Trends Sci. 2025; 22(6): 9686

Can Artificial Intelligence and Machine Learning Predict the Performance of Nano-based Drilling Fluids? A Review

Moamen Gasser^1,2, Mostafa M. Abdelhafiz³, Taha Yehia¹,

Hossam Ebaid¹, Nathan Meehan¹ and Omar Mahmoud^4,*

¹Harold Vance Department of Petroleum Engineering, Texas A&M University, College Station,

Texas 77843-3116, United States

²Ignis H2 Energy, Texas 77042, United States

³Institute for Final Disposal Research, Clausthal University of Technology, Clausthal-Zellerfeld 38678, Germany

⁴Department of Petroleum Engineering, Faculty of Engineering and Technology, Future University in Egypt,

Cairo 11835, Egypt

(^*Corresponding author’s e-mail: [email protected])

Received: 1 January 2025, Revised: 26 February 2025, Accepted: 5 March 2025, Published: 1 April 2025

Abstract

Drilling fluids play a crucial role in the control and functionality of oil and gas well operations. Continuous monitoring, enhancement, and optimization of their properties are essential for successful drilling processes. Recently, a variety of additives, including nanoparticles (NPs) and novel polymers, have been introduced to modify and improve the performance of drilling fluids, addressing the emerging challenges in the field. The behavior of these fluids can change over time or under extreme drilling conditions, necessitating the use of predictive models to optimize their properties, particularly their rheological characteristics. In the past decade, there has been a growing trend of developing new models and correlations through artificial neural networks (ANN) and machine learning (ML) techniques within the petroleum industry. These methods enable the development of mathematical formulas that can predict the behavior of specific parameters based on known variables. Compared to traditional models, ANN and ML offer enhanced reliability and accuracy in predicting drilling fluid properties. This review aims to provide a comprehensive overview of the latest applications and mechanisms of various additives, with a particular focus on NPs, in drilling fluids. Additionally, it highlights the valuable insights and advancements in using ANN and ML techniques to predict and optimize the behavior of drilling fluids, which could pave the way for innovative applications and more efficient utilization of these technologies.

Keywords: Drilling fluids, Nanoparticles, Novel additives, Artificial intelligence, Machine learning

Nomenclature

Introduction

Drilling fluids, also known as drilling muds, are essential in oil and gas drilling operations. They perform several critical functions, including cooling and lubricating the drill bit, carrying drill cuttings to the surface, maintaining pressure control, and stabilizing the wellbore [1,2]. Drilling fluids can be divided into 2 main categories [1]; the liquid-based fluids which are the most common and the gas-based fluids which are rarely used. There are 3 main different types of the commonly used liquid-based drilling fluids; water-based mud (WBM), oil-based mud (OBM), and synthetic-based mud (SBM). The selection of suitable drilling fluid depends mainly on the performance, the cost, and the environmental impact. WBMs are well known for their lower cost than the OBMs and SBMs, their better impact on the environment, and better chemical solubility [3,4]. However, some of their disadvantages are that they might cause problems with the wellbore stability, hydrate the clay formations, and less lubricity than the OBMs. The properties of these fluids - such as rheology, viscosity, filtration, thermal stability, and density - must be continuously monitored and optimized to ensure the efficiency and safety of drilling operations[5-7]. As industry advances, the increasing complexity of reservoirs and drilling environments presents new challenges that require more sophisticated solutions for fluid performance.

In response to these challenges, a variety of additives have been introduced to enhance the properties of drilling fluids. Among the most promising are nanoparticles (NPs) and novel polymers, which offer the potential to improve the rheological, mechanical, and thermal characteristics of drilling fluids. These advanced additives allow for better fluid control under harsh drilling conditions, such as extreme temperatures, pressures, and aggressive chemical environments. However, the behavior of drilling fluids can change over time due to the dynamics of the reservoir or variations in operational parameters. Therefore, effective monitoring and optimization strategies are required to predict and manage these changes.

Several mathematical models are used in describing the non-Newtonian rheological behavior of drilling fluids. Rheological models, such as Power Law, Hershel-Buckley, Casson, and Bingham Plastic models [6,8-10]. A proper model must be selected accurately to illustrate the shear stress/shear rate relationship of the drilling fluids. Over the past decade, there has been a noticeable trend in utilizing artificial intelligence (AI) techniques, such as artificial neural networks (ANN) and machine learning (ML), in the petroleum industry to predict and optimize the behavior of drilling fluids field [11,12]. These data-driven approaches are increasingly replacing traditional models by offering more reliable and accurate predictions of fluid properties based on known parameters [13,14]. By developing mathematical formulas through ANN and ML, it is possible to predict the behavior of drilling fluids under various conditions, which can greatly enhance operational efficiency and decision-making.

This paper aims to present a comprehensive review of the latest advancements in drilling fluid additives, particularly focusing on NPs, and the role of advanced computational techniques in optimizing fluid behavior. Furthermore, the review explores the growing importance of ANN and ML in predicting the performance of drilling fluids and discusses their potential for future applications. Ultimately, this paper seeks to highlight the synergistic effects of innovative additives and predictive modeling techniques, which can pave the way for more efficient, cost-effective, and sustainable drilling operations.

Nanoparticle applications as drilling fluid additives

The drilling fluids are non-Newtonian fluids which means that their viscosities are directly impacted by shear rate. In other words, shear dominates most of the viscosity related functions of drilling fluids. Hence, the sheer viscosity of drilling fluids is the property that is most tracked and optimized. Four viscosity-related parameters are usually measured and optimized for drilling fluid which are plastic viscosity (PV), apparent viscosity (AV), yield point (YP), and gel strength (GS).

According to the standard protocol (API RP 13B-1, 2003), AV is one-half of the dial reading at 600 rpm (1,022 s⁻¹ shear rate) using a direct-indicating, rotational viscometer [5,6]. PV contingent on the solid content size, shape, and distribution and the friction between the inert solids. Minimum PV is always required to save the energy used by the mud pumps to circulate the drilling fluid, reduce losses that occurs due to excrescent equivalent circulation density (ECD) that may fracture the formation, and increase the rate of penetration required [7].

YP is an indication of the ability of the drilling fluids to lift the cutting to the surface. However, high YP can cause high frictional losses which will lead to high ECD. In large diameter wells high YP is regularly used for efficient hole cleaning. In addition, low YP may cause drilled cuttings and barite sag.

GS shows the capability of drilling fluids to suspend the solids and the cuttings cutting in times of no circulation. In other words, GS is the shear stress at very low shear rate after the drilling fluids were allowed to rest for a period. There are 2 types of GS, which are the initial GS or (gel-10 s) and the final GS or (gel-10 min). Both initial and final GS are measured based on the abovementioned protocols by stirring the fluid at high speed then allowing it to rest for 10 s and 10 min, respectively. The maximum value the knob reached at low speed (usually 3 rpm) after the resting time is observed and recorded as initial and final GS.

