Comparison of 1D and 3D reservoir heat transport models and temperature effects on mass transport

Polli, Bruna Arcie; Bleninger, Tobias

doi:10.1590/2318-0331.241920190023

Bruna Arcie Polli

Universidade Federal do Paraná, Curitiba, PR, Brasil

http://orcid.org/0000-0001-7455-0687

Tobias Bleninger

Universidade Federal do Paraná, Curitiba, PR, Brasil

http://orcid.org/0000-0002-8376-3710

E-mails: brunapolli@gmail.com (BAP), tobias.bleninger@gmail.com (TB)

Bruna Arcie Polli: Numerical modeling, data analysis and comparisons, writing.

Tobias Bleninger: Data analysis and comparisons, paper revision and closing.

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Figure 1
Vossoroca reservoir bathymetry, main rivers and location of continuous measurements.

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Figure 2
Vossoroca reservoir temperature profiles measured at the floating platform location (see ).

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Figure 3
Meteorological data measured at the meteorological weather station of Vossoroca reservoir (see ). a) Wind speed (U), b) wind direction (WD), c) air temperature (T_a), d) relative humidity (RH) and e) solar radiation (q_s).

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Figure 4
Inflow and outflow discharge Q of Vossoroca reservoir, and inflow temperature, T_in.

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Figure 5
- Murakami and Ocean heat flux models applied in Vossoroca reservoir

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Figure 6
Temperature in Vossoroca reservoir at the floating platform location. a) Measurements, b) MTCR-1 model and c) Delft3D model.

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Figure 7
Vertical eddy diffusivity (E) in Vossoroca reservoir at the floating platform location a) MTCR-1 model and b) Delft3D.

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Figure 8
Temperature gradients in Vossoroca reservoir at the floating platform location.

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Figure 9
Wedderburn and Lake Number calculated with a) measured data, b) MTCR-1 results and c) Delft3D results at the floating platform location.

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Figure 10
Period of time (in %) that a certain temperature gradient is expected in Vossoroca reservoir during the period of simulation (94 days).

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Figure 11
Monitoring paths and cross-sections (CS) for tracer modeling in Vossoroca reservoir.

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Figure 12
Water temperature and normalized tracer concentration in a longitudinal section in Vossoroca reservoir.

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Figure 13
Normalized tracer concentration in a longitudinal section of Vossoroca reservoir (in this simulation, temperature is not modelled).

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Figure 14
Velocity profiles in points R1, R2 and R3 (see ) in the river tracer modeling.

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Figure 15
Water temperature and normalized tracer concentration in a side arm section in Vossoroca reservoir.

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Figure 16
Water temperature and normalized tracer concentration in a side arm section in Vossoroca reservoir.

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Figure 17
Normalized tracer concentration in a side arm section of Vossoroca reservoir (in this simulation, temperature is not modelled).

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Figure 18
Velocity profiles in points P1 and P2 (see ) in the side arm tracer modeling in Vossoroca reservoir.

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Figure 19
Normalized tracer concentration in points P1 and P2 (see ) in the 2D and 3D side arm tracer modeling in Vossoroca reservoir.

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Figure 12
Water temperature and normalized tracer concentration in a longitudinal section in Vossoroca reservoir.

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Figure 13
Normalized tracer concentration in a longitudinal section of Vossoroca reservoir (in this simulation, temperature is not modelled).

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Figure 14
Velocity profiles in points R1, R2 and R3 (see ) in the river tracer modeling.

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Figure 15
Water temperature and normalized tracer concentration in a side arm section in Vossoroca reservoir.

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Figure 16
Water temperature and normalized tracer concentration in a side arm section in Vossoroca reservoir.

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Figure 17
Normalized tracer concentration in a side arm section of Vossoroca reservoir (in this simulation, temperature is not modelled).

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Figure 18
Velocity profiles in points P1 and P2 (see ) in the side arm tracer modeling in Vossoroca reservoir.

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Figure 19
Normalized tracer concentration in points P1 and P2 (see ) in the 2D and 3D side arm tracer modeling in Vossoroca reservoir.

