14 replies to this topic

[rmarzo]

Dear all, 

 

I was investigating in this amazing forum how the molecular weight affect in the centrifugal compressor performance. My doubts come from this topic: 

 

http://www.cheresour...gal-compressor/

 

According to the Ankur statetment:

 

Gas Horse Power or Gas kW = Polytropic Head*Mass flow rate

 

"Ankur: Polytropic head remains unchanged for a fixed-speed machine, so a change in density will cause a change in the differential pressure."

 

However, in other post : http://www.cheresour...gal-compressor/

 

"Ankur: I don't know where you have read that the polytropic head is independent of the MW of the gas. This is totally incorrect & in fact the MW has a very large influence on the polytropic head & change in MW by a very small number results in an immediate change in the polytropic head. I am quoting from a very reputed book on compressor:"

 

Can anyone help me in this misunderstanding? 

 

Thanks in advance.

 

Regards,

RML

Edited by rmarzo, 15 August 2014 - 03:02 PM.

[Bobby Strain]

You might best answer your question with a visit to this site.

 

http://compressorcalcs.com/

 

Bobby

[PingPong]

An existing centrifugal compressor will develop a certain head at a certain speed and a certain volumetric flowrate. This is shown in the performance curves provided by the compressor vendor.

 

When the compressor does not exist yet, and still needs to be designed and built, the gas molecular weight has a big impact on the required (calculated) polytropic head of the new compressor.

 

It is important that you understand the difference between an existing compressor with a given polytropic head (determined by its number of impellers, impeller diameter, impeller speed) and the required polytropic head for a new compressor that still has to be built for processing a certain mol weight.

 

The quote from Royce Brown's reputable book on compressors, stating:

To determine the number of stages (using the impeller and diffuser defined as the stage), assume 10,000 ft-lb/lb of head per stage. This value can be used if the molecular weight is in the range of 28 to 30. For other molecular weights, this initial value must be modified. As a rule of thumb, lower the head per stage by 100 ft-lb/lb for each unit increase in molecular weight. Conversely, raise the allowable head per stage 200 ft-lb/lb for a unit decrease in molecular weight. The rule of thumb gives the best results for a molecular weight range of 2 through 70. Because this sizing procedure is being used only to establish the rough size of the compressor, the upper range may be extended with some loss in accuracy.

refers to the maximum head that an impeller in a centrifugal compressor usually is designed for, which depends on the MW of the gas. It is only a rule of thumb meant to estimate the number of impellers required.

Edited by PingPong, 15 August 2014 - 03:45 PM.

[rmarzo]

Thanks PingPong,

 

My intention is figure out how compressor (designed yet) could be work when it is operating in a off design point, like for instance, when the MW increase suddenly in the system.

 

In such condition, if the MW varies, the flow rate will change also, since density is affected. But the compressor does not follow the same performance curve. My understanding is that such curve is for a certain compressor at certain speed working with a certain gas at certain inlet conditions. Any changes in those will lead a new performance curve (Hp vs Qv)

 

I am trying to find out and explain why the curve (Hp  vs  Qv) with higher density is shifted up. 

 

Considering now a compressor, designed for operating at certain conditions. 

 

Assumptions:

 

Mass flow constant

Suction pressure constant

Suction pressure constant

Z constant (in reality, does not)

k constant (the same, with changes in gas composition it will change)

Fixed speed

Given curve for initial inlet conditions with a initial gas composition.

 

 

Suddenly the MW increases. What would it happen?

 

 

System curve

==========

Increase in MW, increase in density

 

Density = MW   P    /     R T Z

 

Increase in density, increase the fricction coeficient since Re is proportional to density, and this is proportional to friction factor.

 

Therefore, the slope of the resistance curve of the system becomes steeper, and the intersection with the compressor curve will be at lower flow rate and higher polytropic head.

