Positive Displacement Motor Condition and Performance Prediction Using Surface and Downhole Sensor Data

Abstract

Positive displacement motors (PDM) are utilized to drill deviated and horizontal sections and are a key technology for deep oil/gas and geothermal wells. The energy transferred at the drill bit is delivered from the drillstring and bottom hole assembly (BHA) components. Energy loss due to friction, wellbore problems (tight spots, poor hole cleaning, etc.), and damage to the drillstring reduce the energy delivered to the drill bit. As a result, there is a reduction in drilling efficiency and an increase in nonproductive time. Mud motor fatigue due to cycling loading significantly influences wellbore quality and drilling performance. This chapter aims to develop a framework using surface and downhole data to predict the condition and performance of mud motors. A systematic and automated approach to access data quality and operations recognition is a fundamental element in the study. The borehole trajectory is reconstructed by implementing the survey data with the corresponding generated forces acting on the drillstring. Mud motor operating efficiency is monitored by continuously evaluating the produced differential pressure, power efficiency, and modeled incremental torque produced from each drillstring element. The theoretical and actual torque produced from the motor and the drillstring is compared to establish a correlation with the measured sensor data.

1. Introduction

With the energy demand increasing by around 50% by 2050 [1], the required oil/gas and geothermal wells have become deeper, each associated with technical challenges. By targeting greater depths or longer horizontal sections, the required drilling time, equipment, and technology are much more substantial, and thus the drilling cost exponentially increases (Figure 1).

Figure 1.

Annual US nominal cost per well, drilled footage, and number of wells. Source: The figure is modified from Refs. [2, 3, 4].

Drilling is a destructive action that requires a tool to penetrate the rock. As the drill bit rotates, it requires energy to provide the torque and additional rotation. Positive displacement motors (PDM), with the common terminology of mud motor in the industry, are complex mechanical designs that convert the drilling fluid’s hydraulic energy into mechanical energy transferred to the drill bit [5]. Even though the primary purpose and current utilization of the mud motors are to build angle and control the direction of the drillstring on a deviated section, on many occasions, it is utilized to enhance the drilling performance.

The rate of penetration is a complex variable that is a function of several parameters [6, 7, 8, 9, 10, 11, 12] that can be separated into controlled and uncontrolled, as Figure 2 shows. Variables, including drilling parameters, drilling fluid, drill bit, and well design, are selected and designed before the drilling process or dynamically fluctuate while drilling depending on the formation drilled and unforeseen circumstances. Dynamic simulations and real-time monitoring of the drilling process assist in generating valuable scenarios to identify the optimum drilling parameters and minimize wellbore issues [13, 14, 15]. On the contrary, formation properties are uncontrolled parameters significantly influencing all the controlled variables. The most common practice of obtaining the formation properties is acquiring a core and conducting uniaxial and triaxial compression tests to obtain the unconfined compressive strength (UCS) and confined compressive strength (CCS) values and study the rock sample’s mechanical properties. Several researchers are keen to develop a technology to obtain rock strength while drilling using in-cutter sensing technology [16, 17, 18].

Figure 2.

Rate of penetration as a function of several variables.

The mud motor’s operating efficiency and duty cycle are fully incorporated with the operating parameters and hours, and formation properties [8, 9, 15]. Downhole measurement technologies have demonstrated that the mud motor’s expected rotational speed differs from the actual [19]. The elastomer (stator) deteriorates and reduces the motor’s volumetric efficiency; as a result, there is a decrease in the differential pressure in the power section, which affects the output mechanical energy at the bit [20]. A standard method to evaluate the condition of the mud motor is to perform a wear-off test and calculate the overall efficiency change for a specific interval.

Detection of mud motor failure requires actual drilling data and images that capture the condition of the elastomer. The primary cause of elastomer damage is motor stalling; detecting those events provides information regarding the operating parameters and the corresponding motor response. Data-driven methods and machine-learning algorithms classify the failure modes and mitigate the risks [21, 22].

This chapter aims to establish a workflow that uses physics-based modeling and data-driven analysis. The framework contains data quality oversight, operations recognition, mud motor performance, and drilling efficiency by utilizing low-frequency surface and high-frequency downhole data.

