Hydraulic capsule pipelines

Calliban · 2022-09-09 08:46:04

On Earth, pipelines often provide the most cost effective bulk transportation of liquids and gases. There has been some analysis to suggest that pipelines could provide a cost effective transportation option for solids as well. Pipelines have been used to transport coal slurries and floating coal logs. Pipelines could be useful for transportation of other freight, by sealing it into neutrally bouyant capsules and either allowing capsules to be propelled by the movement of the fluid or by propelling capsules through a notionally static or more slowly moving fluid. I have carried out some fluid mechanics calculations to assess how this concept will perform on energy efficiency grounds on Earth and Mars.

In both cases, I have assumed cast iron pipes, with a roughness of 0.15mm. Calculations were performed for pipe diameters of 0.3m (1'), 1m and 2m. Flowrates were 1, 2 and 3m/s, which is 2.2, 4.5 and 6.7mph, respectively. I have assumed that pipes are straight, with no bends or discontinuities that could effect friction factor. On Earth, the carrier fluid will be water, with temperature of 1°C and 20°C and dynamic viscosity of 0.0017 and 0.001 Pa.s, respectively and density 1000 and 998kg.m-3, respectively. On Mars, the carrier fluid is liquid CO2, with a temperature of 217K, pressure 5.3bar, dynamic viscosity 0.000252 Pa.s and density 1177kg.m-3. I assume that capsules are neutrally bouyant and occupy one half of the volume of the pipe, displacing one half of the liquid. The mass of freight transported per unit time, is therefore one half of the mass flowrate of a pure liquid filled pipe. Based on previous experimental work, I have assumed that the presence capsules and the effect they have on Reynolds number and friction factor, roughly doubles pumping power compared to pumping 100% liquid. The reference pipe length is taken to be 1000km, with pressure drop and pumping power directly proportional to pipe length.

Method:

The pumping power required to push fluid through a pipeline of length, L, is equal to the pressure drop across L, multiplied by pipe cross-section area, multiplied by L. Pressure drop is calculated using the Fanning Equation.
https://chemical-engineering-review.com … drop-pipe/

Friction factor was calculated iteratively, using the Colebrook-White equation.
https://engineerexcel.com/colebrook-white-equation/

Results: Scenario 1: Water.

Temperature: The pumping power required to drive the pipeline is relatively insensitive to temperature. For a cast iron pipe with diameter 1m and flow speed 3m/s, a reduction in temperature from 20°C to 1°C, increased pumping power by 2.4%.

Flow speed: For a 1m diameter pipe, 1°C water temperature and flow speed of 3m/s, pumping power is 386W/m. The implied energy cost of transport is 328KJ/tonne-km. This compares with rail freight which has an energy consumption of 410KJ/tonne-km in the UK. The energy cost per tonne-km is proportional to v^0.9, so is roughly proportional to flow speed. A doubling of pipe diameter, halves the energy cost per tonne-km. The amount of freight delivered through a 1m diameter pipe, with flow speed 3m/s, is 37.2 million tonnes per annum. The delivery mass is proportional to pipe diameter squared, all other variables being constant.
For an extreme case of a 2m diameter pipe and a flow speed of 1m/s, energy consumption is 51KJ/tonne-km. This is one eighth the energy consumption of Earth rail freight, according to wikipedia.

Scenario 2: L-CO2.

For L-CO2, performance is actually very similar to water pipelines. Despite having only a quarter of the viscosity of water, pumping power for a 1m diameter capsule pipeline carrying L-CO2 at 3m/s, is 18% greater than water at 1°C. This is due to the substantially higher density of L-CO2. For a 1m diameter pipe and 3m/s flow speed, energy cost is 369KJ per tonne-km, which is again, comparable to rail freight on Earth. Energy per tonne-km appears to be directly proportional to flow velocity. Reducing pipe diameter from 1m to 0.3m, increased energy per tonne-km by a factor of 4.3, for a common 3m/s flow speed. A 0.3m diameter pipeline, with a flowspeed of 0.33m/s, would deliver 433,000 tonnes of freight per year at an energy cost of 183KJ/tonne-km, about one half of Earth based rail. However, such a low speed may be problematic for some freight. It would take some 35 days for a capsule to traverse a 1000km long pipeline.

I decided to examine an extreme case of a 0.1m diameter pipe, with flow speed of 3m/s. This pipe could deliver 438,000 tonnes per annum at full capacity. Energy cost is 6.16MJ/ tonne-km. This compares to an energy consumption of 1.33MJ/tonne-km for an Earth based truck.
https://www.researchgate.net/figure/Ene … 5_49616876

Conclusions.

