2. ROP models

therefore, it has been of great concern to drilling engineers during the last decades [1, 2]. Maximization of ROP is often directly related to the minimization of drilling costs and, therefore, it is a significant measure of drilling performance. Hydrocarbon accumulations are becoming more increasingly difficult to find and reach in terms of depth and remoteness of location, and therefore more complex wells are being drilled. Effective prediction of ROP becomes imperative in order to improve efficiency of the drilling process, enables drilling engineers, and operations team to properly estimates the time for the drilling phase of operations, the associated costs, and properly phase the operation in order to save cost. ROP prediction also helps to explain the reason behind a sudden slowness in the drilling process, and therefore helps in making informed decisions on the optimization strategy to adopt.

There are several techniques present to predict ROP, each with its own merits and demerits, and there is no acceptable universal model for all conditions, as the nature of the relationships among the parameters that affects ROP is quite complex and unique for each case. Traditional ROP model usually predicts ROP with lots of assumptions and wide range of uncertainties due to the complexity in the interactions of several parameters which affects ROP. ROP follows a complex relationship with several drilling parameters such as string rotation (RPM), weight on bit (WOB), mud weight (MW), flow rate, bit hydraulics, formation properties such as compressive strength, pore pressure gradient; mud properties, mud hydraulics, borehole deviation, size, and type of bit used. In some cases, increasing WOB and RPM could results in decreasing ROP, as there is an interaction of these inputs with other factors that affects ROP. The understating of the underlying complex relationships among these parameters is impor-

Predictive data-driven (PDA) modeling involves searching through complex data to identify patterns and adjust the program actions accordingly. During drilling operations, lots of realtime data are being gathered with quite a number related to ROP but are riddled with lots of uncertainties and complex relationships which are better handled by data-driven analytical techniques. The ability of AI techniques, to work through complex data sets and establish a relationship or trend without prior assumptions has made it endearing to the hearts of engineers who seek to solve complex drilling engineering problems, especially when the geology and rock mechanic parameters differs from well to well, and therefore may have different

Several researches have been carried out in predicting and optimizing ROP using AI techniques. Jahanbakhshi developed an artificial neural network (ANN) modeling for predicting ROP as a real-time analytical approach with encouraging results [5]. Bodaghi et al. showed that optimized SVR has better accuracy and robustness in the prediction of ROP compared to back propagation neural network (BPNN), and is a practicable method to implement for drilling optimization [6]. Also, Shi et al. in their study showed a promising prospect for extreme learning machine (ELM) and upper-layer-solution-aware, in predicting ROP, as they outperform the ANN model [7]. The study of Moraveji and Naderi concluded that response surface methodology, RSM statistical model provides an efficient tool for prediction of ROP as a function of controllable and uncontrollable variables with a reasonable accuracy [8]. Mantha and Samuel, using ANN, SVR, and classification regression trees (CART) in their study, shows ROP follows a complex relationship

tant in the accurate prediction and optimization of ROP [3].

106 Drilling

recommended drilling parameters within a wide range [4].

ROP is an important drilling parameter as a measure of performance in terms of both drilling cost savings and drilling efficiency. It is defined as the slope of the depth evaluated over a short time. It gives a perspective of how fast or slow a particular formation is being drilled or how operational conditions affect the functioning of the drilling system. The mathematical expression of ROP is given as [9]:

$$ROP(t) = \frac{dh}{dt} \tag{1}$$

Factors affecting ROP can be divided into the following [5, 10];


Bit type selection is dependent on the type of formation to be drilled with a significant effect on ROP. Some bits such as roller cone bits with large cone offset angle and long teeth are only practical for soft formations due to fast tooth wear and hence a quick loss of ROP in harder formation. The fixed cutter bit is one where there are no moving parts, but drilling occurs due to shearing, scraping, or abrasion of the rock. Fixed cutter bits can be either polycrystalline diamond compact (PDC) or grit hot-pressed inserts (GHI) or natural diamond. They can also be matrix-body or steel-body, the selection of which depends on the application and the environment of use. Matrix is desirable as a bit material, because its hardness is resistant to abrasion and erosion. It is capable of withstanding relatively high compressive loads, but, compared with steel, has low resistance to impact loading. PDC bits are generally used for drilling soft but firm, and medium-hard, nonabrasive formations that are not sticky. The choice of bit therefore has a significant impact on ROP [9].

