Negative stress during expansion phase

[clariu25]

Hi!
I'm working on a THM model, injecting hot water into a reservoir layer. The geometry is a 3-layer cube, with a very thin reservoir layer in between two surrounding layers. The injection occurs in a loaded state, so the overburden stress is already applied. Because of that, the initial strain is negative everywhere since the model is initially compressed.
I'm exporting manually the stress and strain, using the RankTwoAux AuxKernel and I think there is something wrong in the way I’m computing or interpreting the stress, but I can’t figure out what.
As I inject hot fluid into the system, the main variables (temperature, pressure and displacement) are reacting as expected:

• an increase of P and T induce a positive displacement.

• Strain also behaves as expected, increases near the injection point, decreases at the end of the thermal plume, and remains constant in the rest of the model.

Stress doesn't behaves as I expected. Stress gets more negative (which would mean compression in the nomenclature used in MOOSE) towards the injection point, and gets back to the initial value away from the well. It doesn't increase, as I expected.

If I check the stress over time, there is a small increase at the very beginning of the injection, but later it decreases. The plot is from a point 5m away from the injection, at the mid-depth of the reservoir layer..

The model is large enough (7.5km from the center) so that the pressure is not affected by the boundary conditions. So I'm wondering if it is physically possible in a THM problem to get more compressive stress near the injection point. Has anyone encountered this issue before?

This is how I defined my stress and strain in the materials block:

  [strain]
    type = ComputeSmallStrain
    eigenstrain_names = 'thermal_contribution initial_stress'
    output_properties = total_strain
  []
  [stress]
    type = ComputeLinearElasticStress
    output_properties = stress
  [] 

And these are my Aux_Kernels

  [stress_zz]
    type = RankTwoAux
    variable = stress_zz
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [strain_zz]
    type = RankTwoAux
    variable = strain_zz
    rank_two_tensor = total_strain
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [vol_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = volum_stress
    scalar_type = Hydrostatic
    execute_on = timestep_end
  []
  [vol_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volum_strain
    scalar_type = VolumetricStrain
    execute_on = timestep_end
  [] 

[GiudGiud]

Hello

Stress gets more negative (which would mean compression in the nomenclature used in MOOSE) towards the injection point,

So you are getting the expected compression from injecting hot water ?
Is injecting water supposed to relax the compression? (sorry non-expert here)

and gets back to the initial value away from the well. It doesn't increase, as I expected.

But you would expect the same effect away from the well rather than the stress getting back to the initial state?

[clariu25]

Hello,
Thank you for the quick reply.

What I mean is that I would expect some expansion at some point during the injection. Since both temperature and pressure increase, the material should tend to expand rather than become more compressive. That is why I am confused by the stress becoming more negative close to the injection.

For the second point, I realize I was not very clear. You are right that far away from the well I expect the stress to remain at the initial conditions. I meant that I was expecting an increase of stress, then a decrease and then going back to the initial conditions, just as it happens with the strain. Instead, what I see is that the stress goes from compressive at the injection point to the initial values further away, without signs of expansion.

[GiudGiud]

Maybe the compression from the injection is too strong compared to the thermal expansion and that effect is not showing?

Could you lower the injection pressure and increase the injection temperature?

Also can you please double check that you have turned on thermal expansion in the solid mechanics? I know for the "physics" syntax you have to add the temperature parameter.

[clariu25]

but what would cause the compression during injection? If I pressurize the rock from within, it should try to expand, right? This is my main question/doubt

Yes, I do have the thermal expansion active:

  [thermal_contribution]
    type = ComputeThermalExpansionEigenstrain
    temperature = temperature
    thermal_expansion_coeff = 5e-6
    eigenstrain_name = 'thermal_contribution'
    stress_free_temperature = 'temp_ref'
  []
  [volumetric_strain]
    type = PorousFlowVolumetricStrain
  []
  [strain]
    type = ComputeSmallStrain
    eigenstrain_names = 'thermal_contribution initial_stress'
    output_properties = total_strain
  []
  [stress]
    type = ComputeLinearElasticStress
    output_properties = stress
  []

[GiudGiud]

From these material you should be able to output the stress / strain related to thermal expansion. And compare that effect to injection