Fluids In Concentric Annuli Research Articles

Study of the Hydrodynamic Characteristics of Non‐Newtonian Polymer Solution Fluid in Concentric Annulus Using Computational Fluid Dynamics Methods

AbstractNon‐Newtonian fluids flowing in a concentric annulus have been widely observed in industrial chemical processes. In this study, the hydrodynamic characteristics of a non‐Newtonian fluid (polymer solution) in concentric annulus are investigated using computational fluid dynamics (CFD) modeling and numerical simulation methods. First, a simple grid independence analysis is carried out to select appropriate grid parameters. Then the rationality of the proposed CFD model is confirmed by the near‐wall velocity profiles. Based on the validated model, the effects of the fluid properties and radius ratio on the flow structure characteristics are studied at various inlet velocities. According to the simulated flow fields (i.e., velocity, pressure, strain rate, and wall shear stress), the flow pattern, flow resistance, and residence time distribution characteristics are analyzed in the laminar and turbulent regimes. The presented results show that non‐Newtonian fluids have unique flow behaviors in concentric annulus when compared with Newtonian fluids.

The flow of power-law fluids in concentric annuli: A full analytical approximate solution

This work deals with the zero shear rate (maximum velocity) position parameter λ of a steady laminar axial annular flow of power-law fluids especially polymeric ones. λ is involved in the shear rate, velocity profile and the flow rate calculations, which are essential for studies such as viscous dissipation, convective heat transfer and pressure drop prediction in annuli. However, the analytical explicit expression of λ remains unsolved despite some approximate solutions. In this paper, we will provide a simple and analytically demonstrable expression of λ so that it can be used for parametric investigations, identifications, sensitivity analysis etc. in terms of industrial or laboratory applications.

Explicit flow velocity modelling of yield power-law fluid in concentric annulus to predict surge and swab pressure gradient for petroleum drilling applications

Exact prediction and controlling of surge/swab pressure are required during drilling of hydrocarbon reservoirs and other geological formations that often leads to well control challenges. The existing methods to predict the surge/swab pressure gradient in the wellbore are much implicitly developed, which further reduces the model accuracy. Therefore, the present research aims to develop a novel analytical model by incorporating the explicit flow velocity equations to further improve the efficiency in predicting the surge pressure gradient. The governing flow velocity equations are developed for a concentric annulus exhibiting Couette–Poiseuille flow phenomenon that subsequently used in designing a new analytical model for yield power-law fluids to predict surge pressure gradient. Detailed analysis for the validation of a newly developed model is performed using existing predictive models and experimental data of surge pressure. The statistical analysis exhibits satisfactory outcomes with a maximum error of 5.61% and R2 of 0.988. A detailed analysis on the effect of relevant parameters on surge/swab pressure is also presented. The impact of fluid behaviour index and diameter ratio is found to be highly dependent on surge pressure under varying tripping speeds compared to other drilling parameters such as fluid yield point and consistency index.

Analytical solution for axial flow of a Giesekus fluid in concentric annuli

An exact analytical solution for a Poiseuille flow of a Giesekus fluid in an annulus is obtained, taking into account the effects of the non-linearity of the constitutive equation. The fluid velocity is given in terms of Legendre elliptic integrals and Jacobi elliptic functions. The fluid behaviour is described using the Deborah number along the mobility factor and the radius ratio, while the tangential and the normal stresses are also evaluated.The shear-rate, the velocity and the stress tensor components as function of the involved parameters are graphically represented and analysed in detail.

Entrance Region Flow Heat Transfer in Concentric Annuli with Rotating Inner Wall for Herschel-Bulkley Fluids

A finite difference analysis of the entrance region flow heat transfer of Herschel-Bulkley fluids in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic and thermal boundary layer in concentric annuli with one wall being isothermal and other one being adiabatic. The inner cylinder is assumed to be rotating with a constant angular velocity and the outer cylinder being stationary. A finite difference analysis is used to obtain the velocity distributions, pressure drop and temperature variations along the radial direction. Computational results are obtained for various values of aspect ratio, flow index, Prandtl’s number and Herschel-Bulkley number. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.

A numerical model to predict surge and swab pressures for yield power law fluid in concentric annuli with open-ended pipe

Excessive surge pressure can cause many downhole problems such as loss circulation, leakage, fracture formation, and blowout. Accurately predicting surge and swab pressures can provide a guarantee of safety in a downhole. Multiple research endeavors have been conducted based on close-ended pipes (CEP); however, no exact or approximate models to predict surge and swab pressures have been reported for yield power law (YPL) fluid in an open-ended pipe (OEP). In this paper, an exact numerical model was established to predict surge and swab pressures for YPL fluid in concentric annuli with OEP. Additionally, existing regression models for Bingham plastic (BP) and power law (PL) fluids were modified based on the exact numerical solutions in concentric annuli with OEP. The accuracy of the modified regression model is ±5% and ±15% for BP and PL fluids, respectively. In addition, an accurate (to within 5% error) new regression model was developed to predict surge and swab pressures for YPL fluid in a concentric annulus with OEP on the basis of exact numerical solutions. The effects of fluid properties, annular geometries and drilling parameters on surge and swab pressures in OEP were investigated using an exact numerical model.

