Some Issues in the Processing of Hydrogeological Data
Abstract Generated abstract
This article examines shortcomings in the regional processing of hydrogeological test data from coal-bearing areas and presents a statistical approach using materials from the Tom-Usa district of Kuzbass. It analyzes factors affecting well yields, including surface waters, tectonic disturbances, pumping conditions, lithology, and the depth of the water-bearing zone, and then groups wells to correlate specific yield with the proportion of sandstones and conglomerates within the upper aquifer interval. The study finds that specific yield generally increases with the content of more permeable rocks but decreases and becomes more predictable as the aquifer roof lies deeper, allowing graphical estimation from exploratory drilling data. The proposed method is offered as a preliminary tool that may reduce pumping tests in watershed and slope areas, while river valleys and disturbed zones still require special hydrogeological investigation.
Full Text
SOME ISSUES IN THE PROCESSING OF HYDROGEOLOGICAL MATERIALS
G. P. BOGOMYAKOV
In many coal basins of the Union (Kuzbass, Donbass, and others), an enormous body of factual material on hydrogeological testing of exploratory workings has by now accumulated. However, the processing and generalization of this material, especially on a regional scale, is being carried out inadequately. At the same time, the elucidation of certain regularities makes it possible to assess the hydrogeological situation more correctly in areas explored in detail and to approach the methodology of hydrogeological investigations under analogous conditions on a more substantiated basis.
The methodology for processing hydrogeological data is likewise imperfect and requires further development.
The present article gives an example of the use of a method of mathematical statistics in processing materials for the Tom-Usa coal-bearing district of Kuzbass. This district is situated on the southeastern margin of the basin. Its territory is composed of coal-bearing deposits of the Balakhonka and Kolchugino series of Upper Paleozoic age.
Geological exploration work is being conducted extensively in the district. Many areas have already been explored in detail, and a large body of factual material has accumulated for them.
Analyzing the extensive, though heterogeneous, material on hydrogeological testing of workings, we may note that well yields depend on a large number of both general and particular causes.
Among the most frequently encountered particular factors that noticeably affect well yields under our conditions, we may note the following:
a) the influence of surface water bodies and watercourses,
b) the influence of zones of tectonic disturbances,
c) the influence of the magnitude of drawdown during pumping,
d) the influence of the duration of pumping,
e) the influence of well design.
Various kinds of errors allowed during pumping tests also have a significant influence on the results; however, these errors cannot always be taken into account. Therefore, we do not use materials for several wells where pumping was carried out in an obviously incorrect manner.
It should be noted at once that we equate the results of pumping from wells with the results of injection tests, although we recognize that a complete analogy between them cannot be drawn. During pumping, the drilling mud remaining in the well is removed from the well; in addition, many fractures in the rocks are cleared. All this leads to an increase in ...
inflow of water into the well. When water is poured into a well, the fractures are colmatated by drilling mud, which reduces the specific rates of water consumption. Thus, pouring tests should give somewhat understated results in comparison with pumping tests.
In our case, a favorable circumstance is that the duration of pumping tests is considerably greater than the duration of pouring tests. If, for example, the duration of pumping for each lowering is almost always more than 10–15 hours, the duration of pouring tests is usually 3–5 hours, sometimes somewhat longer. We know that increasing the duration of pumping (of course, up to certain limits) at an unchanged drawdown leads to a decrease in the yield of a well, whereas with an increase in the duration of pouring the water absorption of the well decreases. Consequently, on the one hand, a certain colmatation of fractures understates the data on water absorption in wells; on the other hand, the shorter duration of pouring tests, in comparison with pumping tests, overstates these data.
Let us consider in more detail the influence of the causes listed above on the yields of wells drilled in the region.
a) The influence of surface waters on the inflow of water was manifested in a number of wells drilled on the Tom–Usa interfluve, in the valleys of the Kiyzak, Olzheras, and other rivers. Most often these wells were laid down for the purpose of prospecting groundwater, or as production wells for the water supply of individual industrial facilities and the settlements adjacent to them; therefore they were located in river valleys, where the water level lies close to the ground surface. In some cases the distance to a river, or to some oxbow lake in the river floodplain, was less than the radius of influence of pumping.
