© The Author(s), published by EDP Sciences, 2025

1 Introduction

In a world where awareness of global warming and climate change is growing, it is crucial to convert the renewable energy sources [1]. In addition to fulfilling the Paris Agreement, renewable energy sources are essential to ensuring universal access to affordable energy [2]. Because of this, practically all nations in the world currently have energy support programs and targets for renewable energy sources. It is anticipated that wind power generation will play a significant part in this worldwide energy revolution [3]. By the 2050s, it is anticipated that wind power would supply more than one-third of the world’s electricity requirements [4].

Due to the numerous advantages (i.e., advantages to prevent either social conflicts from competitive land uses, or social unrest issues) that the offshore environment can provide; a significant number of future projects are therefore predicted to be offshore [5]. A power plant, often known as a wind farm, is required to harness wind energy, convert it to electricity, and send it to the primary electrical grid. In an offshore wind farm, the primary components are the wind turbines, cables, and substations [6, 7]. Figure 1a shows the common arrangement of an offshore wind farm. Wind turbines are merely generators that transform wind energy into electrical energy. Numerous wind turbines are put in at once in one place for financial reasons, such as lowering planning, building, and maintenance costs. The offshore substation receives the electric power generated by the turbines through cable connections. The voltage of the electricity is enhanced and stabilized there before being exported to land. The offshore electric power is added to the primary electrical system through an onshore substation [6, 10].

Figure 1 (a) Layout of a typical offshore wind farm; (b) Common types of foundations used to support offshore turbines [6, 8]; (c) The installation of offshore wind farms [9].

The world’s wind power capability is not spread equally. With 43.2% of the world’s capacity, Asia has the most potential, then Europe with 32.1%. North America’s stake is 18.5%. It is curious to notice that only ten countries account for 84% of the world’s wind power when the spatial distribution is created by nation. China is by far the biggest provider, accounting for 35% of all wind energy produced worldwide. The United States comes in second with 17% of the total. Then comes Germany, India, Spain, the United Kingdom, France, Brazil, Canada, and Italy [11]. All projections for the expansion of wind energy in the future seem promising [12].

The sizes, designs, and power output of wind turbines vary. A rotor drives a power generator that is positioned horizontally in a wind turbine system, which is now the most used arrangement. The rotor, the nacelle, the tower, the transition piece, and the base make up a wind turbine’s basic components. Figure 2 depicts the different parts of a wind turbine. Many wind turbines in use today rotate around a center on a flat axis and contain three blades, or less frequently, two blades. However, there are wind turbines whose axis of rotation is vertical to the surface of the earth. The power generator is positioned at ground level, making these turbines independent of wind direction and simpler to maintain. They are only employed in small-scale projects, however, and are less effective in converting wind energy into electricity. The rotor of a wind turbine, which houses the blades and the hub is essential to the effectiveness of power generation. Using the aerodynamic force generated by the rotor blades, the wind turbine turns wind energy into electricity. The air pressure on one side of the blade drops as the wind moves across it; as a result, the pressure difference between the two sides of the blade produces both lift and drag. The rotor spins because the force of the lift is greater than the force of the drag. The blades’ size, shape, and number can all vary, and they are made to be strong enough to withstand forces acting on them while yet providing the optimal aerodynamic performance for the desired energy efficiency. If the turbine is a direct drive turbine, the rotor is connected to the generator directly. If not, the connection is made through a shaft and a gearbox, which accelerates rotation. Electricity is produced as a result of the conversion of aerodynamic force into generator rotation. The main shaft, the brake, the gearbox, and the generator are additional crucial parts that are placed inside the nacelle. Through the yaw mechanism, the nacelle can spin horizontally to let the rotor be pointed in the direction of the wind for the generation of the most power. The tower, which is made out of tubular steel, supports each of these parts. Larger, more dependable, more efficient wind turbines would be possible with the improvement of all the many components mentioned [8, 13, 14]. In less than two decades, the average size of offshore wind turbines has increased by about three times. Specifically, from 2.2 MW with a 50-meter-diameter rotor in 2000 to 6.6 MW and a 100-meter-diameter rotor in 2018. All the advancements in wind turbine technology will become more obvious in the coming years, when turbines with capacities greater than 10 MW and greater than 15 MW will be on the market by 2022 and 2030, respectively [6–8].

Figure 2 Main components of a wind turbine [8].

The most crucial design factor for wind turbines is their foundations, which frequently decide the project’s financial feasibility as a whole. The capital expenditure of the foundation is 20% of the whole expenditure (including turbine, foundation, electrical infrastructure, and other costs) of an offshore wind farm. The foundation is rather simple when a turbine is located on land. It is composed of a concrete slab heavy enough to provide enough force and moment to withstand the bending moments and motions of the loads acting on the turbine [6, 15, 16]. On the other hand, the design of offshore foundations is more challenging since they have a substantial impact on the dynamic characteristics of the entire turbine construction, in addition to accounting for a sizeable portion of the overall cost. Whether the stability is assured by the bulk of the foundation body (i.e., a gravity base foundation) or whether the structure is embedded or anchored in the sea floor defines the static principle of offshore foundation (i.e., monopile). Many different offshore foundation designs have been created over the years [8, 9, 17]. Figure 1b displays a few of the most popular styles of offshore foundations.

