Chapter 8 - Presentation and analysis of the main outputs
In this chapter we use the selected configuration described in Ch. 5 to test the behavior of the numerical model by varying the regional geothermal gradient (0-20-40 K/km) and the conductive vs convective heat transmission inside the geothermal reservoir.
Output Analysis
Conductive Temperature field in the Computational Domain
Using the selected configuration (Tab. 1) and the selected mesh (Fig. 1), the temperature field in the domain is analyzed, at different time steps (50 ka, 150 ka, 250 ka and 350 ka), with thermal gradient = 0 K/km and in conductive heat transmission in the geothermal reservoir.
The temperature field for 50 ka, 150 ka, 250 ka and 350 ka output is shown in Figs 2 and 3.
k cp ρ T Porosity Thermal diffusivity
Cap Rock 1.5 1,100 2,200 / / 6.20 10-7
Geothermal Reservoir 2.7 900 2,650 / 0.05 1.13 10-6
Crystalline basement 2.5 1,100 2,750 / / 8.26 10-7
Magma 1.7 1,200 2,750 900 / 5.15 10-7
Table 1 Summary of basic physical parameters used for the numerical simulations
d) c) b) a)
Fig. 1 Heat3D X-Z selected mesh 60 km x 10 km. The points are considered in the next figures: a) centre of Magma Chamber (MC) (column 60); b) 5 km far from centre of MC (column 50); c) 10 km far from centre of MC (column 40);
d) 20 km far from centre of MC (column 20).
a)
b) c)
d) e)
Fig. 2 Temperature field in the domain - t (°C) vs z (m) for different time steps (at 50 ka, 150 ka, 250 ka and 350 ka).
Thermal gradient 0 K/km. Conductive heat transmission in the geothermal reservoir.
a) in the centre of magmatic chamber full temperature field; b) in the centre of magmatic chamber with temperature field cut-off at 400 °C; c) 5 km far from the centre of MC; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC.
The diagrams of Fig. 2 show some very important features:
1) the thermal anomaly attenuates laterally to negligible already at 10 km from magma reservoir centre (Fig. 4d), that is just 5 km from its margin, where the total gradient built after 350 ka is only 10 K/km. At 20 km from MC centre there there is no sign of thermal anomaly (Fig. 4e);
2) The proximal thermal profiles at 0 and 5 km (Fig. 4a-c) show a substantial modification respect to initial conditions, where the magma chambers cools to less than half of its initial temperature transferring heat upward where the thermal gradient rises quickly within the first 150 ka and then progressively tends to stabilize so that the temperature differences between 250 ka and 350 ka are minimal; this pattern suggests that the chosen initial conditions thermally inflate the reservoir on time scales of 250 ka, and then the gain over time, though still occurring, is negligible. This result is important as it stresses the relevance, in geothermal modeling, of reliable geochronological datasets that allow to constrain the life-span of magma chambers.
3) the shape of thermal gradients in the geothermal reservoir is complex above MC whereas is linear laterally away (10 km)
a)
b)
c)
d)
e)
Fig. 3 Temperature field evolution in the domain. Thermal gradient 0 K/km. Conductive heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
The same kind of data shown in Fig. 2 are shown in Fig. 4, for simulations within a geothermal gradient of 20 K/km, in conductive heat transmission within the geothermal reservoir.
a)
b) c)
d) e)
Fig. 4 Temperature field in the domain for different time steps (at 50 ka, 150 ka, 250 ka and 350 ka). Thermal gradient 20 K/km. Conductive heat transmission in geothermal reservoir.
a) in the centre of magmatic chamber full temperature field; b) in the centre of magmatic chamber with temperature cut-off at 600 °C; c) 5 km far from the centre of MC; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC .
The time-temperature pattern shown by these simulations is the same as previous, and identifies (a) an horizonal length scale of 10 km from MC centre wherein the thermal anomaly attenuates to negligible and (b) a time-scale of 150 ka for attaining almost stable thermal conditions that then persist to the end of simulation at 350ka
Under the same conditions, in Fig. 5 the temperature field at 50 ka, 150 ka, 250 ka and 350 ka repsectively is shown.
a)
b)
c)
d)
e)
Fig. 5 Temperature field in the domain. Thermal gradient 20 K/km. Conductive heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
Fig. 6 and Fig. 7 show the evolution over time of temperature during the cooling of MC with regional geothermal gradient of 40 K/km, in conductive heat transmission within the geothermal reservoir.
a)
b) c)
d) e)
Fig. 6 Temperature field in the domain for different time steps (initial configuration, 50 ka, 150 ka, 250 ka and 350 ka).
