Equal percentage valve

A small compromise has to be made to equal percentage to ensure the flow through the valve is zero when the valve is fully shut but, in general, if F is the flow and V the percentage valve position then, by definition 

The constant A can be eliminated by defining F ojc as the flow with the valve 100% open, i.e. 

If p is the liquid density then control valves are characterised by the coefficient (C ) 

For a linear valve Cy is constant, but for an equal percentage valve 

If the pressure drop across the valve exceeds the pressure drop across the rest of the process then it will change relatively little as the flow changes. A linear valve will then provide better linearity. If the pressure drop across the valve is relatively small then an equal percentage will perform better. But oversizing a linear valve has a more detrimental effect than oversizing an equal percentage valve so the latter is often chosen to provide more robust control as process conditions vary. 

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Equal-percentage valves are often used when the pressure drop available over the control valve is not constant. This occurs when there are other pieces of equipment in the system that act as fixed resistances. The pressure drops over these parts of the process vary as the square of the flow rate. We saw this in the examples discussing control valve sizing. 

Over a threefold load change, the performances of linear and equal percentage valves are almost identical. When the pressure drop across the valve is less than 25% of the system drop, the equal... 

FIG. 8-51 Heat-transfer rate in sensible-heat exchange varies nonlinearly with flow of the manipulated fluid, requiring equal-percentage valve characterization. 

An alternate method is to calculate the ratio R from the individual measurements of flows A and B, and use this calculated ratio as the measurement input into a manually set ratio controller (RIC). In this case the loop gain varies with both the ratio R and the flow B. Because the loop gain varies inversely with flow B, this can cause instability at low rates. Therefore, the use of equal-percentage valve characteristics is essential to overcome this danger (Figure 2.48). 

Figure 2.63 illustrates the effect of the distortion coefficient (Dc) on the characteristics of a linear and an equal-percentage valve. As the ratio of the minimum to maximum pressure drop increases, the Dc drops and the equal-percentage characteristics of the valve shift toward linear and the linear characteristics shift toward QO. In addition, as the Dc drops, the controllable minimum flow increases, and therefore, the rangeability (the flow range within which the valve characteristic remains as specified) of the valve also drops. 

These figures illustrate the effects of the distortion coefficient (DJ on inherently linear (left) and inherently equal-percentage valves (right), according to Boger. 

In order to stay within 25% of the theoretical valve gain, the maximum flow should not exceed 60% in a linear valve and 70% of full flow in an equal-percentage valve. In terms of valve lift, these flow limits correspond to 85% for an equal-percentage and 70% for linear valves. 

Select the type of valve characteristic to use. Table 19.1 lists the typical characteristics of various control valves. Study of Table 19.1 shows that an equal-percentage valve must be used if a rangeability of 20 is required. Such a valve has equal stem movements for equal-percentage changes... 

FIGURE 19.14 (a) Inherent flow characteristics of valves at constant pressure drop (b) effective characteristics of a linear valve (c) effective characteristics of a 50 1 equal-percentage valve. 

Figure 19.14b and c give definite criteria for the amount of pressure drop the control valve should handle in the system. This pressure drop is not an arbitrary value, such as 5 lb/in2, but rather a percent of the total dynamic drop. The control valve should take at least 33 percent of the total dynamic system pressure drop if an equal-percentage valve is used and is to retain its inherent characteristics. A linear valve should not take less than a 50 percent pressure drop if its linear properties are desired. 

Number of constraints Equal-percentage valve characteristic Resistance in temperature sensor Valve resistance... 

For many process control applications it is possible that the pressure drop across the valve will have more effect on flow rate than will the valve position. The relationship between pressure drop and flow rate at constant valve position is the square-root expression for flow through an orifice. This relation introduces a nonlinearity in the control system which complicates the analysis of the system except insofar as it can be linearized. For equal-percentage valves the effect of changing pressure drop in the lift-flow characteristic of the valve is small, but for linear valves the effect is large. 

Figure 15.18 shows how7(x) varies with stem position for three types of valves a quick opening valve, an equal percentage valve, and a linear valve, where... 

FIGURE 15.18 Inherent valve characteristics for a quick opening (QO), linear, and equal percentage valve (=%). 

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