Simulation of BM2.1-BCE RAWRA / TUL Technical University of - - PowerPoint PPT Presentation

Simulation of BM2.1-BCE

RAWRA / TUL Technical University of Liberec, Czech Rep.

• M. Hokr, D. Frydrych

Processes in the simulation code ISERIT

• Heat conduction
• Vapor diffusion
• Water adsorption – non-equilibrium
• Mobile and adsorbed water
• Concentrations/densities C_a, C_b

[kg/m3]

) , , ( 100 ) , , ( ) , , ( ) , , ( ) , , (

) ( 1 ) ( ) 1 ( ) (

b a b a b a b a b a

C C T b a a b a C C T a b a b C C T C C T C C T v

C C C t C C D t C t C t C T t T c γ ϕ ε τ ε ε ε χ λ         − = ∂ ∂ ∇ ⋅ ∇ = ∂ ∂ − + ∂ ∂ ∂ ∂ + ∇ ⋅ ∇ = ∂ ∂

IM IM IM M M M

REV Cb Ca

Constitutive relations

• Heat conductivity on water content
• Heat capacity on water content and temperature

– Additive:

• Diffusion coefficient on water content and

temperature

– D=D(T).D_r(w)

• Sorption curve [water_content(RH)] on

temperature

– w=w(ϕ).w_r(T) , w(ϕ) linear in our simulations

• Saturated vapor density on temerature
• Additional parameters

– Tortuosity, rate of adsorption

( ) ( )

5 . 732 ) 15 . 273 ( 38 . 1 ~ ,

1 1

+ − + = = T c T c c

dry eff

ρ ρ χ η χ

Features of analysis

• The coupling features not fully used
• 3D model (1/4 symmetry, linear tunnel), simplification on top heater

shape, backfill and tunnel floor

• Water transport only in the buffer
• Fixed (constant) thermal parameters
• Constant temperature boundary (11degC outer, 16degC tunnel

surface)

• Block size 15m×15m×35m
• EOT: considered at switching-off the heater
• Numerical:

– Linear finite elements, implicit “monolithic” scheme, simple iterations for non-linear terms – 13227 nodes, 66758 elements (tetrahedra) – 20 times steps (variable)

Material parameters

8930 385 392 Heater 1850 1400 0.44 sand 1720 2000 1.5 buffer 2630 1100 3.6 Rock + Backfill &floor density Heat capc. Heat cond.

Model mesh

Results: temperature buffer

• 7
• 6
• 5
• 4
• 3
• 2
• 1

1 10 20 30 40 50 60 70 80 90 100

BCE 0days BCE 7days BCE 49days BCE-EOT Model 0d Model 7d Model 49d Model EOT

Distance from the top of backfill [m] Temperature [°C]

10 20 30 40 50 60 70 1 2 3 4 5 6 BCE 1d BCE 10d BCE 50d BCE EOT Model 1d Model 10d Model 50d Model EOT Temperature Distance from the center

Results: temperatures rock

• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

10 15 20 25 30 BCE 0d BCE 7d BCE 49d BCE EOT Model 0d Model 7d Model 49d Model EOT Temperatu Distance from the tunnel

• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

10 15 20 25 30 35 40 BCE 0d BCE 7d BCE 49d BCE EOT Model 0d Model 7d Model 49d Model EOT Temperature Distance from the tunnel

Temperature contours - EOT

• Effect of nonsymmetry given by tunnel direction

Tunnel width Tunnel length

Temperature contours buffer

Parameter optimization

• UCODE program by USGS, optimization by

repeated running of the model

• Only for steady-state temperature (large

computational time)

• Two different sets of observations considered
• Estimated parameters: four thermal

conductivities, tunnel temperature and tunnel surface heat exchange coefficient (various combinations)

Optimization results 1st part

• Observations: T7 (8x), T8 (8x), HT (6x)
• SOSR=sum (T_obs – T_mod)^2

fit measure lam_R lam_B lam_S lam_F T_tunn coef_tunn SOSR starting 3.6 1.5 0.44 3.6 11 50 196 T2 3.11 1.47 0.544 105 starting 3.6 1.5 0.44 3.6 16 50 132.2 T3 3.491 1.442 0.52 92.9 starting 3.491 1.442 0.52 3.6 16 50 92.9 T4 3.425 14.94 91.7 T5 3.425 1.442 0.52 3.6 15.81 709 !! 91.05 T6 3.449 1.442 0.52 2.842 15.81 709 90.9 parameter

Optimization results 2nd part

• Observations: T7 (8x), T8 (8x), HT (6x), BT(10x), RT(6x)
• SOSR=sum (T_obs – T_mod)^2

fit measure lam_R lam_B lam_S lam_F T_tunn coef_tunn SOSR starting 3.6 1.5 0.44 3.6 15.8 709 154.4 T7 3.656 1.514 0.482 3.6 16.68 709 124.3 T8 122.2 T9 122.6 T10 3.632 1.514 0.482 10.59 !!! 16.68 50 123 T11 3.656 1.514 0.482 3.6 16.73 110.1 !!! 123.3 parameter

Parameter optimization results

10 20 30 40 50 60 70 80 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BCE EOT Model start Fir nr 2 Fit nr.4 Fit nr.7 Řada1 Řada2 Řada3 Temperature Distance from the center

• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

10 15 20 25 30 35 40 BCE EOT Model fit 2 Model fit 7 Model fit 4 Model start Temperature Distance from the tunnel

• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

10 15 20 25 30 BCE EOT Model fit 2 Model fit 7 Model fit 4 Model start Temperatu Distance from the tunnel

• 7
• 6
• 5
• 4
• 3
• 2
• 1

1 20 40 60 80 100

896 Model fit 2 Model fit 7 Model fit 4 Model start Distance from the top of Temperature [°C]

Water content

• Only for buffer part
• Technical problem in

fully coupled code:

– Initial condition as a solution of steady- state problem – Variable temperature (11-16degC) – Water content not in equilibrium (steady state)

kg/m3 w% 13.3 26.6 150d EOT

18 19 20 21 22 23 24 25 200 400 600 800 1000 1BX01-BCE 1BX06-BCE 1BX07-BCE 1BX12-BCE 1BX16-BCE 1BX17-BCE BX1 BX6 BX7 BX12 BX16 BX17

Conclusion

• Temperature can be predicted satisfactorily

even with simple linear heat conduction

• Fit of steady state is good, but in unsteady

phase the model underpredicts T

• Optimization can decrease the total error (sum

square residuals) by 10-50%

• Different results of optimization for different sets
• f observations
• Distribution of moisture not captured

• Thank you for your attention