The most striking example in this respect is provided by data for wells Nos. 399 and 404. Both wells are located on the Tom–Usa interfluve, in the immediate vicinity of oxbow lakes. The specific yield of well No. 399 after prolonged pumping with three drawdowns of the level (pumping in 1953) was 3.79 l/sec. When pumping was stopped, the level recovered almost instantaneously. An even greater specific yield, equal to 6.0 l/sec, was obtained for well No. 404, and it was possible to lower the level by only 0.35 m. The initial diameters of both wells were 131 mm, the final diameters 101 mm.
At the site of well No. 404, a production well was drilled with an initial diameter of 24″ and a final diameter of 8″ (well No. 131a). The specific yield of this well was 14 l/sec, and the maximum drawdown reached was 2.57 m. Both this well and the other wells were drilled in deposits of the Balakhon series, and no zones of disturbance were encountered by them. For wells that penetrated deposits of the Balakhon series within the territory of the region, specific yields of no more than 1.0 l/sec are characteristic. The rocks exposed at the sites of wells Nos. 399 and 404 are analogous to the rocks of this suite in other areas, and it is quite evident that the high yields in these wells are due to the influence of surface waters.
b) Tectonic disturbances may exert a great influence on well yields. In the Tom–Usa region, zones of rock crushing associated with tectonic disturbances have been encountered by many wells; however, they did not have a noticeable effect on the inflow of water in all wells. Most often the fractures in the zones of tectonic disturbances of the region are closed (usually filled with calcite) and do not transmit water. Crushing zones with increased permeability were encountered by only a small number of wells (wells Nos. 738, 770, 833, and some others).
which are due mainly to the influence of surface waters or zones of tectonic disturbances, then these causes are not determining ones and may be disregarded (of course, with a certain degree of allowance). The main factors on which well yields depend may be considered the following:
a) the degree of permeability of the rocks,
b) the thickness of the aquiferous zone penetrated by the well.
The degree of permeability of the rocks, in turn, is governed by the porosity and the degree of fracturing of the rocks (only “active” fracturing is meant). For the coal-bearing deposits of the district that interest us, the predominant role is played by the fracturing of the rocks.
The degree of fracturing, and consequently also the degree of permeability of the rocks, should vary depending on the lithological composition and on their depth below the ground surface. Undoubtedly, different lithological varieties are not equally affected by weathering processes, and at the same time the intensity of these processes diminishes with the depth of occurrence of the rocks.
The decrease in the fracturing of rocks with the depth of their occurrence is very well confirmed by the cores of exploratory wells. Thus, within the first two or three tens of meters from the surface, the core is very strongly crushed and is represented by separate angular fragments bounded by cracks with distinct traces of water circulation (usually these are brown ferruginous coatings on the walls of the cracks). At a depth of 30–60 m, although fairly strong fracturing is still observed, the core consists of separate columns up to 10–15 cm high, and sometimes more. By 80–100 meters, only isolated thin open cracks remain in the rocks. Under normal drilling conditions, at a depth of more than 100 m from the ground surface, the core in ordinary cases comes out in columns up to 0.5 m long and often longer, while permeable cracks occur rarely and are very thin.
Proceeding from the indicated character of fracturing, one may expect that the main inflow of water to a well will be observed in the zone 0–100 m from the surface. Below we shall present data confirming this proposition.
The thickness of the aquiferous zone penetrated by a well undoubtedly has a great influence on the well yield; therefore, when assessing the water abundance of rocks, it must be taken into account. However, under the conditions of the district we cannot everywhere determine with justification the base of this zone. This is due to the gradual attenuation of rock fracturing noted above. Nevertheless, we believe that the thickness of the aquiferous zone can be taken into account by knowing the depth at which it occurs. Indeed, if the water-bearing capacity of the rocks dies out at some definite depth from the surface, then the thickness of the saturated zone will decrease with increasing depth of occurrence of the saturated rocks.
In addition, taking into account the depth of occurrence of the saturated rocks helps to take into account also the degree of permeability of the rocks. The smaller this depth, the higher the permeability of the saturated rocks, and, conversely, the greater it is, the less permeable are the rocks that make up the aquiferous zone.