RPM: this is the revolutions per minute which represents the rotational speed of the drill string. The top drive system (TDS) is a revolutionary introduction into the rig system in the early 1980s, it provides clockwise torque to the drill string to drill a borehole. Figure 1 shows an experimental result which proves that ROP usually increased linearly with increasing values of RPM up to a certain point for a particular formation illustrated as segment a-b, provided all other drilling parameters are kept constant, after which ROP starts to diminish as seen in segment b-c. Point b, is called "the bit floundering point."

segment b-c followed by only a slight increase in ROP at a high value WOB in segment c-d. In extreme cases, a further increase in WOB will lead to a decrease in ROP as seen in segment d-e.

Rate of Penetration Prediction Utilizing Hydromechanical Specific Energy

http://dx.doi.org/10.5772/intechopen.76903

109

• Hydraulic factors: this refers to the bit hydraulics, and the two main hydraulic factors with significant effects on ROP are (i) jet velocity, and (ii) bottom hole cleaning. Significant improvement in ROP could be achieved if proper nozzles were selected for a proper jetting action at the bit as drilling fluids flows at a determined flowrate through the drill string and the bit nozzles into the annulus. This promotes better cleaning action at the bit

Bottom hole cleaning is an important mechanism of removing drilled cuttings from the face of the bit. The jetting action of the mud passing through the bit nozzles has to provide enough velocity and cross flow across the surface of the bit to remove the newly drilled cuttings effectively as the bit penetrates the formation. This will prevent bit balling and regrinding of drilled cuttings by moving them up the annulus to maximize drilling

• Drilling fluid properties: the two main mud properties with significant impact on hole

Mud density: aside serving as the primary control of the well, that is, prevention of formation-fluid intrusion into the wellbore, the mud density functions as mechanical stabilization of the wellbore. Increasing the mud density beyond required to serve the aforementioned functions, is detrimental to ROP, and may cause induced losses by fracturing the formation under the in-situ stress condition. An increase in the mud density causes a decrease in ROP. This is because it causes an increase in bottom hole pressure

The point at which this occurs is called floundering point.

cleaning are the mud density and viscosity.

face as well as bottom hole.

Figure 2. Typical response of ROP to WOB.

efficiency of the bit.

Weight on bit (WOB): the WOB represents the amount of axial force applied onto the bit which is then transferred to the formation causing it to break. The significance of WOB as a factor affecting ROP can be seen as illustrated in Figure 2. The figure shows zero ROP until the inertial breaking WOB is applied to the formation at point a. The ROP increases rapidly with increasing WOB as observed in segment a-b; then, a linear increase in ROP is observed in

Figure 1. Typical response of ROP to RPM.

Figure 2. Typical response of ROP to WOB.

Bit type selection is dependent on the type of formation to be drilled with a significant effect on ROP. Some bits such as roller cone bits with large cone offset angle and long teeth are only practical for soft formations due to fast tooth wear and hence a quick loss of ROP in harder formation. The fixed cutter bit is one where there are no moving parts, but drilling occurs due to shearing, scraping, or abrasion of the rock. Fixed cutter bits can be either polycrystalline diamond compact (PDC) or grit hot-pressed inserts (GHI) or natural diamond. They can also be matrix-body or steel-body, the selection of which depends on the application and the environment of use. Matrix is desirable as a bit material, because its hardness is resistant to abrasion and erosion. It is capable of withstanding relatively high compressive loads, but, compared with steel, has low resistance to impact loading. PDC bits are generally used for drilling soft but firm, and medium-hard, nonabrasive formations that

RPM: this is the revolutions per minute which represents the rotational speed of the drill string. The top drive system (TDS) is a revolutionary introduction into the rig system in the early 1980s, it provides clockwise torque to the drill string to drill a borehole. Figure 1 shows an experimental result which proves that ROP usually increased linearly with increasing values of RPM up to a certain point for a particular formation illustrated as segment a-b, provided all other drilling parameters are kept constant, after which ROP starts to diminish as seen in segment b-c. Point b, is called "the bit floundering point." Weight on bit (WOB): the WOB represents the amount of axial force applied onto the bit which is then transferred to the formation causing it to break. The significance of WOB as a factor affecting ROP can be seen as illustrated in Figure 2. The figure shows zero ROP until the inertial breaking WOB is applied to the formation at point a. The ROP increases rapidly with increasing WOB as observed in segment a-b; then, a linear increase in ROP is observed in

are not sticky. The choice of bit therefore has a significant impact on ROP [9].

