Three‐dimensional incompressible flow calculations using the characteristic based split (CBS) scheme

In this paper, the characteristic based split scheme is employed for the solution of three‐dimensional incompressible viscous flow problems on unstructured meshes. Many algorithm related issues are discussed. Fully explicit and semiimplicit forms of the scheme are explained and employed in the calculation of both isothermal and nonisothermal incompressible flows simulation. The extension of the scheme to porous medium flows is also demonstrated with relevant examples. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of porous disc receiver configurations on performance of solar parabolic trough concentrator

In this article, heat transfer enhancement of line focus solar collector with porous disc receiver is studied with water and therminol oil. A three dimensional (3-D) numerical simulation of porous disc enhanced receiver is carried out using commercial CFD software Fluent 6.3 to evolve the optimum configuration. The 3-D numerical model is solved by renormalization-group based k-ε turbulent model associated with standard wall function. The effect of porous disc receiver configurations (solid disc at bottom; porous disc at bottom; porous disc at top; and alternative porous disc) on performance of the trough concentrator is investigated. The effect of porous disc geometric parameters (φ, θ, W, H and t) and fluid parameters (Pr and m) on heat transfer enhancement of the receiver is also studied. The numerical simulation results show that the flow pattern around the solid and porous discs are entirely different and it significantly influences the local heat transfer coefficient. The porous disc receiver experiences low pressure drop as compared to that of solid disc receiver due to less obstruction. The optimum configuration of porous disc receiver enhances the heat transfer rate of 221 W m⁻¹ and 13.5% with pumping penalty of 0.014 W m⁻¹ for water and for therminol oil-55, heat transfer rate enhances of 575 W m⁻¹ and 31.4% with pumping penalty of 0.074 W m⁻¹ as compared to that of tubular receiver at the mass flow rate of 0.5 kg s⁻¹. The Nusselt number and friction factor correlations are proposed for porous disc receiver to calculate heat transfer characteristics. The porous disc receiver can be used to increase the performance of solar parabolic trough concentrator.     

Contributions to numerical developments in shock waves attenuation in porous filters

The paper deals with the numerical method of the compressible gas flow through a porous filter emphasizing the treatment of the interface between a pure gaseous phase and a solid phase. An incident shock wave is initiated in the gaseous phase interacting with a porous filter inducing a transmitted and a reflected wave. To take into account the discontinuity jump in the porosity between the gaseous phase and the porous filter, an approximate Riemann solver is used to compute homogeneous non-conservative Euler equations in porous media using ideal gas state law. The discretization of this problem is based on a finite volume method where the fluxes are evaluated by a “volumes finis Roe” (VFRoe) scheme. A stationary solution is determined with a continuous variable porosity in order to test the numerical scheme. Numerical results are compared with the two-phase shock tube experiments and simulations of a shock wave attenuation and gas filtration in porous filters are presented.      

Hydrodynamic models of the residual oil distribution in water-flood reservoirs

Models of the residual oil saturation distribution are proposed for linear, axisymmetric, and general flows. The steady displacing fluid flow model makes it possible to find equilibrium residual oil saturation distributions corresponding to given flow regimes by treating the porous medium with capillary-trapped oil as a medium with permeability that depends on the displacement conditions. The dynamics of the mobilized globules of the residual oil are excluded from consideration. The simulation results indicate that the residual oil saturation distribution after stimulation of the wash-out zone by means of enhanced oil recovery techniques is generally essentially nonuniform. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–104, May–June, 2000.     

Modélisation du transport réactif en milieu poreux : schéma itératif associé à une combinaison d'éléments finis discontinus et mixtes-hybridesModelling reactive transport in porous media: iterative scheme and combination of discontinuous and mixed-hybrid finite elements

The sequential iterative approach (SIA) scheme is the most efficient method for modelling reactive transport in porous media with the operator-splitting approach. A combination of finite discontinuous and finite mixed-hybrid elements is a powerful method for solving solute transport in porous media, but the use of this method for SIA scheme induces numerical difficulties. In this paper, a new method is developed to solve reactive transport by using both the SIA scheme and a combination of finite discontinuous and finite mixed elements. The proposed method is tested by modelling a column experiment. To cite this article: J. Carrayrou et al., C. R. Mecanique 331 (2003).     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

An augmented Lagrangian approach to simulating yield stress fluid flows around a spherical gas bubble

We simulated the flow of a yield stress fluid around a gas bubble using an augmented Lagrange approach. The piecewise linear equal‐order finite elements for both the velocity and the pressure approximations proposed and analyzed by Latché and Vola in 2004 were applied. A mesh adaptive strategy based on this element‐pair choice was also proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme was formulated for general Herschel–Bulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble were provided to validate the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

