Elsevier

Powder Technology

Volume 339, November 2018, Pages 728-746
Powder Technology

Review
Settling velocity of drill cuttings in drilling fluids: A review of experimental, numerical simulations and artificial intelligence studies

https://doi.org/10.1016/j.powtec.2018.08.064Get rights and content

Abstract

In this paper, a comprehensive review of experimental, numerical and artificial intelligence studies on the subject of cuttings settling velocity in drilling muds made by researchers over the last seven decades is brought to the fore. In this respect, 91 experimental, 13 numerical simulations and 7 artificial intelligence researches were isolated, reviewed, tabulated and discussed. A comparison of the three methods and the challenges facing each of these methods were also reviewed. The major outcomes of this review include: (1) the unanimity among experimental researchers that mud rheology, particle size and shape and wall effect are major parameters affecting the settling velocity of cuttings in wellbores; (2) the prevalence of cuttings settling velocity experiments done with the mud in static conditions and the wellbore in the vertical configuration; (3) the extensive use of rigid particles of spherical shape to represent drill cuttings due to their usefulness in experimental visualization, particle tracking, and numerical implementation; (4) the existence of an artificial intelligence technique - multi-gene genetic programming (MGGP) which can provide an explicit equation that can help in predicting settling velocity; (5) the limited number of experimental studies factoring in the effect of pipe rotation and well inclination effects on the settling velocity of cuttings and (6) the most applied numerical method for determining settling velocity is the finite element method. Despite these facts, there is need to perform more experiments with real drill cuttings and factor in the effects of conditions such as drillstring rotation and well inclination and use data emanating therefrom to develop explicit models that would include the effects of these. It should be noted however, that the aim of this paper is not to create an encyclopaedia of particle settling velocity research, but to provide to the researcher with a basic, theoretical, experimental and numerical overview of what has so far been achieved in the area of cuttings settling velocity in drilling muds.

Introduction

Apart from changing a dull bit or making a connection, drilling operations may be suspended temporarily for a variety of other reasons. Whatever the reason for suspending the drilling activity, the circulation of drilling mud also ceases. This termination of the flow of the drilling fluid causes the cuttings that were moving up to the surface to begin settling out of the mud and settling in the wellbore [130]. As the cuttings settle in large quantities, several wellbore problems such as stuck pipe, high torque and drag, decreased bit penetration into the formation, troubles in running casing pipes downholeetc would be encountered [5,32,58,128,150]. Over time, researchers have found that calculating the velocity at which cuttings settle out of the mud and accumulate at the bottom of the wellbore serves as a means of assessing the efficiency of cuttings transport out of the well [4,58,204]. Additionally, the knowledge of the settling velocity when determined, serves vital purposes during drilling. Baldino et al. [18] lists two of these purposes to include: (1) aids in understanding the profile of the cuttings concentration which in turn improves control on the wellbore pressure leading to better wellbore stability and (2) enables an estimate of the depth from which the cuttings are generated to be done. On the reverse side, erroneous calculation of cuttings settling velocities leads to imprecise determination of cuttings concentration and, hence, incorrect wellbore pressure estimates, as well as inaccurate lag times [10].Due to the practical significance of the settling velocity phenomenon; within the oil well drilling community, cuttings settling in drilling muds has continued to be an area of active research leading to an avalanche of studies accruing to its database. Consequently, studies ranging from experimental, mathematical modelling, numerical, simulation and the use of artificial intelligence abound in literature. Firstly, the use of experiments to study cuttings settling in drilling muds can be a practical way of determining the settling velocity of particles in fluids. As a result, there are numerous experiments about spherical or non-spherical particles settling in Newtonian or non-Newtonian fluids for decades [201]. Secondly, according to Rao [149], numerical techniques make the solutions of engineering challenges economical due to its high but inexpensive computational power. In comparison with experiments, numerical simulations give satisfactory checks over setting up the problem without having need for closure relations [202]. Thirdly, artificial intelligence techniques such as artificial neural network, support vector machines, genetic programming etc. can predict to a reasonable degree of accuracy complex phenomena such as settling velocity of cuttings whose factors or parameters have a non-linear relationship. This area has also received its fair share of research outputs with various artificial intelligence based predictive models dotting the landscape. The use of artificial intelligence became imperative because despite the existence of numerous mathematical models for predicting settling velocity of particles in non- Newtonian fluids, there exists a huge lacuna because existing mathematical models fail to predict field data effectively [141]. However, the area of mathematical modelling has been deliberately left out in this review and would be the subject of another paper. The purpose of this review therefore is to prepare summaries of experimental, numerical simulations and artificial intelligence techniques that have been applied to the study of the settling velocity phenomenon that would strengthen the connections between new research and the accumulated body of knowledge in the literature. In order to achieve this purpose, this study first reviews the historical studies into the settling velocity phenomenon. Next, a definition of settling velocity and the factors affecting it are showcased. Then, a summary of the settling velocity experimental details and major findings from the experiments as found in the literature are reviewed, tabulated and discussed. Afterwards, the applications of artificial intelligence techniques in estimating settling velocity are discussed. Next, numerical simulations and modelling applied to the settling velocity phenomenon are presented. Then the challenges facing the use of the settling velocity study methods discussed in this work follows while a comparison of the three methods follows thereafter. The learnings from the study, the proposed future research directions and the conclusions make up the last three sections of the study.

