recordValidityThresholds

Thresholds of the validity analysis of the ATES_L4 model (defaults with literature sources)

Extends from TransiEnt.Basics.Icons.Record (Icon for records).

Information

1. Purpose of model

Record collecting all thresholds used by the validity analysis function ValidityAnalysis. Each default value is taken from the literature or derived from it; the source is given in the description of each parameter.

2. Level of detail, physical effects considered, and physical insight

(Purely technical component without physical modeling.)

3. Limits of validity

- The thresholds marked as derived (E_Darcy_ok, N_NRGF_ok, f_warn) are engineering choices and not taken directly from the literature.

- The thresholds for the natural regional groundwater flow were determined for low-temperature ATES with annual cycles (Bloemendal and Hartog 2018; Tas et al. 2025).

- The LTE thresholds are based on numerical studies (Gossler et al. 2020) and laboratory experiments with uniform spherical grains (Lee et al. 2025).

4. Interfaces

(no elements)

5. Nomenclature

$E_\mathrm{ok}$	`E_Darcy_ok`	non-Darcy share of the pressure gradient up to which Darcy's law is fulfilled, default 0.01 [-]
$E_\mathrm{max}$	`E_Darcy_max`	non-Darcy share of the pressure gradient above which Darcy's law is violated, default 0.10 [-]
$c_\mathrm{visc}$	`c_Ergun_visc`	viscous coefficient of the Ergun equation, default 150 [-]
$c_\mathrm{inert}$	`c_Ergun_inert`	inertial coefficient of the Ergun equation, default 1.75 [-]
$d_\mathrm{LTE}$	`d_LTE`	grain diameter up to which LTE holds for all flow velocities, default 7 mm [m]
$v_\mathrm{s,LTE}$	`v_s_LTE`	seepage velocity up to which LTE holds for all grain diameters, default 1.6 m/d [m/s]
$d_\mathrm{LTNE}$	`d_LTNE`	grain diameter from which significant LTNE effects were measured, default 20 mm [m]
$q_\mathrm{LTNE}$	`q_LTNE`	Darcy velocity from which significant LTNE effects were measured, default 12 m/d [m/s]
$N_\mathrm{ok}$	`N_NRGF_ok`	displacement number up to which the natural regional groundwater flow is negligible, default 0.1 [-]
$N_\mathrm{max}$	`N_NRGF_max`	displacement number above which displacement losses dominate, default 1 [-]
$\mathrm{Ra}_\mathrm{crit}$	`Ra_crit`	critical Rayleigh-Darcy number, default 4π² [-]
$q_\mathrm{0,crit}$	`q_0_crit`	characteristic buoyancy flow velocity from which buoyancy-driven flow becomes significant, default 0.05 m/d [m/s]
$f_\mathrm{warn}$	`f_warn`	fraction of Ra_crit and q_0_crit from which a warning is issued if buoyancy is switched off, default 0.5 [-]

6. Governing Equations

(no equations)

7. Remarks for Usage

Pass a modified instance to ValidityAnalysis to change single thresholds, e.g. thresholds = Records.ValidityThresholds(N_NRGF_ok = 0.2). The criteria and the meaning of each threshold are described in the documentation of ValidityAnalysis.

8. Validation

(no validation or testing necessary)

9. References

Beernink, S., Hartog, N., Vardon, P. J., Bloemendal, M., 2024: Heat losses in ATES systems: The impact of processes, storage geometry and temperature. Geothermics 117, 102889, https://doi.org/10.1016/j.geothermics.2023.102889.

Bloemendal, M., Hartog, N., 2018: Analysis of the impact of storage conditions on the thermal recovery efficiency of low-temperature ATES systems. Geothermics 71, 306–319, https://doi.org/10.1016/j.geothermics.2017.10.009.

Ergun, S., 1952: Fluid flow through packed columns. Chemical Engineering Progress 48, 89–94.

Gossler, M. A., Bayer, P., Rau, G. C., Einsiedl, F., Zosseder, K., 2020: On the limitations and implications of modeling heat transport in porous aquifers by assuming local thermal equilibrium. Water Resources Research 56, e2020WR027772.

Lee, H., Gossler, M., Zosseder, K., Blum, P., Bayer, P., Rau, G. C., 2025: Laboratory heat transport experiments reveal grain-size- and flow-velocity-dependent local thermal non-equilibrium effects. Hydrology and Earth System Sciences 29, 1359–1378, https://doi.org/10.5194/hess-29-1359-2025.

Nield, D. A., Bejan, A., 2017: Convection in Porous Media. 5th edition. Springer, New York, https://doi.org/10.1007/978-3-319-49562-0.

Tas, L., et al., 2025: Efficiency and heat transport processes of low-temperature aquifer thermal energy storage systems: new insights from global sensitivity analyses. Geothermal Energy 13, 2, https://doi.org/10.1186/s40517-024-00326-1.

Zeng, Z., Grigg, R., 2006: A criterion for non-Darcy flow in porous media. Transport in Porous Media 63, 57–69, https://doi.org/10.1007/s11242-005-2720-3.

10. Version History

Model created by Markus Gillner (markus.gillner@tuhh.de) on 01.10.2026

Parameters

Type	Name	Default	Description
Darcy's law
Real	E_Darcy_ok	0.01	Non-Darcy share of the pressure gradient up to which Darcy's law is regarded as fulfilled (derived)
Real	E_Darcy_max	0.10	Non-Darcy share of the pressure gradient above which Darcy's law is violated, Fo = 0.11 (Zeng and Grigg 2006)
Real	c_Ergun_visc	150	Viscous coefficient of the Ergun equation (Ergun 1952)
Real	c_Ergun_inert	1.75	Inertial coefficient of the Ergun equation (Ergun 1952)
Local thermal equilibrium
SI.Length	d_LTE	7e-3	Grain diameter up to which LTE holds for all flow velocities (Gossler et al. 2020)
SI.Velocity	v_s_LTE	1.6/86400	Seepage velocity up to which LTE holds for all grain diameters, 1.6 m/d (Gossler et al. 2020)
SI.Length	d_LTNE	20e-3	Grain diameter from which LTNE effects > 5 % were measured (Lee et al. 2025)
SI.Velocity	q_LTNE	12/86400	Darcy velocity from which LTNE effects > 5 % were measured for d >= d_LTNE, 12 m/d (Lee et al. 2025)
Natural regional groundwater flow
Real	N_NRGF_ok	0.1	Displacement number up to which the natural regional groundwater flow is negligible (derived)
Real	N_NRGF_max	1	Displacement number above which displacement losses dominate, R_th/u = 1 a for annual cycles (Bloemendal and Hartog 2018)
Buoyancy switch
Real	Ra_crit	4*pi^2	Critical Rayleigh-Darcy number (Nield and Bejan 2017)
SI.Velocity	q_0_crit	0.05/86400	Characteristic buoyancy flow velocity from which buoyancy-driven flow becomes significant, 0.05 m/d (Beernink et al. 2024)
Real	f_warn	0.5	Fraction of Ra_crit and q_0_crit from which a warning is issued if buoyancy is switched off (derived)