Study on the influencing factors of rock-soil thermophysical parameters in shallow geothermal energy

ZHU Xi, ZHANG Qing-lian, WANG Wan-li, LIU Yan-guang

1The Institute of Hydrogeology and Environmental Geology, CAGS, Shijiazhuang 050061, China,

2 Shijiazhuang University of Economics, Shijiazhuang 050031, China.

Abstract: Thermophysical parameters are the main parameters affecting the utilization efficiency of shallow geothermal energy. Based on the research and evaluation data of shallow geothermal energy in capital cities of China, this paper analyzes the differences between two testing methods and finds that data measured in in-situ thermal conductivity test is closer to the actual utilization. This paper analyzes the influencing factors of thermophysical parameters from lithology, density, moisture content and porosity: The thermal conductivity coefficient of bedrock is generally higher than Quaternary system loose bed soil; as for the coefficient of bedrock, dolomite, shale and granite are higher while gabbro, sandstone and mudstone are lower; as for the coefficient of loose bed, pebble and gravel are higher while clay and silt are lower. As the particle size of sand decreases, the thermal conductivity coefficient declines accordingly. The thermal conductivity coefficient increases linearly with growing density and decreases in logarithm with growing moisture content as well as porosity; specific heat capacity decreases in logarithm with growing density, increases in power exponent with growing moisture content and decreases linearly with growing porosity. The thermal conductivity coefficient is high when hydrodynamic condition is good and vice versa. The conclusions of this paper have guiding significance for the research, evaluation and development of shallow geothermal energy in other areas.

Keywords: Shallow geothermal energy; Thermophysical property; Influencing factor;Distribution rule

Introduction

As a widely distributed new energy with clean,environmentally friendly and economically applicable features, shallow geothermal energy is easy to use and has great potential (WANG Gui-ling et al. 2012). For decades, the use of shallow geothermal energy has been developing rapidly relying on ground-source heat pump technology: Since United States established the first ground-source heat pump system in the 1940s,domestic and foreign universities began to study heat pump technology in the 1960s; in 1970s,countries like Switzerland and Netherland established demonstration projects; in 1990s, the application of ground source heat pump system was gradually popularized; in the 21stcentury, the ground source heat pump technology and its application has been developing rapidly. The ground source heat pump market in China is growing quickly with a growth rate of over 30%since 2004, which is far higher than the world average growth rate of 20% to 22% over the same,making China rank the second in the world(ZHENG Ke-yan, 2012).

The thermal storage property, thermal conductivity property and other thermo-dynamic properties of rock-soil layer are determined by its thermal conductivity, specific heat capacity and thermal diffusivity coefficient, which are collectively referred to as thermophysical para-meters. Thermophysical indicators are also the key factors affecting the design of ground source heat pump engineering (LIN Wen-jing et al. 2012).Currently, there has not been any study on the influencing factors of thermophysical parameters at a national level. Based on the research and evaluation data of shallow geothermal energy in capital cities of China, this study analyzes the influencing factors of thermophysical parameters,providing basis for the research and analysis as well as the development and utilization of shallow geothermal energy.

1 Research methods

Thermophysical properties test of rock-soil mass mainly includes thermal conductivity coefficient, specific heat capacity and thermal diffusivity coefficient (HU Ping-fang et al. 2008).

Thermal conductivity coefficient is the quantity of heat passing through per unit of horizontal cross-sectional area in per unit of time when the vertical temperature gradient is 1℃/m (YU Wei-zhi, 2012). Rocks and soil are inorganic non-metallic materials composed by a variety of grains, so the internal thermal conduction is achieved by crystal lattice or lattice vibration (XU Mo et al. 2011). The more compact materials combine, the easier vibration of molecules in solid transmits and the bigger the thermal conductivity coefficient will be (ZHANG Yan-jun et al. 2011).

