# Perforated Pipe Distributor Sizing Calculations

Perforated Pipe Distributors have been discussed many times on “Cheresources”. How to design a perforated pipe distributor also known as a sparger has been a frequent question on the forum. Some general replies without providing in-depth methodology of sizing a distributor can be seen in the queries raised.

Perry’s Handbook (8th Edition) has a brief sub-section on perforated pipe distributors in Section 6, Fluid & Particle Dynamics which I had gone through critically but which was not to my satisfaction.

Since I do have a penchant of finding and developing engineering calculations, I was continuously on the look-out for something related to perforated pipe distributors. Last week I struck gold, when I found a company design manual providing detailed calculations for perforated pipe distributors. I had a critical look at it and found it to be better than anything I had found and read earlier related to perforated pipe distributors. I could even develop an excel workbook for perforated pipe distributor from this very informative design procedure.

Today’s blog entry is meant to provide the stepwise calculations for a perforated pipe distributor including the design equations. Both liquid and gas pipe distributors are covered. Gas pipe distributors follow the same design steps as that for liquid pipe distributors except for some minor variations in the design procedure. Both Metric units and USC units have been provided in the methodology.

Let us straight away get to the steps for sizing a Perforated Pipe Liquid distributor:

Step 1:
Initially set the pipe size of the pipe distributor, same as the pipe size feeding the pipe distributor

Step 2:
Calculate the Reynolds number, Rei, of the inlet stream to the pipe distributor using the following equation:

Metric Units:
Rei = 1.27*Q*ρ / (d*μ)

USC Units:
Rei = 50.6*Q*ρ / (d*μ)

where:
Q = Volumetric flow Rate, liters/s (gpm)
ρ = Liquid Density, kg/m3 (lb/ft3)
d = inside diameter of pipe, mm (inch)
μ = Liquid Viscosity, Pa.s (cP)

Step 3:
Find the fanning friction factor f (dimensionless), for the given flow regime. For turbulent flow some values for fanning friction factor based on pipe size are provided in the attached table.

Step 4:
Calculate the Kinetic Energy per unit volume of the inlet stream, Ek, kPa (psi) from the following equations:

Metric Units:
Ek = 810*α*ρ*Q2 / (d4)

USC Units:
Ek = 1.8*10-5*α*ρ*Q2 / (d4)

where:
Ek = Kinetic energy per unit volume of the inlet stream, kpa (psi)
α = velocity correction factor (use α = 1.1 for turbulent flow and 2.0 for laminar flow)

Step 5:
Calculate the pressure change ΔPp along the distributor pipe due to friction and momentum recovery from the following equations:

Metric Units:
ΔPp = ((4000*f*L*J/α*d) – 1)*Ek

USC Units:
ΔPp = ((48.0*f*L*J/α*d) – 1)*Ek

where:
f = fanning friction factor, dimensionless
L = Length of perforated distributor pipe, m (ft)
J = dimensionless factor (Use J = 0.35 as an initial value)

Step 6:
Find the required pressure drop, ΔPo across the distributor holes by multiplying the greater of Ek or ΔPp by 10. If the calculated value of ΔPo is less than 1.75 kPa (0.25 psi) make it equal to at least 1.75 kPa (0.25 psi).

Step 7:
Calculate the required total area of the pipe distributor holes, Ao, using the following equations:

Metric Units:
Ao = 22.3*(Q / C)*sqroot (ρ/ΔPo)

USC Units:
Ao = 3.32*10-3*(Q / C)*sqroot (ρ/ΔPo)

where:
Ao = Total required hole area, mm2 (in2)
C = flow coefficient, dimensionless (as a first value consider C = 0.60)

Step 8 (Guidelines for choosing hole diameter and hole-to-hole linear distance):
a. Minimum hole diameter ≈ 1/2-in. (13 mm) to avoid plugging and to limit the number of holes to a reasonable value. In very clean service, smaller holes may be considered, but in severely fouling service, 1/2-in. (13 mm) holes may be too small.
b. Maximum hole diameter = 0.2 times inside diameter of distributor.
c. The ratio of hole diameter, do, to inside pipe diameter, di, should be between 0.15 and 0.20 when the criterion ΔPo = 10 Ek is used. If it is necessary to use do /di < 0.10, then make ΔPo = 100 Ek.
d. To provide sufficient pipe strength, the minimum distance (edge-to-edge) between adjacent holes should approximately equal the hole diameter.
e. Within the limitations imposed by the above requirements, a larger number of small holes are preferred over a smaller number of large holes.
f. If slots are used instead of holes, the slot width should be at least 1/2-in. (13 mm).

