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ammonia compressor efficiency to calculate mass flow

ammonia compressor efficiency to calculate mass flow

ammonia compressor efficiency to calculate mass flow

(OP)
I need to evaluate the performance of a heat exchanger (evaporator)

The exchanger evaporates ammonia
In order to do the calculation I need to know the ammonia mass flow. Which is not meassured directly.

The only information I have got is about the compressor which runs after the evaporator and has the following conditions meassured:

the ammonia vapour is compressed with a compressor from 82mbar (abs)(Saturation pressure) to 13.1 bar (abs)Discharge temperature (84.9°C)(superheated)

The Motor Ampere is meassured with 257 Ampere
The Voltage is unknown, I pressume it is 380V

My question:
Can I calculate the mass flow by
m * (enthalpy outlet - enthalpy inlet) = P compressor = 257 * 380. ???

I pressume I need to take into account the efficency of the compressor. I do not have any information about the type of compressor, Can anyone advice?
What kond of efficiency can one use??


RE: ammonia compressor efficiency to calculate mass flow


Before attempting to answer are you sure the suction pressure isn't gage pressure, namely 1.082 bar abs. ?

RE: ammonia compressor efficiency to calculate mass flow

(OP)
sorry you are half right, it is actually 0.82 bar and the temperature is about -33° the vapour is slightly over heated (about 4K)

thanks for the hint

RE: ammonia compressor efficiency to calculate mass flow

themroc:

Is this a mechanical refrigeration application with an Ammonia evaporator acting as the cold source for your process or utility fluid?  If so, why not just tell us that; it would be much simpler because then we could analyze and inquire why you don't just supply the vaporizer heat load.  That's the way a conventional mechanical refrigeration system is usually designed - not by trying to find out how much refrigerant vapor your compressor is going to handle.

I have some misgivings about your basic data besides what I've stated:

1) what exactly are you trying to figure out - in total?  You say you want to "evaluate" the evaporator and then you ask about how to calculate the compressor horsepower (or whatever you mean by "P compressor".
2) You state you do not have any information about the type of compressor.  This is not only strange, it's not what a responsible engineer would accept.

Is this a real-life application or is this a conceptual or academic question?  Please tell us ALL of the facts and the basic data as well as your scope of work - and then we can help you out in an organized and intelligent manner.  Otherwise, we're only half-guessing at just exactly what you have.



RE: ammonia compressor efficiency to calculate mass flow


FWIW, you may compare results with the following ballpark data I took from old notes for an oil-flooded twin-rotor screw compressor on anhydrous ammonia working on a properly-maintained system.

With the evaporator and condenser conditions indicated by you and no economizer, the motor would be consuming about 3.5 HP/TR, and the ammonia flow rate to the evaporator would be about 12 kg/h per TR.

1 TR = 3,000 kcal/h.

RE: ammonia compressor efficiency to calculate mass flow

With a reciprocating compressor you can also estimate CFM
by knowing displacement and RPM of cylinders.  Knowing an average specific volume between intake and outlet you'll have an estimated mass rate.

RE: ammonia compressor efficiency to calculate mass flow

380 volts, not familar with that.  If I ssume 480 Volts and 257 amps on 3 phase, that appears to be 150 HP or 112 KW.  At the available conditions, the compressor could compress 680 Kg/hr (based on a reciprocating compressor of 82% effiency.  The resulting evaporator could remove 175,000 Kcal/hr. If the compressor is a lower effiency screw type, the values would drop to 425 Kg/hr and 110,000 Kcal/hr.

RE: ammonia compressor efficiency to calculate mass flow

dcasto:

With all due respect, your estimates are just whispers in the wind.  There is no way you can estimate/predict any duties, horsepower requirement, or condenser cooling requirements where the Original Poster (OP) hasn't revealed anything about his refrigeration cycle yet other than he's using Ammonia and his compressor suction & discharge pressures.  This is not enough information to generate what you state.  One needs to know the evaporator conditions and the condenser conditions.

Of course, one can establish a base - like ASHRAE does - and fix the conditions of both the evaporator and condenser.  But you haven't stated that.  Consequently I have to say that your estimates are meaningless unless they have a basis.  This doesn't mean your estimates are wrong; it just means they lack a basis - and that's essential in engineering.

