Advanced prediction for field strength parameters of rock using drilling operational data from impregnated diamond bit

Journal of Petroleum Science and Engineering 187 (2020) 106847

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Advanced prediction for field strength parameters of rock using drilling operational data from impregnated diamond bit Mingming He a, b, *, Ning Li a, b, Jiwei Zhu a, b, c, Yunsheng Chen b a

State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, 710048, China Shaanxi Key Laboratory of Loess Mechanics and Engineering, Xi’an University of Technology, 710048, China c Research Center of Eco-hydraulics and Sustainable Development, The New Style Think Tank of Shaanxi Universities, Xi’an, 710048, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Analytical model Rock strength parameters Impregnated diamond bit Drilling logging data

Field drilling can be a continuous, fast, and reliable technology to predict the cohesion, internal friction angle, and unconfined compressive strength (UCS) of rock in petroleum engineering. Herein, a theoretical model is established in an impregnated diamond bit considering some effective parameters including friction parameter, crushed zone, and bit geometry parameter. A novel method is proposed to determine field strength parameters including the cohesion, internal friction angle, and UCS of four types of rock using drilling logging data. Many drilling experiments in the field are conducted using a drilling process monitoring apparatus to obtain drilling logging data (thrust force, torque, penetration rate, and rotation speed). Experimental results on weak, mediumstrong, and strong rock show that drilling with an impregnated diamond core bit includes two fully dependent and simultaneous processes: rock cutting and frictional contact, the dominant role of which is dependent on the cutting point. The cohesion, internal friction angle, and UCS estimated from the proposed method for the four types of rocks are close to those from standard laboratory tests. This practical method can provide practical, fast, and reliable estimation for field strength parameters of rock and should be highly beneficial to field applications in rock engineering.

1. Introduction The unconfined compressive strength (UCS) of rock has become the most typical measurement of strength in most classification systems of rock mass in civil, mining, and petroleum engineering. The procedure to determine the UCS has been standardized by the International Society for Rock Mechanics (ISRM, Ulusay and Hudson, 2007) and the American Society for Testing and Materials (ASTM, 2010). The UCS test requires well-prepared samples; sample preparation is time consuming, costly, and difficult as well as destructive, in particular the polishing and rectification of the sample ends (Kalantari et al., 2018). Hence, alter­ native indirect methods such as point load, scratch, Schmidt hammer, and block punch tests have been developed to determine the UCS (Pal­ assi and Emami, 2014; Naeimipoura et al., 2018; He et al., 2019a, 2019b). However, to evaluate complex field conditions and related ef­ fects on field rock (Ma et al., 2015; Liu et al., 2018), the indirect methods present some limitations (Naeimipoura et al., 2018). The results from those methods only contain limited information regarding in-situ rock and may not necessarily reflect the properties of field rock (Richard

et al., 2012). Therefore, a new method for continuously and reliably measuring the field strength parameters of rock is crucial for the design of underground structures founded in rock. During the past 50 years, drilling has shown promise as a method for determining field strength and drillability of rock (Richard et al., 2012; Munoz et al., 2016a, 2016b; Taheri et al., 2016). In this method, the continuous and fast determination of field rock strength is enabled using measured drilling logging data from the drilling process. Apart from the advantage of continuous measurement, the method is applied as a quasi-nondestructive field method that is easily facilitated because of its nonsampling and simple movement (Kalantari et al., 2018). A signifi­ cant benefit of drilling is that the assessment of field conditions can be provided for field rock strength measurements. Therefore, researchers have established many methods to estimate rock strength based on force limit and energy equilibria. Force-equilibrium-based models include the “indentation model” (Evans, 1962), “shear model” (Nishimatsu, 1972), and “bit models” (Merchant, 1945; Detournay and Defourny, 1992; Gerbaud et al., 2006; Chiaia et al., 2013; Wojtanowicz and Kuru, 1993; Nakajima and Kinoshita, 1979; Franca, 2010; Roxborough and Philips,

* Corresponding author. State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, 710048, China. E-mail address: [email protected] (M. He). https://doi.org/10.1016/j.petrol.2019.106847 Received 29 August 2019; Received in revised form 10 December 2019; Accepted 20 December 2019 Available online 27 December 2019 0920-4105/© 2019 Elsevier B.V. All rights reserved.

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Journal of Petroleum Science and Engineering 187 (2020) 106847

1975; Hareland, 2010). However, except the Nakajima and Kinoshita (1979), and Gerbaud et al. (2006) model, the crushed zone has not been mentioned in the proposed relations between drilling data and rock strength. Kalantari et al. (2018) developed an analytical model to esti­ mate rock strength parameters using a T-shaped drag bit. Many re­ searchers (Teale, 1965; Karasawa et al., 2002a, 2002b; Ohno et al., 2004; Bingham, 1964; Wolcott and Bordelon, 1993; Hoberock and Bratcher, 1996; Burgess and Less, 1985; Pessier and Fear, 1992; Warren, 1987; Li and Itakura, 2012) have used various approaches to determine the UCS of rock during drilling based on the specific energy by Teale (1965). Moreover, several researchers developed a linear relationship between the intrinsic specific energy and UCS of rock (Munoz et al., 2016a, 2016b, 2017). Analytical models based on energy equilibrium can resolve the problem of the crushed zone during drilling. However, an explicit relationship between rock UCS and drilling logging data has been primarily circumstantial hitherto. Herein, a theoretical model is established based on the force limit equilibrium in an impregnated diamond bit considering the effective parameters of friction, crushed zone, and bit geometry. According to the proposed model, a new method is proposed to determine the field strength parameters including the cohesion, internal friction angle, and UCS of four different types of rocks. In this study, some drilling exper­ iments in the field were conducted by a drilling process monitoring apparatus (DPM) to obtain drilling operational data (thrust force, tor­ que, penetration rate, and rotation speed) using two independent wireless motors. In addition, the effects of various factors such as fric­ tions, crushed zone, and bit geometry on the estimated strength pa­ rameters were evaluated. The obtained strength parameters of rocks from the drilling method were compared with results from standard laboratory tests.

