Narrow Annulus Research Articles

On the efficient non-linear solver for hydraulic fracturing and well cementing simulations based on Anderson acceleration

The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration (AA) algorithm to fixed-point (FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing, the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production (fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.

Forming Mercury from Excited Initial Conditions

Mercury is notoriously difficult to form in Solar System simulations, due to its small mass and iron-rich composition. Smooth particle hydrodynamics simulations of collisions have found that a Mercury-like body could be formed by one or multiple giant impacts, but due to the chaotic nature of collisions, it is difficult to create a scenario where such impacts will take place. Recent work has found more success forming Mercury analogues by adding additional embryos near Mercury’s orbit. In this work, we aim to form Mercury by simulating the formation of the Solar System in the presence of the giant planets Jupiter and Saturn. We test out the effect of an inner disk of embryos added on to the commonly used narrow annulus of initial material. We form Mercury analogues with core-mass fractions (CMFs) > 0.4 in ∼10% of our simulations, and twice that number of Mercury analogues form during the formation process but are unstable and do not last to the end of the simulations. Mercury analogues form at similar rates for both disks with and without an inner component, and most of our Mercury analogues have lower CMFs than that of Mercury, ∼0.7, due to significant accretion of debris material. We suggest that a more in-depth understanding of the fraction of debris mass that is lost to collisional grinding is necessary to understand Mercury’s formation, or some additional mechanism is required to stop this debris from accreting.

Influence of fluid viscosity hierarchy on the reverse-circulation displacement efficiency

Reverse-circulation cementing is an alternative strategy for well cementing where the cementing fluids are injected directly into the annulus from the surface. This cementing strategy can reduce downhole circulation pressures compared to conventional circulation cementing and potentially eliminate the need for retarders in the cement slurry. In reverse-circulation operations, the fluid hierarchy will normally involve density-unstable combinations along the annulus. Since the annular geometry prevents the mechanical separation of fluids, reverse-circulation cementing is associated with a risk of slurry contamination and mixing during placement. Although reverse-circulation cementing has been known for several decades and is used for cementing of both onshore and offshore wells, it remains unclear whether conventional circulation job design guidelines apply to reverse-cementing or indeed how fluid properties should be optimized for such operations. The purpose of the current study is to contribute to the understanding of buoyant annular displacements, with a particular focus on the role of viscosity hierarchy on the annular displacement in vertical and near-vertical annuli.We present a combined experimental and numerical study of density-unstable downward displacements in a downscaled, narrow concentric annulus. A transparent annulus flow loop was used to conduct downward displacements. A high-speed camera and a mirror arrangement were used to track the displacement. Numerical simulations of the experiments and selected other cases were performed using the open-source OpenFOAM computation framework. We study Newtonian and mildly shear-thinning fluids, and our study aims to determine whether it is more efficient to use a displacing fluid with higher viscosity or lower viscosity than the displaced fluid while maintaining a constant average viscosity for the fluid pair. The experimental and numerical results, which are in good qualitative agreement, demonstrate that the viscosity hierarchy of the fluids significantly affects the displacement flow features. Our results show that a more viscous displaced fluid leads to faster growth of the instabilities and, as a result, less efficient displacement. Oppositely, we observe less tendency for finger growth and a more diffusive mixing region for more viscous displacing fluids. The effect of the viscosity hierarchy can get stronger by increasing the inclination of the annulus and the viscosity difference between the fluids from 0.006 to about 0.02 Pa⋅s. The findings can assist in the selection of fluid properties for future reverse-circulation displacement operations.

A Case of Mitral Valve Replacement for Mitral Stenosis with Narrow Annulus after TAVI and PTMC

A Case of Mitral Valve Replacement for Mitral Stenosis with Narrow Annulus after TAVI and PTMC

Ozaki Procedure Plus Aortic Annular Enlargement in an Extremely Narrow Aortic Annulus: A Surgical Challenge.

We report a 19-year-old woman with a history of percutaneous aortic valve (AV) balloon valvuloplasty 3 years ago. She was admitted with severe symptomatic AV stenosis with narrow aortic annulus. We decided to perform AV reconstruction with autologous pericardium. However, surgical findings revealed a very narrow AV annulus with a unicuspid valve; therefore, an AV enlargement was added.

