EXPERIMENTAL STUDIES OF THE DEPENDENCES OF TECHNOLOGICAL DRILLING PARAMETERS

V. I. Zvarygin

(Presented by the scientific seminar of the Department of Exploration Engineering)

The principal factors affecting drilling productivity are:

a) the design of the bit (quality, number, shape, and arrangement of the cutters);
b) technological drilling regimes;
c) properties of the rocks.

In order to determine optimal bit designs and technological drilling regimes, and to establish the dependence between technological parameters, special laboratory studies were set up.

Research Methodology

To solve the stated problem, a ZIV-75 drilling unit was used. The axial pressure on the bit was applied by means of S. A. Volkov’s regulator. The weights for producing the axial pressure were preliminarily weighed through Volkov’s system on a DS-0.2 dynamometer.

To record the circumferential force and axial pressure, as well as for visual observation of the magnitude of the torque, an experimental setup was developed and assembled. The electrical system of the laboratory setup consisted of the following parts:

1. A type S-0.75 stabilizer.
2. A two-channel bridge circuit using semiconductor devices, with a step-down input transformer.
3. Two filters. The filters were mounted on the same chassis as the bridge circuit.
4. A VS-24 rectifier.
5. A two-channel dynamometer with inductive sensors.
6. An N-700 oscillograph.

Figure 1 shows the electrical circuit of the laboratory setup.

To record the mechanical drilling speed, the following device was manufactured. A wooden platform was attached to the rear part of the vertical box of the machine; a sheet of millimeter paper was pinned to it. Between the locknut and the handwheel of the feed-nut brake, a bracket was fastened, in the lower part of which a ruler was installed. As the drilling tool deepened, the spindle together with the bracket moved downward; the ruler, pressed against the sheet of millimeter paper, also moved downward. During drilling, on the li-

… at the stand every 5–10 sec. marks were made with a pencil. After a series of experiments was carried out, the paper was removed and analyzed. From the magnitude of the drilling time interval and the magnitude of the advance between the marks, which was calculated on millimeter paper, the mechanical drilling speed was computed.

The experiments were carried out on cores of various rocks, having a diameter of 115 mm: sandstone, siltstone, marble. The length of the specimens was 15–30 cm. To study the technological regimes, standard core bits TP-3 and MR-6 with a diameter of 46 mm were used. To compensate for errors in the measurement results due to wear of the bit cutters, with each bit experiments were carried out on the same rock according to the following scheme: first drilling was carried out at speed I, speed II, speed III, then at speeds II, III, and I, and finally at speeds III, I, and II, i.e., over all drilling intervals it was carried out at all three speeds. The measurement results were summed, and the average value for each speed was determined. Under the same conditions, 10 experiments were carried out.

Fig. 1. Electrical measuring circuit of the laboratory setup.
a — schematic diagram; b — instrument connection diagram.

Study of the Dependence of Circumferential Forces on Axial Pressure

Determining the dependence of the circumferential forces acting during the drilling process on the bit on the magnitude of the axial pressure is of great importance for calculating certain technical quantities: the energy consumption of drilling, the strength of the cutters and of the drilling tool. An increase in energy expenditure affects the cost of drilling. In addition, the delivery of a large amount of energy to the bottomhole is limited by the strength of the drill string. All this makes it necessary to seek ways of reducing the energy consumption of drilling while maintaining or even increasing drilling productivity.

To determine the influence of axial pressure on circumferential forces, special experiments were set up on the laboratory installation described above. Drilling was carried out at a rotational speed equal to 405 per min, with TP-3 and MR-6 bits 46 mm in diameter, in sandstones and siltstones taken from the Anzher deposit. The TP-3 bits were fitted with eight thin plates of hard alloy; the MR-6 bits, with twelve cutters of form 1301. The interval of advance co…

were 20–30 cm. As the cutters became dull, they were sharpened on a sharpening machine.

For each given axial load, 10 experiments were carried out. The axial load in the experiments was 140, 230, 290, and 350 kg.

The results of processing the oscillograms are entered in Table 1.

Table 1

E. F. Epshtein [1], when drilling ore, granite, and sandstone with hard-alloy crowns, obtained the following data (Table 2).

