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Volume 28 Issue 1
Feb.  2017
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Spatial Variation of Hydraulic Conductivity Categories in a Highly Heterogeneous Aquifer: A Case Study in the North China Plain (NCP)

  • Compared with research on spatial variation of hydraulic conductivity (K), less effort has been made researching different grades of K value in the North China Plain (NCP). In this study, 3D spatial distribution models of different grades of K were established by considering the effects of clay fraction content and uniformity coefficient (Cu). The K value can be divided into five grades: very low, low, permeable, high, and very high groups. The volume percentages of these clusters were 3.06%, 36.01%, 55.70%, 4.82%, and 0.41% for the first aquifer; 0.016%, 9.56%, 88.25%, 2.16%, and 0.014% for the second aquifer; and 0.04%, 17.74%, 84.21%, 0.001%, and 0.01% for the third aquifer. It is concluded that the high and very high K values are fully affected by burial depth and that the very low, low, and permeable K values are mainly controlled by depositional environment and are partially influenced by burial depth. The burial depth became the main influencing factor only within the same depositional environment, causing the overall K to decrease with depth. The variations of very low, low, permeable, high, and very high categories of K values with depth are described in this study. This can provide useful information for non-technical decision makers to achieve sustainable development of deep groundwater resources.
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    [3] DesRoches, A. J., Butler, K. E., Pelkey, S., 2012. Influence of Fracture Anisotropy and Lithological Heterogeneity on Wellfield Response in a Fluvial Sandstone Aquifer of the Carboniferous Moncton Subbasin, Canada. Hydrogeology Journal, 21(3): 559-572. doi:10.1007/s10040-012-0931-6
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    [8] Gégo, E. L., Johnson, G. S., Hankins, M., 2001. An Evaluation of Methodologies for the Generation of Stochastic Hydraulic Conductivity Fields in Highly Heterogeneous Aquifers. Stochastic Environmental Research and Risk Assessment, 15(1): 47-64. doi:10.1007/s004770000060
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    [10] Giambastiani, B. M. S., McCallum, A. M., Andersen, M. S., et al., 2012. Understanding Groundwater Processes by Representing Aquifer Heterogeneity in the Maules Creek Catchment, Namoi Valley (New South Wales, Australia). Hydrogeology Journal, 20(6): 1027-1044. doi:10.1007/s10040-012-0866-y
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    [25] Post, V. A., Simmons, C., 2010. Free Convective Controls on Sequestration of Salts into Low-Permeability Strata: Insights from Sand Tank Laboratory Experiments and Numerical Modelling. Hydrogeology Journal, 18(1): 39-54. doi:10.1007/s10040-009-0521-4
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    [27] Ronayne, M. J., Houghton, T. B., Stednick, J. D., 2012. Field Characterization of Hydraulic Conductivity in a Heterogeneous Alpine Glacial Till. Journal of Hydrology, 458/459: 103-109. doi:10.1016/j.jhydrol.2012.06.036
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    [31] Sakata, Y., Ikeda, R., 2013. Depth Dependence and Exponential Models of Permeability in Alluvial-Fan Gravel Deposits. Hydrogeology Journal, 21(4): 773-786. doi:10.1007/s10040-013-0961-8
    [32] Schultz, G., Ruppel, C., 2002. Constraints on Hydraulic Parameters and Implications for Groundwater Flux across the Upland-Estuary Interface. Journal of Hydrology, 260(1-4): 255-269. doi:10.1016/s0022-1694(01)00616-3
    [33] Schön, J. H., 1996. Physical Properties of Rocks-Fundamentals and Principles of Geophysics. In: Helbig, K., Treitel, S., eds., Handbook of Geophysical Exploration-Seismic Exploration. Pergamon, London. 583
    [34] Shao, J. L., Cui, Y. L., Hao, Q. C., et al., 2014. Study on the Estimation of Groundwater Withdrawals Based on Groundwater Flow Modeling and Its Application in the North China Plain. Journal of Earth Science, 25(6): 1033-1042. doi:10.1007/s12583-014-0493-8
    [35] Shi, J., Li, Y., Zhang, Y., et al., 2011. The Program Designitation of Spontaneous Potential Application in Water Resistivity Estimation. World Well Logging Technology, 4: 36-50 (in Chinese with English Abstract)
    [36] Slater, L., 2007. Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries-A Review. Surveys in Geophysics, 28(2/3): 169-197. doi:10.1007/s10712-007-9022-y
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Spatial Variation of Hydraulic Conductivity Categories in a Highly Heterogeneous Aquifer: A Case Study in the North China Plain (NCP)

