 # Some questions about time step and pressure source term

Hi,all
I have some questions about the codes of ogs6.

1. Is the time we set for simulation a real time？For example, if I set the start time 0 and end time 20, does it mean a 20 seconds simulaiton time?
2. the source term of pressure for THM process means injection rate, right? the value of it changes with the scale of our model, I guess. So what is the relationship between them specifically? I always want to find an appropriate injection rate, but I don’t know whether it is right.

Hi,
there are no units set in OGS but for very few constitutive relations which require temperature to be in Kelvin, for example. Otherwise the units are free for the user to decide. Most prefer to stay in SI system and then your end time of 20 would mean 20s.
For the second part of the question maybe @joergbuchwald can answer it in detail, but from lines for the RHS in THM FEM the dimensions for the weak integral are L^3/T, where L is the unit of length (say m) and T is the unit of time (say s). Then the source term integral must be of the same units. Then the values for the source terms are given in units of 1/T.

For changing the scales I would suggest to write down the weak form of the equations being solved and make a variable substitution for quantities you are interested. For example for time scale changing from seconds to hours all quantities related to time must be scaled with 3600 accordingly, e.g. the viscosity.

Not so easy for me to write down the whole procedure but the Wikipedia is a good starting point: Nondimensionalization - Wikipedia

I hope I could clarify some points.

– d

Thank you. I will read the text. Hope it can help.
Since the water’s viscosity is mentioned, I have another question about the water’s density. I notice that in many benchmarks the density of water’s density is the linear function of temperature, but the slope is 4e-4, which is too small in my mind. I read some text and it seems that the gradient of the water’s density change with temperature is near -1. So what is the reason for a 4e-4 definition of the slope? Or the water’s density is just a constant value in most conditions?

For the temperature source term the unit is Watts, so for the pressure it should be accordingly.
Concerning the temperature change: Not sure where you got the one from.
However, -4e-4 corresponds to the volumetric thermal expansion at ~40 °C: Volumetric - or Cubic Thermal Expansion
(Keeping in mind that the sign here matters: so a thermal expansion coefficient of 4e-4 corresponds to a negative value in the slope)
If you just think about the definition of the thermal expansion coefficient it becomes clear that a value of one is unrealistic.

Dear Dr. Jörg Buchwald
-4e-4 is from Tests/Data/ThermoHydroMechanics/Linear/Point_injection/square_1e2.prj · master · ogs / ogs · GitLab. According to this website(Water - Density, Specific Weight and Thermal Expansion Coefficient), the density of water should be a function of temperature, right? So, I find in this prj code, Tests/Data/ThermoHydroMechanics/Linear/Point_injection/square_1e2.prj · master · ogs / ogs · GitLab, the density of water has been assumed as a linear function based on the temperature, and the slope is -4e-4.
If it use SI system, e.g. density is kg/m3, the slope should be close to -1(if I draw a line between 0℃ and 300℃ ), not -4e-4?

Ah, so this is what you mean…
The density is already factored out: OGS: [case] Linear
Therefore, the unit is 1/K.

Thanks, Dr. Jörg Buchwald. I have another two simple questions.
First,

I just want to confirm that the unit mentioned in this sentence is the unit of thermal expansion coefficient. Right?

Second, could you give us more details about the temperature and pressure source terms, like their definitions and settings in OGS6 and how to determine the value of them in different kinds of models. Do I need to apply nondimensionalization to the PDEs?
For example, (1) if I know both the injection and production volumetric rate are 8.91e-5 m3s-1 in a geothermal exploitation, what value should I set for the pressure source term? like this Tests/Data/HydroMechanics/NodalSourceTerm/nodal_source_test.prj · master · ogs / ogs · GitLab, should I change the value of `nodal_flux` from 0.001 to 8.91e-5 directly? (2) If I know the temperature source is 773.15 K in the formation stage of a geothermal reservoir, what value should I set for the temperature source term? Directly change to 773.15? Tests/Data/ThermoHydroMechanics/Linear/Point_injection/square_1e2.prj · master · ogs / ogs · GitLab

Yes, the slope is identical to the negative volumetric thermal expansion coefficient as the density is already factored out.

Do I need to apply nondimensionalization to the PDEs?

The main thing is you have to be consistent with unit. So if you use SI units everywhere then everything should be fine now.
(1) The documentation of the HydroMechanics example can be found here: A test with nodal source term
(I’m not really working with this process my self so I have to look up things myself. However, according to this example the value of 0.001 correspond to a mass flux. If you not sure about units, scaling tests might help: Just look what happens to the response if you change certain parameters, like the density etc. In the future we will work on a better documentation on units and conventions in ogs6, but this might take a while…
(2) If you need to set the temperature to a specific value instead of having a heat flux, you should use Dirichlet boundary conditions.

Thanks for your reply.
Btw, do you have any examples (prj code) using the source term of pressure in THM process? If you have, please link here. I think I can learn something from that. Thanks!