Table 2

From the experimental data obtained by us and the published experimental materials of E. F. Epshtein, the following conclusions follow:

1) the tangential forces acting on the crown during the drilling process do not depend on the type of rock;

2) when drilling rocks with hard-alloy crowns, the dependence remains the same as when cutting with a single cutter;

3) the experimental data once again confirm the theoretical conclusions made by us earlier.

Investigation of the dependence of the mechanical drilling rate on axial load

As a result of processing the experimental material on drilling sandstones and aleurolites at different axial loads, the following data were obtained (Table 3).

Table 3

Using the tabular data, a graph was constructed (Fig. 2), analysis of which makes it possible to draw the following conclusion: the mechanical drilling speed of sandstones with bits having sharp cutters, at low axial pressure, increases up to a certain limit less intensively than at high loads. Moreover, at high loads (above \(P_0\)) the dependence of the mechanical drilling speed on axial pressure, within the investigated range, is linear in character. The same results were obtained by E. F. Epshtein [2], who carried out experiments on clayey, carbonaceous, and sandy shales, sandstones, limestones, and marble; by N. I. Lyubimov and V. I. Morozov [3] in drilling plagiogranite, gabbro-norite, keratophyre, basalt, gabbro, labradorite, skarn, marble, diabase, and basalt; by F. I. Kucheryavyi [4] in drilling gneiss and iron ore; by V. M. Trofimov [5] in drilling sandstones and sandy and clayey shales, etc.

Fig. 2. Graph of the dependence of the mechanical drilling speed:
a) on axial pressure: 1 — for sandstone, 2 — for siltstone; b) on the number of revolutions: 1 — for low-abrasive sandstone of category VI, 2 — for low-abrasive sandstone of category VIII, 3 — for abrasive sandstone of category VI, 4 — for abrasive sandstone of category VIII, 5 — for siltstone, 6 — for marble.

As the investigations show, for most rocks (including sandstones and siltstones) the straight-line dependence of the mechanical drilling speed on axial pressure passes either through the origin of coordinates or very close to it; therefore it may be considered that, when drilling with sharp cutters, the mechanical drilling speed for the rocks investigated by us is directly proportional to the magnitude of the axial pressure.

Investigation of the dependence of the mechanical drilling speed on the number of revolutions of the bit

The investigation to determine the dependence of the mechanical drilling speed on the number of revolutions of the bit was carried out on sandstones, siltstones, and marble with TP-3 and MR-6 bits 46 mm in diameter at 203, 405, and 810 revolutions per minute. To eliminate additional friction due to the matrices of the TP-3 bits, the rear angle of the cutters was ground off. The dependence of the mechanical drilling speed on the number of revolutions for various-

of the rocks has a different character. Even for one and the same rock with different mechanical properties, this dependence is different.

At the initial moment of drilling (3–5 sec), for all the rocks tested, the dependence of the mechanical drilling rate and the rotational speed of the bit has a linear character.

With a prolonged drilling time, for low-abrasive sandstones and siltstones the dependence curve has a quadratic function (Table 4, Fig. 2, b)

\[ v_{\text{mech}} = k \sqrt{n}, \]

where \(k\) is the proportionality coefficient.

In the figure the theoretical curves are shown by dashed lines.

One of the reasons for the lag in the rate of increase of the mechanical drilling rate behind the number of revolutions of the bit is wear of the cutters. As the rotational speed of the bit increases, wear of the cutters occurs more intensively, as a result of which the rate of mechanical drilling speed decreases.

Table 4

The phenomenon of intensive wear with an increase in the number of revolutions is especially clearly observed in highly abrasive sandstones. At a bit speed of 810 revolutions per minute, the prismatic cutters of MR-6 bits wear heavily, while the hard-alloy plates of TP-3 bits wear out and even chip at the corners. As a result, the rate of increase of the mechanical drilling speed drops sharply, and in some cases no increase in mechanical speed occurs; even a decrease is observed.

A. D. Imas [6], when drilling sandstones, found that at 300–400 revolutions per minute the curve has a maximum of mechanical speed, after which the curve descends, and at 500 rpm the mechanical drilling rate decreases to \(v_{\text{mech}}\), corresponding to drilling at 200 rpm.