Recently, the oil industry is giving nanotechnology growing interest and expectations. NPs opened the door to the development of nano-fluids that can be used for drilling [15,16], production, and well stimulation applications. The optimistic performance of NPs can be attributed to their tiny sizes and their extraordinarily massive surface area to volume ratio. Nanotechnology might play an important role in all the aspects of the petroleum industry. NPs are key factors in the coming developments as they are friendly to the environment, more efficient and used in small quantities so they are less expensive materials. Many applications of NPs are still in the laboratory and research phases; however, their significant impact might fast their field applications. Different types of NPs have been investigated as rheological property controllers, fluid loss reducers, and shale stabilizers in many drilling fluid applications [17-19] brief discussion about the most valuable findings in the field of using them as drilling fluid property modifiers will be summarized herein.

In 2011, Amanullah et al. [20] formulated and investigated 3 nano-based drilling fluids. It was noticed that without using chemical additives it was difficult to stabilize the NPs in the drilling fluid. To reach a stabilize and homogeneous nanofluid, highly effective surfactants or polymers with high neutralizing capabilities were used. Further, Jung et al. [21] examined the rheological behavior of 5 wt. % bentonite drilling fluids containing ferric oxide NPs of 3 and 30 nm at different temperatures (20 - 200 °C) and pressures (1 - 100 atm). The results revealed an increase in the yield stress and viscosity by increasing the concentration of NPs. Later, Abdo and Haneef [22] produced and tested a new type of clay NPs that is mainly composed of montmorillonite. The drilling fluid formulated using this clay NPs with bentonite was found to have low viscosity and high GS at high pressure/high temperature conditions.

Ferric oxide NPs can maintain optimal rheological properties, reducing the filtration, and forming thin/low-permeable filter cake when used at small concentrations. Further, a custom-made magnetic iron oxide and iron oxide clay hybrid NPs were found to be able to improve the properties of bentonite-based and low solid content bentonite based drilling fluids under downhole conditions [23-28]. Moreover, a combination of Multi-Walled Carbon Nanotube (MWCNT) and nano silica, which showed improvements in PV, YP and GS of the drilling fluid as well as a fluid loss reduction lubricity and shale inhibition at temperatures up to 250 °F and pressures up to 500 Psi [29,30]. The fluids having NPs showed no phase-separation unlike the base-fluid that suffered from sagging effect and had 2 visible separate layers of fluids Figure 1 [31,32].

According to Aftab et al. [33], Zinc oxide NPs-acrylamide composite enhanced the lubricity of the WBM by 25 % as well as slightly increased the rheological properties (AV, YP, GS) of the treated fluids. Nizamani et al. [34] investigated a drilling fluid having titania-bentonite based nanocomposite as an additive at low (80 °F) and high (150 °F) temperatures. The base mud met the required operating values at 80 °F but it failed to meet them at 150 °F. Addition of titania-bentonite nanocomposite showed an improvement in the rheological properties as the AV, YP, GS increased by 19, 64 and 40 %, respectively. The addition of 1 g of titania nanocomposite at 150 °F helped in maintaining the rheological properties of the fluid at the correct operating values.

Figure 1 Sagging effect of the prepared drilling fluid after 3 weeks (a) without any additives and (b) with NPs [31].

Adding Fe₂O₃ NPs at small concentration yielded better rheological and filter cake characteristics of bentonite-based drilling fluids. However, the addition of silica NPs decreased the YP but showed better rheological stability [35-38]. Also, adding 0.05 vol % silica dioxide NPs can reduce the power consumption by up to 27 % [39]. It was also reported that the surface charge of NPs and their stability in suspension played a key role in NPs’ dynamics with the other drilling fluid additives as revealed from zeta potential measurements. Moreover, the effect of using different types of NPs (Fe₂O₃, Fe₃O₄, ZnO and SiO₂) with a bentonite-based drilling fluid was evaluated [40]. A thorough discussion about the interaction of NPs with bentonite was presented in this study. Figure 2 shows the embedding of iron oxide NPs in the randomly formed pore structure on the surface of bentonite particles and the weak edge-to-edge platelet structure in the case of using SiO₂ NPs at elevated temperatures

Figure 2 Schematic illustration shows the embedding of iron oxide NPs (Fe₂O₃ or Fe₃O₄) in the randomly formed pore structure on the surface of bentonite particles and the weak edge-to-edge platelet structure in the case of using SiO₂ NPs at the elevated temperatures [35].

Al₂O₃, CuO, SiO₂ and MgO NPs were examined at different concentrations and conditions with WBM [41-43]. The addition of NPs increased the GS with the best performance when adding higher concentration of CuO. However, increasing the concentration of Al₂O₃ and MgO decreased the gelation. Adding NPs were also reported to improve YP and PV at the studied conditions [41]. In 2018 a new type of NPs (Yttrium oxide, Y₂O₃) was introduced to be used as a drilling fluid additive at low and high pressure/temperature conditions [44]. It was found that the PV, YP, and GS increased with the increase in the concentrations of NPs at ambient temperature and pressure. It was also noticed that they decreased with the increase in temperature but with different reduction percentages. Further, WBM that doesn’t contain any NPs produced a very high shear thinning behavior and lost its viscosity and the ability to suspend cuttings. However, the mud treated with NPs was found to be more stable under high pressure and temperature with neither high thinning shear behavior nor high thickening shear behavior. Optimum concentration of Yttrium oxide NPs was reported to be 2.5 g [44].

It was found that with the increase in the concentration of the ZnO nanowires the reduction rate of density with the increase in the temperature becomes smaller. Using the same concept, the rate of reduction in the fluid viscosity with the increase in temperature was found to be decreasing with the increase of the ZnO nanowires concentration [45]. Later, Aramendiz et al. [46] checked both SiO₂ and Graphene-NPs (GNPs). A significant improvement in the filtration properties were observed when using a mixture of 0.5 wt. % of SiO₂ and 0.25 wt. % of GNPs with a neglect effect on the spurt loss, PV, and YP. However, the GNPs samples yielded higher gel strength compared to the fluids containing SiO₂ NPs. adding graphene oxide NPs enhanced the stability of both fresh water and saline water in the saline environment [47]. In addition, nano graphene the thermal stability and the shale swelling properties of the salt polymer WBM at High Temperature High Pressure (HTHP) conditions [48].