The decision is mostly influenced by the depth of the water at the site and the size of the building that will be built there. The foundations are positioned immediately on the seabed for a maximum water depth of 60 m. However, in deeper waters, floaters that are tethered to the seabed are used as platforms for the wind turbines (Fig. 2) [7, 18].

The overall capacity of offshore wind energy at the end of 2018 was 23 gigawatts with about 80% originating from Europe. The median volume of an offshore wind farm has significantly expanded during the past few years, mostly because of advancements in wind turbine technology [19]. Figures 3a and 3b respectively show the growth in the average volume of offshore wind farms and the average rated power of a wind turbine. For example, in 2008, the average offshore wind farm had a capacity of 100 MW and contained 33 turbines with an average capacity of 3 MW. Approximately 82 turbines with an average capacity of 6.8 MW each made up the average size of a wind farm in 2018, which was an increase of 561 MW from a decade earlier.

Figure 3 (a) Average size of offshore wind farms in the given year; (b) Average size of wind turbine size in the given year [19].

As wind farms using the most recent wind technology are put into operation, these figures are only anticipated to rise. For instance, the 174 turbines in the 1,200 MW Hornsea Project 1 will have an average rated capacity of 6.8 MW apiece, making it the largest offshore wind farm in the world by 2020 [19]. With the new greater capacity of wind farms, it appears that there is already an effort to move offshore wind farm locations farther from the shore and to deeper sea depths [20, 21]. Figure 4, which displays the average sea depth and separation from the coast of offshore wind farms around the world based on their size and stage of construction, illustrates this tendency. Based on this data, it can be deduced that the normal offshore wind farm’s average water depth is about 27 m, while the typical distance from the shore is about 35 km [21, 22].

Figure 4 Average depth of water and distance from shore of offshore wind farms [22].

Understanding the drillability performance of offshore wind turbine foundations with an emphasis on the interaction between soil and large-diameter drilling bits is the main goal of this study. It is crucial to have a full understanding of the mechanisms driving rates of drilling penetration within the soil layers to forecast the time scale of a given wind farm project in a given area of consideration offshore. Since the performance of offshore wind turbines is a complicated problem involving several interfaces, the major goal of the current challenge is to simplify the actual situation. Therefore, simplifying the rate of prediction equations due to shallow drilling environments leads to significant efficiency in computations and predictions while still maintaining accuracy. As a result, the following describes this study’s purpose and scope:

• Develop an innovative and scalable model for predicting drilling rates below the mud line for shallow-hole drilling.

• Test the model with actual drilling parameters to understand the quality of the match.

• Propose the developed model to be used for large-diameter drilling as hydrocarbon drilling bits are significantly smaller in diameter compared to the hole sizes for offshore wind farm structure monopile sizes.

• Outline directions for future supplementary research while presenting a straightforward design approach that considers the use of actual hydrocarbon drilling data to forecast the long-term drilling performance of offshore wind farm structures.

The objective of this study is to create data-driven models that forecast ROP for top-hole drilling for the monopile installation of wind farm structures. Our suggested model may be systematically calibrated using data from any field and is modeled after the Bourgoyne and Young (B&Y) model of ROP prediction, which is commonly used in the oil and gas industry. The B&Y model was established for the oversimplified drilling scenario using vertical wells with roller-cone bits. Therefore, it is an ideal model for drilling conditions for the wind farm structures as the depths are very shallow compared to hydrocarbon drilling and the verticality is maintained. Once a reliable prediction model is established from the hydrocarbon well drilling, we use the model to predict drilling rates for large-diameter hole sizes that apply to monopiles of wind farm structures. As an outcome, the rate of penetration vs. hole size drilled plot will be shown for the worst-case scenario (assuming the strongest rock drilling environment). Briefly, this study is innovative in several key ways:

• It is one of the first to focus on predicting the Rate Of Penetration (ROP) specifically in offshore large-diameter wells, a crucial parameter for improving drilling efficiency and reducing costs in deepwater operations.

• By sharing comprehensive drilling data from 17.5-inch wells, the study contributes valuable insights to the existing literature. This data can significantly enhance our understanding of ROP dynamics in offshore large-diameter wells, which has direct implications for developing and optimizing offshore drilling techniques. Additionally, the findings may prove especially beneficial for offshore wind energy projects, where efficient drilling processes are critical for the installation of wind turbines and related infrastructure.

2 Materials and methods

The presence of an accurate model for forecasting ROP is crucial for obtaining the best drilling parameters when drilling holes for windfarm structure installation (as in Fig. 1b) is essential as increasing ROP greatly lowers drilling costs.

The following are the main research goals for this study:

• Researching the impact of various drilling functions on ROP (rate of penetration) during an actual drilling operation.

• Creating a general ROP model for top-hole sections of drilling in low-deviated wells for the design of wind farm foundational structure.

• Test the ROP model using the hardest rock that can be drilled.

• Use of the ROP prediction approach for drilling wind farm monopiles.

Bourgoyne and Young’s (B&Y) model of ROP prediction was used in this study, so it is important to understand the theory behind this method. The multiple regression method by Bourgoyne and Young [23] was developed to forecast ROP in vertical wells drilled using roller-cone bits. Numerous factors that affect ROP are considered by Bourgoyne and Young’s model. This includes depth, Weight on Bit (WOB), Threshold WOB, rotary speed of drilling string (rpm), pore pressure gradient, formation strength, pump rate, drilling mud weight, mud viscosity, bit cutter wear, bit size, and bit nozzle diameter. We believe that this model is enough to predict the rates of penetration for the wind farm drilling scope because of the relatively simple conditions. Understanding the suggested ROP modeling approach requires an explanation of modeling approaches and drilling parameters that affect ROP.

