Page 451 - Chemical process engineering design and economics

432 Chapter 8

and because Q = AQ VQ, the volumetric flow rate,

f(P,- 2)V /2
P
Q= Cyl ———— I (8.7)
I n )

which is a formula used by valve manufacturers to size valves for incompressible
fluids. Because the valve coefficient, Cy, contains the orifice area, C is not a con-
v
stant for any particular valve but varies with the position of the valve stem and
hence the valve plug. The units used for Cy by valve manufacturers are gal/min for
flow rate and Ibp/in2 for pressure. Thus, Cy has units of gal-in/min-lbi;1'2
Sizing valves requires calculating Cy for the design flow rate and then se-
lecting an appropriate valve from a manufacturer. The valve coefficient contained
in manufacturers' catalog is the maximum coefficient. If the valve were sized at
the normal operating flow rate, the system would then be out of control if an upset
should occur. To avoid this, Chalfin [9] recommends sizing a control valve for a
flow rate that is 30% greater than the normal operating flow rate.
The designer, to insure good process control, specifies the pressure drop
across the valve. At low-pressure drops, the valve characteristic curve is distorted
resulting in poor control. Boger [10] and Moore [11] discuss this effect. The valve
characteristic curve is a plot of the valve opening against flow rate. There are sev-
eral rules of thumb in the engineering literature for assigning the pressure drop
across a control valve. Sandier and Lukiewicz [29] recommend a pressure drop of
30 to 50% of the frictional pressure drop - also called the dynamic pressure drop -
in the system and a minimum of 5 to 10 psi (0.345 to 0.67 bar). Forman [12] states
the assigned pressure drop is not an arbitrary value like 5 psi (0.345 bar). He rec-
ommends a pressure drop of 33% of the frictional pressure drop for a linear valve
and 50% for an equal-percentage valve [12]. For a valve that has a linear charac-
teristic curve, the flow rate varies linearly with valve opening. For a valve that has
an equal-percentage characteristic curve, the flow rate varies non-linearly with
valve opening. Power consumption increases with increasing frictional pressure
drop. Thus, the assigned pressure drop should not be any larger than necessary for
adequate control. Example 8.1 illustrates the procedure for valve sizing.
Example 8.1 Valve Sizing______________________________

What size valve will be required to control the flow rate of 50 gal/min (0.169
3
m /min) of brine (rj = 1.2), if the frictional pressure drop in the system, excluding
the valve, is 15 psi (1.03 bar)? Assume a linear valve.

Q (design) = 1.3 (50) = 65 gal/min (0.246 nrVmin).

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