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Table 1
Delft3D model set-up and calibration parameters for Vossoroca reservoir modeling related to turbulence and surface heat flux.

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Table 2
Mean heat flux calculated with Murakami and Ocean models.

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Table 3
MTCR-1 and Delft3D model set-up for Vossoroca reservoir modeling.

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Table 4
Mean Absolute Error (MAE) and Standard Deviation (SD) for 1D and 3D modeling of Vossoroca reservoir at the floating platform location.

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Table 5
Mean Absolute Error (MAE) and Standard Deviation (SD) in the 1D and 3D modeling at the measured points in Vossoroca reservoir at the floating platform location.

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Table 6
Temperature gradients and physical indices comparison between measured data, 1D and 3D modeling at the floating platform location (duration, in days, of gradients occurring out of 94 days of simulation).

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Table 7
Difference in percentage between advective and dispersive tracer mass transport considering or not temperature effects.

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Table 8
Difference in percentage between advective and dispersive transport considering temperature and not considering temperature in the side arm tracer modeling.

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(1)

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(2)

	Description	Delft3D set-up
ν_H^back (m²s^-1)	background horizontal eddy viscosity	0
D_H^back (m²s^-1)	background horizontal eddy diffusivity	0.001
ν_V^back (m²s^-1)	vertical eddy viscosity	0
D_V^back (m²s^-1)	background vertical eddy diffusivity	0
L_oz (m)	Ozmidov length scale	0
H_Secchi (m)	Secchi depth	1.8
c_e (-)	Dalton number (evaporative flux)	0.0013
c_H (-)	Stanton number (heat convection)	0.0013

Mean heat flux	Murakami	Ocean
Q_eb (Wm^-2)	-1.23	-1.89
Q_ev (Wm^-2)	3.32	72.3
Q_co (Wm^-2)	1.25	29
Q_sn (Wm^-2)	106.1	109.6

	MTCR-1	Delft3D
Period	94 days	94 days
Number of layers	85 (0.2 m)	20 (0.88 m)
Time step	2 min	3 s
Grid (horizontal)	-	15 m x 15 m
Processing time	1 min	10 days

Error	MTCR-1	Delft3D
MAE (°C)	1.18±0.84	0.50±0.31

Depth (from surface)	MTCR-1 (°C)	Delft3D (°C)
1 m	1.10±0.11	0.46±0.15
3 m	0.87±0.01	0.72±0.04
5 m	1.30±0.02	0.63±0.04
7 m	1.60±0.02	0.38±0.03
9 m	1.18±0.01	0.48±0.005
11 m	1.04±0.01	0.48±0.002
Bottom	1.20±0.07	0.36±0.001

Days	Measurements	1D Modeling	3D Modeling
ΔT>1 °C	79	49	78
ΔT>2 °C	61	42	62
ΔT>3 °C	53	25	54
W>1	91	93	91
L_N>1	91	83	85

Cross-section (CS)	Advective transport (%) ^* * Positive sign means that mass transport through the cross-section is higher in the modeling with temperature; Negative sign means that mass transport through the cross-section is higher in the modeling without temperature	Dispersive transport (%)*
1	-0.24	+71.3
2	+1.9	-110.3
3	+3.2	-129.8
4	+10.7	-109.3
5	+17.3	0.0
6	+27.2	0.0
7	+36.2	-154.9
8	+39.7	-421.2

Cross-section	Advective transport (%) ^* * Positive sign means that mass transport through the cross-section is higher in the modeling with temperature; Negative sign means that mass transport through the cross-section is higher in the modeling without temperature.	Dispersive transport (%)*
1	+9.1	-96.3
2	+2.0	+1.9
3	+4.5	+62.1
4	+4.5	0.0
5	+5.7	-30.8

[1] E-mails: brunapolli@gmail.com (BAP), tobias.bleninger@gmail.com (TB)

Brasil

Brasil

Comparison of 1D and 3D reservoir heat transport models and temperature effects on mass transport

Comparação de modelos 1D e 3D de transporte de calor e efeitos de temperatura no transporte de massa

ABSTRACT