ANALYSIS OF THE DEPENDENCE OF PENETRATION RATE ON PRESSURE IN SHOT DRILLING

I. S. MITYUSHKIN and V. I. MOLCHANOV

In the summer of 1952, under production conditions, the Department of Prospecting conducted experiments aimed at studying the operating regimes of shot drilling. The experimental data, verified by additional tests on an instructional drilling rig, make it possible to draw certain conclusions about the optimal drilling regime.

By the optimal drilling regime is meant the combination of parameters that ensures the maximum penetration rate under given geological and technical conditions.

The principal parameters of the regime are:

a) the number of revolutions of the tool (bit), $n$ rpm,
b) pressure on the bit, $C$ kg,
c) flushing of the borehole, $W$ l/min,
d) method of feeding and dosing the shot, $q$ kg.

The present article is devoted to studying the question of the influence of pressure on the penetration rate. The character of this dependence may be represented by a certain curve with a clearly expressed maximum penetration rate at a certain optimal pressure on the bit.

The decline in penetration rate at pressures above the optimum is explained differently by different investigators.

There are three points of view.

1. The maximum on the curve corresponds to the strength limit of the shot. “The critical pressure for standard cast-iron shot is approximately 30 kg/cm²” and further: “The critical pressure depends not only on the shot, but also on the material of the bit and the properties of the rock, although the influence of the latter within the investigated intervals is small” (I. A. Ostroushko, “Destruction of Rocks in Drilling,” pp. 235, 237).

2. The decrease in penetration rate at pressures above the optimum is explained by excessively rapid crushing of the shot. This point of view is held by S. A. Volkov and I. A. Ostroushko. They believe that, at high pressures, cast-iron shot is ground down so quickly that it does not have time to perform useful work in destroying the rock. “Hard and brittle steel shot is rapidly ground down and therefore cannot work under high loads. In general, as brittleness increases, steel shot in its properties approaches cast-iron shot” (I. A. Ostroushko, p. 238).

From consideration of these two points of view it follows that the limiting pressure at the bottom hole is limited by the shot: it must be such that the shot under the end of the bit is not crushed, but remains round, and in order to ensure maximum penetration it is necessary to have strong shot (in particular, steel shot).

1. The low penetration rate at high pressure on the bit is explained by the squeezing of the shot out from under the end of the bit. In the opinion of the proponents of this point of view, shot at high pressures cannot remain under the end of the bit.

the bit, but is squeezed out to the side. No working particles remain between the bit and the rock, and the bit rests directly on the rock. “With an insufficient quantity of shot, the normal drilling process was disrupted because the shot came out from under the bit” (I. A. Ostroushko, p. 237).

The point of view set forth in the present article differs completely from those enumerated above.

We shall begin the explanation of the maximum on the curve in the coordinates “penetration rate \(U\)—pressure \(C\)” with a critical examination of the factual material.

The graphs given below (Figs. 1 and 2) were obtained on the experimental rig of the drilling test site of the Department of Exploration Engineering of the TPI. The purpose of the investigation was to determine the dependence of shot consumption and penetration rate on the pressure on the bit.

The results of these experiments are presented in the form of an observation table and graphs (Table 1, Figs. 1 and 2).

First of all, certain concepts should be clearly distinguished, namely: (a) hourly shot consumption and (b) shot consumption per meter. The first gives an idea of the quantity of shot used per hour of net drilling. The second gives an idea of the quantity of shot consumed per 1 linear meter of drilling. These two concepts reflect the essence of the bottom-hole process and make it possible to consider the dependence of penetration rate on pressure from a different point of view.

It does not seem possible to explain the optimum pressure on the bottom hole by the strength limit of the shot, because cast-iron brittle shot essentially splits under any pressure on the bit. At a pressure of \(2\ \mathrm{kg/cm^2}\) at the face of the bit, cast-iron shot gives particles exactly the same as at a pressure of \(40\ \mathrm{kg/cm^2}\), with the only difference that in the first case more time is needed for the shot to split.

Table 1

The strength limit of the shot is a constant quantity. If the maximum of the curve is to be explained by the strength limit of the shot, then why, with one and the same shot, with one and the same bit, but with different numbers of bit revolutions, is the maximum of the curves obtained under identical conditions not constant, but instead regularly decreases with an increase in the number of revolutions?

At a number of revolutions \(n = 90\) rev/min, the maximum occurs at a pressure \(C = 32\ kg/cm^2\), whereas at \(n = 380\) rev/min it corresponds to a pressure \(C = 22\ kg/cm^2\).

In other experiments this discrepancy lies in an even larger interval (Graph 1 in the article by V. I. Molchanov, included in this same collection).