    Corresponding author: Jiansheng Shi, tiger7886@gmail.com
  • 1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
  • 2. Institute of Hydrogeology and Environmental Geology, Shijiazhuang 050061, China
  • 3. China Geological Survey, Beijing 100037, China

Abstract: Compared with research on spatial variation of hydraulic conductivity (K), less effort has been made researching different grades of K value in the North China Plain (NCP). In this study, 3D spatial distribution models of different grades of K were established by considering the effects of clay fraction content and uniformity coefficient (Cu). The K value can be divided into five grades: very low, low, permeable, high, and very high groups. The volume percentages of these clusters were 3.06%, 36.01%, 55.70%, 4.82%, and 0.41% for the first aquifer; 0.016%, 9.56%, 88.25%, 2.16%, and 0.014% for the second aquifer; and 0.04%, 17.74%, 84.21%, 0.001%, and 0.01% for the third aquifer. It is concluded that the high and very high K values are fully affected by burial depth and that the very low, low, and permeable K values are mainly controlled by depositional environment and are partially influenced by burial depth. The burial depth became the main influencing factor only within the same depositional environment, causing the overall K to decrease with depth. The variations of very low, low, permeable, high, and very high categories of K values with depth are described in this study. This can provide useful information for non-technical decision makers to achieve sustainable development of deep groundwater resources.

0.   INTRODUCTION
  • A better understanding of hydraulic properties such as transmissivity (T), storativity (S), porosity (P), and hydraulic conductivity (K) is a prerequisite for solute transport, managing groundwater resources, and designing remediation measures (Tayfur et al., 2014). Among the various chemical and physical properties, K is one of the most important properties of a hydrogeological system, and developing an adequate understanding of K has remained one of the fundamental challenges to hydrogeology researchers (Gueting and Englert, 2013). It is highly correlated to the surface water infiltration and runoff, groundwater recharge, site monitoring, as well as the movement of dissolved contaminants in aquifers. However, for a proper description of groundwater flow and contaminant migration, an estimate of the K value at the aquifer scale is insufficient (Qian et al., 2009). Accurate knowledge is also required of the spatial distribution of K which is caused by various geological processes, such as deposition, dissolution, erosion, and faulting. During the past a few decades, K heterogeneity has attracted worldwide attention. Soltani et al. (2008) reported that K heterogeneity strongly influenced physical dispersion and the characteristic shape of effluent profile. Compared with the homogeneous K field, researchers concluded that different distributions of K can result in a 41% increase in the average time to compliance for pump and treat remediation (Güngör-Demirci and Aksoy, 2010). Post and Simmons (2010) used sand tank experiments and numerical models to investigate the influence of K heterogeneity on the solute transport process, and they indicated that salinization was rapid and occurred predominantly by free convective flow around the low K region. Gueting and Englert (2013) investigated the impact of K on plume behavior at the source zone and found that tracer injection into high K zones caused early arrival, and enhanced transverse and reduced longitudinal spreading. They also reported that tracer injection into low K regions caused late arrival, and reduced transverse and enhanced longitudinal spreading. The spatial variation of K is of such importance to the evaluation of groundwater resources that numerous researchers have attempted to characterize the spatial variation of K using various methods, including zonal methods, geo-statistical representation, moment equation methods (MEM), Monte Carlo simulation methods (MC), inverse methods, and ensemble Kalman filter methods (EnKF) (Jardani et al., 2013; DesRoches et al., 2012; Min et al., 2012; Boschan and Nœtinger, 2012; Ronayne et al., 2012; Tong et al., 2012; Straface et al., 2011; Zhang et al., 2011; McArthur et al., 2010; Ouellon et al., 2008). These studies have found that K values can vary in space, time, and flow direction with maximum values over 6 orders of magnitude larger than minimum values (Dewandel et al., 2012; Giambastiani et al., 2012; Gégo et al., 2001). At the opposite, porosity and other hydrogeological parameters do not exhibit such a broad range of variation. Therefore, it is widely recognized that understanding flow and transport in low and high K regions is crucial for a proper description of the internal properties of a groundwater system. Understanding the impact of low K values is essential for geological disposal of toxic waste and groundwater resources evaluation (Soltani et al., 2008). For example, Huysmans and Dassargues (2012) demonstrated that the aquifer response to groundwater extraction was mainly affected by a low K value, and Rübel et al. (2002) indicated that low K media can limit the renewal rate of deep groundwater resources and thus water supply. More importantly, regions with low K values are usually selected for landfilling of industrial waste. High K regions are the main transport pathway of pollutants, where exact knowledge is important in solving a number of environment geology problems.

