gravity fluid feed to an underground mine down a vertical mineshaft. 1

[ECD40]

I'm looking for some hydraulic flowrate help with a problem that I'm trying to solve.

The problem is that a fluid of 1.24 specific gravity, has to be delivered down a mine shaft which is 3,300 feet deep, but I don't want to build any static head in the pipe. Therefore, it needs to be designed as a free flowing 'drain-pipe', with the top open to the atmosphere. The flowrate is 1,250 USgpm. This is well beyond any plumbing formula for rainwater down-comers.

Does anyone have any idea what formula would apply to such a massive 'free-fall' of liquid, so that the pipe can be sized. Also, what would the terminal velocity of the fluid be inside of the pipe. I might put a turbine in the pipeline after some later thought, but that is not the current issue.

Any help will be appreciated.

thanks,
ECD40

 

[MikeHalloran]

Can you slant drill a couple miles to the bottom?


Mike Halloran
Pembroke Pines, FL, USA

 

[MikeHalloran]

Assuming you can't slant drill, estimate the major diameter of a pipe helix that would fit in the shaft.
... yes, lining the shaft, all the way down.






Mike Halloran
Pembroke Pines, FL, USA

 

[katmar]

There are two ways to approach this and achieve no static head build up. Both assume that the driving force is gravity only. You can either use self venting flow, or design on the basis that the static head available exactly matches the friction head - thus giving a zero pressure gradient.

For self venting flow at 1250 USgpm you would require a diameter of 18" or larger. The flow that would result in the friction exactly matching the static head would depend weakly on the viscosity, but assuming a viscosity of 5 cP gives a diameter of 3.9" (99 mm). Any size between these extremes would result in various degrees of gurgling, slugging and pressure build up.

There was a looong discussion on this way back in thread378-81608

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

Katmar has it nailed here and I won't try to adjust any of these numbers.

You need though to give us a bit more data.

Truly vertical?
What is happening at the bottom? - You will only be able to stop flow at the top and let the contents continue to pour out with an air gap into a pond or tank. Any attempt to stop flow at the bottom will build up a considerable pressure very quickly so this open end will need to be absolutely guaranteed - can you do this?

What level of pressure can you stand?

Some sort of multiple sections or zig zags will break up the flow and reduce velocity. I find it difficult to work out for any vertical system how you would start / stop / commission this system without the first fluid not achieving free fall velocities of probably hundreds of metres a second at the bottom with consequencial huge impact forces.

A sectional diagram or a bit more info would be good.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[katmar]

LittleInch is correct to raise the problematic nature of the start and stop operations, and these aspects were discussed in the thread I referenced earlier. The start up relies on the feed to the top of the vertical section not being a bottleneck. You have to feed the vertical portion fast enough to ensure the pipe runs full. To get a zero pressure gradient in this example the velocity would be about 10 m/s. This is close to the terminal velocity of a rain drop falling through air so you won't get droplets falling at hundreds of metres per second.

But when liquid flows at these rates then bends need to be thoroughly anchored. The mechanical aspects are much more difficult to design than the hydraulics. Definitely no valves in the line (other than the very beginning) and the best way to do it is to charge a small tank on the surface with the quantity you need to transfer, and then just drain the full contents to the underground tank and avoid the need to stop the flow.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

OK - I perhaps went a bit overboard on the velocity, but even 10m/sec hitting something at the bottom with an SG of 1.24 (what is this stuff??) is going to be pretty big force and as a transient force even bigger.

A series of cascades might be a lot easier??

Why not use a steel pipe or even a small diameter high pressure flexible. 1000m at 1.24SG is only 125barg. Not really that high in small bore pipe terms?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[ECD40]

To all who responded - thank you.

The thread referred to regarding diesel delivery down a shaft or decline is common to all underground mines and they operate with no problem as a 'drainpipe', vented to atmosphere and discharging into a holding tank. Normally, the pipe size is no larger than a 2" schedule 80 steel pipe.

In my case, the volume of fluid is huge, the mine shaft is vertical and it already exists, therefore the pipe will be vertical. The hydraulics should be the same or similar to a rainwater downcomer, open at the top and discharging to atmosphere or into a holding tank with little or no back-pressure. There will be no 'water-hammer' effect by design. When we 'pour' the fluid into the open topped vertical pipe, it will accelerate to some terminal velocity and break-up into streams and droplets. The pipe discharge can be submerged in the underground receiving atmospheric pressure tank, so that no head will build up in the pipe.

If you think of your house rainwater downcomers in a heavy storm, the eaves-troughs can be overflowing, because the downcomer entry is overloaded and submerged, but the discharge pipe is still not running full at the exit. I think that this is where 'normal' hydraulic formulae do not apply, as we do not have a full pipe flow to which Bernoulli et al's formulae apply.

So this is the dilemma and challenge - what formula does apply to free fall liquids in a vertical pipe? The plumbing codes don't even come close to these kinds of volumes. With a mineshaft at 3,300 feet deep, I cannot afford to have the wrong size pipe installed. I only have one good shot at getting this right, as it will cost $$millions to install the pipe(s) in the shaft - right size or wrong size!