The cost per foot drilled is obviously and directly influenced by the bit’s rate of penetration and rate of bit wear. The three factors recognized and analyzed as having the greatest impact on penetration rate are (1) bit type, (2) formation characteristics, and (3) drilling fluid parameters. (4) Bit operational circumstances (bit weight and rotary speed), (5) bit hydraulics, and (6) bit tooth wear [24].

Bit type: The choice of bit type has a significant impact on the penetration rate.

Formation characteristics: The most significant formation characteristics influencing penetration rate are the elastic limit and final strength of the formation. By plotting the drilling rate as a function of bit weight per bit diameter and then extrapolating back to a zero-drilling rate, the threshold force, or bit weight (W/d), necessary to begin drilling was determined. The results of this method’s laboratory correlation are displayed in Figure 5 [25, 26].

Figure 5 Relation between rock shear strength and threshold [24].

Drilling fluid properties: The drilling fluid’s characteristics that have reportedly been linked to the penetration rate include (1) density, (2) rheological flow properties, (3) filtration characteristics, (4) solids content and size distribution, and (5) chemical composition [26, 27]. The following formula provides the link between the rate of penetration and overbalance [24]:$$\log \left(R/R_0\right)=-m\left(P_{\mathrm{bh}}-P_f\right),$$(1)where R: penetration rate; R₀: penetration rate at zero overbalance; P_bh: bottom hole pressure in the borehole; P_f: formation fluid pressure; and m: the slope of the line.

Operating conditions: Numerous studies [24, 28] showed the impact of bit weight and rotary speed on penetration rate. When all other drilling factors are kept constant, an experimental plot of penetration rate vs. bit weight often takes on the pattern depicted in Figure 6.

Figure 6 Typical response of penetration rate to increasing bit weight [24].

Before applying the threshold bit weight, a significant penetration rate cannot be reached (Point A in Fig. 6). When bit weight is increased by reasonable amounts, the penetration rate then rises quickly (Segments a–b in Fig. 6). At moderate bit weights, a linear curve can frequently be seen (Segments b–e in Fig. 6). However, at higher bit weight values, future bit weight increases only marginally enhance the penetration rate (Segments c–d in Fig. 6). In some instances, the penetration rate drops off at excessively high bit weight values (Segments d–e in Fig. 6). This kind of conduct is frequently referred to as bit floundering. The ineffective bottom hole cleaning at higher rates of cuttings generation or a complete penetration of the cutting element into the hole bottom are typically to blame for the poor responsiveness of penetration rate at high values of bit weight. Figure 7 is a typical plot of penetration rate vs. rotary speed that was obtained when all other drilling variables were held constant.

Figure 7 Typical response of penetration rate to increasing [24].

To determine the relationship between bit weight, rotary speed, bit size, and rock strength [26] created a theoretical equation for rolling cutter bits. The equation was created because of the following finding in single tooth impact tests [24]:

• The square of the depth of cutter penetration determines the crater volume.

• The rock strength has an inverse relationship with the depth of cutter penetration. The penetration rate R under these circumstances is given by

$$R=\frac{K}{S^2}{\left[\frac{W}{d_b}-{\left(\frac{W}{d_b}\right)}_t\right]}^{2}N,$$(2)

This theoretical relationship is predicated on flawless bit tooth penetration and imperfect bottom hole cleaning. Utilizing experimental data taken at relatively low bit weights and rotating speeds corresponding to Segments a–b in Figures 6 and 7, the theoretical equation of [26] can be confirmed. Bingham [25] proposed the drilling equation below considering extensive laboratory and field data:$$R=K{\left(\frac{W}{d_b}\right)}^{a_5}N,$$(3)where K: constant of proportionality that includes the effect of rock strength; a₅: bit weight exponent.

The threshold bit weight was negligible in equation (3), and the bit weight exponent needs to be calculated empirically for the current circumstances. However, even though some of this data displayed behavior resembling that depicted by Segments b–e in Figure 7, a constant rotary speed exponent of one was utilized in the Bingham equation.

According to Hook’s law, a stress change is proportional to a strain change.$$∆\sigma =E∆ϵ.$$(4)

The stress change for axial tension in a drill string is determined by dividing the bit weight change (axial tension) by the drill pipe’s cross-sectional area. The variation in drill pipe length per unit length is equivalent to the variation in strain. As a result, Hook’s law is$$\frac{∆W}{A_{\mathrm{s}}}=E\frac{∆L}{L}.$$(5)

Solving this expression for ΔL gives$$∆\mathrm{L}=\frac{\mathrm{L}}{{\mathrm{EA}}_s}∆W.$$(6)

By multiplying this equation by the amount of time Δt needed to drill off the bit weight ΔW, one can determine the average penetration rate that was observed for that change.$$R=\frac{∆W}{∆t}=\frac{L}{{\mathrm{EA}}_s}\frac{∆W}{∆t}$$(7)

Bit Tooth Wear: Due to tooth wear, most bits generally drill more slowly as the bit run continues. Abrasion and chipping cause the milled tooth rolling cutter bits’ tooth length to continuously decrease. The following model was published by Gallle and Woods [29]: $$R\propto {\left(\frac{1}{0.928125h^2+6h+1}\right)}^{a_7},$$(8)where h: fractional tooth height that has been worn away, and a₇: an exponent. The exponent (a₇) for self-sharpening wear of milled tooth pieces was suggested to have a value of 0.5. the main bit type covered in the article. In a more current piece. Bourgoyne and Young [23] proposed a comparable but less intricate link is evidenced by:$$R\propto e^{-a_{7}h}.$$(9)Bourgoyne and Young [23] recommended calculating the exponent a₇ using the observed reduction in penetration rate with tooth wear for earlier bits ran under comparable circumstances.