    On the other hand, the groundwater supply from shallow aquifers is insufficient or unsuitable to support current local water demand for drinking, irrigation, and industry due to the growing pressure of urban populations and industrial development. Deep groundwater has become the main source of water supply for large cities and towns. To achieve sustainable development of deep groundwater resources in the North China Plain (NCP), more information is needed on the variation of K with depth. Sakata and Ikeda (2013) investigated the depth dependence of K in various depositional environments. Jiang et al. (2009) revealed that K decreased exponentially or logarithmically with depth and that decay exponents varied on the order of 10-2 to 10-4 at specific sites; Saar and Manga (2004) employed four methods to describe the remarkable variation of K with depth for different depth scales. However, to the authors’ knowledge, few similar studies have been conducted for variation of different categories of K with depth.

    Therefore, the aim of this paper is to describe the spatial distribution of different grades of K value for three different aquifers, respectively. In the prior literatures (Genereux et al., 2008; Tijani and Nton, 2008), K values have been typically classified into five different grades: very low (-∞, 0.001 m/d], low (0.001, 0.1 m/d], permeable (0.1, 10 m/d], high (10, 100 m/d], and very high (100, +∞ m/d). It is well known that K is not only a function of the grain shape, porosity, water content, tortuosity, and specific surface, but also depends on the clay fraction content, uniformity coefficient (Cu), and geochemical composition (Vienken and Dietrich, 2011). Numerous studies indicated that lower clay fraction content and Cu values are the necessary conditions for higher K value compared to other influencing factors (Doro et al., 2013; Tijani and Nton, 2008). Therefore, the clay and Cu values were used to identify the high and very high K values from its 3D spatial distribution model, which is established using the geo-statistical methods.

    Water quality in the NCP is slowly reaching an alarming stage due to the intense development of industrial and urban areas which is resulting in a variety of environmental and ecological problems, including the expanding of desertification in arid areas, groundwater contamination, saline intrusion, and land subsidence. Based on the considered influences of clay fraction content and Cu on higher K value, the spatial variation of the very low, low, permeable, high, and very high K values of a pediment region of the NCP was characterized. This study can provide information for developing policies to protect deep groundwater resources and for understanding the exchange of water and pollutants between surface and surrounding groundwater systems.

    Based on the above analysis, the remainder of this article is organized as follows: Section 1 describes the proposed method and study area in detail, the dependence of different grades of K with depth is presented and discussed in Section 2, and Section 3 provides concluding remarks

1.   MATERIALS AND METHODS
  • The study area is located in the NCP between latitudes 37°43′N-37°52′N and longitudes 114°31′E-114°39′E, with a total area of 240 km2. The region is characterized by a semi-arid continental climate; the average annual temperature is 11-14.5 ℃, and the summer maximum and winter minimum are 39.8 and -26.2 ℃, respectively. The annual precipitation ranges from 400 to 800 mm. This region belongs to the hydrogeological unit of Taihang Mountain pediment, from the top to the bottom, the Quaternary systems can be divided into three subzones according to the lithologic properties, geological age, and depositional sequence: the Hutuo River alluvial-pluvial fan, the Huaisha River alluvial-pluvial fan, and the Xiao River alluvial-pluvial fan. The study area contains three aquifer systems. The first aquifer was formed in the Late Pleistocene, and mainly contains silt clay, silt, silt sand, and fine sand grains. Surface water hydrology in this region is represented by the Xiao River. The first aquifer has a close hydraulic connection with the surface water, and therefore the Xiao River and precipitation are the main sources of recharge for this aquifer. Groundwater pollution in this aquifer is so serious that it is unsuitable for drinking and irrigation purposes. Second aquifer is the current main exploitation sector with a floor burial depth of 70-90 m. The third aquifer is confined aquifer with depths varying from 105 to 120 m (Shao et al., 2014). Compared to the first aquifer, the second and third aquifers were formed in the Middle Pleistocene, their grain sizes are larger, and the lithology mainly includes silt, silt sand, fine sand, and medium sand. The climate of study area is characterized by the continental semi-arid, and the aquifers are dominated by fluvial deposits with a complex multi-layered framework. More noteworthy, serious environmental problems such as seawater intrusion, saline connate water invasion into fresh groundwater, and land subsidence are caused by the rapid growth of groundwater. Therefore, the climate condition, depositional facies, and hydrogeology condition of study area are typical in the North China, which can help in generalization of the finding results of this study.