All further thoughts and comments will be appreciated.

Thanks,
ECD40

 

[katmar]

Why is your application any different from the diesel situation? The liquid density is higher, and you want a high flow rate, but hydraulics are hydraulics and I cannot see why the pipe will not run full if you get the feed arrangement right.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[cvg]

google 2-phase flow in vertical pipes. this has been researched quite a bit
you need to avoid bubble and slug flow and probably stick with annular flow

http://www.tandfonline.com/doi/pdf/10.1080/18811248.1989.9734366

 

[bimr]

Another reference:

http://www.eng-tips.com/viewthread.cfm?qid=326191

 

[miningman]

I believe some of my old mining engineering text books have most of the answers here, but of course I cant locate the relevant sections right now. Please take the following comments as "constructive criticism" Don't even think about signing off on a design like this without consulting an experienced shaft engineer. WEird things happen in shafts in excess of about 1500 feet deep. I have worked in 6300 foot shafts and only consider myself partially qualified. Katmar' estimate of an 18 inch pipe seems very high to me. If I remember correctly , one can get 3000 gpm thru a 6 inch line... this is when the frictional loss per 100 feet is 100 feet. Ie this is the absolutely theoretical maximum..... imagine drilling a 6 inch hole from underground into the bottom of a huge lake or the ocean.. This is for clean water obviously.

If I were to try to determine an answer to your query , I would want to know EXACTLY what your liquid at 1.24 SG is. It sounds like hydraulic backfill , and once again , weird things happen when moving hyd fill.. both vertically and horizontally.

Personaly I'd be very nervous extrapolating diesel fuel calculations into this scenario.

 

[katmar]

It is good to have comments from an experienced engineer like miningman and I agree totally with his cautionary comments. The 18" that I calculated was for self venting flow. If I use miningman's design criterion of having the frictional loss per 100 feet to be 100 feet then I calculated the 3.9" ID that I posted earlier. Using a 4" pipe for 1250 USgpm (31 ft/s) compares fairly closely with miningman's 3000 USgpm in a 6" line (33 ft/s).

If this fluid contains solid particles then the velocities required to achieve a zero pressure gradient become a concern for erosion.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[ECD40]

Thanks for all of the interest and contributions being made, so I'll try to respond as best that I can.

To Katmar. When we send diesel fuel down the mine, it goes in batches. The pipeline is not allowed to contain a column of fuel by code, so the hydraulics are similar to a rainwater leader - ie., open on the top and bottom so that its a straight through flow. The pipe is therefore running only part full in the cross section. The time it takes for the diesel fuel to run down the pipe in batches is not important.

To Miningman. Your comments would apply to running the pipe full, but that will pressurize the line by whatever head builds up. That is what I'm trying to avoid by treating the line as a drainpipe or rainwater leader. The SG is very high but it's not backfill. I'm not at liberty to reveal exactly what I'm doing yet, as the project is very confidential. I'll reveal more as time goes on.

To bimr. Thanks for that reference regarding the diesel flow. For the benefit of all, I'm copying what you said elsewhere regarding the work done by Dawson and Kalinske - as follows:-
[If you desire to limit the terminal velocity, then you need to limit the flow of fluid into the pipe since the terminal velocity is related to fluid flow.
In a report done by Dawson and Kalinske - "Report of Hydraulics and Pneumatics of Plumbing Drainage Systems' they developed the formulae. The terminal velocity is related to fluid flow and diameter according to the equation:

Vt = 3.0 (q/d)^(2/5) and
Lt = 0.05(Vt)^2

Where Vt is terminal water velocity (fps), and Lt is the developed length to develop terminal velocity (ft). From these formulae it was determined for various standard pipe sizes terminal velocity is about 10-15 fps, and that this velocity is achieved within 10-15 feet of fall.
What this means is that the velocity of falling fluid is about the same regardless if it is falling 2-3 stories, or 100 stories.]
The terminal velocity of 10 - 15 fps is more than where the IAMPO flowrates settle in.

To all. I've pursued the rainwater analogy idea and found what seems to be a reasonable approximation to the issue with the pipe in the mineshaft (see attachment). The pipe does not run full as the fluid is in 'free fall' within the pipe, but neither can it reach the 'free fall' terminal velocity of an unconstrained fall. (Note that much of the fluid will be running down the walls of the pipe as well as away from the walls). According to the source, which is IAMPO, an 8" diameter vertical pipe can carry 913 USgpm. By extrapolation, 1,250 USgpm requires between an 8" and 10" diameter pipeline, running at 7/24th full. In the above Dawson and Kalinski formula the units are inches of pipe diameter and USgpm for fluid flow. I've tried the Dawson and Kalinski formula, but have not yet reconciled the two sources. Maybe there is a problem between the Dawson and Kalinski work (University of Iowa Studies - Bulletin 10 - Report on Hydraulics and Pneumatics of Plumbing Drainage Systems - 1937) and what I'm trying to do. Their lab test pipe was 30 feet long - mine is 3,300 feet long, so the hydraulic results can vary considerably.