When drilling a non-abrasive rock, owing to a substantial decrease in wear at different numbers of revolutions, the dependence should be rectilinear. To confirm this assumption, experiments were carried out on drilling marble. The results (Fig. 2, b) of the experiments indeed show a rectilinear dependence \(v_{\text{mech}} = f(n)\). A rectilinear dependence for marble was also obtained by other researchers [3].

It is interesting to note that, for the rocks studied by N. A. Lyubimov and V. I. Morozov [3], the dependences \(v_{\text{mech}} = f(n)\) have an analogous character. For basalt-type rocks the dependence \(v_{\text{mech}} = f(n)\) is analogous to that for abrasive sandstone, while for epidote-garnet skarn it is analogous to that for slightly abrasive sandstone and siltstone.

Thus, on the basis of the foregoing, it may be concluded that, for nonabrasive rocks (of the marble type), the dependence of the mechanical drilling rate on the number of revolutions is linear; for slightly abrasive rocks this dependence has the form

\[ v_{\text{mech}} = k\sqrt{n} \]

and for abrasive rocks it has a more complex character.

Study of the Dependence of the Peripheral Force on the Number of Revolutions of the Bit

The results of processing oscillograms obtained when drilling sandstones, siltstones, and marble (Table 5) show that, for all the rocks we tested, the peripheral force changes very little with an increase in the number of revolutions.

Table 5

Despite the substantial decrease in the mechanical drilling rate when the number of revolutions of the bit is increased (as is evident from the graphs presented above), the peripheral forces decrease very little. Some investigators [4, 6] attribute such increased values of the peripheral forces for breaking the rock, when the rotational speed of the bit is increased, to strengthening of the rock at an increased rate of load application.

On the basis of the experimental data obtained, it may be concluded that the peripheral force acting on the bit practically does not depend on the number of revolutions.

Study of the Dependence of the Depth of Cutter Penetration on the Number of Revolutions

In the process of cutting rock, the cutter, under the action of horizontal and axial forces, will continuously shear off in front of it rock elements of various sizes. After each large chip, the cutter, as a result of the action of the axial load and the small value of the horizontal load, will penetrate by some amount \(\Delta h\). If the cutting process proceeded very slowly, and the horizontal (peripheral) forces imparted to the cutter were arbitrarily large, then, obviously, at sufficient values of axial pressure, clearance, and cutter strength, the cutter could penetrate into the rock indefinitely, since after a large chip the possibility is created for the cutter each time to deepen by some amount. However, in drilling the cutter has some

a certain speed of motion, as a result of which, after the cutter has penetrated by an amount \(h\), it subsequently “does not have time” to enter the intervals between spalls, since the front face of the cutter is constantly in contact with the rock. Moreover, the higher the speed of movement of the cutter, the smaller the depth to which the cutter will penetrate (up to a certain speed of movement \(n_k\)).

To determine the influence of the number of revolutions of the bit on the penetration depth of the cutters, the results obtained in studying the dependence \(v_{\text{mech}} = f(n)\) may be used. In this case, the total penetration depth of the cutters was determined as the quotient obtained by dividing the mechanical drilling rate by the number of revolutions of the bit:

\[ h=\frac{v_{\text{mech}}}{n}. \]

To determine the penetration depth of the cutters at a small number of bit revolutions (\(n = 1\) rpm), the spindle was rotated manually with a wrench. The material processed in this way is presented in Table 6 and in the form of graphs (Fig. 3,a).

Table 6

Analyzing the graph obtained, the following is easy to note:

1. For the rocks studied, within the range of bit rotation speeds from 1 to 203 per minute, the penetration depth of the cutters decreases sharply (by approximately a factor of 4).

2. At bit rotation speeds above 203 per minute, for sandstones and aleurolites the rate of decrease in penetration depth is sharply reduced. Moreover, the rate of decrease for abrasive sandstones is lower than for slightly abrasive sandstones and aleurolites. Evidently, somewhere within the range of rotation speeds from 1 to 203 per minute there exists that limiting point which we earlier denoted by \(n_k\). At rotation speeds above \(n_k\), the penetration depth should remain constant (marble), but in fact, owing to wear of the cutters, it decreases (sandstones and aleurolites).