Mohre–Coulomb failure equation. Additionally, Fig. 1 shows that the three different media of diamond blade, compressed crushed zone, and failed rock are in contact. To model a drilling process, it is necessary to consider the intersecting helicoid trajectories (Mellor, 1978). For an impregnated diamond bit, when the penetration rate and rotation speed are v and w, respectively, the depth of penetration per rotation h can be calculated as (Kalantari et al., 2019)

2. Developed analytical model

In the n–t coordinate system shown in Fig. 1, the force Ft of the diamond blade that results from the torque (T) of an impregnated dia­ mond bit is the tangential acting force along the rotation of bit. The normal force Fn of the diamond blade that results from bit weight (W) is along the penetration of the bit. Each of the tangential force Ft and normal force Fn involves some components including cutting, frictional, and normal forces at the back end of diamond blade:

h¼

2v 60kw

(1)

where h is the depth of penetration per rotation, k is the number of cutters, v is the penetration rate, and w is the rotation speed, respec­ tively. The penetration depth is the same for all the diamond blades; this is reasonable in a stationary regime, owing to the progressive wear of the indenters (Kalantari et al., 2019). According to the cutting and failure characteristics of rock (Wang et al., 2018; Kalantari et al., 2019), the cutting model can be proposed based on the following assumptions: � Owing to the cutting width being significantly larger than the depth of penetration per rotation, the rock-cutting problem can be simpli­ fied as a plane-strain problem. � The cut region and crushed zone follows the Mohr–Coulomb criterion. � For a diamond core bit, the amount of displacement per rotation along penetration movement or depth of penetration per rotation for each diamond blade is the same for all the diamond blades. � The cutting model neglects the effect of rock anisotropy, water, and temperature. � Rock is an ideal elastic body, ignoring the effect of the pores, microcracks, discontinuities, etc.

In general, the drilling process in rock is performed in a helicoid motion simultaneously through two continuous stages: penetration and cutting process. The penetration and cutting stages must be performed simultaneously and continuously. Fig. 1 shows an impregnated diamond bit during drilling. For a diamond blade, we can assume that the dia­ mond blade is a pentahedron. The rake angle of the diamond blade is a, as shown in Fig. 1. During drilling, the diamond blade moves downward and penetrates into the rock. The penetration depth is created propor­ tionally to the drilling rate. During drilling, owing to the continuous downward and forward movements of the diamond blade, the crushed zone in front of the diamond blade is controlled by the rake angle of the diamond blade, as shown in Fig. 1. The minimum amount of compres­ sive stress in the crushed zone can be obtained based on the

Ft ¼ Fct þ F wt

Fh cos a þ 2F h tan θ

Fn ¼ F cn þ Fwn þ 3Fh sin a

(2) (3)

where Fcn is the normal components of the cutting force, Fct is tangential components of the cutting force, Fwn is the normal components of the friction force, Fwt is the tangential components of the friction force in the front end of diamond blade, respectively, Fh is a normal force in the back

Fig. 1. Geometry and mechanism of the acting forces in the proposed analytical model. 2

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Journal of Petroleum Science and Engineering 187 (2020) 106847

After some algebraic manipulation, the shear strength τo and hy­ drostatic pressure σo in the No. 2 crushed zone can be obtained from Eqs. (17) and (18):

end of diamond blade, Fh sin a is the frictional force between the dia­ mond blade and rock sides. The relationships among these parameters can be expressed as F cn ¼ F ct tanða þ θ Þ

(4)

F wt ¼ Fwn tan θ

(5)

0

τo ¼ σo tan ϕ

(6)

W ¼ kFn

(7)

0

T ¼ kFn

D1 þ D2 2

Fh cosða þ βÞ A

(9)

σ1 ¼

Fh sinða þ βÞ A

(10)

(20)

Fct tan a A tan2 a

τo cos ψ sin ψ

(21)

τ ¼ σo cos ψ sin ψ þ τo sin2 ψ

(22)

σ o cos ψ sin ψ þ τo sin2 ψ ¼ σ o sin2 ψ

0

σ1 tanϕ

CA cos ϕ F ¼ cosða þ ϕ þ βÞcos β

∂σ o ¼0 ∂ψ ψ¼

π 4

(25) ϕ ð

0

2

ϕ Þ

0

σo ¼

2C cosðϕ ϕÞ 0 0 ð1 þ tan ϕ tan ϕ Þ½cosðϕ ϕÞ sin2 ðϕ

τo ¼

2C cosðϕ 0 ð1 þ tan ϕ tan ϕ Þ½cosðϕ ϕÞ

0

0

(12)

0

0

ϕÞ�

ϕÞ þ sinðϕ

(28)

(29)

Fh cos a þ 2Fh tan θ

(30)

After some algebraic manipulation from Eqs. (29) and (30), the relationship between the tangential force Ft and normal force Fn can be obtained as 0

2AC cosðϕ

0

ϕÞ½1 þ tan ϕ tan a 0

ð1 þ tan ϕ tan ϕ Þ½cosðϕ

2CA cos ϕð2 tan θ cos a cosða þ ϕÞ

h

Finally the minimum value of F can be calculated as ðaþϕ Þ� 2

0

(27)

