A New Mechanical Specific Energy Model for Composite Impact Drilling

Abstract

Composite impact drilling technology is one of the important techniques to increase drilling speeds in deep hard formations. In order to evaluate the efficiency of drilling with a composite impactor in real time and effectively, and to further improve the drilling speed in deep formations, the mechanical specific energy (MSE) model of drilling with a composite impactor was studied. Based on previous theoretical studies on MSE, and considering the effect of the composite impactor on the axial and torsional impact of the drill bit during operation, a new MSE model for composite percussion drilling was established. The results show that the evaluation of the drilling efficiency by MSE obtained by this calculation model is consistent with the actual situation of a Lufeng X well. It can be more widely used in wells drilled with composite impact tools and meet the needs of field operations.

1. Introduction

With the continuous development of oil and gas exploration and development to deep and ultra-deep wells, problems such as low rock-breaking efficiency of a PDC bit (Poly-crystalline Diamond Compact Bit) and head failure due to stick–slip vibrations are becoming more and more frequent in deep hard formations. As a drilling tool that can convert hydraulic energy into periodic axial and circumferential impact force, the composite impactor can effectively reduce the stick–slip vibration of the drill bit and achieve the purpose of increasing the ROP (Rate of Penetration) (Liu et al. 2016) [1]. MSE refers to the mechanical work required to destroy a rock per unit volume (Teale 1965, Chen 2014) [2,3], which can be used as an objective method to evaluate drilling efficiencies. As early as 1965, Teale proposed a calculation model of MSE based on a large number of experiments (Teale 1965) [2], which was also the original model of MSE calculations. Later, various conditions and working conditions were considered by Pessier and Fear (1992) [4], Duprlest et al., (2005) [5], Duprlest and Koederitz (2005) [6], Cherif (2012) [7], and Chen (2014) [8]. The MSE model was adjusted to improve its accuracy. As a new speed-up method for deep hard formations, composite impact drilling technology has achieved good application effects in the field (Su 2019) [9]. Researchers have also done some kinematics and dynamics studies on this technology (Wang 2019) [10], but there is no relevant research on the MSE model of drilling with composite impact technology. Therefore, based on the theory of MSE, a new MSE model of composite impact drilling is established by considering the effect of a composite impactor on the drill bit’s axial impact force and torsional impact force during operation. This model can be used to evaluate and analyze the drilling efficiency and working condition of drill bit in the process of compound impact drilling, optimize the drilling parameters and further improve the drilling speed.

2. Materials and Methods

2.1. Rock-Breaking Mechanism of Composite Impact Drilling

A compound impactor is a drilling speed accelerating tool developed by sheenstone (Shenzhen, China) Oil Tools Co., Ltd. (Su 2019) [9]. The tool adopts an all-metal design and is suitable for deep hard and high-temperature formations. It mainly includes structures such as throttle nozzles, converters, axial hammers and circumferential pendulums. As shown in Figure 1, during the drilling process, the drilling fluid forms a pressure difference between the axial hammer and the circumferential pendulum through the action of the throttle nozzle and the converter, and the axial hammer reciprocates in the axial direction to generate the axial impact load, which can increase the drill bit, the cutting depth of the cutting teeth into the rock; the axial pendulum produces the torsional impact load in the circumferential direction, which can reduce the stick–slip effect of the PDC bit. The composite impact load formed by the two is transmitted to the bit to achieve the torsional impact rock-breaking effect.

2.2. Mechanical Specific Energy Calculation Model of Composite Impact Drilling

Based on a large number of experiments, Teale took into account the influence of factors such as bit weight, bit diameter, rotational speed, mechanical penetration rate and torque on the working efficiency of the bit. In 1965, he first proposed the calculation model of MSE, which was also the original model of MSE (Teale 1965) [2]:

$$MSE=\frac{WOB}{A_b}+\frac{120\pi \cdot N\cdot T}{A_b\cdot ROP}$$

(1)

where MSE is mechanical specific energy, N is bit rotating speed, T is torque, ROP is rate of penetration, $A_b$ is the bit area and WOB (Weight on bit) is the weight on bits of the surface measurement.