2. Torque modeling

2.1 Mud motor and drill bit

The mud motor consists of several parts, with the main components being (1) a power section, (2) a transmission shaft, and (3) a bearing assembly. The internal assembly of the power section consists of the rotor and the stator, which are geometrically aligned to provide a smooth rotational movement. The geometrical design is primarily the lobes, which allow us to determine the mud motor’s output rotational speed and torque. As the drilling fluid is circulated inside the drillstring and enters the power section, the helical design of the rotor and the configuration with the stator allow the rotor to rotate. The motor rotates when the drilling fluid enters under pressure in the cavities between the stator and rotor.

The required power the mud motor has to provide depends on several parameters, including weight on bit (WOB), which is axial force, drill bit wear state, and rock properties. In the case of a polycrystalline diamond compact (PDC) drill bit, the PDC cutter penetrates the rock and shears the formation. Due to the rotating motion, a tangential force component $\left({\mathit{F}}_{\mathit{t}}\right)$ acts on the cutter and is a function of the depth of cut (DOC). Figure 3 illustrates the cutting process with a sharp and a blunt cutter, where the wear flat area has been developed.

Figure 3.

Cutting process with a sharp and blunt PDC cutter [23].

The total tangential force is equal to Eq. (1):

$$F_{\mathit{t}}=F_{\mathit{t}}^c+F_{\mathit{t}}^f$$E1

The drill bit’s produced torque $\left(T_{\mathit{bit}}\right)$ is the summation of the tangential force produced from each cutter $\left(N_c\right)$ and is a function of the cutter’s radial location $\left(r_c\right)$. The torque at the drill bit is calculated according to Eq. (2):

$$T_{\mathit{bit}}=\sum _{n=i}^{N_c}{\left(F_{\mathit{t}}{r}_c\right)}_i$$E2

As the wear flat area $\left(A_{\mathit{\text{flat}}}\right)$ starts developing, for the same applied axial force $\left(\mathrm{WOB}/F_n\right)$, the generated torque increases. This creates complexity in detecting and evaluating the condition of the mud motor. Since the mud motor is connected with a shaft to the drill bit, it is assumed that the $T_{\mathit{\text{motor}}}=T_{\mathit{bit}}.$ The power section performance of the mud motor is illustrated with power curve graphs and shows the relationship of rotational speed with flow rate and torque with differential pressure. In the actual drilling process, since the drilling fluid is non-Newtonian (shear stress has no linear relationship with shear rate), we perform a rotating off-bottom procedure with the same flow rate utilized to drill the upcoming section. By knowing the coefficients $c_1$ (torque factor, ft-lb/psi), $c_2$ and $c_3$ (require fitting equation) from the power curves, the motor torque can be calculated as follows (Eq. (3)):

$$T_{\mathit{\text{motor}}}=c_1\mathrm{\Delta }P$$E3

where $T_{\mathit{\text{motor}}}$ [ft-lbf] and $\Delta \mathit{P}$ is the differential pressure [psi]. The rotational speed of the mud motor and the total rotational speed that is transferred to the drill bit are equal to (Eqs. (4) and (5)):

$$N_{\mathit{\text{motor}}}=c_2\mathrm{\Delta }{P}^2+c_{3}Q$$E4

$$N_{\mathit{\text{total}}}=N_{\mathit{\text{string}}}+N_{\mathit{\text{motor}}}$$E5

where $N_{\mathit{\text{motor}}}$ is the motor rotational speed [RPM], Q is the flow rate [GPM], and $N_{\mathit{\text{string}}}$ is the surface rotational speed of the drillstring provided by the top drive system. The motor has an input of the hydraulic energy (HHP) of the drilling fluid and an output of the mechanical energy (HP) to the shaft as per Eq. (6):

$$\mathit{HHP}=\frac{Q\mathrm{\Delta }P}{1714}\text{and}\mathit{HP}=\frac{T_{\mathit{\text{motor}}}}{550}\left(\frac{2\pi }{60}\right)N_{\mathit{\text{motor}}}$$E6

The motor efficiency is derived from output work and input work as per Eq. (7):

$$\eta =\frac{\mathit{\text{output}}}{\mathit{\text{input}}}=\frac{\mathit{HP}}{\mathit{HHP}}$$E7

2.2 Drillstring

Theoretically, while drilling vertical sections, the downhole torque equals the surface torque. Thus, the surface measurements are a good representation of the downhole conditions. On deviated and curved sections, parts of the drillstring are in contact with the wellbore and generate additional torque due to the rotating action. Additional variables such as wellbore tortuosity, poor hole cleaning, and tight spots increase the torque produced from the drillstring. Thus it is essential to differentiate the produced toque from all different elements and be able to evaluate the condition of the mud motor. Figure 4 demonstrates a deviated wellbore and the incrementally applied forces to each drillstring component.