Thus, summing up to some extent, it may be said that the degree of permeability of the aquiferous zone depends both on the lithological composition of the rocks and on the depth of occurrence of the aquiferous zone from the ground surface. The thickness of the aquiferous zone can be taken into account by knowing the depth of occurrence of the saturated rocks. Consequently, if well yields are determined mainly by the degree of permeability of the rocks and by the thickness of the aquiferous zone, then they should depend on the lithological
composition of the water-bearing rocks and the depth at which these rocks occur below the ground surface.
The study of such relationships is of considerable importance, since it opens the way to a preliminary, more or less approximate assessment of the water abundance of rocks without carrying out special hydrogeological testing of wells, i.e., on the basis of exploratory-drilling data.
Proceeding from this, we attempted to establish the indicated relationships for the Tom-Usinsk district.
Since, owing to insufficient data, it was not possible to determine the dependence of well yields on each lithological variety separately, we divided all the rocks occurring within the coal-bearing sequence into two groups. The first group includes conglomerates and sandstones (with various cement), and the second includes siltstones, argillites, coaly argillites, and coals.
To determine the dependence of specific yields on the content of sandstones and conglomerates, we constructed several graphs. On one of them we plotted data on specific yields and on the sum of the thicknesses of individual beds of sandstones and conglomerates penetrated by a well below the roof of the water-bearing rocks or below the groundwater level in the absence of pressure; however, no regular relationship could be established in this way. This is quite understandable, since when the depth of a well increases beyond 100 meters, weakly fractured or almost monolithic rocks are encountered; that is, the well yield does not increase, whereas the content of sandstones and conglomerates changes. Therefore, on another graph, specific yields were plotted as a function of the sum of the beds of sandstones and conglomerates (in %) occurring in water-bearing rocks down to a depth of 100 meters.
From this graph (Fig. 1) it is evident that an increase in the content of sandstones and conglomerates leads to some increase in specific yields; however, the scatter of the points is very large, and no conclusions
Fig. 1. Graph of the dependence of specific well yields on the sum of sandstones and conglomerates in the water-bearing zone (in % of the thickness of the zone).
can be drawn. Apparently, other factors have a major influence here, such as the unequal degree of permeability of the same rocks in different areas and at different depths of their occurrence below the ground surface.
In order to take into account the influence of the depth of occurrence of the rocks, we constructed graphs of the dependence of specific yields on the content of sandstones and con—
conglomerates in the aquifer zone (down to a depth of 100 m) for several groups of wells, combined according to the depth at which the watered rocks occur in them (Fig. 2).
On the basis of the available factual material, we have distinguished four such groups. The first group includes wells (35 in number) in which the depth of occurrence of the watered rocks is 0–1.5 m; the second (comprising 24 wells) consists of wells with a depth of occurrence of the upper boundary of the aquifer zone of 1.5–10 m; the third (19 wells), 10–25 m; and the fourth (27 wells), >25 m.
Fig. 2. Graphs of the dependence of the specific yields of wells on the sum of sandstones and conglomerates in the aquifer zone at different depths of occurrence of the upper boundary of the aquifer rocks.
A — depth of occurrence of the upper boundary of the aquifer rocks 0–1.5; Б — depth 1.5–10.0 m; В — depth 10.0–25.0 m; Г — depth 25.0 m.
Considering Fig. 2, several conclusions may be drawn. First, the relationship between the specific yields of wells and the sum of sandstones and conglomerates in the watered zone is revealed much more clearly in these graphs than in Fig. 1.
Second, the greater the depth of occurrence of the aquifer zone, the tighter this dependence. With increasing depth of occurrence of the watered rocks, the influence of the content of sandstones and conglomerates in the aquifer zone on well yields decreases. In other words, as the depth of occurrence of the rocks increases, there is not only a general decrease in the degree of their water permeability, but also an erasure of differences in the water permeability of individual lithological varieties.
Third, from these same figures it is evident that, where the watered rocks occur shallowly, the scatter of points on the graph is large, while with increasing depth the deviations of the points from some mean line decrease.
