Can increasing backpressure increase the flow of a flashing liquid? 3

[JKoenders]

Suppose there's a pipe connecting two vessels that is very long relative to its diameter, and there is a pressure differential between the tanks driving the flow of liquid through the pipe. Now suppose that somewhere along the length of this pipe the pressure-drop causes the fluid to flash, creating a two phase flow regime.

My understanding is that the two phase flow will cause a greater pressure drop along the pipe than if the material remained in liquid phase. So, conceptually speaking, could adding a restriction (such as by throttling a valve, or adding an orifice) at the downstream end of the pipe increase flow through the pipe by forcing the material to remain in the liquid phase until it gets to the end of the pipe?

This logic, while counter-intuitive, seems sensible to me. Intuitively, though, I would think that adding any restriction must decrease the flow, and removing a restriction must increase the flow.

Is there any truth to this theory, or is my intuition correct?

 

[BigInch]

Why not? A similar comparison makes sense for carbon dioxide lines. Although its not 2 phase flow, CO2 lines are pressured up to run in the dense phase, thereby reducing pressure drop per unit volume delivered to a fraction of what it would be in the gas phase alone. LPG gomponents are also transported in the liquid phase and "flashed" for final use.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Latexman]

No, adding a restriction decreases flow.

The pressures at the beginning and ending of the pipe are fixed. You did not mention temperature, but I assume these are fixed too. Therefore, the % flashed is a state function depending only on it's initial T and P and it's final T and P, and it is not impacted by what's in between. The only thing that is impacted by the amount of restriction in the line is the flow rate. The % flashed will be constant.

Good luck,
Latexman

 

[zdas04]

This is a very hard concept for some people to grasp, and I had a meeting once where I thought the only possible outcome was violence. The argument goes like this:

1. Flow rate is a function of dP across a pipe length
2. Increasing dP means greater flow
3. Therefore adding flow restriction increases flow

The fallacy in this circular nonsense is that statement 1 and 2 are only true at a constant resistance to flow. If you add resistance between the inlet and the outlet then you change the system response to flow and a fixed dP will give you less flow. If you remove resistance between the inlet and outlet then a fixed dP will result in more flow.

This is the reason that any flow equation has to be solved iteratively--you guess a flow for a dP and calculate a friction factor, use that factor to recalculate the flow, use that flow to recalculate the friction, repeat until the change in the answer is acceptably small. The argument above skips all that pesky iteration and gets a wrong and counter-intuitive answer.

I had this argument with a 30 year Engineer who thought he had found the meaning of life in the statement "increased dP results in higher flow rates so we should be adding restriction". I thought about how to correct his thinking without bitch-slapping him and came up with the term "parasitic pressure drop" to include friction, multi-phase interference, and hydrostatic resistance. These parasitic terms decrease the effectiveness of the flow conduit and reduce the amount of fluid that can flow for a given whole-pipe dP. Everybody in the room got it except this grey-hair (he was younger than me) who kept writing the AOF equation (q=c(Pup^2-Pdown^2)^n) on the board saying that since "c" was a constant more pressure drop was good. He never did understand that "c" was no more constant than ambient temperature. I ended up walking out of the room and writing a white paper on the problem. Maybe someday someone will read it.

David

 

[Zapster]

wisepeppy, I agree that it seems that flow might increase by placing an orifice on the discharge end of the pipe where you only have two phase flow exiting the orifice and single phase (liquid) upstream of the orifice. I had thought about this scenario regarding condensate flashing creating two phase flow for much of a line compared to flashing across an orifice on the end of the line with single phase upstream. I was not interested enough to do the math. Seeing how you brought up the topic, why don’t you make the flow calculations and let us know the results. The most compelling argument for this type of reasoning would be a simple flow analysis to make or break the argument.

 

[BigInch]

Here's something to consider for you guys.

As Latexman suggests, in evaluating this problem from a pipeline dP vs flow perspective you must maintain the same pipeline physical boundary conditions. Assume the primary boundary conditions are inlet pressure, outlet pressure and pipeline length. Adding a restriction within that framework to an interior point of the pipeline DECREASES differential pressure in the first segment of pipeline, and INCREASES the differential pressure in the second segment. Considering only one phase flow of the fluid What would normally be expected is that, due to the lesser differential pressure in the first segment, that flowrate in that segment would tend to go down, and due to the higher differential pressure in the segment segment, the flowrate in the second segment would tend to go up. That poses a quandry, because then the mass flow in segment one would not be equal to the mass flow in segment 2, neglecting possible changes in density. Thus a transient flow scenario would be initiated and stay in effect until (if) the flow in segment 1 was equal to the flow in segment 2. That would tend to orbit about the initial flowrate, until steady state was achieved. I think undoubtedly, the average flowrate transmitted during the transient state would probably tend to remain the same as the initial flowrate.