Thermal diffusivity coefficient refers to the physical quantity that reflects the speed of temperature homogenization in heterogeneous materials, namely, the higher thermal diffusivity is,the quicker temperature changes diffuse, from the perspective of temperature. Thermal diffusivity coefficient=thermal conductivity coefficient/density heat capacity. The bigger thermal diffusivity coefficient is, the shorter time it needs to reach homogeneous temperature within materials.

Specific heat capacity refers to internal energy absorbed or released by per unit mass of material when the temperature of this unit changes. When the materials absorb or release a certain amount of thermal energy, the higher the capacity is, the less significantly the temperature goes up or down.With higher capacity, materials of the same quality absorb or release more internal energy when unit temperature changes.

Rock-soil thermalphysical index testing currently involves two testing methods, namely,indoor thermalphysical property testing and in-situ thermal response testing. Indoor thermalphysical property testing is to collect rock-soil samples from drill holes and transport them back to the laboratory, and to use special testing equipment(e.g. laser thermal conductivity meter) to test the thermal physical property of the samples to directly obtain testing data; in-situ thermal response testing is to make use of instruments (e.g.GH-12FT05/1 in-situ thermal response testing meter provided by Beijing Huaqing Ronghao New Energy Development Co., Ltd) to calculate the thermalphysical parameter in initial conditions (in terms of temperature, pressure, moisture content,etc.). Both testing methods are very common in real shallow geothermal energy development.Sampling and testing should be in accordance with Regulations for Investigation into Rock-Soil Engineering (GB50021-2001) and Standards for Geotechnical Testing Methods (GB/T50123-1999).

2 Influence factors of thermalphysical parameters

Thermalphysical property of rock-soil mass is very closely related with the cause of its formation,the geological age of its formation and the geological environment it is in, and all these factors are usually reflected in specific indicators like lithological characters and substance composition, structure, construction, density,porosity (or porosity factor), moisture content,saturation, pressure, temperature and rate of decay,etc. Variance in rock-soil thermalphysical property is resulted from combined action of the above-mentioned indicators. Differences in these indicators, to a large extent, reflect variance in rock-soil thermalphysical property. Therefore, we can study relevant indicators so as to further study thermalphysical property of rock-soil mass.

There are multiple factors influencing the thermalphysical property of rock-soil mass, which are mutually affecting as well in a very complex way. According to part of the data from investigation and evaluation of shallow geothermal energy in capital cities of 29 provinces, we can conduct an analysis of the main factors, including testing methods, lithology, density, moisture content and porosity, etc., and analyze in detail how each factor influences thermalphysical parameters.

2.1 Mineral composition, stratum lithology

Mineral constituents and contents in rocks differ, and their conductivity coefficients vary from one another. There is a remarkable difference between thermalphysical parameters of different minerals; if there is a high content of minerals with higher thermal conductivity coefficient within a piece of rock, then the thermal conductivity coefficient of this rock is larger, and vice versa.The thermal conductivity coefficient of feldspar and micalex is 5.30 W/(m·℃), biotite, chlorite 5.51 W/(m·℃), calcite 5.56W/(m·℃), hornblende, pyroxene and olivine 5.19 W/(m·℃); quartz 7.12 W/(m·℃); water 0.59W/(m·℃) (measured at 18℃) (WANG Nanet al. 2012).

Physical properties of different rock-soil masses vary significantly from one another.Thermalphysical parameters of materials with different lithology are counted and analyzed (Table 1) (data are assessed according to Standard for Soil Testing Methods GB_T50123-1999), according to data investigated and evaluated from capital cities of 29 provinces, and as a conclusion, how lithology exerts an influence on thermal- physical property is calculated: Rock has the highest thermal conductivity coefficient, sandy soil and silty soil are in the middle, and the thermal conductivity of clayey soil is the lowest (Fig. 1).