Thermal gradient 40 K/km. Conductive heat transmission in geothermal reservoir.
a) in the centre of magmatic chamber full temperature field; b) in the centre of magmatic chamber with temperature cut-off 700 °C; c) 5 km far from the centre of MC; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC.
a)
b)
c)
d)
e)
Fig. 7 Temperature field in the domain. Thermal gradient 40 K/km. Conductive heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
This simulation shows similar patterns to the previous although the external “forcing” provided by the regional geothermal gradient appears to anticipate the attainment of stable gradient conditions at less than 150 ka
From the comparison of data obtained by the set of simulations in 0, 20 and 40 K/km regional geothermal gradients, some information can be deduced for the conductive regime:
1. In correspondence of the centre of the Magma Chamber (MC) and laterally to 5 km away (i.e. at the margin of MC), the variation of temperature in the geothermal reservoir rises quickly up to 150 ka and then stabilizes till 350 ka with an exponential trend as a function of time.
2. 10 km far from the centre of MC, in function of time, thermal effect of MC produces a linear increasing of temperature that continues to increment over time. The linearity depends on the physical parameters in the basement, reservoir and cap rock.
3. 20 km far from the centre of MC, there is a negligible effect in temperature for the thermal contribution of MC compared with the external field contribution (thermal gradient in the domain).
4. Thermal gradient in the domain acts like a relevant external force for the temperature dynamic.
The same analysis implemented for conductive heat transmission in geothermal reservoir can implemented for convective heat transmission in geothermal reservoir.
Conductive-Convective Temperature field in the Mesh Domain
Under convective heat transmission in the geothermal reservoir, the temperature field in the domain, with different time steps (at 50 ka, 150 ka, 250 ka and 350 ka) and regional geothermal gradient = 0 K/km is analyzed in Fig. 8.
The temperature field for 50 ka, 150 ka, 250 ka and 350 ka output is shown in Fig. 9.
a)
b) c)
d) e)
Fig. 8 Temperature field in the domain - t (°C) vs z (m) - for different time steps (at 50 ka, 150 ka, 250 ka and 350 ka).
Thermal gradient 0 K/km. Convective heat transmission in geothermal reservoir.
a) in the centre of magma chamber full temperature field; b) in the centre of magma chamber with temperature field till 400 °C; c) 5 km far from the centre of MC with temperature field cut-off at 400 °C; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC.
The temperature field for 50 ka, 150 ka, 250 ka and 350 ka output is shown in Fig. 9.
a)
b)
c)
d)
e)
Fig. 9 Temperature field in the domain. Thermal gradient 0 K/km. Convective heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
The same data with thermal gradient of 20 K/km, in convective heat transmission in geothermal reservoir, is in Fig. 10. The temperature field for 50 ka, 150 ka, 250 ka and 350 ka is shown in Fig. 11.
Finally, the case with thermal gradient of 40 K/km, in convective heat transmission in geothermal reservoir, is in Fig. 12. The temperature field for 50 ka, 150 ka, 250 ka and 350 ka is shown in Fig. 13.
a)
b) c)
d) e)
Fig. 10 Temperature field in the domain for different time steps (initial configuration, 50 ka, 150 ka, 250 ka and 350 ka). Thermal gradient 20 K/km. Convective heat transmission in geothermal reservoir.
a) in the centre of magma chamber full temperature field; b) in the centre of magma chamber with temperature field cut-off at 500 °C; c) 5 km far from the centre of MC; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC.
a)
b)
c)
d)
e)
Fig. 11 Temperature field in the domain. Thermal gradient 20 K/km. Convective heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
Finally, the same data, proposed so far, is presented for the thermal gradient 40 K/km in Fig. 12 and 13.
a)
b) c)
d) e)
Fig. 12 Temperature field in the domain for different time steps (initial configuration, 50 ka, 150 ka, 250 ka and 350 ka). Thermal gradient 40 K/km. Convective heat transmission in geothermal reservoir.
a) in the centre of magmatic chamber full temperature field; b) in the centre of magmatic chamber with temperature cut-off at 700 °C; c) 5 km far from the centre of MC; d) 10 km far from the centre of MC; e) 20 km far from the centre of MC.
a)
b)
c)
d)
e)
Fig. 13 Temperature field in the domain. Thermal gradient 40 K/km. Convective heat transmission in geothermal reservoir. a) 0 ka; b) 50 ka; c) 150 ka; d) 250 ka and e) 350 ka)
The main obvious difference between this set of simulations and the previous is the more effective convective thermal plume that rises the temperatures within the geothermal reservoir; on the other side, there are also significant similarities such as:
1. Most of the thermal variation in the geothermal reservoir occurs within 150 ka from the beginning of simulations, leading to amost steady conditions until the end of simulations at 350 ka;
2. At 10 km far from the centre of MC the thermal variations are limited. Convection in the geothermal reservoir affects the slope igradient and interestingly the larger increase in T at the top of the geothermal reservoir corresponds to a decrease at its base;
3. 20 km far from the centre of MC, there is no effect on temperature for the thermal contribution of MC.