3. Drilling performance prediction and optimization based on mechanical specific energy technologies

#### 3.1. Confined compressive strength

Teale's laboratory experiment showed that MSE was numerically close to the unconfined compressive strength (UCS) of the formation at maximum drilling efficiency [6]. However, the tests were conducted at atmospheric conditions. In the real drilling process, MSE is numerically close to the CCS of the formation at maximum drilling efficiency. In other words, when drilling achieves a maximum drilling efficiency, the minimum MSE is reached and is roughly equal to the CCS of the rock drilled [14].

$$MSE(\text{min}) = \text{CCS} \tag{43}$$

3.2.2. Drilling performance prediction and optimization method

efficiency.

MSE is the amount of energy required to destroy a unit volume of rock and it provides a means of evaluating and optimizing drilling performance. By comparing MSE to the predicted CCS, as well as by comparing actual ROP to the predicted ROP, drilling performance and bit condition can be evaluated. The drilling performance can be evaluated and predicted by Eqs. (44) and (46). When MSE is equal to the predicted CCS, or actual ROP is equal to the predicted ROP, it indicates that drilling performs well and the bit is operating at its peak

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Drilling performance optimization based on MSE technologies means real-time analyzing of MSE and adjusting drilling parameters accordingly to minimize drilling problems and maximize ROP. When a bit is operating at its peak efficiency, the ratio of energy to rock volume will remain relatively constant, and MSE is nearly equal to the CCS of the formation. This relationship is used operationally by observing whether the minimum MSE is equal to the CCS of the formation while adjusting drilling parameters such as WOB or RPM to maximize ROP. If the minimum MSE remains equal to the CCS of the formation while increasing WOB, the bit is assumed to be still efficient. If MSE increases significantly and is much higher than the CCS of the formation, the bit has foundered and drilling problems may occur, such as vibrations, bit balling, bottom hole balling and dull bits. The driller then determines the most likely cause of founder and drilling problems, and adjusts parameters accordingly. Adjustments continue to

Based on the relations between MSE, drilling parameters and ROP, an appropriate predicting and optimizing method can be proposed by analyzing bottom-hole conditions of drilling and determining the reasonability of drilling parameters. Figure 4 is the flow chart of the drilling

As shown in Figure 4, when MSE(min) = CCS, and ROP/WOB = constant >0, it is in the region B as Figure 5 [12] indicate. MSE is low and nearly equal to CCS. The slope of the line is relatively constant for a given formation, bit and rotary speed. The drilling efficiency remains at its peak efficiency. In this region, the bit is not constrained by a unique inefficiency, it simply needs more energy. Just by increasing WOB or RPM, the ROP will increase greatly and eventually approach the founder point. When ROP/WOB6¼constant > 0, it is close to the highest ROP that can be achieved with the current system and reached the region C. But if ROP further increases, then bit balling and bottom hole balling will occur. Therefore drilling parameters should be better set in the area near to the founder point to ensure that drilling performs efficiently and safely. Real-time MSE surveillance can be used to find the founder point. If MSE remains constant, the bit is efficient, if the MSE rises, the system is foundering.

When MSE(min) > CCS, it is in the region C, MSE is high and even several time of CCS. As ROP increases, down hole cuttings accumulate, which leads to bit balling, bottom hole balling, and constrains the energy from bit transfer to the rock, as a result ROP drops. If WOB further increases, vibrations will occur and ROP will decrease greatly. In this region, in order to extend

be made until the MSE value is minimized equally to CCS of the formation.

performance prediction and optimization method [12].

Therefore, MSE can be used to detect the peak drilling efficiency by surveilling MSE to see if the MSE(min) is roughly equal to the CCS of the rock drilled.

The widely practiced and accepted method for calculating CCS of rock is as follows [18].

$$\text{CCS} = \text{LCS} + D\_p + 2D\_p \cdot \frac{\sin \phi}{1 - \sin \phi} \tag{44}$$

In bottom-hole drilling conditions, for permeable rock, the bottom hole confining pressure can be expressed as

$$D\_p = E \mathbf{C} D\_p - P\_p \tag{45}$$

#### 3.2. Drilling performance prediction and optimization for directional or horizontal drilling

#### 3.2.1. Rate of penetration model based on mechanical specific energy

The rock strength at the rock-bit interface is best defined by CCS. Given the MSE model of directional or horizontal drilling takes the mechanical efficiency (Em) of the new bit into account, so we can assume that MSE is equal to the CCS of the formation. Substituting MSE in terms of CCS, then ROP can be predicted as follows [12].

$$ROP = \frac{13.33 \cdot \mu\_b \cdot RPM}{D\_b \left(\frac{\text{CCS}}{E\_m \cdot WOB \cdot \epsilon^{-\mu\gamma\_b}} - \frac{1}{A\_b}\right)}\tag{46}$$

The above ROP model is relatively simple. By using this model we can quickly predict the ROP with reasonable accuracy for all of the bit types, according to the formation properties and the drilling environment. One limitation of the ROP model is that it does not recognize the founder point of any given bit, which means it can predict a higher ROP than is achievable as WOB and RPM increase beyond the bit's optimum combination [23].