Table 1 Thermalphysical parameters of rock-soil mass with different lithology

According to the statistics, dolomite has the highest thermal conductivity coefficient, which is up to 2.8 W/(m·℃), and that of limestone and shale is relatively high as well; among all rocks,sandstone and mudstone are the mostly widely spread, and the thermal conductivity coefficient of the former is 1.86 W/(m·℃), and that of the latter is 1.79 W/(m·℃); thermal conductivity coefficient of pebble, sand, silt, silty clay and clay decrease in sequence, but with a small difference. Clay’s thermal conductivity coefficient is 1.37 W/(m·℃),the lowest in the list. Patterns about specific heat capacity are roughly opposite to those of thermal conductivity coefficient: silty clay has the highest specific heat capacity, which is 1.35 KJ/kg℃, and that of clay and silt is slightly lower; next is pebble,and stones normally have low specific heat capacity, among which gabbro’s is 0.46 KJ/kg℃,the lowest. Specific heat capacity of silt, silty clay and clay can be significantly affected by other factors (for instance, moisture content), and there is no obvious pattern that could be drawn. Pebbles are the highest in thermal diffusivity, which is up to 1.40 m2/s, and next are silt, granite, gabbro, etc.,and clay has the lowest, which is 0.53 m2/s.Thermal diffusivity refers to the ratio of thermal conductivity to the product of density and specific heat capacity, representing rock’s capacity to reach a balanced inner temperature.

Fig. 1 Thermalphysical parameters of materials with different lithology

Among sandy soils, the bigger the particle size is, the higher the thermal conductivity coefficient will be, and the coefficient of gravelly sand,medium-coarse sand and fine sand decreases in sequence (Table 2). Medium-coarse sand has the lowest specific heat capacity and silty sand the highest. There is no obvious regular pattern about thermal diffusivity. According to patterns drawn from statistics collected in all provincial capital cities, the thermal diffusivity of sandy soil is generally higher than that of clay and silt, and particularly gravelly soil and pebble soil have higher thermal diffusivity than other types of rock-soil; the variance between rocks with different thermal diffusivity is relatively large, in a majority of the cities, rocks have higher thermal diffusivity than silt, and the thermal diffusivity of bedrock is low in a few cities.

From thermalphysical parameters of each lithology category, it is seen that the more compact the structure of the rock-soil mass is, the higher its thermal conductivity will be, and vice versa.However, specific heat capacity follows an opposite pattern: The specific heat capacity of quaternary system loose bed soil is generally higher than that of bedrock, and clayey soil has bigger specific heat capacity than sandy soil and pebble bed. There is a big difference in specific heat capacity between soil masses in quaternary system loose bed soil, and due to high mineral content in clay, the porosity is relatively high, so as the moisture content; therefore, its specific heat capacity is high, and that of gravel pebble is lower.This shows that silt and clay are more capable of absorbing and releasing energy, while fine sand and gravel pebble are not. Thermal diffusivity in pebbles and sandy oil are higher than that of other lithology categories.

Table 2 Thermalphysical parameters of sandy soil

There is no obvious correlation between rock type and stratigraphic age (LU Qing-zhi et al.2005). For example, the stratigraphic conditions are very complex in Guangzhou area, from overlying Quaternary system to the base of metamorphic rock in Proterozoic, more than ten strata have been successfully deposited, including Devonian system, Carboniferous system, Permian system, Triassic system, Jurassic system,Cretaceous system and tertiary system, etc.Analysis shows that most thermalphysical features of rocks are not evidently correlated with their age of deposition or formation; some rock that have been formed for long have higher thermal conductivity, to a large extent, due to the fact that they have experienced intense compaction and thus becoming denser.

These features indicate that rocks are better than soil layers in absorption of heat, while soil layers are more effective in heat storage than rocks due to higher moisture content in soil layers.Rock-soil mass with coarse particles is good at release heat but poor in accumulating heat; by contrast, rock-soil mass with fine particles is good at accumulating heat and poor in releasing heat.From the perspective of developing shallow geothermal energy, rock-soil mass layers need to be effective in heat release for the convenience of heat conduction.

