Dependence of the Diameter of Dewatering Wells on the Type of Pump Used

N. D. Smirnov

(Presented by the scientific seminar of the Faculty of Hydraulic Engineering Construction)

Modern hydraulic engineering construction is, as a rule, associated with the need for artificial lowering of the groundwater level by as much as 50 meters. This is achieved by constructing deep wells—boreholes equipped with deep artesian-type pumps (VAN, ATN, NA, and others), by means of which continuous pumping of water is carried out, with its discharge through special collector pipes beyond the cofferdam enclosing the excavation during the work.

The number of deep wells—boreholes—at large hydraulic-engineering projects reaches several hundred; the diameters of the wells vary within the range from 100 mm (4″) to 500 mm (20″), depending on the water-bearing capacity of the soils.

Dewatering works involve considerable material and financial expenditures, which consist of the costs of drilling well-boreholes and equipping them with water-intake filters, and of the costs of operating deep pumps.

The cost of drilling a borehole increases with an increase in its diameter; the cost of operating deep pumps also increases with an increase in the power (capacity) of the deep pump.

Observations of the operation of wells during their service and measurements of the water pumped from the wells have shown that in individual cases the pumps operate at only 10% of their design capacity.

The analysis of these causes is the task we set ourselves in the present work.

Choice of Pump Type

The water-transmission capacity of a well may be calculated by S. K. Abramov’s formula

\[ f = 120 \pi r_c \sqrt[4]{k}\, l_f, \tag{1} \]

where \(f\) is the water-transmission capacity of the well, m\(^3\)/day;
\(r_c\) is the radius of the well in meters;
\(k\) is the filtration coefficient, m/day;
\(l_f\) is the length of the water-intake part (filter) of the well, in m.

The water-transmission capacity of the well, determined by Abramov’s formula, must exceed, or in the extreme case be equal to, the discharge of the well \(Q\):

\[ f \geq Q. \tag{2} \]

Using formula (1), we determine the water-yielding capacity of wells with diameters of 150; 200; 250; 300; 350 and 400 mm, with the filtration coefficient of the aquifer equal to 5; 10; 15; 20; 25; 30; 35; 40; 45 and 50 meters per day, and with the length of the well filter equal to 1.0; 2.0; 4.0; 5.0; 6.0; 8.0; 10.0; 12.0 m.

The cases considered cover the possible range of application of deep wells for dewatering works, since in soils with a filtration coefficient of more than 50 meters per day artificial lowering of the groundwater level is not used, while a well filter length of more than 10–12 meters is likewise never encountered in the dewatering practice of hydraulic-engineering construction.

Table 1.

Well with a diameter of 150 mm

Well capacity, m³ per day

Note: The limits of applicability of the VAN-7 pump are bounded by the bold line.

Table 2

Well with a diameter of 200 mm

Well capacity, m³ per day

Note: The limits of applicability of ATH-8 type pumps are bounded by the bold line.

Table 3

Well with a diameter of 250 mm

Well capacity, m³ per day

Note: The limits of applicability of ATH-10 type pumps are bounded by the bold line.

Table 4

Well with a diameter of 300 mm

Well capacity, m³ per day

Table 5

Well with a diameter of 350 mm

Well capacity, m³ per day

Table 6

Well with a diameter of 400 mm
Well capacity, m³/day

Our domestic industry produces deep-well pumps of the artesian type for wells with diameters of 4″ and larger.

For dewatering work, the most widely used have been: for wells with a diameter of 150 mm, VAN-7 pumps with a capacity of 15 m³/hour; for wells with a diameter of 200 mm, ATN-8 pumps with a capacity of 18–50 m³/hour; for wells of 250 mm, ATN-10 pumps with a capacity of 50–100 m³/hour; for wells of 300 mm, 12 NA pumps with a capacity of 150 m³/hour; for wells of 350 mm, ATN-14 pumps with a capacity of 150–250 m³/hour; for wells of 400 mm, ATN-16 pumps with a capacity of 300–500 m³/hour.

Let us consider the limits of application of these pumps for dewatering.

