modelHeatCapacitorStone

Same model as HeatCapacitorStone but with FluidModel for density calculation of fluid

Information

1. Purpose of model

Lumped thermal capacitor representing one control volume of a saturated confining layer (aquitard). The stored heat is that of the combined solid matrix and pore fluid, computed from a porosity-weighted volumetric heat capacity. The single heat port couples the element to the surrounding thermal resistor network.

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

L2: Single ideally mixed (lumped) control volume with one uniform temperature. Only thermal storage is modeled; heat transport between elements is handled externally by thermal resistors. Heat capacity is constant (no temperature dependency).

3. Limits of validity

- No internal temperature distribution; the whole volume is at one temperature.

- Constant, porosity-weighted heat capacity (no temperature or pressure dependency).

- No fluid flow (impermeable confining layer); only conductive coupling via the heat port.

4. Interfaces

port: heat port to the surrounding thermal resistor network (Heat)

5. Nomenclature

	T	temperature of the element (state) [K]
$\dot{Q}$	port.Q_flow	heat flow rate into the element [W]
	U	inner energy of the element [J]
	C	heat capacity of the element [J/K]
	n_c	porosity of the confining layer [-]
$\rho_l$	rho_l	density of the pore fluid [kg/m³]
$\rho_{sc}$	rho_sc	density of the solid in the confining layer [kg/m³]
$c_{p,l}$	Cp_l	specific heat capacity of the pore fluid [J/(kg·K)]
$c_{p,sc}$	Cp_sc	specific heat capacity of the solid in the confining layer [J/(kg·K)]
	A_q	cross-sectional (annular) area of the control volume [m²]
	z_c	height of the control volume [m]

6. Governing Equations

Porosity-weighted heat capacity of the saturated control volume:

C = (n_c*rho_l*Cp_l + (1-n_c)*rho_sc*Cp_sc) * A_q * z_c

Energy balance (lumped capacitor):

C * dT/dt = port.Q_flow

Inner energy of the element:

dU/dt = C * dT/dt

7. Remarks for Usage

Instantiated as an array inside ImpermeableLayer to provide thermal storage for the upper and lower aquitard. The variant HeatCapacitorStone_WithFluidModel adds a fluid property model and is the one actually used by ImpermeableLayer; use this simpler variant where constant fluid properties are sufficient. Material properties are taken from the Subsurface_Basic (Parameters) record.

8. Validation

Tested in check model "ATES.Validierung.Buoyancy.Val_homogenLayer"

9. References

(no remarks)

10. Version History

Model created by Markus Gillner (markus.gillner@tuhh.de), May 2026

Model revised by Markus Gillner (markus.gillner@tuhh.de), June 2026

- Replaced the generic Modelica Standard Library documentation with a model-specific 10-section description.

Parameters

Type	Name	Default	Description
SI.Density	rho_sc		Density of solid in aquitard
SI.Density	rho_l		Density of liquid in aquitard
SI.SpecificHeatCapacity	Cp_sc		Specific Heat Capacity of solid in aquitard
SI.SpecificHeatCapacity	Cp_l		Specific Heat Capacity of liquid in aquitard
SI.DimensionlessRatio	n_c		porosity of aquitard
SI.Temperature	T_start		Start temperature of the confining layers
SI.Pressure	p_initial		initial pressure of confined layer
SI.Area	A_q		Circular ring area of CV
SI.Length	z_c		Height of the volume of the confining layer
SI.Mass	m	(n_crho_l + (1 - n_c)rho_sc)(A_qz_c)	Mass of the control volume
SI.HeatCapacity	C	(n_crho_lCp_l + (1 - n_c)rho_scCp_sc)(A_qz_c)	Heat capacity of element
TILMedia.VLEFluidTypes.BaseVLEFluid	water	simCenter.fluid1	Heat carrier

Connectors

Type	Name	Default	Description
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a	port

Components

Type	Name	Description
SI.Temperature	T	Temperature of element
SI.TemperatureSlope	der_T	Time derivative of temperature (= der(T))
SI.Energy	U	Inner energy of stone
ClaRa.SimCenter	simCenter
TILMedia.VLEFluid_pT	bulk