According to the rock-breaking mechanism of drilling with the composite impact tool mentioned previously, the energy of rock breaking by composite impact drilling mainly comes from the work done by four forces: weight on bit, torque, axial impact force generated by impact hammer and circumferential torsion force generated by the pendulum. In hard formations, hydraulic energy is mainly used to clean rock cuttings at the bottom of wells, and its contribution to the energy of broken rock is negligible here (Chen 2016) [11]. In the actual drilling process, the mechanical energy provided by the power drilling tool to the bit cannot be used to break rock, so the influence of mechanical efficiency needs to be considered (Duprlest et al. 2005, Duprlest and Koederitz 2005, Cherif 2012) [5,6,7]. Considering the above factors comprehensively, the mechanical-specific energy equation at each impact can be expressed as follows:

$$MSE=E_m\left(\frac{E_W}{A\cdot ROP}+\frac{E_T}{A\cdot ROP}+\frac{E_a}{A\cdot ROP}+\frac{E_t}{A\cdot ROP}\right)$$

(2)

where $E_m$ is the mechanical efficiency of the bit, which can be measured by core experiments or retrieved from the logging data of adjacent wells. $E_W$ is the axial energy generated by surface WOB on the bit. Chen pointed out that the WOB measured by surface WOB indicator is measured under surface conditions (Chen 2014) [8], which is greatly different from the actual bottomhole WOB, and the relationship between the bottomhole WOB and surface WOB is obtained through research:

$$WO{B}_b=WOB\cdot e^{-\mu {\gamma }_b}$$

(3)

where $WO{B}_b$ is the bottomhole actual weight on the bits, $\mu$ is the coefficient of friction of the drill string, usually the value of 0.35 (Li 2009) [12] and ${\gamma }_b$ is the inclination of the bottomhole. Therefore,

$$E_W=WO{B}_b\cdot ROP=WOB\cdot e^{-\mu {\gamma }_b}\cdot ROP$$

(4)

$E_T$ is the rotational kinetic energy generated by the surface rotary table on the bit and is a function of torque. Pessier took the influence of the sliding friction coefficient into consideration and expressed torque as a function of the bit weight (Pessier and Fear 1992) [4]. By substituting Equation (3), we obtain the torque generated by the surface turntable on the bit:

$$T_b={\mu }_b\frac{D_{b}WO{B}_b}{36}={\mu }_b\frac{D_{b}WOB\cdot e^{-\mu {\gamma }_b}}{36}$$

(5)

where $T_b$ is the torque on the bit generated by the surface turntable and $D_b$ is the bit diameter. Therefore,

$$E_T=120\pi N{T}_b=3.33{\mu }_b\pi N{D}_{b}WOB\cdot e^{-\mu {\gamma }_b}$$

(6)

$E_a$ is the impact energy generated by the axial impact hammer in the composite impactor on the bit, and $E_t$ is the torsion energy generated by the circumferential pendulum in the composite impactor on the bit:

$$E_a=F_a{v}_a$$

(7)

$$E_t=F_t{v}_t$$

(8)

where $F_a$ is the axial impact force of an axial hammer on the bit, $v_a$ is the final velocity of the impact motion of the axial impact hammer, $F_t$ is the circumferential torsional force exerted by the circumferential pendulum on the bit and $v_t$ is the final circumferential velocity of a circumferential pendulum.