This section traces the historical development of studies on cuttings settling velocity in drilling muds. The concept of settling velocity dates back to the pioneering work presented by [176]and is known as the Stokes equation [10]. The other researchers who followed include: Oseen [139], Rubey [156], Rouse [155], Pigott [142]; Williams and Bruce [199]. It must however be noted that the works of these early men are no doubt pre-cursors for the development of modern studies on settling velocity. However, presenting a detailed history of studies on settling velocity would be a herculean task due to the vast number of publications dating back to the 17th century. To put the original research problem into the proper historical perspective of the engineering application, we first mention that extensive historical accounts are provided in earlier review papers. Hence, rather than present individual studies from the onset from 1845 up until now, it is pertinent to situate the historical development in the light of previous reviews by other researchers. The reviews done by Walters and Tanner [192]; Chhabra et al. [42]; Brown and Lawler [31]; Le Roux [110] and Sadat-Helbar et al. [158] are good reads in this regard.

This section highlights previous review studies on the phenomenon of settling velocity. Five major reviews are available in literature. The focus of each review and the major findings of each review work are presented below:

  • (a)

    Walters and Tanner (1992): Shah et al. [164] reports that there exists critical reviews of particle settling velocity phenomenon by Chhabra [36,37], however, the review by Walters and Tanner [192] likely falls among one of the earliest review papers on settling velocity during this period.

  • (b)

    Chhabra et al. (1999): This review covered experimental results from 19 independent studies covering the periods from 1937 to 1996. From the review, researchers experimented on various non-spherical particles with shapes ranging from cylinders, needles, cones, prisms, discs, rectangular, parallel piped and cubes. From the review, about 1900 data points were collated while 5 correlations were tested for their predictive capacity. The major findings from this review is that the best method of estimating drag is that of Ganser [63] which uses the equal volume sphere diameter and sphericity of particle.

  • (c)

    Brown and Lawler (2003): This review covered researches throughout the 20th century. The main focus was on drag on spheres and settling velocity. <16 papers were reviewed with 480 data points collated. From the data collated, the authors developed two new correlations applicable for Reynolds numbers <2 × 105 and settling velocity prediction for Reynolds number <4000. They suggested that the Fair and Geyer [208] equation for drag that involves trial and error should be discarded. They added that the correlation of Clift et al. [209] appears to model sphere drag best though with a few deficiencies.

  • (d)

    Le Roux (2005): This review was tilted towards the settling velocity of natural sediment grains in air and water. Though thorough and wide in its coverage, the review does little to address works involving non-Newtonian fluids.

  • (e)

    Sadat-Helbar et al. (2009): The review presented by these authors spanned from works done between 1933 and 2007. The review essentially studied the works of 17 researchers from which they isolated 22 correlations. They modified some of these correlations to obtain newer ones.