Bit Hydraulics: The advent of the jet-type rolling cutter bits in 1953 demonstrated that a better jetting motion at the bit might result in appreciable increases in penetration rate [24]. Many believe that the bit’s flounder point is influenced by the level of hydraulics that are attained at the bit. A hypothetical illustration of the kind of conduct frequently reported is shown in Figure 8.

Figure 8 The expected relationship between bit hydraulics and penetration rate [24].

Eckel [30] discovered that penetration rate might be associated with a Reynolds number (N_RE) group provided that while operating at constant bit weight and rotary speed:$$N_{\mathrm{RE}}=K\frac{\mathrm{\rho }\mathrm{vd}}{{\mu }_a},$$(10)where K: a scaling constant; p: drilling density; v: flow rate; d: nozzle diameter; and μ_a: apparent viscosity of drilling fluid at 10,000 s⁻¹_.

As a sample of shear rates present in the bit nozzle, a shear rate of 10.000 s⁻¹ was selected. Even though the sealing constant K is rather arbitrary. Eckel [30] utilized a constant value of 1/1976 to produce a useful range for the Reynolds number group. Figures 9 and 10 provide an overview of Eckel [30] research findings.

Figure 9 Penetration rates as a function of bit Reynolds number [24].

Figure 10 Experimentally observed effect of bit weight and bit [24].

Penetration rate equation: It is quite complicated and only partially understood how the significant drilling factors that have been mentioned affect penetration rate. Particular a given cutting element penetration into the formation, the drag bit’s rate of penetration is given by Bourgoyne et al. [24]$$R=L_{\mathrm{pe}}{n}_{\mathrm{be}}N,$$(11)where L_pe: effective penetration of each cutting element; n_be: effective number of blades, and N: rotary speed.

Several writers have developed penetration rate equations for rolling cutter bits. Assuming that the effects of bit weight, rotational speed, tooth wear, etc. on penetration rate are all independent of one another and that the composite effect can be calculated using an equation of the form:$$R=\left(f_1\right)\left(f_2\right)\left(f_3\right)\left(f_4\right)\dots \left(f_n\right),$$(12)where the functional relationships between drilling factors and penetration rate are represented by the functions f₁, f₂, f₃, etc. The functional relationships that are selected are frequently based on patterns seen in both laboratory and field studies. While some authors have opted to employ curve-fitting techniques to produce empirical mathematical formulas, others have opted to define the functional connection graphically. Only two or three of the drilling variables have been modeled using some rather straightforward mathematical formulae. The Bingham model is one illustration.

The Bourgoyne and Young model is arguably the most comprehensive mathematical drilling model that has been applied to rolling cutter bits. To represent the impact of the majority of the drilling factors outlined in the preceding section, they suggested utilizing eight functions. Equation (12) can be used to define the Bourgoyne-Young drilling model using the following functional relations:$$f_1=e^{2.303a_1}=K,$$(13) $$f_2=e^{2.303a_2\left(\mathrm{10,000}-D\right)},$$(14) $$f_3=e^{2.303a_3{D}^{0.69}\left(g_p-9\right)},$$(15) $$f_4=e^{2.303a_{4}D\left(g_p-{\rho }_c\right)},$$(16) $$f_5={\left[\frac{\left(\frac{W}{d_{\mathrm{b}}}\right)-{\left(\frac{W}{d_{\mathrm{b}}}\right)}_t}{4-{\left(\frac{W}{d_{\mathrm{b}}}\right)}_t}\right]}^{a_5},$$(17) $$f_6={\left(\frac{N}{60}\right)}^{a_6},$$(18) $$f_7=e^{-a_{7}h},$$(19) $$f_8={\left(\frac{F_j}{1000}\right)}^{a_8},$$(20)where D: true vertical well depth, ft; g_p: pore pressure gradient, lbm/gal; p_c: equivalent circulating density: (W/d_b)_t : threshold bit weight per inch of bit diameter at which the bit begins to drill, 1000 lbf/in; h: fractional tooth dullness; a₁ to a₈: constants that must be chosen based on local drilling conditions; F_j : hydraulic impact force beneath the bit, lbf, given by the below formula:$$F_j=0.01823C_{d}q\sqrt{\rho ∆P_b},$$(21) $$∆P_b=\frac{8.311\times {10}^{-5}\rho q^2}{C_d^2{A}_t^2}.$$(22)