Figure 4.

Forces acting on the drillstring for an inclined and curved section. Source: Modified from Ref. [24].

The buoyancy weight of the drillstring is derived, and it is a function of the density of drilling fluid filling the wellbore. Wellbore friction models are then developed, which are then used to compute the axial (tension), frictional, and normal contact forces [25, 26, 27, 28]. Depending on the upward or downward movement of the drillstring in the wellbore, the tension force per element is calculated as Eq. (8):

$$F_{T\left[\mathit{top}\right]}=W_B\mathrm{\Delta }\mathit{L}\left(cosa\pm \mu sina\right)+F_{T\left[\mathit{\text{bottom}}\right]}$$E8

where $W_B$ is the buoyancy weight [lb/ft] of a component in the drillstring, $\Delta \mathit{L}$ is the component step length [ft], $\mu$ is the coefficient of friction, and a is the inclination $\left[{}^o\right]$. The drillstring is divided into elements of a certain step length $\left(\Delta ,\mathit{L}\right)$, and cumulative tension and torque are calculated at the top of each element. On a curved section, the dogleg angle $\left(\theta \right)$ has to be considered, as shown in Eq. (9):

$$\begin{array}{r}{F}_{T\left[\mathit{top}\right]}=W_B\mathrm{\Delta }\mathit{L}\left[\frac{sin{a}_{\mathit{top}}-sin{a}_{\mathit{\text{bottom}}}}{a_{\mathit{top}}-a_{\mathit{\text{bottom}}}}\pm \mu \frac{cos{a}_{\mathit{top}}-cos{a}_{\mathit{\text{bottom}}}}{a_{\mathit{top}}-a_{\mathit{\text{bottom}}}}\right]\\ +F_{T\left[\mathit{\text{bottom}}\right]}\left(e^{\pm \mathit{\mu \theta }}\right)\end{array}$$E9

For a soft string torque and drag model, each incremental element is in contact with the wellbore and produces a normal/contact force $\left(F_N\right)$, a function of the tension and coefficient of friction. The normal contact force is equal to Eq. (10):

$$F_N=\sqrt{{\left(F_T\mathrm{\Delta }\varphi sin\left(\frac{a_{\mathit{top}}+a_{\mathit{\text{bottom}}}}{2}\right)\right)}^2+{\left(F_T\mathrm{\Delta }a+W_B\mathrm{\Delta }\mathit{L}sin\left(\frac{a_{\mathit{top}}+a_{\mathit{\text{bottom}}}}{2}\right)\right)}^2}$$E10

where $\varphi$ is azimuth $\left[{}^o\right].$ While drilling, the applied weight on the bit (WOB) affects the tension force, either rotating or sliding mode. The produced torque is calculated as Eq. (11):

$$T=T_{\mathit{\text{bottom}}}+\mu F_{N}r$$E11

where $\mu$ is the coefficient of friction and r is the radius of the tool joints.

3. Data quality and operations recognition

Depending on the operating parameters, the differential pressure value fluctuates while drilling. To evaluate the mud motor’s condition and performance, obtaining the differential pressure for on and off-bottom operations is crucial. The recognition of operations encountered while drilling has been a subject of interest for many years [29, 30, 31]. In addition, drilling data quality and reliability are important factors in assessing the operations successfully. The current method utilizes unprocessed drilling data to recalculate several variables and evaluate the validity and accuracy of each attribute and the entire dataset [32]. For each attribute ϒ, we calculate its validity as follows (Eq. (12)):

$$Q_V^{\mathrm{\Upsilon }}=\frac{1}{T}\sum _{i=i}^{T}V\left\{\begin{array}{cc}V=0& \forall {\mathrm{\Upsilon }}_i\ne C_i\\ V=1& \forall {\mathrm{\Upsilon }}_i=C_i\end{array}\right.$$E12