Other review works relating to the cuttings settling velocity phenomenon are highlighted below. These reviews are related to development of predictive models either by modification of existing ones or by the outright development of new ones.

  • (f)

    Shah et al. (2007): These authors collated the settling velocity data from five previous authors' work and re-analyzed them using the approach proposed by Shah. The data of each author were analyzed separately and correlations were developed for each case. They also combined all the data sets and developed a new model from the combined data set. The new model was found to be an improvement to the existing models in the literature to predict the spherical particle settling velocity in power law liquids.

  • (g)

    Barati et al. (2014): These authors collated and reviewed sixteen settling velocity correlations with a bid to improving the range of applicability and accuracy of the models. They did this using the shuffled complex evolution algorithm. The outcome of using this algorithm was that the range and accuracy of ten new correlations were improved. In comparison with other existing models, they reported that the new correlations on the basis of the sum of squared of logarithmic deviations fitted the experimental data up to 96%.

  • (h)

    Ramírez (2017): This work presented an evolutionary trend of developed sphere drag correlations required to deal with the settling of spherical particles in fluids. The work chronologically arranged the models historically starting from the work by [176] and terminated in 2013. A total of 13 relationships were isolated with their range of applicability. However, commenting on this work, Barati and Neyshabouri [19] highlighted three areas which are worth noting namely: 1. That there exists newer approaches one of which is the high-resolution numerical simulation beyond the two categories of relationships between drag coefficient of a sphere and the Reynolds number of the particle put forward by Ramírez [148]. 2. The existence of a new concept termed appropriate drag introduced by [55]as opposed to the customary drag. 3. The existence of new empirical models with high accuracy developed using multi-gene genetic programming.

The concept of settling velocity is a widely known concept due to the fact that settling occurs in a number of operations in industries such as the oil and gas industry, mining industry, chemical industries such as waste water treatment, pharmaceutical industries, food and process engineering operations [43,58]. Despite its widespread application, the definition of settling velocity remains practically the same. The settling velocity of a solid particle is defined as the rate at which the solid particle settles in a still or quiescent fluid [16]. According to Shahi and Kuru [165], the settling velocity of a particle in a fluid is defined as the constant velocity reached by a particle when all the forces acting upon it are balanced. It is sometimes referred to as terminal velocity or fall velocity [198]. In cuttings transport during drilling, settling velocity is also referred to as cuttings slip velocity [15,87,162,204].However, in vertical and near vertical well drilling, the slip velocity concept is used to represent minimum transport velocity. Particle slip velocity is fluid velocity minus particle velocity [5,11,79]. At this juncture therefore, it would not be out of place to define settling velocity in the context of cuttings transport in wellbores as follows: The settling velocity of cuttings essentially stipulates whether cuttings of any size will separate against the upward moving mud in the annulus or whether the mud system would have enough residence time for cutting particles before they settle at the bottom of the wellbore especially when mud circulation is stopped. Following this definition stated for cuttings settling velocity, it is observed that the definition tilts towards hinging the rate of settling on the size of drill cuttings. It must however be stressed here that when a well is drilled, cuttings comprising large, medium, small and fine sized particles are generated. As a result, the distance between the cuttings become so small that they collide with one another, hence their rates of settling is no longer dependent on cuttings size, rather on cuttings concentration. This type of settling is called hindered settling [157].

This section focuses on highlighting the factors on which the settling velocity of cuttings in drilling muds is dependent. In order to make this section unambiguous, these factors would be categorized into three namely: (a) Factors relating to the cuttings (b) Factors relating to the mud and (c) Factors relating to the wellbore.

  • (a)

    Factors relating to the drill cuttings

The following are the parameters relating to the drill cuttings that affect the settling velocity of cuttings:

  • (1)

    Cuttings size and diameter

During wellbore drilling, cuttings are churned out in multitudes of sizes [181]. The multiple sizes in which they come make their settling velocity in the mud behave differently. Results from experimental works from researchers such as Chien [43] indicate that, the velocity of particle settling in a mud increases with increasing particle diameter; however, the rate of increase differs from one another depending on the differences in the range of the particle-size.

