Flow behaviour

Over the last decade some of the major oil companies have been using vast amounts of outcrop derived measurements to design and calibrate powerful computer models. These models are employed as tools to quantitatively describe reservoir distribution and flow behaviour within individual units. Hence this technique is not only important for the exploration phase but more so for the early assessment of production profiles. 

One of the major differences in fluid flow behaviour for gas fields compared to oil fields is the mobility difference between gas and oil or water. Recall the that mobility is an indicator of how fast fluid will flow through the reservoir, and is defined as... 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

The practical and computational complications encountered in obtaining solutions for the described differential or integral viscoelastic equations sometimes justifies using a heuristic approach based on an equation proposed by Criminale, Ericksen and Filbey (1958) to model polymer flows. Similar to the generalized Newtonian approach, under steady-state viscometric flow conditions components of the extra stress in the (CEF) model are given a.s explicit relationships in terms of the components of the rate of deformation tensor. However, in the (CEF) model stress components are corrected to take into account the influence of normal stresses in non-Newtonian flow behaviour. For example, in a two-dimensional planar coordinate system the components of extra stress in the (CEF) model are written as... 

Metzener, A. B. and Whitlock, M., 1958. Flow behaviour of concentrated dilatant suspensions. Trans. Soc. Rheol. 2, 239-254. 

In the specific case of polymer melts these almost invariably are of the pseudoplastic type. In such cases the flow behaviour index n is less than 1 the greater the divergence from Newtonian behaviour the lower its value. 

Effect of increase of On viscosity On flow behaviour index On critical shear rate On sharkskin... 

When a fluid is flowing along a channel which has a uniform cross-section then the fluid will be subjected to shear stresses only. To define the flow behaviour we may express the fluid viscosity, rj, as the ratio of shear stress, r. 

Design methods involving polymer melts are difficult because the flow behaviour of these materials is complex. In addition, flow properties of the melt are usually measured under well defined uniform conditions whereas unknown effects such as heating and cooling in processing equipment make service conditions less than ideal. However, sufficient experience has been gathered... 

Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

Chapter 4 describes in general terms the processing methods which can be used for plastics and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

Plug-flow behaviour has been shown in this type of reactor by the use of tracer studies (Table 8.6). 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

The flow behaviour of suspensions of coarse particles is completely different in horizontal and vertical pipes. In horizontal flow, the concentration of particles increases towards the bottom of the pipe, the degree of non-uniformity increasing as the velocity of flow is decreased. In vertical transport, however, axial symmetry is maintained with the solids evenly distributed over the cross-section. The two cases are therefore considered separately. 

For an incompressible viscous fluid (such as the atmosphere) there are two types of flow behaviour 1) Laminar, in which the flow is uniform and regular, and 2) Turbulent, which is characterized by dynamic mixing with random subflows referred to as turbulent eddies. Which of these two flow types occurs depends on the ratio of the strengths of two types of forces governing the motion lossless inertial forces and dissipative viscous forces. The ratio is characterized by the dimensionless Reynolds number Re. 

The flow behaviour of a material is described by the relationship between the force acting on the sample of a material, and the effect of this force. The effect may be elastic deformation or viscous flow. For technological and historical reasons, the standard measuring technique has been to force the sample to undergo a predetermined shear rate and measure the force required. 

The value of critical concentration depends strongly on the pectin being used. Figure 2 gives the viscosity curves of two different pectins at the same concentration of 2.5 % w/w. The different production parameters, that have been used for these pectins, have strongly influenced their flow behaviour. The enzymatic reduction of the molecular weight down to... 

The above model of settler flow behaviour, combined with entrainment backmixing was used by Aly (1972) to model the unsteady-state extraction of copper from aqueous solution, using Alamine 336 solvent. An identification procedure for the relevant flow parameters showed an excellent fit to the experimental data with very realistic entrainment backmixing factors, fL = fQ = 3.5 percent, the fraction of well-mixed flow in the settlers, (XX = ay = 5 percent and an overall mass transfer capacity coefficient, Ka = 25 s->. 

The stagewise model with backmixing is an essential component of any model representation of a stagewise extraction column. As shown in Sec. 3.3.1.5 the non-ideal flow behaviour is represented by the presence of the N stages in... 

At the molecular level there are several important differences between polymeric fluids and small-molecule fluids. Because of these differences the flow behaviour of polymeric fluids is not similar to that of small-molecule fluids, which are satisfactorily described by Newtonian fluid dynamics. There are several salient features of macromolecular architecture that influence the flow behaviour ... 

Introduction of the reptation concept by De Gennes [43] led to further essential progress. Proceeding from the notion of a reptile-like motion of the polymer chains within a tube of fixed obstacles, De Gennes [43-45], Doi [46,47] and Edwards [48] were able to confirm Bueche s 3.4-power-law for polymer melts and concentrated polymer solution. This concept has the disadvantage that it is valid only for homogeneous solutions and no statements about flow behaviour at finite shear rates are analysed. 

Taking into account the relevance of the range of semi-dilute solutions (in which intermolecular interactions and entanglements are of increasing importance) for industrial applications, a more detailed picture of the interrelationships between the solution structure and the rheological properties of these solutions was needed. The nature of entanglements at concentrations above the critical value c leads to the viscoelastic properties observable in shear flow experiments. The viscous part of the flow behaviour of a polymer in solution is usually represented by the zero-shear viscosity, rj0, which depends on the con-... 

J. Gotz, K. Zick, V. Lehmann, D. Grog, M. Peciar, (Analysis of the mixing and flow behaviour of beer mashes in a stirring vessel by means of NMR flow experiments), in preparation. 

J Mewis. Flow behaviour of concentrated suspensions predictions and measurements. Int J Miner Proc 44-45 17-27, 1996. 

The flow behaviour of rubber on a mill is dependent on the material, nip width, roll speed and temperature, and certain combinations can give flow instabilities, the worst case from the mixing point of view being bagging , i.e., loss of adhesion of the rubber compound to the mill rolls. A decrease in nip width, an increase in speed or temperature, can overcome this problem. 

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