Hydraulic pipeline capsules may offer some logistical advantages for transportation of non-perishable goods on Earth and Mars. The main limitation of such pipelines is their low speed. A 3m/s flow rate is about one third of the average velocity of rail freight. This makes pipelines unsuitable for delivery of goods where time limitations are important. Low speed also directly impacts the amount of freight that a pipeline can carry per annum and thus the number of tonne-km delivered per year. This is a problem because the marginal capital cost of a pipeline depends on the ratio between capital cost and flow rate of goods through the pipeline. However, safety prevents railways from operating without substantial gaps between trains, whilst pipelines face no such limitations. Pipelines are in many ways easier to build and maintain than railways. A leak could lead to loss of flow, but no catastrophic damage would occur to either the pipeline, its surroundings or stranded payload. A damaged rail track on the other hand, could be catastrophic. It is therefore reasonable to expect a pipeline to be cheaper to build and maintain than a railway of comparable capacity (2m diameter, 3m/s). A water pipeline 2m in diameter with a flow speed 3m/s, would have energy consumption of 143KJ/tonne-km, which about one third that of rail freight.

On Mars, the calculations are complicated by the fact that gravity is only 2/5g and air resistance is practically zero. This means that rail freight would have one third of the energy consumption of Earth based rail and the energy efficiency advantage of a pipeline disappears. The need for pressurisation of L-CO2 also complicates pipeline design. Using water based pipelines is impractical on Mars. Whilst it is possible to add salts that will keep water technically a liquid at -50°C, its viscosity is comparable to honey or maple syrup. Not something we can pump at reasonable energy cost. Heating the water is impactical for the same reason. I therefore conclude that pipelines offer significant advantages for bulk freight transportation on Earth, but the case appears to be weaker on Mars, as both rail and pipeline options are comparable in terms of freight delivery flow rate and energy consumption.

Finally, the long-duration of pipeline transportation and lack of direct labour involvement in the conveyance itself, makes short term variations in input power less significant. On Earth, we could drive freight pipelines using directly coupled, mechanical wind power, i.e. using the turbine shaft to directly drive a centrifugal pump without intermediate electricity generation. Such turbines do not need any copper or rare earth elements. Blades can polymer and carbon fibre or even wood. The tower could be steel, or masonry or even rammed earth, depending upon size. The shaft and pumps can be steel of varying grade. On Earth, it may even be practical to use open ditches instead of pipelines in some locations. On Mars, PV panels would power centrifugal pumps driven by DC motors with direct drive. This obviates the need for power transmission to pumps along the pipeline. On both Earth and Mars, pipelines can be powered using directly harvested energy without storage. This eliminates the need for batteries or other energy storage technologies.

Last edited by Calliban (2022-09-09 09:38:21)

NewMarsMember · 2022-09-09 09:41:49

For Calliban re new topic

Best wishes for success with this interesting new topic!

Thanks for providing numbers for readers to work with.

If anyone not already a member would like to add to this topic, please see the Recruiting topic for procedure.

(th)

Calliban · 2022-09-09 17:28:40

Thanks Tom.

Precast, reinforced concrete pipes would appear to be the most suitable material for construction of capsule pipelines here on Earth. They are used to construct sewers and storm drains and have a demonstrated 100+ year service life.
https://precast.org/precast-product/pipe/#

They are already manufactured with internal diameter 2.1m. This is just about ideal to carry containers that are interchangeable between rail, truck and pipeline.
https://www.jdpipes.co.uk/products-and- … crete-pipe

In the UK, there is an extensive rail network. However, this has become increasingly tailored to passenger traffic, which tends to limit its usefulness for freight. For the UK to reduce the oil requirements of freight transport, we can either build dedicated freight railway lines or a parrallel freight system involving pipelines, allowing rail to serve passenger traffic.

Last edited by Calliban (2022-09-09 17:38:42)

tahanson43206 · 2022-09-09 19:28:59

For Calliban re new topic ....

Before we get too far along here, please comment on the engineering of grade.

My (vague) recollection is that Roman engineers (and others of antiquity) found that a grade of ? 2 degrees ? was about right for routing water over great distances.

Does the "lay of the land" in Britain favor long distance runs at such a gentle grade?

If a grade is favorable for descent, do you have a plan for ascent, or would be pipe be a one-way run, with rail or something else as the alternative?

The coasts of an island would seem well suited for non-elevation runs, but in that case, would impellers be required to move the water along?

Your long opening post includes mention of pumps, so I would assume those would be at the high end of a line?

Also .... salt water is more readily available than fresh water (in many locations on Earth) so building a system that uses salt water might make sense?

