Eccentric Annulus Research Articles

Performance of turbulence models for single phase and liquid-solid slurry flows in pressurized pipe systems

In hydraulic engineering, turbulent flow is the most encountered flow regime in closed conduits. Because of the difficulty and complexity of the turbulence mechanism dominated by fluctuations, it is very important to model the turbulence mechanism correctly. Numerous models are developed by researchers in order to characterize turbulence. However, it is crucial to choose the model that gives the correct results. In this study, the performance of some well-known turbulence models is comparatively investigated. Extensive computational fluid dynamics (CFD) simulations and experimental analysis of water flow in the rough pipe, eccentric and concentric annulus, and liquid-solid slurry flow in the eccentric annulus are presented. The accuracy of turbulence models is verified with the experiments that have been conducted and presented data by Sorgun, 2010). Reasonable agreements are obtained between CFD simulations and experiments. Results show that the RNG κ-ϵ gives better results than the other turbulence models for the water flow through the rough pipe and eccentric annulus. For the water flow through the concentric annulus, the EARSM model outperforms the other turbulence models. All models except SSG showed similar performances in the estimation of the pressure difference for slurry flow.

Spiral laminar flow of yield-power-law fluids in partially blocked annulus

During drilling of directional and horizontal wells, cutting beds inevitably form in highly deviated and horizontal sections. Because of the centralizer, both concentric and eccentric annuli can exist in both highly deviated and horizontal sections. Existing studies on the helical laminar flow of a non-Newtonian fluid in partially blocked concentric and eccentric annuli are mainly based on numerical models, laboratory experiments, and computational fluid dynamic (CFD) simulations. Directly applying the research results to drilling engineering is difficult. To accurately and conveniently predict the pressure gradient of helical laminar flow with a fixed horizontal cutting bed, this work first presents a new model based on fluid mechanics to compute the pressure loss of a yield-power-law (YPL) flow in partially blocked concentric and eccentric annuli in a laminar helical-flow state. Second, the Fluent software is used to simulate the helical laminar flow of the YPL fluid with a fixed horizontal cutting bed. The existing experimental measurements, mathematical model calculation, and Fluent software simulation results are used to verify the proposed simplified model. The results show that the predicted results of the simplified model agree well with the existing numerical results, existing experimental data, and CFD simulation results; the error is only ±5%. The new simplified model can achieve accurate and convenient prediction of the pressure gradient of a spiral laminar flow in an annulus with a fixed horizontal cutting bed.

Using particle image velocimetry to evaluate the displacement efficiency of drilling mud in horizontal well cementing

For a horizontal well cementing, successful displacement of the drilling mud from the annulus using the cement slurry were paramount for achieving zonal isolation. This study evaluated the displacement efficiency of drilling mud from the annulus by applying particle image velocimetry incorporating the development of a large-scale displacement efficiency device. Displacement efficiency measurements revealed that increasing the injection displacement and reducing the eccentricity cleans up residual drilling mud and significantly improves displacement efficiency. Slurry density significantly affected displacement efficiency, because high- and light-density slurries were shown to lead to low velocities and to increase the boundary layer thickness of the drilling mud. High injection displacement swirling flows were found to be more effective for reducing drilling mud adhesion to the casing and wellbore walls. The eccentric annuli tended to result in a narrow channel, which results significantly reducing the displacement efficiency owed to the laminar fluid flow.

Performance of Dual Phase non-Newtonian Fluid in an Eccentric Annuli with Rotation of Inner Cylinder

The eccentric annular flow is a flow with special considerations; it forms a vital part of practical industrial flow analysis. In this work eccentric, dual phase flow through horizontal wells are simulated with the help of CFD. In horizontal annuli, flow occurs in an adverse pressure gradient condition, that makes the particle inside it susceptible to reversed flow. Thus the flow has to be analyzed in a three dimensional manner. Moreover, the non-Newtonian behavior of the fluid makes the problem really challenging in numerical and physical aspects. The results of this work clarify the relationship between different flow characteristics with the speed of inner wall rotation. The flow characteristics include swirl of flow, wall shear stress, and axial velocity.