where $Q_V^{\mathrm{\Upsilon }}$ is the validity score of the attribute, ${\mathrm{\Upsilon }}_i$ and $C_i$ are the original and recalculated values of the attribute at the $i^{\mathit{th}}$ sample and T represents the total number of data points. The accuracy of the attribute is calculated (Eq. (13)):

$$Q_A^{\mathrm{\Upsilon }}=\frac{1}{T}\sum _{i=i}^T\frac{\mid {\mathrm{\Upsilon }}_i-\mid {\mathrm{\Upsilon }}_i-C_i\Vert }{{\mu }_{\gamma }}$$E13

where ${\mu }_{\gamma }$ represents the mean value of the attribute in the dataset. The validity and accuracy of the dataset are calculated as Eq. (14):

$$Q_V=\frac{1}{N}\sum _{k=i}^N{Q}_V^k\text{and}{Q}_A=\frac{1}{N}\sum _{k=i}^N{Q}_A^k$$E14

A particular procedure adheres to determine the motor differential pressure during drilling. This is called rotating off-bottom operations and the drill bit is off-bottom. When the bit touches the bottom of the wellbore, WOB and standpipe pressure (SPP) increase. The difference between the SPP on and off-bottom is the differential pressure on the motor. The differential pressure values are a function of the motor design, the rotor and stator state, applied WOB, etc. The following Figure 5 demonstrates the required workflow from data quality to modeling.

Figure 5.

Workflow from data quality to modeling.

On an interval of approximately 3000 ft, a few hundred operations are continuously repeated to drill the section successfully. Automated operations recognition allows the establishment of a suitable roadmap that provides a comprehensive and reliable method to evaluate the drilling process. As described in the previous paragraphs, the differential pressure on the motor subtracts the SPP on and off-bottom. But while on-bottom, the algorithm must consider the most recent off-bottom SPP value. Thus, once the recognition of the operation has been successfully established, the data are separated into three modes:

• Standpipe pressure rotating (MODE 1)

• Standpipe pressure sliding (MODE 2)

• Standpipe rotating off-bottom (MODE 3)

Then, after calculating the $\mathrm{\Delta }\mathit{P},$ the data are exported for each node. Additional variables and calculations occur during the process, including drilled footage in rotating and sliding modes, average rate of penetration (ROP), depth of cut, and mechanical specific energy (MSE). The indicated variables can either be exported per section or the formation drilled, depending on the analysis.

4. Case study: Forge well 16A (78)-32

4.1 Original data set

The data utilized for the current case study are obtained from the geothermal field in Utah Forge from the well 16A (78)-32. It is a deviated well with a complex lithology and multiple bottom-hole assemblies (BHA) utilized for each section. The following Figure 6 demonstrates the actual design of the well.

Figure 6.

Actual well trajectory for the well 16A (78)-32.

Drilling is a complex process, and conducting a comprehensive analysis requires various amounts of data, including drilling data, daily drilling operation reports and surveys [33], well drilling summary [34], well logs, and downhole data [35].

4.2 Vertical section 1600–5100 ft

While a mud motor is used to drill a deviated section, on several occasions, it is utilized on vertical intervals to provide additional rotations to the drill bit and enhance the drilling efficiency. The 12.25-in section is drilled with two PDC drill bits runs. In addition, the BHA has a positive displacement motor (6 5/8 mud motor with 7/8 5.9 stages) and a shock sub. The current configuration of the mud motor is to provide and achieve high torque, with the torque factor $\left(c_1\right)$ equal to 15.7 ft-lb/psi. The coefficients $c_2$ and $c_3$ (rotational factor) equal −0.000009 and 0.155 RPM/gal, respectively. As illustrated in Figure 6, operations recognition plays an important role in evaluating and understanding the drilling data. For the current case study, having computed the on and off-bottom operations, the standpipe pressure rotating off-bottom is illustrated in Figure 7.

Figure 7.

Computed standpipe pressure during rotating off-bottom. Each data point represents the SPP’s average value for the entire operation duration [24].

