Inconsistency of 3D_Beier_sandbox.prj with Beier article

Hello everyone,

I’m working on 2U BHE modeling and I’m looking at 3D_Beier_sandbox benchmark. But I ran into a problem.
According to the figures below, in Beier’s article, the value of the inner radius of the U-shaped pipe is 0.02733 meter, but in the beier_sandbox.prj the value of the inner diameter of the pipe (0.013665 meter) is equal to a quarter of the value of Beier.

Although the results of running the beier_sandbox.prj match the results of Beier’s article, the diameters are different.
Please can someone explain the reason?

Thanks in advance

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You use in OGS diameter no radius and the units in OGS in meter no cm.


2*0,013665= 0,02733cm *100= 2,733 m.

Hello @akoutelidakis,
I think you made a mistake.
The radius in Beier’s article is equal to 0.02733 meters, which means the diameter of the pipe is equal to 2*0.02733 = 0.05466, while the value of 0.013665 is written inside 3D_Beier_sandbox.prj code

Dear yasinahmadpoor,

Thank you very much for raising the issue and paying attention to the details. I had a quick look at the input files and also Beier’s paper. I also remembered that I had the same problem couple of years ago when setting up this benchmark.

Short answer to your question:
Table 1 in Beier’s paper is wrong. The values were given in diameter, not radius.

Long reasoning:

  • Argument #1

Assuming the U-tube pipe has a outer radius of 3.34 cm, then you have 6.68 cm outer diameter for 1 pipe. As we have 2 pipe in the cross section, we need at least a borehole of 2 x 6.68 = 13.36 diameter. In this case we can not insert 2 x 6.68 pipes in the 12.6 cm borehole. This actually gave me trouble when calculating the thermal resistance. I got a Non-a-Number (NaN) error when blindly put those values into OGS. Then the program crashed.

  • Argument #2

This forced me to dig around the internet, trying to understand what exactly is the dimension of those pipes. Please have a look at this webpage, which explains what a SDR 11 pipe is. The following table lists the specifications of these pipes.

So we are talking about 1 inch SDR 11 pipe. According to the above table, it has a outer diameter of 1.310 - 1.320 inch, which is about 3.34 cm. That confirms my suspicion that it should be diameter in Beier’s table.

According to the webpage, SDR 11 means: SDR = Diameter / Wall Thickness = 11
Assuming it’s a diameter of 3.34 cm, then we have wall thickness of 3.34 / 11 = 0.3035 cm. That’s exactly what we have adopted (or 0.003035 m as in OGS prj file).

I hope the above info helps to resolve your puzzle.

Best regards,

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ِDear @HBShao,

Based on your reasoning, the correct inner and outer diameter of the pipe is 2.733 and 3.34 cm respectively, but the value of the diameter placed in the prj file is equal to half of inner diameter (2.733 / 2 = 1.3665 cm), in other words, in the prj file, the value of the inner radius is inserted, while the inner diameter should have been written. Am I right?

Dear @yasinahmadpoor,

you are right, when you simulate the benchmark case, do forget to change the internal radius to the internal diameter value accordingly. The benchmark input files did not update in time. Sorry for the confusing.

Best regards,
Chaofan Chen

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