If precise drilling data are available, they can be used to calculate the constants a₁ through a₈ from previous drilling data gathered in the region. Both calculations for drilling optimization and the detection of changes in formation pore pressure can be done using the drilling model. If precise drilling data are available, they can be used to calculate the constants a₁ through a₈ from previous drilling data gathered in the region. Both calculations for drilling optimization and the detection of changes in formation pore pressure can be done using the drilling model. The main representation of the function f₁ is the influence of bit type and formation strength on penetration rate. However, it also takes into account the impact of drilling variables not taken into account by the drilling model, such as mud type and solids content. For determining the values of a₁ through a₈ using past drilling data gathered in the area’s multiple regression technique can be applied to find the exponential equation for f₁. The constant a₁ can be simply calculated in terms of the common logarithm of an observed penetration rate thanks to the coefficient “2.303”. The impact of compaction on penetration rate is modeled by the functions f₂ and f₃. The consequences of undercompaction seen in overly pressurized formations and the increase in rock strength brought on by standard depth compaction are both simulated by the functions f₂ and f₃. The function f₄ models how overbalance affects penetration rate. This function has a value of 1.0 when there is no overbalance, which occurs when the bottom hole pressure in the well and the formation pore pressure are equal. The functions f₅ and f₆ model how bit weight and rotational speed affect penetration rate. In areas with relatively soft formations, like the US Gulf Coast, the threshold bit weight is typically quite small and can be disregarded. Drilloff tests stopped at very low bit weights in more capable formations can be used to estimate the threshold bit weight. The bit flounder point serves as the upper limit for the function of f₅, which must be determined by drilloff testing. Drilloff tests can also be used to determine the constants a₅ and a₆. Reports of a₅ values range from 0.5 to 2.0, whereas those of a₆ values range from 0.4 to 1.0 [24].

The impact of tooth wear on penetration rate is modelled by the function f₇. A value of 1.0 for the word “f₇” indicates no tooth wear. Tooth wear is frequently negligible when tungsten carbide insert bits are used and operated at moderate bit weights and rotational speeds, hence this term can be disregarded. For milled tooth bits, typical values of a₇ range from 0.3 to 1.5 [24].

The impact of bit hydraulics on penetration rate is modeled by the function f₈. As often has values between 0.3 and 0.6 in real life. It is wise to choose the best a₂ through a₈ average values for the different formation types in the target depth range. However, the strength of the formation being drilled affects the value of f₁. The word “f₁” is used to describe the formation’s drillability and is represented in the same units as the penetration rate. The penetration rate that would be experienced in the specified formation type (under typical compaction) when drilling with a fresh bit at 0% overbalance, 4,000 lbf/in bit weight, 60 rpm rotary speed, and 10,000 ft depth is the drillability in numbers [24]. Using drilling information gathered from prior wells in the area, it is possible to calculate the drillability of the different formations.

3 Results and discussion

In this study, field data from seven wells, located in both offshore oil and gas fields, were gathered to evaluate the proposed technique for predicting the Rate of Penetration (ROP). These wells are situated in two distinct regions: The North Sea, UK, and the Shah Deniz field in the Caspian Sea, Azerbaijan. The geographical locations of these wells are illustrated in Figure 11. The data collected from these wells spans a wide range of downhole conditions and drilling operations, making them ideal for assessing the general applicability and reliability of the ROP prediction models under varying conditions.

Figure 11 Locations of the selected fields (Shah Deniz field in Azerbaijan and North Sea Fields in the UK) for this study.

The wells used in this study were drilled using different types of drilling rigs, each employing distinct drilling techniques and configurations depending on the well depth, formation characteristics, and other operational considerations. The primary objective of this study is to create and evaluate ROP prediction models that are applicable across a variety of drilling scenarios, each reflecting different geological formations, drilling phases, and equipment types. By including wells from different regions and drilling conditions, we aim to assess the performance of the proposed model in predicting ROP under a broad spectrum of subsurface environments, which is essential for optimizing offshore drilling operations.

To evaluate the effectiveness of the ROP prediction model, the wells were grouped according to the geological characteristics of their respective fields. The first three wells, located in the North Sea, were selected as representative wells for this study. The North Sea wells were chosen because they are drilled in conditions that are similar to those found in the seabed areas designated for offshore wind farms in the UK. These sites typically feature a combination of relatively soft to medium-hard soil layers, which are comparable to the conditions likely to be encountered when drilling for offshore wind farm foundations. Therefore, these wells serve as a suitable test case for evaluating the model’s performance in predicting ROP for offshore wind farm construction, where similar soil conditions are expected.

In addition to the North Sea wells, three wells from the Shah Deniz field in the Caspian Sea were selected to test the model’s predictive power under different soil conditions. The Shah Deniz field is known for its complex and heterogeneous reservoir formations, which range from softer shale layers to much harder rock formations. These wells provide a varied set of data points, allowing us to assess how well the ROP model can adapt to diverse subsurface conditions and predict drilling performance in both soft and hard formations. By including these wells, this study gains a broader perspective on the model’s applicability in regions with a wide range of geological challenges, which is crucial for offshore drilling operations in other parts of the world.

Finally, to further evaluate the robustness of the proposed ROP prediction model, a well from the Shah Deniz field was selected that penetrated through a very hard formation with high pore pressure. This well was drilled through a particularly tough section, where the formation exhibits a high unconfined compressive strength and significant pore pressure differentials, making it a challenging environment for drilling operations. The data from this well is being used as a “conservative case” to simulate the worst-case scenario for offshore wind farm drilling, where very hard formations with high pore pressure are encountered. By testing the model on this well, we aim to demonstrate its capability to predict ROP even in the most difficult drilling conditions, which are representative of the harder rock formations that may be encountered when drilling foundation piles for offshore wind turbines.