In our opinion, this should indicate that the degree of permeability of the rocks in different areas in the near-surface zone is subject to greater fluctuations than at depth. And this is quite understandable, since the permeability of the rocks here is influenced by a considerably larger number of factors than at depth.
In addition to the unequal action of weathering processes, which is most strongly manifested in the zone close to the ground surface, the position in the section of more or less permeable rocks may in these cases exert a great influence on the water abundance of the rocks. To explain this, let us consider the following example: the depth to the top of the watered rocks in two wells located in different areas is 1.0 m; the sum of sandstones and conglomerates in the 1.0–100.0 m zone is 75% in both wells.
In one well the upper part of the aquifer zone is composed of sandstones and conglomerates, while in the other it is composed of argillites and siltstones. Since the permeability of these lithological varieties, provided that they occur close to the ground surface, is different (as has already been confirmed above), the well yields must also be unequal. At the same time, since the differences in the degree of permeability of individual lithological varieties decrease with increasing depth of occurrence of the rocks, the influence of the position in the section of sandstones and conglomerates will decrease as the depth to the top of the aquifer zone increases.
It is evident from Fig. 2 that in each of the graphs the points are located near some curve, i.e., a correlative relationship is indicated between them.
In all four graphs these curves have the form of a power function \(y = B\sqrt{x}\), and consequently, on a logarithmic scale they should be straight lines; or, denoting \(\lg B = b\), we obtain
\[ \lg y = a \lg x + b. \]
If \(y\) is the specific yield of a well, \(x\) is the sum of sandstones and conglomerates in the watered zone, in %, and we now denote the depth of occurrence of the watered zone by \(Z\), then for a definite value \(Z = Z_1\) the equation of the logarithmic straight line will be:
\[ \lg y = a_1 \lg x + b_1. \]
For another value \(Z = Z_2\),
\[ \lg y = a_2 \lg x + b_2 \quad \text{and so on.} \]
The values \(a_1\) and \(b_1\), \(a_2\) and \(b_2\), etc., can be found with quite sufficient accuracy by the correlation method. As an example, let us consider the determination of \(a_3\) and \(b_3\) for \(Z_3 = 18.5\) m (wells with a depth to the aquifer zone of 10–25 m).
For convenience, we place all the initial and calculated data in a table (Table 1). Having found the logarithms of the different values of \(x\) and \(y\), we find for them the arithmetic mean values \(\lg x_0\) and \(\lg y_0\). After this, the deviations from the arithmetic means, the squares of these deviations, and their products are calculated (i.e., we calculate \(\lg y - \lg y_0\), \(\lg x - \lg x_0\), \((\lg y - \lg y_0)^2\), \((\lg x - \lg x_0)^2\), and \((\lg y_0 - \lg y_0)\cdot(\lg x - \lg x_0)\). The arithmetic mean...
Table 1
Initial data and calculation of the correlation curve at \(Z = 18.5\ \mathrm{m}\)