Boundary domain integral method for transport phenomena in porous media

A boundary domain integral method (BDIM) for the solution of transport phenomena in porous media is presented. The complete, so‐called modified Navier–Stokes equations (Brinkman‐extended Darcy formulation with inertial term included) have been used to describe the fluid motion in porous media. Velocity–vorticity formulation (VVF) of the conservative equations is employed. In this paper, the proposed numerical scheme is tested on a particular case of natural convection and the results of flow and heat transfer characteristics of a fluid in a vertical porous cavity heated from the side and saturated with Newtonian fluid are presented in detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Passive control of the flow around a square cylinder using porous media

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two‐dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier–Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

Fundamental Study of Pore Morphology Effect in Low Tension Polymer Flooding or Polymer–Assisted Dilute Surfactant Flooding

Low Tension Polymer Flooding or Polymer Assisted Dilute Surfactant Flooding is generally deployed as a method to produce additional oil trapped in oil reservoirs after waterflooding. Fundamental study of microscopic mechanisms and pore-level phenomena in Polymer Assisted Dilute Surfactant Flooding needs more investigation. Of particular concern and interest is to probe into and document the effect of pore morphology and structure on microscopic phenomena occurring at pore level. No previous works on the effect of pore morphology in Polymer Assisted Dilute Surfactant Flooding has been reported in the literature. In this study, one-quarter five-spot glass micromodels were deployed to examine the effect of porous media morphology and structure on microscopic mechanisms as well as macroscopic behavior of Polymer Assisted Dilute Surfactant Flooding. Four types of pore morphologies were employed to study this factor. Results show that the pore geometric properties in a porous medium will dictate the degree of displacement front instability, capillary imbalance, viscous fingering, wetting characteristics and its distribution, and finally magnitude of ultimate oil recovery. We also found that the formation of flow scheme is dramatically influenced by the pre-designed injection scheme.     

STREAMLINE-BASED MATHEMATICAL MODEL FOR CO2 MISCIBLE FLOODING

According to the research theory of improved black oil simulator, a practical mathematical model for C02 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening andmiscible oil field.reservoir dynamic management of the CO2 miscible oil field.     

Improved non‐staggered central NT schemes for balance laws with geometrical source terms

In this paper we extend the non‐staggered version of the central NT (Nessyahu–Tadmor) scheme to the balance laws with geometrical source term. This extension is based on the source term evaluation that includes balancing between the flux gradient and the source term with an additional reformulation that depends on the source term discretization. The main property of the scheme obtained by the proposed reformulation is preservation of the particular set of the steady‐state solutions. We verify the improved scheme on two types of balance laws with geometrical source term: the shallow water equations and the non‐homogeneous Burger's equation. The presented results show good behaviour of the considered scheme when compared with the analytical or numerical results obtained by using other numerical schemes. Furthermore, comparison with the numerical results obtained by the classical central NT scheme where the source term is simply pointwise evaluated shows that the proposed reformulations are essential. Copyright © 2004 John Wiley & Sons, Ltd.     

A semi‐discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow

In this paper, we develop a new Godunov‐type semi‐discrete central scheme for a scalar conservation law on the basis of a generalization of the Kurganov and Tadmor scheme, which allows for spatial variability of the storage coefficient (e.g. porosity in multiphase flow in porous media) approximated by piecewise constant interpolation. We construct a generalized numerical flux at element edges on the basis of a nonstaggered inhomogeneous dual mesh, which reproduces the one postulated by Kurganov and Tadmor under the assumption of homogeneous storage coefficient. Numerical simulations of two‐phase flow in strongly heterogeneous porous media illustrate the performance of the proposed scheme and highlight the important rule of the permeability–porosity correlation on finger growth and breakthrough curves. Copyright © 2013 John Wiley & Sons, Ltd.     

A simple strategy for constructing bounded convection schemes for unstructured grids

Due to the great geometrical flexibility, popularity for unstructured grid methods in fluid dynamics has been increasing in recent years. In parallel with this interest there is a need for bounded second or higher order convection schemes which can be implemented easily in the unstructured setting. In the present work a simple strategy for achieving convective boundedness in the context of a vertex‐centered unstructured finite volume algorithm is demonstrated. Testing is carried out on an inviscid oblique step problem using both structured and unstructured grid arrangements. Further testing for numerical diffusion is done using a distorted grid in a two dimensional channel. The proposed scheme is straightforward to implement and is found to perform well for the cases considered. The overall algorithm converges well and the limiter appears to introduce little extra numerical diffusion beyond that inherently present in the base scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

Coalescence of oil drops on the skeleton of a porous medium in filtering a water-oil mixture

Two mathematical models of filtration coalescence of oil drops when a water-oil mixture moves through a porous material are proposed. In the first model, coalescence is interpreted as the process of sorption, i.e., the accumulation of the oil phase on the pore surface up to a definite critical value above which the larger drops involved by a filtration flow stall. The second model assumes that the motion of the sorbed oil and the entire mixture obeys the generalized Darcy laws. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 118–124, November–December, 1998.     

