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Volume 16 Issue 3
Sep 2005
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Article Contents
Abstract
INTRODUCTION
HYDROGEOLOGICAL CONDITION OF GEOTHERMAL WATER IN RESEARCH AREA
ESTABLISHING A MATHEMATICAL MODEL
IDENTIFICATION OF THE MATHEMATICAL MODEL
PLANNING THE EXPLOITATION OF THE GEOTHERMAL WATER
CONCLUSIONS
References
Journal of Earth Science  > 2005  >  16(3): 262-267.
Dongyan Liu, Yunju Luo, Xinrong Liu. Mathematical Model of the Geothermal Water Resources in the South Hot Spring System in Chongqing. Journal of Earth Science, 2005, 16(3): 262-267.
Citation: Dongyan Liu, Yunju Luo, Xinrong Liu. Mathematical Model of the Geothermal Water Resources in the South Hot Spring System in Chongqing. Journal of Earth Science, 2005, 16(3): 262-267.
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Mathematical Model of the Geothermal Water Resources in the South Hot Spring System in Chongqing

  • College of Civil Engineering, Chongqing University, Chongqing 400045, China

Funds:

the Applied and Fundamental Foundation of Chongqing 8020

the Natural Science Foundation of Chongqing 102075120040022

More Information
  • Corresponding author: Luo Yunju, E-mail: Luoyunju123@163.com
  • Received Date: 28 Mar 2004
  • Accepted Date: 30 Jun 2005
    Abstract

  • The geothermal waters of south hot spring, small hot spring and Qiaokouba in Chongqing, are all part of the south hot spring geothermal water system. Exploitation has caused a decline in the water levels of the south and small hot springs, which have not flowed naturally for 15 years. Now, bores pump geothermal water to the springs. If the water level drops below the elevation of the rivers, river-water will replenish the geothermal water, destroying this resource. It is therefore an urgent task to model the geothermal water system, to enable sustainable development and continued use of the geothermal water in Qiaokouba. A numerical simulation of the geothermal water system was adoptedand a quantitative study on the planning scheme was carried out. A mathematical model was set up to simulate the whole geothermal water system, based on data from the research sites. The model determined the maximum sustainable water yield in Qiaokouba and the two hot springs, and the south hot spring and small hot spring sustainable yields are 1 100 m3/d and 700 m3/d from 2006 to 2010, 1 300 m3/d and 1 000 m3/dfrom 2011 to 2015, and 1 500 m3/d and 1 200 m3/d from 2016 to 2036. The maximum exploitable yield is 3 300 m3/d from 2006 to 2036 in Qiaokouba. The model supplies a basis to adequately exploit and effectively protect the geothermal water resources, and to continue to develop the geothermal water as a tourist attraction in Chongqing.

     

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  • South hot spring, small hot spring and Qiaokouba represent, between them, the geothermal waters of the south hot spring system in the south hot spring anticline in Chongqing. The south hot spring anticline is a geothermal water storage system. It extends from north to south in the central part of Chongqing. It is 45 km long from south to north and 2 km wide. The south hot spring and small hot spring, in the middle of the anticline, are well-known tourist attractions for their geothermal waters. Excessive exploitation led to a gradual decline in the water level of the south and small hot springs, until the water level dropped below the elevation of their outcrop. The two hot springs have not flowed naturally since the early 1990s. Currently, the south and small hot springs receive geothermal water pumped by bores, for the development of a recreation enterprise. At present, there are three developers exploiting geothermal water through the use of bores in Qiaokouba in the south of the anticline, roughly 16 km from the south and small hot springs. Geothermal water is not generally a regenerative resource and, once severely depleted, may not recover. As such, use of the south hot spring geothermal water system must be planned in order to protect the geothermal water resources effectively and avoid over exploitation.

    The use of geothermal water in Qiaokouba is causing the water level of the south and small hot springs to decline. As the geothermal water level drops, normal temperature water will replenish the geothermal water, destroying the geothermal water resources. It is therefore an urgent task to plan the geothermal water use in the south hot spring geothermal water system, to ensure that the south and small hot springs remain sustainable, while at the same time the geothermal water can be rationally exploited and utilized in Qiaokouba.