0

(15)

2CA cos ϕ cosða þ ϕÞ

ϕÞ�

Fn ¼ Aσ o tan a þ Aσ o tan ϕ þ Fwn þ 3F h sin a

Ft ¼ Fn tan θ þ

¼

0

0

ϕÞtan ϕ 0 sin2 ðϕ

Ft ¼ Aσo þ Aσ o tan ϕ tan a þ Fwn tan θ

(14)

CA cos ϕ cos½π4 þ ðaþϕ Þ�cos½π4 2

ϕÞ þ sinðϕ

Now, considering the normal and tangential acting forces in diamond blade as well as Eqs. ((2), (3), (5), (6), (17) and (18), the tangential force Ft and normal force Fn can be obtained as

Eq. (13) is derived in respect to β to obtain the minimum value of Fh. Then the value of β can be calculated as

aþϕ Þ ð 2

(26)

The minimum values of σo and τo are obtained as

(13)

∂F h ¼0 ∂β

sin2 ψ tan ϕ þ tan ϕ cos ψ sin ψ tan ϕ� (24)

Eq. (24) is derived in respect to ψ to obtain the minimum value of σ o. Then the value of ψ can be calculated as

If τ1 σ 1 tanϕ is replaced with the cohesion C in Eq. (11), and after some algebraic manipulation in Eq (12), the normal force Fh in the back end of diamond blade can be calculated as h

0

C ¼ σo ½cos ψ sin ψ þ tan ϕ sin2 ψ

where C is the cohesion of intact rock, ϕ is the internal friction angle of intact rock.τ1 and σ1 are taken from Eqs. (9) and (10), then we have Fh sinða þ βÞtan ϕ ¼ τ1 A

(23)

τo cos ψ sin ψ þ C

If τo is replaced with σotanϕ0 (from Eq. (6)) and after some algebraic manipulation, the cohesion can be obtained as

(11)

τ1 ¼ σ1 tanϕ þ C

Fh ¼

F cn A

where ψ is the angle of shear plane in front of the blade. The values of τ and σ from Eqs. (21) and (22) are assigned in the Mohr-Coulomb failure criterion of rock, then we have

where A is vertical cross-sectional area of cut, β is the angle of shear plane in the back of the blade, σ1 and τ1 are hydrostatic pressure and shear strength, respectively. The Mohr-Coulomb failure criterion of rock can be given as

4

τo ¼

σ ¼ σo sin2 ψ

(8)

τ1 ¼

β¼

(19)

Also in the potentially fail face of wedge, shear τ and normal σ tractions can be calculated as

where a, θ, θ , ϕ , τo , σo , D1, and D2 are the rake angle of diamond blade, contact friction angle between the bottom face of diamond blade and rock, contact friction angle between cutting face of diamond blade and compressed crushed zone, frictional angle between compressed crushed zone and intact rock, shear strength, hydrostatic pressure in compressed crushed zone, bit inner radius, and bit outer radius, respectively. T is bit torque, W is weight on bit. Now, for the normal force in the back end of diamond blade ignoring the friction force between the back end of diamond blade and compressed crushed zone (No.1 crushed zone, see Fig. 1), we have

π

Fct tan Fcn A A tan2 a

0

0

Fh cosða þ βÞ A

σo ¼

0

ϕÞ

0

ðtan a þ tan ϕ Þtan θ�

sin2 ðϕ

0

ϕÞ þ sinðϕ

0

ϕÞ�

3 sin a tan θÞ (31)

(16)

Eq. (31) shows that the normal force Fn and tangential force Ft are affected by cutting and friction during drilling, which occur simulta­ neously and are dependent on each other. The slope of this equation (Eq. (31)) is dependent on the contact friction angle between the diamond blade end wearing face and the rock. In many studies, drilling experi­ mental results show a linear relationship between the normal and tangential acting forces during rock penetration (Kalantari et al., 2018, 2019; Detournay and Defourny, 1992; Teale, 1965). Furthermore, they

Now, considering the No. 2 crushed zone (see Fig. 1), the tangential and normal components of the cutting force can be calculated as F ct ¼ Aσ o þ Aτo tan a

(17)

F cn ¼ Aσ o tan a þ Aτo

(18)

3

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Journal of Petroleum Science and Engineering 187 (2020) 106847

show that the penetration depth significantly affects the response of drilling. The intersection of the two forces was primarily located in the cutting point, which is a combination of cutting and friction processes (Dagrain, 2001, see Fig. 2). For a low thrust force (Fn < the force of the cutting point), the diamond blade only penetrates into the rock at a low

0

0

the side of diamond blade, frictional angle (ϕ ) between the intact rock and compressed crushed zone, rake angle (a) of the diamond blade, and internal friction angle of intact rock (ϕ). The slopes of Eqs. (34) and (35) are only dependent on the rock properties. Hence, when Eq. (34) is divided by Eq. (35), the linear relationship of Ft –Fn can be obtained as 0