  • Forty-two boreholes were drilled in the study area for collecting depositional samples (Fig. 1). Between 2010 and 2012, core samples from these boreholes were collected with split-spoon samplers with rotary drill rigs. Out of 42 boreholes, 28 ones had depths of approximately 120 m and the remaining had depths of 220 m. A large body of geophysical log data were collected from 42 locations including spontaneous potential (SP), natural gamma (NG), and apparent resistivity (AR). The cores from the boreholes were split into two halves, with one half taken for sampling purpose and the other half being retained. Before sampling, drill mud should be removed from the split core surface using a clean knife to eliminate contamination on grain size analysis. Therefore, a total number of 4 072 core samples, 0.1 m long, were collected from these boreholes at depths based on changes in grain size. The grain size distributions of these samples were tested using the Malvern-Mastersizer 3000.

    Figure 1.  Study area and sample locations.

  • In order to characterize the spatial distribution of different grades of K, three steps were involved in this paper. The first step was to calculate the K values of the 4 072 core samples collected from the study area. There have been many approaches used to determine the K values, some of which have been in use since the nineteenth century. These available methods can be divided into three main types: in-situ tests (pumping test, slug test, tracer test, direct-push methods, and heat-transport test), laboratory tests (grain size method and permeameter testing), and other methods (geophysical well logging, visual assessment, and inverse numerical modeling) (Tayfur et al., 2014; Pliakas and Petalas, 2011). Each method has its own advantages and disadvantages. The pumping test has proven to be the most reliable method for determining K value; however, this method is relatively expensive and mainly dependent on the geometry and hydraulic boundaries of the study area (Slater, 2007). Although costs of the slug test are fairly low, it can only be used to estimate K values in the vicinity of a single well. Grain size methods are relatively quick and inexpensive and numerous measurements can be made at many locations; however, it can not evaluate the anisotropy of K values because the depositional structure is destroyed during sampling; geophysical well logging methods are strongly affected by various factors, such as aquifer lithology, material source and type of cementation, fluid properties, and borehole conditions, which can lead to uncertainty in estimated K value.

    A large number of grain size distribution, SP, and AR data were available, providing a foundation for applying grain size methods to determine K values. Therefore, the Kozeny-Carman-Bear equation (Soupios et al., 2007) was selected to estimate K values for this paper.

    where K is the hydraulic conductivity value, d is the average grain size diameter (μm), δw represents the fluid density (0.998 2 g·cm-3 at 20 ℃), μ is the dynamic viscosity (0.019 g·cm-1·s-1 at 20 ℃), and g denotes the acceleration of gravity (980 cm·s-2), φ represents the porosity value of sample (Khalil and Santos, 2011).

    The φ that is required in Eq. (1) and was calculated using Archie’s law (Soupios et al., 2007), which is only valid in clay free medium saturated with water and relates bulk resistivity, porosity, and the resistivity of the fluid within the pores according to Eq. (2)

    where Ro represents the bulk resistivity of the rock in the undisturbed zone (Ω·m), Rw denotes the fluid resistivity (Ω·m), m is known as the cementation factor, and a is a factor depending on lithology (Khalil and Santos, 2011), for a clay-free medium, the ratio of Ro/Rw is known as the intrinsic formation factor, Fi.

