In last month’s column, we discussed how to use a piping system model for operator training, system troubleshooting and improvements. This month, we will discuss one of the fundamental engineering principles used to build a piping system model.

A core attribute of this type of model is the ability to determine the fluid energy anywhere in the system. If we think of it as an energy balance, we can see the interactions and contributions of each of the various components found in each circuit. If each piece of equipment and interconnecting piping is accurately described in the model, then the model will show how the total flow of fluid energy in and out of the system works under any expected flow rate or set of boundary conditions.

Every piping system consists of pump, process and control elements. Pump elements add all the fluid energy needed to operate the system. Process elements use the energy to move the fluid through the process steps or provide the desired service. Control elements use the remainder of the energy to maintain or improve the quality of the product or service. This concept is described in Equation 1.

*(Graphics courtesy of the author)*

Figure 1 shows the flow diagram for a portion of a heater drain system typically found in a steam power plant. The condensate is pumped from the drain tank through the drain pump where the flow then goes into two separate circuits. Circuit 1 continues through heat exchanger EX01, then through control valve LV01 and flow meter FM-01 into the Heater 01, where Circuit 1 ends. Circuit 2 continues through heat exchanger EX01, through control valve LV02, through flow meter FM-02 and into Heater 02, where Circuit 2 ends.

Circuit 1 has a flow rate of 400 gallons per minute (gpm), and Circuit 2 has a flow rate of 350 gpm. The flow rate through the system provides the levels in Heater 01 and Heater 02 established by the set points for level control valves LV01 and LV02. Knowing the entire flow is supplied by the drain pump, we can determine that the flow rate through the pump is 750 gpm (summing the flow rates through Circuits 1 and 2). The boundary conditions (i.e., hydraulic grade, or HG) for the drain tank and Heaters 01 and 02 can be seen in Figure 1 and represent the energy levels at the ends of the system.

Next, we will look at how the energy is used within the system. The manufacturer’s supplied pump curve can help determine the head produced by the drain pump. Given a specific flow rate, the pump curve indicates the corresponding head produced by the pump with the installed impeller. With the pump curve embedded in our model, this determination is completed automatically and responds to any system changes. For our test, the model calculates 241 feet of head.

Looking at the process elements, we will start with the inlet condition in the drain tank. Because this is the start of the system, the starting energy for both circuits is equal to the surface liquid level and pressure in the drain tank and establishes the inlet boundary condition (127.5 feet of head). Heater 01 is the end point for Circuit 1, and Heater 02 is the end point for Circuit 2. Knowing the liquid level and the pressure in each tank, we can calculate the energy of the fluid at each of these points using the Bernoulli Equation. Our model uses this equation to determine the energy levels in Figure 1.

The energy consumed in the pipeline and other transport process elements can be calculated using the Darcy Equation, and the energy consumed in heat exchangers EX01 and EX02 is based on manufacturer test data.

Next, we will look at the control elements. The purpose of LV01 is to regulate the flow through Circuit 1 to maintain a constant liquid level in Heater 01. LV02 does the same for Circuit 2 and Heater 02. The head loss across each control valve can be calculated using the flow rate through the valve and the position of the control valve, along with the manufacturer’s valve test data. This data is included in the system model to determine the head loss.

FM-01 and FM-02 indicate the flow rate through each circuit. They are considered control elements because they contribute to the process quality of the process. There is head loss across each flow meter that can be calculated using the sizing equations for the flow meter. These equations are based on industry standards or the manufacturer’s supplied test data and are entered into the model for each device.

The resulting energy loss or gain for each of the elements is determined by the calculations in the model and are listed Table 1, which shows that the pump energy for each circuit is 241 feet of fluid.

Because the drain pump is common in both circuits, the head gain for the circuits is the same. In addition, the head loss in the common pipelines connecting the drain tank and the drain pump used by both circuits is the same.

Finally, because the drain tank provides the starting energy of the system and is shared by both circuits, the drain tank is used for calculating both circuits.

The results indicate that the energy the pump puts into the system (241 feet of head) is equal to the losses from the process and control elements for each circuit; the energy going into the system (energy in) equals the energy consumed by the system (energy out). This phenomenon sheds some light on the efficiency of our sample system: Only two-thirds of the energy added to the fluid is used to process and transport the fluid.