Interactive coupled sample
Thermo-hydro-mechanical processes in porous media
Porous materials deform, conduct heat, and transmit fluids at the same time. Adjust the loading below to see how heat gradients, pore-pressure gradients, and effective stress combine inside a saturated sample.
hot boundary
pore water flux
external stress
Physical principles
Three fields, one porous skeleton
A representative elementary volume contains mineral grains, connected pore space, and a pore fluid. THM theory tracks temperature, pore pressure, and displacement as primary fields, then closes the problem with material laws.
Thermal transport
Heat moves by conduction through the composite solid-fluid medium and by advection when pore water carries thermal energy.
q_T = -lambda_eff grad(T) + rho_w c_w v T
Fluid mass balance
Pore pressure changes when fluid enters, leaves, expands thermally, or is squeezed by deformation of the pore volume.
v = -(k / mu) (grad(p) - rho_f g)
Effective stress
The skeleton responds to effective stress, not total stress alone. Pore pressure unloads grain contacts while thermal expansion adds eigenstrain.
sigma' = sigma - alpha_B p I
Mathematical model
Balance laws plus constitutive closure
The standard small-strain THM problem couples conservation of energy, conservation of fluid mass, and quasi-static momentum balance.
Energy conservation
(rho c)_eff dT/dt = div(lambda_eff grad T) - rho_f c_f v dot grad T + Q_T
The left side stores heat in the solid-fluid mixture. The right side accounts for conduction, advective heat transport by flowing water, and sources such as injection or reactions.
Coupling map
How one field drives another
Select a coupling path to see the mechanism. Strong THM effects usually appear when more than one path is active at the same time.
T -> H
Thermal pressurization
Heating expands pore fluid and grains by different amounts. In low-permeability rock, fluid expansion cannot drain quickly, so pore pressure rises and effective stress falls.
dp ≈ Lambda dT, where Lambda depends on compressibility and expansion mismatch.
Scales and regimes
When coupling matters
Coupling is governed by material properties and time scales. Use the sliders to compare diffusion, advection, and deformation response for a representative length.
Pressure and temperature equilibrate over roughly L2 / c.
Pe = v L / D compares advective transport with diffusive smoothing.
Advection and diffusion both shape the response.