Temperature dependent fluid properties for borefield

[mwetter]

This issue is to test the effect of temperature dependent media properties for the borefield models.

[LoneMeertens]

@mwetter, @Vbraciszewski: I created a very small working example in my fork so we can reproduce/compare the behavior quickly:

• example branch: https://github.com/LoneMeertens/modelica-buildings/tree/issue4483_TempDepFluPropBorefield

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Short summary / diagnosis

The current borefield implementation computes the convective resistance using

Buildings.Fluid.Geothermal.Borefields.BaseClasses.Boreholes.BaseClasses.Functions.convectionResistanceCircularPipe

(used inside Buildings.Fluid.Geothermal.Boreholes.BaseClasses.Boreholes.BaseClasses.InternalHEXOneUTube). Concretely the model sets for example:

Modelica.Blocks.Sources.RealExpression RVol1(y=
  Buildings.Fluid.Geothermal.Borefields.BaseClasses.Boreholes.BaseClasses.Functions.convectionResistanceCircularPipe(
    hSeg=hSeg,
    rTub=borFieDat.conDat.rTub,
    eTub=borFieDat.conDat.eTub,
    kMed=kMed,
    muMed=muMed,
    cpMed=cpMed,
    m_flow=m1_flow,
    m_flow_nominal=m1_flow_nominal))
"Convective and thermal resistance at fluid 1"

Modelica.Blocks.Sources.RealExpression RVol2(y=
  Buildings.Fluid.Geothermal.Borefields.BaseClasses.Boreholes.BaseClasses.Functions.convectionResistanceCircularPipe(
    hSeg=hSeg,
    rTub=borFieDat.conDat.rTub,
    eTub=borFieDat.conDat.eTub,
    kMed=kMed,
    muMed=muMed,
    cpMed=cpMed,
    m_flow=m2_flow,
    m_flow_nominal=m2_flow_nominal))
"Convective and thermal resistance at fluid 2"

Because RVol1 and RVol2 are computed from that function using the (reference) fluid properties provided as inputs, the value is effectively fixed for the full simulation (a RealExpression evaluated from fixed inputs unless the model actively updates it each step).

Function convectionResistanceCircularPipe workflow

1. Fixes reference fluid properties as inputs (ρ, µ, cp, k)
2. Compute Reynolds number Re based on fixed fluid properties and actual mass flow (each time step)
3. Selects a Nusselt correlation depending on Re (laminar / transitional / turbulent)
4. Computes convective heat transfer coefficient → RVol

Why this can be undesirable

• The HTF temperature in the borehole changes during the simulation → µ, ρ, cp, k change.
• Changes in fluid properties change the Reynolds number and can cause regime switches (laminar ↔ transitional ↔ turbulent).
• Regime switches change the Nusselt correlation, which can cause large jumps in RVol, strongly affecting the heat transfer between fluid and ground.
• If a constant medium is used (fixed ρ), the temperature dependence of density is neglected, meaning pumping power differences caused by density changes are not captured.

To demonstrate the effect, I implemented four minimal cases (combinations of whether the convective resistance is updated each time step and whether the medium has temperature-dependent properties).

Case definitions

• UTube
  Default borefield model where the convective resistance is computed once using reference properties.

• UTubeTdep
  Modified borefield model that updates RVol1 and RVol2 each time step using the instantaneous HTF properties.

• Medium
  Fixed medium:
  Buildings.Media.Water

• MediumTdep
  Temperature-dependent medium:
  Buildings.Media.Specialized.Water.TemperatureDependentDensity

Compact results (values from my runs)

Case (label)	CPU integration (s)	one grid interval (ms)	initialization (s)	RVol1 (seg1)	RVol2 (seg1)	µVol1 (Pa·s)	µVol2 (Pa·s)
UTube, Medium (reference)	0.123	0.246	1.10	0.002	0.002	0.0010	0.0010
UTubeTdep, Medium	0.892	1.78	0.996	0.002	0.015	0.0010	0.0010
UTube, MediumTdep	13.00	26.10	0.977	0.002	0.002	0.0008	0.0013
UTubeTdep, MediumTdep	24.00	48.60	0.979	0.002	0.015	0.0008	0.0013

Columns explained

• CPU integration (s): solver CPU time for integration (main solver).
• one grid interval (ms): CPU time per grid interval (diagnostic).
• initialization (s): initialization CPU time.
• RVol1 / RVol2: convective resistances for segment 1 (volumes 1 and 2).
• µVol1 / µVol2: dynamic viscosities for segment 1 (volumes 1 and 2).