Later, NPs-based KCL-Polymer drilling fluid was formulated and examined based on the rheological and filtration characteristics. The impact of 4 different types of NPs with one of them having 2 particle sizes had been tested at 5 different concentrations. Based on the rheological properties of the tested nano-based fluids, higher NPs-concentrations (greater than 0.5 wt. %) were found to negatively affect the properties of KCL-Polymer mud because of the agglomeration of the excessive NPs. Adding 0.3 wt. % of nanotitanium, nanoaluminium-15 nm, and copper oxide NPs were found to cause a reduction in the PV of drilling fluid by 72, 10, and 10 %, respectively. On the other hand, using both nanosilica and nanoaluminium-40 nm increased the PV. Nanotitanium at 0.3 wt. % showed an increase of 30 % in the YP compared to the base-fluid, which implies less solids sagging and higher drilled cuttings carrying capacity. An increase in the GS was observed when using any concentration of nanosilica with the highest at NPs’ concentration of 0.7 wt. %, which caused an increase in gel-10 s and gel-10 min by 26 and 38 %, respectively. However, all the other NPs at the same concentration were found to have minimal or no effect on gel strength. Figure 3 shows the effect of NPs on the PV and YP of the KCl-Polymer mud [19]. Moreover, silicon oxide can improve the rheological properties, lubricity and colloidal stability of the OBM [49].

The impact of different NPs (Al₂O₃, TiO₂ and CuO) on the rheological and filtration properties of WBM was investigated [50-52]. Cellulose nanofibers cellulose nanocrystals and different factors like flow rate, rheological properties, and hole size were studied in parametric research to explain their effect on the efficiency of cutting transport and hole cleaning [53-55]. Moreover, the influence of dual-functionalized cellulose nanocrystals on the toxicity, thermal tolerance, rheological and filtration properties of bentonite based drilling fluids have been investigated under variant temperatures [56]. The results revealed that NPs can be used as a promising additive to improve rheological behavior. In addition, using NPs has improved hole cleaning efficiency. The abovementioned study showed both the size of the cuttings, and the rheological properties have the largest effect on the hole cleaning efficiency. On the other hand, when the rheological properties were elevated the effect of the flow rate was minimal. Furthermore, especially in holes with big diameters, the addition of NPs enhanced the cleaning of the wellbore significantly regardless of the cutting sizes. Recently, Aftab et al. [57] showed that WBM treated with titania-bentonite nanocomposite has improved lubricity at different temperatures.

Figure 3 Impact of NPs on the (a) PV and (b) YP of the KCl-Polymer mud [19].

In 2021 the addition of synthetic zinc oxide NPs to WBM was investigated at 25 [58], 40, and 80 °C [59]. At 40 °C and 0.1 wt % concentration the YP and gel-10 s have increased by 61.54 and 125 %, respectively. While, at elevated temperatures the lower NPs concentrations show better enhancements for the rheological properties. Also, 0.05 wt. % concentration of ZnO NPs showed an increase of 60 and 50 % for YP and gel-10 s. The addition of ZnO and associative polymer with ratio of 0.1 to 1, respectively showed the highest impact on rheology, filtration and shale inhibition [58]. The effect of aluminum oxide and copper oxide on KCl-Polymer WBM was investigated. The addition of both NPs within the range of 0.3 - 0.5 wt. % improved the rheological parameters. While the filtration characterization was improved on the addition of 0.5 and 1 wt. % of aluminum oxide and copper oxide, respectively. Also, SEM and EDX have shown that the addition of NPs smoothens the surface and made it less pours compared to the base fluid [60].

Later in 2021, Mirzaasadi et al. [61] have extracted silica oxide from agriculture wastes (rice husks) and then silica NPs were produced using 2 different approaches; one without any chemical addition and the other with chemically treating. The purity of the chemically treated and untreated NPs was 97.4 and 94.5 %, respectively, determined by x-ray fluorescence method (XRF). The effect of both NPs on WBM rheology and thermal stability were studied at 121.11 and 148.88 °C, which simulates the downhole conditions. The study showed that both NPs improved the rheological properties but increased the filtration loss. The chemically treated NPs prevented thermal degradation and improved rheological properties more than the untreated NPs. Among the tested the concentrations 3 % of chemically treated NPs showed better effect in enhancing the properties of the drilling fluids [61].

A comparison between the effect of silica oxide and copper oxide NPs on the polyamine based non-damaging drilling fluids and bentonite-based drilling fluids. Silica oxide NPs acted as a mud thicker in non-damaging drilling fluids while having the opposite effect on the bentonite-based drilling fluid. The addition of copper oxide NPs worked as mud thinner in both drilling fluids [62]. Furthermore, copper oxide and zinc oxide were used to enhance the thermal, electrical, and filtration properties of Polyethylene glycol-based and polyvinylpyrrolidone-based drilling fluids. It was observed that the addition of NPs to the drilling fluids enhanced all the above mentioned properties at room temperature [63]. Moreover, aluminum oxide nanorods were used to develop a thermally stable ethyl octanoate ester-based drilling fluid. The rheological properties for both the base and the nanomodified drilling fluid samples were measured at low (2.6 °C), room (26.8 °C) and elevated (70 °C) temperatures. While the filtrate loss was measured at the room temperature and 690 KPa. The addition of aluminum oxide nanorods enhanced the thermal stability of the drilling fluids over the wide range of the investigated temperatures [64].

In 2023, a systematic study of the influence of nano-additives of various concentrations, average sizes, and composition on the temperature dependence of the viscosity and rheological behavior of WBM was conducted [50]. Typical compositions of drilling fluids, such as water suspensions of various clay solutions and gammaxan-based polymer solutions, were considered. Hydrophilic silicon and aluminum oxides NPs were used as nano-additives at concentrations ranging from 0.25 to 3 wt. %. The average NPs size varied from 10 to 151 nm. The temperature of drilling fluids varied from 25 to 80 °C. It was found that the addition of NPs leads to a significant change in the rheological properties of WBM depending on the temperature. With increasing temperature, the yield stress and consistency index of drilling fluids with NPs increase, while the behavior index, on the contrary, decreases. This behavior depends on the size of the NPs. As the particle size increases, their influence on the temperature dependence of the drilling fluids’ viscosity increases. In general, it was shown that the addition of NPs makes the viscosity of drilling fluid more stable with regard to the temperature, which is an essential fact for practical application [50].

A modified polystyrene micro-nano spheres (MPS) was synthesized, then characterized, and tested to achieve wellbore stability by changing the hydrophobicity of the shale surface and plugging the micro-nano pores [65]. The inhibition and plugging performance of MPS were evaluated through linear expansion, shale recovery, and plugging of polytetrafluoroethylene (PTFE) microporous membrane. Contact angle, pore size distribution, and SEM analysis were performed to study the inhibition and plugging mechanisms of MPS. The results showed that MPS was spherical with a particle size distribution of 91 - 712 nm and had good thermal stability. The MPS had excellent compatibility with drilling fluids and better inhibition than KCl, polyamines, and SiO₂. When using PTFE microporous filter membrane as a filtration medium, the API filtration loss volume of 3 wt. % MPS aqueous solution was only 42 mL, while that of the solution without MPS was 260 mL. The pore size of the PTFE microporous membrane decreased after plugging. The MPS adsorbed on the shale surface to form a hydrophobic layer, which could weaken the hydrophilicity of shale. The contact angle of shale slices treated with 2 wt. % MPS was 108.2 °. Furthermore, SEM observations indicated that MPS can improve the quality of mud cakes and plug the small pores [65].