  • (2)

    Cuttings shape

Cuttings come in various shapes as the well is being drilled. More often than not, their shapes are irregular and cannot be fitted to any known shape. This does not exclude the fact that some may be near spherical, conical, triangular etc. In drilling, the shapes of drill cuttings are defined in relation to how it approximates to the shape of a sphere. This is termed sphericity. The sphericity of a solid particle by definition is the degree to which the shape of a solid particle approaches that of a sphere [16].According to Kamyab et al. [99], sphericity in quantitative terms varies from 0 to 1 with 1 representing a perfect sphere. In comparison, the characteristics of cuttings with irregular shape are markedly different from cuttings having a spherical outlook during the process of settling. According to Baldino et al. [18], irregularly shaped cuttings usually exhibit trajectories somewhat spiral in outlook and they vibrate and rotate while they fall. However, the works of Luo [114] and Reynolds and Jones [151] indicate that in a power law fluid, an irregularly shaped particle has a lower settling velocity compared to its spherically shaped counterpart having the same density. Therefore, as the particle shape deviates from a spherical surface, a higher drag force is obtained, thus decreasing the particle terminal velocity [50,53,183].

  • (3)

    Cuttings density

The main factor that propels cuttings to settle out of a mud system and into a wellbore is the gravity factor. The cuttings generated have a measurable density and varies between a specific gravity range of 2.4 to 2.8 while the mud specific gravity varies between 0.9 and 1.8 [204]. Thus cuttings would naturally settle easily if the mud is at rest in the wellbore.

  • (b)

    Factors relating to the drilling fluid

Listed below are drilling fluid parameters that have notable effects on the settling velocity of cuttings:

  • (1)

    Drilling fluid density

The density of a drilling mud is the ratio of the sum of the masses of the various mud components to the sum of their volumes. It is an important property necessary for limiting the effects of formation pressures. In relation to settling velocity, high mud density reduces the cuttings settling rate [87].

  • (2)

    Drilling fluid viscosity

Fluid viscosity is one of the main properties of a drilling mud that enables it to transport drill cuttings out of a wellbore. Experimental findings indicate that as fluids become more viscous, the rate of settling of a particle in it decreases [43]. However, from the experimental work of Hopkin [87], the yield value of mud is the most important component of viscosity affecting cuttings settling velocity. Simply put, the thicker (more viscous) the fluid, the longer the settling time, the thinner (less viscous) the fluid, the faster the settling time.

  • (3)

    Drilling fluid velocity

During mud circulation, the flow is more often than not turbulent in nature. It is always challenging to calculate the frictional drag on cuttings, since the coefficient of drag coefficient is dependent on the Reynolds number of the particle [181].Four theories are available which provide explanatory insight as to how turbulence affects the velocity of settling particles. Of these four theories, three of them suggest that the mechanisms of non-linear drag, loitering and vortex trapping decrease the velocity of settling particles [135].

  • (c)

    Factors relating to the wellbore

The wellbore parameters that have a strong influence on the settling velocity of cuttings are highlighted below:

  • (1)

    Wellbore configuration

The configuration of a wellbore may largely be divided into vertical and deviated. The way cuttings settle in either of these well configurations differ. It must be stated however, that due to their cost effectiveness, there are more vertical wells drilled than deviated wells [128].However, cuttings settle easily in deviated wells than in vertical wells [5].

  • (2)

    Confining walls

If a wall or some sort of a boundary exists or is adjacent to the settling particle then wall effect takes place [60].Confining walls decrease the settling velocities by imposing a retardation effect or friction force on the settling particles near them (Clift et al. [209] [48,119,152]). Wall factor, (Fw), is defined as the ratio of the velocity of settling of a particle in presence of confining walls to the velocity of settling of the particle in the absence of confining walls [119]. Many theoretical and experimental studies to determine wall factors for spherical particles settling in Newtonian fluids in tubes of varying cross sectional area and over a wide range of Reynolds numbers abound in the literature. Examples are found in the works of Bohlin [26]; Miyamura et al. [127]; Tullock et al. [186]; Chhabra [38];Chhabra [39] and Chhabra [40]. However Richardson et al. [152] reports that when the diameter of the tube or vessel is about 100 times greater than that of the settling particles the walls effect on settling velocity diminishes.