zdas mentions a similar argument where people supposedly also forget that the pipeline physical boundary conditions must remain the same; ie. nothing happened to inlet pressure - outlet pressure; that remains the same. Upstream dP was decreased, downstream segment was increased, thus the loss of flowrate upstream obviously cannot be miracuously transported to the beginning of second segment to be flashed. The iteration that he mentions needs to be calculated beween the first segment's flowrate and the second segment's flowrate and continue until both are equal to thereby achieve steady state. Since no more, or no less mass could possibly enter the pipeline's inlet, if inlet pressure and outlet pressure remained equal, the final flowrate should eventually equal the initial flowrate.

Considering only the most basic fluid mechanics problems, the above is true.

However the above arguments NEGLECT density changes and possible changes in friction factor per unit mass. They also do not address possible changes in even simple flow regimes, such as passing from turbulent to laminar flow at some point in the pipeline, not to mention potential phase changes.

I don't know if it was your intention to allow consideration of those effects in your original question.

Considering the case of CO2, where inlet pressure might be 2000 psia and final outlet pressure is 15 psia, and considering scenarios where the "orifice" is located at the beginning or the end of the pipeline, while keeping those in/outlet pressures constant, the orifice plate located at the end of the pipeline increases the transported mass to levels much higher than those possible than if the "orifice" were to be located at the beginning of the pipeline. In that analogy however, if the phase change occured at the orifice plate located upstream, segment 2 might require an even a higher differential pressure causing the overall dP to have to be increased. If you place the orifice plate at an optimum point, maybe the dP in segment 2 could be made equal.

You can see the same process in batch mode when looking at LNG transport. Its liquified, filled into LNG carriers and transported at a liquid at 1/600th of gas volume, then gasified at the end. If you did it all at low pressure, you'd have a lot more friction loss (600 NG gas phase carriers in this case) for the same mass.

If any don't believe, kindly please explain in your opinion why CO2, LPG, LNG and even liquid O2 and liquid N2 and others are transported with the "orifice plate" located at the end of the transport process. For the case of LNG, typical economics of the transport mechinisms and refrigeration cost available dictate that LNG should be the method used when pipelines are expensive to build (very deep water) and sources are more than 2000 miles away from destinations. In the case of O2 and N2, its not possible to pipeline up to a Saturn V. The mileage factor goes up, when the pipelines are located on relatively cheep right of ways in farm country. This would seem to indicate conclusively that the friction factor of a given phase and the length of the line considered against the pressure lost/unit mass transported has an definit impact on where the "orifice plate" should be used, or not used, and if used, where it should be located in the transport process.

But admittedly, and going totally by experience, short natural gas lines, less than 3000 miles, should not usually have an orifice plate added to increase dP to liquid phases, but CO2 lines should. Depends on friction factor in the phase vs the phases' mass transport ratio.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[zdas04]

BigInch,
As I was reading your excellent analysis I had a thought--if you put a restrictive orifice in the middle of the pipe the dP between the inlet and outlet is meaningless. You have a dP between the head of the pipe and the orifice of some amount. Then you have a dP across the orifice. Then you have a dP from the outlet of the orifice to the foot of the pipe. The dP across the orifice can be huge depending on the size of the hole. So your statement that the orifice "DECREASES the differential pressure in the first segment of pipeline, and INCREASES the differential pressure in the second segment" is not necessiarily true. The dP in the orifice could easily result in a DECREASE of the dP in both segments by reducing q and therefore friction.

David

 

[BigInch]

Well... yes, then let's be technically correct, any device in the pipeline, including pipe is considered as a "flow element", basically anything having flow and a pressure drop, so to steer the analysis along the lines you suggest, we really should be talking about 3 flow elements, with corresponding flows and resultant pressure drops distributed to each element. Therefore an orifice plate element with a small hole, would have the exact same effect as a very short length very small diameter pipe. Increasing the pressure drop by decreasing the diameter of the hole would raise the outlet pressure of element #1 and reduce the inlet pressure of element #3. So, then when the orifice plate is added into the line, we don't know the flow in the new 2nd element (the orifice plate element), so a more correct iteration process would start with the old flowrates in segments (elements) 1 and 3 and a 0 in element 2, then, since dP in 1 and 3 decreased, the flow in the 1st and 3rd would decrease and we would quickly discover that the continueity equation would require us to increase the flow in the 2nd element, not in the downstream segment as I said when I "grouped" the orifice effect with the last downstream segment before (or, more accurately, neglected to mention the orifice plate at all).