Entrance Region Flow Heat Transfer in Concentric Annuli with Rotating Inner Wall for Bingham Fluid

A finite difference analysis of the entrance region flow heat transfer of Bingham fluid in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic and thermal boundary layer in concentric annuli with one wall being isothermal and other one being adiabatic. The inner cylinder is assumed to be rotating with a constant angular velocity and the outer cylinder being stationary. A finite difference analysis is used to obtain the velocity distributions, pressure drop and temperature variations along the radial direction. Computational results are obtained for various values of aspect ratio N, Bingham number B and Prandtl’s number. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.

Entrance Region Flow in Concentric Annuli with Rotating Inner Wall for Herschel–Bulkley Fluids

A finite difference analysis of the entrance region flow of Herschel–Bulkley fluids in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic boundary layer in concentric annuli with the inner cylinder assumed to be rotating with a constant angular velocity and the outer cylinder being stationary. A finite difference analysis is used to obtain the velocity distributions and pressure variations along the radial direction. With the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. Computational results are obtained for various non-Newtonian flow parameters and geometrical considerations. A significant asymmetry is found in the entrance region which is gradually reduced as the flow develops. For smaller values of aspect ratio and higher values of Herschel–Bulkley number the flow is found to stabilize more gradually. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.

A new utility calculation model for axial flow of non‐Newtonian fluid in concentric annuli

A new utility approach that is independent of the rheological model is presented for the flow of non‐Newtonian fluids in concentric annulus. The novel model was developed without assuming that the generalised flow index remains constant over all shear rate ranges. Based on the slot model, the flow rate expressions for all common rheological models flowing in annuli were obtained, such as the Herschel–Bulkley model, the Robertson–Stiff model, and the Four‐parameter model, and they all can be solved numerically to obtain accurate wall shear rate and shear stress. Following Metzner and Reed's study, we defined a generalised flow index for non‐Newtonian fluid flow in annuli. Through a theoretical analysis, we also defined a new effective diameter for non‐Newtonian fluid flow in annuli, which accounts for the effects both of annulus geometry and fluid rheology but which is different from that was proposed by Reed and Pilehvari. Through the generalised effective diameter we linked non‐Newtonian annular flow with Newtonian pipe flow. A general annular Reynolds number expression was derived from this method for conditions under which the generalised flow index is variable. A theoretical calculation method for the generalised flow index and a uniform pressure loss calculation model for non‐Newtonian flow in concentric annuli were developed, which are applicable to all time‐independent non‐Newtonian fluid. The predictions of this model have been compared with an extensive set of data from the literature. The comparisons of different fluids in different size annuli show very good agreement over the entire range of flow types.

Axial laminar flow of viscoplastic fluids in a concentric annulus subject to wall slip

The flow of non-Newtonian fluids in annular geometries is an important problem, especially for the extrusion of polymeric melts and suspensions and for oil and gas exploration. Here, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel–Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided. The simplifications of the analytical model for Hershel–Bulkley fluid subject to wall slip also provide the analytical solutions for the axial annular flows of Bingham plastic, power-law, and Newtonian fluids with and without wall slip at one or both surfaces of the annulus.

A Mechanistic Model for Predicting Frictional Pressure Losses for Newtonian Fluids in Concentric Annulus

A mathematical model is introduced estimating the frictional pressure losses of Newtonian fluids flowing through a concentric annulus. A computer code is developed for the proposed model. Also, extensive experiments with water have been conducted at Middle East Technical University, Petroleum and Natural Gas Engineering Department Flow Loop and recorded pressure drop within the test section for various flow rates. The performance of the proposed model is compared with computational fluid dynamics (CFD) software simulated annulus flow section and various criteria such as crittendon, hydraulic diameter and slot flow approximation as well as experimental data. The results showed that the proposed model and experimental results are in good agreement for almost all cases when compared with the other criteria and CFD software. Also, the proposed model could estimate the frictional pressure losses for both laminar and turbulent flow regimes within an error range of ±10%.

Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

AbstractAn integrated approach is presented for the flow of Herschel–Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner–Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel–Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi‐analytical and empirical equations, is provided which describe fully the flow of Herschel–Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types.

Entrance region flow of a power-law fluid in concentric annuli with rotating inner wall

The laminar flow of a power-law non-Newtonian fluid in the entrance region of a concentric annulus is investigated numerically. The inner cylinder rotates with a constant angular velocity while the outer cylinder is stationary. Using the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. A Crank Nicolson method is used to obtain the velocity components and the pressure at each step of the axial direction. The development of the axial velocity profile, transverse (radial and tangential) velocity profiles, pressure drop have been studied. Computations are obtained for various axial positions and various flow indices.