    In this work, the values of the coefficients a and m were obtained from previous studies (Soupios et al., 2007; Schön, 1996), bulk resistivity Ro was derived from AR data, and SP data were converted to fluid resistivity Rw using the Eqs. (3) and (4) (Shi et al., 2011; Sun and Chu, 1992), and these two values were used to calculate the Fa for each depth.

    where E is SP value of each core sample, S denotes diffusion and absorption electromotive coefficient (-67.6 at 20 ℃), Fa (the ratio of Ro to Rw) denotes the apparent formation factors, and Rm is the mud resistivity, which was calculated using a theoretical formula Eq. (5).

    where Rst is the standard value of mud resistivity at 18℃ (equal to 2.87 Ω·m), and T is the temperature of mud. Let the mud temperature be equal to 20 ℃ in this region, and therefore the Rm value is equal to 2.74 Ω·m.

    The three aquifer systems of the study area are comprised of silt clay, silt, silt sand, fine sand, and medium sand. Previous studies demonstrated that Archie’s law is only valid for clay-free and clean sediments and that the clay effect needs to be removed to estimate the Fi and φ. In order to estimate K values of core samples, an additional corrective step for clay content was required. For this reason, the Waxman-Smits model was considered (Waxman and Smits, 1968), and their equation is as follows

    where the BQ coefficient is associated with the influences of surface conduction. When no clay particles exist, the Fa becomes equal to the Fi. When (1/Fa) is drawn versus (Rw), the relation will theoretically result in a straight line, and 1/Fi represents the intercept of the straight line, their slope is denoted by the value BQ/Fi (Devarajan et al., 2006).

    Currently, the K value of each sample can be predicted using Eqs. (1)-(6) with the grain size distribution and geophysical logging data. It has been acknowledged by different studies that K is a complex function of grain shape, water content, porosity, soil structure, depth, and clay particles, however, these influencing factors play a different role in K distribution. Some authors reported that the effects of porosity on K can be neglected compared to other factors, the empirical formulas do not employ the porosity value to calculate K (Vienken and Dietrich, 2011; Winter and Disse, 2010). Sakata and Ikeda (2013) revealed exponential decay in K with depth in the mid-fan above 30 m depth, however, this vertical decreasing trend was not observed in the fan toe. The clay fraction content and Cu have an especially significant influence upon high K values. Numerous studies have proven that lower clay fraction content ( < 6%) and Cu ( < 10) are the necessary conditions for high K values ( > 10 m/d) (Doro et al., 2013; Zhang et al., 2006; Zhu et al., 2005). Therefore, the second step was to establish 3D spatial distribution models of K, clay fraction content, and Cu using the Sequential Gaussian Simulation (SGS) method (Monjezi et al., 2011), which were employed to select the high K value.

    The SGS method was applied to establish the 3D spatial distribution models of three parameters in the study area because of its ability to produce conditioned random-correlated fields of parameters in a Bayesian statistical framework. Since the early 1990s, the SGS method has gained popularity due to its simplicity, flexibility, and reasonable CPU time (Deutsch and Journel, 1998). To keep the length of this paper, the computation process of the SGS algorithm is not discussed. Detailed information can be obtained in the prior literatures (Karacan et al., 2012; Ma et al., 2012; Yunsel, 2012; Monjezi et al., 2011).

    The final step was to classify the K values into five different grades. The classification process was performed as follows.

    (1) The 3D spatial distribution model was divided into 312, 500 square elements. The grid spacing is 100 m in both X and Y directions, the spacing in the Z direction was highly dependent on the thickness of the three aquifers; xi represents the ith (i=1, 2, …, m, m=312, 500) square element, which had three calculated values, namely clay fraction content, Cu, and K.

    (2) Divided the K value of xi element into one of five different grades via four threshold values, i.e., 0.001, 0.1, 10, and 100 m/d.

    (2.1) If the K value of the xi element was less than 10 m/d, then it would be classified into the very low (-∞, 0.001 m/d], low (0.001, 0.1 m/d] or permeable (0.1, 10 m/d] group according to the K value.

    (2.2) If the K value of the xi element was 10-100 m/d and clay fraction content < 6% and Cu < 10, then it was classified into the high group (10, 100 m/d]. If the clay fraction content or Cu condition was not met, then it was placed in the permeable cluster.

    (2.3) If K value of the xi element was greater than 100 m/d, only it simultaneously satisfies these two necessary conditions as well as high groups, and then it would be classified into very high (100 m/d, +∞) cluster; otherwise it was included into the permeable group.