Unfortunately, it did not seem possible for us to find this point \(n_k\) for the rocks studied because of the lack of the necessary equipment.

Studies of the dependence of the mechanical drilling rate on the number of revolutions at low rotation speeds were carried out by F. A. Shamshev and I. M. Mlodik [2]. However, these studies were conducted on rocks that differ from those studied by us in drillability. Assuming that the mechanical drilling rate is directly proportional to the drillability of the rocks, we shall reduce the values obtained by F. A. Shamshev (for ease of comparison) to the values of mechanical rate obtained by us for sandstones. For this purpose, the mechanical drilling rate (obtained by E. F. Shamshev) at various numbers of revolutions is divided by 1.5 and

from the obtained \(v_{\text{mech}}\), we shall determine the depth of penetration of the cutter. In the same way we shall cite the penetration depth when drilling gneisses, according to the materials processed by F. I. Kucheryavy [4]. The average values of the depth of penetration of the cutters, obtained as a result of our experiments and the cited values of cutter penetration according to the materials of F. A. Shamshev and F. I. Kucheryavy, are given in Table 7.

Table 7

The obtained graph (Fig. 3,b) makes it possible to draw the following conclusions: 1) within the range of rotational speeds 1—200 per min the depth of penetration of the cutters decreases sharply, 2) the decrease in the depth of penetration of the cutters is inversely proportional to the number of revolutions, 3) when the number of revolutions is increased from

Fig. 3. Graph of the dependence of the depth of penetration of bit cutters on the number of revolutions:
a) 1 — for slightly abrasive sandstone, 2 — for abrasive sandstone; 3 — for siltstone; b) 1 — according to the materials of F. A. Shamshev, 2 — according to the materials of F. I. Kucheryavy, 3 — according to experimental data from drilling sandstone at the initial moment of drilling.

1 to 200 per min, for both sandstones and siltstones, as well as for gneiss, the depth of penetration of the cutters decreases by a factor of 4.

Conclusions

1. As a result of the experimental studies it has been established that the circumferential force acting on the bit when drilling various rocks amounts to one half of the axial pressure.

2. The circumferential force for the rocks tested does not depend on the lithological composition of the rock or on the rotational speed of the bit.

3. For the rocks tested, the mechanical drilling speed may be taken, with a small error, as directly proportional to the magnitude of the axial pressure.

4. The dependence of the mechanical drilling speed on the number of revolutions of the bit is complex in character. For slightly abrasive sandstones and siltstones it may be expressed by the function \(v_{\text{mech}} = k\sqrt{n}\).

5. The principal reason for the decrease in the rate of growth of the mechanical drilling speed with increasing rotational speed of the bit is the more intensive wear of the cutters at high numbers of revolutions.

6. As the number of revolutions of the bit increases from 1 to 200 per min, the depth of penetration of the cutters decreases, for the rocks studied, by approximately a factor of 4. With a further increase in the rotational speed of the bit, the rate of decrease in the depth of penetration of the cutters drops sharply. For slightly abrasive sandstones and siltstones, at a number of revolutions above 200 per min, the depth of penetration of the cutters is inversely proportional to the square root of the number of revolutions of the bit.

Literature

1. E. F. Epshtein. Theory of Drilling-Cutting of Rocks with Hard Alloys. GONTI, 1939.

2. E. F. Epshtein. Wear of Hard Alloys during Friction against Rocks in Core Drilling. Gostoptekhizdat, 1952.

3. N. I. Lyubimov, V. I. Morozov. The influence of drilling regimes on the rate of penetration of boreholes by carbide bits. Razvedka i okhrana nedr, No. 2, 1956.

4. F. I. Kucheryavyi. On the relationship between the rotational speed of a drill bit, the thickness of the layer removed by the cutter, and the energy intensity of the rock-destruction process. Razvedka i okhrana nedr, No. 8, 1957.

5. V. M. Trofimov. On stresses arising beneath the cutters of bits during drilling. Izvestiya vysshikh uchebnykh zavedenii. Geologiya i razvedka, No. 7, 1962.

6. N. N. Pavlova, L. A. Shreiner. Destruction of Rocks under Dynamic Loading. Nedra, 1964.