Combined Effects of Temperature, Salinity and Viscosity Changes on Groundwater Flow in the Xinzhou Geothermal Field, South China

Abstract

The distribution of groundwater temperature and flow can be used to describe the hydrogeological process in a geothermal system, which is of great significance to the exploitation of geothermal resources. The traditional gravity-driven groundwater system theory takes less consideration of thermal convection, resulting in a deviation in the investigation of geothermal systems. The rise of water table and the acceleration of the flow of geothermal water in the discharge section suggest the existence of geothermal buoyancy. The changes in temperature, salinity and viscosity comprise the physical basis for the formation of geothermal buoyancy. Geothermal buoyancy due to free heat convection in a fault-controlled discharge section is discussed in the Xinzhou geothermal field, South China. The geothermal buoyancy is the additional pressure head created by the increase in temperature, increase in salinity and decrease in viscosity. At the convection point, geothermal buoyancy appears and forms a maximum of + 417.6 m. Geothermal buoyancy gradually decreases in the discharge section due to temperature domination. The salinity effect and viscosity effect on geothermal buoyancy are minor and negligible, respectively. Comparing the vertical velocity of geothermal water in the discharge section (32.47 × 10⁻³ m/d) and the average vertical circulation velocity (3.15 × 10⁻³ m/d), the geothermal buoyancy has an obvious acceleration effect on groundwater flow in the discharge section. The geothermal buoyancy at typical points provides the framework and control points for geothermal water flow in the discharge section of a geothermal system.

Appendix

Geothermal Buoyancy Generated by Viscosity Changes

The viscosity (η) of a liquid is controlled by temperature, and it is related to the internal friction (τ) between particles in a liquid, which can be expressed as (Ariman et al., 1973; Chevalier et al., 1988):

$$\tau \, = \, \eta \cdot {\text{d}}u/{\text{d}}y$$

(10)

where du is the difference in velocity between the two liquid layers, and dy is the distance between the two liquid layers.

The kinematic viscosity (ν) and the viscosity have the following relationship:

$$\nu \, = \, \eta /\rho$$

(11)

The kinematic viscosity (ν) is related to the temperature of geothermal water and expressed as Eq. 5.

The temperature increase leads to internal friction decrease, resulting in viscosity decrease (Mukhopadhyay and Layek, 2008). The relationship between internal friction and pressure can be expressed as:

$$P_{\tau } = \, \tau /s \, = \, \rho gh_{\tau }$$

(12)

where P_τ is the hydrostatic pressure generated by internal friction, s is the area of action of internal friction, and h_τ is hydraulic head generated by internal friction.

The hydraulic head generated by viscosity change is the change value of h_τ (Δhτ). By substituting Eqs. 10 and 11 into Eq. 12, the value of Δhτ can be calculated using Eq. 6.

Rayleigh Number

The temperature Rayleigh number is defined as:

$$Ra_{T} = \frac{{g\beta_{T} L^{3} \Delta T}}{{v\alpha_{T} }}$$

(13)

where g is the acceleration due to gravity, β_T is thermal expansion coefficients, L is the vertical dimension of the convection cell, ∆T is the temperature difference between the top and the bottom, v is the kinematic viscosity, and α_T is the thermal diffusivity. For this study, g = 9.8 m/s², β_T = 0.644 × 10^-3, L = 4338.72 m, ∆T = 154–83 = 71 ℃, v = 0.17 × 10^-6 m²/s, α = 1.6 × 10^-7. The calculated temperature Rayleigh number is 1.34 × 10²⁴.

The salinity Rayleigh number can be defined as:

$$Ra_{S} = \frac{{g\beta_{s} L^{3} \Delta S}}{{v\alpha_{S} }}$$

(14)

where β_S is salinity expansion coefficients, ∆S is salinity difference between the top and the bottom walls, and α_S is salinity diffusivity. For this study, g = 9.8 m/s², β_S = 0.222 × 10^-8, L = 4338.72 m, ∆S = 1.952–1.650 = 0.302 g/L, v = 0.17 × 10^-6 m²/s, α_S = 1 × 10^-4. The calculated salinity Rayleigh number was 3.16 × 10¹³.