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# Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

## Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
Dear All,

The subject topic has been discussed extensively on many platforms but I see many contradictions between platforms, books and online literature.

I always like to refer to William Forsthoffer books about rotating equipment and compressors. In his book, he mentions that an increase in gas density (i.e. molecular weight) results in a reduction of gas relative velocity through the impeller which results in an increase in gas tangential velocity which in turn increases the head generated by the impeller for a given impeller tip speed. Also, the surge limit flow increases and the choke limit flow decreases resulting in a reduced stable flow range and a reduced turndown.

However, in the well known below head equation, the head is inversely proportional to MW meaning that in a case where MW increases and all the other parameters are fixed, the head decreases.

𝑯𝒆𝒂𝒅_𝒑𝒐𝒍𝒚 =((𝒌 * 𝒏_𝒑𝒐𝒍𝒚)/(𝒌 −𝟏)) * ((𝒁_𝒂𝒗𝒈 * 𝑹 * 𝑻_𝟏)/𝑴𝑾)*((𝑷_𝟐/𝑷_𝟏 )^(((𝒌−𝟏))/(𝒌 * 𝒏_𝒑𝒐𝒍𝒚 ))−𝟏)

With that being said, I have two questions:

1. I believe that the first relation which is explained in Forsthoffer's book is relating MW with the head developed by the impeller given a fixed tip speed. On the other hand, the head formula is relating MW with the head required by the compressor to achieve a fixed compressor ratio. Is my understanding correct or is there a real contradiction between the book and the formula regarding the head and MW relationship?

2. Forthoffer does not explain why does the gas relative velocity decrease with an increase in MW. The only way I see this relationship is that for a given impeller volumetric flow rate (constant flow coefficient) and impeller exit area, when the density increases, the velocity of the gas (i.e. gas relative velocity) has to reduce to keep the volumetric flow rate through the impeller constant. Is this understanding correct?

On a separate note but related to compressor impellers, Forthoffer mentions that in the old days, the first stage impeller used to be an open impeller since they can generate much higher heads than closed impellers due to the high stresses developed on closed impellers at high flow rates. I understand that he means that the volumetric flow rate at the first stage impeller is higher than the subsequent impeller stages hence, higher stresses are developed at the first stage impeller compared to subsequent impeller stages. Do you agree?

I was having a discussion about this issue (i.e. higher stresses at the first impeller) with one compressor OEM and he told me that in certain cases, the material for the first stage impeller must be of exotic material like Inconel 825 while the subsequent stages can be in Stainless steel depending on the H2S and chloride content in the gas and the stresses developed on the first stage impeller. I do not really understand this argument by the OEM. Does anyone understand the rationale behind the use of Inconel for the first stage impeller in these special cases?

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

2/ Correct.

3/ Agreed. Dependency of stresses on inlet flow coefficient (which are higher at first impeller) is explained and detailed in a book by Klaus Ludtke "Process centrifugal compressors" (unsurpassed). The 'trend' is that the stresses are higher on first impeller.

4/ Yes I think there is a rational behind this OEM argument.

Wet H2S content generates SSC risk which pushes for some stainless steel selection. The material is to be selected based on yield strength and severity of service. Chlorides dissolved in condensed water, on the other hand, generate an other type of corrosion risk whereby stainless steel might not cope pushing for Inconel. I am not sure if Inconel is selected based on yield strenght vs. stresses. It is more of a threshold of chlorides content.

Inconel is very expensive (it would be golden plating/very expensive to quote this material for the complete impeller arrangement). So the it is an option to determine impeller most stringent in terms of stress but it is not necessarily a conservative option.

I believe the rational which may be more predominant in fact is that 1st impeller (as it is suction) is subject to highest humidity / closest to dew point, possibly subsequent impeller are less at risk of being in wet service (super heated) based on settle out and operational condition. The other thing to consider is that casing is also in contact with process gas, so if they Inconel825 is included on first impeller you may wonder what have they done as solution for the statoric part.

In general, these difficult situations must be strongly mitigated by past reference ; the mechanisms of failure and corrosion are understood but always difficult subject, so conservative approach is in order.

If you plan an escape, you must succeed as if you fail, you will be punished for trying. Never say or write down your plan. Heart is the only place where secrecy is granted.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

Suspect what the book author is alluding to is that the polytropic head coeff, usually abbreviated to μp, increases with increasing mol wt, and by extension, the head developed by the compressor at a given tip speed increases. See if you can find some discussion of this term in this book.

On the other hand, the head required for a given pressure ratio decreases with increasing gas mol wt.