#### 3.2.2. Drilling performance prediction and optimization method

3. Drilling performance prediction and optimization based on mechanical

Teale's laboratory experiment showed that MSE was numerically close to the unconfined compressive strength (UCS) of the formation at maximum drilling efficiency [6]. However, the tests were conducted at atmospheric conditions. In the real drilling process, MSE is numerically close to the CCS of the formation at maximum drilling efficiency. In other words, when drilling achieves a maximum drilling efficiency, the minimum MSE is reached and is roughly

Therefore, MSE can be used to detect the peak drilling efficiency by surveilling MSE to see if

The widely practiced and accepted method for calculating CCS of rock is as follows [18].

CCS <sup>¼</sup> UCS <sup>þ</sup> Dp <sup>þ</sup> <sup>2</sup>Dp � sin <sup>ϕ</sup>

In bottom-hole drilling conditions, for permeable rock, the bottom hole confining pressure can

3.2. Drilling performance prediction and optimization for directional or horizontal drilling

The rock strength at the rock-bit interface is best defined by CCS. Given the MSE model of directional or horizontal drilling takes the mechanical efficiency (Em) of the new bit into account, so we can assume that MSE is equal to the CCS of the formation. Substituting MSE

ROP <sup>¼</sup> <sup>13</sup>:<sup>33</sup> � <sup>μ</sup><sup>b</sup> � RPM

The above ROP model is relatively simple. By using this model we can quickly predict the ROP with reasonable accuracy for all of the bit types, according to the formation properties and the drilling environment. One limitation of the ROP model is that it does not recognize the founder point of any given bit, which means it can predict a higher ROP than is achievable as WOB and

CCS Em�WOB�e

�μγ<sup>b</sup> � <sup>1</sup> Ab

Db

MSEð Þ¼ min CCS (43)

Dp ¼ ECDp � Pp (45)

(46)

<sup>1</sup> � sin <sup>ϕ</sup> (44)

specific energy technologies

144 Drilling

3.1. Confined compressive strength

equal to the CCS of the rock drilled [14].

be expressed as

the MSE(min) is roughly equal to the CCS of the rock drilled.

3.2.1. Rate of penetration model based on mechanical specific energy

in terms of CCS, then ROP can be predicted as follows [12].

RPM increase beyond the bit's optimum combination [23].

MSE is the amount of energy required to destroy a unit volume of rock and it provides a means of evaluating and optimizing drilling performance. By comparing MSE to the predicted CCS, as well as by comparing actual ROP to the predicted ROP, drilling performance and bit condition can be evaluated. The drilling performance can be evaluated and predicted by Eqs. (44) and (46). When MSE is equal to the predicted CCS, or actual ROP is equal to the predicted ROP, it indicates that drilling performs well and the bit is operating at its peak efficiency.

Drilling performance optimization based on MSE technologies means real-time analyzing of MSE and adjusting drilling parameters accordingly to minimize drilling problems and maximize ROP. When a bit is operating at its peak efficiency, the ratio of energy to rock volume will remain relatively constant, and MSE is nearly equal to the CCS of the formation. This relationship is used operationally by observing whether the minimum MSE is equal to the CCS of the formation while adjusting drilling parameters such as WOB or RPM to maximize ROP. If the minimum MSE remains equal to the CCS of the formation while increasing WOB, the bit is assumed to be still efficient. If MSE increases significantly and is much higher than the CCS of the formation, the bit has foundered and drilling problems may occur, such as vibrations, bit balling, bottom hole balling and dull bits. The driller then determines the most likely cause of founder and drilling problems, and adjusts parameters accordingly. Adjustments continue to be made until the MSE value is minimized equally to CCS of the formation.

Based on the relations between MSE, drilling parameters and ROP, an appropriate predicting and optimizing method can be proposed by analyzing bottom-hole conditions of drilling and determining the reasonability of drilling parameters. Figure 4 is the flow chart of the drilling performance prediction and optimization method [12].

As shown in Figure 4, when MSE(min) = CCS, and ROP/WOB = constant >0, it is in the region B as Figure 5 [12] indicate. MSE is low and nearly equal to CCS. The slope of the line is relatively constant for a given formation, bit and rotary speed. The drilling efficiency remains at its peak efficiency. In this region, the bit is not constrained by a unique inefficiency, it simply needs more energy. Just by increasing WOB or RPM, the ROP will increase greatly and eventually approach the founder point. When ROP/WOB6¼constant > 0, it is close to the highest ROP that can be achieved with the current system and reached the region C. But if ROP further increases, then bit balling and bottom hole balling will occur. Therefore drilling parameters should be better set in the area near to the founder point to ensure that drilling performs efficiently and safely. Real-time MSE surveillance can be used to find the founder point. If MSE remains constant, the bit is efficient, if the MSE rises, the system is foundering.