0

0

Ft cosðϕ ϕÞcosða þ ϕÞ þ cos ϕð2 tan θ cos aÞ½cosðϕ ϕÞ sin2 ðϕ ϕÞ þ sinðϕ ϕÞ� ¼ 0 0 0 0 Fn cosðϕ ϕÞcosða þ ϕÞ þ 3 cos ϕ sin a½cosðϕ ϕÞ sin2 ðϕ ϕÞ þ sinðϕ ϕÞ�

depth, and the drilling energy is dissipated only in the rock cutting; the friction between the diamond blade and rock bottom sides is negligible. When the thrust force occurs beyond the cutting point, the diamond blade of the impregnated diamond bit penetrates deeply into the rock and creates a penetration depth. When friction and cutting occur simultaneously, including the pure cutting and the friction between the diamond blade and rock sides, the linear relationship of Ft –Fn in the impregnated diamond bit represents the theoretically pure cutting for Fn ¼ 0 (see Eq. (31)). For a low thrust force (Fn < the force of cutting point), the value of the friction force Fwt between the diamond blade and rock bottom sides is negligible. The normal force of the impregnated diamond bit can be transferred to the compressed crushed zone. This is the result of the friction and rake angle between the compressed crushed zone and dia­ mond blade. In this case, Eqs. (29) and (30) can be rewritten as 0

Ft ¼ Aσo þ Aσ o tan ϕ tan a

In the right of Eq. (36), there are four parameters a, ϕ , ϕ and θ, which are constant. Hence, the value of Ft/Fn is a constant as follows (Kalantari et al., 2018, 2019) 0

Ft 1 ¼ ¼ constant 0 Fn tanða þ θ Þ

(ϕ ), internal friction angle of intact rock (ϕ), and rake angle (a) of the diamond blade. The normal force of the diamond blade from the impregnated diamond bit is transferred to the rock owing to the crosssectional area. Hence, using Eq. (31) or (37), friction appears when drilling with the impregnated diamond bit. In the diamond blade, the friction between the diamond blade end side wearing face and rock, acting as a resistant force, is crucial for cutting. For a high thrust force (Fn > the force of the cutting point), the friction between the cutting side and crushed zone becomes a resistant force in the penetration process for transferring the normal force to the crushed zone. If a weight is imposed on the impregnated diamond bit, the penetration depth for the diamond blade becomes larger. Owing to the cutting force acting as a dominant force, the cutting process is crucial for drilling. According to Eqs. (34), (35) and (37), for a high thrust force (Fn > the force of cutting point), the contact friction (θ) at the side of the diamond blade, frictional angle between the compressed crushed zone and intact 0

(33)

0

Fn ¼ Aσo tan a þ Aσo tan ϕ þ 3F h sin a

By substituting Eqs. (16) and (27) into Eqs. (32) and (33), respec­ tively, the axial force Fn and tangential force Ft can be calculated as 0

Ft ¼

0

2CAð1 þ tan ϕ tan aÞcosðϕ ϕÞ 0 0 0 0 ð1 þ tan ϕ tan ϕ Þ½cosðϕ ϕÞ sin2 ðϕ ϕÞ þ sinðϕ

ϕÞ�

2CA cos ϕð2 tan θ cos aÞ þ cosða þ ϕÞ

(34) 0

2CAðtan a þ tan ϕ Þcosðϕ 0 0 0 ð1 þ tan ϕ tan ϕ Þ½cosðϕ ϕÞ sin2 ðϕ 6CA cos ϕ sin a þ cosða þ ϕÞ

Fn ¼

0

ϕÞ 0 ϕÞ þ sinðϕ

(37)

For a high thrust force (Fn > the force of the cutting point), the relationship between the normal force Fn and tangential force Ft is dependent on the contact friction (θ) at the side of the diamond blade, frictional angle between the compressed crushed zone and intact rock

(32)

F h cos a þ 2Fh tan θ

(36)

rock (ϕ ), and rake angle of the diamond blade (a) are dominant factors. For the diamond core bit, the shape of each diamond blade impregnated in the bit is irregular, thereby resulting in the difficulty and limitation of the measurement of rake angle of each diamond blade. For a diamond core bit (see Fig. 1), owing to the irregular shape of diamond grains in a bit, the rake angle (a) of the diamond blade cannot be measured accu­ rately; therefore, it is assumed as an unknown parameter. We can use the following five steps to estimate the strength parameters of rock: 0

ϕÞ� (35)

where A � Bh=2, and B is the shape parameter of the cutter. The linear relationship of Ft –A and Fn –A are dependent on the contact friction (θ) at

(1) According to Eq. (37), we can calculate the value of a þ θ using the experimental results of the linear Ft –Fn relation for a low thrust force (Fn < the force of cutting point). According to Eq. (31), the value of the contact friction (θ) using the experimental results of the linear Ft –Fn relation for a low thrust force. The 0

contact friction angle θ of the diamond blade side wearing face and the contact friction angle θ in the cutting face are almost the same in the cutting and friction processes (Kalantari et al., 2018). Subsequently, the rake angle (α) can be obtained according to Eqs. (31) and (37). (2) The linear slope from Eqs. (34), (35) and (37) in low thrust forces are important. Using the obtained rake angle (α) and the value of (θ0 ) from the slope of the linear Ft –Fn curve in a high thrust force, after some algebraic manipulations of Eqs. (17) and (18) to 0

Fig. 2. Synthetic model for drilling (modified from Dagrain, 2001). 4

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Journal of Petroleum Science and Engineering 187 (2020) 106847

estimate the internal friction angle of rock, the value of ϕ0 can be calculated as 0

0

ϕ ¼ arc tan

tanða þ θ Þ tan a 0 1 tan a tanða þ θ Þ

(38)

(3) Using the estimated friction angle (ϕ ) from Eq. (38), the internal friction angle (ϕ) can be calculates as (Kerisel, 1975; Gerbaud et al., 2006) 0

2 0 ϕ ¼ tan 1 ð tan ϕ Þ

(39)

π

(4) The slopes in Eq. (34) and Eq. (35) can obtained from the plotted drilling data (Ft –h andFn –h) in low thrust forces (Fn < the force of the cutting point) in the impregnated diamond bit. Using the