Suspect the reasoning for more exotic materials at the first stage impeller may also be for corrosive wet gas applications. Past the first impeller, the gas would be superheated in terms of water and hence less corrosive.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

". . . that an increase in gas density (i.e. molecular weight) results in . . ."

fyi, molecular weight is not the same as gas density.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

There are other factors that affect gas density, but a doubling of molecular weight doubles the gas density. Avogadro's number.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
rotw and george

Thank you for your responses. I believe the first three points in my initial thread are agreed upon by both of you. I am not sure what is the polytropic coefficient that George is referring to and it is not really discussed in the book I am referencing.

For the point regarding the first impeller stresses, why does higher volumetric flow rates create higher stress levels on the shroud of the first impeller than the subsequent impellers? I understand that the subsequent impellers are having lower volumetric flow rates due to the compression of the gas but at the same time, the subsequent impellers are subjected to higher pressures than the first impeller. Am I missing something?

For the choice of material of the first impeller, I have typically seen spark eroded or electrochemical machining method of construction for the first impeller with Inconel material for the first impeller while the subsequent impellers are welded/brazed with SS material. I understand that the spark eroded or ECM construction has no weak points like in welded/brazed impellers and since the first impeller is subjected to higher stresses, this method of construction is more favorable. However, with regards to the material of construction, what do you mean by "Wet Gas"? I have seen the same term in the API 617 datasheet and never understood if "Wet" refers to H2O vapor content in the gas or the heavy hydrocarbons content (for example propane, butane, pentane, etc). Also, why does H2O vapor or heavy hydrocarbons pose an increased risk of SSC? I know that SSC does not need H2O for it to take place.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
pmover,

I know that molecular weight is not the something as density. However, maintaining all the other parameters equal (i.e. temperature, pressure, compressibility factor, etc.) density increases with molecular weight increase.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

Wet gas usually refers to gases with water content equal to or exceeding equilibrium dewpoint. Some modes of corrosion require water vapor or liquid water to be present.

Suspect the author is alluding to mu_p here. For some reason, the icon for loading up mathematical symbols doesnt load up now.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

For the point regarding the first impeller stresses, why does higher volumetric flow rates create higher stress levels on the shroud of the first impeller than the subsequent impellers? I understand that the subsequent impellers are having lower volumetric flow rates due to the compression of the gas but at the same time, the subsequent impellers are subjected to higher pressures than the first impeller. Am I missing something?

Reasoning should not be in terms of pressure but in terms of stress. As materials mechanics fundamentals, it should be a given. Did you try to access the information of the book (K. Ludtke) I referred to in the above post? It says at page 78 (from par. 3.1.8 Impeller Stress Analysis)
"Tangential or hoop stresses are by far the dominant stress components in an impeller under centrifugal load.
In this 2D-impeller equally high stresses occur in the impeller bore on the rear side of the hub (location A) and in the inner rim of the cover disk at the impeller eye (location B). With increasing eye diameter (i.e. increasing flow coefficient) the cover disk stresses increase in absolute terms and in relation to the bore stresses."

However, with regards to the material of construction, what do you mean by "Wet Gas"? I have seen the same term in the API 617 datasheet and never understood if "Wet" refers to H2O vapor content in the gas or the heavy hydrocarbons content (for example propane, butane, pentane, etc). Also, why does H2O vapor or heavy hydrocarbons pose an increased risk of SSC? I know that SSC does not need H2O for it to take place.

For CO2 corrosion to happen you need to have water and CO2 dissolved in water liquid phase (so not hydrocarbons in liquid phase which can be concurrently present, but indeed water). Something to keep in mind is that presence of other gas compounds in the hydrocarbon gas mixture however (CO2 and/or H2S going by memory) can however impact the water dew point curve, but that is on a side note.
It is generally admitted that if the relative humidity is below ~80% the service can be considered dry.

I know that SSC does not need H2O for it to take place.

Your should try to read NACEMR0175 / ISO15156 standard. The entire concept of SSC risk analysis (severity) according to NACEMR0175 is based on pH (which means aqueous media) and H2S partial pressure. By the way, if you have no water content, then "pH" does not hold any physical meaning. SSC corrosion involves reaction of H2S with steel which generates hydrogen atoms. For these atoms to enter steel, some conditions must coexist and that includes material subject to stress and H2S + water presence. Refer to my above comment with respect to humidity level.

If you plan an escape, you must succeed as if you fail, you will be punished for trying. Never say or write down your plan. Heart is the only place where secrecy is granted.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

pmover,

I know that molecular weight is not the something as density. However, maintaining all the other parameters equal (i.e. temperature, pressure, compressibility factor, etc.) density increases with molecular weight increase.