Numerical study of steady and periodic mixed convection of Bingham fluid in a narrow annulus with the exact Bingham model

This article numerically investigates the mixed convection of Bingham fluid in a narrow annulus. The temperature of the inner fixed cylinder ( θ i ) is higher than that of the outer one ( θ o ), which rotates at a constant angular velocity. An OpenFOAM solver, icoFoam, which works based on the finite volume method and the PISO algorithm, is modified to perform the simulations. The modified solver can solve unsteady heat transfer problems for Bingham fluids without using regularization methods. After validating the solver, it solves the problem in different conditions to show the effect of relevant parameters, such as Reynolds number, Bingham number, and aspect ratio, on the flow field and thermal performance of the enclosure for constant amounts of Grashof and Prandtl numbers. The results are presented as streamlines and isotherms, the size and shape of the unyielded regions, the local and mean Nusselt number, and the torque coefficient. The results demonstrate that the flow is steady at Re = 10 for all Bingham numbers, and a decrease in the Reynolds number may result in an unsteady flow depending on the value of the Bingham number. The flow’s time history reveals that at a fixed Reynolds number, the flow shifts from periodic to steady-state by enhancing the Bingham number so that the flow becomes entirely steady for a given Bingham number. An interesting phenomenon is observed, the formation, movement, and disappearance of the plug zones (unyielded regions) for the periodic flow at Re = 1 and Bn = 5 .

Viscous Theory for the Vibrations of Coaxial Cylinders: Analytical Formulas for the Fluid Forces and the Modal Added Coefficients

Abstract This article addresses the small-amplitude forced beam vibrations of two coaxial finite-length cylinders separated by a viscous Newtonian fluid. A new theoretical approach based on an Helmholtz expansion of the fluid velocity vector is carried out, leading to a full analytical expression of the fluid forces and subsequently of the modal added mass and damping coefficients. Our theory shows that the fluid forces are linear combinations of the Fourier harmonics of the vibration modes. The coefficients of the linear combinations are shown to depend on the aspect ratio of the cylinders, on the separation distance, and on the Stokes number. As a consequence, the linear fluid forces do not have, in general, the same shape as the forced vibration mode, so that the fluid makes it possible to couple vibration modes with different wave numbers. Compared to the previous works, the present theory includes the viscous effects of the fluid, accounts for the finite length of the cylinders, does not rely on the assumption of a narrow annulus, and covers in a unique formulation all types of classical boundary conditions for an Euler–Bernoulli beam. The theoretical predictions for the modal added mass and damping coefficients (self and cross) are corroborated numerically, considering rigid, pinned-pinned, and clamped-free vibrations.

Calculation of Cementing ECD for Well Annuli with Narrow or Varied Radial Sizes

In this present work, cement slurry flowing in well annuli with narrow or varied radial sizes is investigated, whose purpose is to precisely calculate the equivalent circulating density (ECD) during well cementing in the petroleum industry. The theoretical Metzner-Reed (MR) method and the direct numerical simulation (DNS) are applied to calculate the cementing ECD for different types of cement slurries by considering both the Bingham and Power-Law rheological models. The cementing ECD calculated by the theoretical MR method is verified to be in accordance with the DNS result. Moreover, for the narrow annulus, the cementing ECD is demonstrated to be sensitive to the rheological model. In addition, based on the obtained DNS results, the accuracies of the cementing ECD calculated by three commercial software, including DRILL BENCH (DB), LANDMARK (LM), and PVI, are compared, to determine their corresponding adaptability for different rheological models. According to the detailed comparisons, LM shows the highest accuracy in calculating the cementing ECD for the Power-Law fluid, while PVI is optimal for the Bingham fluid. However, sharp fluctuations of the calculation errors are observed when DB is applied.