  • (3)

    Pipe rotation

The rotation of the drillpipe during drilling affects the settling velocities of cuttings in a mud [181].According to Hopkin [87], experimental investigations indicate that particles that are thin and flat turn on their edges and leads to a huge variation in their measured settling velocities. This was the same findings made by Williams and Bruce [199] as they report that when mud flow is laminar, the drill cuttings turn over due to a torque effect exerted on them. This shows that rotation of the drill pipe re-orientates the particles causing them to settle slowly.

Table 2.1 summarizes the published information related to particle settling velocity experiments in drilling muds. The available information about the wellbore type, particle type, the particle diameter and density, mud type and the properties of the mud used are the main parts of the table. A brief and general overview of the table is presented here.

  • (a)

    An oil and gas wellbore may typically not be drilled vertically all the way through to its total depth [115]. Thus, a vertical well may contain one or more bend sections. The effect of the configuration of the well trajectory in this case is important when modelling settling velocity of cuttings. It is observed that 98% of the studies in this regard have focused only on a vertical well configuration except for the work done by Baldino et al. [18].

  • (b)

    The particle shape that was commonly used was mainly spherical with >50% of the experimental studies carried out with spherical glass particles rather than real drill cuttings. A plausible explanation for this is that particles of a known shape such as spheres offer a huge reduction in the complexity of numerical simulations and models. However, attempts have been made by some researchers to replicate what happens in the field where real drill cuttings of various shapes, sizes and orientations were used. The works of Aswad and Rashid [16] and Baldino et al. [18] are very good reads in this regard.

  • (c)

    The particle diameters range from micrometres to centimetres. Comparatively, many used millimetre sized particles; however, the maximum size was approximately 100 mm.

  • (d)

    Very light particles with density of approximately 1.2 g/cm3(e.g. plastic particles) to very heavy particles that have density of approximately 8000–15,000 kg/m3 (e.g. steel, tungsten carbide) have been used to represent drill cuttings.

  • (e)

    In most of the experiments, the settling velocity is determined for just a particle at a time in a fluid. However, only a few researchers looked at the settling velocities of two or more particles at a time.

  • (f)

    More Newtonian fluids were used as the test fluid compared to the non - Newtonian fluids with about 67% of the Newtonian fluid used being water and 40% of the non – Newtonian fluid used was carboxymethyl cellulose.

  • (g)

    Most of the test fluids used by the researchers were transparent to enhance settling visualization. Such fluids include water, glycerine, polyacrylamide, carbopol solution, carboxymethyl cellulose, laponite solution and hydroxyethyl cellulose except for the works of Briscoe et al. [30] and Du Plessis and Ansley [54] wherein they used water based bentonite solution.

  • (h)

    Only one researcher –Walsh and Rao [191] considered the effect of fluid temperature on settling velocity.

  • (i)

    Though most of the researchers carried out their experiments with fluids in static mode, the works of Brucato et al. [210] Jacobs et al. [92] and Jacobs et al. [93] are some exceptions to this. These researchers conducted their experiments with the fluid subjected to various degrees of turbulence.

This section highlights the major findings from the experimental researches on particle settling velocity. In order to situate the experimental research findings in a context that makes understanding easy, the factors each researcher considered during the course of their research are highlighted and are summarized in Table 2.2. The available information about the factors considered for each experiment and the major finding of each experiment are the main parts of the table. A brief and general overview of the table is presented here.

  • (a)

    From the table, it is noticed that various factors ranging from particle shape size and diameter, fluid rheological properties and wall effect were the most studied factors affecting particle settling velocity in drilling muds.

  • (b)

    From the table, mud viscosity is agreed by most of the researchers as the most influential rheological property that affects the settling velocity of cuttings. This implies that as the fluid become more non-Newtonian, the settling velocity will be decreased.

