Improving inefficiencies provides opportunities for energy savings.

A significant factor in the design of a pumping system is the flow variation required by the process. Several pumps in parallel, variable speed pumps, pumps with on-off control and pumps with a control valve are some of the methods available for flow variation. A widely used method in the industry is to use control valves, generally located on the pump discharge in the pipe supplying process fluid. The flow could be used for different purposes—such as maintaining the level in a process vessel or in a boiler drum, or maintaining the flow in a pipeline or in the tubes of a fired heater. To understand how flow can be varied by a control valve, the system designer and operator need to understand the basic principles of how control valves behave.

## The Control Valve

The flow rate through a control valve depends on the size of the valve, the pressure drop over the valve, the stem position and the flow properties. A simplified design equation for non-flashing liquids, ignoring the effects of the connected fittings, can be derived from References 1, 2 and 3 as Equation 1.

Where: F = Fluid flow through the control valve Cv = Valve flow coefficient (at the full open) x = Valve stem position f(x) = Fraction of the valve size coefficient at any given valve stem opening indicating the inherent flow characteristics of the valve ∆Pv = Pressure drop across the control valve sp.gr. = Specific gravity of the fluid More detailed equations are available in the standards (References 1 and 2) and publications of the control valve manufacturers (Reference 4), also for flashing liquid services. The most common type valve characteristics are equal percentage, linear and quick opening type. Because of the distortion in valve characteristics in the extreme conditions of full open and full shut and because of the performance of the valve actuator and spring, the usable range is less than 0 percent to 100 percent.

Typically, this range is limited to about 10 percent to 90 percent of the valve opening. Distortion also occurs because of system losses that vary the pressure drop across the control valve in its operating range and result in valve characteristics that are different from the valve’s theoretical characteristics (Reference 6). The present analysis is based on a linear control valve, which is often the choice when constant control valve gain (the magnitude ratio of the change in flow through the valve to the change in valve travel under conditions of constant pressure drop) is required for accurate control of parameters, such as level or flow control. Processes require flow variations, either during plant capacity ramp up or ramp down. Flow variation is also required to handle fluctuations in the process parameters—such as drum level, thermal load variation requiring adjustment of cooling or heating fluid flow, or for adjusting pressure variation. To ensure controllability, the flow variation should not demand that the valve open either less than 10 percent or greater than 90 percent.

When specifying the pump and control valve, the designer must first develop the system head curve. The system head curve is the head required (m) to be developed by the pump at different flow rates in cubic meters per hour (m3/hr), ignoring the losses across the control valve. For systems comprised of static and dynamic losses such as the one shown in Figure 1, the system head curve can be represented as shown in Equation 2.

Figure 1. System with one control valve

Hs = Hstatic + q x flow2 (Equation 2) Where: Hstatic = A constant, sum of the static head and pressure difference between source and destination q = A multiplying factor between the dynamic head and the square of the flow, which is a constant in turbulent flow condition Figure 2 shows a system head curve that was developed using: Hstatic = 50 m q = 0.009 [m head/ (m3/hr flow)]