Friction factor of shear thinning fluids in non-circular ducts—a simplified approach for rapid engineering calculation

This work reports on an investigation of the relationship between the Reynolds number and the friction factor of the fully developed laminar flow of power-law fluids through non-circular cross-sections (elliptical, concentric annuli, symmetrical L-shape, isosceles triangle, eccentric annuli, and square duct with a central cylindrical core), with the aim of providing a simple method for rapid and simplified engineering calculations. The friction factor—Reynolds number relation has been derived for non-circular ducts on the basis of the modified Reynolds number proposed by Metzner and Reed. It has been shown that the proposed correlation enables a prediction of the friction factor for the fully developed laminar flow of shear thinning fluids in non-circular cross-sections by using a calculation method similar to the method used for laminar flow of a Newtonian fluid. The correlation that is provided has been validated by analytical and numerical methods. It has been found that the proposed method can be used to determine the friction factor with high accuracy. This method yields a friction factor with a deviation of less than 5% in comparison with the conventional method.

Numerical simulation of non-Newtonian fluid flow in partially blocked eccentric annuli

A cuttings bed formed on the lower side of the wellbore is the most common drilling problem confronted when horizontal or highly deviated wells are drilled. The phenomenon is undesirable and has a detrimental effect on wellbore hydraulics and drilling performance. To achieve an efficient drilling operation, hydraulics optimization should be implemented by precisely predicting annular pressure loss and other hydraulic parameters.The accumulation of cuttings at the lower side of horizontal or highly inclined wellbores, combined with wellbore eccentricity and fluid rheological properties, create a complex behavior of pressure loss. In this study, a numerical approach is used to investigate the influence of the aforementioned factors. A numerical solution is performed for laminar flow of non-Newtonian fluids. A non-orthogonal, boundary-fitted curvilinear coordinate is developed, which is based on elliptic partial differential equations (PDE) to accommodate annular flow geometry with arbitrary cross-sections. Finite difference numerical schemes adapted to the coordinates is then used to analyze the problem. The numerical model determines the effect of hydraulic parameters of fluid flow thorough an irregularly shaped annulus and considers the following factors: flow rate, fluid rheological parameters, annular geometry and bed appearance. Numerical predictions from the model are verified against existing models and experimental data in literature; and good agreements are obtained. The developed numerical model can be combined with a 1-D solids transport model for designing oil and gas well drilling operations.

An experimental and numerical study on effect of longitudinal finned tube eccentric configuration on melting behaviour of lauric acid in a horizontal tube-in-shell storage unit

• Enhancing the melting performance of a PCM in a LHTES system through the enrichment of natural convection mode of heat transfer. • Different configurations of triple fin arrangement are simulated and compared for different angles between fins in bottom annulus. • Stephan number and different eccentric arrangement of a longitudinally finned HTF tube are studied for a concentric double pipe heat exchanger. • Temperature variation, melt fraction distribution and heat storage potentiality in PCM are studied for determining the effective heat exchanger having fastest melting rate. • Results indicate that the smaller angle between bottom fins with maximum eccentric distance of HTF tube shows the best melting performance. Melting characteristics of lauric acid in a horizontal shell and finned tube-type storage unit has been studied numerically and experimentally. The low thermal conductive nature of phase change materials (PCMs) have pre-eminently constricted the advantage of such storage systems for various applications hence an attempt has been made to provide the finned tube in the storage container to enhance the heat transfer rate between the heat transfer fluid (HTF) and PCM for three different eccentric position ( e = 12 mm, 18 mm and 24 mm) of a finned HTF tube from the centre of outer tube in concentric configuration ( e = 0 mm). The present work aims on the use of minimum fin length by covering 36% of the annular length of a concentric arrangement for enhancing the melting rate of a phase change material (PCM) particularly to increase the natural convection effects besides sustaining the conduction effects. The melting rate of PCM in an annular is analysed with different angles of 60⁰, 120⁰ and 180⁰ between fins in the bottom annulus of the storage unit at different eccentric positions of the inner tube. The results obtained through numerical calculations are found in agreement with experimental results. The enhancement in the melting rate of PCM has been examined and it has been found that the melting rate is 21% higher at the maximum eccentric annulus as compared to the concentric configuration due to enhanced domination area for natural convection effects which also increases the uniformity in temperature distribution in PCM. The eccentric behaviour for the enhancement of melting performance has been effectively achieved in the fin configuration having an angle of 60º between the fins in the bottom annulus. It has been observed that the increase in Stefan number enhances the melting rate of PCM irrespective of the eccentric position of the inner tube and the heat storage rate in an eccentric annulus is 18.7% higher in comparison to the concentric annulus.

