A nearly fully opened valve allows increasing flow—hence higher production—while eliminating a bottleneck or pinch in the system is possible.

The calculation assumed a fixed bypass flow of 10 percent of flow at BEP, and the pressure drop of the control valve at design was fixed to a travel of 70 percent. The control valve featured an ideal equal-percentage characteristic and a rangeability of 25 and 50, respectively.

Calculation results are shown in Figure 4 and are based on pump characteristic Curve I. The relative maximum flow rate is plotted versus A, the relative pressure drop of the control valve at design. Parameter B constitutes the system’s relative dynamic pressure loss. The same calculation was performed based on the pump’s characteristic, as demonstrated by Curve II (see Figure 5).

Figure 4. Maximum flow dependent on relative pressure loss of control valve, variable A, based on Curve I of Figure 2. Parameter B represents the relative dynamic pressure loss of system.
Figure 5. Maximum flow dependent on relative pressure loss of control valve, variable A, based on Curve II of Figure 2. Parameter B represents the relative dynamic pressure loss of system.

A comparison of those figures demonstrates the great influence of the pump’s characteristic on the maximum flow rate: The flatter the pump curve, the larger the maximum flow rate at a given relative pressure drop of the control valve. Doubling the rangeability of the control valve increases the maximum flow rate to a small amount.

The previous scenario may be highlighted by another example having a configuration like the system in Figure 1 and where a control valve of low rangeability (base case) is replaced by valves with higher ones.

The H-Q diagram in Figure 6 contains the pump’s characteristic and the system’s pressure drop curve without the loss of the control valve.

Figure 6. Example of the influence of a control valve’s rangeability on maximum flow rate.

Adding the control valve’s pressure loss, which had been fixed to ΔHRV = 3 m at a dimensionless travel of YS = 70 percent, results in an operating point 1 (base case) that matches the design flow rate and a bypass of 10 m3/h.

The plot in Figure 6 shows several scenarios, with duty points at various maximum flow rates due to different control valves’ rangeabilities. The maximum flow rate QS is determined by a travel of 100 percent—a totally open control valve.

The pressure loss curve of the system with different rangeabilities of the control valves was calculated using the appropriate rated Cv, converting it into the frictional loss factor, which is subsequently used in the Bernoulli equation.

The friction loss factor decreases with increasing rangeability; in an extreme case, it becomes more or less equivalent to that of a full bore pipe having the length of the valve.

Based on the design flow rate QS, the relation Qmax/QS may be taken from Figure 6:

• Point 1 (base case): R = 25; Qmax/QS ≈ 109 percent with linear characteristic of control valve
• Point 2: R = 25; Qmax/QS ≈ 113 percent for equal-percentage characteristic
• Point 3: R = 150; Qmax/QS ≈ 114 percent for equal-percentage characteristic—a straight pipe replacing the control valve resulting in Qmax/QS ≈ 115 percent

This example illustrates that a high rangeability typically does not have a great effect, but this result depends on the individual system and the parameter chosen.

Additionally, at the same design pressure loss and design travel of the control valve, an equal-percentage valve characteristic allows a higher maximum flow rate because of a steeply increasing Cv.

Nevertheless, whenever the travel approaches 100 percent, controllability may deteriorate because a small change of travel causes a relatively large change in flow rate.

## Conclusion

Qualitatively, the steeper a pump’s characteristic falls, the smaller the maximum flow rate, and the higher the relative dynamic pressure loss of the system, the smaller the maximum flow rate.

The parameter “design flow rate” and “design pressure loss and travel” of the control valve establish the reference values. As a result, increasing a specified design flow rate by 10 percent, for example, without also increasing the pressure the pump delivers does not mean that the system will necessarily achieve this flow rate.

References

1. Yu, F.C., “Easy way to estimate realistic control valve pressure drops,” pp. 45-48, Hydrocarbon Processing, August 2000
2. Unnikrishnan, G., “Visualize pump and control valve interaction easily,” pp. 51-56, Hydrocarbon Processing, August 2007
3. Jerdal, W.A. et al., “Dimensionless Characteristics of Pumps With Specific Speeds nq = 20…80,” pp. 546- 550, Transaction ASME, Vol. 124, June 2002
4. Green, D.W., Perry R.H., “Perry’s Chemical Engineers’ Handbook,” 8th ed., Section 8, p. 8-83
5. To read other Efficiency Matters articles, go here.