For the same flow rate, it is expected to have a linear increase of the standpipe pressure with the true vertical depth (TVD), but depending on the selection of the drilling parameters, it can differ. By utilizing the values of SPP for rotating off-bottom, the differential pressure on the motor is accurately calculated while drilling, as is shown in Figure 8. For tortuosity zero, the surface torque equals the downhole torque on a vertical section. Motor stalling or micro-stalling are events in which a sudden increase of differential pressure is observed. An indication of a motor stall or micro-stall is an instantaneous peak in standpipe pressure that does not correspond to a forced change in flow rate. Standpipe pressure (SPP) peak selection is controlled by two parameters: (1) peak prominence and (2) peak width. In case the increase in pressure is due to an increase in flow rate, then these changes in flow rate at the selected peak are used to disregard the corresponding value as a valid stall. Motor stalling detection requires a high-frequency downhole, allowing us to evaluate the duration of the stall and its impact on motor efficiency [36, 37, 38]. Depending on the duration, it can also be detected from surface measurements but requires downhole data for validation.

Figure 8.

Computed mud motor differential pressure and torque using surface sensor data [24].

The concept of energy efficiency for a given activity is to utilize less energy to perform the same task. In drilling engineering, it is expressed as the required amount of energy to drill a volume of rock, termed mechanical specific energy (MSE) [39, 40]. Axial and rotational energy is transferred from the surface to the drill bit via the drillstring. However, energy losses occur due to vibrations, drag, stator-rotor misalignment in the mud motor, etc. Thus, to evaluate the drilling efficiency concerning the actual energy transferred to the drill bit and the energy provided from the surface to perform the drilling action, it is different from the surface and downhole MSE [37, 38]. Theoretically, if we neglect wellbore tortuosity and vibrations for a vertical section, the surface and downhole MSE are equal. The surface MSE is equal to Eq. (15):

$${\mathit{MSE}}_{\mathit{\text{surface}}}=\frac{4{\mathit{WOB}}_{\mathit{\text{surface}}}}{D^2\pi }+\frac{480T_{\mathit{\text{surface}}}\left(N_{\mathit{\text{motor}}}+N_{\mathit{\text{surface}}}\right)}{D^2\mathit{ROP}}$$E15

where $T_{\mathit{\text{surface}}}$ is the surface torque (ft-lbf) and $N_{\mathit{\text{motor}}}$ is the mud motor rotational speed. To calculate the downhole MSE we need to know the actual axial force that is transferred to the drill bit and the mud motor torque. In principle, the most reliable and accurate method to obtain the downhole WOB is to have a measurement while drilling (MWD), which can measure it. On the other hand, the current methodology to obtain the mud motor torque is an excellent approximation for an intact PDM assembly. The downhole MSE is given in Eq. (16):

$${\mathit{MSE}}_{\mathit{\text{downhole}}}=\frac{4{\mathit{WOB}}_{\mathit{\text{downhole}}}}{D^2\pi }+\frac{480T_{\mathit{\text{motor}}}\left(N_{\mathit{\text{motor}}}+N_{\mathit{\text{surface}}}\right)}{D^2\mathit{ROP}}$$E16

Figure 9 shows that except for formations 1 and 2, the energy required to drill the additional six formations is significantly higher, corresponding to an insufficient drilling process. This formation corresponds to the second drill bit utilized for the interval and demonstrates lower performance.

Figure 9.

Surface and downhole mechanical specific energy for the eight formations drilled [24].

In elastomer fatigue due to cyclic loading, motor efficiency often decreases with operational time. Figure 10 illustrates the motor efficiency as a function of time and differential pressure. Efficiency reduction can be related to main factors, including the operational procedure of the rotating off-bottom and on-bottom operations. In case the flow rate during the operations differs, the computed differential pressure at the motor is inaccurate; the described scenario was observed while drilling formation four shows (approximately 80 hours) with the efficiency significantly lower for the differential pressure—400 psi than other formations. Nevertheless, motor efficiency shows no significant decrease with operating hours, indicating a steady motor condition.

Figure 10.

Motor efficiency to time and differential pressure for each drilled formation [24].