| Item No. | Well No. | \(y\) | \(X\) | \(\lg y\) | \(\lg x\) | \(\lg y-\lg y_0\) | \(\lg x-\lg x_0\) | \((\lg y-\lg y_0)^2\) | \((\lg x-\lg x_0)^2\) | \((\lg y-\lg y_0)\cdot(\lg x-\lg x_0)\) |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 24 | 0,10 | 50,6 | −1,0000 | 1,7042 | −0,3185 | −0,1613 | 0,1014 | 0,0260 | 0,0514 |
| 2 | 158 | 0,20 | 82,7 | −1,3010 | 1,9175 | 0,0175 | 0,0538 | 0,0003 | 0,0029 | −0,0009 |
| 3 | 194 | 0,26 | 88,55 | −1,4150 | 1,9472 | 0,0965 | 0,0835 | 0,0093 | 0,0070 | 0,0081 |
| 4 | 348 | 0,40 | 80,35 | −1,6021 | 1,9050 | 0,2836 | 0,0413 | 0,0804 | 0,0017 | 0,0117 |
| 5 | 388 | 0,17 | 91,1 | −1,2304 | 1,9547 | −0,0881 | 0,0910 | 0,0078 | 0,0083 | −0,0080 |
| 6 | 398 | 0,35 | 72,8 | −1,5441 | 1,8618 | 0,2256 | −0,0019 | 0,0509 | 0,0000 | −0,0004 |
| 7 | 422 | 0,15 | 70,1 | −1,1761 | 1,8457 | −0,1424 | −0,0180 | 0,0203 | 0,0003 | 0,0026 |
| 8 | 423 | 0,25 | 67,6 | −1,3979 | 1,8296 | 0,0794 | −0,0341 | 0,0063 | 0,0012 | −0,0027 |
| 9 | 448 | 0,19 | 87,7 | −1,2788 | 1,9430 | −0,0397 | 0,0793 | 0,0016 | 0,0063 | −0,0031 |
| 10 | 449 | 0,30 | 77,2 | −1,4771 | 1,8873 | 0,1586 | 0,0236 | 0,0252 | 0,0056 | 0,0037 |
| 11 | 660 | 0,22 | 63,8 | −1,3424 | 1,8048 | 0,0239 | −0,0589 | 0,0057 | 0,0035 | 0,0014 |
| 12 | 668 | 0,20 | 94,0 | −1,3010 | 1,9731 | −0,0175 | 0,1094 | 0,0003 | 0,0120 | −0,0019 |
| 13 | 748 | 0,30 | 77,6 | −1,4771 | 1,8899 | 0,1586 | 0,0262 | 0,0252 | 0,0007 | 0,0042 |
| 14 | 762 | 0,32 | 84,1 | −1,5051 | 1,9248 | 0,1866 | 0,0611 | 0,0348 | 0,0037 | 0,0114 |
| 15 | 765 | 0,08 | 51,8 | −2,9031 | 1,7143 | −0,4154 | −0,1494 | 0,1726 | 0,0223 | 0,0621 |
| 16 | 766 | 0,10 | 48,7 | −1,0000 | 1,6870 | −0,3185 | −0,1767 | 0,1014 | 0,0312 | 0,0563 |
| 17 | 768 | 0,20 | 64,0 | −1,9010 | 1,8062 | −0,0175 | −0,0575 | 0,0003 | 0,0033 | 0,0010 |
| 18 | 829 | 0,35 | 86,9 | −1,5441 | 1,9390 | 0,2256 | 0,0753 | 0,0509 | 0,0057 | 0,0170 |
| 19 | 872 | 0,18 | 75,0 | −1,2553 | 1,8751 | −0,0632 | 0,0114 | 0,0040 | 0,0001 | −0,0007 |
| Sum | −13,0516 | 35,4102 | −1,4383 +1,4384 |
−0,6572 +0,6559 |
0,6987 | 0,1418 | 0,2131 |
... are equal:
\[ \lg y_0=-\frac{12.9484}{19}=-0.6815; \]
\[ \lg x_0=\frac{35.4102}{19}=1.8637. \]
We compute the value of the correlation coefficient, indicating the closeness of the relationship, by the formula:
\[ r=\frac{\Sigma(\lg y-\lg y_0)\cdot(\lg x-\lg x_0)} {\sqrt{\Sigma(\lg y-\lg y_0)^2\cdot\Sigma(\lg x-\lg x_0)^2}}; \]
\[ r=\frac{0.2131}{0.06987\cdot0.1418} =\frac{0.2131}{0.3148}=0.677. \]
We calculate the probable error of the correlation coefficient by the formula:
\[ \varepsilon_r=\pm0.674\,\frac{1-r^2}{\sqrt{n}}, \]
where \(\varepsilon_r\) is the probable error of the correlation coefficient,
\(r\) is the correlation coefficient,
\(n\) is the number of points for which the relationship is calculated
\[ \varepsilon_r=\pm0.674\,\frac{0.542}{\sqrt{19}} =\pm\frac{0.3653}{4.359}=0.084. \]
It is considered that if the quantity \(r\pm3\varepsilon_r\) retains its sign in both cases, i.e., if \(r>3\varepsilon_r\), then the correlation is good and the relationship is proven. In our case the correlation coefficient is greater than its probable error not by a factor of three, but by a factor of eight \((0.677:0.084=8.1)\); consequently, the existence of the relationship is beyond any doubt.