    (3) Advance to the xi+1 element.

2.   RESULTS AND DISCUSSION
  • Based on the above analysis, the workflow to characterize the spatial distribution of different grades of K values in the study area involves the following steps. The first step was to estimate the K value of each sample using Waxman-Smits model and Kozeny-Carman-Bear equation according to grain size, AR, and SP data. The Rw and Ro values of each sample were obtained according to Eqs. (3) and (4), which can be employed to calculate Fi using Eq. (6). The reciprocal of the calculated apparent formation factor (1/Fa) and its corresponding Rw values for the different depth are plotted in Fig. 2 for both sand and clay layers.

    Figure 2.  Linear regression line between (1/Fa) and (Rw) at different deep layer.

    From Fig. 2, it is clear that the relation between 1/Fa and Rw was characterized by a straight line. The intrinsic formation factor (Fi) varies between 0.22 and 18.18 as calculated from intercept values in Fig. 2. Through a similar method, the Fi values of core samples at different depths were obtained and were used to estimate porosity values via the most widely used modified form of Archie’s law. Subsequently, the K values of 4 072 samples were determined via the Kozeny-Carman-Bear equation.

    Figure 3 illustrates the grain size distribution, SP, AR, porosity, calculated K values, and measured K values of borehole S6 with depths from 25 to 120 m. It can be seen from this figure that the selected borehole was installed in an aquifer composed of fine sand and medium sand. The estimated porosity increased during burial from initial values of about 0.22 near the surface to values greater than 0.42 at approximately 85 m burial depth, which is inconsistent with conventional knowledge. A large body of papers has reported that porosity decreases with depth due to increased compaction and other physical or chemical effects. However, the shallow stratum of borehole S6 was formed by an alluvial-pluvial fan toe of several rivers, the sorting of these samples is poor, and the pore space between coarser sediments is filled by small size particles which cause a lower porosity value. In contrast, the deep stratum of S6 was only composed of Hutuo River alluvial-pluvial fan. These samples are better sorted and their grain size is larger, and therefore their porosity values are higher.

    Figure 3.  The log, grain size, K, and porosity values showing the multiple layer aquifer system in the study area. K1 is the hydraulic conductivity values determined by grain size method, K2 is the hydraulic conductivity values measured by permeability tests, P denotes the porosity values of samples, SP represents the spontaneous potential value, AR denotes apparent resistivity value, d50 is the average grain size diameter (μm).

    The K1 varied in the range of 3.20 to 73.20 m/d with an average value of 23.52 m/d for this borehole. In order to verify the accuracy of the Kozeny-Carman-Bear equation, twenty-five core samples with depth from 25 to 120 m were collected to carry out the laboratory permeability tests, their values ranged from 0.02 to 28.9 m/d with a mean value of 12.80 m/d. The K2 values obtained from permeability tests is a factor of two of K1, and they have the similar variation with depth. The K1 values determined by grain size method are reasonable for this paper. In addition, it is observed that the K1 and grain size diameter is more sensitive to depth than porosity, reflecting that the trend of rock properties with depth can be more easily identified through K1 and grain size diameter. Although the K values determined from grain size have been used for geotechnical problems as well as for the protection of groundwater resources, a variety of application limits exist. The values of K determined from grain size analysis reflect neither horizontal nor vertical aquifer properties due to sediment structure are destroyed during sediment sampling (Song et al., 2010). K values from grain size, pumping tests, slug tests, and laboratory permeability tests are substantially different, Schultz and Ruppel (2002) argued that K determined from pumping tests accounted for groundwater flow averaged over a larger scale (4-50 m), whereas that determined from grain-size analysis represented the permeability of sediments averaged over a small scale (∼0.1 m). In this paper, K estimates from laboratory permeability tests with TST-55 represented static properties of sediments averaged over a very small scale (~0.04 m), and therefore its value slightly smaller than K value estimated by grain size method. In addition, with respect to the different depositional environment and sediment samples, the accuracy of grain size methods is different. Rosas et al. (2013) identified the most effective grain size method for several depositional environments such as beach, dune, and offshore; Cheong et al. (2008) demonstrated Beyer’s equation is adequate for determining K of very fine sand, while Sauerbrei’s equation can be used for determining K of sand and sandy clay. Therefore, the depositional sequence and sediment sample must be understood carefully before determining K values from grain size method.

