at PI-101 matches, validating the model at PI-101.
Figure 3. The manufacturer supplied head loss as a function of flow rate through heat exchanger HX-101.
Looking at the graph for 1,000 gpm, the heat exchanger has a head loss of 23.3 feet of fluid, which results in a total energy of 177.89 feet at the discharge of HX-101 (201.19 – 23.3). Because no pressure gauge is located at the outlet of HX-101, this pressure value cannot be validated.
The pipeline connecting the heat exchanger to the inlet of the flow meter is 50 feet of 8-inch steel schedule 40 pipe with a single gate valve. This results in a head loss of .85 feet of fluid. The total energy at the inlet of the flow meter is 177.04 feet (177.89 – 0.85). Because there is no pressure gauge at this location, this value cannot be validated.
The next item in the system is the flow meter FT-101. This meter is designed according to the American Society of Mechanical Engineers (ASME) standard MFC-3M Measurement of Fluid Flow in Pipes Using Orifices, Nozzles and Venturi. The formula to calculate the permanent (non-recoverable) pressure drop across the flow meter is included in the reference standard. That information is also be provided by the manufacturer of the flow element.
The manufacturer's supplied differential pressure graph for flow element FT-101 shows that at 1,000 gpm the differential pressure is 1.35 pounds per square inch (psi), equating to a head loss of 3.14 feet of fluid. The total energy at the outlet of the flow element is 173.9 feet (177.04 - 3.14). Because there is no pressure gauge at this location, this value is also not validated.
The head loss in the 50-foot section of 8-inch steel schedule 40 pipeline with no valves and fitting is 0.78 feet. The total energy at the inlet of the control valve FCV-101 is 173.12 feet (173.9 - .78). Because there is no pressure gauge at this location, this value is also not validated.