Control Valve Homework help!

Hi,

Slightly off the PLC topic but i'm sure there are people on here with good experience... So I have no practical experience of control valves at all. I have a question which is asking me to size a control valve. This is the question:

A valve is required to regulate the flow of natural gas. Details of the gas are given in table below. It can be assumed that the pipe size and the valve size are the same [i.e. piping geometry does not have to be allowed for].

• Determine the required valve size in inches from the range of sizes given in the data sheet [the data sheet gives a range of nominal pipe sizes (NPS) in inches].

• Estimate the percentage the chosen valve would have to be open to carry the required flow.

Natural Gas
Required volumetric flow rate [@ STP] 2.8 x 10^6 litre per minute
Density [@ STP] 0.752 kg per m3
Specific heat ratio 1.31
Inlet pressure 20 bar gauge
Outlet pressure 6 bar gauge
Inlet Temperature 20 °C

What I am struggling with is calculating the required Kv value. I know the formula for a compressible fluid.

Kv = Qm/(31.6Y)*sqrt(x*p1*density)

What I cannot work out however is Y, the expansion factor. The formula for Y is

Y = 1 - (x/3Fk*Xt)

but I cannot work out how to find a value for Xt. Xt is the critical pressure differential ratio. Everything I have been reading, mostly the Emerson Control Valve Handbook suggests that you select the Kv/Cv value and then look and basically estimate that the Xt value specified by the valve manufacturer.

but if I haven't worked out the Cv value yet, how can you estimate the Xt value? I think i must be missing something otherwise it seems a bit like plucking a valve size out of thin air!

thanks

Picking a valve size is an iterative process (a.k.a educated guess and check). The general steps to sizing a valve for gas:

1. Check for choked flow (X_max < deltaP / P1)? For this you need the manufacturer's Xt value. (X_max = Fk * X, where Fk = ratio of specific heats / 1.4)

2. Estimate Cv using any of the flow equations. Example mass flow equation: m' = N_6 * F_p * Cv * Y * sqrt(x * P1 * rho), x = deltaP/P1

For the expansion factor, Y, you can 1) look up using a table, 2) calculate using Y = 1 - x/ 3*FK*Xt

Homework help

hello, I am struggling with the same question

Cv = alternative flow coefficient (gallons/min)
Kv = flow coefficient (M^3h^-1)
Y = expansion factor
Qm = mass flow rate (kg/hour)
xT = critical pressure differential ratio
x = pressure differential ratio
Fl= liquid pressure recovery coefficient
Fk = specific hear ratio factor
k = specific heat ratio

x=(p1-p2)/p1

xT = Fk * x

xT < x

Y = 1 - x/( 3 x Fk x xT )

Kv= Qm / ((2/3) x 31.6 x √ Fk x xT x P1 x p1)
Working out as follows

x= (20-6)/20 = 0.7

Fk = k / air specific heat ratio

Fk = 1.31/1.4
Fk = 0.94

xT = Fk * x
0.94 x 0.7 = 0.658

because xT < x = 0.658<0.7 flow through the valve is choked

Expansion factor Y

Y = 1 - x/( 3 x Fk x xT )

Y= 1- 0.7/( 3 x 0.94 x 0.658)

Y = 0.623

Although this is the expansion factor because the flow is choked a value of 2/3 or 0.667 is used.

I am now struggling to kind a value for Qm which is mass flow rate. I believe once i have this value i can then incorporate it into Kv= Qm / ((2/3) x 31.6 x √ Fk x xT x P1 x p1) to find the valve flow coefficient