2.2 Density

Density is the most fundamental physical property of rock-soil mass. It can be drawn from previous experiences that in the three-phase composition (solid, liquid and gas) of rock-soil mass, solid enjoys the greatest thermal conductivity, the next being liquid, and gas has the lowest thermal conductivity.

There is a large amount of data concerning density and thermal conductivity coefficient collected from investigation and evaluation of shallow geothermal energy in 29 provincial capital cities, among which density values are repetitive.The mean value of thermal conductivity coefficient corresponding to repetitive density values is calculated, and then a regression analysis is conducted with density values and thermal conductivity (Fig. 2) after deleting repetitive data.As a result, it is seen that density of rock-soil mass is in direct proportion to thermal conductivity coefficient, i.e. the denser the rock-soil mass is, the higher its thermal conductivity is.

Fig. 2 Correlation between rock-soil mass density and thermal conductivity

Equation of linear regression: y=1.166+0.473x

Correlation coefficient: R2=0.763

Similar to thermal conductivity, the mean value of specific heat value corresponding to repetitive density values is calculated, and the data then is screened and a regression analysis is conducted with density values and specific heat capacity (Fig.3). The results illustrate that rock-soil mass density has an exponential relation with specific heat capacity: when the rock-soil mass gets denser, the specific heat capacity declines exponentially.

Fig. 3 Correlation between rock-soil mass density and specific heat capacity

Equation of linear regression:

y=6132.542-1.411ex

Correlation coefficient: R2=0.708

When the data is analyzed according to lithology categories, it is seen that the patterns of density of rock-soil mass of all lithology categories are generally in line with the general pattern,namely, in the same rock-soil layer, the denser it is,the more compact the rock-soil mass is and the higher its thermal conductivity is; vice versa.Specific heat capacity is in inverse proportion to density. Thermal conductivity is closely related with particle composition within rock-soil mass;the more compact the particles are, the higher its mineral content and thermal conductivity performance tend to be, so as its thermal conductivity coefficient.

2.3 Moisture content

Moisture content indicates the percentage of the quality of free water content in the total quality of soil mass. There is a large amount of data concerning moisture content and thermal conductivity coefficient collected from investigation and evaluation of shallow geothermal energy in 29 provincial capital cities, among which moisture content values are repetitive. The mean value of thermal conductivity coefficient corresponding to repetitive moisture content values is calculated, and then a regression analysis is conducted with moisture content values and thermal conductivity (Fig. 4) after deleting repetitive data. As a result, it is seen that moisture content of rock-soil mass has a logarithmic relation with thermal conductivity coefficient; when moisture content goes up, thermal conductivity coefficient declines logarithmically. In Fig. 4, the high value part on the left mainly refers to rocks,with a lower moisture content compared with silt and clay, but a much higher thermal conductivity coefficient.

Fig. 4 Correlation between rock-soil mass moisture content and thermal conductivity

Equation of linear regression: y=2.945-0.81ln x

Correlation coefficient: R2=0.744

Then the mean value of specific heat value corresponding to repetitive moisture content values is calculated, and then the data is screened and singular points are removed, and next a regression analysis is conducted with moisture content and specific heat capacity (Fig. 5). The two sets of values are in power function relations: when moisture content increases, specific heat capacity goes up as well.

Fig. 5 Correlation between rock-soil mass moisture content and specific heat capacity

Equation of linear regression:

y=1116.428+x0.97

Correlation coefficient: R2=0.95

Specific heat capacity of rock-soil mass mainly depends on its air and water content. Due to the fact that the specific heat capacity of water is remarkably higher than that of air, the more moisture there is in rock-soil mass, the higher its specific heat capacity tends to be; by contrast, the more air it contains, the lower the moisture content will be, so as the specific heat capacity.