Again, without any concrete basic data and a scope of work explaining what the OP is doing, we're all guessing (or as we would state it here in Texas, "p_ _ _ing in the wind").

RE: ammonia compressor efficiency to calculate mass flow

i stated my basis, 150 HP at 82% effiency, with the pressures set by themroc.  Simple refrigeration cycle. I gave an alternative at a lower effiency (62%).  Now if themroc measures the heat rejection near one of the values I've stated he can enterpolate the effiency and then ask himself it thats a reasonable value or can they make an economic justification to replace the system.

RE: ammonia compressor efficiency to calculate mass flow


To dcasto, the temperatures of the gas entering the compressor at say, 0.8 bar, and the liquid upstream the reducing valve weren't given.

If, through heat exchange with the condensed ammonia, usually done to remove any droplets by vaporization, vapors entering the positive displacement compressor heat up by 40-50oC, their specific volume may increase by more than 20% defeating the estimate of throughput.

Of course, this enthalpy exchange wouldn't be lost since the liquid entering the evaporator would be cooler. Agree ? smile

BTW, one interesting item I found many years ago when dealing with (anhydrous) ammonia refrigeration is that the liquid has a specific heat capacity equal or greater than water. Any comment ?

RE: ammonia compressor efficiency to calculate mass flow


My own comment: the change in BHP/kg ammonia vapor compressed as a result of superheat at suction would change, but not by much, so as to thwart a rough estimate.

RE: ammonia compressor efficiency to calculate mass flow


Let's clarify the subject during the weekend.

Since BHPadiabatic/(kg/h) is proportional to the absolute suction temperature, to [(k/(k-1)] and to [(p2/p1)(k-1/k)-1], roughly speaking a 20% increase in absolute suction temperature would result in a 14% increase in BHP/(kg/h) for a constant volumetric efficiency and the given pressure ratio.

On the other hand, 4 K superheat wouldn't mean an appreciable change in the said BHP to mass rate ratio.

RE: ammonia compressor efficiency to calculate mass flow

(OP)
Dear all thanks for your replies.
I was out of office for some days, therefor no clarification.

We designed and delivered an heat ammonia evaporator.
When designing it I based my design on the information delivered.
At this time it was not clear for what purpose the exchanger was designed.
The following conditions were given:
Evaporation on the tube side with ammonia (quality 0.067) entering the exchanger at a pressure of 1.3bar absolute (t sat = -28.9°C) Requirement was to evaporate 1320kg/hr with a superheat of about 4K.
This was the design sucction pressure for an compressor which compressed the gas.
The ammonia is heated via syltherm a heat transfer fluid. (t inlet -17.2 / outlet - 25°C) Heat transfered 457kW.

Now in service we got the feedback that the exchanger does not perform. It is based on the heat load of the shell side heating fluid. Which only meassured about 280kW.

The thing is according to them this is the value they base the exchanger duty on. Apparently they do not measure the ammonia mass flow.
But they state that the exchanger is not performing well. In addition they give the compressore information of the current perfomance so I wondered whether it is possible to calculate from this the mass flow in order to calculate the tube side duty of the exchanger?
Following conditions meassured of the compressor:
___________
The ammonia vapour is compressed with a compressor from 82mbar (abs)(Saturation pressure) to 13.1 bar (abs)Discharge temperature (84.9°C)(superheated)

The Motor Ampere is meassured with 257 Ampere
The Voltage is unknown, I pressume it is 380V
__________

In addition they state that there are dropplets present in the succion stream. But they meassure a temperature of -33°
The saturation temperature at this point would be about -37°C. Indicating a superheat of the ammonia. Is it possible that you get droplets in a superheated flow?





RE: ammonia compressor efficiency to calculate mass flow

Themroc,

Can you indicate how is the ammonia preflash attained ? Is there a level-controlled flooder feeding the exchanger by gravity while simultaneously venting the vapor produced in the preflash ? Can you explain the 1.3 bar at the inlet of the vaporizer and 0.82 bar at the outlet ?

The data just now supplied indicates the original design considered a degree of subcooling for the liquid ammonia prior to the expansion valve. Can you comment on that ?

Yes, droplets can coexist with superheated vapor for a certain time until equilibrium is reached. If the residence time in the suction pipe, from the vaporizer to the compressor, is short enough droplets may reach the compressor. Is there a KOD at the compressor suction ?