Mercury’s formation within the early instability scenario

The inner solar system’s modern orbital architecture provides inferences into the epoch of terrestrial planet formation; a ∼100 Myr time period of planet growth via collisions with planetesimals and other proto-planets. While classic numerical simulations of this scenario adequately reproduced the correct number of terrestrial worlds, their semi-major axes and approximate formation timescales, they struggled to replicate the Earth–Mars and Venus–Mercury mass ratios (∼9 and 15, respectively). In a series of past independent investigations, we demonstrated that Mars’ mass is possibly the result of Jupiter and Saturn’s early orbital evolution, while Mercury’s diminutive size might be the consequence of a primordial mass deficit in the region (potentially the result of the growing Earth’s early outward migration). Here, we combine these ideas in a single modeled scenario designed to simultaneously reproduce the formation of all four terrestrial planets and the modern orbits of the giant planets in broad strokes. By evaluating our Mercury analogs’ core mass fractions, masses, and orbital offsets from Venus, we favor a scenario where Mercury forms through a series of violent erosive collisions between a number of ∼Mercury-mass embryos in the inner part of the terrestrial disk. We also compare cases where the gas giants begin the simulation locked in a compact 3:2 resonant configuration to a more relaxed 2:1 orientation and find the former to be more successful. In 2:1 cases, the entire Mercury-forming region is often depleted due to strong sweeping secular resonances that also tend to overly excite the orbits of Earth and Venus as they grow. While our model is quite successful at replicating Mercury’s massive core and dynamically isolated orbit, the planets’ low mass remains extremely challenging to match. Indeed, the majority of our Mercury analogs have masses that are 2–4 times that of the real planet. Finally, we discuss the merits and drawbacks of alternative evolutionary scenarios and initial disk conditions (specifically a narrow annulus of material between 0.7-1.0 au). We argue that the results of our N-body accretion models are not sufficient to break degeneracies between these different models, and implore future studies to apply further cosmochemical and dynamical constraints on terrestrial planet formation models.

Хирургическое лечение клапанного аортального стеноза в сочетании с узким корнем аорты. Место задней аортопластики у взрослых. Обзор потребности в этой операции, техник ее выполнения и нашего опыта

Aim: to describe the current state of the problem of surgical expansion of the aortic root during aortic valve replacement. Aortic valve replacement is a radical operation aimed at reducing the symptoms of chronic heart failure, reducing left ventricular overload, regressing its hypertrophy, and thereby increasing the quality and life expectancy of the patient. For the greatest success of the operation, the replacement should be made with the appropriate valve size suitable for the particular patient. Materials and methods. The latest literature data on the place of surgical expansion of the aortic root in the problem of treating aortic stenosis were studied. The own experience of these operations during the implantation of mechanical and biological prostheses in the aortic position in the practice of the cardiosurgical department of the Belgorod Regional Clinical Hospital is presented. Results. The study is devoted to the actual problem of choosing the right size of the prosthesis, the frequency of additional surgical procedures for its placement. Many studies have established an association between prosthesis-patient mismatch (PPM) and surgical outcome. The association of prosthesis-patient mismatch with long-term survival is inverse, although sometimes reported as ambiguous. We reviewed the literature and our experience with the surgical management of narrow aortic root situations to determine the incidence of PPM and the need for an additional surgical procedure of posterior aortoplasty to accommodate the appropriate size of the prosthesis. The results of modern meta-analyses, multicenter studies and limited series of operations presented in the literature are reviewed. The experience of the cardiosurgical department of the Belgorod Regional Clinical Hospital for the period 01.01.2015-30.04.2023 in aortic valve replacement with a small size of the aortic ring (17-20 mm) is presented. The study material consisted of 303 patients. As prosthesis-patient mismatch, we defined all cases of posterior aortoplasty with implantation of an appropriately sized aortic prosthesis. According to modern studies, the incidence of prosthesis-patient mismatch in aortic valve replacement without aortic root plasty is 11-33%. The frequency of posterior aortoplasty in adults is, according to different authors, 5-40%. Our experience has shown that the situation of PPM, which required aortic plasty, occurred in 14.8% of cases of implantation of stented biological prostheses, in 17.3% of cases of implantation of mechanical bicuspid prostheses. In general, on average, aortic plasty was performed in 15.8% of cases. Prosthetic-patient mismatch in aortic valve replacement occurs at a relatively constant rate. Posterior aortoplasty allows implanting the calculated size of the prosthesis and avoiding this problem. Conclusion. Surgery to patch the aortic root to accommodate an adequately sized prosthesis in the aortic position is required in 15-30% of patients with narrow aortic annulus. It allows you to get good hemodynamic results. The surgical risk of the operation is low.