Machine Learning Methods for Herschel–Bulkley Fluids in Annulus: Pressure Drop Predictions and Algorithm Performance Evaluation

Accurate measurement of pressure drop in energy sectors especially oil and gas exploration is a challenging and crucial parameter for optimization of the extraction process. Many empirical and analytical solutions have been developed to anticipate pressure loss for non-Newtonian fluids in concentric and eccentric pipes. Numerous attempts have been made to extend these models to forecast pressure loss in the annulus. However, there remains a void in the experimental and theoretical studies to establish a model capable of estimating it with higher accuracy and lower computation. Rheology of fluid and geometry of system cumulatively dominate the pressure gradient in an annulus. In the present research, the prediction for Herschel–Bulkley fluids is analyzed by Bayesian Neural Network (BNN), random forest (RF), artificial neural network (ANN), and support vector machines (SVM) for pressure loss in the concentric and eccentric annulus. This study emphasizes on the performance evaluation of given algorithms and their pitfalls in predicting accurate pressure drop. The predictions of BNN and RF exhibit the least mean absolute error of 3.2% and 2.57%, respectively, and both can generalize the pressure loss calculation. The impact of each input parameter affecting the pressure drop is quantified using the RF algorithm.

Turbulent displacement flow of viscoplastic fluids in eccentric annulus: Experiments

We study displacement flows in strongly eccentric annuli, where the in situ fluid is viscoplastic and the displacing fluid is Newtonian. This mimics the situation found in the cementing of horizontal oil and gas wells. In this configuration, it is common that the yield stress of the displaced fluid prevents displacement from the narrow side of the annulus, where it remains static. We address the question of whether a turbulent flow of the displacing fluid will be effective in removing the static narrow side channel and by what means. The flows proceed with rapid displacement along the wide side of the annulus, leaving behind a gelled channel of fluid on the narrow side. The narrow side is displaced either slowly or not at all. This depends on both the yield stress of the displaced fluid and the turbulence characteristics of the displacing fluid. We influence the latter through the use of drag-reducing polymers. We show that secondary flows in the turbulent displacing fluid are essential to the displacement and also the increased pressure drops in the turbulent flow. We hypothesize that the displacement is enhanced by the transmission of normal stresses into the gelled layer.

Two-phase flow simulations at [formula omitted] inclination in an eccentric annulus

Co-current two-phase simulations of gas-liquid flow with mixture velocities from 1.2 to 4.2 m/s were run in a partially eccentric annulus and compared with entirely eccentric and concentric experimental data collected at the Institute for Energy Technology in Norway. The gas-phase was sulphur hexafluoride (SF6) for all cases, while the liquid-phase was Exxsol D60 for the horizontal cases and a mixture of Exxsol D60 and Marcol 82 for the inclined case. The outer diameter of the annulus was 0.1 m for all cases, while the inner diameter was 0.05 m in the horizontal configuration and 0.04 m for the inclined configuration. The purpose of this paper is to explore the effect of the holdup fraction, mixture velocity, and interior pipe’s position on the pressure gradient and flow regime, in effect a study of the pressure gradient and holdup fraction transients. The comparisons between simulations and experiments indicate that moving the pipe from an entirely eccentric to the partially eccentric configuration has a drastic impact on the pressure gradient. In all 4 cases where the inner pipe was changed from a completely eccentric geometry in the experiments to a less eccentric configuration in the simulations, we notice an increase of 48–303% of the mean pressure gradient. Comparatively, the 4 cases where the pipe was moved from a concentric experimental configuration to a more eccentric configuration in the simulations result in less drastic pressure gradient changes. Two cases were within 22% of the experimental results for mean, maximum, and minimum pressure gradient, while the last two cases exceeded the minimum and mean pressure gradients by 25–250%, respectively. The flow regime is rarely significantly affected by a change in eccentricity; 2 out of the 8 horizontal cases indicate either a transition from wavy flow to slug flow or significantly larger waves. The most prominent and frequent discrepancies identified were altered slug and wave frequencies. The last case, a 4o inclined, partially eccentric simulation was compared to an entirely eccentric experiment and results in a 0.2 Hz increase in wave frequency, up from the experimental 0.56 Hz and a 49% increase in the mean pressure gradient.