Nano-WBM was prepared using nano-copper oxide and multiwalled carbon nanotubes (MWCNTs) as modification materials [66]. The effects of the temperature and concentration of the NPs on the rheological properties were studied using a rotational rheometer and viscometer. Also, the influence of 2 NPs on the filtration properties was studied using LTLP filtration apparatus, as well as a scanning electron microscope (SEM). It is found that MWCNTs with a concentration of 0.05 w/v % have the most obvious influence on the NWBDFs, which improves the stability of the gel structure against temperature and decreases the filtration rate. Also, a theoretical model predicating the YP and the PV as a function of the temperature considering the influence of the NPs was developed based on DLVO theory [66]. Tahr et al. [67] inspected the investigations’ results and any gains made by utilizing a new material in drilling fluids. As biodegradable materials, the filtration and rheological capabilities were indicated to be significantly improved by the powders of rice husk and pomegranate peel. Titanium oxide NPs and nano-clay also significantly altered the drilling fluid’s characteristics. Therefore, these qualities may be enhanced, and the wellbore stability may be provided by combining these 2 unique materials - titanium and pomegranate peel.

Ultrafine barite was utilized to obtain good suspension stability. Also, the method of modifying zwitterionic polymers on the surface of nano-silica was used to develop a temperature-resistant and salt-resistant fluid loss reducer FATG with a core-shell structure, and it was applied to ultra-fine clay-free WBM [68]. The results showed that the filtration loss of clay-free drilling fluid containing FATG can be reduced to 8.2 mL, and AV can be reduced to 22 mPa·s. The clay-free drilling fluid system obtained by further adding sepiolite reduced the filtration loss to 3.8 mL. After aging at 220 °C for 15 d, it had significant salt tolerance, the filtration loss was only 9 mL, the viscosity did not change much, a thinner and denser mud cake was formed, and the viscosity coefficient of the mud cake was smaller. The linear expansion test and permeability recovery evaluation were carried out. The hydration expansion inhibition rate of bentonite reached 72.5 %, and the permeability recovery rate reached 77.9 %, which can meet the long-term drilling fluid circulation work in the actual drilling process [68].

An industrially prepared silica NPs coated with AEAPTS ([3-(2-Aminoethylamino) propyl] trimethoxy silane) was used as an additive to enhance the rheology and control filtration of WBM [69]. Silica NPs were coated separately in a 2-step process, which involved the addition of a hydroxyl group first and then coating with AEAPTS. Different rheological and filtration tests were done with varying NPs concentrations of 0.2, 0.3, and 0.4 w/v %. The rheological values of the mud samples were recorded both before and after the thermal aging of mud in the roller oven at 105 °C for 16 h. The filtration test was carried out according to API standards with 100 psi differential pressure for 30 min. Both PV and AV of the drilling fluid were found to be increasing with silane-coated silica NPs when tested at 30 and 60 °C. The degradation in the rheology of the base mud without NPs after thermal aging was found to be around 60 % which was reduced to around 20 % with the addition of the coated silica NPs. Also, a remarkable reduction in the filtrate volume, when compared with base mud, was achieved with the addition of the silane coated NPs [69].

Martin et al. [70] aimed to establish the optimum concentration of a cationic surfactant that would successfully modify the surface of silica NPs and thereafter, evaluate the performance of modified nano silica as a rheological and filtration property enhancer in WBM. The surface of silica NPs was successfully modified by adding Hexadecyltrimethylammonium bromide (CTAB) to silica solution. Different mud formulations containing modified nano silica with varying zeta potential values, SNP3 -S2, SNP3 -S4, SNP3 -S5, SNP3 -S6, and SNP3 -S7 with −17.7, 20, 28.2, 35.4, and 37.1 mV, respectively, were investigated. Results showed that modified nano silica with the highest absolute value of zeta potential enhanced drilling mud rheology as temperature increased from 149 to 232 °C. The optimal amount of CTAB was found to be between 1.0 and 2.0 wt. %. Filtration loss was reduced by 11.4, 17.6, and 29.5 % on average for mud samples SNP3-S5, SNP3-S6, and SNP3-S7, respectively, at all temperatures. Mud cake thickness was reduced by 19.9, 11.6, and 28.7 % on average by mud samples SNP3-S5, SNP3-S6, and SNP3-S7, respectively, at all temperatures [70]. Figure 4 shows the interaction between unmodified silica NPs and bentonite as well as the interaction between modified silica NPs and bentonite.

Figure 4 Interaction between unmodified silica NPs and bentonite (top) and Interaction between modified silica NPs and bentonite (bottom) [70].

In 2024, CuO NPs were synthesized using a natural extract from Colocasia esculenta leaves and the potential of the biogenic CuO NPs to enhance the lubricity in mud had been explored [71]. The ability to form a continuous and thin lubricating film at the mud-drill string interface was expected to reduce the frictional resistance between them significantly. Besides this, the filtration and rheological performance of the developed mud had been investigated. The formulation exhibited significant enhancements in lubricity, with a 27 % increase, and filtering performance, with a 48 % increase. The rheological profile, which exhibited shear-thinning behavior, demonstrated strong agreement with the Herschel-Bulkley model. Furthermore, the NPs showed the capability of reducing the negative effects of heat-induced deterioration on the characteristics of mud [71]. This highlights their potential as advantageous substances for drilling operations conducted at high temperatures. The results emphasize the advancement of drilling fluid technologies that are both environmentally benign and economically feasible.

Ahmed et al. [72] synthesized SiO₂/g-C₃N₄ NPs hybrid and investigated its addition in different concentrations to WBM and studied the impact on the rheological and fluid loss properties of the fluids. The studies were carried out at various SiO₂/g-C₃N₄ NPs concentrations under before hot rolling (BHR) and after hot rolling (AHR) conditions. The outcomes demonstrated that the rheological and fluid loss properties were enhanced by the addition of SiO₂/g-C₃N₄ NPs, as it worked in synergy with other additives. Additionally, it was discovered that the NPs improved the drilling fluid thermal stability. The experimental findings indicate a significant influence of SiO₂/g-C₃N₄ NPs on base fluid properties including rheology and fluid loss as the most remarkable, especially at higher temperatures. The significant improvements in YP and gel-10 s were 55 and 42.8 % under BHR and 216 and 140 % under AHR conditions, respectively. Permeability plugging test fluid loss was reduced by 69.6 and 87.2 % under BHR and AHR conditions, respectively, when 0.5 lb/bbl NPs were used in formulations [72].