The equation of the straight regression line has the form:
\[ \lg y-\lg y_0=R^{\lg y}_{/\lg x}(\lg x-\lg x_0), \]
where \(R^{\lg y}_{/\lg x}\) is the regression coefficient. It is determined by the formula
\[ R^{\lg y}_{/\lg x}=r\,\frac{\sigma_{\lg y}}{\sigma_{\lg x}}. \]
In this formula \(r\) is the correlation coefficient,
\(\sigma_{\lg y}\) and \(\sigma_{\lg x}\) are the root-mean-square deviations for the values \(\lg y\) and \(\lg x\).
\[ \sigma_{\lg x}=\sqrt{\frac{\Sigma(\lg x-\lg x_0)^2}{n-1}}; \qquad \sigma_{\lg y}=\sqrt{\frac{\Sigma(\lg y-\lg y_0)^2}{n-1}}, \]
\[ \frac{\sigma_{\lg y}}{\sigma_{\lg x}} = \sqrt{\frac{\Sigma(\lg y-\lg y_0)^2} {\Sigma(\lg x-\lg x_0)^2}}. \]
Consequently:
\[ R^{\lg y}_{\lg x}=0,677 \sqrt{\frac{0,6987}{0,1418}}=0,677\cdot 2,220=1,503. \]
Hence the equation of the desired straight line will be:
\[ \lg y-\lg y_0=1,503\;(\lg x-\lg x_0); \]
\[ \lg y+0,6815=1,503\;\lg x-1,503\cdot 1,8637 \]
\[ \lg y=1,503\;\lg x-3,483. \]
We calculate the mean error of this equation by the formula:
\[ S_{\lg y}=\sigma_{\lg y}\sqrt{1-r^2} =\sqrt{\frac{\sum(\lg y-\lg y^0)^2}{n-1}}\,\sqrt{1-r^2} =0,145. \]
Having carried out similar calculations, we find the equations of straight lines also for the other three groups of wells. The results of the calculations are summarized in Table 2.
Table 2
Data for calculating regression equations for all values
| \(Z_{\mathrm{avg}}\) | \(r\) | \(\varepsilon_r\) | \(\dfrac{r}{\varepsilon_r}\) | \(a\) | \(b\) | Equation | \(S_{\lg y}\) |
|---|---|---|---|---|---|---|---|
| 0,7 | 0,646 | 0,066 | 9,8 | 2,035 | −4,080 | \(\lg y=2,035\;\lg x-4,080\) | 0,264 |
| 4,0 | 0,675 | 0,075 | 9,0 | 2,049 | −4,201 | \(\lg y=2,049\;\lg x-4,201\) | 0,222 |
| 18,5 | 0,677 | 0,084 | 8,1 | 1,503 | −3,483 | \(\lg y=1,503\;\lg x-3,483\) | 0,145 |
| 45,3 | 0,629 | 0,078 | 8,3 | 1,302 | −3,315 | \(\lg y=1,302\;\lg x-3,315\) | 0,120 |
The data presented in Table 2 show that in all four cases, i.e., at different depths of occurrence of the roof of the watered rocks, a relationship between the specific yields of wells and the content of sandstones and conglomerates in the watered zone undoubtedly exists. The mean error of the equation decreases rather sharply as the depth of occurrence of the roof of the water-bearing zone increases.
In order to represent graphically the equations obtained above, let us calculate the values of \(y\) for a series of values of \(x\).
Table 3
Calculated data for constructing correlation curves
| \(Z_{\mathrm{avg}}\) | 40 | 50 | 60 | 70 | 80 | 90 | 100 | \(\alpha\) | \(\beta\) |
|---|---|---|---|---|---|---|---|---|---|
| 0,70 | 0,15 | 0,24 | 0,35 | 0,47 | 0,62 | 0,79 | 0,98 | 84 | 45 |
| 4,0 | 0,12 | 0,19 | 0,28 | 0,38 | 0,50 | 0,64 | 0,79 | 66 | 40 |
| 18,5 | 0,08 | 0,12 | 0,16 | 0,20 | 0,24 | 0,28 | 0,33 | 40 | 28 |
| 45,3 | 0,06 | 0,08 | 0,10 | 0,12 | 0,15 | 0,17 | 0,20 | 32 | 24 |
In Table 3, $\alpha$ is the error in the direction of overestimation, $\beta$ is the error in the direction of underestimation, in %.
