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# applying heat load in BHE and varying input T?

Hi all,

I am using T2Well with TOUGH2 to model a borehole heat exchanger and was wondering if it was possible to apply a heat load to the BHE? I have tried something of the form below:

GENER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8
A1000HTR 1                   1     HEAT1 6.360e+03 0.000e+00 0.000e+00 0.000e+00

to inject into the inlet, but this does not seem to be working as expected. My temperature in the borehole is not changing much i.e. 0.01 degrees at 100 days.

I was also wondering if it was possible to vary input T for the BHE model and how I might go about this?

Kind regards,

Hannah Doran

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• Hi Hannah,

Your heat source term looks correct (when I display it with a uniform-width font, so I can check the column alignment).  Check the temperature in element A1000, I would expect it to increase more than 0.01 degrees.  Also check that the density and  heat capacity of the material for A1000 are normal, and that the volume and connections for A1000 are correct.

You can do a time-dependent temperature boundary condition.   In TOUGH3 you can do it directly with the TIMBC block, but if you are using TOUGH2, it is a little more complicated.  The TOUGH2 User's guide explains what to do on pages 62-63.  The example is for a prescribed P boundary, but I have used this technique for a prescribed T boundary.  To get T(t), use the fact that heat flow rate Q can be written as Q = dE/dt, where E is internal energy, and E=rho C V T.  Thus, Q = rho C V dT/dt.  So if you have a desired T(t) boundary condition, take the derivative and multiply by density and heat capacity and volume of the boundary material, and specify the resulting Q(t) in the GENER block. You should also set either rho or C or V to a very large value so the temperature stays at the prescribed value.  It took me some trial and error to figure out that C=1e10 would work on my computer and produce the desired result.  By making rho or C huge and keeping V normal, T stays at the prescribed value but P varies normally.  For all variables to stay at the prescribed values, make V huge instead.

Christine

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• Dear Hanna,

I understood you want to apply a heat load to your entire BHE. But you applied the heat load by  just injecting heat into the BHE inlet (eleme A1000). As apparently you have not added any fluid flow, it is not surprising that the rest of the BHE does not experience the desired T change. I imagine the desired heat load should be applied by assign a fluid flow through the BHE with the desired inlet T, if your model allows that approach.

Otherwise, if you cannot model any fluid flow through the BHE, then I think you should inject heat into all the elements belonging to the BHE. The details on how assign a prescribed heat injection are given by Christine.

Regards,

Alfredo

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• Thank you both for your replies,

I have been having a play and have managed to obtain the correct T down the wellbore when I inject 0.58 kg/s and impose an inlet initial T = 11 degrees within INCON.

I then tried a dynamic inlet T approach using a GENER table following Christine's approach:

GENER----1----*----2----*----3----*----4----*----5----*----6----*----7----*----8
T0000HTR 1                  20     HEAT  0.000e+00 0.000e+00 0.000e+00 0.000e+00
-0.0000000e+00 0.1440000e+03 0.1531789e+03 0.1629428e+03
0.17332920e+03 0.1843776e+03 0.1961302e+03 0.2086320e+03
0.22193070e+03 0.2360770e+03 0.2511251e+03 0.2671324e+03
0.28416000e+03 0.3022730e+03 0.3215405e+03 0.3420362e+03
0.36383840e+03 0.3870303e+03 0.4117004e+03 0.4379432e+03
0.0000000e+00 6.2993591e+01 5.9200810e+01 5.5723755e+01
5.2395516e+01 4.9275420e+01 4.6342498e+01 4.3589776e+01
4.1044748e+01 3.8591996e+01 3.6298288e+01 3.4159999e+01
3.2134172e+01 3.0237739e+01 2.8449439e+01 2.6769808e+01
2.5192227e+01 2.3711201e+01 2.2312473e+01 2.1002325e+01

with an imposed mass flow rate of 0.58 kg/s and setting 11 degrees again for the inlet cell and an artificial infinite volume cell above. Note there is just one vertical connection T0000A1000 between the artificial and inlet cell. However, setting the artificial cell to an initial T value I think is preventing the dynamic T increasing above 11 degrees. Is there a way to overcome this? I do not think I can remove the artificial cell as it is needed for the inlet and outlet points in T2Well.

Kind regards,

Hannah

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• I guess you should remove the inactive cell at DHE input and use GENER to inject your variable fluid rate history by assigning the injection enthalpy corresponding to your desired inlet T vs time.

The inactive cell with proper P shall be maintained at DHE outlet . In this way you will inject the desired rate and enthalpy history while T2Well will compute P losses along  the DHE as well as the heat exchange between the DHE and surrounding grid elements.

Alfredo

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