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www.cmr.no © Christian Michelsen Research AS
Simulation of a Geothermal System in COMSOL Multiphysics
Knut-Erland Brun
Comsol Workshop 10/6/2011
www.cmr.no © Christian Michelsen Research AS
Outline
Background – geothermal energy
Comsol model
Geometry
Implementing physics
Meshing
Preliminary results
Outlook
3 Comsol Workshop 10/6/2011
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Geothermal energy
Geothermal Heat Pump
Comsol Workshop 10/6/2011 4
Illustration: Comfortbrygga.no
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Geothermal energy
Geothermal Heat Pump
Natural Geothermal Systems – e.g. Iceland
1-3 km – or less
Comsol Workshop 10/6/2011 5
www.cmr.no © Christian Michelsen Research AS
Geothermal energy
Geothermal Heat Pump
Natural Geothermal Systems – e.g. Iceland
1-3 km – or less
Enhanced Geothermal System («Hot Dry Rock»)
3-5 km – or more
Comsol Workshop 10/6/2011 6
Fracture-dominated porous media
• Earth-science module • Model fractures as internal boundaries
• BC: fluid flow along a fracture
www.cmr.no © Christian Michelsen Research AS
Geothermal energy
Geothermal Heat Pump
Natural Geothermal Systems – e.g. Iceland
1-3 km – or less
Enhanced Geothermal System («Hot Dry Rock»)
3-5 km – or more
Comsol Workshop 10/6/2011 7
Fracture-dominated porous media
• Earth-science module • Model fractures as internal boundaries
• BC: fluid flow along a fracture
www.cmr.no © Christian Michelsen Research AS
Geothermal energy
Geothermal Heat Pump
Natural Geothermal Systems – e.g. Iceland
1-3 km – or less
Enhanced Geothermal System («Hot Dry Rock»)
3-5 km – or more
Comsol Workshop 10/6/2011 8
Fracture-dominated porous media
• Jan’s work…
www.cmr.no © Christian Michelsen Research AS
Geothermal energy
Geothermal Heat Pump
Natural Geothermal Systems – e.g. Iceland
1-3 km – or less
Enhanced Geothermal System («Hot Dry Rock»)
3-5 km – or more
Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 9
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Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 10
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Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 11
Jan’s best tip:
• Parameterize everything! • Total control of all ‘parameters’; initial values, BC,
subdomain settings, etc. • Easy to make parametric sweeps
• Also geometric properties and mesh-values!
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 12
Jan’s best tip:
• Parameterize everything! • Total control of all ‘parameters’; initial values, BC,
subdomain settings, etc. • Easy to make parametric sweeps
• Also geometric properties and mesh-values!
www.cmr.no © Christian Michelsen Research AS
Wellbore Heat Exchanger – Physics/Geometry
Comsol Workshop 10/6/2011 13
Simple axial / single pipe
Axial symmetry
Flexible model: rwell : 0.10 - 0.15 m
rrock: 10 – 20 m
Depth 300 m – 5 km
www.cmr.no © Christian Michelsen Research AS
Wellbore Heat Exchanger – Physics/Geometry
Comsol Workshop 10/6/2011 14
Fluid inlet
Fluid outlet
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Wellbore Heat Exchanger – Physics/Geometry
Comsol Workshop 10/6/2011 15
d
rrock
rwell
Fluid inlet
Fluid outlet
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Heat transfer by forced convection
• 𝜙𝑇 = ℎ𝐴(𝑇ℎ − 𝑇𝑙)
• 𝑇ℎ − rock temperature
• 𝑇𝑙 − fluid temperature
Heat transfer by conduction
• 𝜙𝑇 = 𝑘𝑇𝛻𝑇
Comsol Workshop 10/6/2011 16
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Heat transfer by forced convection
• 𝜙𝑇 = ℎ𝐴(𝑇ℎ − 𝑇𝑙)
• 𝑇ℎ − rock temperature
• 𝑇𝑙 − fluid temperature
Heat transfer by conduction
• 𝜙𝑇 = 𝑘𝑇𝛻𝑇
Comsol Workshop 10/6/2011 17
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Heat transfer by forced convection
• 𝜙𝑇 = ℎ𝐴(𝑇ℎ − 𝑇𝑙)
• 𝑇ℎ − rock temperature
• 𝑇𝑙 − fluid temperature
Heat transfer by conduction
• 𝜙𝑇 = 𝑘𝑇𝛻𝑇
Comsol Workshop 10/6/2011 18
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 19
Heat transfer by forced convection
• Continuity or ‘Thin thermally resistive layer’?
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Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 20
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 21
Mesh
• Difficult geometry: • Long, thin pipe • Need small, high-quality elements in the pipe • Need large elements in rock to reduce
computation time
• Implement a mesh-refinement parameter
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 22
Mesh
• Difficult geometry: • Long, thin pipe • Need small, high-quality elements in the pipe • Need large elements in rock to reduce
computation time
• Implement a mesh-refinement parameter
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 23
Mesh
• Difficult geometry: • Long, thin pipe • Need small, high-quality elements in the pipe • Need large elements in rock to reduce
computation time
• Implement a mesh-refinement parameter
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 24
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 25
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 26
www.cmr.no © Christian Michelsen Research AS
Comsol Model of a Wellbore Heat Exchanger
Comsol Workshop 10/6/2011 27
www.cmr.no © Christian Michelsen Research AS
Preliminary results
Comsol Workshop 10/6/2011 28
The effect of a thin thermally resistive layer
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Preliminary results
Comsol Workshop 10/6/2011 29
Cut-line plot
Continuity of temperature. The ‘jump’ in the rock temperature observed about
r=0.45 m is assumed due to interpolation of the solution using 2nd-degree
polynomials.
www.cmr.no © Christian Michelsen Research AS
Preliminary results
Comsol Workshop 10/6/2011 30
Table plot
Outflow temperature after 200 days. Observe the small difference this layer
makes; it can be quantified to less than 0.1 ˚C
www.cmr.no © Christian Michelsen Research AS
Outlook – further work
Study behavior for three cases – both fluid and rock temperature
500 m well
1 km well
5 km well
Imitate the behavior of a U-pipe by mirroring the model at z=-d (total
depth = 2d)
Future model: Coaxial
Comsol Workshop 10/6/2011 31