RE: ammonia compressor efficiency to calculate mass flow

(OP)
25361,
The 1.3 bar was the design condition.

Now they run the exchanger under different conditions, for the 1.3 the outlet condition due to the pressure drop was about 1.18 bar.

I refer to the 0.82 because I have got for this value data from logs for the compressor. For the 0.82 bar the inlet pressure of the exchanger was about 0.89 bar.

What do you understand under the ammonia pre flash? Is that commonly used in this kind of applications?

According to the operator the ammonia is not subcooled when entering the evaporator ir as a quality of about 5%.

What is a KOD.

Thanks themroc?

RE: ammonia compressor efficiency to calculate mass flow


Besides, can you explain the 1.3 bar at the inlet of the vaporizer and 820 mbar at the outlet ?

Has the condenser operation been checked ?

Is there a KOD at the compressor suction ?
Is there a strainer at the compressor suction ? What type of compressor is being used ?

On another direction altogether, has the user checked the flash point or the viscosity of the syltherm fluid to verify whether it suffered a change with time ?

RE: ammonia compressor efficiency to calculate mass flow


Sorry for the duplication of questions due to my pressing the submit post button too soon.

I understand the clients moved to "vacuum" conditions to get lower ammonia temperatures to compensate for the worsened performance of the exchanger. Right ?

I call preflash the vaporization that occurs after the expansion valve which is the 5% quality you mentioned. I assume the vaporizing takes place on the shell-side. Am I right ? What type of vaporizer is this ?

A KOD is knock out drum usually provided with a demister to remove liquid droplets from the vapor. It usually has a coil to subcool the ammonia from the condenser, while superheating the vapors to vaporize droplets coming from the vaporizer.

RE: ammonia compressor efficiency to calculate mass flow

(OP)
In fact the client did a whole series of check at different operation conditions in order to check the performance of the exchanger.

In this case the vapourisation takes place on the tube side.
It is a horizontal BEM type evaporator.

As far as I know there is no KOD installed, at leased  I do not see anything on the flow sheet.

RE: ammonia compressor efficiency to calculate mass flow

Themroc:

Thank you for finally giving us ALL of the facts.  However, some things don’t make for common sense:

You say your client has a suction pressure on his compressor that registers 82 mbarA.  This can’t be correct.  Either you or they have made an error or are reading the pressure wrong.  82 mbarA yields an ammonia saturated temperature of -74 oC and I don’t believe that you have an operation that is producing that level of refrigeration.  You also may have just made a typo error and really mean that you have 840 mbarA suction pressure.  If so, please clarify.  If you are going to insist on using the SI system, then I suggest you stick to one set of units (like barA) instead of measuring and reporting in different units which only creates conversion problems – as noted.

You state your ammonia vaporizer has the liquid ammonia vaporizing in the tube side.  Is this a vertical unit?  You also state that the vaporization is taking place at 1.3 barA and -28.9 oC.  But then you say that the ammonia is compressed from 82 m barA (840 mbarA?) to 13.1 barA.  That means that there must be a pressure drop of 460 mbar (6.7 psi) in the suction piping going to the ammonia compressor(s).  This is an excessive amount of pressure loss for an ammonia mechanical refrigeration system.  I would have expected 0.5 psi or thereabouts.  My point here is that this is very inefficient.

You are correct in noting that the compressor suction cannot possibly have ammonia “droplets” if the actual temperature is -33 oC.  This temperature, as you state, indicates superheating and droplets (liquid) cannot physically exist in a superheated state.  Superheat applies only to the gaseous state – not the liquid state.

If the evaporator that you designed is not transferring the specified 457 kW (1,559,350 Btu/h) then something is obviously wrong.  However, this would entail believing the information coming from people who also allege that liquid droplets exist in a superheated suction to the compressor.  Consequently, I would suggest that you or your representative investigate the application and get to the real facts in the field.

From the application data you supply it is obvious to me that the ammonia compression is being done in a 2-stage cycle.  This type of cycle usually has an “economizer” type of intercooler, of which there are at least 2 varieties.  Depending on the mechanical configuration and type of intercooler, you will have varying refrigeration efficiencies and the Bhp requirements (as well as the compressor capacity) will vary depending on the efficiencies.  That’s why I maintain that the best way to determine the amount of ammonia evaporated is to make an accurate heat balance around the evaporator.  This should be easy to do since you can measure the Syltherm flow rate and the inlet/outlet temperatures.  This is far more accurate than assuming a variety of conditions that, as seen with recent data, don’t exist.

