non-Newtonian Fluids In Pipes Research Articles

Model inference using the Akaike information criterion for turbulent flow of non-Newtonian crude oils in pipelines

The friction factor is a crucial parameter in calculating frictional pressure losses. However, it is a decisive challenge to estimate, especially for turbulent flow of non-Newtonian fluids in pipes. The objective of this paper is to examine the validity of friction factor correlations adopting a new informative-based approach, the Akaike information criterion (AIC) along with the coefficient of determination (R 2). Over a wide range of measured data, the results show that each model is accurate when it is examined against a specific dataset while the El-Emam et al. (Oil Gas J 101:74–83, 2003) model proves its superiority. In addition to its simple and explicit form, it covers a wide range of flow behavior indices and generalized Reynolds numbers. It is also shown that the traditional belief that a high R 2 means a better model may be misleading. AIC overcomes the shortcomings of R 2 as a trade between the complexity of the model and its accuracy not only to find a best approximating model but also to develop statistical inference based on the data. The authors present AIC to initiate an innovative strategy to help alleviate several challenges faced by the professionals in the oil and gas industry. Finally, a detailed discussion and models’ ranking according to AIC and R 2 is presented showing the numerous advantages of AIC.

Simplified method for estimating heat transfer coefficients: constant wall temperature case

This work completes a previous study (Cruz et al., in J Heat Transf 134:091703, 2012) by evaluating the performance of the simplified method proposed therein for calculating the Nusselt number for laminar flow of non-Newtonian fluids in pipes with constant wall temperature. The methodology was tested using the Herschel-Bulkley, Bingham, Casson and Carreau-Yasuda generalized Newtonian models, and also the simplified form of the Phan-Thien–Tanner viscoelastic model. The error of the approximate methodology is below 3 %, except for yield stress fluids, for which the maximum error increases to 7.4 % for the cases analyzed, which cover a wide range of shear viscosity curves. An explicit expression of Nusselt number for Casson fluids is also presented.

An Explicit and Continuously Differentiable Flow Equation for Non-Newtonian Fluids in Pipes

Summary A simple model approximates Herschel-Bulkley (HB) non-Newtonian fluids in laminar flow in pipes. It is continuously differentiable and explicit in the frictional pressure gradient. Such properties are needed for control, real-time optimization, and prediction in drilling operations. The accuracy of the new model is evaluated by comparing it with a numerical implementation of the implicit HB model and some representative approximations used in the literature. Very little loss in accuracy is experienced compared with the implicit solution.

Buoyancy driven slump flows of non-Newtonian fluids in pipes

We present results of a comparative experimental-numerical study of the buoyancy-driven slumping flow of two non-Newtonian fluids in a horizontal closed pipe. This type of flow occurs during the abandonment of horizontal oil and gas wells, when sealing the well through the setting of cement plugs. In our study, both of the fluids exhibit shear-thinning behaviour and one of the fluids has a yield stress. The yield stress is necessary in order for the flow to have a static equilibrium. We have studied the effects of changes in density difference and of small deviations from perfectly horizontal. The effects of these parameters on the interface shape and on the slump length versus time were analyzed. Comparison of numerical and experimental results shows broadly similar trends, but with some qualitative differences also observed, possibly due to interfacial effects at the interface. We also compare the slump length and shape against existing analytical results that predict the maximal static slump length.

Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders

In general, purely axial flows of non-Newtonian fluids are not possible in straight pipes of non-circular cross section. The secondary flow pattern for the flow of various non-Newtonian fluids in pipes of non-circular cross section has been studied by many authors. The method which is used is invariably a perturbation technique using either the driving force for the problem or one of the material constants as the parameter for the expansion. The former implies that the solution is a perturbation of the state of rest, while the latter implies that the null solution corresponds to the Newtonian solution. However, in many problems of practical relevance, flows of a particular non-Newtonian fluid, with specific values for the non-Newtonian parameters (not necessarily small), take place under a finite driving force, making such approaches of dubious value. For instance, as a consequence of perturbing in the driving force, the secondary flows appear only at the fourth order. In this paper we use a perturbation technique in which the perturbation parameter is a geometric measure of the departure from the geometry in which rectilinear flow is possible. Such an approach allows one to study perturbation of flows which are not the null state, and this, in turn, leads to secondary flows at first order.