Fig. 1

Labels visible in the figure:

• Penetration rate, cm/min
• Shot consumption, kg/min
• Shot consumption, kg/h
• Pressure on the bit, kg/cm²
• Curve labels:
• \(v\), cm/min
• \(Q\), kg/min
• \(q\), kg/h

Fig. 2

Labels visible in the figure:

• Penetration rate, cm/min
• Shot consumption, kg/min
• Shot consumption, kg/h
• Pressure on the bit, kg/cm²
• Curve labels:
• \(v\), cm/min
• \(Q\), kg/min
• \(q\), kg/h

The maximum on the curves also cannot be explained by excessively rapid crushing of shot at pressures above the optimum. If it is assumed that this phenomenon occurs, then a sharp increase in the hourly consumption of shot would undoubtedly be observed here. The hourly consumption of shot, however, remains constant when the pressure varies within the limits from 15 to 40 kg/cm\(^2\).

If the hourly consumption of shot depended on the pressure on the bit and on the speed of its rotation, this would be reflected in the instructions for shot drilling. The instructions, however, recommend the rate of shot charge only as a function of the drilling diameter and of the hardness of the rocks. The factual material obtained in carrying out the experiments likewise refutes the extrusion of shot from under the bit at pressures above the optimum.

If it were observed, then, first, in the pressure interval above the optimum the hourly consumption of shot would be equal to zero; but in this interval shot is nevertheless consumed in the same amount.

Second, the end face of the bit would in all cases have a polished rock surface. A polished surface of the end face occurs only in cases of a complete absence of shot, whereas in the presence of even an insignificant amount of shot it has a rough character.

Extrusion of shot from under the end face of the bit, as such, does indeed occur in cases of abnormal wear of the bit (an arrow is formed).

As is clear from what has been said above, none of the viewpoints listed above is sufficiently convincing. A more convincing explanation of the maximum on the curve can be found by considering the relation of the forces acting on the bit. The action of the shot on the rock through the bit will evidently not be indifferent to the character of the relation of these forces.

Acting on the bit are: 1) the rotating force \(P_{vr}\), transmitted by the motor of the rig and equal to \(\dfrac{M_{kr}}{r_{sr}}\cdot\eta\); 2) the friction force \(F_{tr}\), caused by the axial pressure \(C\) and by the character of the rubbing surfaces. Calculated as the friction force of the annular heel, it is equal to \(fC\); 3) the adhesion \(A\), equal to \(P_{vr} - F_{tr}\); 4) the axial pressure \(C\).

The actual destructive force is the resultant of two forces: the adhesion \(A\) and the axial pressure \(C\)

\[ \overline{R}=\overline{A}+\overline{C}. \]

When the axial pressure \(C\) changes, the friction force changes and, consequently, so does the difference \(P_{vr}-F_{tr}=A\), which leads to a change in the magnitude and direction of the resultant \(\overline{R}\).

At some value of \(C\) the friction force balances the rotating force. The adhesion \(A\) then tends to \(O\) \((A \to O)\), and the resultant \(\overline{R}\), in magnitude and direction, approaches the normal

\[ \angle \rho \to 90^\circ . \]

When \(C=O\), the difference \(P_{vr}-F_{tr}=A\) also tends to \(O\).

\[ \angle \rho \to O. \]

In the first case, rock destruction is of low productivity, because only the force of direct compression is present; in the second, there will be no rock destruction at all, because the bit does not touch the rock.

Useful work, evidently, can be obtained at some intermediate value of \(C\), that is, the destructive force must be applied at a certain angle \(\rho\).

The most advantageous angle of application of the destructive force \(R\) is the angle complementary to the friction angle \(\rho=90-\varphi\), where \(\varphi\) is the friction angle.

For $\rho = 90 - \varphi$, the adhesion $A$ is numerically equal to $fC$, where $f$ is the coefficient of friction.

Under the established optimum regime, the rotating force is $P_{\mathrm{rot}} = 2 f C_{\mathrm{opt}}$. This equality indicates the most advantageous ratio of the forces acting on the bit, which ensures the maximum on the curve $U = \Phi(C)$.

The optimum pressure on the bottom hole is determined as

$$ C_{\mathrm{opt}} = \frac{P_{\mathrm{rot}}}{2f}. $$

If this equality is violated, unproductive consumption of shot takes place. The same quantity of shot per hour of net drilling performs different work, and this is understandable: only at $C_{\mathrm{opt}} = \frac{P_{\mathrm{rot}}}{2f}$ will the action of the shot on the rock be effective.

This equality simply and convincingly explains the reason for the regular shift of the maximum of the curves toward lower pressures as the number of revolutions of the bit increases.

An increase in the number of revolutions causes a decrease in the rotating force. The most advantageous ratio

$$ C_{\mathrm{opt}} = \frac{P_{\mathrm{rot}}}{2f} $$

will be established at a smaller value of $C_{\mathrm{opt}}$, as is indicated by the series of curves obtained at different numbers of revolutions of the bit.

Analysis of a large number of curves $U = \Phi(C)$ shows that the maximum of any of them corresponds to

$$ C_{\mathrm{opt}} = \frac{P_{\mathrm{rot}}}{2f}. $$