When MSE(min) > CCS, it is in the region C, MSE is high and even several time of CCS. As ROP increases, down hole cuttings accumulate, which leads to bit balling, bottom hole balling, and constrains the energy from bit transfer to the rock, as a result ROP drops. If WOB further increases, vibrations will occur and ROP will decrease greatly. In this region, in order to extend

but also drilling system specific. Figure 6 shows a classic drill-off curve [5]. The point at which the ROP stops responding linearly with increasing WOB is referred to as the founder point where the ROP is maximized. The corresponding WOB at this point is taken to be the optimum WOB. Figure 7 shows field data from three drill-off tests with an insert bit [5, 14]. It indicates that the bit is prone to founder with high RPM, and the optimum WOB decreases obviously with the increase of RPM of bit. Moreover, the founder point changes greatly with the change of RPM of bit. In rotating drilling with PDM, the surface rotation is superimposed on PDM rotation, the RPM of bit is high and could be changed greatly. It not only makes the bit be easy to reach the founder point even at low WOB, but also makes the founder point be difficult to be identified. MSE surveillance provides an objective assessment of the drilling efficiency and an

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Figure 6. Relationship between the traditional ROP versus WOB plot [14].

Figure 7. Field data from three drill-off tests [5].

Figure 4. Flow chart of drilling performance prediction and optimization [12].

Figure 5. Relationship between the traditional ROP vs. WOB plot and the new MSE vs. ROP plot [12].

the range of balling period and maximize ROP, nozzles and flow rates can be modified to achieve the highest hydraulic horsepower per square inch (HSI) possible with the available rig equipment. If reaching the rated power of the equipment, WOB should reduce, and drilling parameters should be set in the intersect area between region B and region C.

#### 3.3. Drilling parameters optimization for rotating drilling with PDM

Real-time optimization of drilling parameters during drilling operations aims to optimize WOB, RPM for obtaining maximum ROP [24, 25]. The process is not only formation specific

Figure 6. Relationship between the traditional ROP versus WOB plot [14].

but also drilling system specific. Figure 6 shows a classic drill-off curve [5]. The point at which the ROP stops responding linearly with increasing WOB is referred to as the founder point where the ROP is maximized. The corresponding WOB at this point is taken to be the optimum WOB. Figure 7 shows field data from three drill-off tests with an insert bit [5, 14]. It indicates that the bit is prone to founder with high RPM, and the optimum WOB decreases obviously with the increase of RPM of bit. Moreover, the founder point changes greatly with the change of RPM of bit. In rotating drilling with PDM, the surface rotation is superimposed on PDM rotation, the RPM of bit is high and could be changed greatly. It not only makes the bit be easy to reach the founder point even at low WOB, but also makes the founder point be difficult to be identified. MSE surveillance provides an objective assessment of the drilling efficiency and an

Figure 7. Field data from three drill-off tests [5].

the range of balling period and maximize ROP, nozzles and flow rates can be modified to achieve the highest hydraulic horsepower per square inch (HSI) possible with the available rig equipment. If reaching the rated power of the equipment, WOB should reduce, and drilling

Real-time optimization of drilling parameters during drilling operations aims to optimize WOB, RPM for obtaining maximum ROP [24, 25]. The process is not only formation specific

parameters should be set in the intersect area between region B and region C.

Figure 5. Relationship between the traditional ROP vs. WOB plot and the new MSE vs. ROP plot [12].

3.3. Drilling parameters optimization for rotating drilling with PDM

Figure 4. Flow chart of drilling performance prediction and optimization [12].

146 Drilling

objective tool to identify the founder point. Therefore, real-time optimization of drilling parameters for rotating drilling with PDM can be performed by identifying the founder point of the bit in specific formation drilling based on MSE surveillance.

As aforementioned, MSE is the amount of energy required to destroy a unit volume of rock. When a bit is operating at its peak efficiency, the ratio of energy to rock volume will remain relatively constant. The minimum MSE is reached and it correlates with the CCS of the formation. This relationship is used operationally by observing whether the MSE(min) is roughly equal to the CCS of the formation while adjusting drilling parameters such as WOB or RPM to maximize ROP. If the MSE(min) remains roughly equal to the CCS of the formation while increasing WOB, the bit is assumed to be still at its peak efficient. If the MSE(min) increases significantly and is much higher than the CCS of the formation, the bit has foundered. The causes of founder are bit balling, bottom hole balling and vibrations. If the causes of founder are not addressed when they occur, overall drilling performance will suffer and tools will be damaged.

Bit balling and bottom hole balling are terms used to describe build-up of material on the bit and bottom hole that inhibits transfer of a portion of the WOB to the cutting structure. They usually occur in soft formations, and can be relieved by increasing flow rates and reducing WOB. When drilling in hard formation with a PDM, bit balling and bottom hole balling are unlikely to occur, while vibrations are very common. Down hole vibrations include three modes: whirl (lateral), stick-slip (torsional) and bit bounce (axial). They amplify loads downhole, resulting in a host of bit and tool failures that not only increase the number of trips required, but also the costs of tool repair and replacement. Actually these vibrations in rotating drilling with PDM could be effectively eliminated by adjusting WOB or RPM on the surface.