Cuttings transport: On the effect of drill pipe rotation and lateral motion on the cuttings bed

Drill pipe rotation is considered a relevant factor for cuttings transport and hole cleaning. However, in the term “rotation” is often used as a moniker for the combination of plain drill pipe rotation around its own axis and more complex lateral motion, as many laboratory setups feature an unconstrained drill string. Lateral motion is generally considered to benefit the transports of cuttings due to increased bed agitation. By means of Computational Fluid Dynamics, we have investigated the effect of synchronous and asynchronous whirling drill string motion on the cuttings bed and cuttings transport for water and a more viscous, shear-thinning fluid using the Two Fluid Model in conjunction with the Kinetic Theory Of Granular Flows and closures from soil mechanics to rheologically describe granular matter. The dynamic mesh capability of ANSYS Fluent R17.2 is exploited to account for the orbital motion of the drill string. In addition, three base cases (negative eccentric, concentric, and positive eccentric) are investigated for comparison. Whirling motion helps tremendously to disperse the solids into the main flow region and hence improves the quality of cuttings transport and hole cleaning, with synchronous whirl by far outperforming asynchronous whirl due to the cumulative tangential and radial velocities. The effect is much more prominent for water than for the more viscous, shear-thinning fluid because the latter already shows a comparatively good cuttings transport performance. Moreover, in case of the more viscous, shear-thinning fluid, the positive eccentric annulus provides an even better cuttings transport capability, if comparison is made on equivalent pressure gradients. Because of the higher viscosity level, the whirling motion reduces the axial throughput, which despite the increased bed agitation results in worse performance compared to the positive eccentric case.

Mathematical Analysis of Entropy Generation in the Flow of Viscoelastic Nanofluid through an Annular Region of Two Asymmetric Annuli Having Flexible Surfaces

In this manuscript, the authors developed the mathematical model for entropy generation analysis during the peristaltic propulsion of Jeffrey nanofluids passing in a midst of two eccentric asymmetric annuli. The model was structured by implementation of lubrication perspective and dimensionless strategy. Entropy generation caused by the irreversible influence of heat and mass transfer of nanofluid and viscous dissipation of the considered liquid was taken into consideration. The governing equations were handled by a powerful analytical technique (HPM). The comparison of total entropy with the partial entropy was also invoked by discussing Bejan number results. The influence of various associated variables on the profiles of velocity, temperature, nanoparticle concentration, entropy generation and Bejan number was formulated by portraying the figures. Mainly from graphical observations, we analyzed that, in the matter of thermophoresis parameter and Brownian motion parameter, entropy generation is thoroughly enhanced while inverse readings were reported for the temperature difference parameter and the ratio of temperature to concentration parameters.

Mud/Cement Displacement in Vertical Eccentric Annuli

Summary A successful cement placement can provide zonal isolation and environmental safety. Effective design of cement placement and mud removal affects all the stages of the wellbore life, from drilling ahead to production. Accurate predictions of fluid displacement in the wellbore are vital to design fluid properties and plan the cementing job. In this work, an analytical model is developed to simulate the displacement of fluids in eccentric annuli. This paper presents an analytical method for the solution of cement/mud displacement and evaluation of interfluid contamination during displacement in vertical eccentric annuli. This new approach starts by addressing the problem of single-fluid flow in eccentric annuli by analytically solving the governing transport equations for a flow inside an unwrapped annulus. The solution is then extended to a system of two fluids in a vertical annulus by adjusting the boundary conditions for displacement. The model is completed by adding the time-dependent calculation of interface between the two fluids, enabling the accurate determination of the amount of interfluid mixing and displacement efficiency. The analytical method proposed is used to simulate single- and multifluid flows and study the effect of fluid properties of cement, spacer, and drilling mud at different flow rates on displacement efficiency for both concentric and eccentric vertical annuli. Noting that the drilling fluids are non-Newtonian, the concept of apparent viscosity is used, accounting for variable apparent viscosity at different annular gaps. 3D computational-fluid-dynamics (CFD) simulations were performed and the results were compared with the analytical solution. Moreover, instability of the interface in all cases was studied, and the analysis offers an understanding of the role of fluid properties and proposes applicable optimized design to enhance the displacements. The amount of interfluid mixing and contamination that occurs during the displacement was calculated for both methods. The analytical solution and CFD produce results within a 13% difference, which sufficiently validates the analytical model. Evidence was gathered to support that the improper design of fluid properties and flow rate along with a highly eccentric annulus can lead to substantial cement contamination. This can lead to underdesigning the amount of fluids to be pumped to provide a complete mud removal and an efficient cement placement. On the other hand, learnings and models developed allow the optimization of fluid properties that can lead to the best outcomes, even for a highly eccentric annulus. The present work aims to take part in addressing the undeniable importance of a complete cement displacement by means of a semianalytical solution for the fluid displacement coupled with the interface-instability analysis, attempting to provide a realistic prediction of the amount of interfluid mixing and cement contamination, along with qualitative judgements on the quality of the cementing job. This methodology is intended to offer improvement techniques for the displacement and provide enhancements for practical industrial applications.

