07/29/2014
Last month’s column described the process of creating an energy cost balance sheet for a piping system (see Figure 1). The manufacturer’s curve was used to calculate the cost of operation for the centrifugal pump. This column explains how to perform the detailed cost calculation for other items in the system.
Evaluating Parts
Figure 1 shows the operating data from the installed plant instrumentation. This operating data and the manufacturer’s equipment data sheets will be used to calculate the differential pressure and flow rate through each item. With that information, the cost of electrical power and the annual rate of operation, the annual operating cost and energy use can be calculated for each item in the system’s energy cost balance sheet. To calculate the operating cost for an item in the system, its head loss and corresponding flow rate must be determined. Insufficient installed instrumentation means these values need to be calculated with data from the equipment manufacturers.Figure 1. The operating data from installed plant instrumentation and elevations of selected tanks and equipment
Determining Pump Flow Rate
Last month’s column calculated a pump head of 235 feet (ft) and a flow rate of 4,000 gallons per minute (gpm). From the pump curve, it was determined that the pump had an efficiency of 83 percent at its flow rate. The pump’s operating costs were calculated after looking at the pump’s motor efficiency, annual hours of operation and cost of electrical power. So how was the flow rate through the pump of 4,000 gpm established? The flow to the destination tank is 2,500 gpm, but because there is no flow element in the bypass circuit, the pump’s total flow rate cannot be calculated. Without this value, the pump efficiency and power consumed also cannot be calculated. The pump curve is the key to this process because it provides manufacturer-supplied test data on how the pump operates for its flow range. Knowing the pump’s total head, the pump curve can be entered on the head axis and move across until the known pump head value intersects the pump curve. Dropping straight down on the pump curve gives the flow rate, and the intersection point provides the pump efficiency. In Figure 1, the process pump’s discharge pressure is 102.8 pounds per square inch (psig). Centrifugal pump curves use head instead of pressure, so the discharge pressure must be converted to feet of fluid using Equation 1. Where: H = Head in feet of fluid P = Pressure in lb/inch2 ρ = Fluid density in lb/ft3 144 is a conversion factor for ft2 to in2 A pressure gauge is not installed on the pump suction, so a temporary gauge was mounted on a suction vent. The temporary suction pressure gauge reads 1.7 psig, resulting in 3.95 ft of fluid. Subtracting the discharge and suction heads (239 ft minus 3.95 ft), the pump’s total head is 235 ft. Reading from the pump curve (see Figure 2), the resulting flow rate through the pump is 4,000 gpm, and the pump is 83 percent efficient.Figure 2. Determining the flow rate and pump efficiency from calculated total head of 235 ft
Next, the cost to operate the system’s process elements will be evaluated using their flow rates and head loss.
Static Head Cost
The static head accounts for the difference in fluid energy between the destination and supply tanks. Per the Bernoulli equation, fluid energy is composed of three types of head: elevation, pressure and velocity. Because the fluid is at rest in the supply and destination tanks, the velocity head has no value (see Equation 2). Where: ZB = Elevation of tank bottom in ft LFS = Level of fluid surface above tank bottom in ft PFS = Pressure on fluid surface in psi ρ = Fluid density in lb/ft3 1 = Supply tank 2 = Destination tank The static head is the energy difference between the supply and destination tanks. It remains the same regardless of the flow rate between the tanks. The static head can be used to calculate the annual operating cost due to the head component within the process circuit. The 2,500 gpm flow rate through the process circuit is used in the annual operating cost formula (see Equation 3). The 83 percent pump efficiency comes from the pump curve with a 4,000 gpm flow rate. The pump efficiency applies to the 4,000 gpm flow rate because the pump supplies both the process and bypass circuits. Inserting the static head pump efficiency, flow rate, hours of operating and cost of power results in an annual energy cost of $22,800 for the static head. Where: Q = Flow rate H = Head ρ = Fluid density ηρ = Pump efficiency ηm = Motor efficiencyProcess Element Cost
Process equipment—characterized by a head loss that is a function of flow rate—is the next item in the energy cost balance sheet. In the system shown in Figure 1, the process element has no installed pressure gauges. The manufacturer’s equipment data sheet will be used to calculate head loss. The manufacturer’s supplied data sheet could have a curve showing the pressure drop and head loss for a range of flow rates, a Cv value or a single value of pressure drop versus a given flow rate. For this example, the manufacturer provided a 14.4 psi pressure drop with a flow rate of 3,000 gpm. To determine the pressure drop through the process element at 2,500 gpm, the Cv must be calculated using the manufacturer’s supplied data points of 3,000 gpm and 14.4 psi (see Equation 4). Where: Cv = Flow coefficient Q = Volumetric flow rate in gpm dP = Differential pressure in psi SG = Specific gravity The differential pressure across the process element is 10 psi, after calculating the Cv of the process elements, the specific gravity of the process fluid and the flow rate using Equation 5. The 10 psi differential pressure converts to 23.3 ft head loss across the process equipment. The head loss results in a $5,592 annual energy cost for the process element as calculated in Equation 6.Piping Cost
The head loss in a pipeline can be calculated using the Darcy equation (see Equation 7). However, Equation 8 makes calculating the head loss with the flow rate in gallons per minute and pipe inside diameter in inches easier. Where: hL = pipeline head loss in ft f = Darcy friction factor (unitless) L = pipe length in ft D = pipe inside diameter in ft v = fluid velocity in ft/s g = gravitational constant in 32.2 ft/s2 Q = volumetric flow rate in gal/min d = inside pipe diameter in inches In this example, we’ll calculate the head loss for a 50-foot suction pipeline made of 16-inch schedule 40 steel. Two gate valves and a sharp edge transition lie along the pipeline from the tank. The pipeline is passing 4,000 gpm of a fluid with a fluid density of 62 lb/ft3 and viscosity of 0.68 centipoise. The steps required to arrive at the pipeline’s head loss are listed below along with the intermediate results.- Reynolds number = 1.23 x 106 unitless
- Relative roughness = 0.00012 in
- Darcy friction factor = 0.0135 unitless
- Pipe head loss = 0.44 ft
- Valve and fitting loss = 0.57 ft
- Pipeline head loss = 1.01 ft
http://kb.eng-software.com/questions/575/Pipeline+Head+Loss+Calculation+Process.) The head losses for the circuit’s remaining pipelines are added to obtain the total pipeline head loss in Table 1.
Table 1. Pipeline summary, calculated head loss and annual operating costs for the pipelines in the process circuit
The operating cost for the pipelines is $5,376, after plugging in the sum of the pipeline’s head loss and the flow element, as shown in Equation 9.