 

 

 

Compressor curve

=============

 

Buuuuut, the compressor does not follow the same curve than the initial one. As consequence of the MW increase, density increases, and frictional internal looses are higher now for any flow rate. Therefore, the compressor shall offer higher power, thus higher polytropic head (mass flow constant). Considering, just the compressor behaivour (no the system),  we could say that for the same Qv, the politropic head will be higher because more power comes from fixed rpm driver (it fits its torque to the resistance torque, giving a new operation torque. At fixed rpm, the power then will increase). Therefore, the curve (Hp vs Qv) is shifted up for higher density as it is reflected in the attached figure. (Source:  "Centrifugal Compressors. Principles of operation and control." - A. Eli Nisenfeld)

 

Take into account that the discharge pressure will increase also. Higer politropic heand and constant and higher density, higher differential pressure. Because of inlet pressure remains fixed, discharge pressure will increase.

 

 

 

Operation point

===========

 

Considering this new compressor curve and the new system curve, the interaction will light the new operation point.

 

Please, correct me if I am wrong. I am so interested in this analysis

 

 

Regards,

RML

Attached Files

•  densityimpact.png   24.16KB   13 downloads

Edited by rmarzo, 15 August 2014 - 05:15 PM.

[Bobby Strain]

So, you didn't follow my advice. All the appropriate relationships are shown when you complete data entry and calculate power. Ping understands compressor behavior. So he doesn't need any explanation of the effect of gas MW on compressor performance. You seem to struggle with compressor behavior. So, take a look at the site I suggested. When you perform the calculations with two different molecular weights with fixed inlet and discharge pressure, you see from the equations that the required head is reduced for higher MW. The equation describing head does not contain MW explicitly; R is a function of MW. And you will observe this in comparing the two cases. If you want to determine the discharge pressure with an existing machine, then use trial and error to calculate the discharge pressure until the head is the same in both cases. To examine system behavior with changing MW, you need dynamic simulation software. And lots of information to describe the machine and piping system.

 

Bobby

[rmarzo]

So, you didn't follow my advice. All the appropriate relationships are shown when you complete data entry and calculate power. Ping understands compressor behavior. So he doesn't need any explanation of the effect of gas MW on compressor performance. You seem to struggle with compressor behavior. So, take a look at the site I suggested. When you perform the calculations with two different molecular weights with fixed inlet and discharge pressure, you see from the equations that the required head is reduced for higher MW. The equation describing head does not contain MW explicitly; R is a function of MW. And you will observe this in comparing the two cases. If you want to determine the discharge pressure with an existing machine, then use trial and error to calculate the discharge pressure until the head is the same in both cases. To examine system behavior with changing MW, you need dynamic simulation software. And lots of information to describe the machine and piping system.

 

Bobby

 

Bobby, I know so far you and Ping don't need a explanation of compressor behavior, my intention was to explain what my understanding is to see if someone could say at what point I am confused.

 

I looked an eye on the site you recommended. Actually, I developed a similar tool in excel.

 

I tried the thing you explained. when we have a certain machine and MW changes, I used trial and error to find the new discharge pressure with the new MW, and I found a solution. But, from the begining, the thing that is making me confuse is ... Why is the polytropic head, (at off-design point)¨developed by a existing compressor, constant when MW changes? I can't reach that concept. Does anyone explain this?

Edited by rmarzo, 16 August 2014 - 03:13 AM.

[PingPong]

Increase in density, increase the fricction coeficient since Re is proportional to density, and this is proportional to friction factor.

Re is not proportional to density (common misunderstanding but wrong), but proportional to mass flowrate.

 

At first you stated that mass flow is constant, so Re is constant.

 

But then you talk about the same Qv .....

 

we could say that for the same Qv, the politropic head will be higher because more power comes from fixed rpm driver (it fits its torque to the resistance torque, giving a new operation torque. At fixed rpm, the power then will increase). Therefore, the curve (Hp vs Qv) is shifted up for higher density as it is reflected in the attached figure.

Polytropic head is determined by the compressor, not by the driver. For the same Qv but a higher MW the power will increase because the mass flowrate increases. The dimension of Hp can be written in several ways, one is in kJ/kg.