Predicting Single-Phase and Two-Phase Non-Newtonian Flow Behavior in Pipes

Improved and novel prediction methods are described for single-phase and two-phase flow of non-Newtonian fluids in pipes. Good predictions are achieved for pressure drop, liquid holdup fraction, and two-phase flow regime. The methods are applicable to any visco-inelastic non-Newtonian fluid and include the effect of surface roughness. The methods utilize a reference fluid for which validated models exist. For single-phase flow, the use of Newtonian and power-law reference fluids are illustrated. For two-phase flow, a Newtonian reference fluid is used. Focus is given to shear-thinning fluids. The approach is theoretically based and is expected to be more accurate for large, high-pressure pipelines than present correlation methods, which are all primarily based on low-pressure, small-diameter pipe experimental data.

The flow characteristics of fluidized magnetite powder in an inclined open channel

The flow characteristics of a fluidized bed of magnetite in an inclined open channel were studied experimentally. Data were obtained on the effects of mass feed rate of solids, channel inclination, superficial gas velocity and channel length on the depths of flowing beds of 139-μm and 169-μm magnetite particles. It was observed that channel inclination and superficial gas velocity have very pronounced effects on the bed depth and shape of the free surface profile of the flowing bed. Under some operating conditions, the flow became unstable, resulting in the formation of flow-rate oscillations. The effect on flow behavior of a narrow defluidized region caused by a discontinuity in the distributor plate was also studied. For certain operating conditions, it was possible to apply the liquid analogy approach, based on the laminar flow of non-Newtonian fluids in pipes, to the flowing bed of magnetite. A friction factor versus generalized Reynolds number correlation, characterized by a power-law model and originally developed for laminar flow of non-Newtonian fluids, showed good agreement with the experimental results. The flowing bed of 139-μm magnetite displayed different non-Newtonian characteristics, depending on the superficial gas velocity and depth of the bed. For a superficial gas velocity of 2.3 u mf and 40 mm bed depth, the flowing bed behaved like a Bingham plastic fluid, while at a 55-mm bed depth it exhibited pseudoplastic behavior.

Invariant solutions of the equation of non-steady laminar flow of a non-newtonian fluid in pipes

A method of obtaining particular solutions of the equations of the laminar flow of non-Newtonian fluids in pipes based on a group-theoretic analysis of differential equations is considered. Invariant solutions are given for point and tangential transformations satisfying the natural boundary conditions.

Extended Lévêque solution for heat transfer to non-Newtonian fluids in pipes and flat ducts

The problem of predicting the rate of heat transfer through the wall of a duct in which a nonNewtonian fluid is flowing in laminar regime is analyzed in the present contribution. The effect of heat generation by viscous dissipation is also considered. In this work an alternative route, to deduce an extension of the Lévêque solution, is presented up to terms including the effect of the Brinkman number. The results so obtained are compared with previous results showing that our final expression, valid for pipes as well as flat ducts, produces extremely good results within the range of validity of the variables which is specified.

Non-steady two-phase stratified laminar flow of polymeric liquids in pipes

A numerical method of solution is given for the non-steady two-phase stratified. laminar flow of various non-Newtonian fluids in pipes. In particular, the Ellis fluid model is chosen to illustrate inelastic shear thinning effects. It is shown that the method can be applied to the non-steady multi-phase stratified laminar flow of some non-Newtonian fluid models. An Oldroyd six constant model is used to illustrate the fully elastic flow. It is found that the presence of two phases of the same kind of immiscible liquids tends to suppress the typically viscoelastic response to time dependent situations that the same liquids would exhibit as a single phase. Overshoot of flow rates is reduced, if not completely eliminated in both the generation and decay of steady flows. In two-phase pulsatile flows, the flow enhancement is less marked and the time dependence of the individual flow rates can be significantly different. Theoretical results are used to interpret some of the flow instabilities encountered during the capillary flow of polymeric liquids.

General solutions of the heat equation in finite regions

Using a finite integral transform an analytical solution is found for a large class of heat transfer problems. This solution is obtained in form of infinite series and contains quasi-steady and transient terms. It is shown that the Ölçer's conductive heat transfer solution [2,3] is a special case of the general solution obtained. The latter can also be applied when studying heat transfer in laminar and turbulent flows of Newtonian and non-Newtonian fluids in pipes and ducts, temperature development in the entrance region of MHD channels and elsewhere.