The greater relative deviations of the specific yields are explained, in addition to the reasons noted above, by the fact that we take wells not with a definite depth of occurrence of the aquifer zone—for example, 18.5 m—but a group of wells with a depth of occurrence of the watered rocks of 10–25 meters. It is quite natural that, if there is a sufficient amount of initial data, these intervals (of depths of occurrence of the aquifer zone) can be reduced; then the errors in determining the specific yields will decrease.
Of course, part of the errors is probably due to the unequal degree of permeability of the rocks and to various kinds of errors in pumping tests.
Using the computed values of $x$ and $y$, we construct graphs of the dependence of specific yields on the sum of sandstones and conglomerates in the watered zone, for different depths of occurrence of this zone (Fig. 2).
By superimposing all the obtained curves on one graph (Fig. 3), we can, by interpolation, find the specific yields for any (of course, within the limits of the graph) relationship between the sum of sandstones and conglomerates in the aquifer zone and the depth of occurrence of this zone. In other words, we can find the values of $y$ for any values of $x$ and $Z$.
Fig. 3. Graph of the dependence of the specific yields of wells on the sum of sandstones and conglomerates in the aquifer zone at different depths of occurrence of the upper boundary of the aquifer rocks.
However, for better interpolation of the dependence of $y$ on $Z$, this graph can be modified by constructing the dependence of $y$ on $Z$ at definite values of $x$ (Fig. 4). In order for the graph to be more compact and convenient to use, we construct it on a semilogarithmic scale. Along the horizontal axis the values of $Z$ are plotted, and along the vertical axis, $\lg y$. To construct the dependence of $y$ on $Z$, at definite values of $x$, the points are taken from the graph shown in Fig. 3.
Thus, knowing the lithological composition of the rocks penetrated by a well and the depth of occurrence in it of the aquifer zone, one can, using the indicated graph (Fig. 4), determine what the specific yield of the given well should be. Consequently, from the data of exploratory drilling we have the possibility of judging, with sufficient justification, the degree of water abundance of the rocks.
Hydrogeological observations on exploratory wells, obligatory when drilling all wells, make it possible to establish (jointly—
but, with the study of core, the presence or absence in them of more or less large zones of rock crushing with increased water permeability. For those wells that have encountered such zones, it is impossible to determine the inflow of water or absorption by the method set forth above; therefore, if necessary, they must be tested by pumping or injection tests.
Fig. 4. Graph of the dependence of the specific yields of wells on the depth of occurrence of the upper boundary of the water-bearing zone and the sum of sandstones and conglomerates, in % of the thickness of the water-bearing rocks.
The materials presented above show that the greatest errors in such a determination of the water abundance of rocks are possible in those cases when the depth of occurrence of the water-bearing rocks is small. As the depth of occurrence of the water-bearing rocks in the well increases, the accuracy of determining the specific yield by the proposed method increases. On this basis, it should be concluded that, for exploratory wells located on watershed areas and on slopes, the number of pumping tests can be substantially reduced.
In river valleys, and especially near large bodies of water or watercourses, well yields are subject to large fluctuations. At the same time, the question of protective pillars around such bodies of water often arises here; therefore, determination of the water abundance and water permeability of rocks within river valleys is of great importance. It is quite understandable that determination of the water abundance of rocks by the method proposed above, from wells located in river valleys, can only be preliminary at the first stage of investigations. In such areas it is necessary to carry out special hydrogeological investigations.
The data presented above show that the use of the method of mathematical statistics, together with a careful analysis of the geological setting and hydrogeological data, makes it possible to-
to approach the question of a preliminary, to one degree or another approximate, assessment of the water-bearing capacity of rocks on the basis of exploratory drilling data, without carrying out special hydrogeological testing.
In many cases such an assessment is necessary and often, apparently, will be sufficient.
REFERENCES
Shamansky L. I. Mathematical Processing of Exploration Materials. GONTI, 1936.
“Kuzbassuglegeologiya” Trust
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