Fig. 4. (a) Drill bit geometry, and (b) Part of drilled rock samples.

m for the cutting process. The thrust force servomotor and torque servomotor function independently during drilling. The DPM can accurately measure the thrust force, torque, and drilling depth in a self-control manner, separately. With increasing drilling depth, it can automatically save the drilling operational data in an Excel file. The DPM with the maximum collection ability of 500 data per seconds can accurately complete several hundred sets of drilling data storage. In this experiment, the rotation speed (w) and penetration rate (v) are imposed as control parameters, while the thrust force and torque can be obtained as the drilling response. An impregnated diamond bit (see Fig. 4) is used as a drill bit in this DPM. The variation of the thrust force and torque with an increasing drilling depth for argillaceous sandstone is shown in Fig. 5. The thrust force and torque are obtained by many repeated tests. Fig. 5 shows that after the initial drilling stage, the thrust force and torque tend to be in the stationary drilling state (Detournay et al., 2008). The measurements of drilling data have been repeated many times in the stationary drilling state. As this DPM is a crawler type, it can easily be adopted for outcrop field drilling.

parameters (θ, ϕ , ϕ, a) obtained from the steps (1)–(3) and the slope of Fn –h (orFt –h), the cohesion C can be calculated according to Eq. (34) or Eq. (35). Subsequently, we can use the slopes of Eqs. (31), (34) and (37) from test results and Eqs. (38) and (39) to 0

solve the five parameters (θ , ϕ , ϕ, a, and C). (5) Using the obtained cohesion and internal friction angle from the proposed method, based on the Mohr–Coulomb criterion, the UCS of rock (qc) can be calculated as 0

qc ¼

2C cos ϕ 1 sin ϕ

0

(40)

where qc is the UCS of intact rock. 3. Drilling equipment We have developed a drilling process monitoring apparatus (DPM, He et al., 2019a; see Fig. 3) and used the DPM to estimate the field strength parameters of the in-situ rock. The DPM can be used for drilling in fields of an inner diameter 60 mm, outer diameter 70 mm, and drilling depth 50 m. It can continuously measure and record drilling logging data such as thrust force (Fn), torque (T), penetration rate (v), rotation speed (w), drilling depth, and penetration depth per rotation (h). Two different servomotors are applied to measure the thrust force (Fn) and torque (T). The thrust force servomotor can provide the maximum thrust force capacity of 18 kN for the penetration, and the torque servomotor can provide a reliable torque force with a maximum capacity of 2458 N

4. Experimental results In this study, a large number of field drilling tests have been con­ ducted on rocks with different UCSs in sandstone as weak rocks, lime­ stone and marble as medium-strong rocks, and granite as a strong rock (see Fig. 4(b)). Granite is a black cloud quartz feldspar. Its main minerals of granite are quartz, potassium feldspar, and plagioclase, whereas its secondary mineral is biotite. Its natural density is 2.60–2.64 g/cm3,

Fig. 3. An overview of the drilling process monitoring apparatus (DPM). 5

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Journal of Petroleum Science and Engineering 187 (2020) 106847

Fig. 5. Variations of measured (a) torque, and (b) thrust force with drilling depth in different test repetitions on sandstone.

moisture content is 0.44–0.46%, longitudinal wave velocity is 5010–5108 m/s. The crumb structure of sandstone is subcircular, the debris content is 86%, and the interstitial content is 14%. The single mineral debris in the main debris of rock is dominated by potassium feldspar, and rock debris is dominated by volcanic and pyroclastic rocks. The natural density is 2.45–2.51 g/cm3; the moisture content is 2.43–2.46%; the longitudinal wave velocity is 2488–2531 m/s. Lime­ stone is primarily gray, brittle, calcareous, and uniform particles, and its features are uneven oblique fractures. The main minerals of limestone are calcite, dolomite, and pyrite. Its natural density is 2.58–2.63 g/cm3, moisture content is 0.82–1.03%, longitudinal wave velocity is 4853–5106 m/s. The marble is gray at the sampling site and contains two main mineral components, namely, dolomite and calcite, and has a density of 2.59–2.62 g/cm3. The longitudinal wave velocity of the rock samples is 3850–4117 m/s. The physical information of the rocks is presented in Table 1. Owing to the significant effect of discontinuities in rocks arising from determining the mechanical properties of intact rock using drilling logging data, the selected specimens were obtained from homogeneous, uniform, and integrate rocks, which may reduce the effect of the dis­ continuities on the result obtained from this proposed method. We performed conventional laboratory tests and drilling tests on the same type of rock. For each type of rock, the number of drilling tests per­ formed using the impregnated diamond bit is more than five, with many repetitions in similar conditions. Furthermore, we performed all drilling tests rapidly to avoid the effects of environmental factors (humidity and temperature) on the test results. The specimens selected were obtained from the same rock layer to maintain the uniformity of the specimens. Each sample was processed into a cylindrical shape of standard sample size ϕ50 mm � 100 mm (diameter � height). The nonparallel error of the end face of the sample was <0.005 mm, and the section unevenness error was <0.02 mm; the smooth vertical diameter error was <0.3 mm. The UCS, cohesion, and internal friction angle of each rock type were measured in a laboratory using the WDT-1500 testing machine (He et al., 2018) according to the ISRM testing procedure and guidelines (Fairhurst and Hudson, 1999). The standard test results are shown in Table 1. An impregnated diamond bit of outer diameter 70 mm and inner diameter 60 mm was used to conduct the drilling tests, as shown in Fig. 4