To obtain an overview and correlate the mud motor efficiency with the drill bit’s wear state, the drill bit’s depth of cut (DOC) must be obtained. As a wear flat area develops on an individual cutter, the axial force must increase to maintain the same DOC. The depth of cut is equal to Eq. (17):

$$\mathit{DOC}={\frac{\mathit{ROP}}{N_{\mathit{\text{total}}}}}^{}\ast 0.2\ast 25.4$$E17

Figure 11a demonstrates that the ratio of DOC over WOB decreases with increase in depth. The averaged values were obtained for each drilled formation. However, the downhole MSE shows an increase, which differs from the decrease in the DOC/WOB ratio (Figure 11b). The main aspect is to differentiate the reason for the additional produced torque, which, in this case, is generated due to bit wear rather than the mud motor. This can be correlated with the high axial vibrations that subsequently produce micro-chipping and spalling at the PDC cutters [33].

Figure 11.

(a) Ratio of depth of cut with applied weight on bit, (b) average downhole mechanical specific energy for each drilled formation.

4.3 Deviated section: Interval 5878–7294 ft

Complexity increases while drilling deviated intervals on hard rocks. The current deviated section is on a granite layer in which four drill bits runs were required, with the same mud motor, to drill until 7294 ft. The tripping-to-surface operations and the corresponding tripping-to-bottomhole were separated manually to reduce computational time. Thus, the data were separated into four individual data sets and combined after the processing. The mud motor is a 6 1/2-in 7/8 5.7 stages with a fixed 1.5 deg. bend sub.

Steering of the drillstring is achieved through a semi-automated transition from rotating to sliding mode. The energy from the drillstring dissipates due to the increase of the frictional component in the drillstring and, thus, the reduction of ROP. Even though the same framework was utilized to access the data quality, an additional challenge was observed from the perspective of operations recognition. High-frequency data is usually an additional benefit to conducting an analysis, but in the case of a low rate of penetration, accurate operations recognition is more challenging (Figure 12). The following Table 1 provides drilling data with a sampling frequency of 0.1 Hz. The dataset was also available with a sampling frequency of 1 Hz. Since the ROP was lower in the deeper part of the section, it created a challenge for the algorithm to perform excellently in recognizing the continuous transition on different operation modes. It is observed that a single miscalculation of the rotating off-bottom and on-bottom SPP can significantly reduce the accuracy of evaluating the differential pressure.

Figure 12.

The recalculated ROP shows more comprehensive values than the original. In several circumstances, utilizing the original value is unreliable method for operations recognition.

Data point	Depth [ft]	Block position [ft]
Data 1	5607.24	44.22
Data 2	5607.30	44.16
Data 3	5607.36	44.11
Data 4	5607.36	44.11
Data 5	5607.42	43.95

Table 1.

Unprocessed drilling data for the given run of BHA#21.

Depth is given in the dataset as Depth Hole Total Vertical Depth.

Block position is utilized not only to calculate the rate of penetration but also to obtain the measured and bit depth. A condition is applied to resolve the barrier of obtaining the instantaneous depth change and ROP, by utilizing surface measurements and rig variables. For precise and accurate output of the algorithm, the following threshold has to be considered for each well and section:

• Surface RPM is used for sliding and rotating modes. In several cases, the surface RPM during sliding mode can be about 20 RPM, which creates an additional challenge to identify it as sliding mode.

• Maximum and minimum block position, critical hookload, and standpipe pressure. To accomplish that, a manual assessment is conducted to identify the critical block position, hookload, and standpipe pressure.

• Initial bit depth for each section. In case the bit depth is not given, as it was described, the bit depth is calculated, but if the data are separated per day, then a manual estimation of bit depth as the initial data point is obtained with trial and error.

Subsequently, the algorithm performs excellently, identifying the rotating and sliding mode intervals and calculating the downhole torque. Wellbore quality, excessive lateral and torsional vibrations, and poor hole cleaning have a negative impact on drilling efficiency since the surface energy transferred to the drill bit dissipates with additional drag and torque produced from the drillstring. It is challenging to identify if the additional torque is produced from the drill bit/mud motor or the drillstring without integrating surface and downhole data (measured and computed). To demonstrate the reliability of the methodology, the simulation utilizes the actual BHA and survey data to estimate the torque while rotating off-bottom. An important step is that the torque values must be incremental and represent a real-time/dynamic scenario. The torque measured at the surface is equal to Eq. (18):

$$\sum _{i=2}^n{T}_i=T_{\mathit{\text{motor}}\left(i\right)}+\sum _{i=2}^n{T}_{i-1}+\sum _{i=2}^n\mu F_{N\left(i\right)}{r}_i$$E18

The combined simulated torque while rotating off-bottom with the estimated torque from the mud motor during the rotating mode is displayed in Figure 13 and it is correlated with the actual measured torque at the surface.

