Paulo R. de Souza Mendes

A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids

A constitutive model for elasto-viscoplastic thixotropic materials is proposed. It consists of two differential equations, one for the stress and the other for the structure parameter, a scalar quantity that indicates the structuring level of the microstructure. In contrast to previous models of this kind, the structure parameter varies from zero to a positive and typically large number. The lower limit corresponds to a fully unstructured material, whereas the upper limit corresponds to a fully structured material. When the upper limit is finite, the model represents a highly shear-thinning, thixotropic, and viscoelastic liquid that possesses an apparent yield stress. When it tends to infinity, the behavior of a true yield-stress material is achieved. Predictions for rheometric flows such as constant shear rate tests, creep tests, SAOS, and large-amplitude oscillatory shear (LAOS) are presented, and it is shown that, in all cases, the trends observed experimentally are faithfully reproduced by the model. Within the framework of the model, simple explanations are given for the avalanche effect and the shear banding phenomenon. The LAOS results obtained are of particular importance because they provide a piece of information that so far is absent in the literature, namely a quantitative link between the Lissajous–Bowditch curve shapes and rheological effects such as elasticity, thixotropy, and yielding.

Obstruction of pipelines due to paraffin deposition during the flow of crude oils

Heavy hydrocarbons tend to precipitate off waxy crude oils as they flow through tubes. The precipitated paraffin deposits on the tube inner wall, narrowing the flow passage and eventually reducing drastically the rate of flow. A simple theory that gives the thickness of deposited layer as a function of axial position and time is presented. Experiments were carried out in order to validate the theoretical model. Results are presented in the form of time evolution of axial distributions of pressure, temperature and layer thickness. It is shown that the simple model is capable of predicting the correct order of magnitude of important engineering quantities such as pressure and flow rates as functions of time.

Heat transfer to non-Newtonian fluids in laminar flow through rectangular ducts

Abstract Heat transfer to non-newtonian fluids flowing laminarly through rectangular ducts is examined. The conservation equations of mass, momentum, and energy are solved numerically with the aid of a finite volume technique. The viscoelastic behavior of the fluid is represented by the Criminale-Ericksen-Filbey (CEF) constitutive equation. Secondary flows occur due to the elastic behavior of the fluid, and, consequently, heat transfer is strongly enhanced. It is observed that shear thinning yields negligible heat transfer enhancement effect, when compared with the secondary flow effect. Maximum heat transfer is shown to occur for some combinations of parameters. Thus, there are optimal combinations of aspect ratio and Reynolds numbers, which depend on the fluids mechanical behavior. This result can be usefully explored in thermal designs of certain industrial processes.

Inelastic constitutive equations for complex flows

A new class of inelastic constitutive equations is presented and discussed. In addition to the rate-of-strain tensor, the stress is assumed to depend also on the relative-rate-of-rotation tensor, a frame-indifferent quantity that brings information about the nature of the flow. The material functions predicted by these constitutive equations are given for simple shear and uniaxial extension. A special case of these equations takes the Newtonian form, except that the viscosity is a function of the invariants of both kinematic tensors on which the stress depends. This simple constitutive equation has potential applications in liquid flow process simulations, since it combines simplicity with the capability of responding independently to shear and extension, as real liquids seem to do. Finally, possible forms for the new viscosity function are discussed.

Heat transfer to viscoplastic materials flowing laminarly in the entrance region of tubes

Abstract Heat transfer in the entrance-region flow of viscoplastic materials inside tubes is analyzed. The flow is laminar and the material viscosity is modeled by the Herschel–Bulkley equation. The conservation equations are solved numerically via a finite volume method. Two different thermal boundary conditions are considered, namely, uniform wall temperature and uniform wall heat flux. The effect of temperature-dependent properties is also investigated. The Nusselt number is obtained as a function of the axial coordinate, yield stress, and power-law exponent. Results show that the same trend is observed for the two thermal boundary conditions, but the Nusselt numbers are always higher for the isoflux-wall cases. The length of the entrance region decreases as the material behavior departs from the Newtonian one. Finally, it is observed that neglecting the temperature dependence of material properties may introduce important errors in the heat transfer coefficient.

Heat transfer to viscoplastic materials flowing axially through concentric annuli

Abstract Heat transfer in the entrance-region laminar axial flow of viscoplastic materials inside concentric annular spaces is analyzed. The material is assumed to behave as a generalized Newtonian liquid, with a modified Herschel–Bulkley viscosity function. The governing equations are solved numerically via a finite volume method. Two different thermal boundary conditions at the inner wall are considered, namely, uniform wall heat flux and uniform wall temperature. The outer wall is considered to be adiabatic. The effect of yield stress and power-law exponent on the Nusselt number is investigated. It is shown that the entrance length decreases as the material behavior departs from Newtonian. Also, it is observed that the effect of rheological parameters on the inner-wall Nusselt number is rather small.

Bingham’s model in the oil and gas industry

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.

The quasilinear large-amplitude viscoelastic regime and its significance in the rheological characterization of soft matter

We present a novel approach for using large-amplitude oscillatory shear flow experiments (LAOS) to determine—in a simple, direct, and robust manner—the mechanical behavior of materials that possess a microstructure and may exhibit solidlike, liquidlike, viscoelastic, viscoplastic, and/or thixotropic behavior. As the stress amplitude and frequency are independently varied, two classes of motion are observed: (i) structure-changing motions, characterized by a nonsinusoidal response, when the stress amplitude is large enough to cause microstructural changes and the frequency is of the order of the reciprocal of the time scale of microstructural changes; and (ii) constant-structure motions, characterized by a sinusoidal response, when either the stress amplitude is not large enough to cause microstructural changes or the stress amplitude is large enough to cause microstructural changes but the frequency is much larger than the reciprocal of the time scale of microstructural changes. For a commercial hair gel,...

Crossflow of viscoplastic materials through tube bundles

Abstract The flow of viscoplastic materials through staggered arrays of tubes is analyzed. The mechanical behavior of the materials is assumed to obey the generalized Newtonian liquid (GNL) model, with a viscosity function given by the biviscosity law. The governing equations of this flow are solved numerically using a finite-volume method with a non-orthogonal mesh. For a representative range of the relevant parameters, results are presented in the form of velocity, pressure and viscosity fields. The pressure drop is also given as a function of rheological and geometric parameters.

Flow of elasto-viscoplastic liquids through a planar expansion-contraction

The steady flow of incompressible elasto-viscoplastic liquids through a planar expansion–contraction is investigated. A novel constitutive model is employed to describe the mechanical behavior of the flowing liquids. Numerical solutions of the constitutive and conservation equations were obtained via a finite element method to investigate the role of elasticity, yield stress, and inertia. The fields of velocity, stress, elastic strain, and rate of strain were obtained for different combinations of the governing parameters. It was observed that these fields, as well as the shape and position of the yield surface, are all strong functions of elasticity, yield stress, and inertia. The trends observed agree well with previous numerical and visualization results available in the literature. The present work offers a detailed study on the effects of elasticity, presenting, in particular, the fields of elastic strain.