  • (c)

    On the effect of particle shape, the authors were in unison in their submission that spherical particles follow the vertical path during settling, while the irregular shaped particles follow different and unstable paths and orientations such as springing, circular, oscillating etc. Additionally, most of the researchers are in agreement with the idea that the orientation of particles will decrease the settling velocity of irregularly shaped particles. As the particle diameter or volume increased, the settling velocity will increase.

  • (d)

    All the researchers who worked on evaluating the effects of particle size on cuttings settling velocity were unanimous in their submissions that small particle sizes exhibit less velocity of settling; while settling velocity of cuttings increased with the shape factor and mud rheology increase reduces particle settling velocity.

  • (e)

    The surface roughness has little or no effect on the settling velocity of cuttings in drilling muds.

The search for an all-encompassing model for the prediction of the settling velocity phenomenon has led researchers to try virtually all possible techniques. So it's no surprise that the field of artificial intelligence (AI) has been popping up in academic journals in recent years as a potential solution. Table 2.3 shows the research efforts towards using artificial intelligence techniques in predicting settling velocity. Seven papers were found in the literature relating to this. From the review, the artificial neural network technique is the most widely used. In Zhang et al. [205], comment on the works of Li et al. [111] and Rooki et al. [153] on using artificial intelligence namely artificial neural network (ANN) to predict the wall factor effect and settling velocity of particles in non-Newtonian fluids respectively, they submitted that the method of using ANN in predicting the settling velocity phenomenon provides wider adaptability in that it eliminates the restriction of fluid types and flow regimes on predictions of particles settling in various fluids at different flow regimes. Other artificial intelligence techniques such as support vector machine and multi gene genetic programming-a variant form of genetic programming were also applied. However, artificial neural networks (ANNs) and support vector machines (SVM) when used in prediction of settling velocity were not capable of providing a practical prediction equation which makes their usage disadvantageous. Multi gene genetic programming as used by Barati et al. [20,21] was capable of providing a practical prediction equation for drag coefficient determination, thereby giving the technique an edge over the other AI techniques. In addition to being able to evolve a mathematical expression for predicting any phenomena, Pandey et al. [140] adds the following as other unique characteristics of multi-gene genetic programming: (a)The mathematical expression evolved by multi-gene genetic programming can be analyzed further to find which variables impact the final prediction and in what specific manner (b) The multi-gene genetic programming method eliminates errors due to various assumptions since it is a data-driven methodology which relies on experimental data to build models.

Numerical simulations aid the proper understanding of the characteristics of solid–liquid suspensions irrespective of the fluid type (Newtonian or non-Newtonian). While numerical simulations come in various forms, the line of distinction among them can be drawn based on their level of detail on the one hand, and the size of the systems they are capable of handling on the other hand [70]. Without claiming to be exhaustive, a brief review is provided of some of the available applications of numerical simulation and modelling to the settling velocity phenomenon (Table 2.4). The focus of the researchers, the algorithm they used, the method of discretization and grid type as well as the findings they made is presented in the table. The following are the observations from the works presented in the table.

  • (a)

    The following are the numerical techniques used by researchers for simulating particle settling: Lattice-Boltzmann technique, arbitrary Lagrangian –Eulerian technique, discrete element method, immersed boundary method and distributed Lagrangian multiplier method.

  • (b)

    The common denominator these numerical techniques have is that fluid flow is governed by the Navier-Stokes equations while the motions of the particles are governed by Newton's equations of motion.

  • (c)

    The numerical techniques seem to be computationally unit intensive for 3-D flows.

  • (d)

    Numerical examples show that finite element method can be used as efficient tools for simulating the settling velocity phenomenon as shown in Table 2.4 where it is the most widely used.

Even though there exist so much literature on the concept of settling velocity ranging from experimental researches, development of model equations, prediction using artificial intelligence, numerical modelling and simulations and so on, researches on the settling velocity phenomenon continues to face perplexing challenges. This section reviews existing drill cuttings settling velocity methods and their shortcomings. Table 2.5 are examples of the areas that pose new challenges to our understanding of the settling velocity phenomenon.

From Table 2.5, it is evident that no one method of estimating cuttings settling velocity is completely foolproof. Despite this, the consolation is that the existing methods provide valuable insight into the settling velocity phenomenon while the various challenges throws up new study areas for interested researchers.

