modelMultiWell

Information

This model simulates aquifer thermal energy storage, using one or multiple pairs of cold and hot wells.

To calculate aquifer temperature at different locations over time, the model applies physical principles of water flow and heat transfer phenomena. The model is based on the partial differential equation (PDE) for 1D conductive-convective transient radial heat transport in porous media

ρ c (∂ T(r,t) ⁄ ∂t) = k (∂² T(r,t) ⁄ ∂r²) - ρ_w c_w u(∂ T(r,t) ⁄ ∂t),

where ρ is the mass density, c is the specific heat capacity per unit mass, T is the temperature at location r and time t, u is water velocity and k is the heat conductivity. The subscript w indicates water. The first term on the right hand side of the equation describes the effect of conduction, while the second term describes the fluid flow.

The pressure losses in the aquifer are calculated using the Darcy's law

Δp = ṁ g ⁄ (2 π K h ln(rMax ⁄ rWB)),

where ṁ is the water mass flow rate, g is the gravitational acceleration, K is the hydraulic conductivity, h is the thickness of the aquifer, rMax is the domain radius and rWB is the well radius. The pressure losses in the wells are calculated using Modelica.Fluid.Pipes.BaseClasses.WallFriction.Detailed.pressureLoss_m_flow.

Spatial discretization

To discretize the conductive-convective equation, the domain is divided into a series of thermal capacitances and thermal resistances along the radial direction. The implementation uses an array of Modelica.Thermal.HeatTransfer.Components.HeatCapacitor and Modelica.Thermal.HeatTransfer.Components.ThermalResistor. Fluid flow was modelled by adding a series of fluid volumes, which are connected to the thermal capacitances via heat ports. The fluid stream was developed using the model AixLib.Fluid.MixingVolumes.MixingVolume. The geometric representation of the model is illustrated in the figure below.

Typical use and important parameters

By default, the component consists of a single pair of wells: one cold well and one warm well. The number of paired wells can be increased by modifing the parameters nPai. The effect is a proportional increase of thermal capacity, and the mass flow rate at port_a and port_b is equally distributed to the pairs of well, thus all pairs have the same mass flow rates and temperatures, and the quantities at the fluid ports is for all well combined, as is the electricity consumption PTot for the well pumps.

To ensure conservation of energy, the wells are connected via fluid ports. To avoid thermal interferences, make sure that the aquifer domain radius rMax is large enough for your specific use case.

Circulation pumps are included in the model and they can be controlled by acting on the input connector. The input must vary between [1, -1]. A positive value will circulate water clockwise (from port_Hot to port_Col, thus extraction from the cold well and injection into the warm well). A negative value will circulate water anticlockwise.

The temperature values in the warm and cold aquifers can be accessed using TAquHot and TAquCol. These temperatures correspond to the temperatures of each thermal capacitance in the discretized domain. The location of the thermal capacitance is expressed by rVol.

Implementation

The model computes the flow resistance of the cold well and the cold acquifer. Because of symmetry, the warm side has the same flow resistances. To reduce the number of equations in the model, the flow resistance of the warm side is set to the same flow resistance as on the cold side, but with the sign reversed.

Parameters

Connectors

Components

Contents

Name	Description
Medium	Medium in the component

Revisions

• September 22 2023, by Alessandro Maccarini and Michael Wetter:
  First Implementation.