Flow Of non-Newtonian Power-law Fluid Research Articles

Analysis of flow of power-law non-Newtonian fluids in hollow fiber membrane modules

The primary objective is to analyze the flow of non-Newtonian fluid in the hollow fiber membrane module on the basis of the power-law model. The problems of both filtration and permeation of power-law fluids through the fiber wall are solved numerically

Non-Newtonian fluid flow development in a circular pipe

Laminar non-Newtonian power-law fluid flow development in a pipe has been obtained by studying a hydrodynamically equivalent Newtonian analogue of the problem. Several integral solutions of the problem have been presented and their predictions have been compared with another similar solution.

Darcy-Forchheimer natural, forced and mixed convection heat transfer in non-Newtonian power-law fluid-saturated porous media

The governing equation for Darcy-Forchheimer flow of non-Newtonian inelastic power-law fluid through porous media has been derived from first principles. Using this equation, the problem of Darcy-Forchheimer natural, forced, and mixed convection within the porous media saturated with a power-law fluid has been solved using the approximate integral method. It is observed that a similarity solution exists specifically for only the case of an isothermal vertical flat plate embedded in the porous media. The results based on the approximate method, when compared with existing exact solutions show an agreement of within a maximum error bound of 2.5%.

Heat transfer to non-Newtonian power-law fluid past a continuously moving porous flat plate with heat flux

The analysis of heat transfer to the non-Newtonian power-law fluid flow past a continuously moving flat porous plate in presence of suction/injection with heat flux has been presented. We have obtained the solution using the method of successive approximations, starting with zero approximation. It has been observed that the results obtained forn=1 are in good agreement with the corresponding results for Newtonian fluid. For various values of flow indexn and the suction/injection parameter, temperature profiles and rate of heat transfer have been presented graphically. The effect of suction is to decrease in temperature and the rate of heat transfer, while reverse nature occurs for injection.

Transient spherical flow of non-newtonian power-law fluids in porous media

The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.

Well Test Analysis for Two-Phase Flow of Non-Newtonian Power-Law and Newtonian Fluids

Analysis of injectivity and falloff test data is considered during two-phase flow of non-Newtonian and Newtonian fluids. The non-Newtonian fluids considered are power-law fluids. Two sets of relative permeability data representing preferentially water wet and oil wet systems are considered. The conditions under which saturation gradients develop are thoroughly investigated. The effects of finite radius skin region and rock compressibility on pressure response are also investigated. During two-phase flow of power-law and Newtonian fluids, saturation gradients do not develop under most practical conditions. Injectivity and falloff data can be analyzed using available techniques with appropriate definitions of dimensionless variables for two-phase flow. When saturation gradients exist, the response of this transition region is not interpretable by available methods.

Unsteady thermal entrance heat transfer of power-law fluids in pipes and plate slits

An instant-local similarity method is proposed to analyze the unsteady state Graetz problems. Unsteady heat transfer for fully-developed laminar flow of power-law non-Newtonian fluids in the thermal entrance region of pipes and plate slits, with viscous dissipation considered, is studied. For the unsteady thermal entrance heat transfer problems, only large Graetz numbers (small normalized axial distance) are concerned and the normalized time from transient up to steady state is of order 10 −1; therefore, the instant-local similarity approach gives results of high accuracy. The effects of the flow index, viscous dissipation and Graetz number on the heat transfer rate are demonstrated with numerical solutions. The corresponding steady-state Graetz problems are studied by the local similarity method whose solutions agree very well with the extended Leveque solutions particularly for large Graetz number and Brinkman number.

Pressure Transient Behavior of Non-Newtonian/Newtonian Fluid Composite Reservoirs

Abstract Pressure transient theory of flow of non-Newtonian power-law fluids in porous media is extended to non-Newtonian/Newtonian fluid composite reservoirs. This paper examines application of non-Newtonian and conventional (Newtonian) well test analysis techniques to injectivity and falloff tests in wells where different amounts of non-Newtonian fluids have been injected into the reservoir to displace the in-situ Newtonian fluid (oil and/or water). Early time pressure data can be analyzed by non-Newtonian well test analysis methods. Conventional semilog methods may be used to analyze late time falloff data. The location of the non-Newtonian fluid front can be estimated from well tests using the radius of investigation equation for power-law fluids. An equation for calculating shear rates and apparent viscosities for power-law fluids in reservoirs is presented. An example problem is used to illustrate observations and solution techniques.