(a). The drilling operational parameters include the penetration rate and rotation speed of each rock type. The penetration rates of limestone, granite, marble, and sandstone were set as 0.1–1.2 mm/min. Rotation speeds of 200–600 rpm were applied for each rock type. The DPM was operated with different penetration rates and rotary speeds. The DPM measures the torque and thrust force for drilling in different depths and subsequently saves the data in an Excel file. The curve thrust force and torque versus drilling depth for sandstone are presented in Fig. 5, which shows that the values approach a constant rate (stationary state) after an initial violation in the surface. The thrust force and torque changed at different penetration rates and rotation speeds. Hence, a drilling test with different penetration rates and rotation speeds was repeated a few times under the same condition (see Fig. 5). The thrust force and torque force were obtained in the stationary state of the drilling operation. The recorded torque force and thrust force in the stationary state were used to estimate the rock strength parameters. Fig. 6 shows the plots of torque force versus penetration depth per rotation, and thrust force versus penetration depth per rotation for limestone, granite, marble and sandstone, separately. As shown, the torque and thrust forces increase linearly with increasing penetration depth in the cutting process and the cutting and friction processes. Within the ranges of Fn < the force of cutting point, the normal pene­ tration force Fn increases progressively with the penetration depth and subsequently saturates at a limit value when the penetration depth reaches a critical value (Lhomme, 1999). At shallow penetration depths, the negligible friction force between the diamond blade and rock bottom sides conform entirely. Hence, any increase in the cutting force associ­ ated with the pure cutting process is from the increase in the penetration depth (h) before the penetration depth reaches the critical depth of penetration (Detournay et al., 2008; Zhou and Detournay, 2014). Beyond the critical value of the penetration depth, the normal compo­ nent of the frictional force reaches a stable value and the effective contact stress reaches a limited value (Rostamsowlat, 2018). In this stage, the increment of the cutting response is governed by the pure cutting of the diamond blade. These findings from the impregnated diamond bit are consistent with the results of other type of bits (Adachi, 1996; Dagrain, 2006; Detournay et al., 2008; Rostamsowlat et al., 2018; Rostamsowlat, 2018). Fig. 7 shows the plots of torque force versus thrust force data for

Table 1 Obtained physical information and strength parameters for rocks from standard tests. Rock type

Density (g/cm3)

Moisture content (%)

Longitudinal wave velocity (m/s)

Cohesion, C (MPa)

Internal friction angle, ϕ(� )

USC, qc (MPa)

Sandstone Limestone Marble Granite

2.45～2.51 2.58～2.63 2.59–2.62 2.60～2.64

2.43～2.46 0.82–1.03 1.56–1.83 0.44～0.46

2488–2531 4853–5106 3850–4117 5010–5108

5.8 10.7 8.23 17.1

40 56.3 53.4 63.2

24.8 74.3 60.2 145.2

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Journal of Petroleum Science and Engineering 187 (2020) 106847

Fig. 6. The plots of torque force versus depth of penetration per rotation, and thrust force versus depth of penetration per rotation for (a, b) limestone, (c, d) granite, (e, f) marble and (g, h) sandstone.

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Journal of Petroleum Science and Engineering 187 (2020) 106847

Fig. 7. The plots of torque force versus thrust force data for (a) limestone, (b) granite, (c) marble and (d) sandstone.

limestone, granite, marble, and sandstone, separately. A pair of torque and thrust forces was obtained from different drilling operational data, and each of their data points is represented in Fig. 7. Owing to the dependence on the predominating cutting process, the cutting points are changed for the different thrust forces in the Ft–Fn relation of the impregnated diamond bit. Generally, the drilling rotary process of rock is performed through two stages: penetration and cutting, where the fraction process is performed perpendicular to the penetration move­ ment, ignoring the axial direction of the friction process owing to the low friction force (Kalantari et al., 2018). If drilling is dominated by the friction process, the data points of the Ft–Fn relation follow a linear path with a high intercept. If the drilling is dominated by cutting, the points on another path follow the same path as that of the Ft–Fn linear relation (Dagrain, 2001). For the impregnated diamond bit, the obtained data between the two paths of the Ft–Fn linear relation perform a combination of friction and cutting processes. The data from the two paths were primarily located on the cutting point. The cutting and friction processes are dependent on the applied force Fn (see Fig. 7). In other words, the dominance of the cutting point for the impregnated diamond bit de­ pends on the diamond blade end wearing and penetration depth per rotation. When the diamond blade end wearing is low and negligible (Fn < the force of cutting point), the incremental cutting response is gov­ erned by pure cutting. For the applied force Fn > the force of the cutting point, the penetration depth increases with the increasing thrust force, and the friction and cutting processes are provided simultaneously (see Fig. 7). When the drilling test was performed by the impregnated diamond bit during cutting, the diamond blades of the impregnated diamond bit penetrated into the rock and created a penetration depth. Rock was cut during drilling rotation. For the cutting and friction processes, the slope

of the Ft–Fn linear equation is a function of the contact friction, while the intercept value is dependent on the penetration depth, which correlates with the crushed zone, rock properties, and bit geometric parameters, as shown in Eq. (31). Using least-squares regression, the correlation be­ tween the thrust and torque forces for the cutting and friction processes is a linear curve in the impregnated diamond bit (see Fig. 7). Their correlation coefficients are almost larger than 0.9. This linear correla­ tion satisfies Eq. (31). Therefore, two trend lines are observed, one ob­ tained from the cutting process with the impregnated diamond bit and the other from the cutting and friction processes. The impregnated diamond bit trend lines from the cutting process pass almost from the origin of the coordinates, the small error from which can be neglected. The obtained trend lines from the cutting and friction processes have intercepts with relatively low slopes. According to the obtained slopes of Ft–Fn linear curves during the cutting process and the cutting and friction processes in Fig. 7, the rock mechanical parameters can be calculated based on the proposed method. Owing to the uniformity of the bit material at the cutting face and end wearing face, the contact friction angle in the cutting face (θ’) and the contact friction angle in the end wearing face of the diamond blade (θ) are almost the same (Kalantari et al., 2019). The calculated Table 2 Obtained strength parameters for rocks from drilling tests.