The drilling techniques employed for these wells varied depending on the formation types and depths. In general, tricone bits were used for drilling the shallow sections of the wells, where the formations were softer and less challenging to penetrate. In deeper sections, the formation became harder and more resistant to drilling, Polycrystalline Diamond Compact (PDC) bits were used. PDC bits are known for their ability to drill through harder formations more efficiently and are commonly used in deepwater drilling operations. The use of different bit types across the wells provides additional insights into the performance of the ROP prediction model under a range of drilling conditions.

For the ROP prediction, this study exclusively used the Bourgoyne-Young (B&Y) drilling model, which is based on eight functional relationships (equations) as outlined in Section 2. These equations have been widely used in the oil and gas industry for predicting ROP in various drilling environments, and they form the foundation of many ROP prediction models used for offshore drilling operations. In this study, these well-established methods, have been honed for oil and gas exploration, were adapted and applied in a new context – the foundation design of offshore wind farms.

The adaptation of the B&Y model for wind farm foundation design is a novel aspect of this research. While the oil and gas industry has long relied on this model for well planning and drilling optimization, its application to offshore wind farm drilling represents a new frontier. Offshore wind farm installation often requires the drilling of deep, large-diameter holes for the foundation piles, and the ability to accurately predict ROP in these conditions is essential for cost-effective project planning and execution. Therefore, by leveraging the well-established techniques from the oil and gas industry, this study aims to provide a reliable methodology for predicting ROP in the context of offshore wind farm foundation installation, contributing valuable insights for the renewable energy sector.

In summary, this study utilizes field data from seven wells across two different offshore regions – the North Sea and the Shah Deniz field – to test and evaluate the B&Y ROP prediction model in a variety of downhole conditions. The diversity in well locations, soil types, and drilling phases ensures a comprehensive evaluation of the model’s predictive power, making it an essential tool for optimizing drilling operations in offshore wind farm projects. By adapting proven oil and gas industry models to offshore wind farm construction, this research provides a foundation for more accurate and efficient drilling techniques for renewable energy infrastructure.

Tables 1–3 show the achieved correlation coefficients for wells in different geological settings. Table 4 demonstrates coefficients reported from the literature.

North Sea wells: The rationale behind using the Bourgoyne and Young (B&Y) model in this study is to calibrate its model parameters (a₁–a₈) in such a way that the predicted Rate of Penetration (ROP) closely matches the actual ROP values observed during drilling operations. The goal is to minimize the difference between the two sets of values, ensuring that the model provides an accurate representation of real-world drilling conditions. To achieve this calibration, Excel’s Solver feature was utilized to automatically adjust the parameters by minimizing the sum of the squared errors between the predicted ROP values (ROP_predicted) and the actual ROP values (ROP_actual). This optimization technique allows for fine-tuning the model’s parameters to best fit the data, ensuring that predictions are as accurate as possible.

Figures 12–14 illustrate the results obtained from calibrating the B&Y model using drilling data from three wells – Well N-1, Well N-2, and Well N-3 – located in the North Sea. These figures show how the model’s predicted ROP values align with the actual ROP values measured during drilling operations, providing a clear picture of the model’s predictive accuracy. Figure 15 offers a comparative analysis of ROP_predicted vs ROP_actual for these three wells, allowing for a direct evaluation of how well the B&Y model performs in predicting drilling performance in this offshore environment.

Figure 12 ROP prediction for Well N-1 (17.5 in the borehole) in the North Sea.

Figure 13 ROP prediction for Well N-2 (17.5 in the borehole) in the North Sea.

Figure 14 ROP prediction for Well N-3 (17.5 in borehole) in the North Sea.

Figure 15 ROPactual vs. ROPpredicted for (a) Well N-1, (b) Well N-2 and (c) Well N-3 in the North Sea.

As seen from Figures 12 to 15, the B&Y model provides a relatively good prediction of ROP, even in challenging offshore drilling conditions like those found in the North Sea. The model performs well overall, particularly in formations where the soil strength is high. However, it should be noted that the soil layer is approximately 120 m below the mud line is quite strong and hard, which results in ROP values generally being below ~40 m/h through that interval. This characteristic is a result of the challenging drilling conditions in this deeper section of the well. After this depth, the soil becomes softer, and an increase in ROP is observed, reflecting a transition to more easily drillable formations.

Despite these general trends, the B&Y model does not fully capture the peaks in ROP observed within the hard soil interval. These ROP peaks likely result from localized variations in the formation, tool interactions, or other dynamic drilling factors that the model does not account for. This highlights a limitation of the B&Y model in accurately predicting ROP in all formations, especially in situations where sharp, short-term variations in drilling conditions occur.

Based on these observations, we conclude that the B&Y model is most effective in predicting ROP in formations that are consistently strong or hard, provided that certain operational conditions are met. These conditions include:

• Normal pore pressure regime: The model assumes a hydrostatic pore pressure condition within the soil layers, where the pressure exerted by the fluid column in the wellbore is balanced with the pore pressure of the surrounding formation.

• Minimal overbalance: The model performs best when the difference between the mud weight and the pore pressure (i.e., the overbalance) is kept to a minimum. A minimal overbalance reduces the risk of borehole instability and improves the accuracy of the model’s predictions.