Figure 1. Typical response of ROP to RPM.

108 Drilling

segment b-c followed by only a slight increase in ROP at a high value WOB in segment c-d. In extreme cases, a further increase in WOB will lead to a decrease in ROP as seen in segment d-e. The point at which this occurs is called floundering point.

• Hydraulic factors: this refers to the bit hydraulics, and the two main hydraulic factors with significant effects on ROP are (i) jet velocity, and (ii) bottom hole cleaning. Significant improvement in ROP could be achieved if proper nozzles were selected for a proper jetting action at the bit as drilling fluids flows at a determined flowrate through the drill string and the bit nozzles into the annulus. This promotes better cleaning action at the bit face as well as bottom hole.

Bottom hole cleaning is an important mechanism of removing drilled cuttings from the face of the bit. The jetting action of the mud passing through the bit nozzles has to provide enough velocity and cross flow across the surface of the bit to remove the newly drilled cuttings effectively as the bit penetrates the formation. This will prevent bit balling and regrinding of drilled cuttings by moving them up the annulus to maximize drilling efficiency of the bit.

• Drilling fluid properties: the two main mud properties with significant impact on hole cleaning are the mud density and viscosity.

Mud density: aside serving as the primary control of the well, that is, prevention of formation-fluid intrusion into the wellbore, the mud density functions as mechanical stabilization of the wellbore. Increasing the mud density beyond required to serve the aforementioned functions, is detrimental to ROP, and may cause induced losses by fracturing the formation under the in-situ stress condition. An increase in the mud density causes a decrease in ROP. This is because it causes an increase in bottom hole pressure

beneath the bit causing a chip hold-down effect. Hence, regrinding of drilled cuttings with adverse effect on penetration rate.

Viscosity tends to decrease ROP as it increases in drilling fluids. Plastic viscosity is the resistance of the drilling fluid to flow caused by mechanical friction within the fluid. With high viscosity, cuttings tend to remain stuck on the bottom of the hole causing their re-drilling and this leads to reduction in the performance of the bit. It affects the hydraulic energy available at the bit nozzles for cleaning due to parasitic frictional losses in the drill string [9].

#### 2.1. ROP empirical models

There has been many proposed empirical ROP models in the last 3 decades; however, three of them are quite popular for estimating ROP, they are (i) Maurer's ROP model, (ii) Galle and Woods ROP model, and (iii) Bourgoyne-Young ROP model.

### 2.1.1. Maurer's model

Maurer [11] developed a ROP model based on a theoretical penetration equation as a function of WOB, RPM, bit size, and rock strength derived for a roller-cone type bit. A mathematical relation between rate of drilling, WOB, and RPM based on perfect hole cleaning condition was achieved as a function of depth. The ROP equation was thus given as:

$$\frac{dF\_D}{dt} = \frac{4}{\pi d\_b^2} \frac{dV}{dt} \tag{2}$$

model to capture the effects of changes in the various drilling parameters. They proposed an eight function empirical relationship to model the effect of most of drilling variables [1]. The

ROP d ¼ f <sup>R</sup> a1; ::…; a8; p2;…:; p<sup>8</sup>

Here, a1 = formation strength parameter, a2 = exponent of the normal compaction trend, a3 = under compaction exponent, a4 = pressure differential exponent, a5 = bit weight exponent,

Approaching the drilling process as a closed system in terms of energy input in the form of applied drilling parameters, and a corresponding output, in the form of ROP, brought about the concept of specific energy (SE). This concept was first introduced by Teale in [13]. Further work has been done to fully capture the mechanical and hydraulic energy input and their relationship with ROP. The HMSE concept states that "the energy required to remove a unit volume of rock comes primarily from the torque applied on the bit, the weight on bit (WOB), and the hydraulic force exerted by the drilling fluid on the formation" [14]. Specific energy is therefore a significant measure of drilling performance, especially of the cutting efficiency of