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Rock type

ϕ (� )

θ ; θ(� )

ϕ(� )

C (MPa)

qc (MPa)

Sandstone Limestone Marble Granite

49.6 71.5 70.3 75.02

11.31 16.7 14.04 14.6

38.7 60.7 62.3 67.2

5.16 10.08 8.79 15.82

22.39 72.28 71.26 157.04

0

0

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Journal of Petroleum Science and Engineering 187 (2020) 106847

parameters of the rocks including the frictional angle (θ ; θ), frictional

sandstone are 60.7� , 67.2� , 62.3� , and 38.7� respectively; the calculated internal friction angles are close to the results from the standard test (56.3� , 63.2� , 53.4� , and 40� , respectively). For weak rocks such as sandstone, the internal friction angle estimated from the proposed for­ mula is slightly low. However, for moderate and hard rocks, the esti­ mated internal friction angle is relatively high owing to the existence of a boundary layer of failed rock in the cutting face. In the proposed

0

angle (ϕ ) between the compressed crushed zone and intact rock, and internal friction angle (ϕ) are given in Table 2. According to Fig. 7, the variations of torque and thrust forces with the penetration depth in the cutting process are large. The correlations between the torque and thrust forces and the penetration depth per rotation for the cutting and friction processes are a linear curve, obtained using least-squares regression (see Fig. 7). Their correlation coefficients R2 are almost larger than 0.91, which satisfies Eq. (37) or (44). Based on the slopes of linear Ft–h (or Fn–h) curves obtained during drilling, the cohesion of rocks can be calculated. Subsequently, the UCS of rock (qc) can be calculated from Eq. (40) (see Table 2). 0

model, the variations of the estimated ϕ and ϕ with the slope b of the Ft–Fn linear curve are shown in Fig. 8. When the slope b changes from 0.9 0

to 3.2, the estimated values of ϕ are 35.3� –76.3� and 24.3� –69.06� for ϕ. These ranges almost encompass the range of friction angles of all rocks. The slope of the Ft–h or Fn–h linear curve from an impregnated dia­ mond bit was used to estimate the cohesion of rocks. To obtain the cohesion of rocks, the values of internal friction angle ϕ and friction 0

5. Discussion

angle ϕ of rock were used. According to Eq. (34) and Eq. (35), the slope of the Ft–Fn linear curve in the cutting and friction processes and the rake angle a of the impregnated diamond bit was used. As shown in Fig. 6, the slopes of the linear Fn–h curve for limestone, granite, marble, and sandstone during drilling are 29.2, 55.6, 23.5, and 9.98, respectively. According to Eq. (35), the estimated cohesion from the slope of the linear Fn–h curve for limestone, granite, marble, and sandstone are 10.08, 15.82, 7.52, and 5.16 MPa, respectively, which are almost close to the results of the standard test (10.7, 17.1, 8.23, and 5.8 MPa, respectively). The error values by comparing with the standard test values are 5.8%, 7.5%, 8.6%, and 11% for limestone, granite, marble, and sandstone, respectively. The obtained cohesion for all rocks is slightly low compared with the standard test results. This can be attributed to the slightly high penetration depth per rotation h (Eq. (35)) owing to more plastic deformity, caused by the high plastic deformities during drilling, especially in soft rocks (Warren, 1987). Moreover, ac­ cording to Eq. (35), the estimated cohesions from the slope of the linear 0

For the impregnated diamond bit, the shape of each diamond blade impregnated in the bit is irregular, resulting in the difficulty and limi­ tation in determining the rake angle of the diamond blades. During drilling, the diamond blade may wear out and change the shape of the diamond blade. Therefore, we assume that the rake angle a is an un­ known variable, and the value of the rake angle can be estimated approximately using Eqs. (31) and (37). As shown in Fig. 7, the slopes of the trend lines for the cutting and friction processes in limestone, granite, marble, and sandstone are 0.31, 0.26, 0.25, and 0.2, respec­ tively. Using Eq. (31), the values of contact friction angle (θ) in the diamond blade side wearing face for rocks were calculated as 16.7� , 14.6� , 14.04� , and 11.31� for limestone, granite, marble, and sandstone during cutting and friction processes. The contact friction angle θ in the cutting face and the contact friction angle θ of the diamond blade side wearing face are almost the same in the cutting and friction processes 0

(Kalantari et al., 2018). We can replace θ with θ in Eqs. (31) and (37), and the value of the rake angle a can be estimated as 9.9� , 5.6� , 14.8� , and 19.3� correspondingly. In these cases, the rake angle of the diamond blades is considered as a < 20� . For rake angles <20� , Fig. 7 shows that their effects on the estimated parameters from the proposed method are negligible (Bingham, 1964; Roxborough and Philips, 1975; Hibb and Flom, 1978; Hoover and Middleton, 1981; Karasawa and Misawa, 1992; Li et al., 1993; Richard et al., 1998, 2012; Sinor et al., 1998). Therefore, according to Eqs. (31) and (37)–(39), we can estimate the internal friction angle of the rocks. The slopes of the Ft–Fn linear curve for the cutting process in limestone, granite, marble, and sandstone are 0.502, 0.31, 0.55, and 0.93, respectively. Based on Eq. (38), the values of 0