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[BigInch]

So, yes, the system flowrate would quickly be seen to decrease according to the increased friction of the entire system. The 0 flow in the orifice plate could not possibly reach the original values of the flows in elements 1 and 3. We could only maintain the original flowrate, if somehow we managed to compensate for the new added frictional resistance, for example, by increasing the inlet pressure, or reducing the outlet pressure, BUT then that's changing the boundary conditions, so we couldn't do that and stay within the original boundary conditions of the original problem.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[BigInch]

Once again neglecting phase changes and any possible friction factor-unit mass variance between phases.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Latexman]

It's clear to me that an orifice at the end of the line gives more flow than the same orifice at the beginning of the line in flashing two phase flow, but that's not the OPs question.

The OP is asking will adding an orifice to the line give more flow than just the pipe alone in flashing two phase flow. After reading the excellent, rapidly growing responses, I believe the consensus is no, the flow will decrease.

Right? Or, is that just my view of the world?

Just trying to clarify

Good luck,
Latexman

 

[JKoenders]

My thought was that this scenario, if possible, may only hold true in certain very specific situations, so even if I did the math and showed that it did not hold true for one scenario, I've by no means disproved the concept. I was hoping that someone could show me that the concept was bogus before I spent any time doing any calculations. At this point I'm just curious if, conceptually, the theory is plausible or complete bubkis.

The scenario where the orifice plate is either at the front or back of the pipe makes sense, and clearly shows that the same collection of components can produce a different effect when assembled in a different order, because of the conditions they impart on the fluid within. Maintaining liquid flow until the end of the pipe is more favorable than flashing at the front of the pipe. Same mechanical restriction, but the additional resistance caused by the two-phase flow is avoided when the orifice is put at the end of the pipe.

So, is it plausible that if you have no orifice, and then add one at the end of the pipe, that the resistance added by the orifice is less than the resistance you remove from the system by preventing two phase flow. Sort of a return-on-investement situation - put 1 in to get 2 out. Again, probably situation-dependent, but is there any situation, within the confines of the boundaries established, where this is possible?

One post by BigInch suggests that this is done intentionally when transporting liquified gases - that the orifice is added at the end of the pipe, in order to prevent two phase flow, and thereby increase overall mass flow rate verses having no orifice at all. Is this true?

 

[BigInch]

I know for certain that is how CO2 pipelines operate, although its not necessarily gassified at what you might want to call the precise "end of the pipeline"; perhaps just after the end of the pipeline, but it also seems to make little difference where you say the exact end of the pipeline actually is. The physics is that its transported as a supercritical fluid and, as I understand it, is pumped into certain types of oil wells in a liquid phase as a means of enhancing oil recovery. It increses well pressure and the resultant CO2-oil mixture has a reduced viscosity, so is better able to flow through the fissures.

It turns out that its much cheaper to transport CO2 by pipeline in the (single) dense supercritical phase, where its neither liquid or gas, even though relatively high pressures are required to do so. The friction factor per amount of mass transported is very much lower than if it was transported as either a gas or a liquid phase alone.

The following is from the Midwest Regional Carbon Sequesturization and Storage Project, "Final Report" of 2005.

CO2 may be transmitted via pipeline as a low pressure gas or a supercritical fluid. Pipeline transmission as a supercritical fluid (compressed to 1073 – 3046 psi (7.4 - 21 MPa)) is considered the most reliable and
cost effective method for transporting large amounts of CO2. In the supercritical phase CO2 has
characteristics of both a liquid and gas, maintaining the compressibility of a gas while having some of the
properties, such as density, of a liquid. Low viscosity is important for pipeline transport and the viscosity
of CO2 in the supercritical phase is the same as in the gas phase, which is 100 times lower than in the
liquid phase. Important from a cost standpoint, supercritical transport allows for substantially higher
throughput through a given pipe cross-section than transport as a lower pressure gas.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[BigInch]

Latexman,

Certainly fluid flow would decrease, at least for typical fluids transported in a single phase. However, if as in the CO2 example the orifice plate held the CO2 in the dense phase for a longer length of pipeline segment than you would have if the orifice plate was not included, it appears that the mass flow rate would increase, although the overall pressure drop could plausibly remain equal, or even be very much less than the original, since such a large reduction in friction factor occurs in the SC phase (its the same as the gas phase friction factor) but the mass is very much higher. In that scenario you could easily add a perhaps short region of pipe where 2 phase, or even multiple phase gas/liquid/supercritical flow might exist, let's make it right after an orifice plate close to the end of the pipeline. So, if we're talking about CO2, it would seem that you can't make that typical theory hold for all cases.