The composite impactor converts the hydraulic energy of the drilling fluid to 80% torsional impact and 20% axial impact through an energy distribution device. Since the influence of hydraulic energy on rock breaking is ignored, it can be considered that the composite impactor distributes 80% of the flow to the circumferential pendulum and the remaining 20% to the axial hammer through the energy distribution device. Based on the conservation of mass law and Bernoulli equation, the axial impact force, the axial impact velocity, the torsional impact force and the torsional impact velocity can be, respectively, expressed by the following formulas:

$$F_a=\Delta p_a{A}_a=\frac{1}{2}\rho \left(\frac{0.04Q^2}{A_2{}^2}-\frac{0.04Q^2}{A_1{}^2}\right)A_a$$

(9)

$$v_a=\frac{\Delta p_a{A}_a}{m_a}t$$

(10)

$$F_t=2\Delta p_t{A}_t=\rho \left(\frac{0.64Q^2}{A_2{}^2}-\frac{0.64Q^2}{A_1{}^2}\right)A_t$$

(11)

$$v_t=\frac{\Delta p_t{A}_t\left(R_1+R_2\right)}{2\left(J_1+J_2\right)}t$$

(12)

where $\Delta p_a$ is the pressure drop resulting from drilling fluid flow through an axial hammer, $A_a$ is the stress area of the impact hammer, $\rho$ is the drilling fluid density, $Q$ is the drilling fluid rate, $A_2$ is the throttle nozzle area, $A_1$ is the tool area of the upper part of the composite impactor, $m_a$ is the mass of the axial impact hammer, $t$ is the single impact time of the composite impactor, which can be determined by the impact frequency, $\Delta p_t$ is the pressure drop resulting from drilling fluid flowing through a circumferential pendulum, $A_t$ is the stressed area of a circumferential pendulum, $R_1$ is the external radius of the circumferential pendulum, $R_2$ is the inner radius of the circumferential pendulum, $J_1$ is the circumferential pendulum moment of inertia and $J_2$ is the moment of inertia of the converter. Therefore,

$$E_a=\frac{\Delta p_a{}^2{A}_a{}^2}{m_a}t=\frac{{\rho }^2{A}_a{}^2{Q}^4{\left(A_1{}^2-A_2{}^2\right)}^{2}t}{2500m_a{A}_1{}^4{A}_2{}^4}$$

(13)

$$E_t=\frac{\Delta p_t{}^2{A}_t{}^2\left(R_1+R_2\right)}{\left(J_1+J_2\right)}t=\frac{{\rho }^2{A}_t{}^2{Q}^4\left(R_1+R_2\right){\left(A_1{}^2-A_2{}^2\right)}^{2}t}{2500\left(J_1+J_2\right)A_1{}^4{A}_2{}^4}$$

(14)

Combined with Equations (2), (4), (6), (13) and (14), the calculation model of MSE under the condition of compound impact drilling is obtained.

$$\begin{array}{c}MSE=E_m\left(\frac{WOB·e^{-\mu {\gamma }_b}}{A}+\frac{13.33{\mu }_{b}NWOB·e^{-\mu {\gamma }_b}}{D_b·ROP}+\frac{\Delta p_a^2{A}_a^{2}t}{m_{a}A·ROP}+\frac{\Delta p_t^2{A}_t^2\left(R_1+R_2\right)t}{A\left(J_1+J_2\right)·ROP}\right)\hfill \\ =E_m\left(\frac{WOB·e^{-\mu {\gamma }_b}}{A}+\frac{13.33{\mu }_{b}NWOB·e^{-\mu {\gamma }_b}}{D_b·ROP}+\frac{{\rho }^2{A}_a^2{Q}^4{\left(A_1^2-A_2^2\right)}^{2}t}{2500m_{a}A{A}_1^4{A}_2^4·ROP}+\frac{64{\rho }^2{A}_t^2{Q}^4\left(R_1+R_2\right){\left(A_1^2-A_2^2\right)}^{2}t}{625A\left(J_1+J_2\right)A_1^4{A}_2^4·ROP}\right)\hfill \end{array}$$

(15)