Abdullah et al. [73] conducted a comparative analysis between hydrophobic nanosilica (HNS) and potassium chloride (KCl), a widely used shale inhibitor but has negative impact on the environment and subsurface activities, to better understand how HNS can effectively manage water and shale interactions by restricting mud filtration into the formation. In this work, shale samples were collected from the Kolosh Formation in the Kurdistan Region of Iraq, known for being one of the most challenging formations to drill. Investigations into the properties of drilling fluid were conducted using LTLP and HTHP filter press, alongside analyzing rheological properties at 3 different temperatures (25, 50 and 75 °C). In addition, the impact of the HNS on clay swelling was examined using the liner swelling meter test, shale dispersion test and capillary suction time test. The obtaining results revealed that the shale hydration in the drilling fluids was reduced 24.36 - 15.53 % and the shale recovery at high temperatures was improved from 80.2 to 94 % by adding 0.4 wt. % HNS[73]. Furthermore, HNS demonstrated improved clay suspension in the capillary suction time test wherein the suspension time reduced from 303 to 80 s at the same HNS concentration. Utilizing HNS effectively reduced clay swelling in all experiments and enhanced the rheological properties of the mud, showcasing stability across a range of temperatures and significantly reducing the formation of filter cake and fluid loss. Figure 5 illustrates the results of shale dispersion test for the base mud and drilling fluids with KCl and HNS with 4 different concentrations of 0.05, 0.1, 0.2 and 0.4 wt. %.

Figure 5 The result of shale dispersion test for the base mud and drilling fluids with KCl and HNS with 4 different concentrations of 0.05, 0.1, 0.2 and 0.4 wt. % [73].

Bardhan et al. [74] introduced Mesoporous Nano-Silica (MNS) to enhance WBM’s inhibitive, rheological, and fluid loss characteristics. MNS was synthesized with a particle size of 134.47 nm and zeta potential of −32.2 meV. MNS was added to the fixed base formulation at varied concentrations (0.05, 0.1, 0.2, 0.5 and 1 wt. %) and were subjected to hot rolling at 180 °C temperatures at 100 psi pressure for 16 h to evaluate the influence of thermal aging on the properties of the drilling fluid. The rheological investigation was performed at 25 and 70 °C while the inhibitive properties were checked via shale recovery test and capillary suction timer. The filtration properties were examined at 100 psi and 500 psi pressure at 150 °C. The results revealed that MNS can substantially improve the thermal properties of WBM, maintaining rheological characteristics and drastically reducing fluid loss while imparting some shale inhibitive properties, which may be attributed to either the size effect or the synergistic influence of materials. After hot rolling PV of MNS-infused mud was 77 % better than that of the base mud [74]. Figure 6 presents the PV at 25 and 70 °C variations with increasing concentrations of MNS in the drilling fluids before and after hot rolling.

Figure 6 PV at 25  and 70 °C variations with increasing concentrations of MNS in the drilling fluids before and after hot rolling [74].

Promising drilling fluid additives

Different rheological models as well as new additives have been introduced in the literature. Some of them showed optimistic performance. A pioneer trial had been presented by Vipulanandan and Mohammed [75] by introducing the hyperbolic model to predict the rheological behavior of bentonite WBM. In this study, acrylamide polymer was added to bentonite-based drilling mud at different concentrations. The results showed that the addition of bentonite increased the yield stress, while the addition of acrylamide polymer decreased the yield stress depending on the bentonite content. Also, the addition of bentonite increased the maximum shear stress. while the addition of 0.24 wt. % acrylamide polymer reduced the maximum shear stress as well as decreased the AV. The authors compared between the rheological parameters predicted using their hyperbolic model and that of Herschel-Bulkley [9]; Casson [10] models. The hyperbolic model was found to be more effective in predicting the shear stress, strain rates, and thinning behavior than the other models. Moreover, the model was the only one that can predict the maximum shear stress while the other 2 models can only predict the finite shear stresses [75].

In 2015, ball-milled functionalized -COOH carbon NPs with average size of 10 nm was dispersed in the drilling fluid sample with different concentrations ranging from 0 to 1 wt. %. The addition of NPs enhanced the thermal conductivity by 6 % and increased the viscosity of the nano-modified drilling fluid compared to the base fluid [76]. Green synthesized α-MnO₂ NPs can help improve the thermal degradation of the polymer WBM under harsh conditions. Adding a small concentration of 0.01 w/v % of α-MnO₂ NPs can improve the rheological properties and they keep increasing with the increase of concentration. Both HTHP and Low Temperature Low Pressure (LTLP) filtrate loss are reduced compared to the base fluid and the electrical conductivity increased on the addition of NPs [77].

Later, in 2018 the shear stress-shear strain rate was predicted for bentonite WBM treated with bentonite-based nano clay using the hyperbolic model [78]. The study aimed to reduce the fluid loss of the drilling fluids, alter the rheological properties, and improve the electrical resistivity using the nano clay particles. For all the drilling fluids studied in this work and compared to the other rheological models, Vipulanandan rheological model predicted shear stress-shear strain rate relationships better. Furthermore, the addition of 1 wt. % of nano clay particles yielded more than double the maximum shear stress tolerances and yield stresses for all cases except the one containing 8 wt. % bentonite at 25 °C.

In 2017, Afolabi et al. [79] investigated the mutation in rheological properties of bentonite mud on the addition of silica NPs using an optimization-based statistical approach. A feasible area was constructed for multiple parameters using an overlaid contour plot. The concentrations of 6.3 wt. % bentonite and 0.94 wt. % silica NPs were selected to be the optimal factors for minimum rheological properties using the steepest method. The rheological properties of the formulated mud were evaluated using the hyperbolic model [40] and compared with other rheological models. The shear stress limit and the rheological properties of the nano modified drilling fluids were precisely predicted using response surface design and the hyperbolic model [75], respectively. Figure 7 shows the overlaid contour plots of PV, YP, AV, and shear stress limit [79,80].

In 2016, a local bentonite clay had been collected from South Hamam, Egypt and investigated versus a commercial one in formulating drilling fluids [81]. The mineralogical and elemental analysis of the local bentonite had shown that it is composed mainly of Na-montmorillonite with the elemental composition shown in Tabel 1. The local bentonite had been activated using a constant ratio of polyvinylalchol, chitosan which was mixed with various ratios of N-vinyl-2-pyrolidene with and without diethyleglycal dimethylacrylate. The new prepared composition polymers were evaluated as filter loss additives and viscosifier. The results showed that the increase in the 3 mixtures concentrations increased the rheological properties of the fluids such as the PV, AV, YP and gel-10 s and gel-10 min. However, the efficiency of the formulated drilling fluids increased with the increase in the cross links in the polymer mixture and the decrease in the amount of N-vinyl-2-pyrrolidone [81]. Later, the effect of different types of clays like Organophilic clay with associative polymer, clay NPs, barite and bentonite NPs on the rheological, filtration and shale inhibition properties of the water based drilling fluids at harsh well like conditions [82-84].

In 2022, a combination of inorganic nanomaterials with organic macromolecules were used to formulate and test a potential filtrate loss reducer and rheology modifier called PAASM-CaCO₃. PV, AV, and YP were measured at ambient temperature and atmospheric pressure while the filtrate loss was recorded at temperatures up to 180 °C and pressures up to 3.5 MPa. PAASM-CaCO₃ was capable of increasing the PV and AV and reduce the volume of filtration compared to the base fluid [85]. Furthermore, a hybrid of NPs can significantly reduce the filtration volume in HTHP fluid loss and particle plugging tests at differential pressures up to 1,000 Psi [86].