RE: ammonia compressor efficiency to calculate mass flow

(OP)
Montemayor,
thanks for your comments, as I staed earlier (reply 3) there was atypo and it is in fact 820mBar absolute.

The 1.3 bar was the design pressure at the inlet of the evaporator

The 0.82bar was the actually meassured suction pressure at the compressor. (see sommend 12 Dec 06 8:32)

The evaporator type is horizontal.
It is probably better to do a heat balance around the evaporator. I intended to do this and therefore was quiet keen to know the mass flow of the ammonia. But because this was not meassured I thought there is a way to find it out using the compressure inlet and outlet conditions.

Thanks for the help.

RE: ammonia compressor efficiency to calculate mass flow


If the client arbitrarily changed the compressor's conditions from a suction pressure of 1.1 down to 0.8 bar, with the same discharge pressure 13.1 bar, as fixed by the condenser, while the suction temperature dropped from 248 K to 240 K, the ratio HP/(kg/r) is supposed to increase according to the equation I mentioned above.

Namely, for the same BHP, less kg/h ammonia vapor would circulate at the lower pressure, the small increase in latent heat would probably not compensate for the diminished flow rate.

One assumes there are no inward leaks of air when working under vacuum.

RE: ammonia compressor efficiency to calculate mass flow

26362,  The temperature was given at the inlet of the compressor as 4 degrees of superheat and the temperature upstream of the reducing valve is the saturation temperature.

As for the temperature rise and specific volume change going through the compressor, that doesn't matter only the specific volume at the suction dictates the compressor capacity.

The enthaphy entering the cooler is soley dependant on the condensor outlet conditions since the enthalphy across the reducing valve is zero.

I looked at the PH diagram and found that at 250 psia and 100 F, ammonia hac a heat capacity of about .8 BTU/lb-DegF


themroc,
The change from 1.1 to .8 bars will tranlste to a 30% decrease in mass througput and a 1 % lower duty in the chiller



RE: ammonia compressor efficiency to calculate mass flow


To dcasto, I do not disagree with your points, except for the isenthalpic expansion meaning that the change in enthalpy is ~zero, not that the enthalpy is zero.

Please note that themroc's question was what happens with the ratio HP/(kg/h) of the compressor when the suction conditions drop from 1.1 bar and 248 K down to 0.8 bar and 240 K, with a constant discharge pressure of 13.1 bar as fixed by the condenser.

I have a small disagreement with Montemayor concerning the presence of droplets in a superheated vapor. Not about the theory or the definition of superheat, but with the facts.

This is a short-lived (let's say, transient) non-equilibrium situation that may happen in refrigerants when the superheated vapor flows in parallel with a droplet-containing saturated stream, and in particular when the superheat ΔT (as driving force) is small. Besides, the density of the droplets being almost 800 times greater than that of the vapor, they may tend to collect and coalesce.

In gas quenching, it has been noted that when the flows of mass and heat are opposite, as for gas cooling with humidification, the overall heat transfer coefficient would be 0.3 to 0.8 times what we'd expect from heat transfer alone.

On the other hand, when both, mass and heat, flow in the same direction, as for gas cooling and dehumidification, the OHTC may be 1.5 to 3 times higher than what could be expected from heat transfer alone.

Therefore, if the residence time is short, there is a chance that while bulk temperatures indicate a degree of superheat there still may be drops of liquid refrigerant reaching the compressor.

Comments are appreciated.

RE: ammonia compressor efficiency to calculate mass flow

25362, Sorry if I wasn't clear, but yeah, the delta enthalpy is 0.  

In more detail (give us all a break here 'cause we do not have every P&ID, manufacturers data book, etc..) The HP/(kg/hr) will increase by 10%, but the compressors ability to move gas will decrease by 30%.  Net effect is a 30% less than design in kg/hr to the HX available heat transfer, less some amount for a change in the heat transfer coefficient for being at a reduced rate (less than 5% here).  There will be a corresponding 10% increase per kg/hr for a net of the compressor running at 77% of its original design amps.

