Can increasing backpressure increase the flow of a flashing liquid?
Can increasing backpressure increase the flow of a flashing liquid?
(OP)
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?
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?





RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
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
RE: Can increasing backpressure increase the flow of a flashing liquid?
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
RE: Can increasing backpressure increase the flow of a flashing liquid?
RE: Can increasing backpressure increase the flow of a flashing liquid?
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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
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
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
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?
Just trying to clarify
Good luck,
Latexman
RE: Can increasing backpressure increase the flow of a flashing liquid?
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?
RE: Can increasing backpressure increase the flow of a flashing liquid?
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.
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
RE: Can increasing backpressure increase the flow of a flashing liquid?
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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
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
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
Good luck,
Latexman
RE: Can increasing backpressure increase the flow of a flashing liquid?
(whether the current is concentrated towards the surface or not).
Fe
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
Unless maybe we are in another dimension.
Fe
RE: Can increasing backpressure increase the flow of a flashing liquid?
In my original post, I should have said "My understanding is that the two phase flow will cause greater resistance in the pipe than if the material remained in liquid phase." The total pressure drop will remain the same between the two tanks regardless of where the orifice is or isn't, it's just a matter of where that pressure drop occurs and what it does to the fluid in the pipe. The theory is that if the major component of the pressure drop occurs at the end of the pipe, the liquid is allowed to expand to a vapor where there are no hinderences, as opposed to flashing mid-way along the pipe and having high-resistance two-phase flow along the rest of the pipe. Can the resistance added by an orifice that forces liquid-phase flow be less than the resistance of two-phase flow along the pipe?
BigInch, you have my permission to solicit input from wherever you like, but I'd prefer that the conversation doesn't stray too far from the original constraints of the problem (flashing liquid, constant tank pressures / available dP, fixed system geometry).
An alternative consideration to adding the orifice to delay flashing, however, would be to increase the downstream tank pressure, which would effectively create the same scenario within the pipe. The dP from the front end of the pipe to the front of the orifice (orifice scenario) or to the end of the pipe (increased downstream pressure scenario) are identical if flashing is occuring right at the end of the pipe in both scenarios.
Thus, another way to pose the question is, can a saturated liquid flow at a greater mass flow rate with less available dP than a two-phase system in the same pipe with a higher available dP? Keep in mind that when I say dP here, I mean the available driving force to push the flow; i.e. the difference in the tank pressures.
RE: Can increasing backpressure increase the flow of a flashing liquid?
In the case of CO2, if you have your upstream pressure at let's say 2000 and the outlet tank at 1500 psia (I hope both of those pressures really are in the supercritical phase) you could get a higher mass throughput than if you had the inlet pressure at 1000 and the outlet tank pressure at 500 psia, where (I think) it would be flowing as a liquid. And that would probably be more mass throughput than if it was at 550 and 50, where let's say for argument's sake that it would probably be 2phase flow.
And these things really don't have to be supercritical flow either, say if you were flowing CokaCola. If you kept the pressure above your solution pressure for the quantity of CO2 in the flowstream, you'd have 1 phase flow, or a water line with air near the soluable limits, if you kept your pressure above the solution pressure for that quantity of air, 1 phase flow. Or just water alone, if its above the vapor pressure, 1 phase flow, below the vapor pressure its all vapor, or in and out of 2 phase, if the pressure varies enough at the high low points.
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
NOPE, my simulator can't find a solution where that will happen.
RE: Can increasing backpressure increase the flow of a flashing liquid?
If your inlet pressure is over supercritical pressure, you'll be flowing sc for a little while, no. Whether you'll do that for the entire length of the pipeline or not will depend on the backpressure you're holding.
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
Compositepro and dcasto have really summed up the scenarios nicely.
If I understand correctly, your recommendation is to increase the system inlet and outlet pressures so that the cumulative losses due to friction and orifice plate do not drop the pressure to a point where flashing occurs. Essentially, shifting the entire transport process above the critical point.
In the more general case, where you may not be able to freely change inlet and outlet pressures beyond a limit, you may not be able to shift the process into supercritical region.
IMHO adding the orifice plate in that case will only suppress the flow rate.
RE: Can increasing backpressure increase the flow of a flashing liquid?
**********************
"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/
RE: Can increasing backpressure increase the flow of a flashing liquid?
That is not within the confines of the problem statement, however. The upstream pressure is fixed, and the fluid will flash by time it reaches the downstream pressure.
I think the pipe extension scenario clears it up. To reastae the idea: keeping the material a liquid (or supercritical fluid) until the end of the pipe, by increasing backpressure (however that might be done), will increase flow. It is obvious, however, that in the situation where the pressure profile (and therfor phase profile) is shifted downstream by adding pipe on the end, that the flow rate upstream of the flash point will not increase, but rather decrease. How could more pipe, with two phase flow at the end, flow more than the shorter pipe? If you include the proposed end-of-line orifice on the short pipe, and compare to the upstream-of-flash-point portion of the elongated pipe, the pressure profile, phase, and length of pipe, upstream of the flash point in both situations is identical, and therefor the flow must be the same. So, if it's obvious that a longer pipe must decrease flow, then the addition of the orifice must also decrease flow. Agreed?
RE: Can increasing backpressure increase the flow of a flashing liquid?
Regarding the discussion around supercritical CO2 pipelines (and LNG lines), is it possible that rather than maintain the same inlet pressure and using an orifice to hold backpressure that what is really going on is that we are jacking the inlet pressure and then we have to install an orifice on the outlet to take away the extra pressure we put into the system in order to hold everything supercritical (or in the case of LNG as a liquid). In this case, we would trade off the cost of generating the extra pressure against the savings in pipe size associated with gaseous or 2-phase flow but we wouldn't be getting something for nothing as we had to invest extra capital in additional equipment in order to generate the additional pressure. We just made a determination that for a given length of pipeline, the extra pressure paid off.
This is a different argument than suggesting that we are providing the same inlet pressure and adding pressure drop (e.g., restriction orifice) to gain savings in friction which would amount to getting something for nothing - all we had was the cost of an orifice and we increased mass flow?
Again, I'm just trying to wrap my head around it as the arguments proposed on both sides of the debate seemed on their faces to make sense. This is the only way I can rationalize the fact that CO2, LNG, etc are definitely transported in SC or liquid states against the analogy presented by Wisepeppy which also appears to make complete sense.
RE: Can increasing backpressure increase the flow of a flashing liquid?
In your method you only include the cost of compression. You also have to realize that the cost of generating the pressure is only one cost of many. Actual transportation cost is not a linear function of increasing the operating pressure, which can be balanced against the cost of generating that pressure. You still need to include the costs of minimizing the loss of that pressure as you try to meet the final objective, transport to point B. For typical fluids that is basically only pipe diameter. The larger diameter, the lesser the friction cost. But for some fluids, ...
again considering CO2, after compression to a liquid, the cost of further compression to supercritical regions I would guess is nearly linear with pressure, but the cost of friction when in that critical phase will be 1/100th of what it is in the liquid phase, so assuming that compression all the way to SCritical doesn't cost 100 X compression only to a liquid, its a good deal.
**********************
"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/