Figure 7 Overlaid contour plots of: (a) PV, (b) YP, (c) AV, and (d) shear stress limit [79].

Table 1 Elemental analysis of the local bentonite collected from South Hamam, Egypt using X-ray florescence [81].

Further, glass beads were investigated in various sizes of 90 - 150 and 250 - 425 μm as rheological property modifiers as well as drilling fluid lubricators [31]. For this aim, different samples were prepared with different sizes and concentrations of the glass beads. It was found that an optimum concentration of 4 ppb of glass beads reduces the coefficient of friction by 28 % compared to the base mud. In addition, increasing concentration of the glass beds increased the PV and the increase above 8 ppb increased the YP significantly. On the other hand, the increase of glass beads concentration from 2 to 6 ppb decreased the GS while at high concentrations of 6 to 12 ppb the GS slightly increased [31].

Adewle and Najimu [87] investigated the mutation in WBM performance on the addition of date seed based. Moreover, they investigated rheological/filtration properties, density, and thermal stability of WBM on the addition date-seed and the influence of particle size, date-pit fat content, and date-pit loading on the drilling fluids. It was revealed that particles with size less than 75 nm enhanced both the rheological and filtration properties of the WBM. However, the best performance was determined to be achieved on the dispersion of 15 to 20 wt. % date-pit to the base WBM. Figure 8 shows images of the date-pit processing (upper) and the effect of the date-pit loading on the shear thinning behavior (lower-left) and the AV and GS (lower-right) of the drilling fluid [87].

Figure 8 (Upper) date-pit processing, (Lower) effect of date-pit loading on the rheological performance of the drilling fluid [87].

In 2020, Ismail et al. [88] explored the feasibility of applying henna-leaf extracts and hibiscus-leaf extracts as ecological being products in WBM, which might minimize the environmental hazards. Rheological and filtration characterizations were carried out at 78 and 300 °F. The results of the low viscosity polyanionic cellulose were compared to plant extracts results. It was revealed that the volume of filtrate was dramatically decreased between 62 - 76 % on the addition of henna-leaf extracts and hibiscus-leaf extracts as well as significant improvement in the mud cake and rheological characteristics of the WBM. Furthermore, the viscosity and inhibition properties of WBM were both progressed when using both extracts as promising additives. Further, compatibility test data confirmed that the green additives are compatible with the other base fluid additives. The swelling behavior of sodium bentonite verified that the green plants are effective in inhibiting bentonite swelling. Figure 9 shows images of the leaf extracts and powder after processing henna (upper-left) and hibiscus (upper-right), and mud cake filter cakes (lower) for different test fluids [88].

Figure 9 (Upper) Leaf extracts and powder after processing henna and hibiscus, (Lower) mud cake filter cakes for different test fluids [88].

Khan et al. [89] examined the combination of hydrophobic ionic liquid (Trihexyltetradecyl phosphonium bis (2,4,4-trimethyl pentyl) phosphinate) - (Tpb-P) and cationic gemini surfactant (GB) as a WBM additive for clay swelling inhibition. Different concentrations of the combined ionic liquid and gemini surfactant were used to prepare the drilling fluids ranging from (0.1 to 0.5 wt. %), and their performances were compared with the base drilling fluid. The wettability results showed that novel drilling fluid having 0.1 % Tpb-P - 0.5 % GB wt. % concentration has a maximum contact angle indicating the highly hydrophobic surface. The linear swelling test yielded the least swelling of bentonite at a concentration of 0.1 % Tpb-P - 0.5 % GB wt. % combined solution. Furthermore, the results of the capillary suction test (CST) also suggested improved performance of the combined solution at 0.1 % Tpb-P - 0.1 % GB concentration [89].

The application of okra mucilage for the prevention of shale swelling was the objective of several studies [90,91]. Okra mucilage (hibiscus esculents) was extracted from the okra plant and used – as an alternate green additive – at 3 different concentrations (5, 10 and 20) vol. % for linear swell test at atmospheric conditions for 24 h on bentonite wafers. Further zeta potential, particles size and capillary suction timer test (CST) were conducted. An experimental study revealed that okra mucilage reduced the swelling of bentonite. For instance, 10 and 20 vol. % of okra mucilage solutions reduced the swelling by 36.8 and 50.5 %, respectively. Also, the Okra mucilage decreased the zeta potential of clay and increased its particle size. CST time decreased initially at low concentration and increased with concentration [90]. In the second study [91], the composition of okra powder was diagnosed by X-ray fluorescence (XRF) and Fourier-transform infrared spectroscopy (FTIR), and its thermal stability was tested using thermal gravimetric analysis (TGA). Then the okra powder was mixed in various concentrations (1, 2 and 3 g) in 350ml of WBM and its performance was compared with starch-based drilling fluid. The addition of okra reduced fluid loss in different proportions at different concentrations. For instance, drilling fluid with 3g okra concentration had 42 % lower fluid loss as compared to the base fluid. The cake thickness was reduced upon the addition of okra. The addition of okra powder also increased the viscosity and GS of the WBM. TGA analysis of okra powder showed that it has strong thermal stability as compared to starch [91]. Later in 2022, the okra mucilage showed comparable performance to the commonly used clay stabilizer (KCl) used in the industry [92]. It was observed that okra mucilage reduced the fluid loss and provided a thin filter cake. The rheological properties were improved with the addition of okra mucilage. The increase in clay particles and reduction in zeta potential showed the inhibition properties of the okra mucilage. In addition, okra mucilage reduced friction and provided lubricity, which suggests that okra mucilage could be a green and environmentally friendly alternative clay swelling inhibitor [90-93]. Figure 10 showed the scanning electron (SEM) micrograph images of filter cakes of the base mud and those of the base mud modified with 10 % okra mucilage [92].

Figure 10 Scanning electron micrograph images of filter cakes (a,b) base mud and (c,d) base mud modified with 10 % okra mucilage [92].

The formulation of a drilling fluid modified with a combination of NPs with their unique properties and cost-effective biodegradable materials (pomegranate peel powder, and Prosopis farcta plant powder) was the aim of another study [94]. The drilling fluids were identified and recognized using scanning electron microscopy (SEM), X-ray diffraction (XRD), and Fourier transform infrared spectroscopy (FTIR) techniques. Furthermore, experimental tests were conducted to investigate the performance of the newly formulated drilling fluid in improving fluid loss characteristics. The results showed that adding 0.3 wt. % of pomegranate peel powder to the reference (base) drilling fluid reduces the filter loss volume to 7.9 mL compared to the reference fluid (11.6 mL). As the optimal concentration of TiO₂ was mixed with 0.3 wt. % of pomegranate peel powder then added to the reference fluid, the filter loss volume was reduced to 8.6 mL [94].