The three methods for estimating cuttings settling velocity are compared in this section. The comparison is made using four criteria namely: The basic features of each method, their applications, their advantages and their disadvantages. From Table 2.6, it is seen that all three of these seemingly diverse methods used for estimating cuttings settling velocity are inextricably interwoven that no one method seems independent of the other. Take the following instances. First, the interdependence between numerical simulation and laboratory experimentation of cuttings settling velocity is evident in that numerical simulation offers the opportunity to carry out experimental studies of phenomena which are not possible in the laboratory while the results of most numerical simulations are more often than not validated using experimental results [171]. Second, since artificial intelligence (AI) is largely data driven, data generated from laboratory experiments on cuttings settling velocity (whether small or large scale) is seen as a way of improving the capabilities of AI [45].

In conclusion, it is seen that the interaction among experiments, numerical simulations and artificial intelligence is a three way street where each side benefit from each other. Continued interaction and improvements in each of these methods as highlighted in the future research directions section of this work can only add to its progress.

Section snippets

Derivatives from the review

This study made an examination on the settling velocity phenomenon with special interest in settling behaviour of cuttings in drilling muds. There was a wide literature spectrum to choose from– from the experimental to numerical simulation and the use of artificial intelligence. Based on this review, the following are noted:

  • 1.

    Well thought out theoretical, experimental, numerical and artificial intelligence studies of particle settling have been done and have resulted in a better understanding of

Future research directions

This review of existing literature on the cuttings settling velocity in muds has not just generated novel insights into the phenomenon of cuttings settling during wellbore drilling but also throws up areas that require further research. These areas include the following:

For the use of experiments:

  • 1.

    It is worth noting that enormous work from inception to date (year on year basis) has focused on varying the size and/or the density of cuttings and fluid properties and measuring the subsequent

Conclusions

This paper reviewed the works of previous researchers on the experimental, numerical and artificial intelligence applications to the cuttings settling velocity in drilling fluids with the outputs of those researches presented. It started with the definition of particle settling velocity, highlighted the factors affecting particle settling velocity before delving into the many experimental and modelling parts of the study. On the basis of the outcomes of the above review, the following

Funding

No funding was provided for this research by any individual or corporate organisation.

Conflicts of interest

No conflicts of interest exist.

Acknowledgement

The authors would like to appreciate the management of the University of Uyo for providing an enabling environment to carry out this research.

References (171)

  • R.P. Chhabra

    Motion of spheres in power law (viscoinelastic) fluids at intermediate Reynolds numbers, a unified approach

    Chem.Eng. Process

    (1990)
  • R.P. Chhabra

    Wall effects on terminal velocity of non-spherical particles in non-Newtonian polymer solutions

    Powder Technol.

    (1996)
  • R.P. Chhabra et al.

    Drag on discs and square plates in pseudoplastic polymer solutions

    Chem. Eng. Sci.

    (1996)
  • R.P. Chhabra et al.

    Drag on non-spherical particles: An evaluation of available methods

    Powder Technol.

    (1999)
  • N.N. Clark et al.

    Drag coefficient of irregular particles in Newton's settling regime

    Powder Technol.

    (1989)
  • G. Dazhi et al.

    The drag on a sphere in a power-law fluid

    J. Non -Newtonian Fluid Mech.

    (1985)
  • R. Di Felice et al.

    The settling velocity of a single sphere in viscous fluid: the effect of neighbouring larger spheres

    J. Powder Technol.

    (2012)
  • F. Dioguardi et al.

    A new shape dependent drag correlation formula for non-spherical rough particles: Experiments and results

    Powder Technol.

    (2015)
  • R. Elgaddafi et al.

    Settling behaviour of spherical particles in fibre-containing drilling fluids

    J. Pet. Sci. Eng.

    (2012)
  • R. Elgaddafi et al.

    Settling behaviour of particles in fiber-containing Herschel Bulkley fluid

    J. Powder Technol.

    (2016)
  • J. Faitli

    Continuity theory and settling model for spheres falling in non-Newtonian one- and two-phase media

    Int. J. Miner. Process.

