Calculation of Pipe size

[Govind Rao]

We are into coal gasifier manufacturing and operation. I would like to know, the method to calculate the diameter of pipes to transport producer gas of 8000 Normal cubic meter per hour capacity at 500 degree celcius at 5 Kpa pressure

[admin]

In order to calculate pipe diameter you should know pipe length to check pressure drop through it. Also if some resistances (valves, elbows, tee, valves etc.) are present it should be known also as well as entrance and exit height differences.

But for the reference you can assume some velocity that should not be higher. For gas flowing I would suggest maximum of 10 m/s (or maybe less). With that assumption you can use pipe diameter calculator to calculate pipe diameter at:
http://www.pipeflowcalculations.com/flowrate/

In calculator you should enter flow rate at real conditions. You said that the flow is 8000 normal m3/h, and that pressure is 5 kPa with temperature 500 C. To calculate flow ate real conditions I have used same calculator first to calculate relation between density at normal and on your conditions by entering pressures and temperatures. Here are results from report for normal conditions:

6. pressure of gas (p): p : 101.325 kPa
7. density (ρ): ρ : 0.71513265 kg/m3
8. temperature (T): T : 0 C
9. gas constant (R): R : 519 J/kgK

and for your conditions is:

6. pressure of gas (p): p : 106.325 kPa
7. density (ρ): ρ : 0.26502603 kg/m3
8. temperature (T): T : 500 C
9. gas constant (R): R : 519 J/kgK

so at your conditions density is 0.265/0.715 = 0.37 times lower so actual volume flow rate is that much higher than on normal conditions

Q = 8000 / 0.37 = 21621 m3/h.

Now with this flow rate in calculator you have following results:

1. volumetric flow rate (q):
q : 21621 m3/h

2. mass flow rate (w):
w : 5730.128 kg/h

3. diameter (D):
D : 874.4638 mm

4. velocity (v):
v : 10 m/s

5. cross section area (A):
A : 600583.8 mm2

6. pressure of gas (p):
p : 106.325 kPa

7. density (ρ):
ρ : 0.26502603 kg/m3

8. temperature (T):
T : 500 C

9. gas constant (R):
R : 519 J/kgK

[Govind Rao]

Thank you for the prompt reply. Could you please explain in details of theoretical calculations behind this. I would be highly obliged.

[admin]

For basic pipe diameter calculation theory you can click on theory button on the top of calculator while pipe diameter calculator opened. That theory page can also be found here:

http://www.pipeflowcalculations.com/pip ... locity.php

In the calculator it is important to enter flow rate at real conditions. You said that flow rate should be 8000 normal m3/h. Normal conditions are for p=101325 Pa and T=0 C. What you actually need is that amount (weight) of gas being transported, so as you have T=500 C, gas has much less density, so in therms of volume, bigger volume has to be transported in order to have same amount (weight) as required.

Using continuity equation you can calculate flow rate at different conditions:

Q1 * rho1 = Q2 * rho2

where 1 is for normal conditions and 2 is for other conditions.

In your example Q1 = 8000 Nm3/h, rho1 = p1 / RT1 = 101325 / R (0+273)
Q2 = ? , rho2 = p2 / RT2 = (101325 + 5000) / R (500 + 273)

So Q2 = Q1 * rho1 / rho2 = Q1 * (p1 / RT1) / (p2 / RT2) = Q1 * (p1/p2) * (T2/T1) = 8000 * (101325 / 106325) / (773 / 273) = 21586 m3/h

[Govind Rao]

Thank you once again for the prompt reply. You have assumed an velocity of 10 m/s. Is there any way (excluding the losses as informed by you) to assume the velocity as suggested by you? what i mean is how to assume.

[admin]

Velocity is depending on the pressure difference from start to finish. If you do not know it, than you can not calculate velocity.

[Govind Rao]

Can you eloborate on this please. How to go about?