Boiling in Porous Media: Model and Simulations

We present a modelization of the heat and mass transfers within a porous medium, which takes into account phase transitions. Classical equations are derived for the mass conservation equation, whereas the equation of energy relies on an entropy balance adapted to the case of a rigid porous medium. The approximation of the solution is obtained using a finite volume scheme coupled with the management of phase transitions. This model is shown to apply in the case of an experiment of heat generation in a porous medium. The vapor phase appearance is well reproduced by the simulations, and the size of the two-phase region is correctly predicted. A result of this study is the evidence of the discrepancy between the air – water capillary and relative permeability curves and water – water vapor ones.     

Microtomography of Imbibition Phenomena and Trapping Mechanism

Water imbibition during the waterflooding process of oil production only sweeps part of the oil present. After water disrupts the oil continuity, most oil blobs are trapped in porous rock by capillary forces. Developing an efficient waterflooding scheme is a difficult task; therefore, an understanding of the oil trapping mechanism in porous rock is necessary from a microscopic viewpoint. The development of microfocused X-ray CT scanner technology enables the three-dimensional visualization of multiphase phenomena in a pore-scale. We scanned packed glass beads filled with a nonwetting phase (NWP) and injected wetting phase (WP) in upward and downward injections to determine the microscopic mechanism of immiscible displacement in porous media and the effects of buoyancy forces. We observed the imbibition phenomena for small capillary numbers to understand the spontaneous imbibition mechanism in oil recovery. This study is one of the first attempts to use a microfocused X-ray CT scanner for observing the imbibition and trapping mechanisms. The trapping mechanism in spontaneous imbibition is determined by the pore configuration causing imbibition speed differences in each channel; these differences can disrupt the oil continuity. Gravity plays an important role in spontaneous imbibition. In upward injection, the WP flows evenly and oil is trapped in single or small clusters of pores. In downward injection, the fingering phenomena determine the amount of trapped oil, which is usually in a network scale. Water breakthrough causes dramatic decrease in the oil extraction rate, resulting in lower oil production efficiency.     

Miscible displacement from fractured porous media

A model of miscible displacement of incompressible fluids from a fractured porous medium is proposed. The model describes the process of displacement of oil by solvents, the cycling process of displacement of aliphatic hydrocarbon gas by dry gas at low repressions on the formation, and other processes of single-phase multicomponent displacement from fractured porous media. Problems relating to the pumping of a neutral admixture and admixture slugs through a fractured porous reservoir are solved.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–110, November–December, 1989.The authors are grateful to K. S. Basniev, A. K. Kurbanov, V. I. Maron, and M. I. Shvidler for useful discussions.     

Influence of physically nonlinear deformation on short-term microdamage of a fibrous material

The structural theory of short-term damage is generalized to the case where the undamaged isotropic matrix of a fibrous composite with transversely isotropic fibers deforms nonlinearly, with microdamages occurring only in the matrix. The basis for this generalization is the stochastic elasticity equations for a fibrous composite with porous matrix whose skeleton deforms nonlinearly. Microvolumes of the matrix meet the Huber-Mises failure criterion. The damaged microvolume balance equation is derived for the physically nonlinear material of the matrix based on the properties of the ultimate microstrength distribution. Together with the equations relating macrostresses and macrostrains of the fibrous composite with porous nonlinear matrix, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the dependences of macrostresses and microdamages on macrostrains are proposed. Uniaxial tension curves are plotted for a fibrous composite with linearly hardening matrix.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 88–97, October 2004.     

结构可控多孔聚酰亚胺含油薄膜的制备及性能研究

利用SiO2硬质微球作模板制备得到多孔聚酰亚胺薄膜,通过改变SiO2微球的含量可以实现聚酰亚胺薄膜孔隙率及内部孔结构的精确控制.利用多孔聚酰亚胺薄膜的多孔结构,真空浸油得到聚酰亚胺含油薄膜.分别对聚酰亚胺含油薄膜的热稳定性能、含油性能及摩擦磨损行为和寿命进行了考察.结果表明:含油薄膜最大含油率可达40.6%,其小孔径特点决定了含油薄膜具有较高的油保持率;润滑油自身的挥发温度决定了含油薄膜的使用工况,其浸入并未对多孔薄膜本身热稳定性能产生影响;润滑油的存在很大程度上提高了多孔聚酰亚胺薄膜的磨损寿命,并随着薄膜含油率的增加而延长;在低转速摩擦条件下,含油薄膜呈现干摩擦和油润滑2种摩擦方式.