Solid Fluid Flow Research Articles

Modeling Fully Coupled Oil–Gas Flow in a Dual-Porosity Medium

A finite element model has been developed to simulate two-phase, (i.e., oil and gas) flow and solid deformation in a dual-porosity medium. The model accounts for coupling between solid deformations and fluid flow in both the primary medium (representing the matrix pores and solid) and the secondary medium (used to represent fractures in the present study). The model is verified against relevant analytical solutions and then applied to the problem of an inclined wellbore under generalized plane strain conditions, subjected to a three-dimensional in situ state of stress in a fractured formation saturated with oil and gas. A parametric study has been carried out to demonstrate the effect of dual-porosity parameters, phase saturations, and interaction between the two media. The implementation of double effective stress laws in the present study is a significant deviation from some classical dual-porosity models and helps to incorporate the effect of deformation of the secondary medium (representing the fractures).

Chaotic advection in a cavity flow with rigid particles

The effect of freely suspended rigid particles on chaotic material transport in a two-dimensional cavity flow is studied. We concentrate on the understanding of the mechanism how the presence of a particle affects the dynamical system of the flow. In contrast to the case studied by Vikhansky [“Chaotic advection of finite-single bodies in a cavity flow,” Phys. Fluids 15, 1830 (2003)], we show that even a regular periodic motion of a single particle can induce chaotic advection around the particle, as a result of the perturbation of the flow introduced by the freely rotating solid particle. This perturbation is of a hyperbolic nature. In fact, stretching and folding of the fluid elements are guaranteed by the occurrence of the hyperbolic flow perturbation centered at the particle and by the rotation of the freely suspended particle, respectively. The fluid-solid flow problem has been solved by a fictitious-domain/finite-element method based on a rigid-ring description of the solid particle. A single-particle system is studied in detail in view of the dynamical systems theory and then extended to two- and three-particle systems.

Mirror fluid method for numerical simulation of sedimentation of a solid particle in a Newtonian fluid

The mirror fluid method is proposed for simulating solid-fluid two-phase flow. The whole computational domain is modeled as an Eulerian one for the fluid with a Lagrangian subdomain embedded in it. The boundary condition is enforced implicitly on solid-fluid surface segments by mirror relations. Thus, the total flow is solved in the one domain, in which the solid particle region is replaced with the virtual flow as the mirror image of outside flow. The mirror fluid method is implemented to compute the motion of a rigid spherical or elliptic particle in a Newtonian fluid for the purpose of method validation. The control volume formulation with the SIMPLE algorithm incorporated is used to solve the governing equations on a staggered grid in a two-dimensional coordinate system. A number of numerical experiments on falling particles are performed and the computational results are in good agreement with the reported experimental data.

Reply to Comment on “Steady-state 226Ra/ 230Th disequilibrium in mantle minerals: implications for melt transport rates in island arcs” by R. George, M. Reagan, S. Turner, J. Gill, B. Bourdon

We agree with George et al. that high 226Ra/ 230Th and correlated Ba/Th, 238U/ 230Th, and other elemental and isotopic ratios are the result of fluid addition to the wedge. The Feineman and DePaolo [Earth Planet. Sci. Lett. 215 (2003) 339–355] manuscript addresses more specifically the pathway followed by the fluid en route to the surface. In particular, we address whether the 226Ra/ 230Th data directly yield the total time available for the fluid to migrate from the point of origin in the slab to the melting region in the wedge, and ultimately to the surface with the melt. All of the processes involved in generating arc volcanism would of necessity have to take place very rapidly within the constraints proposed by George et al. The alternative is that the upward fluid movement is hindered by the fluid flow regime and solid mantle flow, allowing more time for reaction with the mantle wedge. There is evidence in the U-series data for more than one time scale, and our model helps to explain how this could come about. The extent to which grainscale 226Ra/ 230Th disequilibrium affects the inferred melt transport time is yet another issue, and this could be achieved either with the small-degree melt mechanism we discussed or by additional effects associated with melt and fluid migration at later stages in the melt generation process. We agree that the final melt transport event is likely to happen quickly. One of the most puzzling features of volcanic arcs is that the volcanic front emerges considerably behind the presumed location of primary water release from the subducting slab (depth to slab is ∼120 km beneath the volcanic front, as opposed to the predicted ∼80 km). This offset between the expected site of fluid release and the location of the volcanic front can be attributed to coupled transport of the fluid—in the form of hydrous minerals, such as amphibole and/or phlogopite in the wedge [J. Geophys. Res. 97 (1992) 2037–2070] or redirection of the melt due to flow and stresses in the mantle matrix as the magma slowly percolates upward [J. Geol. 95 (1987) 285–307]. In either case, the fluid and/or melt is required to ascend slowly, at least for some part of its journey, to explain the location of the volcanic front. Furthermore, 238U/ 230Th disequilibria in arc lavas seem to suggest a relatively long interval for fluid addition (∼30–60 ka) [Science 292 (2001) 1363–1366; Earth Planet. Sci. Lett. 179 (2000) 581–593; Geochim. Cosmochim. Acta 61 (1997) 4855–4884], which is difficult to reconcile with the 226Ra/ 230Th disequilibrium observed in the lavas. For these reasons, we sought to find a means whereby apparently short-lived isotopic disequilibria could be maintained during complex fluid and melt migration in the mantle wedge. Below, we address a few of the main issues presented by George et al. [Earth. Planet. Sci. Lett. this issue] in their comment.

