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 IM IM IM • Water adsorption – non-equilibrium C b • Mobile and adsorbed water REV C a • Concentrations/densities C_a, C_b M M M [kg/m3] ∂ ∂ C T = ∇ ⋅ λ ∇ + χ b c ( T ) v ( T , C , C ) ( T , C , C ) ( T , C , C ) ∂ ∂ t t a b a b a b ∂ ∂ ε C C ε + − ε = ∇ ⋅ ∇ a b ( 1 ) ( D C ) a a ∂ ∂ τ ( T , C , C ) t t a b   ∂ C C 1   = − ϕ γ b a ( C )   b ( T , C , C ) ε ∂ 100 t C a b   a

Constitutive relations • Heat conductivity on water content • Heat capacity on water content and temperature ( ) ( ) ~ – Additive: = χ = η χ ρ + ρ − + c c , T c 1 . 38 ( T 273 . 15 ) 732 . 5 eff dry 0 1 1 • 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

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

Model mesh

Results: temperature buffer 1 Distance from the top of backfill [m] Temperature [°C] 0 70 Temperature 0 10 20 30 40 50 60 70 80 90 100 BCE 1d BCE 10d 60 BCE 50d -1 BCE EOT Model 1d 50 -2 Model 10d Model 50d 40 Model EOT -3 30 -4 20 BCE 0days BCE 7days -5 BCE 49days 10 BCE-EOT Model 0d Model 7d -6 Distance from the center Model 49d 0 Model EOT 0 1 2 3 4 5 6 -7

Results: temperatures rock 0 0 Distance from the tunnel Temperature Distance from the tunnel Temperatu 10 15 20 25 30 35 40 10 15 20 25 30 -1 -1 -2 -2 -3 -3 -4 -4 BCE 0d BCE 0d -5 -5 BCE 7d BCE 7d BCE 49d BCE 49d BCE EOT -6 -6 BCE EOT Model 0d Model 0d Model 7d Model 7d -7 -7 Model 49d Model 49d Model EOT Model EOT -8 -8

Temperature contours - EOT • Effect of nonsymmetry given by tunnel direction Tunnel length Tunnel width

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 parameter 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

Optimization results 2nd part • Observations: T7 (8x), T8 (8x), HT (6x), BT(10x), RT(6x) • SOSR=sum (T_obs – T_mod)^2 parameter 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 optimization results 0 1 Temperature Distance from the tunnel Distance from the top of 10 15 20 25 30 35 40 -1 Temperature [°C] 0 0 20 40 60 80 100 -2 -1 -3 -2 -4 -3 -5 BCE EOT -4 Model fit 2 896 -6 -5 Model fit 7 Model fit 2 Model fit 7 Model fit 4 -7 -6 Model fit 4 Model start Model start -8 -7 0 80 Temperatu Temperature Distance from the tunnel BCE EOT 10 15 20 25 30 Model start -1 70 Fir nr 2 Fit nr.4 60 -2 Fit nr.7 Ř ada1 50 Ř ada2 -3 Ř ada3 40 -4 30 BCE EOT -5 Model fit 2 20 -6 Model fit 7 10 Model fit 4 -7 Distance from the center Model start 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8

Water content 150d EOT • Only for buffer part • Technical problem in fully coupled code: – Initial condition as a 25 1BX01-BCE 1BX06-BCE 1BX07-BCE 1BX12-BCE solution of steady- 1BX16-BCE 1BX17-BCE 24 BX1 BX6 BX7 BX12 state problem 23 BX16 BX17 22 – Variable temperature 21 (11-16degC) 20 – Water content not in 19 18 equilibrium (steady 0 200 400 600 800 1000 state) 13.3 26.6 w% kg/m3

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 of observations • Distribution of moisture not captured

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