> 120π:N:T Ab:ROP <sup>þ</sup>

ROP <sup>¼</sup> <sup>120</sup>π:N:<sup>T</sup> <sup>þ</sup> <sup>1154</sup>η:Δpb:<sup>Q</sup>

Here, HMSE = hydromechanical specific energy in psi, F = WOB in lbs, N = RPM, T = TORQ in

in gallons per minute, η = dimensionless energy reduction factor depending on bit diameter,

The use of HMSE-derived ROP model drilling parameters have been proposed in this study because it fully captures the relevant controllable parameters that affects ROP. Also, from an operational point of view, it is valuable because it provides a reference point for measuring drilling efficiency and performance of the drilling process in terms of measuring energy input and corresponding output in terms of ROP. The SE concept became a key element for the fast drill process (FDP) [16]; the process of drilling with the highest possible ROP in terms of technical and economical limits. In early 2004, Exxon Mobil Corporation used the process to

Ab:HMSE � F

1154η:Δpb:Q

� � (7)

, ROP = rate of penetration in ft/hr, Q = mud flow-in rate

8

!

i¼2 aipi

<sup>¼</sup> Exp a<sup>1</sup> <sup>þ</sup><sup>X</sup>

a6 = rotary speed exponent, a7 = tooth wear exponent, and a8 = hydraulic exponent.

2.1.4. Hydromechanical specific energy ROP model (HMSE)

bits and rock hardness [15]. The equation form is:

lb-ft, Ab = bit cross sectional area in in<sup>2</sup>

and Δpb = pressure loss at bit in psi.

HMSE <sup>¼</sup> <sup>F</sup>

Ab þ

� � (4)

Rate of Penetration Prediction Utilizing Hydromechanical Specific Energy

, (5)

http://dx.doi.org/10.5772/intechopen.76903

111

Ab:ROP (6)

equation form is

Rearranging

Here, FD = footage drilled by bit (ft), t = time (h), V = Volume of rock removed, db = diameter of bit.

#### 2.1.2. Galle and woods' model

Galle and Woods, in their work, investigated the effects of bit cutting structure dullness, WOB, and RPM on ROP, rate of tooth wear and bearing life for roller cone bits. The result of their work is a presentation of graphs and procedures for field applications to determine the best combination of constant WOB and RPM [12]. They presented a drilling rate equation as follows:

$$\frac{dF\_D}{dt} = \mathbb{C}\_{\text{fl}} \frac{\overline{W}^k}{a^p} r \tag{3}$$

Here, Cfd = formation drillability parameter, a = 0.028125h2 + 6.0 h + 1 time, hr, h = bit tooth dullness, fractional tooth height worn away, in, p = 0.5 (for self-sharpening or chipping type bit tooth wear), k = 1.0 (for most formations except very soft formations), 0.6 (for very soft formations), r = RPM function, <sup>W</sup>= function of WOB and db, such that <sup>W</sup> <sup>¼</sup> <sup>7</sup>:88WOB db .

#### 2.1.3. Bourgoyne and Young ROP model

The most popular of the ROP model is Bourgoyne and Young ROP model used to calculate the ROP. In their work, they presented a mathematical relationship using a complex drilling model to capture the effects of changes in the various drilling parameters. They proposed an eight function empirical relationship to model the effect of most of drilling variables [1]. The equation form is

$$
\bar{ROP} = f\_R(a\_1, \dots, a\_8, p\_2, \dots, p\_8) \tag{4}
$$

$$=\exp\left(a\_1 + \sum\_{i=2}^{8} a\_i p\_i\right),\tag{5}$$

Here, a1 = formation strength parameter, a2 = exponent of the normal compaction trend, a3 = under compaction exponent, a4 = pressure differential exponent, a5 = bit weight exponent, a6 = rotary speed exponent, a7 = tooth wear exponent, and a8 = hydraulic exponent.