New Iterative Coupling Between a Reservoir Simulator and a Geomechanics Module

SummaryInteractions of solid mechanics and fluid flow have been studied by numerous researchers for the past several years. Different methods of coupling such as full and iterative coupling have been used. Nevertheless, the accuracy and the large run time of the coupled solid-mechanics fluid-flow model are outstanding issues that prevent the application of the coupled model in full-field studies. In this work, a novel relationship of porosity as a function of pressure, temperature, and mean total stress is developed for iterative coupling of stress and flow. The new formula not only improves the accuracy of the coupling but also reduces substantially the number of coupling iterations. The latter feature decreases significantly the CPU time. The new approach was implemented in a modular, iteratively coupled system. The rapid convergence provides the equivalent of a fully coupled method that is necessary to investigate complex coupled problems. The main advantage of this type of coupling is that a geomechanics module can be easily coupled with different reservoir simulators. The paper gives some comparisons of results obtained by the new porosity formula with another formulation.

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.

The effect of interparticle cohesive forces on the simulation of fluid flow in spout-fluid beds

As reflected in the literature, solid-fluid flow characteristics in spouted beds can vary widely when particles are coated by a suspension. This work is aimed at describing the effect of interparticle forces on airflow distribution in conical spouted beds of inert particles coated by Eucalyptus black liquor. The simulator developed earlier is modified to incorporate this effect. Two corrective functions with adjustable parameters are introduced into the simulator gas-flow model to generate the minimum spouting conditions in beds wetted by this liquor. These functions are assumed to be dependent on characteristic suspension groups and bed height. Using the particle swarm optimization (PSO) technique, expressions for these functions are obtained. Simulated results are presented and discussed to validate this technique. Implications of these results on drying Eucalyptus black liquor in conical spouted beds are analyzed.

A 3D conjugate heat transfer model for continuous wire casting

A three-dimensional (3D) model of heat transfer and equilibrium-solidification for a continuous wire casting process has been established using a commercial fluid dynamics programme, Fluent ®. The melt/solid interface was not tracked explicitly. Instead a liquid fraction value was used for each control volume in the domain. Thermal profiles in the melt and throughout the casting assembly were calculated along with solid fraction profiles and fluid flow velocity vectors. 3D visualisation of the melt behaviour inside the casting channel was possible, thus enabling optimum processing windows to be predicted. Fluid flow visualisation also assists the improvement of casting channel design.

Methods for multiphase computational fluid dynamics

This paper presents an overview of the physical models for computational fluid dynamic (CFD) predictions of multiphase flows. The governing equations and closure models are derived and presented for fluid–solid flows and fluid–fluid flows, both in an Eulerian and a Lagrangian framework. Some results obtained with these equations are presented. Finally, the capabilities and limitations of multiphase CFD are discussed.

A new modification of the immersed boundaries method for fluid–solid flows: moderate Reynolds numbers

In this study we consider a combination of an interpolation technique with the D’Alambert principle that allows the direct numerical simulation of fluid-solid flows on a regular rectangular grid. The method models a no-slip boundary with the second-order accuracy interpolation scheme without explicit calculation of the forces that the particles exert at the fluid. The method is applicable for a wide range of Reynolds numbers from creeping flows up to Re≈100.