    The topography of the south hot spring anticline is one of "hill parallel to valley". The mountains extend in accordance with the axis of the anticline, and the axis extends in an NNE direction. The Yangtze River is to the north of the south hot spring anticline (the water level of the river is 167 m), the Huaxi River runs through the middle of the anticline (water level is 209.5 m), and the Qingshui River is to the south (level is 200 m). The rivers run from east to west. The Huaxi and Qingshui rivers eventually join the Yangtze River. The rivers' water level is lower than the geothermal water level and the rivers do not replenish the geothermal water. There is no hydrodynamic relationship between the normal temperature water and the geothermal water. There are three outcrops of geothermal water: the Zimushan hot spring in the north, the small and south hot springs in the center, and Qiaokouba hot springs in the south (Fig. 1).

    Figure  1.  The hydrogeological sketch of south hot spring anticline.
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    From the axes of the anticline to both of its limbs, there is, by turn: mudstone and marlite of the Lower Triassic Feixianguan Formation (T1f), the Jialingjiang Formation (T1j), the first stratum (T1j1) limestone, the second stratum (T1j2) limestone, dolomite rock and salt-soluble breccias, the third stratum (T1j3) mainly of dolomite rock and dolomite-limestone, the fourth stratum (T1j4) dolomite rock; the dolomite of the Middle Triassic Leikoupo Formation (T2l) and sandstones of the Upper Triassic Xujiahe Formation (T3xj) (Figs. 1-2). The Quaternary formations (Q) are mudstones on both sides of the Huaxi River or over the T1j stratum. T1j and T2l are aquifers. T1j2 is the main aquifer; T1j1 is the second aquifer; T1j3, T1j4 and T2l are aquitards. The T1f stratum in between the T1j stratum of the limbs of the anticline is a pervious bed; another T1f is a confining stratum in a pervious bed; the remaining T1f is a confining stratum (li, 1987).

    Figure  2.  The geological section from small hot spring to south hot spring.1.mudstone; 2.limestone; 3.salt-soluble breccia; 4.marlite; 5. limestone-dolomite; 6. dolomite; 7. bore; 8. hot spring; 9. Huaxi River.
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    The geothermal water in the research area is brackish water containing SO4-Ca or SO4-Ca·Mg with a total salinity of 2.16-2.62 g/L and a pH value of 7.6-7.7. The karst outcrops in the south hot spring anticline are not large-scale, and are replenished by precipitation. The geothermal water comes primarily from precipitation through the recharge area on the outcrop of the karst area in the north of the Tongluoxia anticline. The Tongluoxia and south hot spring anticline are uniform. The precipitation is heated at 2 000 m depth in the T 2l+T1j strata of the Tongluoxia anticline, and becomes the geothermal water (Hadzisehovic and Dangic, 1995; li, 1987). The geothermal water flows from north to south, pouring into the south hot spring anticline at its north end and flowing to the middle (south and small hot springs).

    The burial depth of T1j+T2l is shallow, and dip is slight, so the geothermal water temperature is steady at about 45 ℃, and the flow is a horizontal planar flow (Luo and Zeng, 1991).

    Generalizing Model

    The aquifer of stratum (T2l +T1j) is generalized to be a confined aquifer. The T1f stratum in between the T1j stratum of the limbs of the anticline is a pervious bed; the other T1f stratum is impervious. T3xj and Q are over T2l + T1j, and there is no precipitation replenishment of the geothermal water, so T3xj and Q are the ceiling of the aquifer. The boundaries between the T2l+T1j and T3xj strata are boundaries excluding water on both sides and the south end of the south hot spring anticline. The geothermal water comes from the Tongluoxia anticline into the northern end of the south hot spring anticline. The geothermal water has not been exploited in the northern end, so the northern end is the boundary of the fixed head. The geothermal water flows from north to south in the south hot spring anticline, its hydraulic gradient is 0.16 %-0.38 %, and it is medium-low, constant temperature geothermal water, regarded as a liquid during calculation (Grassi et al., 1994).