Yang et al. [95] used styrene, butyl acrylate, acrylamide, and 2-acrylamide-2-methylpropanesulfonic acid as the main raw materials to synthesize a polymer nanolatex (SBAA) employing a conventional emulsion polymerization approach (one-pot method). SEM, TEM, and PSD experiments demonstrated that SBAA is a NP with a particle size of around 150 nm and a distinct core-shell structure. The TGA analysis revealed that SBAA had a decomposition temperature of 296 °C. The experimental results showed that SBAA could reduce the medium pressure filtration loss by around 33 % compared with the basic bentonite fluid, and the reduction rate after aging at 200 °C is around 41 %. Moreover, it can reduce the filtrate loss velocity of WBM in heterogeneous pores, and the effects of filtration reduction and mud cake quality enhancement outperform those of commercial nanosilica particles [95].

Rambutan waste, one of Malaysia’s most produced fruit wastes, was regarded for the first time as a filtering additive in WBM [96]. Rambutan peel contains cellulose fibers that act as rheological modifiers. Rambutan fiber increases the pressure on the crack of the plug and reduces the loss of liquids. Low, medium, and high concentrations of rambutan waste (0.01, 0.1 and 0.5 g) were used to prepare samples of mud to compare the rheological and filtration properties of WBM. The results showed that by increasing the concentration of rambutan waste samples, the properties such as PV, YP, and GS are gradually increased. Furthermore, rambutan additives significantly improved the filtering performance by reducing the loss of filters and the thickness of mud cakes. It was observed that 0.01 g of raw rambutan peel reduced filtrate loss from 9 to 4 mL compared to 9 mL of base liquid. In addition, the lowest concentration of rambutan additive produced the thinnest mud cake of 1.09 mm compared to 2.82 mm of base liquid, respectively [96]. Figure 11 reveals a schematic illustration for the preparation of rambutan waste WBM, and the influence of different concentrations of rambutan waste on the drilling fluid properties.

Figure 11 (Upper) the preparation of rambutan waste WBM, (Lower) the effect of different concentrations of rambutan waste on the drilling fluid properties [96].

Fadairo and Oni [97] reported an examination of eggshell NPs (ESN) to enhance the efficiency of WBM at elevated temperature. The study was based on previous reported literature which revealed that ESN can withstand a lot of heat and at the same time retain their properties under extreme conditions. ESN was added at various weighted amounts to the petroleum industry’s approved mud composition for an elevated temperature well to design eggshell-boosted WBM samples. Filtration and rheological tests were conducted under HTHP conditions. The results showed that ESN helps WBM to withstand drilling operations in elevated temperature formations by delaying thermal degradation up to 270 °C. Specifically, the Fluid sample with 5 lb/bbl of ESN exhibited an 8 % reduction in HTHP filtrate volume when compared with an equal volume of commercial calcium carbonate (CCC), while a larger quantity of ESN (6 lb/bbl) yielded a 17 % reduction. Additionally, the inclusion of 5 lb./bbl of ESN was observed to be more effective than an equal quantity of CCC at 250 °C as it yielded a 28 % increase in 10 min GS. However, the rheological properties of 5 lb./bbl of ESN were not as effective as CCC at LTLP conditions which may be due to the presence of organic matter as a constituent of ESN at any temperatures below 200 °C [97].

A novel biosynthesized nanofluid system integrated with a natural surfactant was developed to tackle biological challenges and reduce the damage to hydrocarbon formations [98]. This innovative approach combines biosurfactants and NPs systems in WBM to minimize formation damage during hydrocarbon extraction while prioritizing environmental sustainability. Rheological measurements revealed that the PV and YP increased to 67.9 cP and 29.71 Pa, respectively, at a concentration of 0.1 wt. % zinc oxide NPs. The biosurfactant (Chuback) enhanced wettability by reducing the contact angle. This reduction, a crucial factor in wettability, led to a decrease of 51.53 % in the contact angle of WBM on sandstone slabs and 52.32 % on carbonate slabs, compared to more hydrophilic surfaces [98]. The research findings indicate that the optimized fluid obtained through Design of Experiments can significantly enhance the operational efficiency of drilling and production by minimizing the negative impacts on reservoir permeability. Finally, images taken before and after the flood using Computed Tomography Scans (CT-Scan) showed that the green additives proposed in the WBM have improved the factors that reduce formation damage.

Based on the articles reviewed in this work, 17 % of the additives used in the drilling fluids investigations contained silica while 16 % of the literature used iron to test its effect on the drilling fluids. Only 2 % used MgO NPs to enhance the properties of the bentonite WBM while 10 % used uncommon additives like yttrium oxide NPs and Nano ATR Figure 12. A compressive summary for the reviewed paper, the type of the investigated drilling fluids, the additives used, the experimental conditions, and the investigated parameters are listed in Table 2.

Figure 12 Comparison between the usage percentages of different additives.

Table 2 Summary of the presented papers in this review.

(R)*: Rheological measurements; (F)**: Filtration measurements; API: room temperature and 100 psi

Machine learning and artificial intelligence applications

AI can be defined as the teaching of computers to perform an action or series of actions that usually require human intelligence to be done. AI can use either explicit approaches like writing a code or implicit techniques like using ML algorithm. On the other hand, ML is teaching the computers how to do a certain task without telling it how to perform this task, instead you provide it with appropriate number of exemplars [99]. Hence, ML is located within the domain of AI, while AI is located within the computer science (CS) domain which has a common domain with data science domain as shown in Figure 13. The petroleum filed like a lot of the other fields has grown an interest in utilizing AI and ML techniques to optimize the several operations[11].

Figure 13 Different domains of computer science branches.

ANN is one of the widely used algorithms in the petroleum field especially in the drilling fluids applications with over 54 % [13]. ANN is a powerful tool that can simulate the human brain learning process through creating networks of artificial neurons. The ANN can learn and train by experience with appropriate learning examples just as people do (i.e. they build their awareness by detecting the relationships and patterns in the data) [100]. Neurons are fully connected and, in a network, shaped form. Neurons act like messengers sending and receiving impulse. However, each neuron can have multiple inputs, it will generate only one output then pass it to the neurons in the next layer which results as an intelligent artificial brain capable of predicting, learning, and recognizing patterns (Figure 14). Artificial neurons can also be referred to as processing elements (PEs), single units and/or simply neurons. An ANN is usually created by from hundreds of PEs which are entirely connected with weights (coefficients). PEs construct the structure of ANN as they are marshaled in the input layer, the hidden layer(s) and the output layer (Figure 14). The power of neural computations comes from connecting neurons in a network. Each PE has weighted input, activation function, and one output. The combination of the weighted inputs controls the activation of the neuron. Each layer has a bias which is the value that combination of the weighted inputs must exceed to activate the neurons and pass the signal to next layer. If the signal is activated, it passes through the transfer function to produce a single output of the neuron that proceeds to neurons in the next layer. The performance and the behavior of ANN is based on the network’s architecture, number of PEs, activation functions of its PEs, and learning rule [100,102].