Figure 13.

Downhole torque during rotating mode and surface-measured torque.

The surface torque increases due to an increase in downhole torque at particular intervals (6150, 6200, 6360, 6950, 7000, and 7400 ft), indicating the influence of the mud motor. The results generally indicate a linear increase in torque (drillstring + mud motor) during the section’s drilling.

It is observed that, in general, the actual and simulated torque match excellently. At approximately 6220 ft the simulated with the actual measurements differ significantly, corresponding to the overall overview regarding wellbore implications. The trend line of the actual data follows the linear increase as a function of depth. The sudden decrease appears due to calculated mud motor torque. A further analysis of the dataset shows that the flow rate utilized during the off and on-bottom operations for that particular interval was different, which caused a miscalculation of the differential pressure at the motor. This approach indicates the necessity of automated operation recognition, mud motor torque evaluation, and real-time modeling.

For the deviated section, a downhole bit box is installed in the BHA to measure the actual downhole rotational speed and vibrations near the drill bit. Operating parameters affect the vibration modes in the drillstring as observed in Figure 14, and the acceleration in the Y and Z-axis is significantly lower during sliding drilling. It is observed that the measured downhole RPM shows sudden decreases in several intervals while drilling in rotating mode. Even though the modeled efficiency of the motor shows a constant trend, the actual fluctuates as a function of the downhole RPM. Nonetheless, a downward trend is not observed throughout the entire interval.

Figure 14.

Calculated RPM for rotating and sliding mode in comparison to downhole and surface measurements.

5. Conclusions

Individual evaluation of the overall drilling and mud motor performance requires extensive data analytics to quantify the uncertainty related to the produced downhole torque. The current workflow is utilized as a diagnostic tool initiated from data quality, followed by operations recognition and physics-based modeling, to evaluate the condition and performance of mud motors. Drilling data quality not only provides the user with a set of data that is qualified for analysis but also allows a rapid and reliable understanding of the drilling process.

The model can predict the efficiency trend for both mud motor runs as a function of operating hours. The calculated mud motor torque is incorporated with the modeled incremental torque produced from the drillstring to relate it with the actual measurements. Monitoring the operational efficiency of the mud motor provides insights regarding the drilling operation and enables evaluation of the drilling performance.

Acknowledgments

The authors thank King Abdullah University of Science and Technology (KAUST) and Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC) for supporting this work.

Conflict of interest

The authors declare no conflict of interest.

Nomenclature

$A_{\mathit{\text{flat}}}$	wear flat area
a	inclination
$c_1$	coefficient
$c_2$	coefficient
$c_3$	coefficient
CCS	confined compressive strength
DOC	depth of cut
$F_{\mathit{t}}$	tangential force
$F_n$	normal force
$F_T$	tension force
$F_N$	normal force
HHP	hydraulic energy
HP	mechanical energy
$N_c$	number of cutters
$N_{\mathit{\text{motor}}}$	motor rotational speed
$N_{\mathit{\text{string}}}$	drillstring rotational speed
$N_{\mathit{\text{total}}}$	total rotational speed at the drill bit
Q	flow rate
r	radius of the tool joints
ROP	rate of penetration
$T_{\mathit{bit}}$	torque on the bit
$T_{\mathit{\text{motor}}}$	mud motor torque
T	drillstring torque
UCS	unconfined compressive strength
$W_B$	buoyancy weight
WOB	weight on bit
$\mathrm{\Delta }P$	mud motor differential pressure
$\eta$	motor efficiency
$\theta$	dogleg angle
$\mu$	coefficient of friction
$\phi$	azimuth

Abbreviations

BHA	bottom-hole assembly
PDC	polycrystalline diamond compact
PDM	positive displacement motor
POOH	pull-out of hole