Skewed Poiseuille-Couette flows of sPTT fluids in concentric annuli and channels

Analytical solutions have been derived for the helical flow of PTT fluids in concentric annuli, due to inner cylinder rotation, as well as for Poiseuille flow in a channel skewed by the movement of one plate in the spanwise direction, which constitutes a simpler solution for helical flow in the limit of very thin annuli. Since the constitutive equation is a non-linear differential equation, the axial and tangential/spanwise flows are coupled in a complex way. Expressions are derived for the radial variation of the axial and tangential velocities, as well as for the three shear stresses and the two normal stresses. For engineering purposes expressions are given relating the friction factor and the torque coefficient to the Reynolds number, the Taylor number, a nondimensional number quantifying elastic effects ( εDe 2) and the radius ratio. For axial dominated flows fRe and C M are found to depend only on εDe 2 and the radius ratio, but as the strength of rotation increases both coefficients become dependent on the velocity ratio ( ξ) which efficiently compacts the effects of Reynolds and Taylor numbers. Similar expressions are derived for the simpler planar case flow using adequate non-dimensional numbers.

Axial Couette–Poiseuille flow of power-law viscoplastic fluids in concentric annuli

The laminar axial flow of non-Newtonian fluids obeying Robertson–Stiff model in concentric annuli is analysed. Fluid flow is produced by the inner cylinder moving along its axis and by the pressure gradient imposed in the axial direction. Both cases (where pressure gradient either assists the moving cylinder or opposes the moving cylinder) are considered. All possible cases with respect to the positions of the plug flow regions are uniquely diversified by the derived semi-analytical criteria using the entry (geometric, kinematic, and rheologic) parameters. The explicit semi-analytical expression is derived for each possible case of the volumetric flow rate.

Explicit pressure drop-flow rate relation for laminar axial flow of power-law fluids in concentric annuli

This paper is an examination of laminar axial flow of power-law fluids in concentric annuli. The objective is to derive an accurate expression relating pressure drop to flow rate over the whole range of entry parameters: aspect ratio of inner-to-outer diameters, flow behavior index, and consistency parameter of the rheological model. Accuracy of the expression enables determination of the influence of individual parameters to the functional dependence of the explicit relation of pressure drop vs. flow rate.

Laminar flow of power law fluids in concentric annuli

Ranger (1994) demonstrated recently that it is possible to achieve higher volumetric flow rate for the laminar flow of incompressible Newtonian fluids in a hollow annular pipe than that in an annulus with the solid core for equal flow areas and pressure gradients. His calculations reveal enhancements of up to 250% in flow rate for certain combinations of the sizes of pipe involved in it. Aside from the theoretical interest in this problem (e.g. Shivakumar and Ji, 1993), this result is of considerable pragmatic importance when different fluids need to be transported between the same points. However, no physical explanation was presented to explain this phenomenon. This note demonstrates that greater enhancements in flow rate are possible for the laminar flow of incompressible power law fluids under the same circumstances. Representative numerical results are presented for a range of combinations of the flow behavior index and geometric parameters to elucidate the interplay between the nonlinear fluid characteristics and the geometrical parameters. The observed trends are qualitatively explained by considering limiting cases and in terms of the results for known geometries

Relationship of Annular and Parallel-Plate Poiseuille Flows for Power-Law Fluids

Abstract This paper deals with both the axial and the tangential annular flows of power-law fluids in concentric annuli, and it specifically focuses on the relation volumetric flow rate Q against pressure drop P. Initially the mutual compatibility of the hitherto obtained results is analyzed, and from this, new results concerning behavior of a parameter λ [a location of maximum axial (tangential) velocity component] are derived. Then, approximative expressions for relations Q against P (independent of A.) are proposed in a sufficiently large region (K,n) where K represents annular aspect ratio and n the flow behavior index n. The deviations of these simple relations from the exact ones are negligible.

Quasisimilarity of flow behavior of power-law fluids in concentric annuli

Axial flow of power-law fluids in concentric annuli is studied. It is shown that this problem has a quasisimilarity solution in a broad range of flow behavior and consistency indices, and an aspect ratio κ of the inner diameter to the outer one. This solution makes it possible to transform the dependence of the flow rate vs. pressure drop for individual κ to a common graph for all κ ⩾ 0.4. The procedure presented fully eliminates the necessity of determining the location of maximum axial velocity.

Numerical Simulation of Laminar Flow of Yield-Power-Law Fluids in Conduits of Arbitrary Cross-Section

A numerical model has been developed to simulate laminar flow of Power-law and Yield-Power law fluids in conduits of arbitrary cross-section. The model is based on general, nonorthogonal, boundary-fitted, curvilinear coordinates, and represents a new approach to the solution of annular flow problems. The use of an effective viscosity in the governing equation of the flow allows the study of the flow behavior of any fluid for which the shear stress is a function of shear rate only. The model has been developed primarily to simulate annular flow of fluids used in drilling and completion operations of oil or gas wells. Predicted flow rates versus pressure gradient for laminar flow of Newtonian fluids in concentric and eccentric annuli, and Power-law fluids in concentric annuli compare very well with results derived from analytical expressions. Moreover, the predictions for laminar flow of Power-law and Yield-Power-law fluids in eccentric annuli are in excellent agreement with numerical and experimental data published in the literature. The model was also successfully applied to the case of laminar flow of Power-law fluids in an eccentric annulus containing a stationary bed of drilled cuttings and the results are presented herein.