 

I don't know Nisenfeld's book so I don't know the context in which he presents that graph, but I find it very strange that at low Qv the Hp for high density gas would be higher than for low density gas, but at higher Qv it is the other way around. In another book I saw a graph that shows that for heavy gas the Hp curve is slightly higher than for light gas over the whole range of Qv.

Edited by PingPong, 16 August 2014 - 03:47 AM.

[rmarzo]

 

Increase in density, increase the fricction coeficient since Re is proportional to density, and this is proportional to friction factor.

Re is not proportional to density (common misunderstanding but wrong), but proportional to mass flowrate.

 

At first you stated that mass flow is constant, so Re is constant.

 

I don't see that. Re = density x characteristic velocity x Diameter  / static viscosity. Could you clarify?

 

 

Anyway, I think the mistake was considering mass flow constant for off-design operation. Is it?

 

But then you talk about the same Qv .....

 

we could say that for the same Qv, the politropic head will be higher because more power comes from fixed rpm driver (it fits its torque to the resistance torque, giving a new operation torque. At fixed rpm, the power then will increase). Therefore, the curve (Hp vs Qv) is shifted up for higher density as it is reflected in the attached figure.

Polytropic head is determined by the compressor, not by the driver. For the same Qv but a higher MW the power will increase because the mass flowrate increases. The dimension of Hp can be written in several ways, one is in kJ/kg.

 

The power increasse. Ok. But the polytropic head? Mass flow increases, power increases... Hp? Here my doubt. Why polytropic head is constant (with regards to the statement of Ankur and Bobby) when a compressor is operating in off-design point, and MW changes? This is not the thing we can see in the figure attached.

 

I don't know Nisenfeld's book so I don't know the context in which he presents that graph, but I find it very strange that at low Qv the Hp for high density gas would be higher than for low density gas, but at higher Qv it is the other way around. In another book I saw a graph that shows that for heavy gas the Hp curve is slightly higher than for light gas over the whole range of Qv.

 

That's true. I note in other sources the thing you said. It is a little bit confuse also.

 

Edited by rmarzo, 16 August 2014 - 04:47 AM.

[rmarzo]

To reinforce my idea I attached a figure:

 

What am I missing? 

Attached Files

•  DSC_0010.JPG   51.63KB   10 downloads

[PingPong]

I don't see that. Re = density x characteristic velocity x Diameter  / static viscosity. Could you clarify?

density x velocity is proportional to mass flow.

One can also write the formula for Re in terms of mass flow and then there is no density (or velocity) in the formula.

 

 

Anyway, I think the mistake was considering mass flow constant for off-design operation. Is it?

Depends on your specific problem or application.

Why do you need to know impact of MW? Is this a specific situation in your plant?Or are you just interested in the theory in general?

 

To reinforce my idea I attached a figure:

 

What am I missing?

I don't know what you mean.

If you run an existing compressor at a lower Qv then delivered Hp will be higher, even if the inlet gas density is the same. If the density is different there may be an additional impact, which none of us can predict, only the compressor vendor can.

Edited by PingPong, 16 August 2014 - 05:44 AM.

[rmarzo]

 

I don't see that. Re = density x characteristic velocity x Diameter  / static viscosity. Could you clarify?

density x velocity is proportional to mass flow.

One can also write the formula for Re in terms of mass flow and then there is no density (or velocity) in the formula.

 

 

 

 

Anyway, I think the mistake was considering mass flow constant for off-design operation. Is it?

Depends on your specific problem or application.

Why do you need to know impact of MW? Is this a specific situation in your plant?Or are you just interested in the theory in general?

It is just theory. I want to study how the MW, Temperature and other inlet properties affect to an existing compressor when one of them changes suddenly and the rest remain fixed.

 

To reinforce my idea I attached a figure:

 

What am I missing?

I don't know what you mean. 

If you run an existing compressor at a lower Qv then delivered Hp will be higher, even if the inlet gas density is the same.