• Vertical wellbore: A vertical wellbore configuration simplifies the problem, as it minimizes the impact of factors like cuttings bed accumulation, which can affect the ROP. In non-vertical wells, deviations in trajectory can complicate the prediction due to changes in wellbore geometry.

• Shallower depth: At shallower depths, compaction effects are either minimized or become irrelevant, meaning that the soil properties do not undergo significant changes due to the weight of the overlying material. This allows the B&Y model to more effectively predict ROP without the interference of deep compaction effects.

In summary, while the B&Y model provides a robust framework for predicting ROP in offshore drilling scenarios, its accuracy is contingent on the type of formation being drilled and specific operational conditions. Its performance is optimal for strong, hard formations where minimal overbalance is applied, the wellbore is vertical, and drilling occurs at shallower depths where compaction effects are minimal.

Shahdeniz field wells in the Caspian Sea: To illustrate the practical application of the Bourgoyne and Young (B&Y) model and assess its reliability across different soil conditions, several wells in the Shah Deniz field, located in the Caspian Sea, were selected for testing. These wells provide valuable data for evaluating the model’s performance under varying subsurface conditions. The initial focus was on the top-hole sections or soil layers just beneath the mudline, which are characterized by very soft formations. These soft formations present a particular challenge for ROP prediction because they are less cohesive and exhibit different drilling behaviors compared to harder, more consolidated rock formations.

To test the B&Y model’s ability to predict ROP in such conditions, the actual ROP observed in the soft soil layers of these wells was compared against the values predicted by the model. Figures 16–19 display the calibration results for several wells in the Shah Deniz field. Upon examining these figures, it becomes clear that there is a significant mismatch between the observed and predicted ROP values. In fact, the discrepancies are so pronounced that it is evident that the B&Y model struggles to provide an accurate prediction in these softer formations. The observed ROP values do not align well with the predicted values, suggesting that the model is not well-suited for use in soils with very soft characteristics.

Figure 16 ROP prediction for Well C-1 (26 × 42 in borehole) in Caspian Sea.

Figure 17 ROP prediction for Well C-2 (26 × 42 in borehole) in the Caspian Sea.

Figure 18 ROP prediction for Well C-3 (26 × 42 in the borehole) in the Caspian Sea.

Figure 19 ROPactual vs. ROPpredicted for (a) Well C-1, (b) Well C-2, and (c) Well C-3 in Shahdeniz Field of the Caspian Sea.

This lack of accuracy in predicting ROP for soft soils highlights a key limitation of the B&Y model, particularly when applied to formations with low cohesion or strength. However, it is important to note that the conditions encountered in offshore drilling projects for wind farm construction typically involve much harder soils and rocks. Therefore, while the B&Y model may not be effective for soft soil formations, its predictive capabilities are still valuable and acceptable in scenarios where drilling occurs in stronger, more consolidated formations. This reinforces the notion that the model is most applicable in environments where the soil is hard or moderately hard, similar to those encountered in wind farm site development.

After exploring the performance of the B&Y model in soft and hard soil conditions, it is crucial to consider the worst-case scenario for top-hole drilling, particularly for the construction of offshore wind farm structures. In such cases, it is essential to account for the possibility of drilling through very strong rock formations, which can significantly affect the rate of penetration. To investigate this scenario, Well S-4, located at a depth of approximately 4,900 m True Vertical Depth (TVD), was selected for further analysis. The geological conditions in this well provide an example of a challenging rock formation that could be encountered during deepwater drilling operations.

For Well S-4, the following conditions were considered:

• An 8.5-inch hole size, which is typical for deep drilling operations.

• High pore pressure, which can influence drilling performance by increasing the risk of wellbore instability.

• A very strong rock formation with an Unconfined Compressive Strength (UCS) of approximately 75 MPa, indicating a particularly tough and resistant rock type that would challenge the drilling equipment.

Figure 20 represents the calibration results for Well S-4, which demonstrate that the B&Y model remains applicable, even in such challenging conditions. The model successfully predicts the ROP under these more extreme drilling conditions, indicating that it can still be useful for predicting penetration rates when drilling through very strong rock formations. However, it is important to note that the calibration was performed with specific operating conditions in mind, such as the high pore pressure and the strong rock formations, which are different from the conditions encountered in the softer soils tested previously.

Figure 20 ROP prediction for Well S-4 (8.5 in borehole) in the Shah Deniz field of the Caspian Sea.

Given the successful calibration of the B&Y model for Well S-4, it is logical to extend its applicability by adjusting the model to account for varying hole diameters. By modifying the model to accommodate different drilling conditions, such as changes in hole size, the rate of penetration can be predicted more accurately for a range of scenarios, which is particularly valuable for planning drilling operations in different geological settings.

To explore how varying hole sizes impact ROP, Figure 21 was developed, showing the predicted rate of penetration as a function of changing hole diameter. This analysis provides valuable insights into how hole diameter influences drilling efficiency, helping to optimize drilling operations and plan for the most efficient and cost-effective drilling methods.

Figure 21 ROP vs. hole diameter for worst-case soil condition scenario.

In summary, while the B&Y model may face challenges in predicting ROP for very soft soil layers, it has proven to be effective and applicable in harder formations, such as those found in offshore wind farm development. By considering different geological scenarios, including both soft and hard soil conditions, and analyzing the effects of varying hole sizes, this study highlights the model’s utility for optimizing drilling performance in a range of real-world offshore drilling applications.