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CPU change vs reference (UTube, Medium)

Percent change relative to UTube, Medium (reference values: integration = 0.123 s, one-grid = 0.246 ms, initialization = 1.10 s)

Case	Integration Δ%	One-grid-interval Δ%	Initialization Δ%
UTubeTdep, Medium	+625.2 %	+623.6 %	−9.5 %
UTube, MediumTdep	+10,469.1 %	+10,509.8 %	−11.2 %
UTubeTdep, MediumTdep	+19,412.2 %	+19,656.1 %	−11.0 %

Interpretation

• Enabling MediumTdep (temperature-dependent medium) produces the largest increases in integration cost.
• Updating RVol each step (UTubeTdep) with a fixed medium is more expensive than the (now) very light reference case, but still far cheaper than enabling MediumTdep. This already captures the correct heat‑transfer dynamics inside the boreholes. However, it does not capture the impact of temperature-dependent pumping power: for that, the (more expensive) switch to temperature‑dependent fluid properties is required.

Theoretical pumping-power effect for segment 1 (Vol1 & Vol2)

Assumptions used

• Mass flow is fixed (models use fixed MassFlowSource_T) → hydraulic power ∝ Δp.
• For these % comparisons I ignore density changes (treat ρ constant) and present two friction-regime assumptions:
  • Laminar (Poiseuille): Δp ∝ µ (linear).
  • Turbulent (Blasius, smooth pipe): approx. Δp ∝ µ^0.25 (because f ∝ Re^-0.25 and Re ∝ 1/µ).

Results table

Case	Volume	µ (Pa·s)	Pumping Δ% (laminar ∝µ)	Pumping Δ% (turbulent ≈µ^0.25)
Reference: UTube, Medium	Vol1	0.0010	0.0 %	0.0 %
""	Vol2	0.0010	0.0 %	0.0 %
UTubeTdep, Medium	Vol1	0.0010	0.0 %	0.0 %
""	Vol2	0.0010	0.0 %	0.0 %
UTube, MediumTdep	Vol1	0.0008	−20.0 %	−5.4 %
""	Vol2	0.0013	+30.0 %	+6.8 %
UTubeTdep, MediumTdep	Vol1	0.0008	−20.0 %	−5.4 %
""	Vol2	0.0013	+30.0 %	+6.8 %

Interpretation

• µ: 0.001 → 0.0008 (×0.8) → pumping Δ ≈ −20% (laminar) or −5.4% (turbulent, Blasius).
• µ: 0.001 → 0.0013 (×1.3) → pumping Δ ≈ +30% (laminar) or +6.8% (turbulent).

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Short recommendations / Next steps

Options / Recommendations:

1. Quick fix to improve borefield model: Enable an option to switch convectionResistanceCircularPipe to update fluid properties each time step (using a constant medium). This captures dynamic RVol effects with minimal CPU increase.
2. Accurate pumping power: Use a medium with temperature-dependent fluid properties (Buildings.Media.Specialized.Water.TemperatureDependentDensity) to capture density and viscosity effects. This leads to a significant CPU increase.
3. Flow-regime relevance: The above options are most relevant when the HTF operates near laminar/transitional/turbulent boundaries. It is difficult to know a priori if the system is in this "danger zone".
   • Suggestion: output Reynolds number (Re) in convectionResistanceCircularPipe during simulation to track flow regime and identify critical conditions.

Next steps:

1. Create a similar minimal working example for glycol-water mixtures.
2. Investigate the influence on pumping power more closely by setting up a small closed-loop working example with an active pump and logging Δp(t) and P(t).

[mwetter]

@LoneMeertens : Thanks for the detailed summary and the suggestions.

Regarding the temperature dependent convection coefficient, it would be good to see what the effect on the outlet temperature is if RVol1 and RVol2 are temperature dependent, because this is one in a series of thermal resistances that connect to the soil. So there overall impact on the temperature (or similarly the heat added/removed from the fluid) may be small. Then we can see if option 1 makes sense. I am a bit surprised that computing time increases by a factor of about 7. Likely, this is because now, the thermal calculations depend on the result of the flow distribution, so there is more coupling (via master...LoneMeertens:modelica-buildings:issue4483_TempDepFluPropBorefield#diff-2268d2c723c7e6772096dcdf1dd1c6abf9a8af7ac0a6e68a85a4f119db278420R108).
This may be avoided by introducing a dummy state

tau*der(mDum_flow) = m_flow-mDum_flow // set tau maybe to 2 minutes

and then there is only an algebraic equation via the pressure. For this, I think we can use Medium.p_default as the fluid properties for water and glycol do not vary much with pressure.

Regarding pumping power, I think best is to give users the option to select the medium. A 5% error seems reasonable (acceptable) in many applications, whereas the increase in computing time would make many applications impractical to simulate.