    A Mathematical Model

    Because the hydrogeological conditions are complicated, inhomogeneous and anisotropic, a finite element numerical simulation was adopted in order to reflect the hydrogeological features in the area. The geothermal water resource was quantitatively studied to plan for sustainable exploitation, and the finite element mathematical model was established. The model is expressed as equations (1) to (4)

    		 (1)

    		(2)

    		(3)

    		(4)

    where H is the hydraulic head, m; kxx, kyy are values of the coefficient of conductivity through the unit volume along the x, y coordinate axes, m/d; H0 is the initial hydraulic head, m; H1 is the hydraulic head of boundaries of varying head (the first boundary B1), m; q is the supplement of boundary of constant head (the second boundary B2), m3/d; m is aquifer thickness, m; w is a volumetric flux per unit volume and represents internal sources of water, m3/d; μ is the storage coefficient, m-1; Ω is field of seepage; and n is the outside normal direction of seepage boundary (Chen and Tang, 1997).

    The research area was divided into 266 cells and 282 nodes; the cells on the north end were the constant head boundary. In order effectively to calibrate the model, there were 3 observation points in all 6 bores. There are three bores in the small hot spring area on the east limb of the anticline, two bores in the south hot spring area on the west limb, and Nan'er bore in Qiaokouba. Their actual water levels were compared with the simulated water levels and used to modify the model. However, because the bores are old and damaged, normal temperature water has been infiltrating through to all six bores. There is a little infiltration in the south hot spring ZK1 bore; however the water level of this bore better reflected the variation of the geothermal water level, so it was selected as the point where the simulated water level was contrasted with the actual one.

    On the basis of the mathematical model established using the parameters above, the geothermal water seepage field from 1991 to 1995 was accurately simulated. The simulated water level was compared with data from the ZK1 bore, and then the hydrogeological parameters kxx and kyy were adjusted up or down by 0.05 and 0.1, modifying the model. An accurate mathematical model was acquired when the simulated water level approximated the actual water level (Olowoker and Nwosu, 1997). The parameters μ and initial kxx and kyy adopted in this simulation came from counting and analyzing pumping test data. The pumping test data came from an experiment of single bore and group bores pumping test.

    The area was divided into four partitions according to experiment of pumping test and the characteristics of the aquifer. T2l+T1j3+4 are the first partition, T1j2 is the second partition, T1j1 is the third partition, and T1f is the fourth partition. The initial water level came from the monitored bores, and from counting the hydraulic gradient. The simulated water level was compared with the actual one (Fig. 3). Because the normal temperature water had infiltrated through to the geothermal water in the south hot spring, the actual water level fluctuated. The numerical simulation does not take into account the infiltration, so the simulated water level does not fluctuate; however, the simulated water level approximates the actual one. It shows that the parameters are in accordance with the actual parameters (Table 1), and the mathematical model is accurate.

    Figure  3.  Comparison of simulated water level with actual level on south hot spring ZK1 bore.
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    Table  1.  The hydrogeological parameters
     | Show Table
    DownLoad: CSV

    Natural Replenishment

    The geothermal water flows from north to south in the T1j+T2l stratum. The natural replenishment is the runoff volume, and is defined as equation (5)

    		 (5)

    where Q is the natural replenishment, m3/d; F is the width of the section of geothermal water flowing in the T1j+T2l stratum on the north of the anticline, m; J is the natural hydraulic gradient; Ty is coefficient of transmissibility of parallel to layers of strata (li, 1987), m2/d. The natural replenishment is therefore: Q=1 048×1 807.5×0.35 %=6 629.91 m3/d.

    Zimushan is another hot spring in the north of the anticline, but the Zimushan hot spring is a bore of geothermal water. The bores are mostly used to observe geothermal water flux and level. The seepage field of the south hot spring geothermal water system controls the flux of the Zimushan hot spring bore. The flux of the Zimushan hot spring controls downriver exploitation of south and small hot springs, and Qiaokouba, ensuring sustainable use. Also, the geothermal water of Zimushan hot spring can be utilized.

    The Budget of Yield

    In order to protect the geothermal water resources, it is necessary to ensure that the south and small hot springs can be sustainably developed and the geothermal water reasonably exploited. It is also important to avoid over exploitation, which would cause a decline in the geothermal water level below that of the river water, causing river water to replenish the geothermal water, thus destroying the resource (Kamil and Abdullah, 2004). The mathematical model was adopted to simulate the geothermal water seepage of the south hot spring system, and provide a quantificational study of the planning scheme, which ensures the sustainable development of the south and small hot springs; at the same time, the geothermal water can be exploited and utilized rationally in Qiaokouba. For this purpose, the maximum yield in Qiaokouba and sustainable yields from the south and small hot springs were determined.