Is it possible that the Coriolis effect can make a difference in fluid flowrate by sending the fluid to the pipe wall on a long vertical pipe run?

So I'm still struggling to find the 'correct' and minimum size of pipe to do the job.

Thanks for your continuing comments and valued input.
ECD40

 

[racookpe1978]

So, why not run two pipes in parallel: one a 3 inch "fill"line that the oil runs inside of, and the second periodically connected as a vent line of 2 inch dia going back topside. The air blocks and locked up sections of pure liquid can "pop" off into the vent line if a slug builds up (or relieve vacuum if the slug passes), but you are not buying a huge "just-in-case" line to make sure the 8 (or 18) inch fill line does not get bound up as a single slug of high mass.

 

[ECD40]

To racookepe1978.
Thanks for your comments, but the fluid is neither diesel oil nor backfill (from a previous comment by miningman). The continuous fluid flowrate is 1,250 USgpm with an SG of 1.24 and the vertical pipeline in the shaft is 3,300 feet long.
I've yet to find any similar installation nor any hydraulic formula that properly covers this application.
Nevertheless, I have to install a pipeline that has to be 'fit for purpose'.

So I'm still struggling with this problem.

Regards to all,
ECD40

 

[LittleInch]

ECD40,

Whatever size you choose it will be wrong - that's pipeline type engineering for you.

You need to move away from the data gathering and look at what really matters I think.

What is it you really really need to achieve? Is it a flow of 1250 gpm or greater? Is it lowest cost but somewhere >1000 gpm will suffice? Is it smallest size because installation cost is everything?

The physics of this are that for a full pipe with pressure drop equal to frictional drop then you're looking at a 4" pipe with velocity about 30 fps according to mining man and katmar - Seems right to me. The trick here will be how you stat and stop the flow, but otherwise you have a good answer here which is clearly the most efficient use of pipe. If you get it just right then there will be no build up of pressure as the friction equals the head loss. To start it from empty you might be able to use something like a foam pig and then release it with a full pipe and a tank full on top of your fluid. If it's a decent fit the pig will seal the fluid and fall a the same speed. You need to think how you're going to deal with a foam bullet travelling at 30 fps, but I'm sure you'll figure it out.

At the other extreme you have a pipe diameter of somewhere between 18" and 10" based on "free fall" flow with not all the pipe being used. This will also introduce a LOT of air into your fluid and you need to think about what is happening at the bottom to be able to vent all this air caught up in your fluid which is hurtling down your pipe.

Anything less than 10" or more than 4" and you're into a complex world of slugging, surging and air fighting to go one way while your fluid is trying to go another. Getting any idea of what is going to happen will need some pretty nifty transient analysis tools which are normally designed for fluid going up from oil wells, not down into the ground.

So "I've yet to find any similar installation nor any hydraulic formula that properly covers this application." - well this tells you something - it probably doesn't exist, at least on a steady state formula or graph based solution - too much is going on to do this.

Yo could look at multiple small tubes inside say a 6" pipe and gradually use them in full mode one by one until you hit your flow rate? They run tubes much longer into oil wells so it's easy to add another coiled tube if you don't have the flow.

Let us know what you decide.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[miningman]

Little inch just put into words my exact feelings. Even if this was just straight clean water at SG of 1.0000, theoretical engineering is unlikely to give an exact result. Anyone who thinks this can be calculated needs to realise that atmospheric pressure 3000 feet below sea level is significantly different to that at sea level. What does that do to calculations ?? And without asking the OP to divulge confidential info, there's no way I could start to refine the advice I have given. If its not conventional hydraulic fill, I suspect its some kind of heavy media for experimental cutting of rock or something equally esoteric. I have succcessfully dropped conventional concrete ( SG 2. something) down a 6000 foot deep shaft yet the same activity in a 1500 foot shaft produced all kinds of problems that we never did fully resolve.

I think I would enjoy the mental challenges of being part of a multi disiplinary team working on this problem, but again Little inch is right , eventually somebody is going to have to spend serious construction money in order to evaluate how good the engineering is.

 

[1gibson]

I was wondering about the mile of air also, what does that do to the ambient pressure down there? Do the guys at the bottom have to pop their ears when it starts flowing?

 

[miningman]

I forget most of the engineering values... it just becomes second nature / fact of life after a while. And your damn right we pop our ears , not just at the bottom but as we're travelling up and down. And its not just the changes in pressure due to the weight of air within the shaft ( 0.075# per cu foot) but almost all shafts are also main airways with substantial fan pressures applied to induce / maintain airflow. I rather think that the most experienced piping / hydraulic engineer on this site has never had to consider changes these type of things in their daily life which is why I always recommend that non mining engineers engage the services of a competent shaft engineer for these type of exercises.