Indeed, the problems of predicting, classifying, and controlling neural networks are being faced. This sweeping success can be attributed to a few key factors. Most conventional modeling techniques seek a presumed mathematical formula for the modeling to be efficient. However, on the other hand, ANN models are considered soft models as they don’t demand an exciting mathematical function beforehand and suitable of multivariant calibration modelling [103]. Usually, the presence of clear and unnoisy data sets is very challenging. ANN has the capability and flexibility to safeguard its performance even in the presence of considerable amount of noise in the input data.

Figure 14 ANN general architecture. ANN consists of 3 or more layers; an input layer, an output layer, and one or more hidden layer(s). Each layer consists of number of neurons and are fully connected with weights [101].

ML is a subset of AI around the idea that we should feed the machines with data and let them learn for themselves. If programming is automated, then ML automates the process of automation. In traditional programming, data and program are both run on the computing machine to compute the output but in ML; both data and output are run on the computer together to develop a program. This program can be used in traditional programming [104]. This concept is visualized in Figure 15.

Figure 15 Traditional programming versus machine learning [104].

Every ML algorithm has 3 stages during the process of building the automated model; Representation: The algorithm used to represent the data pattern knowledge. Examples include regressors, classifiers, support vector machines (SVM), model ensembles and others. Evaluation: The way to evaluate the chosen algorithms’ performance. Examples include accuracy, precision, recall, mean squared error, cost function, etc. Optimization: The process of adjusting the model hyper-parameters to improve performance [105].

There are different styles in ML problems [106]; Supervised Learning: Algorithms in which when given a sample of data and its desired outputs, the algorithm approximates a function that maps inputs to outputs. A model is developed through a training phase where prediction is made and then corrected when they proved wrong. The training phase remains until the model reaches to a desired accuracy level on the training data. Unsupervised Learning: Algorithms in which the given sample of data does not contain the desired output. The algorithm learns the inherent pattern of the data without using explicitly provided labels. A model is prepared by inferring structures hidden in the input data. Semi-Supervised Learning: The input data is a mixture of labelled and unlabeled examples, aims to label unlabeled data points using knowledge learned from the labelled data points. The model must learn the structures to organize the data as well as make predictions. Reinforcement Learning: It works the following way, there is a presence of an agent and environment. The agent would be able to take some action on the environment, based on which it would be rewarded or punished.

To build ML model, the appropriate package should be selected for scientific computing, performing different operations, data manipulation and analysis, and data visualization. In addition to having good data, you need to make sure that it is in a useful scale, format and even that meaningful features are included. Steps of building a ML model are [105]; Data Gathering: Different data sets should be collected from many wells and/or fields. Data Pre-Processing: Is a long and burdensome process to get unseen knowledge. Pre-processing of data refers to the transformations applied to the data before feeding it to the algorithm (i.e., cleaning data to have homogeneity by deal with Missing Values and Detecting Outliers). Feature Engineering: Is the process of incorporating domain knowledge to identify attributes from raw data. Relevancy of features to the output varies from one feature to another, so to make the proposed model more accurate, it is mandatory to investigate all the dataset features and assess their importance and focus on features with high relevancy to the output. Algorithm Selection and Training: The field of ML includes an enormous number of algorithms, some of which are easy to use, while some others necessitate more difficult understanding of the algorithms. Predictive modeling is the method of developing a model using historical data to make a prediction on new data where we do not have the answer. It can be described as a mathematical problem of approximating a mapping function (f) from input variables (x) to output variables (y). Table 3 shows a list of the ML algorithms that were duly applied in this research with their advantages and disadvantages [105]. Model Training and Evaluation: Typically, when dataset is separated into a training set and testing set, most of the data are used for training, and a smaller portion of the data are used for testing. Splitting data is an important stage of model evaluation and determining the performance of the model when it is used in real life. Testing model performance on held-out data is the best way to evaluate model accuracy. The most common split of data is 70 % training and 30 % testing parts [107]. This action identifies the precision in the selected algorithm depending on result. A better way to check the accuracy of the model is to see it performs well on data which was not used during training. It’s worth mentioning that diversity of data (not necessarily huge dataset) is a significant factor that enhances the model’s performance and enables model generalization (i.e., model is efficient in forecasting or classifying unseen datasets). For better generalization, cross validation is required during training phase to ensure all portions of dataset are exploited. The nature of ML algorithm and model complexity also play an obvious role in model generalization.

Table 3 The advantages and disadvantages of different ML algorithms [105].

AI and ML have been introduced and used thoroughly to generate more reliable models and correlations in different petroleum engineering aspects. AI and ML have been used for drill bit diagnosis, well-log analysis, surveillance of major drilling and completion activities, and reservoir simulation, encompassing seismic pattern identification, history matching, and reservoir characterization, prediction of permeability and porosity, pressure-volume-temperature (PVT) analysis, production optimization, and well performance evaluation [105,108-125]. Figure 16 shows better summarization of ML applications in the oil and gas industry [105]. In the following lines, we briefly present some of those AI and ML journeys in the field of drilling fluid property prediction.

Figure 16 Applications of AI and ML in oil and gas industry [105].

In 2016, almost 9,000 data points of invert emulsion mud were used as the modeling and testing layer to convert ANN black box to a white box to obtain visible mathematical equation of its rheological properties [126]. The developed ANN can be used to easily predict the dial readings at 600 and 300 rpm, which can then be used to obtain the values of AV, PV, YP as well as the consistency index (k) and the flow behavior index (n) as shown in Table 3. In those equations, x represents the input parameter, j is the number of input variables, N is the number of neurons which was optimized to be 12 for one hidden layer, b₁ is bias of the hidden layer, and b₂ is bias of the output layer, w₁ is weight of hidden layer, w₂ is weight of the output layer. About 70 % of the data were used to train and obtain the mathematical equation [126].

After modeling, 30 % of the data was used to test the developed equations, which showed good values of the average absolute percentage error (AAPE) and the coefficient of correlation (R). The models constructed for the dial readings at 300 and 600 rpm, AV, PV, YP, k, and n gave AAPE of 3.48, 3.7, 3.7, 5, 3, 4.2, and 1.2 %, respectively. In addition, they gave correlation coefficients (R) of 0.898, 0.92, 0.91, 0.91, 0.90, 0.92, and 0.954 for models constructed for the same parameters, respectively. The developed ANN models can save huge times if one knows that AV, PV, YP of the drilling fluids are measured twice a day on the rig in the petroleum fields, while Marsh funnel viscosity, solid content, and density are measured every 10 - 20 min [126,127]. Correlations to predict fluid rheological properties using ANN visible mathematical model are shown in Table 4.

Table 4 Correlations to predict drilling fluid rheological properties using ANN visible mathematical model [126].