(th)

SpaceNut · 2022-09-10 15:28:36

Elon Musk tunnels are all operated by this principle of reduced resistance to forward motion of the object being accelerated from point A to B. These all suffer from the need to ensure that the patron is safe throughout the journey. It does sound like a great cargo system for sure as no fear to spoiled vegies....

Calliban · 2023-03-15 05:47:33

Interesting wordpress article on capsule pipelines.
https://timhowgego.wordpress.com/capsule/what/

Of interest for both Earth and Mars applications. On Mars liquid fuels will be expensive, since we will need to synthesise them from water and CO2. There is also the downside of having to carry a LOX tank in a combustion powered trhck. On Earth, liquid fuels are gradually becoming more expensive. As global supply chains break down, many countries are going to face fuel supply disruptions.

Capsule pipelines could provide a relatively compact way of delivering freight between hubs, which could be located at cities or towns. The capsules may be floating in water or mounted on small wheels in air filled tunnels. Propulsion may be water flow, direct electric (no batteries), compressed air or even gravity. Energy efficiency will be comparable to rail and the energy sources can be the wind or sun harvested close to the pipeline. If all freight was carried this way, then half a dozen large nuclear reactors could power the entire US freight delivery system. A single large reactor could power freight delivery for most European countries.

The main advantage this concept appears to provide over conventional rail is portability. If tunnels are small and can be installed as say 1m diameter steel pipes, then installation costs will be substantially lower than the cost of building conventional rail and it should be possible to build these tubes underground. That means freight tubes can pass under land or streets and can be installed by digging trenches and filling in behind.

On Earth, freight tubes could drastically reduce the amount of diesel needed for package delivery. On Mars, they will become applicable once population passes a threashold and the fuel energy cost of transportation begins to approach the embodied energy of a freight pipeline.

Calliban · 2023-12-05 08:20:33

This reference is the summary report of a 1978 study into hydraulic capsule pipelines.
https://www.osti.gov/biblio/5743024/

A 10" pipeline, moving capsules at 5' per second (1.5m/s), requires a pumping power of 253BTU/ton-mile. This equates to 183.45KJ/tonne-km.

Frictional energy losses per tonne-km are inversely proportional to pipe diameter and proportional to the square of flow speed. A pipe diameter of 2m is large enough to carry most of payloads that are presently transported by road. A 2m pipeline would reduce flow resistance per tonne-km by a factor of 7.8 compared to a 10" pipe. Increasing flow speed to 10' per second (3m/s), would quadruple flow resistance, but would half transit times. At this speed, the energy consumption of transportation would be 94.07KJ/tonne-km, or 0.09407MJ/t-km.

In 2022, UK road transportation delivered some 175bn tonne-km.
https://www.gov.uk/government/statistic … ngdom-2022

Suppose we built a pipeline system that could replace long distance road freight transportation. How much pumping power would be needed? Total pumping energy required would be 175bn x 0.0941 = 16,463,461,543MJ

Averaged over a year, pumping power would 522MW. This is a rather small amount of power to transport the freight for a nation of nearly 70m people. A single 1000MWe nuclear power reactor could do this. Or we could use direct mechanical wind power to pump water through the pipelines. But in this case, the flow speed would be a function of wind speed.

The downside of this type of transportation is that it is slow. For example, the distance from New York to Los Angeles is nearly 4000km. Moving at 3m/s, it would take some 15.4 days to ship freight between these two cities. New York to Chicago (1146km) would take 4.4 days. Winnipeg to Ottawa is 1675km and would take 6.5 days.
https://www.distancecalculator.net/

Pipelines carrying neutrally bouyant capsules could provide us with slow but very energy efficient freight transportation. If we needed to build a nationwide freight transportation system that worked entirely without (direct) use of fossil fuels, this would be a way of doing that. I say 'direct use' because we would need a great deal of concrete, plastic or steel pipes to build the extensive pipeline network. Unless we make these pipes using something other than fossil fuels, we are simply transfering fossil energy consumption from fuel to infrastructure. Maybe in some areas we could use clay lined canals instead of pipes.

The wind has been used to pump water at low heads for drainage for centuries. This wind pump is in Norfolk in England. Thousands more like it were used to drain land in the Netherlands.
https://www.alamy.com/stock-photo-old-w … 06341.html

We could build pumps like this along pipelines and use the wind to pump water through the pipelines. For a modern pump, we would probably use vertical axis wind machines. For a flow speed of just a few metres per second, we could directly couple the vertical axis to a cetrifugal pump without gearing. This would allow the machine to pump water with only one moving part. The rotating turbine and pump would both sit on a single thrust bearing. Such a machine could remain functional for centuries.