Study on the pressure wave velocity model of multiphase fluid in the annulus of dual-gradient drilling

Dual-gradient drilling technology is difficult to detect and deal with well kick, which may cause safety problems such as well control. Once a well kick occurs, the pressure in the narrow annulus increases instantaneously, so it is particularly important to clarify the transmission law of pressure wave. Taking the pressure fluctuation in the annulus of double gradient drilling as an example, considering the boundary between the inner wall of the casing annulus and the outer wall of the drill string, the fluid resistance, the flow field distribution and the multiphase flow, this paper deduces and establishes the multiphase flow pressure wave velocity model in the annulus, and compares the calculation results with the pressure wave velocity model in the circular pipe. The research shows that when the casing and drill string are in the static condition with small roughness and little difference between them, the shear stress on the inner wall of the annulus and the outer wall of the drill string can be treated as equal, and the derivation of the annulus pressure wave velocity model can be simplified. The pressure wave velocity of multiphase flow in annulus is related to casing size, drill string size and multiphase fluid properties. Among them, the gas content is the main influencing factor. With the increase of the gas content, the pressure wave velocity decreases, but the decreasing range will gradually decrease. When the solid content is small, it has little effect on the pressure wave velocity.

Study on the pressure wave velocity model of multiphase fluid in the annulus of dual-gradient drilling

Dual-gradient drilling technology is difficult to detect and deal with well kick, which may cause safety problems such as well control. Once a well kick occurs, the pressure in the narrow annulus increases instantaneously, so it is particularly important to clarify the transmission law of pressure wave. Taking the pressure fluctuation in the annulus of double gradient drilling as an example, considering the boundary between the inner wall of the casing annulus and the outer wall of the drill string, the fluid resistance, the flow field distribution and the multiphase flow, this paper deduces and establishes the multiphase flow pressure wave velocity model in the annulus, and compares the calculation results with the pressure wave velocity model in the circular pipe. The research shows that when the casing and drill string are in the static condition with small roughness and little difference between them, the shear stress on the inner wall of the annulus and the outer wall of the drill string can be treated as equal, and the derivation of the annulus pressure wave velocity model can be simplified. The pressure wave velocity of multiphase flow in annulus is related to casing size, drill string size and multiphase fluid properties. Among them, the gas content is the main influencing factor. With the increase of the gas content, the pressure wave velocity decreases, but the decreasing range will gradually decrease. When the solid content is small, it has little effect on the pressure wave velocity.

Numerical study of temperature–pressure coupling model for the horizontal well with a slim hole

AbstractHorizontal wells with a slim hole (HW‐SH), characterized by high productivity, high environmental protection, and low cost are gradually being introduced into oil and gas extraction processes in high‐temperature and high‐pressure formations. However, the HW‐SH annulus is narrow, and the distributions of temperature and pressure in the wellbore are very different from those of conventional horizontal wells. Furthermore, the mud properties change under the influence of high temperature and pressure. In this study, a numerical model of the transient temperature‐pressure coupling field in an HW‐SH wellbore was developed based on high‐temperature and high‐pressure performance tests of mud, combined with the characteristics of a narrow annulus in HW‐SH. Subsequently, the effects of the ground temperature gradient, displacement, drill pipe speed, annulus size, and joint size on the temperature‐pressure coupling field were analyzed. Measured data from the HW‐SH drilled in the Mahu field in China were used to validate the developed model. The results showed that the ground temperature had a significant effect on the mud density and rheological properties. As the temperature increased, the mud density decreased, and its rheological properties improved. Although pressure also has a large effect on density, it has a negligible effect on the rheological properties of the mud. The coupled temperature‐pressure field model for HW‐SH considering the effects of the temperature and narrow annulus can predict the annulus temperature and pressure with an accuracy of up to 97%. The ground temperature gradient has the greatest influence on the HW‐SH annular temperature, larger than that of the displacement. In addition, the annular size, rotation speed of the drill pipe, and joint size have almost no influence on the annular temperature. Compared to those of conventional horizontal wells, the rotational speed, annulus size, and joint size of the HW‐SH have a greater impact on the annulus pressure.