If the density is different there may be an additional impact, which none of us can predict, only the compressor vendor can. 

 

This is the thing I want to understand, what I can expect when one of the inlet variables changes, just analysing theory. I am not interested in the numerical evaluation, just... MW increase, discharge pressure increase, polytropic head increases... things like that. For this case, according to some sources, the curve Hp-Qv is shifted up, and I am looking for an explanation of how a operation point will move in such case considering also how the system curve changes.

 

 

Thanks for your time.

 

 

 

 

Edited by rmarzo, 16 August 2014 - 06:01 AM.

[PingPong]

I am not interested in the numerical evaluation, just... MW increase, discharge pressure increase, polytropic head increases... things like that. For this case, according to some sources, the curve Hp-Qv is shifted up, and I am looking for an explanation of how a operation point will move in such case considering also how the system curve changes.

I am afraid only the vendor can tell you impact of gas density on Hp-Qv curve.

What I have seen in different textbooks is conflicting.

 

As far as I know there are several aspects to consider:

1) A higher MW gas usually experiences a bigger change in Z through the compressor. Although the Qv in the graph stands for inlet volumetric flow, what really matters is the outlet volumetric flow as that sets the impeller outlet velocity of the gas, and that impeller outlet velocity sets its produced Hp. On top of that a higher MW will result in a higher outlet pressure, which obviously also has an impact on the outlet volumetric flow and impeller outlet velocity.

2) At a given Qv a higher MW (higher density) gas will result in more frictional loss inside the compressor.

3) A higher MW gas often has a lower sonic velocity (at same T), so Mach numbers inside compressor are usually higher for higher MW gas.

Edited by PingPong, 16 August 2014 - 06:26 AM.

[rmarzo]

 

I am not interested in the numerical evaluation, just... MW increase, discharge pressure increase, polytropic head increases... things like that. For this case, according to some sources, the curve Hp-Qv is shifted up, and I am looking for an explanation of how a operation point will move in such case considering also how the system curve changes.

I am afraid only the vendor can tell you impact of gas density on Hp-Qv curve.

What I have seen in different textbooks is conflicting.

 

As far as I know there are several aspects to consider:

1) A higher MW gas usually experiences a bigger change in Z through the compressor. Although the Qv in the graph stands for inlet volumetric flow, what really matters is the outlet volumetric flow as that sets the impeller outlet velocity of the gas, and that impeller outlet velocity sets its produced Hp. On top of that a higher MW will result in a higher outlet pressure, which obviously also has an impact on the outlet volumetric flow and impeller outlet velocity.

2) At a given Qv a higher MW (higher density) gas will result in more frictional loss inside the compressor.

3) A higher MW gas often has a lower sonic velocity (at same T), so Mach numbers inside compressor are usually higher for higher MW gas.

 

 

Thanks for your summary.

 

Just to confirm:

 

At given Qv: Increase MW, density increases, mass flow increase for the same Qv --> internal frictional looses increase --> higher power. However we can't predict if the polytropic head will be higher or not, because maybe the mass flow and power increases are compensate eachother, meanwhile politropic head is unalterable, but it is just a possibility, in fact if we follow the curve for different densities from Nisenfeld, we could say the polytropic head will increase also.

Edited by rmarzo, 16 August 2014 - 08:49 AM.

[PingPong]

At given Qv: Increase MW, density increases, mass flow increase for the same Qv --> internal frictional looses increase --> higher power.

Higher power is not due to increased frictional loss, but simply due to higher mass flowrate at same Hp and same Qv.

 

Gas_power(kW) = mass_flowrate(kg/s) * Hp(kJ/kg) / polytropic_efficiency(fractional)

 

Frictional loss has impact on droop of the Hp-curve, and on shape of the efficiency curve.

[breizh]

marzo,

 

Probably good to read :  http://www.jmcampbel...or-performance/

 

Another good resource is " Compressor selection and sizing "

http://books.google....epage&q&f=false

 

Hope this helps

Breizh