Thermalphysical parameters are not in any simple linear relation with moisture content, and the interactions between the two are restricted by other factors as lithology, density, etc. For instance,in silt and clay, the larger the void ratio is, the lower the density is, and then the moisture content is higher, the contact area within soil mass skeleton smaller, and there will be more void water passing heat, and therefore, the thermal conductivity of soil mass is low and specific heat capacity higher.

2.4 Porosity

Porosity refers to the ratio of volume of pore or void to the total volume of rock-soil mass. With lower porosity (or fracture) ratio, thermal conductivity coefficient tend to fluctuates in a wide range; porosity of loose soil usually falls in the range between 10% and 60%, and its thermal conductivity shows a generally declining trend within value range between 1.0 and 3.0, i.e. there is a negative correlation between porosity and thermal conductivity of loose soil.

There is a large amount of data concerning porosity and thermal conductivity coefficient collected from investigation and evaluation of shallow geothermal energy in 29 provincial capital cities, among which porosity values are repetitive.The mean value of thermal conductivity coefficient corresponding to repetitive porosity values is calculated, and then a regression analysis is conducted with porosity values and thermal conductivity (Fig. 6) after deleting repetitive data.As a result, it is seen that porosity of rock-soil mass has a logarithmic relation with thermal conductivity coefficient; when porosity value goes up, coefficient of heat passage declines logarithmically.

Fig. 6 Correlation between rock-soil mass porosity and thermal conductivity

Equation of linear regression: y=2.105-3.06ln x

Correlation coefficient: R2=0.601

There are two different correlations between porosity and specific heat capacity of rock-soil mass within the range between 1% and 80%: from 1% to 10%, porosity and specific heat capacity are in negative correlation, and from 2% to 80%specific heat capacity increases gradually as porosity goes up. The mean value of specific heat value corresponding to repetitive porosity values is calculated, and the data then is screened and a regression analysis is conducted with porosity values and specific heat capacity (Fig. 7). The results illustrate the correlation coefficient of linear regression is the biggest, and specific heat capacity increases as porosity enlarges.

Fig. 7 Correlation between rock-soil mass porosity and specific heat capacity

Equation of linear regression:

y=547.944+40.897x

Correlation coefficient: R2=0.802

Porosity has an important influence on thermal conductivity performance of rock-soil mass. Heat is passed through mutual contact within particle skeleton of rock-soil, the higher the porosity is, the looser the rock-soil structure tends to be, and the slower heat is conducted, and thus the thermal conductivity coefficient will be lower; on the other hand, higher porosity brings stronger water storage capacity, and thus specific heat capacity is bigger.

To sum up, in terms of stratigraphic condition,geological conditions and stratigraphic distribution of different cities vary a lot, but mostly are overlying quaternary system loose soil cover layer,and in deeper part it is underlying old-time bedrock. In this condition, lithology controls features of thermalphysical parameters: thermalphysical parameters of bedrock, pebbles, gravelly sand, coarse sand, fine sand, silt, silty clay and clay decreases accordingly, and their specific heat capacity increases accordingly. Density, moisture content and porosity affect thermalphysical parameters: The denser it is and the lower the moisture content and porosity are, the bigger the thermal conductivity is, and the smaller the specific heat capacity is; otherwise, the smaller the thermal conductivity is, and the bigger the specific heat capacity is.

3 Patterns of distribution for thermalphysical parameters

Distribution of thermalphysical parameters has their own characteristics in different provincial capital cities. In general, it is affected by factors including lithology, density, moisture content and porosity. Regarding the spatial distribution,thermal-physical parameters are restricted by stratigraphic conditions and hydrogeological conditions as well, in addition to structural factors.