Step 9:
The value of Rei / n should be greater than 4000. If it is not, then a new flow coefficient value "C" should be calculated from the attached chart. Instead of Re shown on the x-axis of the chart use Rei / n for reading the flow coefficient of the chart.

Step 10:
Using the calculated number of holes, find the factor "J" from attached chart and compare this with the assumed value of 0.35. If this revised value of J affects the value of ΔPo by more than 10%, substitute the revised value of J in equation given in Step 5 and repeat the steps starting from calculation of ΔPp.

Perforated Pipe Gas Distributor:

Step 1:
Initially set the pipe size of the pipe distributor, same as the pipe size feeding the pipe distributor

Step 2:
Calculate the Reynolds number, Rei, of the inlet gas stream to the pipe distributor using the following equation:

Metric Units:
Re = 1270*W*ρ / (d*μ)

USC Units:
Re = 6310*W*ρ / (d*μ)

where:
W = gas flow Rate, kg/s (lb/h)
ρ = Liquid Density, kg/m3 (lb/ft3)
d = inside diameter of pipe, mm (inch)
μ = Liquid Viscosity, Pa.s (cP)

Step 3:
Find the fanning friction factor f (dimensionless), for the given flow regime. For turbulent flow some values for fanning friction factor based on pipe size are provided in the attached table.

Step 4:
Calculate the Kinetic Energy per unit volume of the inlet stream, Ek, kPa (psi) from the following equations:

Metric Units:
Ek = 8.10*108*α*W2 / (ρ*d4)

USC Units:
Ek = 0.28*α*W2 / (ρ*d4)

where:
Ek = Kinetic energy per unit volume of the inlet stream, kpa (psi)
α = velocity correction factor (use α = 1.1 for turbulent flow and 2.0 for laminar flow)

Step 5:
Calculate the pressure change ΔPp along the distributor pipe due to friction and momentum recovery from the following equations:

Metric Units:
ΔPp = ((4000*f*L*J/α*d) – 1)*Ek

USC Units:
ΔPp = ((48.0*f*L*J/α*d) – 1)*Ek

where:
f = fanning friction factor, dimensionless
L = Length of perforated distributor pipe, m (ft)
J = dimensionless factor (Use J = 0.35 as an initial value)

Step 6:
Find the required pressure drop, ΔPo across the distributor holes by multiplying the greater of Ek or ΔPp by 10. If the calculated value of ΔPo is less than 1.75 kPa (0.25 psi) make it equal to at least 1.75 kPa (0.25 psi).

Step 7:
Calculate the required total area of the pipe distributor holes, Ao, using the following equations:

Metric Units:
Ao = 2.24*104*(W/C*Y)*(1 / sqroot (ρ*ΔPo))

USC Units:
Ao = 2.24*104*(W/C*Y)*(1 / sqroot (ρ*ΔPo))

where:
Ao = Total required hole area, mm2 (in2)
C = flow coefficient, dimensionless (as a first value consider C = 0.60)
Y = Gas expansion factor, dimensionless

Y is calculated as follows:

Y = 1 - (0.41 + 0.35*β4)*ΔPo/(k*P) for ΔPo/P <0.37 -------(i)

Y = Y0.37 - 0.37*( (ΔPo/P) - 0.37) for ΔPo/P >0.37 --------(ii)

where:
P = Pressure at the inlet of the gas distributor, kPa (abs) (psia)
k = ratio of specific heats, Cp / Cv
β = ratio of hole to the perforated pipe inside diameter (specified earlier as a value between 0.15 to 0.20)
Y0.37 = value of Y calculated using eqn (i) with ΔPo / P equal to 0.37

Steps 8,9 & 10: These remain the same as for Perforated Pipe Liquid Distributors.

This has been a rather detailed description on how to size a perforated pipe distributor and I am hoping that readers and members of "Cheresources" find it useful and can build a excel workbook using the equations and method provided. Please do refer the attachments while reading the text of this blog entry.