As for not getting all the liquid vaporized, this can happen a flooded horizontal super heat controlled exchanger. I'm in the process now of getting rid of one and replacing it with a BKU type, not because I'm convinced it is allowing droplets past, but because it can and if that happens not only do I loose capacity, I may loose the compressor.

RE: ammonia compressor efficiency to calculate mass flow


To dcasto, as I see it, when estimating the mass flow rate you considered just the vapor densities while keeping the compressor to be working with the same volumetric efficiency in both cases.
But what if it were partly unloaded at 1.1 bar and fully loaded at 0.8 bar ?

Regarding your own plans, installing a KO drum on top of the flooded exchanger with suitable droplet-catching devices may be cheaper than replacing it altogether. Have you considered that ?

As an aside, an oil-flooded screw type of compressor could handle some liquid droplets w/o damage.

RE: ammonia compressor efficiency to calculate mass flow

25362:

I seriously doubt there are any droplets in a flow stream that has undergone superheating and overcome a 6.7 psi pressure drop.  The flow is obviously turbulent and well-mixed.  The primary reason I doubt the prescence of any droplets is that it is mere hearsay up to now.

I've undergone this situation where liquid entrainment (without a resultant downstream liquid level) is suspected but only in theory many times in the past.  The end result is that no one has accepted my challenge to catch just a few of these micron-sized "droplets" and saved them in a paper bag for my inspection.  In fact, upon further inquiry, everyone admits they have never seen a refrigerant droplet in a refrigeration compressor suction line existing at -25 oF.  I say this not to reinforce my stubborness and hard-headedness but just to point out that all of the reports of droplets existing in these lines are theoretical - at least those that can't produce a subsequent accumulation of liquid refrigerant.

Please don't interpret my comments as contradictory to taking - and employing - sound engineering judgment and good vapor disengagement practices when feeding a saturated ("wet") refrigerant to a compressor.  On the contrary.  I believe you will find all the systems I've designed and built/installed to be very conservative in that specific section of a refrigeration cycle.  I merely wanted to point out that while the entrainment of droplets may be occurring, it is quite difficult to sustain a saturated liquid drop in a superheated stream that is subject to further heat-up as it approaches the suction valves of a compressor.  And it is quite impossible to prove the prescense or size of the drops within the system under normal conditions - at least in my opinion.  Basically, I believe themroc's client is trying to confuse the issue and point to a defective evaporator design without offering any proof.  I still maintain that themroc's way to prove otherwise is to do a heat and material balance around the evaporator.

Most of the major mechanical refrigeration cycles I've operated in the past have had a small hot gas recycle back to the suction drum as a capacity control + superheating effect to ensure that any liquid accumulating in the lines leading to the compressor suction is "swept" with superheated gas to evaporate it.  

You have done an excellent analysis of this refrigeration system once we were given the factual data.

RE: ammonia compressor efficiency to calculate mass flow


Montemayor, my thanks to you. I fully agree in that we are indeed speaking of seconds or fractions of a second for the droplets to vaporize.

To anyone interested in reading about hot gas quenching with liquid sprays with examples, I suggest the book by
Donald R. Woods: Process Design and Engineering Practice Prentice Hall, ISBN 0-13-805755-9

RE: ammonia compressor efficiency to calculate mass flow

(OP)
Thanks all for your comments.
I see a little bit clearer. In my opinion the droplet issue is also very suspect, according to our client the effect of droplets is clearly noticable due to noise in the compressor. Since I have got no experience at all I belived him in the beginnings. But your comments seams to indicate that this is quiet unlikely. Due to the pressure and temperature measurements I also thought the superheat is sufficient in order to evaporate the remaining droplets.
I will try to find out the actual piping length between evaporator and compressor inlet. This will give an indication for the residence time in the piping.
In this context:
Does anyone have an experience whether the noise level is an indication of droplets pressent in the suction stream?

Annother commend / question reading through all the answers:
The client claims the evaporator does not peform well. I can base my balance only on the shell side single phase heating fluid because here I have the mass flow and temperature difference. Taking this into account He is right and the duty is much lower than expected.
THe problem is that he operates the evaporator at much lower pressure than in the design calculations.
AS I mentioned about 0.82 bar instead of 1.3 bar.
Obviously he does it in order to achieve a higher driving temperature difference in the evaporator.
But I think and I understand that is also your opinion that the penalty for the compressor in succing at a much lower pressure is worse than the gain in driving temperature.
In addition simulations indicate that at the lower ammonia pressure the heat transfer coefficient in the tubes of the evaporator are also decreasing.