Under the condition of continuous pumping of water from wells for deep dewatering, we take the average coefficient of utilization of pump time as 0.8, i.e., we assume that the pump operates on average 16 hours per day. This is confirmed by the practice of many construction projects (Tsimlyansk hydroelectric complex, Kuibyshev Hydroelectric Power Station, Stalingrad Hydroelectric Power Station, etc.).

In this case the average daily capacity of the pumps will be:

for the VAN-7 pump — 200–300 m³/day;
for the ATN-8 pump — 300–800 m³/day;
for the ATN-10 pump — 800–1600 m³/day;
for the 12 NA pump — 2000–2500 m³/day;
for the ATN-14 pump — 2400–4000 m³/day; and
for the ATN-16 pump — 4500–8000 m³/day.

Comparing the daily capacity of pumps and wells, we find the limits of application of the pumps of the listed types in wells of the corresponding diameters.

The limits of possible application of the pumps are entered in Tables 1–6 in the form of a bold contour line.

As a result of the operation carried out, we are convinced that the use of VAN-7 pumps in wells with a diameter of 150 mm, ATN-8 pumps in wells of 200 mm, and ATN-10 pumps in wells of 250 mm is possible within certain limits, which depend on the filtration coefficient and the length of the well filter.

As for the 12 NA, ATN-14, and ATN-16 pumps, their use for dewatering purposes raises doubts, since the capacity of these pumps significantly exceeds the water-intake capacity of the wells in which these pumps can be installed.

Choice of Well Diameter

The discharge of a single well, according to A. A. Krasnopolsky, is equal to

\[ Q = 2\pi M K \sqrt{\frac{S}{\frac{1}{r} - \frac{1}{R}}}, \tag{3} \]

where
\(Q\) — discharge of the well, \(m^3/\)day;
\(M\) — thickness of the aquifer, \(m\);
\(K\) — coefficient of filtration, \(m/\)day;
\(S\) — magnitude of the lowering of the level, \(m\);
\(r\) — radius of the well, \(m\);
\(R\) — radius of influence of the well, \(m\).

Neglecting the term \(\frac{1}{R}\), owing to its small magnitude in comparison with \(\frac{1}{r}\), we have

\[ Q = 2\pi M K \sqrt{r \cdot S}. \tag{4} \]

Let us consider, using formula (4), the change in the discharge of a well as a function of changes in \(r\), i.e., the radius of the well, under the condition \(S = \mathrm{const}\), i.e., with the same magnitude of groundwater-level lowering by wells of different diameters. The results are presented in the form of Table 7.

Table 7

Thus, an increase in the well diameter has an insignificant effect on its discharge.

When determining the discharge of a well as a function of its diameter by the formulas of other authors (for example, S. K. Abramov), the discharge of the well increases to an even lesser degree, since the discharge is a function of the logarithm of the well radius.

To select the optimum well radius, we shall use the unit rates for drilling wells by percussion-cable drilling rigs (Table 8).

Using the data of Tables 7 and 8, we find the relative cost of pumping \(1 \, m^3\) of water from wells of different diameters.

It follows from Table 9 that the relative cost of pumping water in wells of different diameters will be minimal for well diameters of 250 mm and 200 mm.

Table 8

Cost of drilling 1 linear m of well, in rubles.

Table 9

Conclusions

For dewatering in hydraulic-engineering construction, wells of 200 and 250 mm diameter with ATN-8 and ATN-10 pumps should be used, since this gives the greatest economic effect.

The use of wells with a diameter of 300 mm and more cannot be recommended, owing to their low water yield, which does not ensure operation of the ATN-14, ATN-16, and 12NA pumps at full capacity and thereby increases the cost of pumping water.

LITERATURE

1. Abramov S. K. Hydrogeological calculations of water inflow into excavations and artificial lowering of the groundwater level. Ugletekhizdat, 1952.
2. Skaballanovich I. A. Hydrogeological calculations. Ugletekhizdat, 1954.
3. Khokhlovkin D. M. Deep-well pumps for dewatering and water supply. Ugletekhizdat, 1954.
4. Building Norms and Rules, Part IV, Vols. 1 and 2, 1954.
5. Collection of unit rates for construction of the Kuibyshev Hydroelectric Power Station, 1954.
6. Kyrileis V. Artificial lowering of the groundwater level. Gosstroiizdat, 1933.