Looking forward to comments from the knowledgeable forum members.

Regards,
Ankur.

bern307182

Mr. Ankur:

Just one question, on step 9 of both methods says that if Re/n < 4000 you have to recalculate new flow coefficient value "C".

After performing this adjusment, it is compared only dPinitial vs dP0 and if it is in a range of 10% or less then all procedure is completed.

But in some cases if we repeat operation Re/n is <4000. We do not fullfill this condition. Is there any explanation of this situation? or criteria on step 9 is wrong stated?.

ankur2061

bern307182,

The whole idea is to maintain a value of Rei/n > 4000, so that flow is not laminar. At laminar flow, "flow maldistribution" is likely to occur. What it means that you need to adjust the number of holes "n" in such a way that the the value of Rei/n is always greater than 4000. In such a scenario you do not need to adjust the coefficient "C".

Regards,

Ankur.

Strife

Could this procedure be adapted to pipe ladder arrangements in which a single central pipe feeds many lateral pipes drilled with orifices?

Thanks.

suayip.ozturk

Dear Ankur

In the gas calculation step 2: you wrote gas mass flow rate and liquid density-viscosity. What is the reason for that you wrote liquid and gas? ıs liquid outside of gas pipe?

And other my question is:  In step 7, you wrote k coeffient which is the division of Cp/Cv. What are these Cp and Cv. Could you explain them?

ankur2061

Dear Ankur

In the gas calculation step 2: you wrote gas mass flow rate and liquid density-viscosity. What is the reason for that you wrote liquid and gas? ıs liquid outside of gas pipe?

And other my question is:  In step 7, you wrote k coeffient which is the division of Cp/Cv. What are these Cp and Cv. Could you explain them?

suyaip,

Thanks for your comment. It is a typo error and should read "gas" density and "gas" viscosity instead of liquid.

Please refer the links below for Cp & Cv and their ratio.

http://en.wikipedia....i/Heat_capacity

http://en.wikipedia...._capacity_ratio

Regards,

Ankur

suayip.ozturk

Thank you Ankur for your kindly help.

engineer_1

Thank you Ankur for this - it has been extremely helpful. I have one question: now that I have hole area and number of holes, can I determine diameters of each hole? Does it make sense for the last hole to be largest?

Thank you!

brochon

Mr Ankur,

I find this article very useful, thank you for your contribution. I have one question...I notice that the constant (2.24E4) in the equation for Ao for the Gas Distributor is the same for both metric & USC units. Is this correct?

Regards Brian

ankur2061

Mr Ankur,

I find this article very useful, thank you for your contribution. I have one question...I notice that the constant (2.24E4) in the equation for Ao for the Gas Distributor is the same for both metric & USC units. Is this correct?

Regards Brian

Brian,

The USC unit constant in Step 7 for gas distributor is an error. Instead of 2.24E+04 it should read 0.415.

Sorry for the delay.

Regards,

Ankur.

Chem01

Dear Ankur,

For gas, 'd' inside dia of the pipe should be in 'm' not 'mm' as mentioned for Metric units, Pl. confirm.

Regards,

ankur2061

Dear Ankur,

For gas, 'd' inside dia of the pipe should be in 'm' not 'mm' as mentioned for Metric units, Pl. confirm.

Regards,

It is "mm" and not "m".

Chem01

As "L" is in meters, I considered diameter "d" also in meters for consitency. Is it unusual to take mm and m in same equation? like for ΔPp ,anyways I'll use "mm" for d. Thanks

Jovin

I have calculate the value of Y for the beta value less than 0.1 and it is negative and I think for this case the approach will be different. If so,

what will be the calculation approach for the Y if we have beta value less than 0.1.

MrMohasa

I have a question, is it possible to make this case?

delta P for perforated pipe=.34 bar in normal capacity 100%

flow=89 m3/hr

p=538 kg/m3

0.14 cP

D= 6" sch80 => ID=146.36

----------------------------------------

104 hloes with 10 mm Diammeter

------------------------------------------------------------------------------------------

and delta P for perforated pipe=2.09 bar in Design capacity 110%

ankur2061

I have calculate the value of Y for the beta value less than 0.1 and it is negative and I think for this case the approach will be different. If so,

what will be the calculation approach for the Y if we have beta value less than 0.1.

