modelWell_L4

Information

1. Purpose of model

Discretized well model with N_z stacked vertical control volumes. Resolves the temperature and pressure distribution inside the well bore during injection, storage, and production phases. Distributes the total mass flow radially to the aquifer cells proportionally to each cell volume.

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

L4: N_z fully discretized control volumes stacked vertically. Physical effects considered:

• Enthalpy transport in vertical direction (between adjacent well cells)
• Enthalpy exchange with aquifer cells via radial fluid ports
• Heat conduction to surrounding medium via heat ports
• Volume-proportional radial mass flow distribution during production
• Optional partial-well operation: inactive lower cells excluded during a configurable time window

3. Limits of validity

- Radial mass flow is distributed proportionally to cell volume, not driven by a pressure gradient inside the well.

- No wellbore storage effect (compressibility of fluid in well is neglected).

- Cylindrical well geometry with constant radius r_0.

4. Interfaces

fluidPortIn: fluid inlet/outlet to the surface network — top of well (Fluid, bidirectional)

fluidPortOut_radial[N_z]: radial fluid ports to aquifer control volumes, one per vertical cell (Fluid, outlet)

port_a[N_z]: heat ports to surrounding medium per vertical cell (Heat)

5. Nomenclature

	T[N_z]	cell temperature [K]
	p[N_z]	cell pressure [Pa]
	h[N_z]	specific enthalpy of cell fluid [J/kg]
	H_flow_v[N_z]	vertical enthalpy flow rate at top of each cell [W]
	H_flow_r[N_z]	radial enthalpy flow rate from aquifer into cell [W]
	m_flow_v[N_z]	vertical mass flow rate at top of each cell [kg/s]
	m_flow_r[N_z]	radial mass flow rate from/to aquifer per cell [kg/s]
	port_a[j].Q_flow	heat flow from surrounding medium into cell [W]
	V_cell[N_z]	volume of each well cell [m³]
	bulk[j].d	fluid density [kg/m³]
	bulk[j].cp	specific heat capacity of fluid [J/(kg·K)]
	r_0	well bore radius [m]
	H_cell[N_z]	height of each well cell [m]

6. Governing Equations

Energy balance for each well cell j (j = 2 ... N_z; cell j = 1 has no lower vertical neighbour):

Mass continuity for each well cell:

Volume-proportional radial mass flow distribution:

7. Remarks for Usage

Cell index j = 1 is the bottommost cell; j = N_z is the topmost cell connected to fluidPortIn. The parameter No_inactive_well_volumes excludes the lowest cells from the radial distribution during a defined time window [t_well_start, t_well_end], allowing partial-screen operation.

8. Validation

Tested via "ATES.Validierung.Buoyancy.Val_homogenLayer"

9. References

(no remarks)

10. Version History

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

Parameters

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