Analysis of cuttings concentration experimental data using exploratory data analysis

Cuttings transportation is a complex phenomenon involving many inter-acting variables. Experimental investigations on cuttings transport are carried out by different research groups for decades and varying findings are reported which points out to the need for a methodical data analysis approach. In the current paper, six experimental datasets (702 observations) are analyzed using exploratory data analysis (EDA) in a two-fold manner – univariate and multivariate analysis. Univariate analysis shows the asymmetry in distribution for each experimental parameter indicating the need for a nonparametric modeling approach. Multivariate analysis shows the interaction of the experimental parameters among themselves and their influence on downhole cuttings concentration (Cc) using 6D scatter plots and correlation coefficients (Kendall's τ). EDA of the current experimental data reveals the following major findings:•Smaller Cc in concentric vertical wells compared to concentric non-vertical wells.•Drilling fluid flow rate is a dominant operational parameter in vertical wellbore cleaning while string rotation (RPM) is dominant in non-vertical wellbore cleaning.•Little impact of RPM in concentric vertical well and negative eccentric deviated/highly deviated well cleaning. However, RPM together with drilling fluid flow rate provides better cleaning of non-vertical wells with positive eccentricity.•RPM has higher influence on cuttings transport in narrow annulus compared to that in wide annulus.•Assuming drilling fluid of sufficient viscosity and drill string rotation present, low viscous fluid under turbulent flow and high viscous fluid under laminar flow provide better hole cleaning. Further, Kendall's τ indicates apparent viscosity playing a more significant role in cleaning deviated wellbores compared to other inclinations for the current dataset.•Drilling fluid flow rate influences the transport of heavier cuttings and larger cuttings more while RPM has higher influence on the transport of lighter cuttings and smaller cuttings.•Better hole cleaning by heavier drilling fluids than that by lighter fluids.

Transient cutting transport model for horizontal wells with a slim hole

AbstractCompared with conventional drilling methods, the method of drilling horizontal wells with a slim hole (HW‐SH) has advantages, such as high productivity, environment‐friendliness, and low costs. However, during the drilling process, the narrow annulus may become blocked, which may lead to an increase in the annulus pressure if the wellbore is not clean. This often leads to serious drilling accidents, such as sticking and leaking formations. Many models have been used to study the cutting transport law in an annulus, but the influence of drill‐pipe rotation on cutting transport is often ignored and weakened in these models. None of the existing models can effectively simulate the cutting transport law of an entire well section. Therefore, using these models to predict the cutting transport law in the annulus of the HW‐SH will cause significant errors. In this study, the authors first establish a pipeline model of the same size as the on‐site annulus using computational fluid dynamics (CFD). Subsequently, a one‐dimensional (1D) two‐layer model that uses three correction factors to express the influence of drill‐pipe rotation on cutting transport and annulus pressure loss is developed. Finally, the parameters in the 1D model are calibrated using the CFD simulation results to accurately predict the cutting transport behavior and annular pressure loss. From the calculation results of the annulus cutting quality, annulus section‐cutting concentration, and annulus pressure drop, it was observed that the two algorithms proposed in this study have a high degree of coincidence, thereby confirming the reliability of the model. The 1D model provides close to three‐dimensional (3D) accuracy at a much shorter central processing unit time than the 3D CFD models. In addition, the accuracy of the developed model was verified using the results of an indoor pipeline two‐phase flow experiment conducted at the University of Tulsa, without considering the rotation of the drill pipe.

An Electron-scattering Time Delay in Black Hole Accretion Disks

Universal to black hole X-ray binaries, the high-frequency soft lag gets longer during the hard-to-intermediate state transition, evolving from ≲1 to ∼10 ms. The soft lag production mechanism is thermal disk reprocessing of nonthermal coronal irradiation. X-ray reverberation models account for the light-travel time delay external to the disk, but assume instantaneous reprocessing of the irradiation inside the electron-scattering-dominated disk atmosphere. We model this neglected scattering time delay as a random walk within an α-disk atmosphere, with approximate opacities. To explain soft lag trends, we consider a limiting case of the scattering time delay that we dub the thermalization time delay, t th; this is the time for irradiation to scatter its way down to the effective photosphere, where it gets thermalized, and then scatter its way back out. We demonstrate that t th plausibly evolves from being inconsequential for low mass accretion rates characteristic of the hard state, to rivaling or exceeding the light-travel time delay for characteristic of the intermediate state. However, our crude model confines t th to a narrow annulus near peak accretion power dissipation, so cannot yet explain in detail the anomalously long-duration soft lags associated with larger disk radii. We call for time-dependent models with accurate opacities to assess the potential relevance of a scattering delay.

