Thermophysical parameters of brines

Thermophysical parameters of brines such as density, specific heat and dynamic viscosity, change significantly under the influence of temperature and mineralization. The pressure in these correlations is not so important due to the low compressibility factor of water. However, it is essential to know rather precise values of these parameters during evaluation of geothermal venture.

Energetic potential of geothermal source is often estimated assuming parameters of water in temperature 20°C and mineralisation 0 g/kg. Real parameters of geothermal fluid can actually differ a lot from this assumption. In extreme cases, difference can be over a dozen percent [1].

Scientists have developed numerous correlations to estimate the most accurate values of the thermodynamic parameters of water [2,3]. Most of the correlations have been developed for sea water, but the scope of applicability of some of these equations allows them to be used to determine the parameters of geothermal water (brine).

From the point of view of modeling geothermal resources, parameters such as specific heat, density and dynamic viscosity are of key importance. Graphs showing the variability of these parameters as a function of temperature and salinity are presented below.

Relation of specific heat as a function of temperature and mineralisation is presented in Fig. 1. Equation used was taken from Jamieson’a et al. [4]

EQUATION 1

Figure 1 Influence of temperature and mineralization on the specific heat of brines; source: [4]

The variability of specific heat shown in Fig. 1 applies to brines in the temperature range from 0 to 180°C and mineralization from 0 to 180 g/kg. Accuracy within the specified range is ± 0.28% [5]. It can be seen that, in general, for each case the specific heat increases with increasing temperature. Taking into account mineralization, a decrease in the specific heat value is observed with increasing salinity value. For example, geothermal water with a temperature of 80°C and a salinity of 150 g/kg has an approximately 15% lower specific heat value compared to water at the same temperature but characterized by very low mineralization.

Density of brines in function of temperature and mineralisation was presented in Fig. 2. For presented relations, equation by Sharqawy et al. was used [5]. Assumption of constant 0.1MPa pressure was made.

EQUATION 2

Figure 2 Influence of temperature and mineralization on the density of brines; source: [5]

The graph in Fig. 2 allows to determine the density of water with an accuracy of 0.1% at salt concentrations from 0 to 150 g/kg, in the temperature range from 0 to 180°C [5]. The density of water, including brines, decreases with increasing temperature, while for a given temperature it increases with increasing salinity. In Lower Jurassic geothermal reservoirs situated at the Polish Lowland, one can expect geothermal waters with temperatures ranging from 50 to 90°C and mineralization ranging from a few to 150 g/dm³. In such a wide range of temperatures and salt concentrations (mainly NaCl), the density difference in extreme cases can reach up to 100 g/dm³.

Further, Fig.3 shows the relationship between dynamic viscosity as a function of temperature and NaCl concentration. The correlation proposed by Isdale et al. was used. [6, 5]

EQUATION 3

Figure 3 Influence of temperature and mineralization for dynamic viscosity changes, source: [5]

The equation no. 3 used for dynamic viscosity can be applied to waters with salinity from 0 to 150 g/kg and temperatures from 20 to 180°C. Accuracy within the given range is ± 1% [5]. The presented data show that the dynamic viscosity of brines decreases with increasing temperature, while it increases with increasing salinity of the solution. This means that the flow of water with higher salinity will cause greater flow resistance compared to water with low mineralization (at the same temperature). However, it should be noted that the effect of temperature alone is greater than the salt concentration in the solution.

The heating power of geothermal intake is:

EQUATION 4

where

\dot{m}

means mass flow rate of geothermal fluid,

\dot{V}

– volumetric flow rate,

c_{p}

– specific heat, and

Δ T

– the difference between temperature of water extracted and injected. From the above formula, it is clear that product of density and specific heat, called volumetric heat capacity, is relevant when considering heating power of geothermal wells. As can be seen in the previous graphs, the increase in water mineralization affects both of these parameters in the opposite way – in the case of density, it is an increase, while in the case of specific heat – a decrease. It can therefore be seen that the effect of mineralization on the product of these parameters is partially compensated. Fig. 4 shows how the volumetric heat capacity changes with increasing temperature and mineralization. As can be seen in Fig. 4, mineralization has a greater impact on the value of specific heat, because also in the case of volumetric heat capacity, for a given temperature, the value of this parameter decreases with increasing mineralization (at least for temperatures >~25°C). Therefore, it can be seen that the increase in water salinity adversely affects the capacity of the geothermal intake. For example, the volumetric heat capacity of 80 °C water with mineralization of 150 g/dm3 is about 10% lower than that of fresh water at the same temperature.

Rysunek 4. Wpływ temperatury oraz mineralizacji na zmianę objętościowej pojemności cieplnej

Literaturę:

[1] Miecznik M., Błąd szacowania potencjału dla wytwarzania energii elektrycznej w instalacjach binarnych typu ORC związany ze zmiennością parametrów termodynamicznych wody geotermalne, Technika Poszukiwać Geologicznych, Geotermia, Zrównoważony Rozwój 2013(2).

[2] Jamil F., Muhammad Ali H., Khiadani M., Concise summary of existing correlations with thermophysical properties of seawater with applications: a recent review, Applied Thermal Engineering 227 (2023), 120404.

[3] Nayar G.K., Sharqawy H.M., Banchik D.L., Lienharrd V H.J., Thermophysical properties of seawater: A review and new correlations that include pressure dependence, Desalination 390 (2016), s: 1-24.

[4] Jamieson D.T., Tudhope J.S., Cartwright G., Physical properties of sea water solutions: heat capacity, Desalination 7 (1969), s:23-30.

[5] Sharqawy M.H., Liehard V.J.H., Zubair S.M., Thermophysical properties of seawater: A review of existing correlations and data, Desalination and Water Treatment 16(2010), s: 354–380.

Together we work for a green, competitive and inclusive Europe

The project is financed under the Fund for Bilateral Relations through the European Economic Area Financial Mechanism (EEA FM) and the Norwegian Financial Mechanism (NFM) 2014-2021, programme “Environment, Energy and Climate Change”.

Project Operator: Ministry of Climate and Environment