Pulsating flow on non-Newtonian fluids in pipes

Flow rates and power requirements are presented for the pulsating, laminar flow of non-Newtonian power law fluids in pipes under a sinusoidal pressure gradient. A finite difference method of analysis is used which checks against available analytical solutions to within 1 per cent. It is found that for pseudoplastic fluids the pulsations can increase the flow rate above that which would be obtained under steady flow conditions at the same mean pressure gradient. The converse is true for dilatant fluids. However, for all power law fluids, the power required to transport the fluid in pulsating flow is nerver less than that required for the sames flow rate under steady flow conditions.

Unsteady, laminar flows of non-Newtonian fluids in pipes

Velocity profiles for unsteady laminar flows of power law non-Newtonian fluids in pipes have been derived using an explicit finite difference technique. Three unsteady flows have been considered, viz. 1. The transient start-up following the sudden imposition of a constant pressure gradient to a fluid at rest. 2. Oscillatory flow following the imposition of a sinusoidally varying pressure gradient with a zero mean value. 3. Pulsating flow following the imposition of a sinusoidally varying pressure gradient with a non-zero mean. The effects of the major parameters which influence these flows are demonstrated.

Heat exchange in the flow of non-Newtonian fluids

A method is proposed for solution of convective heat-exchange problems for the flow of non-Newtonian fluids in pipes and channels. Problems with a linear rise in the tube wall temperature are investigated in detail.

Numerical Prediction of the Pipeline Flow Characteristics of Thixotropic Liquids

Abstract A numerical technique has been developed to permit establishing the pressure gradient associated with laminar flow of thixotropic liquids through long pipelines. For this purpose the pipeline is divided into a number of radial and longitudinal increments within which rheological properties of the fluid may be considered as constant at any time. Then, provided only that the fluid flow curve is defined at every duration of shear, it is possible to predict the instantaneous pressure gradient at any cross-section along the pipeline for each desired flow rate and pipe size. The technique consists of an iterative integration of shear rate to establish the appropriate value of the wall shear stress at each location. Consistency of fluid in the increment is determined by the flow history of that increment, while the radial flow) associated with variations in velocity profile is accounted for by adjusting the width and radial position of the increment. A number of pressure profiles, computed at each of several flow rates, provide a convenient basis for pipeline design and pump selection. Introduction In recent years, considerable attention has been given to predicting pressure drop associated with the isothermal laminar flow of time-independent non-Newtonian fluids in pipes and annuli. The approach generally has been m develop analytical relationships between flow rate and pressure drop based on simple constitutive models which hopefully provide an approximate description of the rheological properties of the fluid. Analytical solutions are highly desirable since the influence of all pertinent parameters can be readily determined. Unfortunately, however, this approach is restricted to simple flow geometries and frequently leads to erroneous results due to inadequacies in the model. In certain cases a solution may be obtained through applying appropriate numerical techniques For example, a digital computer program is available for predicting the velocity profile and pressure drop encountered by any Newtonian or time-independent non-Newtonian fluid flowing under laminar conditions in a cylindrical pipe or annulus. In this paper the consistency behavior of the fluid need only be described in terms of basic rheological data. Analyzing flow systems involving fluids with time-dependent rheological characteristics is considerably more complicated since substantial changes in consistency may occur because of sustained shear action. This sensitivity to shear frequently persists for several hours. Consequently, variations in pressure drop and/or flow rate resulting from the aging process and addition of unsheared or partially sheared fluid to the system must be considered for purposes of pipeline design. This paper outlines a numerical method for predicting the transient and steady-state laminar flow behavior of a thixotropic liquid in a pipeline of arbitrary length (i.e., at a specified constant flow rate, the instantaneous pressure gradient may be determined at any time after start up and at any location along the pipeline). Several such pressure gradient profiles computed at several flow rates, may be combined to produce a complete portrait of the system response. This flow portrait provides a reasonable basis for pipeline design and for selecting a suitable pump characteristic. TIME-DEPENDENT RHEOLOGICAL BEHAVIOR The most familiar time-dependent rheological properties are those exhibited by thixotropic liquids. Many of these materials, particularly thixotropic crude oils, generally display an apparent yield stress in that a finite pressure gradient is required to initiate flow. Then, under the influence of sustained shear at a constant shear rate, the consistency systematically decreases to some final limiting value. SPEJ P. 369ˆ