Fn–h curve are related to the parameters ϕ, ϕ , and a. The parameter a is related to the measured slope of the linear Ft–Fn curve in the cutting process and cutting and friction processes. In other words, the measured slopes of the linear Ft–Fn curve is responsible for the effect of the parameter a on the estimated cohesion. Hence, owing to the indepen­ dence of the measured slopes of the linear Ft–Fn curve, the effect of the rake angle a on the cohesion is negligible for rake angles <20� in all 0

cases. The parameters ϕ and ϕ are related to the rock and compressed crushed zone, respectively. The effects of these parameters on the esti­ 0

mated cohesion from Eq. (35) show that for 5� � ϕ � 81� and 3:2� � ϕ � 76� , these parameters affect the estimated cohesion (see 0

frictional angle ϕ for limestone, granite, marble, and sandstone are 71.5� , 75.02� , 70.3� , and 51.5� , respectively. Using Eq. (37), the calculated internal friction angle for limestone, granite, marble, and 0

Fig. 9). When the parameters ϕ and ϕ are at the ranges of 35.3� –76.3� and 24.3� –69.06� , respectively, their effects on the estimated cohesion are negligible. These ranges are close to the internal friction angles and 0

Fig. 8. (a) Variations of estimated internal friction angle and friction angle between compressed crushed zone and rock with rake angle. (b)Variations of estimated internal friction angle and friction angle between compressed crushed zone and rock with slope of Ft ~ Fn linear diagram. 9

M. He et al.

Journal of Petroleum Science and Engineering 187 (2020) 106847

Fig. 10. Intrinsic specific energy versus unconfined compressive strength (a is back-rake angle).

Fig. 9. Variations of estimated cohesion from intercept point with rake angle.

contact friction angle of all natural rocks. Therefore, the proposed method can estimate cohesion conservatively for most rocks. Next, the UCS is calculated according to Eq. (40) using the cohesion and internal friction angle of rock obtained from the proposed method. As shown in Table 2, the estimated UCS from the proposed method for limestone, granite, marble, and sandstone are 77.01, 157.04, 60.9, and 22.39 MPa, respectively. The UCS values of the four rocks are 74.3, 145.2, 60.2, and 24.8 MPa from standard tests. Hence, limestone, granite, and marble have been overestimated by 3.6%, 11.6%, and 8.2%, respectively, and sandstone underestimated by 9.7%. Despite the slightly overestimated UCS of rocks with high strength, the proposed method is practical for weak and moderate rocks. Therefore, the pro­ posed method can be used to estimate the UCS of rocks. Moreover, a comparison with the experimental results of recent studies (Richard et al., 2012; Munoz et al., 2016a, 2016b, 2017) was performed to verify the difference among the different drill bits. We used the obtained drilling logging data to calculate the intrinsic specific en­ ergy of the four types of rocks (Richard et al., 2012). The relationship between the intrinsic specific energy and UCS of rocks was obtained, as shown in Fig. 10. The relationship between the intrinsic specific energy and UCS of rocks from the impregnated diamond bit differed with that from PDC cutting (Richard et al., 2012; Munoz et al., 2016a, 2016b, 2017), which was linear. This was because the shape of each diamond blade impregnated in the bit was irregular. Hence, the geometry of the drill bit is an important influencing factor. Additionally, the proposed method was affected by limitations and field conditions such as rock anisotropy, water, temperature, and formation pressure (Ma et al., 2015). In future studies, the existing limitations and deficiencies will be reduced by considering the effects of discontinuities, joint orientation, joint spacing, rock types, rock anisotropy, water, temperature, forma­ tion pressure, and geological rock mass.

cutting and frictional contact, the dominant role of which was depen­ dent on the cutting point. The incremental response of the impregnated diamond bit was similar to the response of a blunt bit below the cutting point and the response of a sharp bit beyond the cutting point. Moreover, the estimated strength parameters for the four rocks using the drilling operational data agreed well with those of the standard test. The test results indicated that the estimated strength parameters of the rocks were within the accepted error range of 15% compared to the results from standard laboratory tests. The drilling test for the estimation of rock strength parameters offered several advantages over conventional tests. The drilling method provided high-resolution and continuous field measurements of rock strength parameters. Additionally, the technique could predict the strength parameters of rock at a speed several orders of magnitude faster than standard laboratory tests. Finally, owing to its minimum requirement for test preparations, this practical method should be highly beneficial for field applications in rock engineering.

6. Conclusions

This study is sponsored by the National Natural Science Foundation of China (Grants No. 51779207 and 11902249) and Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JQ395). The financial support provided by this sponsor is greatly appreciated.

Author contributions section Prof. Li and Dr. He contributed to the conception of the study. Dr. He contributed significantly to analysis and manuscript preparation; Prof. Chen and Dr. He performed the data analyses and wrote the manuscript; Prof. Zhu and Dr. He performed the analysis with constructive discussions. Declaration of competing interest The authors declare no conflict of interest. Acknowledgements

In this study, an analytical model in diamond core bit was developed to determine rock strength parameters such as the cohesion, internal friction angle, and UCS of four types of rocks (high, medium, and weak strength ranges) using drilling operational data. The model was estab­ lished by considering the effects of parameters such as compressed crushed zone, friction, and bit geometry during drilling. The experi­ mental results with high, medium, and weak strength ranges of rock suggested that drilling with the impregnated diamond bit could not be considered as two fully independent processes: “pure cutting” and “frictional contact.” The two simultaneous processes included rock

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