4 Conclusion

This study emphasizes the novelty of utilizing Rate of Penetration (ROP) data for optimizing the foundation design of offshore wind farms. The primary objective was to investigate the drilling parameters and functions that influence ROP and develop accurate formulations for these drilling functions, which were then reported. A key innovation of this study is the selection of three wells from the North Sea, which serve as analogs for wind farm foundation drilling, as these wells are located in regions where offshore wind farm installations are planned. In addition, three wells from the Caspian Sea were chosen to test the applicability of the ROP model to weak formations, focusing specifically on the top-hole section, a critical part of the drilling process for wind farm foundations.

Another novel contribution of this study is the examination of the worst-case scenario for drilling into very hard rock formations under high pore pressure, highlighting the applicability of the ROP model under extreme conditions. This aspect is particularly relevant for offshore wind farm installations, where challenging geological conditions can be encountered during foundation drilling. We demonstrated that the Bourgoyne and Young (B&Y) model is capable of accurately predicting ROP in a wide range of drilling situations, including hard rock formations and abnormal reservoir pressure conditions.

The proposed model is novel in its ability to predict drilling rates for a variety of hole sizes, ranging from 3 to 10 m in diameter, which are typical of the large-diameter holes required for offshore wind farm structures. By testing the B&Y model’s applicability across different hole sizes and geological conditions, this study provides a unique contribution to offshore wind farm drilling, offering a reliable method for estimating ROP in various subsurface environments.

Additionally, this study highlights that the ROP modeling strategy must be tailored to the specific formation being drilled, and the regression coefficients derived for a particular formation should only be applied to similar formations. This emphasizes the need for site-specific modeling in offshore wind farm drilling operations, ensuring that predictions are both accurate and relevant to the local geological context.

Looking forward, this study suggests that future work could involve extending these approaches to include data from various other oil and gas fields, where different bit designs, operational strategies, and geological conditions may be encountered. Such further assessments could lead to a broader application of the model and enhance its generalizability across different types of formations and drilling environments.

Finally, this study proposes the use of Artificial Intelligence (AI) techniques, guided by physical principles, to predict ROP for top-hole sections with varying soil and rock strengths. This approach could lead to improved prediction accuracy by developing more robust correlations and enhancing the model’s predictive power, particularly for complex drilling scenarios.

Acknowledgments

The authors thank the editors and anonymous reviewers for their valuable suggestions. The authors would like to express their great thankfulness to BP for data sharing and Andrew Deeks.

Conflicts of interest

No potential conflict of interest was reported by the author(s).

Author contribution statement

Abbas Abbasov: Conceptualization, Data Curation, Methodology, Investigation, Writing-original draft.

Tural Abbasov: Literature Review, Data Curation, Visualization, Writing-original draft.

Sukru Merey: Investigation, Visualization, Writing-review & editing, Supervision.

References

All Tables

All Figures

	Figure 1 (a) Layout of a typical offshore wind farm; (b) Common types of foundations used to support offshore turbines [6, 8]; (c) The installation of offshore wind farms [9].
In the text

	Figure 2 Main components of a wind turbine [8].
In the text

	Figure 3 (a) Average size of offshore wind farms in the given year; (b) Average size of wind turbine size in the given year [19].
In the text

	Figure 4 Average depth of water and distance from shore of offshore wind farms [22].
In the text

	Figure 5 Relation between rock shear strength and threshold [24].
In the text

	Figure 6 Typical response of penetration rate to increasing bit weight [24].
In the text

	Figure 7 Typical response of penetration rate to increasing [24].
In the text

	Figure 8 The expected relationship between bit hydraulics and penetration rate [24].
In the text

	Figure 9 Penetration rates as a function of bit Reynolds number [24].
In the text

	Figure 10 Experimentally observed effect of bit weight and bit [24].
In the text

	Figure 11 Locations of the selected fields (Shah Deniz field in Azerbaijan and North Sea Fields in the UK) for this study.
In the text

	Figure 12 ROP prediction for Well N-1 (17.5 in the borehole) in the North Sea.
In the text

	Figure 13 ROP prediction for Well N-2 (17.5 in the borehole) in the North Sea.
In the text

	Figure 14 ROP prediction for Well N-3 (17.5 in borehole) in the North Sea.
In the text

	Figure 15 ROPactual vs. ROPpredicted for (a) Well N-1, (b) Well N-2 and (c) Well N-3 in the North Sea.
In the text

	Figure 16 ROP prediction for Well C-1 (26 × 42 in borehole) in Caspian Sea.
In the text

	Figure 17 ROP prediction for Well C-2 (26 × 42 in borehole) in the Caspian Sea.
In the text

	Figure 18 ROP prediction for Well C-3 (26 × 42 in the borehole) in the Caspian Sea.
In the text

	Figure 19 ROPactual vs. ROPpredicted for (a) Well C-1, (b) Well C-2, and (c) Well C-3 in Shahdeniz Field of the Caspian Sea.
In the text

	Figure 20 ROP prediction for Well S-4 (8.5 in borehole) in the Shah Deniz field of the Caspian Sea.
In the text

	Figure 21 ROP vs. hole diameter for worst-case soil condition scenario.
In the text