View source for Archive:000/Hydrogen gas/Pressurized storage

==How much steel: Estimating the ''absolute bare minimum'' required==

In physics, there is a general formula to estimate the theoretical minimum material-to-gas ratio, for ''any material'' containing ''any gas'' at high pressure.

 a = 1.5 R T D / (S M)

{|class="wikitable"
!colspan="2" |Parameters
|-
|<code>a</code>
|The '''ratio''' we're calculating {{minor|'''Mass''' of the container, divided by the '''mass''' of the gas}}
|-
|<code>R</code>
|{{light|''The universal gas constant''}} (<code>8.3144626 J/K/mol</code>) {{minor|The same constant that's used in the ''Ideal Gas Law'' in physics (PV<nowiki>=</nowiki>nRT)}}
|-
|<code>T</code>
|{{minor|&nbsp;}} The maximum storage '''temperature''' {{minor|<small>Relative to ''absolute zero'' (&minus;273&deg;C)</small>}}
|-
|<code>D</code>
|The '''density''' of the material the container is made of
|-
|<code>S</code>
|The '''tensile strength''' of the material the container is made of
|-
|<code>M</code>
|The '''''molar'' mass''' of the gas {{minor|Which, in the case of ''hydrogen gas'' (H<sub>2</sub>), is about <code>2.02 g/mol</code>}}
|}
<tab name="How this formula was obtained" collapsed>
This is based on the general formula for [https://structx.com/Stress_Strain_006.html Spherical Pressure Vessel - Hoop Stress]:
 s = P r / (2 t)
* 's' being the tensile ''hoop stress'' on the material
* 'P' being the pressure of the gas
* 'r' being the <!--(inner)--> radius of the container
* 't' being the thickness of the container wall

'''For our case,''' let's assume that the container is pressurized to its limit - in other words, 's' is also the ''tensile yield strength'' of the material.

We can rearrange the formula to get the wall thickness of the container:
 t = P r / (2 s)

From there, we can get the volume of the container '''material''', approximately:
 Vmat = 4 pi r^2 * t
 (Area of the sphere, times thickness)

Meanwhile the volume of the '''gas''' is:
 Vgas = (4/3)pi r^3
 (Volume of the sphere)

Therefore, the material-to-gas ratio '''BY VOLUME''' is:
 Vmat / Vgas
 = 3t / r
 = 1.5 P/s
 (Yes, everything cancels out except for 'P' and 's'. The ratio is the same '''no matter the size of the container.''')

But we want the material-to-gas ratio '''BY MASS''' instead, so:
 Mmat / Mgas = Vmat / Vgas * Dmat / Dgas
 = 1.5 P/s * Dmat / Dgas

First we need to know the density of the gas (via the ''gas law'' in physics):
 Dgas = P M / R T
* 'P' is the pressure as used earlier
* 'M' is the ''molar mass'' of the gas molecules (chemistry)
* 'R' is the universal ''gas constant''
* 'T' is the temperature

From here, the final equation is:
 Mmat / Mgas = 1.5 R T Dmat / (s M)
 (Yes, 'P' cancels out of the equation. The ratio is the same '''no matter the pressure of the gas.''')

Note that there is '''no safety factor''' in this equation. There is also no accounting for the materials in the gas valve etc. It calculates only the '''theoretical minimum''' material. In real life, you will need a bit more.

{{pn-block|TALK:
* Yes I know it's awkward to use 'M' for molar mass and 'Mgas' for the total mass.
* Yes I know I didn't formally define 'Dmat' but whatever, hopefully people can infer.
* Yes I know that ''relative'' pressure (actual gas pressure minus 1 atm) is what really matters - but that would make the formula more complicated. The simpler formula above works fine if the we assume that the gas is ''significantly'' pressurized. For low pressures close to 1 atm (i.e. a simple balloon, not what this page is about), we could use less material in theory.
}}
</tab>

''Let's apply this formula to a few possible cases below:''

{{dp
|T
|tempC(60)
|Maximum storage temperature
|Chose 60&deg;C because it's just above the highest weather temperature ever recorded on Earth. This doesn't account for future climate change or improper storage of the tanks. In any worst case, the tanks should be designed to vent the gas (or deform?) rather than explode, hopefully.
}}
{{dp
|M
|2.01588 g/mol
|Molar mass of hydrogen gas (H<sub>2</sub>)
}}

===Cheap structural steel===
<div style="background:#DFD">
{{empty}} <br /> {{light|[calculation]}}
</div>

Structural steel is mostly iron & carbon, which are abundant on Earth. The main concern would be the energy needed to process all that steel.

However, this is just a thought experiment, because hydrogen gas is known to react with structural steel anyway. Let's try stainless steel next:

===Stainless steel===
{{dp
|stainless_steel.density
|7.80 g/cc
|Density (weight per volume) of 10.9 alloy steel
|[https://matweb.com/search/datasheet.aspx?matguid=e11dcacd0b2c4cdeae2e2c1b5b0816a1&ckck=1 Ovako ISO 898 grade 10.9 34CrNiMo6 (6499) Steel, +QT]
}}
{{dp
|stainless_steel.yield_strength
|897 N/mm^2
|Tensile yield strength of the stainless steel
|Using "10.9 alloy steel" http://www.volksbolts.com/faq/basics.htm
}}
{{calc
|1.5 R T stainless_steel.density / (stainless_steel.yield_strength M)
||||^ Material-to-gas ratio
}}

Stainless steel contains more than just iron & carbon. It also contains nickel & chromium, which are scarcer resources. {{pn|Need to do an analysis regarding mineral reserves.}}