Apparent viscosity of a fluid–gas mixture

AbstractThe inertia free flow of a one‐dimensional, isothermal fluid–gas mixture in a tube of constant radius is analyzed. The fluid is viscous, non‐Newtonian, and incompressible; the gas is inviscid and compressible. Integration of the equations of continuity, momentum, and state enable the prediction of axial pressure, velocity, density, volumetric flow rate, and shear–stress profiles. Departures from corresponding profiles observed in the flow of non‐Newtonian power‐law fluids are evident. The apparent viscosity of the fluid–gas mixture is computed and compared to that of the fluid alone. A reduction in apparent viscosity is noted. Previously reported experimental evidence of a reduction in viscosity in a non‐Newtonian fluid–gas mixture is recalled and it is claimed that the physical model presented here is capable of explaining the observed reduction in apparent viscosity.

Wellbore Storage and Skin Effects During the Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

AbstractA model recently presented by Ikoku and Ramey for non-Newtonian power-law flow in porous media was extended to flow in finite circular reservoirs. A constant flow rate was stipulated at the wellbore, and two boundary conditions were considered: no-flow outer boundary and constant-pressure outer boundary. The results were used to derive a new expression for the stabilization time for power-law flow in porous media.Wellbore storage and skin effects always distort the transient pressure behavior of wells in petroleum reservoirs. It is important to investigate the consequences of these phenomena and be able to interpret real well test information. This paper considers the effects of skin and wellbore storage on the transient flow of non-Newtonian power-law fluids in petroleum reservoirs.A new numerical wellbore storage simulator was used to study the effects of skin and wellbore storage during the transient flow of power-law fluids in infinitely large and finite circular reservoirs. Results are presented both in tabular form and as log-log graphs of dimensionless pressures vs dimensionless times. The log-log graphs may be used in a type-curve matching procedure to analyze short-time well test data.The early period is dominated by wellbore storage effect. A new expression was obtained for the duration of wellbore storage effect when skin exists for infinitely large reservoirs. This criterion is not valid for finite circular reservoirs with no-flow outer boundary or constant-pressure outer boundary. Results indicate that there is no apparent end of wellbore storage effect for the no-flow outer boundary condition for the values of external radius presented. New relationships were derived for skin presented. New relationships were derived for skin factor and "effective well radius" for power-law flow.

Influence of vibrations of non-Newtonian fluid flow

The influence of vibrations on the exit flow of non-Newtonian power-law fluids from a vessel through capillaries of various diameters is investigated. It is found that the superposition of vibrations can either decrease or increase the time to empty the vessel.

Flow of Non-Newtonian Power-Law Fluids Through Porous Media

Abstract The partial differential equation that describes the flow, of non-Newtonian, power-law, slightly compressible fluids in porous media is derived. An approximate solution, in closed form, is developed for the unsteady-state flow behavior and verified by. two different methods. Using the unsteady-state solution, a method for analyzing injection test data is formulated and used to analyze four injection tests. Theoretical results were used to derive steady-state equations of flow, equivalent transient drainage radius, and a method for analyzing isochronal test data. The theoretical fundamentals of the flow, of non-Newtonian power-law fluids in porous media are established. Introduction Non-Newtonian power-law fluids are those that obey the relation = constant. Here, is the viscosity, e is the shear rate at which the viscosity is measured, and n is a constant. Examples of such fluids are polymers. This paper establishes the theoretical foundation of the flow of such fluids in porous media. The partial differential equation describing this flow is derived and solved for unsteady-state flow. In addition, a method for interpreting isochronal tests and an equation for calculating the equivalent transient drainage radius are presented. The unsteady-state flow solution provides a method for interpreting flow tests (such as injection tests).Non-Newtonian power-law fluids are injected into the porous media for mobility control, necessitating a basic porous media for mobility control, necessitating a basic understanding of the flow behavior of such fluids in porous media. Several authors have studied the porous media. Several authors have studied the rheological properties of these fluids using linear flow experiments and standard viscometers. Van Poollen and Jargon presented a theoretical study of these fluids. They described the flow by the partial differential equation used for Newtonian fluids and accounted for the effect of shear rate on viscosity by varying the viscosity as a function of space. They solved the equation numerically using finite difference. The numerical results showed that the pressure behavior vs time differed from that for Newtonian fluids. However, no methods for analyzing flow-test data (such as injection tests) were offered. This probably was because of the lack of analytic solution normally required to understand the relationship among the variables.Recently, injectivity tests were conducted using a polysaccharide polymer (biopolymer). The data showed polysaccharide polymer (biopolymer). The data showed anomalies when analyzed using methods derived for Newtonian fluids. Some of these anomalies appeared to be fractures. However, when the methods of analysis developed here were applied, the anomalies disappeared. Field data for four injectivity tests are reported and used to illustrate our analysis methods. Theoretical Consideration General Consideration The partial differential equation describing the flow of a non-Newtonian, slightly compressible power-law fluid in porous media derived in Appendix A is ..........(1) where the symbols are defined in the nomenclature. JPT P. 155

Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

Abstract The transient flow behavior of non-Newtonian fluids in petroleum reservoirs is studied. A new partial differential equation is derived. The diffusivity equation is a special case of the new equation. The new equation describes the flow of a slightly compressible, non-Newtonian, power-law fluid in a homogeneous porous medium. This equation should govern the flow of most non-Newtonian oil-displacement agents used in secondary and tertiary oil-recovery projects, such as polymer solutions, micellar projects, such as polymer solutions, micellar solutions, and surfactant solutions. Analytical solutions of the new partial differential equation are obtained that introduce new methods of well-test analysis for non-Newtonian fluids. An example is presented for using the new techniques to analyze injection well-test data in a polymer injection project. project. Graphs of the dimensionless pressure function also are presented. These may be used to investigate the error when using Newtonian fluid-flow equations to model the flow of non-Newtonian fluids in porous media. Introduction Non-Newtonian fluids, especially polymer solutions, microemulsions, and macroemulsions, often are injected into the reservoir in various enhanced oil-recovery processes. In addition, foams sometimes are circulated during drilling. Thermal recovery of oil by steam and air injection may lead to the flow of natural emulsions and foams through porous media. Some enhanced oil-recovery projects involving the injection of non-Newtonian fluids have been successful, but most of these projects either failed or performed below expectation. These results suggest the need for a thorough study of the stability of non-Newtonian fluids at reservoir conditions, and also a new look at the flow of non-Newtonian fluids in porous media. porous media. Many studies of the rheology of non-Newtonian fluids in porous media exist in the chemical engineering, rheology, and petroleum engineering literature. In 1969, Savins presented an important survey on the flow of non-Newtonian fluids through porous media. In some cases, he interpreted porous media. In some cases, he interpreted published data further and compared results of published data further and compared results of different investigators. van Poollen and Jargon presented a numerical study of the flow of presented a numerical study of the flow of non-Newtonian fluids in homogeneous porous media using finite-difference techniques. They considered steady-state and unsteady-state flows and used the Newtonian fluid-flow equation. They considered non-Newtonian behavior by using a viscosity that varied with position. No general method was developed for analyzing flow data. Bondor et al. presented a numerical simulation of polymer presented a numerical simulation of polymer flooding. Much useful information on polymer flow was presented, but transient flow was not considered.At present, there is no standard method in the petroleum engineering literature for analyzing petroleum engineering literature for analyzing welltest data obtained during injection of non-Newtonian fluids into petroleum reservoirs. However, injection of several non-Newtonian oil-displacement agents is an important oilfield operation. Interpretation of well-test data for these operations should also be important. Obviously, procedures developed for Newtonian fluid flow are not appropriate. SPEJ P. 164

The Flow of Power-Law Non-Newtonian Fluids in Concentric Annuli

The Flow of Power-Law Non-Newtonian Fluids in Concentric Annuli

Solutions of Laminar Jet Flow Problems for Non-Newtonian Power-Law Fluids

Solutions are presented for laminar flow of non-Newtonian power-law fluids. The flow configurations cover the two-dimensional plane and radial free jets, the axisymmetrical (circular) free jet, and the plane and radial wall jets. When the flow behavior index is unity, the present results agree well with those already published for the case of Newtonian fluids.