Whirl can be effectively eliminated by reducing RPM while increasing WOB. Stick-slip can be minimized by reducing WOB and increasing RPM. As for bit bounce, if the bouncing is initiated when running high WOB and low RPM, the solution is to increase RPM and reduce WOB. Conversely, if the problem begins with higher RPM and lower WOB, the answer is to reduce RPM and increase WOB. It may also even be necessary to stop surface rotation and simply drill in slide mode (bit rotation is generated only from the PDM) through the problematic formation [26].

adjustment is shown in Figure 8. As drilling with PDM provides much higher RPM at the bit than the conventional rotating drilling could achieve, the bit is easy to reach the founder point even with low WOB. Further increasing WOB or RPM is more likely to decrease ROP and worsen the drilling problems. Moreover, high WOB that will generate excessive torque for the PDM may make PDM stalled, and RPM may also cause excessive vibration of the drill pipe. Therefore, the adjustment for rotating drilling with PDM is to reduce WOB first and then gradually increase WOB, and do the same manipulation for RPM until MSE(min) = CCS. The adjustment should not be in a very wide range. If MSE still much higher than the CCS of the formation after the adjustment of WOB and RPM, down hole conditions should be checked to

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Figure 8. Flow chart of drilling parameters optimization for rotating drilling with PDM [14].

4.1. Field case no.1: verification of MSE model and drilling performance prediction of

In order to verify the accuracy of the MSE model of directional or horizontal drilling, several other key models of MSE (such as Teale model [6], Pessier model [7], Dupriest model [5]) are

see if the bit and PDM were damaged.

directional or horizontal drilling

4. Field case

Assume the bottom hole is effectively cleaned, then based on the above analysis, a drilling parameters optimization method for rotating drilling with PDM can be proposed to maximize ROP and allow operators to drill longer and avoid unnecessary trips. Figure 8 is the flow chart of the drilling parameters optimization method for rotating drilling with PDM [14], and it is based on real-time MSE surveillance to find the founder point of the bit [12]. When MSE (min) = CCS, the bit performs in the region B as shown in Figure 6 and the drilling efficiency remains at peak efficiency. In this region, the bit is not constrained by a unique inefficiency, it simply needs more energy. Given a RPM, just by increasing WOB, the ROP will increase greatly and eventually approach the founder point.

When MSE(min) > CCS, and MSE(min) is even several time of CCS, the bit is floundering and drilling problems may occur. Adjustments of WOB and RPM need to be made until the MSE (min) value is minimized and roughly equal to the CCS of the formation. The process of Drilling Performance Optimization Based on Mechanical Specific Energy Technologies http://dx.doi.org/10.5772/intechopen.75827 149

Figure 8. Flow chart of drilling parameters optimization for rotating drilling with PDM [14].

adjustment is shown in Figure 8. As drilling with PDM provides much higher RPM at the bit than the conventional rotating drilling could achieve, the bit is easy to reach the founder point even with low WOB. Further increasing WOB or RPM is more likely to decrease ROP and worsen the drilling problems. Moreover, high WOB that will generate excessive torque for the PDM may make PDM stalled, and RPM may also cause excessive vibration of the drill pipe. Therefore, the adjustment for rotating drilling with PDM is to reduce WOB first and then gradually increase WOB, and do the same manipulation for RPM until MSE(min) = CCS. The adjustment should not be in a very wide range. If MSE still much higher than the CCS of the formation after the adjustment of WOB and RPM, down hole conditions should be checked to see if the bit and PDM were damaged.

#### 4. Field case

objective tool to identify the founder point. Therefore, real-time optimization of drilling parameters for rotating drilling with PDM can be performed by identifying the founder point

As aforementioned, MSE is the amount of energy required to destroy a unit volume of rock. When a bit is operating at its peak efficiency, the ratio of energy to rock volume will remain relatively constant. The minimum MSE is reached and it correlates with the CCS of the formation. This relationship is used operationally by observing whether the MSE(min) is roughly equal to the CCS of the formation while adjusting drilling parameters such as WOB or RPM to maximize ROP. If the MSE(min) remains roughly equal to the CCS of the formation while increasing WOB, the bit is assumed to be still at its peak efficient. If the MSE(min) increases significantly and is much higher than the CCS of the formation, the bit has foundered. The causes of founder are bit balling, bottom hole balling and vibrations. If the causes of founder are not addressed when they occur, overall drilling performance will suffer and tools