Example:

P=1 MPa, T=300K
Gas #1: CO2 ; MW = 44.01 g/mol
Gas #2: Propane+H2 ; MW = 44.01 g/mol

Calculation relatively to gas #2:
Density deviation (%) ~ 17% (lower for gas#1).

-> So density decreased while MW remained constant, P and T being equal.
Compressibility factor is not a factor you would control, it is resulting for certain set of prevalent thermodynamic conditions (P,T) and mixture.

I have skipped the case of a change in phase.

If you plan an escape, you must succeed as if you fail, you will be punished for trying. Never say or write down your plan. Heart is the only place where secrecy is granted.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
pmover,

I tried reading NACE MR1705 before and to be honest it got me really confused. I am not an expert on material selection and corrosion so that's why I couldn't figure out what they are talking about. I think I have to do more research on these topics.

All the API 617 datasheets that I have come across that referred to the process gas as "WET" had H20 content but nowhere in the datasheet humidity or dew point of the process gas was mentioned. In this case, how do you define when a process as is Wet if you do not know the dew point of the gas. Also, in certain cases, the water content is zero but the methane content was less than 85% and the gas was labeled as "WET". Am I confused between two different definitions?

I was working on a compressor package in which the gas was "DRY" gas with 0 water content but a high H2S content (i.e. 3000 ppm). The client was worried about SSC and emphasized on the material selection for the impeller to deal with the high H2S content of the dry gas. However, since no water content is available and this is a dry H2S service (+ no chloride content as well), then SSC shouldn't take place, correct?. I have read online on sciencedirect that even though water is not present the process gas is still considered sour if it has H2S but SSC cannot occur with water not being present. Do you agree with this statement? Why was the client worried about SSC in this case?

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

All the API 617 datasheets that I have come across that referred to the process gas as "WET" had H20 content but nowhere in the datasheet humidity or dew point of the process gas was mentioned. In this case, how do you define when a process as is Wet if you do not know the dew point of the gas. Also, in certain cases, the water content is zero but the methane content was less than 85% and the gas was labeled as "WET". Am I confused between two different definitions?

I think you are mixing up things. The point of the API617 datasheet mentioning wet flow is to ensure the flow basis is consistent with other datasheet figures (e.g. power consumption). If the basis is "dry" the water content is disregarded irrespective of relative humidity figure.

In the operating condition section, API 617 datasheet contains a bullet point for relative humidity at row#20.
You are making an incorrect statement.

In regard to your latest paragraph, " I have read online on sciencedirect that even though water is not present the process gas is still considered sour if it has H2S but SSC cannot occur with water not being present. Do you agree with this statement? Why was the client worried about SSC in this case?"

I do not know. Maybe the client has deep pockets.

If you plan an escape, you must succeed as if you fail, you will be punished for trying. Never say or write down your plan. Heart is the only place where secrecy is granted.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
rotw,

I believe the client has deep pockets yes. Lol

With regards to the first point, indeed API 617 has a bullet point with RH. However, I have never seen it filled by the vendor or customer in any project even if the gas is WET.

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

(OP)
rotw and george,

I want to really thank you for your time responding to my basic questions on corrosion, etc.

I just want to end this thread with one clarification regarding the usage of WET vs DRY gas. I have done a lot of research today about the subject and everything you have mentioned makes a lot of sense now. However, the only thing that is still confusing me is the definition of Wet gas being a gas with Methane being less than 85% and heavy hydrocarbons constituting more than 15% of the gas composition since these compounds (i.e. propane, butane, etc.) can easily turn into liquids in the gas stream. Please clarify when is the phrase WET indicates water presence and when it indicates heavy hydrocarbons (ethane and higher).

Below link has the definitions I am highlighting:

https://naturalgasnow.org/wet-natural-gas-dry-natu...

### RE: Centrifugal Compressors: Molecular Weight, Head and First Stage Impeller

A gas is water wet when its operating temp is lower than the water dewpoint temp at a given reference pressure. To be safe, given that water content estimates can be prone to some errors when there is H2S, CO2 and/ or high pressure, I would add a margin of safety to the dewpoint temp. ie if the calculated water dewpoint temp of a sour gas is stated to be say 10degC, I would keep some 2-3degC away from this to avoid water dropping out. ie I wouldnt have this gas temp at temp <12-13degC.

Also, the compressor case, during extended pressurised shutdown, can reach min ambient temp, which may be lower than water dewpoint temp. I remember one case where a compressor vendor insisted that pressurised shutdown for a compressor in a similar gas, should only be a for a limited duration, to avoid corrosion concerns resulting from cool down to ambient while pressurised. Beyond this duration, we had to implement auto blowdown of the entire compression train in order to maintain the requested design life for this compressor.

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