Natural convection flow of a suspension containing nano-encapsulated phase change particles in an eccentric annulus

The free convective flow of a Nano-Encapsulated Phase Change Material (NEPCM) suspension in an eccentric annulus is investigated numerically. The inner cylinder is heated and kept at a temperature higher than that of the outer cylinder. The core of the NEPCM particles is made of nonadecane while the shell is made of Polyurethane. The nanoparticles are dispersed in water as the base fluid. The equations governing the flow and heat transfer of the NEPCM suspension in the annulus are developed and written in the non-dimensional form. The numerical solutions of these equations are obtained using the finite element method. The validity of the numerical method is ensured by comparing its predictions to the results of previously published studies. The main outcomes point out to the impact of the volume fraction of the NEPCM particles and Stefan number on the thermal and hydrodynamic characteristics of the suspension. A 5% volume fraction represents the optimal value for heat transfer enhancement. Heat transfer is also enhanced when the fusion temperature of the NEPCM core is far from the temperatures of the hot and cold walls. Furthermore, increasing the annulus eccentricity and moving the inner cylinder towards the top tends to inhibit heat transfer in the annulus.

Rapid classification of primary cementing flows

We develop a simplified approach to predicting the displacement front behaviour of two Herschel-Bulkley fluids displacing one another along a narrow eccentric annulus in turbulent and mixed regimes. The approach involves the use of scaling arguments to reduce the full system of equations to a single hyperbolic equation that models the displacement front evolution. Analysis of the flux function is sufficient to predict whether or not the front will elongate along the annulus. Predictions of the simplified model are compared with a two-dimensional annular displacement model, showing good predictive abilities. The underlying eccentric annular flow is important in the industrial process of primary cementing. More specifically, the proposed method is aimed to provide a quick and reliable computational framework for analyzing primary cementing flows, leading to more successful cementing designs.

Numerical modeling of motion of displacement interface in eccentric annulus during primary cementing

AbstractCementing operations are of major importance to the long‐term zonal isolation and safety of oil and gas wells. As one of the well barriers, the cement sheath is key to the long‐term integrity of the wellbore. If the cement slurry does not completely fill the annulus between the casing and formation during the primary cementing displacement process, a potential leakage channel for subsurface fluids is created. In this study, the motion of the interface between the cement and other displaced fluids was examined during cementing displacement. By dividing an eccentric annulus into two 2D planes along the radial and azimuthal directions, a set of motion models of the interface were developed and solved numerically using a first‐order upwind finite‐difference method. The influences of modified density differenceF*, Bingham numbersB1andB2, plastic viscosity ratiom, eccentricitye*, and diffusion coefficientD*on the motion behavior of the displacement interface were determined. The results indicated that the interface of the eccentric annulus showed serious channeling and a physical mixing phenomenon. Some residual displaced fluid could remain at the casing‐cement and cement‐formation interfaces as a result of the improper design of the fluid parameters. KeepingF* > 0 andB2 < 5 beneficially removed residue from the displaced fluid on the wall, and increasingF*andB1(or decreasingB2,m,e*andD*) was conducive to the smooth motion of the displacement interface. This work showed that the interface motion model could predict the displacement quality and has great potential for improving the design of the primary cementing parameters.

