During my introduction to a piping system fundamentals course at an open-pit copper mine and mill in the southwestern U.S., I stressed the importance of understanding how the individual items of a piping system work together. I then went around the room and asked the attendees what they did at the facility and what they hoped to get out of the course. Each attendee had a specific topic of interest, but the dewatering engineer said his goal was to improve the operation of the dewatering pumps.
Knowing that the mine was in the desert, I asked him how big the pumps were. He mentioned they were mounted on a semi-trailer so they could be moved around the mine, and they were equipped with a second semi for the diesel electric power supply. Even though the operation was in the desert, the rainfall would run off the ground and result in flash floods that could quickly collect in the mine and cause a disruption in production
During the training when I discussed system static head, I emphasized that the static head of the dewatering system amounted to the difference in elevation between the water level at the bottom of the mine and the end of the discharge piping.
When we covered the material on pipeline sizing, the dewatering engineer asked why we needed to perform this calculation. He said his rule of thumb was to size the discharge pipe to that of the pump's discharge flange. For example, if the pump's discharge nozzle was 6 inches, he would use a 6-inch pipe for his discharge header. This column will discuss why this rule of thumb may be costly.
A piping system is made of three elements: the pump elements that add all the fluid energy; the process elements that make the product or provide the service; and the control elements that improve the product quality. Figure 1 shows the piping system details.
In this example system, the pump is an end suction design with a manufacturer's identifier of 10x8-17, operating at 1,770 revolutions per minute (rpm). The pump curve used in this example can be found in Figure 2. Based on the manufacturer's information, the pump suction flange is 10 inches in diameter, and the pump discharge flange is 8 inches in diameter, with the 17 indicating the pump's maximum impeller diameter.
The process elements consist of the supply tank with a liquid level of 0 feet above the common datum. The destination tank has a liquid level of 200 feet above the common datum. A short 14-inch pipeline serves as the pump's suction line with insignificant head loss. The discharge pipe is 3,500 feet in length and is made of steel schedule 40 pipe. We will vary the pipe diameter to demonstrate how changing the pipe diameter affects the flow rate through the system.
Finally, the control elements of the system consist simply of an on/off control for the pump. When the supply tank is pumped down, the pump shuts down to prevent the pump from running dry; when the supply tank is full, the pump is turned on. As a result, all of the energy supplied by the pump is used to move the fluid through the process elements.
Counting the Cost
First, we will look at the system with an 8-inch nominal size discharge pipe. This is the same diameter as the discharge flange on our pump. The resulting flow rate through the system is 1,438 gallons per minute (gpm), resulting in a head loss of 105 feet of fluid in the discharge pipeline. Adding the head loss of the pipeline to the system's static head of 200 feet results in a head of 305 feet for the process and control. The pump curve shows that a flow rate of 1,438 gpm through the pump results in a head of 305 feet. The balanced flow rate through the system is such that the head produced by the pump is equal to the head consumed by the process and control elements.
Next, we will calculate the power cost needed to pump 1,000 gallons of water at 60 F through the 8-inch pipeline using Equation 1.
Table 1 shows how the system operates with various pipe diameters along with the resulting cost per 1,000 gallons pumped. The table demonstrates the interaction between the various elements found in a fluid piping system. As the pipe diameter increases, the head loss in the pipeline decreases along with the fluid velocity. With lower pipeline head loss in the larger pipeline, more of the pump's energy can be used to move fluid.
As the flow rate increases in the pump, the head produced by the pump decreases as demonstrated on the pump curve (see Figure 2). In addition, changing the flow rate through the pump varies the pump efficiency.