Bit balling and bottom hole balling are terms used to describe build-up of material on the bit and bottom hole that inhibits transfer of a portion of the WOB to the cutting structure. They usually occur in soft formations, and can be relieved by increasing flow rates and reducing WOB. When drilling in hard formation with a PDM, bit balling and bottom hole balling are unlikely to occur, while vibrations are very common. Down hole vibrations include three modes: whirl (lateral), stick-slip (torsional) and bit bounce (axial). They amplify loads downhole, resulting in a host of bit and tool failures that not only increase the number of trips required, but also the costs of tool repair and replacement. Actually these vibrations in rotating drilling with PDM could be effectively eliminated by adjusting WOB or RPM on the surface. Whirl can be effectively eliminated by reducing RPM while increasing WOB. Stick-slip can be minimized by reducing WOB and increasing RPM. As for bit bounce, if the bouncing is initiated when running high WOB and low RPM, the solution is to increase RPM and reduce WOB. Conversely, if the problem begins with higher RPM and lower WOB, the answer is to reduce RPM and increase WOB. It may also even be necessary to stop surface rotation and simply drill in slide mode (bit rotation is generated only from the PDM) through the problem-

Assume the bottom hole is effectively cleaned, then based on the above analysis, a drilling parameters optimization method for rotating drilling with PDM can be proposed to maximize ROP and allow operators to drill longer and avoid unnecessary trips. Figure 8 is the flow chart of the drilling parameters optimization method for rotating drilling with PDM [14], and it is based on real-time MSE surveillance to find the founder point of the bit [12]. When MSE (min) = CCS, the bit performs in the region B as shown in Figure 6 and the drilling efficiency remains at peak efficiency. In this region, the bit is not constrained by a unique inefficiency, it simply needs more energy. Given a RPM, just by increasing WOB, the ROP will increase

When MSE(min) > CCS, and MSE(min) is even several time of CCS, the bit is floundering and drilling problems may occur. Adjustments of WOB and RPM need to be made until the MSE (min) value is minimized and roughly equal to the CCS of the formation. The process of

of the bit in specific formation drilling based on MSE surveillance.

will be damaged.

148 Drilling

atic formation [26].

greatly and eventually approach the founder point.

#### 4.1. Field case no.1: verification of MSE model and drilling performance prediction of directional or horizontal drilling

In order to verify the accuracy of the MSE model of directional or horizontal drilling, several other key models of MSE (such as Teale model [6], Pessier model [7], Dupriest model [5]) are carried out and compared against field data. Initially, MSE is calculated respectively by these MSE models using surface measured data and plotted vs. depth. The results are compared with the rock CCS to verify the accuracy of the MSE model of directional or horizontal drilling. Then, the actual ROP and the predicted ROP which is calculated with Eq. (46) are both plotted vs. depth to verify the accuracy of the ROP prediction model, and the drilling parameters WOB, RPM, and MSE are also plotted vs. depth to explain the observed pattern. Furthermore, actual ROP and the predicted ROP of each bit are also plotted.

This well's trajectory is designed with a kick-off point (KOP) at 2925 m with a build rate of 5/ 30 m dogleg severity (DLS) until reaching 90 at 3465 m, and then steered a horizontal section to 4043 m measured depth. The log data of vertical section and horizontal section are used to calculate MSE respectively by Teale model, Pessier model, Dupriest model and the MSE model of directional or horizontal drilling. CCS is determined by Eq. (44) to verify the accuracy of these models. The comparison of MSE calculated results and CCS are showed on Figures 9 and 10 respectively in vertical section and horizontal section. It shows that the calculation errors of Teale model, Pessier model, Dupriest mode are apparently inflated in horizontal section. The MSE estimated with the MSE model of directional or horizontal drilling has the best correlation with CCS, and the order of models from good to poor in accurately predicting correlation effect is the MSE model of directional or horizontal drilling, Pessier model, Dupriest model and Teale model. In vertical section, the correlation effect of MSE model of directional or horizontal drilling, Pessier model, Dupriest model is relatively close, but far better than Teale model. In horizontal section, MSE values calculated with Teale model is more than 10 times of CCS, and MSE values calculated with Pessier model and Dupriest model are several times of CCS. As for the MSE model of directional or horizontal drilling, its MSE values are close to CCS. The correlation effect of the MSE model of directional or horizontal drilling in horizontal section is close to that of in vertical section. So the correlation effect of the MSE model of directional or horizontal drilling is apparently better than Pessier model, Dupriest model and Teale model in both vertical section and horizontal section.

Figure 11 plots the predicted ROP and the actual ROP vs. depth, and the drilling parameters WOB, RPM, and MSE are also included on Figure 11. The predicted ROP is calculated with Eq. (46). As indicated in Figure 11, the predicted ROP matches well with the actual ROP, which reveals that the ROP predict model's prediction accuracy is high, and can fully meet the needs of the field. Therefore, the MSE model of directional or horizontal drilling can be quantitatively applied. Figure 12 plots ROP prediction accuracy of each bit. A, B, and C bit's ROP prediction accuracy respectively are 84.8% (A), 91.2% (B), 76.8% (C). In the section of 2700–2750, 2830–2890 and 3167–3215 m, the predicted ROP is higher than the actual ROP. The drilling parameters WOB, RPM, and MSE plotted vs. depth are used to explain the observed

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Figure 10. Comparison of MSE calculated results and testing CCS in horizontal section.