Workshop Findings

This report outlines scientific issues whose resolution will help advance and define the field of multiphase flow. It presents the findings of four study groups and of a workshop sponsored by the Program on Engineering Physics of the Department of Energy. The reason why multiphase flows are much more difficult to analyze than single phase flows is that the phases assume a large number of complicated configurations. Therefore, it should not be surprising that the understanding of why the phases configure in a certain way is the principal scientific issue. Research is needed which identifies the microphysics controlling the organization of the phases, which develops physical models for the resultant multiscale interactions and which tests their validity in integrative experiments/theories that look at the behavior of a system. New experimental techniques and recently developed direct numerical simulations will play important roles in this endeavor. In gas–liquid flows a top priority is to develop an understanding of why the liquid phase in quasi-fully-developed pipe flow changes from one configuration to another. Mixing flows offer a more complicated situation in which several patterns can exist at the same time. They introduce new physical challenges. A second priority is to provide a quantitative description of the phase distribution for selected fully developed flows and for simple mixing flows (that could include heat transfer and phase change). Microphysical problems of interest are identified––including the coupling of molecular and macroscopic behavior that can be observed in many situations and the formation/destruction of interfaces in the coalescence/breakup of drops and bubbles. Solid–fluid flows offer a simpler system in that interfaces are not changing. However, a variety of patterns exist, that depend on the properties of the particles, their concentration and the Reynolds number characterizing the relative velocity. A top priority is the development of a physical understanding of inertial instabilities which give rise to structural features that have a large range of scales. Important microphysical problems are the understanding of particle/particle interactions, particle/boundary interactions that include the effect of wall roughness, and the influence of particles on fluid turbulence. These behaviors can differ depending on the characteristics of the particles, their size distribution and their concentration. For large concentrations, such as exist in granular flows, instabilities associated with particle–particle interactions often cause separations in systems which are not homogeneous. These instabilities are not well understood. Appropriate averaged equations could provide a way to use an understanding of the microphysics obtained in simple systems to describe more complicated flows. The formulation of these equations presents physical challenges since the structure of the phase distribution could affect the choice of averaging methods and closure relations. Universal computational approaches appear to be out of reach at present.

Chaotic advection of finite-size bodies in a cavity flow

We considered advection of neutrally buoyant discs in two-dimensional chaotic Stokes flow. The goal of the study is to explore a possibility to enhance laminar mixing in batch-flow mixers. Addition of freely moving bodies to periodically driven chaotic flow renders the flowfield nonperiodic [D. F. Zhang and D. A. Zumbrunnen, AIChE J. 42, 3301 (1996)], i.e., the Lagrangian chaos of the bodies motion induces Eulerian chaos of the flow that makes mixing more intensive. The presence of three bodies creates new topological features that do not exist in “pure” fluid. The trajectories of the discs in the augmented phase space tangle and form a braid that leads to so-called topological chaos [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)]. Simulations were performed using a new variant of the immersed boundaries method that allows the direct numerical simulation of fluid–solid flows on a regular rectangular grid without explicit calculation of the forces that the particles exert on the fluid.

Simulation of Particle Impact with a Wedge in Dilute Two-phase Flow

Dilute solid-fluid flow over a wedge in a stationary channel is numerically solved using one-way coupling between fluid and solid particles. The two-dimensional, steady, laminar carrierphaseflow is determined by Galerkin finite-element method using Newton's iteration for primitive variables, pressure, and velocity. Velocity is interpolated biquadratically and pressure is interpolated linearly. Parameter continuation is used to compute solutions for relatively large values of flow Reynolds number. Individual particles are tracked from specified inlet positionsby a fourth-order Runge-Kutta method applied to the equations of motion ofthe particle. Forces acting on the particle include drag, pressure, and inertia. Forces due to particle-particle interaction and Basset forces are neglected. Collisions with the wedge and the walls of the channel are modelled via assumed coefficients ofrestitution in both the normal and the tangential directions. The point of actual impact is determined by interpolation. Results are presented for various parameters, such as particle diameter, wedge angle, Reynolds number, particle density, etc.

Axisymmetric Instability of Fluid Saturated Pervious Cylinders

The emergence of two-phase instability is investigated analytically for the axisymmetric cylinders made of a pervious solid matrix with pores filled with an interstitial fluid. General analytical solutions are derived for a broad range of constitutive models, and are illustrated for a few specific types of solids. For particular combinations of stresses and material moduli, saturated hypoelastic and elastoplastic solids are found to undergo two-phase instability, whereas their dry solid matrices remain stable. Two-phase instability can emerge within stable single-phase solids due to the interaction between solid matrix and fluid flow. The present analysis provides general analytical solutions useful for investigating the instabilities of axisymmetric soil samples subjected to the undrained triaxial tests of geomechanics.

A molecular dynamics approach in simulations of fluid-solid particles flow

In the paper a discrete system of particles carried by fluid is considered in a planar motion. The volumetric density of particles is assumed to be small enough such that they can be treated within the framework of a molecular dynamics model. The fluid is then considered as a carrier of particles. The Landau-Lifshitz concept of turbulence is used to describe the fluctuating part of fluid velocity. This approach is applied to simulate different regimes (laminar and turbulent) and various states of particle motion (moving bed, heterogeneous flow, and homogeneous flow) using only two parameters, which have to be determined experimentally. These two parameters, found for a particular pipe and for a particular velocity from a simple experiment, then can be used for other pipe diameters and different velocities. The computer simulations performed for the flow of particles in pipes at different flow velocities and different pipe diameters agree favorably with experimental observations of the type of flow and critical velocities identifying transitions from one type to another.