#### 2.1.4. Hydromechanical specific energy ROP model (HMSE)

Approaching the drilling process as a closed system in terms of energy input in the form of applied drilling parameters, and a corresponding output, in the form of ROP, brought about the concept of specific energy (SE). This concept was first introduced by Teale in [13]. Further work has been done to fully capture the mechanical and hydraulic energy input and their relationship with ROP. The HMSE concept states that "the energy required to remove a unit volume of rock comes primarily from the torque applied on the bit, the weight on bit (WOB), and the hydraulic force exerted by the drilling fluid on the formation" [14]. Specific energy is therefore a significant measure of drilling performance, especially of the cutting efficiency of bits and rock hardness [15]. The equation form is:

$$HMSE = \frac{F}{A\_b} + \frac{120\pi N.T}{A\_b.ROP} + \frac{1154\eta.\Delta p\_b.Q}{A\_b.ROP} \tag{6}$$

Rearranging

beneath the bit causing a chip hold-down effect. Hence, regrinding of drilled cuttings with

Viscosity tends to decrease ROP as it increases in drilling fluids. Plastic viscosity is the resistance of the drilling fluid to flow caused by mechanical friction within the fluid. With high viscosity, cuttings tend to remain stuck on the bottom of the hole causing their re-drilling and this leads to reduction in the performance of the bit. It affects the hydraulic energy available at the bit nozzles for cleaning due to parasitic frictional losses in the drill string [9].

There has been many proposed empirical ROP models in the last 3 decades; however, three of them are quite popular for estimating ROP, they are (i) Maurer's ROP model, (ii) Galle and

Maurer [11] developed a ROP model based on a theoretical penetration equation as a function of WOB, RPM, bit size, and rock strength derived for a roller-cone type bit. A mathematical relation between rate of drilling, WOB, and RPM based on perfect hole cleaning condition was

Here, FD = footage drilled by bit (ft), t = time (h), V = Volume of rock removed, db = diameter of bit.

Galle and Woods, in their work, investigated the effects of bit cutting structure dullness, WOB, and RPM on ROP, rate of tooth wear and bearing life for roller cone bits. The result of their work is a presentation of graphs and procedures for field applications to determine the best combina-

Here, Cfd = formation drillability parameter, a = 0.028125h2 + 6.0 h + 1 time, hr, h = bit tooth dullness, fractional tooth height worn away, in, p = 0.5 (for self-sharpening or chipping type bit tooth wear), k = 1.0 (for most formations except very soft formations), 0.6 (for very soft

The most popular of the ROP model is Bourgoyne and Young ROP model used to calculate the ROP. In their work, they presented a mathematical relationship using a complex drilling

Wk ap

tion of constant WOB and RPM [12]. They presented a drilling rate equation as follows:

dFD dt <sup>¼</sup> Cfd

formations), r = RPM function, <sup>W</sup>= function of WOB and db, such that <sup>W</sup> <sup>¼</sup> <sup>7</sup>:88WOB

dV

dt (2)

r (3)

db .

dFD dt <sup>¼</sup> <sup>4</sup> πd<sup>2</sup> b

adverse effect on penetration rate.

Woods ROP model, and (iii) Bourgoyne-Young ROP model.

achieved as a function of depth. The ROP equation was thus given as:

2.1. ROP empirical models

110 Drilling

2.1.1. Maurer's model

2.1.2. Galle and woods' model

2.1.3. Bourgoyne and Young ROP model

$$ROP = \left(\frac{120\pi N.T + 1154\eta.\Delta p\_b.Q}{A\_b.HMSE - F}\right) \tag{7}$$

Here, HMSE = hydromechanical specific energy in psi, F = WOB in lbs, N = RPM, T = TORQ in lb-ft, Ab = bit cross sectional area in in<sup>2</sup> , ROP = rate of penetration in ft/hr, Q = mud flow-in rate in gallons per minute, η = dimensionless energy reduction factor depending on bit diameter, and Δpb = pressure loss at bit in psi.

The use of HMSE-derived ROP model drilling parameters have been proposed in this study because it fully captures the relevant controllable parameters that affects ROP. Also, from an operational point of view, it is valuable because it provides a reference point for measuring drilling efficiency and performance of the drilling process in terms of measuring energy input and corresponding output in terms of ROP. The SE concept became a key element for the fast drill process (FDP) [16]; the process of drilling with the highest possible ROP in terms of technical and economical limits. In early 2004, Exxon Mobil Corporation used the process to optimized their drilling operation with a result of an astonishing increase in ROP by 133% proven the concept a useful one [16, 17].