Last edited by Calliban (2023-12-05 09:03:15)

Calliban · 2023-12-05 14:02:25

Archimedes screw pumps are often the choice for pumping large volumes of water at low head. We could attach a vertical screw to a vertical axis turbine.
https://en.m.wikipedia.org/wiki/Archimedes'_screw

The head height associated with a flow speed of 3m/s can be calculated using the Bernouli equation:

V^2/2 = gh

H = V^2/2g = 9/20 = 0.45m

We would have overflows along the pipeline. Overflowing water would drain directly into the screw pump and be lifted by 0.5m and reinjected into the pipeline. The screw itself would by made from thermoplastic, probably polypropylene. The VAWT will be made from wood. The blades can actually be segmented, with each carved from a single piece of wood. The VAWT will be supported by a rammed earth or stone tower. The bearings will be steel wheels running on a steel track on top of the tower. Something like this:

In places where it is sunny but not windy, we could use DC motors to drive screw pumps and couple PV solar panels directly to the DC motors. The pumping power would then be directly proportional to sunlight intensity. One way of avoiding a lot of the demand for copper, is to locate the panels to within a few metres around the DC motor. This avoids the need for inverters and allows us to directly couple the output of panels to the motor. But transmission distance cannot be more than a few tens of metres. We could also mount the PV panels in concrete casings instead of steel and mount them on cast concrete supports. This would cut out a lot the steel needed by the PV panels, as they wouldn't be tracking the sun.

This is one application where PV could be a practical energy source because: (1) Power requirements are low; (2) Most pumping stations will be in the middle of nowhere; (3) Transmission distance from source to load is short, eliminating need for inverters; (4) Energy storage is not anticipated.

The last point is important. We will be transporting goods over long distances and delivery times will typically be measured in days. We can allow higher pumping rates in daytime and lower pumping rates at night. But if we attempt to store energy in batteries, capital and operating costs will explode. For renewable energy costs and embodied energy to be kept under control, energy must be used as directly as possible and energy transitions should be minimised. Which is why I advocate the use of wind power to produce direct mechanical power and solar for direct electric coupling to loads.

Last edited by Calliban (2023-12-05 15:06:29)

kbd512 · 2023-12-05 17:11:49

Calliban,

I think we're going to have to implement something like this for in-continent delivery of freight. The energy and materials trade is worth it over time, since it drastically reduces ongoing requirements for long haul trucks and trains. Population centers are now relatively fixed. The growth surge of the 20th century is over. Maybe this system could be at least partially powered using trompes, although mechanical wind turbines are probably more practical.

Calliban · 2023-12-05 18:00:35

There would need to be junctions at the entrance and end points of these pipelines. These junctions would be shallow ponds, with multiple pipelines entering and leaving each pond. As a capsule exits a pipeline into the pond, hydraulic manipulators would grab it using an electromagnet. It would then be either dragged to the entrance of an outgoing pipeline or onto an off ramp, if that junction is close to its destination.

Ultimately, we want a system where no consumer is more than about 10 miles from an entrance and exit pond. When the containers exit, they will be lifted by crane onto a flat bed heavy truck. We would need to design capsules to allow easy attachment to a towable chassis. If the pipeline system is extensive enough, distribution trucks can be powered by short range energy sources, probably compressed air.

A significant problem with this system would be freezing. One solution to this would be to use saline water. But that magnifies corrosion issues and also creates a land contamination problem in the event of leaks. A partial solution is to lay pipelines in shallow trenches, with at least 1m of soil over the top of the pipe. This insulates against cold weather. Friction in pipes will also generate heat that will help keep water above freezing.

To keep the energy consumption of this system as low as possible, sharp bends in pipes should be avoided. The straighter the pipes are, the longer capsules can be. This allows greater freedom in product geometry. But it also has implications on both maximum loads that can be transported and energy efficiency, as longer capsules allow higher product volume fraction. But ultimately capsule length must always be lower than the width of junction ponds.

If there are temporal variations in traffic through the pipeline, water will be displaced from pipes. We would need surge tanks or reservoirs to absorb this water an ensure it isn't wasted.

Finally, I initially wondered if such capsules could be used for human transportation. But this seems unlikely. There would be no escape from a capsule in emergencies. The only exit points are the junction ponds. Also, pipelines arevprobably too slow for people. At 3m/s, capsules would travel 160 miles per day. So this idea only applies to freight.

Last edited by Calliban (2023-12-05 18:15:13)

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#1 2022-09-09 08:46:04

Hydraulic capsule pipelines

#2 2022-09-09 09:41:49

Re: Hydraulic capsule pipelines

#3 2022-09-09 17:28:40

Re: Hydraulic capsule pipelines

#4 2022-09-09 19:28:59

Re: Hydraulic capsule pipelines

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#6 2023-03-15 05:47:33

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#8 2023-12-05 14:02:25

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