Experimental investigation of tubing collar's influence on hydrodynamic behavior of annular duct flow

Tubing collars’ influence on hydrodynamic behavior of annular duct flow has been investigated using Particle Image Velocity (PIV) technology. PIV has become an efficient method for complex transient flows visualization. A water flow loop with two replaceable variable cross-sections (VCS), 75–90 mm and 90–110 mm, in a 129 mm inner diameter (ID) pipe was used. The whole field of the variable cross-section annulus (VCSA) was visualized, including forward-facing step (FFS), narrow annulus (NA), and backward-facing step (BFS) flow. The VCSA ratio and Reynolds (Re) number influence on streamline distribution, velocity distribution, and turbulence intensity were discussed. Results showed that the recirculation is easier to form in BFS than FFS flow under the same condition. The VCSA ratio affects the formation of recirculation zones and the location of the reattachment point. Reynolds number mainly affects BFS flow by influencing the main velocity component - axial velocity. The turbulence intensity is relatively high in BFS than FFS flow and is larger at y/h>1.0 than y/h<1.0. Furthermore, the streamwise coherent structures reveal that the first two modes are predominant and represent the main characteristics of the flow by proper orthogonal decomposition (POD) method.

Modal added-mass matrix of an elongated flexible cylinder immersed in a narrow annular fluid, considering various boundary conditions. New theoretical results and numerical validation

This paper considers the fluid–structure interaction problem of two coaxial cylinders separated by a thin layer of fluid. The flexible inner cylinder is imposed a small amplitude harmonic displacement corresponding to a dry vibration mode of an Euler–Bernoulli beam, while the external cylinder is rigid. A new theoretical formulation based on the assumption of a narrow fluid annulus is derived to estimate the modal added-mass matrix of the vibrating cylinder. This formulation accounts for the finite length of the flexible cylinder, clearly highlights the effect of the aspect ratio of the vibrating cylinder on the structure of the added-mass matrix, and covers all types of classical boundary conditions in the same theory and can easily be implemented in any numerical computing environment. The diagonal coefficients of the added-mass matrix are shown to increase with the confinement, with the aspect ratio of the flexible cylinder, and are sensitive to the wave-number of the vibration mode. Also importantly, we show that the dry vibration modes generate off-diagonal coefficients that vanish for an infinitely long cylinder. Our theoretical observations are corroborated by an extensive set of CFD numerical simulations, covering all types of classical boundary conditions, different confinement configurations, and different aspect ratios of the vibrating cylinder. The results obtained are presented in graphical form, which can be directly applied in engineering applications.

Oscillatory natural convection of Al2O3-water nanofluid near its density maximum in a narrow horizontal annulus

In order to reveal the oscillatory characteristics of the natural convection of nanofluid, this paper presents a comprehensive numerical work on the oscillatory natural convection of Al2O3-water nanofluid near its density maximum in a narrow horizontal annulus. The influences of nanoparticle volume fraction, Rayleigh number and density inversion parameter on the flow pattern evolution and heat transfer ability are analyzed. Results show that the density inversion of the working fluid affects the velocity and temperature distributions of the natural convection of Al2O3-water nanofluid significantly. Adding nanoparticles is beneficial to stabilizing the flow of nanofluid and keeping the symmetry of the flow structure. The convective heat transfer is enhanced with the increase of the volume fraction of nanoparticles. Furthermore, the evolution of the flow regime with the Rayleigh number at different volume fractions of nanoparticles is summarized.

Effects of wellbore irregularity on primary cementing of horizontal wells, Part 2: Small scale effects

Wellbore irregularities turn the narrow eccentric annulus of primary cementing into a fully three-dimensional (3D) flow geometry. Here we explore the effects of coupling the borehole geometry, reconstructed from high frequency caliper data, with 3D computations of the displacement flow. Displacement flows through circular boreholes with enlargements of varying depths and wavelengths tend to result in both enhanced secondary flows and in residual drilling mud. Short wavelength deep enlargements generally have larger percentage of residual mud. We then perform a frequency analysis of typical caliper data from Northwest Canada, showing that the borehole geometry may typically be reconstructed using the lowest 3–5 dominant frequencies. We present example computations of displacement flows through these geometries. Although the underlying dynamics are those of more uniform annuli, these computations do reveal in that small changes in geometric description can lead to noticeable changes in the displacement mechanics, especially in the fluid present at the walls of the annulus. The conclusion is that borehole irregularity can make a significant difference in cementing horizontal wells, which are anyway already troublesome.