How is actually exactly the pressure level of the cycle maintained.
My understanding is that the compressor determines the succion pressor that means the evaporator exit pressure. So in case the evaporator produces more ammonia vapour mass flow than the compressor can handle at this pressure the pressure will rise automatically, making it easier for the compressor to handle the flow Is this correct?
Would that also mean in case the evaporator produces less vapour mass flow that the succion pressor is reduced?

On the other hand what determines the evaporator inlet pressure? Is this the exit pressure plus pressure drop in the evaporator. Or is the inlet pressure of the evaporator a set value determined by the throtteling valve and all the other pressures (evaporator outlet, compressor inlet) are established from this point?

Sorry for the additional Questions?
but thanks in advance

RE: ammonia compressor efficiency to calculate mass flow

themroc:

From what I see, the issue isn't dead; it has changed complexion or the scope has amplified.  Because of the additional information and explanations, we can now contribute more positive help.  But we need concrete data on:

1. What size, type, model, etc. of ammonia compressor(s) are being used?
2. Is this a 1-stage or 2-stage cycle?
3. What's your capacity control devices on the compressor?
4. How is the evaporator controlled?  Is it on level control?  i.e., is it flooded with refrigerant?  It probably is not since I find it hard to believe that a horizontal BEM type with the refrigerant on the tube side would be.  And this is the difficult part:  for proper industrial control, you should really have a flooded BKU type of evaporator with the refrigerant on the shell side - just as dcasto implies.  I believe dcasto is implying that you have a "DX" type of evaporator and if that is true, then all bets are off on trying to have positive, industrial type of control on the quality of your suction vapor going into the compressor.  With a varying evaporator load and other conditions I don't see how you could successfully design a DX unit for these condtions.  That's why industrial-grade evaporators are almost always of the flooded type.  These you can instrument and control with reliability and dependability.  A DX unit has a scope of design that mandates a steady, predictable evaporator load with ZERO load excursions.

We'll wait for your response with the data to form postiive comments and suggestions.

RE: ammonia compressor efficiency to calculate mass flow

(OP)
Thanks Montemayor,
I will try to find out.

But do you have some experience with droplets in the compressor. Do the produce a loud noise?

RE: ammonia compressor efficiency to calculate mass flow


Unfortunately I have had too many experiences with liquid particles entering reciprocating compressors.  In all these cases I have been called to identify the situation and remedy it.  Liquid particles present a dangerous hazard to a reciprocating compressor when they are in the form of a liquid slug large enough to cancel all the clearances normally available in the cylinder of a recip.  The results can be from mild physical shock to a devastating rupture of the cylinder head cover plates.  It all depends on the size of the invasive liquid slug.

One such recip incident that occurred in a foreign field installation involves a case where wet natural gas was allowed to accumulate liquid in the interstage suction separators without a sight level gage to visually detect the liquid level and to calibrate a defective dP cell used to control that liquid level.  The result was that liquid filled the separator(s) and entered the cylinders.  Fortunately the suction valve design was so weak physically that the suction valves were chattered and this saved the compressor cylinder and other pressure components.  In other cases, I have had to extract cast iron pistons that had pieces of valve components embedded into the face of the piston.  A positive displacement machine is designed to positively displace a given volume - and it will try to do exactly that with every bit of horsepower made available to it.

You can't generalize, as you are doing, just stating that "droplets" are getting through to the cylinder.  You don't know that for sure and you can't prove it until damage results.  If you hear a loud noise it may be that liquid is getting into the cylinder, but that is just one source of trouble.  It could be other factors - depending on the type of compressor, the suction conditions, the mechanical state of the machine, etc., etc.  Up to now, we still have not been told WHAT TYPE of compressor is being used.  If it is a flooded screw, it could take a lot more so-called "droplets" than a recip.  Therefore, it is only guess work without real basic data.

RE: ammonia compressor efficiency to calculate mass flow


I figure the possible entrance of droplets and the resulting devastating consequences, may have been one reason for designing the cylinders of reciprocating compressors horizontal, with the inlet and outlet piping on a vertical line, that is to allow quick draining.  

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