固液二相流における固体間の近接相互作用

In solid-fluid two phase flows, the interaction between particles and particle-wall play important roles. They are deeply related not only to individual motions of the particle but to the formation of meso-scale structure such as particle clouds. Therefore the foundamental study on the interaction of particles has been required for modeling the solid-fluid flow. In this paper, theoretical models of short-range interaction between solids in fluid are briefly reviewed. Then we describe the direct simulation of the sedimentation of a solid particle toward a wall, and discuss the fluid force acting on the particle at finite Reynolds number. Furthermore, it is shown that the fluid effects due to the unsteady motion of the particle are significant role on short-range interaction in liquid.

Experimental study of parameters which influence the energy minimum in horizontal gas–solid conveying

Optimization of pneumatic conveying may be achieved by a reduction of energy consumption by working with the lowest velocities. Based on an experimental approach, our study presents, for various products, the influence of several parameters (diameter, density and the shape of the particles) on the saltation velocity, i.e., the velocity corresponding to the lowest energy losses. The tests were carried out on a pneumatic transport test rig of industrial type composed of stainless pipeline of 80 mm inner diameter for a total length of 36 m. From the experimental results and the Zenz state diagram [F.A. Zenz, Two-phase fluid–solid flow, Ind. Eng. Chem., 41 (12) (1949) 2801–2806.], we analyze the variations of the saltation Froude number according to the solids loading ratio. These results enable us to establish a new correlation, which scans a broad spectrum of solids loading ratio.

Obtainment of High-Fructose Solutions from Cashew (Anacardium occidentale) Apple Juice by Simulated Moving-Bed Chromatography

The simulated moving-bed (SMB) technology has been successfully used in separations in the petrochemical, food, and fine chemicals industries. This work is intended to demonstrate the possibility of using this technology to obtain high-fructose solutions from the cashew apple juice, which may represent an attractive economic alternative for its industrial exploitation. The cashew tree is a native tropical plant abundant in Northeastern Brazil, the commercial value of which relies mainly on the processing of its nut. Despite the high nutritional value of the penduncle of the fruit, the cashew apple, approximately 90% of the crop spoils on the soil. Simulation and experimental results are presented for SMB separation of fructose from glucose, both present (˜40 kg/m3) in the aqueous phase of concentrated cashew apple juice. Kinetic and equilibrium data for fructose and glucose on packed columns using cation-exchange resins are reported. Experimental results for SMB operation at 30°C indicate purities close to 90% in each product (fructose-rich extract and glucose-rich raffinate). Simulated predictions of the unit performance and internal profiles agree well with experimental data. To increase the added value and versatility of the products, either an isomerization step for the raffinate or diverse SMB fluid–solid flow rate ratios may be applied. In this way, a wide range of products may be obtained, from nearly pure fructose to 42, 55, and 90% solutions, which are the standard high-fructose syrup concentrations. If solids content is conveniently raised to the standards of commercial high-fructose syrups, these products may be used as food additives, thus confirming a potentially attractive use of the cashew apple juice.

Electrokinetic and Poroelastic Coupling During Finite Deformations of Charged Porous Media

Due to microstructural interactions between the charged solid matrix and ionic interstitial fluid, hydrated biological tissues and other porous media may exhibit macroscopic coupling between solid deformation, fluid, and electrical flows. In the present manuscript, we develop a variationally motivated finite deformation continuum theory for describing such coupled phenomena. The theoretical formulation combines descriptions of poroelastic and electroquasistatic subsystems along with a continuum electromechanical coupling law, and leads to a five-field finite element formulation. Several axisymmetric problems are presented as examples ofmechanical-to-electrical and electrical-to-mechanical transduction phenomena in common experimental configurations.

A variational formulation for coupled physicochemical flows during finite deformations of charged porous media

Polymer gels, hydrated biological tissues and other charged porous media may exhibit macroscopic coupling between solid deformations and internal fluid, chemical and electrical flows. In this manuscript, we develop a variationally motivated finite deformation theory for describing such coupled phenomena. The formulation combines mathematical descriptions of the power balance associated with solid deformation and fluid and solute flows for an arbitrary number of solute species, and includes the macroscopic phenomenological coupling relations of nonequilibrium thermodynamics. Particular implementations of the theory are discussed for a charged, porous medium interacting with a binary electrolyte and for the addition of a third, possibly charged solute species to such a system. This theoretical framework is suitable for modeling physicochemical interactions in a large class of hydrated porous media.