    At present, the south hot spring yield is 1 000 m3/d and the small hot spring yield 700 m3/d. With the improvements in living standards and more and more demands on tourism development, the geothermal water being removed from the bores is sharply increasing. South hot spring and small hot spring must increase their yields by 2010. The tourist site environment will reach maximum saturation, the person-time also can not increase without limit, and so tourism development should be controlled to a certain degree so as to realize sustainable environmental development. From the analysis of the tourist condition of south hot spring and small hot spring, the yields will increase by 300 m3/d, reaching 1 300 m3/d at south hot spring and 1 000 m3/d at small hot spring, from 2011 to 2015; the yields will increase by 500 m3/d, reaching 1 500 m3/d at south hot spring and 1 200 m3/d at small hot spring from 2016 to 2036 (Manologlou et al., 2004).

    The yields of the south hot spring and small hot spring are 1 000 m3/d and 700 m3/d from 2006 to 2010, 1 300 m3/d and 1 000 m3/d from 2011 to 2016, and 1 500 m3/d and 1 200 m3/d from 2016 to 2026 respectively. The water levels refer to Table 2 in 2036.

    Table  2.  The geothermal water levels in 2036
     | Show Table
    DownLoad: CSV

    Table 2 shows the highest possible sustainable yield is 3 300 m3/d. When the yield is 3 300 m3/d; the lowest water level is 200.3 m, which is 0.3 m higher than the Qingshui River water level in Qiaokouba; it is 209.82 m and 209.57 m in small hot spring and south hot spring, which is 0.39 m and 0.07 m higher respectively than the Huaxi River water level. If the yield is higher than 3 300 m3/d, the lowest water level will drop below the rivers' water level. The river water will then replenish the geothermal water, affecting the quality and changing the temperature, destroying the geothermal water resources. So the yield in Qiaokouba must be less than 3 300 m3/d.

    The yield is 3 300 m3/d, the variety of water level refers to Fig. 4. Figure 4 shows the water level trending towards stabilization in 2026, and steady in 2036. If the geothermal water continues to be exploited at or below this level, the water levels will not decline, and will remain higher than the river water.

    Figure  4.  The variation map of water level of the 3 300 m3/d yield of exploitive bore in Qiaokouba.
    DownLoad: Full-Size Img PowerPoint

    The seepage field is steady in 2036 (Fig. 5). Here, the water levels of south hot spring, small hot spring and Qiaokouba are higher than the river levels they border upon. The geothermal water level is 220 m in the north of the anticline; which is also higher than the Yangtze River water level (167 m). There is steady draw down seepage field from south and small hot springs to Qiaokouba. Because these geothermal waters influx into the south end of the anticline, there is no steady draw down seepage field from the exploitive bore to the end of the anticline; and the field will become the cone of depression. This shows that the geothermal water exploited in Qiaokouba influences the water level of the south and small hot springs, and thus the whole geothermal water system. So the yield of exploitive bore in Qiaokouba must be less than or equal to 3 300 m3/d.

    Figure  5.  The geothermal water seepage field with 3 300 m3/d yield of exploitive bore in 2036.
    DownLoad: Full-Size Img PowerPoint

    The south hot spring, small hot spring and Qiaokouba exploitive well represent the whole geothermal water system. Every exploration of geothermal water use throughout the system should take into account sustainable exploitation. From the simulation, the plan is that the south hot spring and small hot spring sustainable yields are 1 000 m3/d and 700 m3/d from 2006 to 2010, 1 300 m3/d and 1 000 m3/d from 2011 to 2016, and 1 500 m3/d and 1 200 m3/d from 2016 to 2036. The maximum yield of the exploitable well in Qiaokouba is 3 300 m3/d from 2006 to 2036. Adopting these amounts will ensure that the geothermal water resources will be exploited reasonably and adequately, and will effectively protect the geothermal water resources.

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