In 2700–2750 m, MSE value increases and actual ROP reduces greatly, and the predicted ROP is higher than the actual ROP. After the WOB increases from 30 to 52 kN from 2730 to 2766 m, MSE value reduces to the baseline trend and the actual ROP increases. In this section, as the hydraulics and bit rotating speed don't change, so it can't be bit balling and bottom hole inadequate cleaning. Therefore, it is likely that whirl leads energy cannot effectively passed to the bit, as a result actual ROP decreases. And in fact, whirl is also observed in this section. In 2830–2890 m and 3167–3215 m, MSE value increases slowly and actual ROP reduces greatly, trip-out and discovery that bit was badly damaged. Change a new bit and drill with the same

4.2. Field case no.2: drilling parameters optimization for rotating drilling with PDM

To verify the new mechanical specific energy model, drilling data of a 2621-ft section of a vertical well have been used to calculate the profiles of CCS and MSE with depth. The drilling data, including WOB, surface RPM, ROP, mud flow rate and on-bottom PDM differential pressure, were recorded for every 1-ft step from 4072 to 6693 ft. The lithology is limestone and the section was drilled with 22 in bits and a 9:10 lobe ratio PDM. The efficiency of PDM is

drill parameter, MSE value decreases and actual ROP increases.

pattern in Figure 11.

Figure 9. Comparison of MSE calculated results and testing CCS in vertical section.

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Figure 10. Comparison of MSE calculated results and testing CCS in horizontal section.

carried out and compared against field data. Initially, MSE is calculated respectively by these MSE models using surface measured data and plotted vs. depth. The results are compared with the rock CCS to verify the accuracy of the MSE model of directional or horizontal drilling. Then, the actual ROP and the predicted ROP which is calculated with Eq. (46) are both plotted vs. depth to verify the accuracy of the ROP prediction model, and the drilling parameters WOB, RPM, and MSE are also plotted vs. depth to explain the observed pattern. Furthermore,

This well's trajectory is designed with a kick-off point (KOP) at 2925 m with a build rate of 5/ 30 m dogleg severity (DLS) until reaching 90 at 3465 m, and then steered a horizontal section to 4043 m measured depth. The log data of vertical section and horizontal section are used to calculate MSE respectively by Teale model, Pessier model, Dupriest model and the MSE model of directional or horizontal drilling. CCS is determined by Eq. (44) to verify the accuracy of these models. The comparison of MSE calculated results and CCS are showed on Figures 9 and 10 respectively in vertical section and horizontal section. It shows that the calculation errors of Teale model, Pessier model, Dupriest mode are apparently inflated in horizontal section. The MSE estimated with the MSE model of directional or horizontal drilling has the best correlation with CCS, and the order of models from good to poor in accurately predicting correlation effect is the MSE model of directional or horizontal drilling, Pessier model, Dupriest model and Teale model. In vertical section, the correlation effect of MSE model of directional or horizontal drilling, Pessier model, Dupriest model is relatively close, but far better than Teale model. In horizontal section, MSE values calculated with Teale model is more than 10 times of CCS, and MSE values calculated with Pessier model and Dupriest model are several times of CCS. As for the MSE model of directional or horizontal drilling, its MSE values are close to CCS. The correlation effect of the MSE model of directional or horizontal drilling in horizontal section is close to that of in vertical section. So the correlation effect of the MSE model of directional or horizontal drilling is apparently better than Pessier model, Dupriest model and

actual ROP and the predicted ROP of each bit are also plotted.

150 Drilling

Teale model in both vertical section and horizontal section.

Figure 9. Comparison of MSE calculated results and testing CCS in vertical section.

Figure 11 plots the predicted ROP and the actual ROP vs. depth, and the drilling parameters WOB, RPM, and MSE are also included on Figure 11. The predicted ROP is calculated with Eq. (46). As indicated in Figure 11, the predicted ROP matches well with the actual ROP, which reveals that the ROP predict model's prediction accuracy is high, and can fully meet the needs of the field. Therefore, the MSE model of directional or horizontal drilling can be quantitatively applied. Figure 12 plots ROP prediction accuracy of each bit. A, B, and C bit's ROP prediction accuracy respectively are 84.8% (A), 91.2% (B), 76.8% (C). In the section of 2700–2750, 2830–2890 and 3167–3215 m, the predicted ROP is higher than the actual ROP. The drilling parameters WOB, RPM, and MSE plotted vs. depth are used to explain the observed pattern in Figure 11.

In 2700–2750 m, MSE value increases and actual ROP reduces greatly, and the predicted ROP is higher than the actual ROP. After the WOB increases from 30 to 52 kN from 2730 to 2766 m, MSE value reduces to the baseline trend and the actual ROP increases. In this section, as the hydraulics and bit rotating speed don't change, so it can't be bit balling and bottom hole inadequate cleaning. Therefore, it is likely that whirl leads energy cannot effectively passed to the bit, as a result actual ROP decreases. And in fact, whirl is also observed in this section. In 2830–2890 m and 3167–3215 m, MSE value increases slowly and actual ROP reduces greatly, trip-out and discovery that bit was badly damaged. Change a new bit and drill with the same drill parameter, MSE value decreases and actual ROP increases.