    (2017)
  • G.H. Ganser

    A rational approach to drag prediction of spherical and non-spherical particles

    Powder Technol.

    (1993)
  • G. Gheissary et al.

    Unexpected phenomena observed in particle settling in non-Newtonian media

    J. Non-Newtonian Fluid Mech.

    (1996)
  • N. Goyal et al.

    Direct simulations of spherical particles sedimenting in viscoelastic fluids

    J. Non-Newtonian Fluid Mech.

    (2012)
  • M.M. Gumulya et al.

    A new fluid model for particles settling in a viscoplastic fluid

    J. Chem. Eng. Sci.

    (2011)
  • M.M. Gumulya et al.

    The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres

    J. Chem. Eng. Sci.

    (2011)
  • M. Hartman et al.

    Predicting the free fall velocities of spheres

    Chem. Eng. Sci.

    (1989)
  • A. Hazzab et al.

    Measurement and modelling of the settling velocity of isometric particles

    Powder Technol.

    (2008)
  • M.R. Horsley et al.

    Non-Newtonian effects on fall velocities of pairs of vertically aligned spheres

    J. Non-Newtonian Fluid Mech.

    (2004)
  • V. Ilic et al.

    Translation and rotation of spheres settling in square and circular conduits: experiments and numerical predictions

    Int. J. Multiphase Flow

    (1992)
  • W.M. Jones et al.

    The motion of a sphere falling under gravity in a constant viscosity elastic liquid

    J. Non-Newtonian Fluid Mech.

    (1994)
  • L. Khatmullina et al.

    Settling velocity of microplastic particles of regular shapes

    Mar. Pollut. Bull.

    (2017)
  • K. Koziol et al.

    Determination of the free settling parameters of spherical particles in power law fluids

    Chem Eng. Process

    (1988)
  • A.M. Lali et al.

    Behaviour of solid particles in viscous non-Newtonian solutions: settling velocity, wall effects and bed expansion in solid-liquid fluidized beds

    J. Powder Technol.

    (1989)
  • J.P. Le Roux

    Grains in motion: a review

    Sediment. Geol.

    (2005)
  • Y. Lin et al.

    Towards a novel interface design framework: function–behaviour–state paradigm

    Int. J. Hum. Comput. Stud.

    (2004)
  • I. Machac et al.

    Fall of spherical particles through non – Newtonian suspensions

    Chem. Eng. Sci.

    (1995)
  • G.V. Madhav et al.

    Settling velocities of non – spherical particles in non – Newtonian polymer solutions

    J. Powder Technol.

    (1994)
  • G.V. Madhav et al.

    Drag on non-spherical particles in viscous fluids

    Int. J. Miner. Process.

    (1995)
  • A. Mellit et al.

    Artificial intelligence techniques for sizing photovoltaic systems: a review

    Renew. Sust. Energ. Rev.

    (2009)
  • A.D. Ahchin et al.

    A shape-modified size correction for terminal settling velocity in the intermediate region

    J. Powder Technol.

    (1986)
  • R.M. Ahmed

    Fibre containing sweep fluids for ultra deepwater drilling applications

  • R.M. Ahmed et al.

    Fibre sweeps for hole cleaning

  • J.C. Alcerreca et al.

    Simple settling velocity formula for calcareous sand

    J. Hydraul. Res.

    (2013)
  • M.C. Altindal et al.

    Impact of viscoelastic characteristics of oil based muds/synthetic based muds on cuttings settling velocities

  • American Petroleum Institute

    Rheology and hydraulics of oil well drilling fluids

  • A.S. Arabi et al.

    Particle terminal settling velocities in non-Newtonian viscoplastic fluids

    Can. J. Chem. Eng.

    (2016)
  • S.K. Arnipally et al.

    Settling velocity of particles in viscoelastic fluids: a comparison of the shear viscosity vs elasticity effect

  • Z.A.R. Aswad et al.

    New drag coefficient charts for settling spherical and disk particles in shear thinning fluids

  • Z.A.R. Aswad et al.

    The combined effect of irregular shape particles and fluid rheology on settling velocity measurement

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