3.1 Stratigraphic conditions

Thermal conductivity of rocks is generally higher than that of silt and sandy soil, so the following pattern is demonstrated in surface distribution: The thicker the underlying bedrock is and the bigger its area is, the higher the thermal conductivity in this area is, and the lower the specific heat capacity is; on the contrary, if the silt and clay are thinner and with a smaller area, then the thermal conductivity is lower and the specific heat capacity higher.

In landform it shows that areas with high thermal conductivity are usually bedrock mountainous areas or areas where bedrocks are in shallow layers, and thermal conductivity of plain areas is generally lower than that of mountainous areas. In bedrock areas, granite, dolomite,limestone and shale areas are also larger than sandstone and mudstone areas. In plain areas, river terraces and alluvial-proluvial fan areas are higher in thermal conductivity, and other layers are mainly coarse sand and gravelly sand; in eolian deposit and slope deposit areas, strata are mainly composed of clay and silty clay, and thermal conductivity in these areas is lower than that of other areas. Distribution pattern of specific heat capacity is generally opposite to that of thermal conductivity.

3.2 Hydrogeological conditions

Hydrogeological conditions include hydrodynamic power features, water quality, and water yield, etc. These factors are closely correlated with thermalphysical parameters of rock-soil mass. In most cities, distribution of thermal conductivity is in line with distribution of hydraulic gradient.Hohhot, Jinan and Haikou can be seen as examples.In Hohhot, areas with high thermal conductivity are located in plain areas in front of mountains,which are in the north of working areas, with good hydrodynamic conditions and coarse stratigraphic particles, while in the south, the plain area along the Great Heihe River is with fine particles and poor hydrodynamic conditions, and thus the thermal conductivity is low; on the same rock stratum in Jinan, the better hydrodynamic conditions are and the greater water yield is, the higher the thermal conductivity is; in Haikou, areas with high thermal conductivity are located in the north of Changliu and Haikou port in the investigated area, which serve as recharge area, while the south is higher and serve as discharge area, and the thermal conductivity gradually increases from recharge area to discharge area. Distribution pattern of thermal conductivity is generally opposite to that of specific heat capacity. This apparently shows the influence of hydrogeological conditions on thermalphysical parameters.

Main factors that affect thermalphysical parameters are hydrodynamic conditions, which are directly proportional to thermal conductivity coefficient. In areas with good hydrodynamic conditions, water yield is high, so water flow velocity is fast, which is convenient for heat conduction; while poor hydrodynamic conditions bring slow water velocity.

4 Conclusions

Features of thermal parameters are closely correlated with lithology, density, moisture content and porosity of rock-soil mass. Different testing methods lead to different results. Data collected through in-situ thermal response testing method is closer to reality. Stratigraphic lithology and hydrogeological conditions control other distribution patterns.

(1) Thermal conductivity of bedrock is generally higher than quaternary system loose soil bed. Thermal conductivity of dolomite, shale,granite is high, and that of gabbro, sandstone and mudstone is low; in loose soil, pebble and gravel have higher thermal conductivity while clay and silt have lower thermal conductivity, and as for sand, it declines as the particle size decreases. The pattern of specific heat capacity is opposite to that of thermal conductivity. Thermal diffusivity of pebble bed is higher than that of bedrock, which is higher than that of silt and clay.

(2) Density, moisture content and porosity have a significant influence over thermal-physical parameters. Thermal conductivity increases linearly as density gets higher, declines logarithmically respectively as moisture content and porosity go up;specific heat capacity declines logarithmically as density increases, and enlarges power exponentially as moisture content gets higher, and linearly decreases as porosity increases.

(3) Distribution patterns are mainly restricted by hydrogeological conditions and stratigraphic conditions: areas with good hydrodynamic conditions have higher thermal conductivity, and vice versa. Stratigraphic factors are essentially factors including lithology, density and moisture content.

Acknowledgements

This paper is supported by Development and Use of Shallow Part Geothermal Energy below the Earth Surface and Research on Geothermal Reinjection Technology, the Basic Research Funding Project (SK201501).