I am studying rock caverns lined with concrete for compressed air storage. I would like to know if it's possible to convert the permeability coefficient from m/s to m^2 or Darcy. Thank you.

  • $\begingroup$ How do you convert distance traveled in time to an area? $\endgroup$
    – Solar Mike
    Apr 10 at 8:47
  • $\begingroup$ Rather, you are asking how do you convert speed to area? Edit required, I think. $\endgroup$
    – Transistor
    Apr 10 at 9:54
  • $\begingroup$ That's the problem. I think that there's a correlation between the two by means of a hydrostatic term. I can't understand how. I've found permeability expressed both in m^2 and m/s and I wanted to ask how is that possibile. $\endgroup$
    – Davide
    Apr 10 at 10:14
  • $\begingroup$ Quote your sources and give some context and links. $\endgroup$
    – Transistor
    Apr 10 at 10:22
  • 1
    $\begingroup$ To top it all off, CO2 reacts with concrete in even slightly moist conditions. Don't make the Biosphere mistake. $\endgroup$
    – Abel
    Apr 10 at 19:59

The word "convert" is reserved for units that measure the same quantity (like distance in inches or cm). In this case however you need to use the word "calculate" because the units are dissimilar. Yes, the Darcy's Law equation is what you are looking for.

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In SI units, permeability "k" is measured in m2.
In SI units, porous medium gas flux "q" or "Q/A" is measured in (m3/s) / (m2) which reduces to m/s. Q is volumetric flowrate (m3/s) and A is area (m2). Algebraically rearrange q= Q/A as necessary such as Q= q × A.

So to calculate you also need the dynamic viscosity of air "µ" in kg/m-s. Note that this value is temperature and pressure dependent as you can see in this table.

You will also need the differential pressure in Pascals "Δp" in Pa or kg/ms2. The difference in pressure between the inside of our cave and atmospheric pressure.

And finally you will need the length "L" in meters. This is distance the gas must travel through the porous medium or in your case the thickness of your concrete layer.

When you solve the equation, you can confirm you used the correct units by canceling them out.

  • 1
    $\begingroup$ Tip: You can use HTML entities &Omega;, &mu;, &deg;, &times;, etc. as well as <sup>...</sup> and <sub>...</sub> in the posts (but they don't work in the comments). I've converted your squares and cubes so I hope you don't mind. A minor error is that the SI system doesn't have a "unit" for permeability. A better wording might be, "In SI units permeability, k, is measured in , etc. $\endgroup$
    – Transistor
    Apr 11 at 21:34
  • $\begingroup$ @Transistor, Cool, that will be much quicker than cut and paste. And yeah I get lazy with the carrot and forget that not everyone knows what that means. Good call on the rephrasing; I made those changes. Thanks! $\endgroup$
    – ericnutsch
    Apr 11 at 21:46
  • $\begingroup$ @Davide I think you are confused with k (permeability, m^2) and K (conductivity, m/s). k $ K are related to the flow rate as Q = KA.= -kA(dP)/(mu)L. $\endgroup$
    – r13
    Apr 12 at 3:42
  • $\begingroup$ @Davide See this wiki article for more info on the Hydraulic Conductivity, K. en.wikipedia.org/wiki/Hydraulic_conductivity. The article on permeability linked by ericnutsch also addresses the relationship between k & K. $\endgroup$
    – r13
    Apr 12 at 3:58
  • $\begingroup$ Thank you so much. Yes, that was the problem, I didn't understand the difference between k and K. Thank you again. $\endgroup$
    – Davide
    Apr 19 at 10:42

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