Jovin,

Refer the link for calculation of "Y' value baed on ISA equation for compressible flow. Refer page 14 of the link (EPR 4103.3).

http://www.parkersto...cal/ValveEP.pdf

Regards,

Ankur

Ref123

Dear Ankur,

For gas, 'd' inside dia of the pipe should be in 'm' not 'mm' as mentioned for Metric units, Pl. confirm.

Regards,

It is "mm" and not "m".

Hi,

Mr. Ankur. I have balanced the Units and in place of mm, it should be m.

sharjuntj

Dear Ankur,

Thank you very much for your valuable design calculation  method. Actually I am designing a perforated gas distributor for a vaccum vessel in which the outlet perforation area is exposed to a vaccum of 1 Pascal.In the above explained calculations we are getting a perforation area which is lesser than the inlet area of the tube.That doesn't satisfy the conductance principle for a vaccum vessel in which the perforation area of the tube should be atleast equal to the inlet area.So does this calculation is valid for this type of design....??

ankur2061

Dear Ankur,

Thank you very much for your valuable design calculation  method. Actually I am designing a perforated gas distributor for a vaccum vessel in which the outlet perforation area is exposed to a vaccum of 1 Pascal.In the above explained calculations we are getting a perforation area which is lesser than the inlet area of the tube.That doesn't satisfy the conductance principle for a vaccum vessel in which the perforation area of the tube should be atleast equal to the inlet area.So does this calculation is valid for this type of design....??

Please consider minimum distributor hole size as 13 mm (1/2"). Based  on the length of the distributor considering limitations of arranging the distributor pipe in the vessel, provide equidistant holes of 13 mm along the length of the distributor pipe. Since this is a vacuum service the chances of flow maldistribution are negligible.

Regards,

Ankur.

sharjuntj

Dear Ankur,

Thank you very much for your valuable design calculation  method. Actually I am designing a perforated gas distributor for a vaccum vessel in which the outlet perforation area is exposed to a vaccum of 1 Pascal.In the above explained calculations we are getting a perforation area which is lesser than the inlet area of the tube.That doesn't satisfy the conductance principle for a vaccum vessel in which the perforation area of the tube should be atleast equal to the inlet area.So does this calculation is valid for this type of design....??

Please consider minimum distributor hole size as 13 mm (1/2"). Based  on the length of the distributor considering limitations of arranging the distributor pipe in the vessel, provide equidistant holes of 13 mm along the length of the distributor pipe. Since this is a vacuum service the chances of flow maldistribution are negligible.

Regards,

Ankur.

Dear Sir,

Since the flow "mal distribution" is negligible.So it is not necessary to maintain Rei/n of 4000 as per your specification mentioned above right?? and also whether our outlet perforation area can be higher than the inlet tube area for the vaccum system or it can be less also..Please suggest..Thanks in advance..

ankur2061

Dear Ankur,

Thank you very much for your valuable design calculation  method. Actually I am designing a perforated gas distributor for a vaccum vessel in which the outlet perforation area is exposed to a vaccum of 1 Pascal.In the above explained calculations we are getting a perforation area which is lesser than the inlet area of the tube.That doesn't satisfy the conductance principle for a vaccum vessel in which the perforation area of the tube should be atleast equal to the inlet area.So does this calculation is valid for this type of design....??

Please consider minimum distributor hole size as 13 mm (1/2"). Based  on the length of the distributor considering limitations of arranging the distributor pipe in the vessel, provide equidistant holes of 13 mm along the length of the distributor pipe. Since this is a vacuum service the chances of flow maldistribution are negligible.

Regards,

Ankur.

Dear Sir,

Since the flow "mal distribution" is negligible.So it is not necessary to maintain Rei/n of 4000 as per your specification mentioned above right?? and also whether our outlet perforation area can be higher than the inlet tube area for the vaccum system or it can be less also..Please suggest..Thanks in advance..

For gas distributors mal-distribution is negligible. It is more applicable to liquid distributors. I don't see any specific concern for the perforated area being more than the total area of the distributor pipe. Please provide some back-up where it mentions that the perforation area should be less than the total area of the inlet pipe.

Regards,

Ankur.

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