#### 4.2. Field case no.2: drilling parameters optimization for rotating drilling with PDM

To verify the new mechanical specific energy model, drilling data of a 2621-ft section of a vertical well have been used to calculate the profiles of CCS and MSE with depth. The drilling data, including WOB, surface RPM, ROP, mud flow rate and on-bottom PDM differential pressure, were recorded for every 1-ft step from 4072 to 6693 ft. The lithology is limestone and the section was drilled with 22 in bits and a 9:10 lobe ratio PDM. The efficiency of PDM is

Figure 11. ROP predicted result and bottom-hole condition analysis.

70%. MSE is estimated by the new MSE model for rotating drilling with PDM (Eq. (41)). CCS is calculated by Eq. (44) using the field's log data. The comparison of the calculated MSE against CCS is shown in Figures 13 and 14. Figure 13 shows the MSE(min) is roughly equal to the CCS of the formation almost along all the well depth apart from the well sections: 5502–5606 ft, 5948–6045 ft, 6564–6693 ft. In the sections of 5502–5606 ft and 5948–6045 ft, the applied WOB is very high and more than 46 kbl. Severe vibrations were observed in these two sections. In the section of 6564–6693 ft, relatively low WOB is applied and around 8–20 kbl. While trip-out, it is found that the bit was badly damaged. Figure 14 reveals that the MSE values are minimized and have good correlation with the CCS when the ROP is high, while with low ROP the MSE values are obviously higher than the CCS of the formation. Therefore, when drilling with a high efficiency and free of drilling complications, the MSE(min) estimated by the MSE Model for rotating drilling with PDM is roughly equal to the CCS of the formation along all the well depth. This indicates that the MSE Model for rotating drilling with PDM estimates MSE values

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In order to demonstrate the applicability of the proposed drilling parameters optimization method, drilling operation of a 2855-ft interval of an anhydrite and dolostone formation with a 9.5 in PDM and 16 in PDC bit is analyzed to determine the optimum WOB value in the same

with a reasonable approximation and can meet the needs of field applications.

Figure 12. ROP predicted results of different bits type.

Figure 13. MSE and CCS vs depth.

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Figure 12. ROP predicted results of different bits type.

Figure 13. MSE and CCS vs depth.

70%. MSE is estimated by the new MSE model for rotating drilling with PDM (Eq. (41)). CCS is calculated by Eq. (44) using the field's log data. The comparison of the calculated MSE against CCS is shown in Figures 13 and 14. Figure 13 shows the MSE(min) is roughly equal to the CCS of the formation almost along all the well depth apart from the well sections: 5502–5606 ft, 5948–6045 ft, 6564–6693 ft. In the sections of 5502–5606 ft and 5948–6045 ft, the applied WOB is very high and more than 46 kbl. Severe vibrations were observed in these two sections. In the section of 6564–6693 ft, relatively low WOB is applied and around 8–20 kbl. While trip-out, it is

Figure 11. ROP predicted result and bottom-hole condition analysis.

152 Drilling

found that the bit was badly damaged. Figure 14 reveals that the MSE values are minimized and have good correlation with the CCS when the ROP is high, while with low ROP the MSE values are obviously higher than the CCS of the formation. Therefore, when drilling with a high efficiency and free of drilling complications, the MSE(min) estimated by the MSE Model for rotating drilling with PDM is roughly equal to the CCS of the formation along all the well depth. This indicates that the MSE Model for rotating drilling with PDM estimates MSE values with a reasonable approximation and can meet the needs of field applications.

In order to demonstrate the applicability of the proposed drilling parameters optimization method, drilling operation of a 2855-ft interval of an anhydrite and dolostone formation with a 9.5 in PDM and 16 in PDC bit is analyzed to determine the optimum WOB value in the same

Figure 14. MSE and CCS vs ROP002E.

vertical well from 7651 to 10,499 ft. The PDM is a high RPM motor with a 5:6 lobe configuration which provides moderate torque values. PDM unit displacement is 6.67 gal/rev, and the PDM output rotary speed is estimated by Eq. (26).

sections are respectively shown in Figures 16 and 17. From 7651 to 7713 ft, the applied WOB is as high as 34.7.4 kbl, the value of MSE is apparently greater than CCS (MSE(min) > CCS). This indicates that the bit is foundered and the average ROP is 5.9 ft/h. From 7714 to 8094 ft, WOB is adjusted to around 6.6–11 kbl and RPM almost remains at 240, then MSE(min) = CCS and the average ROP increases to 38.1 ft/h. It drills with high efficiency. At around 8084 ft, when WOB further increases from 8.8 to 11 kbl, the MSE value increases obviously and MSE(min) > CCS. From 8095 to 8842 ft, WOB increases to around 17.6 kbl. However, the MSE(min) mounts up to several times of CCS, and the average ROP decreases to 15.1 ft/h. At 8435 ft, when the flow rate increases to 1056.0 gal/min from 1001.6 gal/min and RPM increases to 249 from 240, the MSE

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Figure 16. MSE vs ROP.