Tidal disruption of planetary bodies by white dwarfs – II. Debris disc structure and ejected interstellar asteroids

ABSTRACT We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semimajor axis. We perform the largest yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances, and semimajor axes between 3 and 150 au. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as well as the ejected unbound debris contributing to the population of interstellar asteroids. Unlike previous tidal disruption studies of small asteroids which form ring-like structures on the original orbit, we find that the tidal disruption of larger bodies usually forms dispersed structures of interlaced elliptic eccentric annuli on tighter orbits. We characterize the (typically power law) size distribution of the ejected interstellar bodies as well as their composition, rotation velocities, and ejection velocities. We find them to be sensitive to the depth (impact parameter) of the tidal disruption. Finally, we briefly discuss possible implications of our results in explaining the peculiar variability of Tabby’s star, the origin of the transit events of ZTF J0139+5245 and the formation of a planetary core around SDSS J1228+1040.

Estimating formation leakage pressure using a coupled model of circulating temperature-pressure in an eccentric annulus

The eccentric annulus represents the majority of real-life situations and is attributed to a continuous change of hole-deviation angle and azimuth angle with well depth, leading to a difference in fluid flow and heat transfer mechanisms, compared with a concentric annulus. Errors resulting from ignoring the effect of eccentricity on wellbore circulating pressure and equivalent circulating density can lead to formation leakage. Based on a close relationship between circulating pressure and leakage pressure, a practical approach to predicting formation leakage pressure was established in the eccentric annulus, after running the casing, through the gradual increase of the flow rate and back pressure at the wellhead. Based on the conservation principle of energy and mass, and considering the collective effect of lost circulation and an eccentric annulus on wellbore temperature and pressure, a transient heat transfer model and a fluid flow model were developed and solved to estimate leakage pressure accurately. The numerical solution results were presented, analyzed and tested using a practical example. The results indicated that, with increasing flow rate, annulus pressure increases and temperature decreases. Temperature and pressure in the wellbore have a significant influence on the properties of the rheological parameters of Herschel-Bulkley fluid. Additionally, pressure loss and the equivalent circulating density (ECD) in the annulus were further elevated by setting back pressure at the wellhead, compared with an increase of flow rate. Most relevant is that the validity of the established method was verified through both monitored and calculated data.

The effect of orbital motion and eccentricity of drill pipe on pressure gradient in eccentric annulus flow with Newtonian and non-Newtonian fluids

The correct prediction of the pressure gradient is the fundamental parameter to establish an effective hydraulics program, which enables an optimised drilling process. In the present work, the effect of the orbital motion of the drill pipe on the pressure drop in an eccentric annulus flow with Newtonian and non-Newtonian fluids is studied numerically for both laminar and turbulent regimes using finite volume method (FVM). Furthermore, the effect of eccentricity when the inner pipe makes an orbital motion is evaluated. Different behaviours are observed in laminar and turbulent regimes. In the laminar regime, the simulation results showed that an increase of the orbital motion speed causes a considerable increment of the pressure gradient for the Newtonian fluid. For the power-law, non-Newtonian fluid in the laminar regime, on the contrary, a decrease of the pressure gradient is observed due to the shear-thinning effect. In the turbulent regime the mentioned trends are predicted to be much weaker. As eccentricity increases, the pressure drop of the non-Newtonian fluid decreases with a more pronounced diminish in pressure drop when the drill pipe is in orbital motion for both laminar and turbulent flow regimes.

The effect of orbital motion and eccentricity of drill pipe on pressure gradient in eccentric annulus flow with Newtonian and non-Newtonian fluids

The correct prediction of the pressure gradient is the fundamental parameter to establish an effective hydraulics program, which enables an optimised drilling process. In the present work, the effect of the orbital motion of the drill pipe on the pressure drop in an eccentric annulus flow with Newtonian and non-Newtonian fluids is studied numerically for both laminar and turbulent regimes using finite volume method (FVM). Furthermore, the effect of eccentricity when the inner pipe makes an orbital motion is evaluated. Different behaviours are observed in laminar and turbulent regimes. In the laminar regime, the simulation results showed that an increase of the orbital motion speed causes a considerable increment of the pressure gradient for the Newtonian fluid. For the power-law, non-Newtonian fluid in the laminar regime, on the contrary, a decrease of the pressure gradient is observed due to the shear-thinning effect. In the turbulent regime the mentioned trends are predicted to be much weaker. As eccentricity increases, the pressure drop of the non-Newtonian fluid decreases with a more pronounced diminish in pressure drop when the drill pipe is in orbital motion for both laminar and turbulent flow regimes.