    Currently, the clay fraction content, Cu, and K values of each core sample were obtained. Therefore, the second step was to establish 3D spatial distribution models of these parameters. A statistical summary of these parameters for this paper is presented in Table 1.

    Aquifer Variables Max Min Mean Stand dev Range of variogram (m) Sig
    First aquifer Clay fraction content (%) 29.16 0.02 11.76 5.05 1 629 < 0.05
    Cu 31.06 2.77 5.93 3.86 1 011 < 0.05
    K (m/d) 359.73 0.000 1 7.89 47.28 154 < 0.05
    Second aquifer Clay fraction content (%) 39.28 0.23 14.41 6.17 1 826 < 0.05
    Third aquifer Cu 31.18 2.63 4.93 2.77 1 264 < 0.05
    K (m/d) 306.02 0.000 7 11.83 85.36 195 < 0.05
    Clay fraction content (%) 43.75 0.001 7 12.63 6.02 1 957 < 0.05
    Cu 47.47 2.22 5.47 3.91 1 093 < 0.05
    K (m/d) 315.94 0.000 2 7.61 37.07 915 < 0.05
    Sig. Statistical significance; Stand dev. standard deviation.

    Table 1.  Statistic summary of clay fraction content, Cu, and K values for three aquifers

    It can be seen from this table that K had a wide range of variation, which is consistent with previous results (Min et al., 2012). The first aquifer had the strongest variation, the K value spanned nearly 7 orders of magnitude from approximately 0.000 1 to 359.73 m/d with an average value of 7.89 m/d. Spatial variation of K is one of the most important features of aquifer systems as it strongly affects fluid flow by creating flow barriers or preferential flow paths. The mean value of clay fraction content varied from 11.76% to 14.41%, and average Cu ranged from 4.93 to 5.93 among the three aquifers. The clay fraction content, Cu, and K values were not normal distribution according to the Lilliefors normality test (95% confidence level). To establish 3D spatial distribution models of clay fraction content, Cu, and K via the SGS method, these parameters were transformed to normal distributions using the logarithmic method.

    The final step was to classify the K values into five different grades. The spatial distribution of different grades of K value was characterized through steps (1)-(3) in the “Method” section. Table 2 describes the volume percentages of different grades of K value in these aquifers.

    Aquifer Very low Low Permeable High Very high
    First aquifer 3.060% 36.01% 55.70% 4.820% 0.410%
    Second aquifer 0.016% 9.56% 88.25% 2.160% 0.014%
    Third aquifer 0.040% 15.74% 84.21% 0.001% 0.010%

    Table 2.  The volume percentage of different grades of K value in three aquifers

  • It can be seen from Fig. 4a that the strongest spatial variation of clay fraction content, Cu, and K is present in first aquifer. Their range values are less than that in second and third aquifers, which is attributed to the depositional environment. It has significant effects on these parameters. Hutuo River, Huaisha River, and Xiao River were so active in the late Pleistocene that various alluvial-pluvial fan toes were formed and overlapped. Therefore, changes in micro-facies are violent, and the spatial variation of these parameters is stronger than in the other aquifers (Ma et al., 2012). Figure 4b indicates that defining K values according to rock type is unsuitable for groundwater resource management. Although the lithology in the southeastern part of the second aquifer is all silt sand, K values are variable in this region. This is mainly because the silt sand is formed by two different depositional micro-facies, natural levee and crevasse-splay, respectively. The clay contents of silt sand developed by natural levee are greater than that developed by crevasse-splay (Fig. 4b), therefore, K can vary by several orders of magnitude for the same type of rock. In the third aquifer (Fig. 4c), the higher values of clay fraction content, Cu, and K are all distributed in the southwestern part of the study area. This pattern violates the current hydrogeological paradigm. It is widely recognized that K values, as a rule, should decrease with increasing clay fraction content and Cu. Therefore, the finding indicate that it is not appropriate to use a single geo-statistical method to predict the distribution of higher K values without taking into account the influences of clay fraction content and Cu.

    Figure 4.  Spatial distribution models of clay fraction content, Cu, and K values for the first aquifer (a), the second aquifer (b), and the third aquifer (c).