Figure 17. The average ROP.

Figure 15 plots the drilling parameters versus depth to illustrate the sensitivity of ROP and MSE of this operation to WOB and RPM. MSE vs. ROP and the average ROP of various well

Figure 15. Drilling parameters optimization.

Figure 16. MSE vs ROP.

vertical well from 7651 to 10,499 ft. The PDM is a high RPM motor with a 5:6 lobe configuration which provides moderate torque values. PDM unit displacement is 6.67 gal/rev, and the

Figure 15 plots the drilling parameters versus depth to illustrate the sensitivity of ROP and MSE of this operation to WOB and RPM. MSE vs. ROP and the average ROP of various well

PDM output rotary speed is estimated by Eq. (26).

Figure 14. MSE and CCS vs ROP002E.

154 Drilling

Figure 15. Drilling parameters optimization.

sections are respectively shown in Figures 16 and 17. From 7651 to 7713 ft, the applied WOB is as high as 34.7.4 kbl, the value of MSE is apparently greater than CCS (MSE(min) > CCS). This indicates that the bit is foundered and the average ROP is 5.9 ft/h. From 7714 to 8094 ft, WOB is adjusted to around 6.6–11 kbl and RPM almost remains at 240, then MSE(min) = CCS and the average ROP increases to 38.1 ft/h. It drills with high efficiency. At around 8084 ft, when WOB further increases from 8.8 to 11 kbl, the MSE value increases obviously and MSE(min) > CCS. From 8095 to 8842 ft, WOB increases to around 17.6 kbl. However, the MSE(min) mounts up to several times of CCS, and the average ROP decreases to 15.1 ft/h. At 8435 ft, when the flow rate increases to 1056.0 gal/min from 1001.6 gal/min and RPM increases to 249 from 240, the MSE

Figure 17. The average ROP.

value further inflates. Therefore, when RPM is around 240, the drilling system's optimum WOB is 8.8–11 kbl. At around 8843 ft, WOB is adjust to 8.8–11 kbl, the MSE value is minimized and close to the CCS of the formation. From 8843 to 9842 ft, WOB remains around 8.8–11 kbl, it drills with a relatively high efficiency and the average ROP is 19.4 ft/h. At 9731 ft, the flow rate increased to 1097.6 gal/min from 1056.0 gal/min and RPM increased to 258 from 249. The MSE value is minimized and MSE (min) = CCS while WOB reduced to 7.3–9.5 kbl. At 9888 ft, when WOB increases from 7.3 to 9.5 kbl, the MSE value rockets and MSE(min) > CCS. From 9843 to 10,499 m, WOB increases to more than 26.5 kbl, the MSE value is more than ten times of CCS and the average ROP is 11.2 ft/h. This indicates that when RPM is around 258, the drilling system's optimum WOB is 7.3–9.5 kbl.

Nomenclature

Ab bit area (in<sup>2</sup>

Db bit diameter (in)

Dp ECDp-Pp(psi)

)

CCS confined compressive strength (psi)

ds diameter of the shaft pitch circle (in) ECD equivalent circulating density (ppg)

Em mechanical efficiency of new bit

HHP hydraulic horsepower (hp)

Ls total length of the seal line (in)

MSE mechanical specific energy (psi)

ns number of mud motor stage

Ph pitch of the housing (in)

Pp pore pressure (psi)

<sup>Q</sup> flow rate (gal/min)

ΔPb pressure drop across the bit (psi)

<sup>q</sup> PDM unit displacement (gal/ rev)

ΔPm differential pressure across the PDM (psi)

Lm length of the PDM (in)

i winding ratio

ECDp pressure in psi exerted by an ECD in ppg

Fn the resultant force acting at the contact point (lbf)

MHP mechanical horsepower provided by PDM (hp)

n number of shaft lobes of the motor (winding number)

Fi internal force of drill string produced by bottom hole WOBb (lbf)

Fi<sup>1</sup> internal force of drill string at the upper end produced by bottom hole WOBb (lbf) Fi<sup>2</sup> internal force of drill string at the lower end produced by bottom hole WOBb (lbf)

Dh diameter of the housing (in)

C<sup>f</sup> coefficient of dry friction and is assumed to be constant for all rotational speeds

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Based on the above drilling parameters optimization analysis, it is also found that ROP is sensitive to high WOB values for rotating drilling with PDM, and increasing WOB does not always increase ROP but is more likely to decrease ROP. Moreover, the optimum WOB always changes with RPM for rotating drilling with PDM. The proposed method for optimizing drilling parameters can be used to real time estimate optimum WOB values with different RPM to drill a specific formation interval. It can be effectively and easily used, and is worthy to be applied and promoted.