Let's continue with some unusual scenarios. If an orifice plate with a small hole sheared some kind of a non-Newtonian fluid sufficiently to reduce the friction factor by 20%, the reduction in downstream friction would be 20% less than if the orifice plate wasn't there. If the head loss at the orifice plate was less than that 20% reduction, it would also seem to be able to give the same mass flow, or perhaps even increase mass flow, and do so at a reduced overall pressue loss.

So, for the general case, yes it is true, however in certain specific cases it really depends on the characteristics of the fluid's mass to viscosity ratios in various states along the transport path, even some of which may depend things other than the phases of the fluid.


**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Compositepro]

A restriction will not increase flow. For the restriction to prevent flashing it must reduce the pressure drop in the pipe so that the pressure stays above the flash point. It can only do that by reducing the flow rate.

 

[BigInch]

Compositepro,

2 questions.

How does your logic apply to the non-Newtonian case I mentioned?

How does your logic apply to the supercritical phase of CO2, even when it has 600 times the mass of the gas phase yet the friction factor is the same as the gas?

I don't see how it does.

If we're just under the supercritical phase boundary and we increase the inlet pressure only by 1 psi, theoretically, the pipeline changes from liquid phase to SC phase and the differential pressure drops to 1/100th of what it was when in the liquid phase.

If what caused us to have to increase the inlet pressure by at least 1 psi was the introduction of the orifice plate it wouldn't appear to be so.

Assume the SC phase boundary is 3000 psia and we have a 2999 psia inlet pressure. Pressure drop in the liquid pipeline is 2000 psi. Outlet pressure is 999 psia.

A big holed orifice plate is added to the end of the pipeline giving a dP there of 1 psi at the same time we increase outlet pressure to 2999 psia. Pressure just upstream of the orifice is 3000 psia, SC. Holding the same flowrate, inlet pressure must be 5000 psia as it tries to maintain existing liquid flowrate. The pipeline changes from the liquid phase to SC phase and the differential pressure is now 2000/100 = 200 psi. We can drop inlet pressure to 3200 now.

Inlet pressure is 3200 psia
Pipeline dP in the SC phase is 200 psi
Pressure just upstream of the orifice is 3000 psia
Pressure downstream of the orifice is 2999 psia
We flash that to gas going somewhere.
Mass flow in the pipeline is some multiple (that multiple presumed greater than 1) of what it was in the liquid phase and 600 times that of what it would be if the pipeline was in the gas phase.

At least on the surface, it appears that you could do this. I (with the OP's permission) would like to hear from anybody with supercritical CO2 experience. In the meantime, I'm trying to contact a few I know. Hopefully to arrange a Hysis simulation with CO2.


**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Latexman]

Most non-Newtonian fluids I've come across are time independent on their viscosity versus shear rate response, thus the viscosity changes instantaneously as shear rate changes. In these cases, the lower friction factor in the orifice would not carry downstream.

There are a few time dependent non-Newtonian fluids, but as the high shear, low viscosity would carry downstream of the orifice, the high shear, low viscosity will not be fully realized at the orifice and the resistance in the orifice will be quite high.

We can go round and round on this, but I'd need to see real data to believe it.

Good luck,
Latexman

 

[BigInch]

Yes, but my point was, that it could depend in great part on the fluid's properties, no matter how unusual they might have to be, as to whether adding an orifice plate somewhere into the line will increase pressure drop or decrease pressure drop and that this type of problem might not be so intuitive as it initially sounds. I think it possible that an orifice plate inserted in a pipeline, no matter what the pressure drop is at the orifice plate, could be recovered by a particular fluid's resulting reduced friction factor, if the remaining pipeline happens to be long enough and ... maybe we should take our heads out of the little box once in awhile before we jump to those "I know it is true all the time" responses.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Latexman]

One phenomenon that comes to mind that might help make this happen is "frozen equilibrium", which I have applied in the past to saturated, liquid ammonia going through a restriction to explain the measured pressure drops of the total system. I don't think this is as drastic of a deviation from normal fluid flow and fluid properties as the SC CO2 you mentioned, but I do see your point and it would not surprise me that it might happen.

Good luck,
Latexman

 

[FeX32]

Analogy. Think of it like a simple electrical problem of current flowing through a wire of resistance R. Keeping the voltage potential constant any change in R changes the flow.
(whether the current is concentrated towards the surface or not).


Fe