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.
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.