3. Model Field Application Results

Lufeng Well X is an appraisal well-located in the Pearl River Mouth Basin. The formations of Zhuhai, Enping and Wenchang are mostly sandstone and mudstone, and the borehole wall is easy to collapse, and the bit wear is serious. Therefore, composite impactors are often used in the Lufeng block oil field, which has achieved a good speed-up effect. Taking Lufeng X well as an example, the interval of the well drilled with composite percussion was 2449.22~4100 m. The drilling tool assembly encountered the Paleogene Zhuhai Formation, Enping Formation and Wenchang Formation in one trip to the vertical depth, while the adjacent wells that were not drilled with a composite impactor required three trips to drill in this section on average, with a footage of 1650.78 m. The pure drilling time is 65.39 h, and the average ROP is 25.2 m/h. Its single bit footage and ROP have created records for the same horizon in the area, and the speed-up effect can reach up to 235.8% compared with adjacent wells The performance parameters of the composite impactor are shown in

Table 1. Specifications and parameters of the compound impactor.

Type	Drilling Speed up Tool
Size model	8-1/2″186B
Nozzle	W20 × 1
Upper connection buckle type	NC50 Box
Bit connection type	4-1/2″. REG Box
Largest diameter	7-5/16′ (186 mm)
Displacement	25~40 LPS (400–635 GPM)
Pressure drop	2.0~2.5 MPa (290-363 Psi)
Impact frequency	17~23 Hz
Maximum operating temperature	270 °C
The biggest WOB	160 kN (35 klbs)
The make-up torque	16~20 kN.m (11,792~15,000 ft-lb)

, the appearance dimensions are shown in Figure 2, the physical image is shown in Figure 3 and the dedicated PDC impactor bit used in conjunction is shown in Figure 4.

Using the above MSE calculation model, and according to the relevant geological data of the Lufeng X well, the calculation results of the MSE are obtained, as shown in Figure 5. The 2355–2499.22 m interval was the interval without the composite impactor. It can be seen from the figure that the MSE suddenly increased and the ROP significantly decreased after the increase of weight on the bit. It can be seen that increasing the WOB may not effectively improve the ROP and may even reduce the influence of the bit speed and drilling fluid displacement on the WOB, leading to the decrease of the rock-breaking efficiency of the bit and the bottomhole cuttings cleaning effect. After the replacement of the composite impactor, the MSE was reduced to roughly equal to the CCS (Compressive Strength of rock under Confining pressure) of the rock, especially in the 2500–2900 m interval, where the ROP increased most significantly. In the 2600–2650 m interval, the WOB decreased, MSE decreased and ROP increased and reached a peak, indicating that the rock-breaking efficiency of the bit was the highest. After 2900 m, drill into the Enping formation, the CCS of the rock group compared to the Zhuhai formation is increased, the energy for the broken rock is also increased; in the 2900 m~3650 m interval, MSE compared with the previous interval was increased, but the basic keep in the state of CCS is equal to or slightly greater than the rock WOB are stable fluctuations in this stage; the ROP decreased compared with before, but its stability will remain at a high speed, which shows that the rock fragmentation by this stage and drilling speed are efficient. After 3650 m, the MSE increases and is much higher than the CCS of the rock. As the weight on the bit increases, the ROP decreases and the rock-breaking efficiency of the bit decreases. To achieve a higher ROP, try to reduce the weight on the bit appropriately.

4. Conclusions

Based on the working principle of a composite impactor, a MSE model suitable for composite impactor drilling was put forward and verified by a field case of the Lufeng X well.

Composite impact drilling technology is a new type of drilling acceleration technology. Composite impact devices can convert hydraulic energy into periodic stable axial and torsional impact loads directly acting on the bit, so as to increase the cutting depth of the bit and reduce the stick–slip effect.

The evaluation of the bit efficiency based on the MSE proposed in this paper is in line with the actual situation of the Lufeng X well and can be widely used in oil and gas wells using compound impact drilling technology. The drilling parameters can be optimized through this model, so as to achieve the purpose of optimizing drilling in the construction process.