Non-Newtonian flow along needles

The analysis of incompressible laminar boundary-layer flow of power-law non-Newtonian fluids along thin needles is presented. Similarity velocity profiles and skin friction are obtained for pseudo-plastic, dilatant, as well as Newtonian fluids. Physical insights are gained by examining the effects of the flow behavior index and the needle size on the boundary layer flow.

A variational principle for the two-dimensional boundary-layer flow of non-newtonian power-law fluids

This paper is devoted to the theoretical analysis of steady and unsteady boundary layer problems for non-Newtonian power-law fluid flow using a new variational principle ofHamilton's type. The standard method of variational calculus in the form of partial integration is a basic tool for obtaining approximative solutions. The main characteristic of the variational principle developed here is that all basic rules of variational calculus are preserved. The results are found to be in good agreement with those obtained by other authors. Several examples of practical importance, such as steady flow around a flat plate, a wedge and a circular cylinder as well as impulsive motion of a flat plate and a circular cylinder are considered in detail.

The axisymmetrical boundary layer for a power-law non-Newtonian fluid on a slender cylinder

The axisymmetrical laminar boundary layer flow of power-law non-Newtonian fluids along a slender circular cylinder is investigated by obtaining solutions in series form. The effect of the transverse curvature on the skin friction has been found to be significant at moderate and large distances from the leading edge.

Extrusion of Polymer Melts and Melt Flow Instabilities. III. Theoretical Analysis of Extrusion through a Slit Die

Abstract In the previous sections of this paper we have discussed our own and other experimental studies of flow instabilities in the extrusion of polymer melts as well as various theories of the mechanism of initiation of the instability. It is our belief that one of the keys to a deeper understanding of this phenomenon is a fuller analytical understanding of the stress and velocity fields in the composite reservoir, capillary, and extrudate system. It is to this problem that we turn our attention here. The velocity, stress-field problem in the entrance region of a conduit being fed from a reservoir has received considerable attention for Newtonian fluids. Most authors have followed Schlichting and Goldstein in using boundary-layer theory to analyze this problem. While there are a number of such solutions for viscous non-Newtonian and viscoelastic fluids, they are of little interest for polymer melts. This is not only because they represent a high Reynolds number, inertia-dominated asymptote but because they neglect all phenomena occurring in the reservoir feeding the conduit. Of more interest are the low Reynolds number creeping flow solutions for Newtonian fluids which are based upon the work of Sampson (see also Roscoe and Weissberg). A decade ago Tomita published a pioneering analysis of the creeping flow of a viscous non-Newtonian (power-law) fluid into a sharp edge entrance of a capillary. More recently LaNieve and Bogue have analyzed the creeping flow of a Coleman-Noll second order into the capillary entrance. A recent study of the entry problem has been made by Metzner, Uebler, and Chan Man Fong. The related problem of creeping flow of a viscoelastic fluid in a converging channel or cone has been analyzed by Adams, Whitehead, and Bogue and Kaloni. While the former authors computed the stress field for a second-order fluid and an integral constitutive equation in a presumed velocity field, Kaloni actually evaluated velocity profiles and predicted the formation of secondary flows. A more intuitive, but far less rigorous approach to extrusion of a viscoelastic fluid has been taken by Dexter and Dienes and Smith. These authors presume a virgin material to enter a capillary die in fully developed flow and utilize the theory of linear viscoelasticity to evaluate the stress field.

The laminar‐turbulent transition for flow in pipes, concentric annuli, and parallel plates

Recently Ryan and Johnson proposed a stability parameter for pipe flow. For Newtonian fluids they showed that this parameter Z is proportional to the critical Reynolds number (D anti nu rho/..mu..) and is given by the relation Z = 2 ..sqrt..1/27 N/sub Rec/. They also demonstrated the utility of Z as a stability parameter for the isothermal pipe flow of power-law non-Newtonian fluids. In the present paper a generalized stability parameter will be proposed which is independent of the geometry of the flow system, is proportional to the Reynolds number for Newtonian flow, and contains Ryan and Johnson's results for pipe flows in general as a special case.