    The conventional investigation commonly argue that the dependence of overall K value on depth is mainly due to decreasing porosity because of compaction and other physical or chemical effects (Sakata and Ikeda, 2013). However, the actual spatial variation of K values among the three aquifers in the NCP is contrary to these previous studies. The mean K values of the three aquifers follow the order: second > first > third. More importantly, the spatial variations of different grades of K value are different among these aquifers. It can be seen from Figs. 5a-5c, as well as Table 2 that the volume percentages of high and very high K values decreased with depth from the first to the second and third aquifers. These were the most sensitive parameters to burial depth. There are significant differences in depositional environment between the first aquifer and the other two. The first aquifer was made by an alluvial-pluvial fan toe of several rivers in the Late Pleistocene, while the second and third aquifers were made by an alluvial-pluvial fan of the Hutuo River in the Middle Pleistocene. The grain size distribution of the second and third aquifers is more uniform compared to the first aquifer according to Figs. 5a-5c. Between the first and second aquifer the volume percentages of very low and low K decreased from 3.06% and 36.01% to 0.016% and 9.56%, and the volume percentage of permeable K increased from 55.70% to 88.25%. The second and third aquifers were formed by the same depositional environment, and therefore the burial depth became the major influencing factor. This resulted in the overall K value decreasing from the second to third aquifer. The volume percentages of very low and low K increased from 0.016% and 9.56% in the second aquifer to 0.04% and 15.74% in third aquifer, which have positive effects on the changes in overall K between the second and third aquifers. The volume percentages of permeable K exhibited no obvious changes between these two aquifers. Previous studies have reported that depositional environment is the main controlling factor of K values (Lu et al., 2002); however, this work demonstrated that high and very high K are fully affected by burial depth, rather than depositional environment. It should be noted that the high K value varied slightly with the large decrease from first to second aquifer, while the small decrease from the second to third aquifer was accompanied by a drastic change in high K. This is mainly because the sensitivity of the high K value to depth is different under the upper layer pressure. The very low, low, and permeable K values are mainly controlled by sedimentary environment, and partially influenced by burial depth. Only within the same depositional environment does the burial depth become the main influencing factor and causes the very low, low, and permeable K values decreased with depth.

    Figure 5.  Spatial distribution of diffsrent grades of K values for the first aquifer (a), the second aquifer (b), and the third aquifer (c).

    Overall K values have stronger spatial variation in the vertical direction, and the grades of K make different contribution to this variation. The low K category plays an important role in these changes, and the effects of permeable K are secondary. Although the volume percentages of very low, high, and very high K values have wide ranges, their values in these aquifer systems are so small that it is difficult to cause significant changes in the overall K value.

3.   CONCLUSIONS
  • The aim of this paper is to characterize the spatial distribution of different grades of K value in a highly heterogeneous aquifer based on considering the effects of clay fraction content and Cu values on K. The following conclusions can be drawn from this study.

    (1) It is not appropriate to estimate the higher K values without taking into account the effects of clay fraction content and Cu on K.

    (2) The spatial variation of overall K values in the vertical direction is mainly caused by low and permeable K values.

    (3) Among the three aquifers, the overall K values are partially influenced by burial depth but show a strong dependence on depositional environment. Under the same depositional environment, the K values vary with depth.

    (4) A unique relationship between K and depth is not observed in the NCP. In the vertical direction, only the volume percentages of high and very high K values have a decreasing tendency with the depth. However, a decrease in the volume percentages of very low, low, and permeable Kwith depth is not observed in this article. Therefore, high and very high K value are only controlled by depth, however, both the depositional environment and burial depth are the influencing factors of very low, low, and permeable Kvalues.

    The distribution range of very low, low, permeable, high, and very high zones of K values are described by this work, which can provide useful information for non-technical decision makers to achieve sustainable development of groundwater resources. For example, very low and low K values limit groundwater recharge to underlying aquifers; in this respect, they can also protect the aquifers from contamination. Therefore, the southeastern study area can be used for geological disposal of toxic, domestic, and industrial wastes. The high and very high K regions are critical to water balance and solute transport models, as they are the major transport pathway of the pollutants. Therefore, the sewage discharge and fertilizer utilization in the northeastern part of the study area should be decreased to avoid contaminants migration to groundwater systems throughout this region.

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