Hydrogen in pipes

A paper about to be published completely revises previously held understanding on how hydrogen flows in low pressure pipes, such as the final few hundred metres of the domestic gas distribution network ( which would be relevant if we ever replace any natural gas with hydrogen).

Since 2004 we have thought that we understood this. Now is is apparent that we did not.

Does this affect plans for using hydrogen domestically ?

Not really. The final numbers don’t change that much. It is only at periods of quite low gas demand that the pumping power required to deliver calorific value via hydrogen is nearly 8 times what it was for natural gas:

Fig.1 For five different pipe roughnesses, the ratio of the pumping power required to make up for friciton losses for hydrogen compared with natural gas. The Reynolds’ number is a measure of gas velocity. Most service line pipes have Re < 3000. [Actual compressor power required will be different depending on compressor efficiences.]

What is more worrying is that this work makes it clear that everyone working in this field for the past two decades has made assumptions about gas flow which are quite incorrect. And the concern is that modern process systems computer codes, which are perfectly fine for modelling process plant, may be using the wrong calculations for slow-velocity, low pressure pipes such as the domestic distribution grid. These codes are black boxes and users have no way of finding out how the calculations are done.

Everyone has assumed that Reynolds’ numbers more than about 2,000 mean that the flow is turbulent. This is not right: for a smooth pipe such as polyethylene used today (relative roughness ϵ/D ~ 10^-5), the flow in a circular pipe is only fully turbulent above a Reynolds’ number of more than 10⁹ . It stops being laminar at about 2,300 but then it is in a Blasius and pseudo-Blasius smooth-turbulent regime (shown in the figure by the purple line) for 5 orders of magnitude of gas flow velocity.

There have been very significant advances in the understanding of viscosity in the past 30 years and previously people working in hydrogen techno-economics seemed to have been using old text books, not current research knowledge.

The final numbers do change slightly from what had previously been estimated (estimated for pure methane incidentally, not for natural gas which is a bit different). Hydrogen needs a much higher gas velocity in the pipe to deliver the same useful energy, about 3x, but the exact number we now know is 3.076 times faster (for flows where both the natural gas and hydrogen are in the Blasius regime, something that is actually quite unlikely and rare in the final connection to domestic housing).

Because hydrogen has a low viscosity, the extra gas velocity does not need as high a pressure drop to drive the velocity increase as one might expect. The correct number is that a pressure differential 1.290 times higher is required (in the Blasius regime). This is a bit of a stretch, while the vast majority of distribution pipes will be fine (these run between 75 mbar and 20 mbar above atmospheric pressure), a very few already near the limits of their capability to deliver natural gas will not be able to deliver enough hydrogen.

Unfortunately, at the low gas velocities in the final metres of the distribution network this number can rise to 2.5 times higher, but this is only at times of low demand when there should be adequate pressure gradient ‘headroom’. However it is worrying that gas engineers seem to be totally unaware of this issue, or at least, nothing public has been published about it.

The pressure drop multiplier, as a function of gas velocity, has the same form as Fig.1 above:

Fig.2 How much higher the pressure gradient has to be to delivery the energy-equivalent amount of hydrogen.

So why has the gas delivery industry been so out of date? The Moody diagram which describes the flow of fluids in pipes dates from 1944, but the oil and gas industry has historically used a wonderfully bizarre menagerie of oil-industry specific codes and formulae, such as the Pandhandle equations¹ developed for gases in Texas: these are of course completely inappropriate for hydrogen as they have been calibrated quite specifically for certain natural gas mixtures only.

Fig.3 Updated Moody diagram, showing the laminar/turbulent transition, but also the ‘belly’ and ‘rise’ of the ‘Nikuradse behaviour’. Nikuradse was Prantl’s research student: this is originally from the 1930s.

This has all been re-measured and re-calibrated over the past two decades with two machines at Princeton and Okinawa. There has also been significant theoretical development by Goldenfeld at the University of Illinois.

Fig. 4 The maximum possible boiler efficiency for an air temperature of 5°C and a gas temperature of 8°C for varying condensation temperatures (similar to the return temperature on a central heating system)

The paper also incidentally calculates the form of the boiler efficiency curve for natural gas and for hydrogen, which is perhaps much more significant for those planning on using hydrogen for domestic heating.

Fig.4 shows that a hydrogen fuelled boiler is much less efficient, by about 5% above 70°C, than a natural gas boiler if the condensation temperature in the condensing boiler is warmer than about 63°C. However as the central heating return temperature is decreased, a hydrogen boiler will be slightly more efficient that a natural gas boiler at the same condensation temperature. (This extra efficiency at 50°C was taken into account in the paper when calculating the required hydrogen velocity.)

So a hydrogen boiler really does need to be coupled with a weather-compensation control system in every installation to ensure that hydrogen is not wasted, and it shows that using hydrogen is not a way to avoid having a strong incentive to reduce the flow temperature of your radiators.

Fig.5 The gradients of the lines in Fig.4 showing the strong peaks of efficiency improvement when the return temperature drops just below the dew point temperature for each fuel.

Fig.6 The ratio of friction factors for hydrogen and natural gas to deliver the same useful energy: an enlargement of the flow regimes for most of the gas distribution network. This is not quite the same as the ratio of pressure drops, because of the difference in viscosities and densities.

[minor edits 2024-0320]
Okinawa device size and axes labels on ‘friction loss’ plot, which is now at 30 bar.
Also scfd is a mass unit, not a volume unit.

1. “Where units are in scfd, degrees Rankine, psia, feet, and miles“. scfd is ‘standard cubic foot’ per day, a measure of gas mass delivery. Degrees Rankine have the same interval as degrees Fahrenheit, but with zero at absolute zero: °R = °F + 459.67. psia is pounds (force) per square inch absolute, i.e with respect to zero pressure not with respect to atmospheric pressure. No wonder they got confused.
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