Gravitational migration of fuel in porous media

Fuel migration in a water flowing through a porous medium generally occurs parallel to porous strata, which may not be horizontal. In this case, gravity tends to cause vertical segregation of fluids, depending on their densities. This phenomenon can exert a strong effect on fuel migration. The gravitational force creates the buoyancy force which acts upon the fuel, and may be either parallel or anti-parallel to the water flow direction.In this study, the above effects are investigated using the one-dimensional model of Pistineret al. We go beyond the latter investigation in describing the influence of the gravitational forces upon the movement of fuel saturation fronts in a vertical porous layer against and along the water flow direction.It is found that when the directions of the buoyancy force and of the water flow are anti-parallel, fuel migrates in the direction of the buoyancy force, provided the latter is strong enough. However, in the case of a weak buoyancy force, the direction of migration of the fuel depends on its mass. Small fuel masses move mainly in the direction of the water flow. However, big fuel slugs possessing large masses will move mainly in the direction of the buoyancy force. Slugs, characterized by intermediate masses, have no preferable moving direction and are almost stagnant.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Hydrodynamic Effects in Two-Phase Multicomponent Mixture Flow through a Porous Medium in Oil Reservoirs with a Complex Structure

The features of the hydrodynamic processes in stratified inhomogeneous oil reservoirs are investigated using a numerical solution of the equations of two-phase multicomponent flow through a porous medium. The structures of the two-phase flows caused by the reservoir structure and the hydrodynamic interaction between the phases are analyzed in relation to problems of the displacement of oil by water in ordinary flooding and in the presence of moving thickener slugs.     

Development of a high performance flexible porous burner(FPMB) with an adjustable cooling effect

A high performance flexible porous medium burner that can burn gaseous and liquid fuel with different type of flames(premixed and non-premixed) is proposed. The merit of the combustion within porous medium is that heat is recirculated from the combustion gas to porous medium at upstream wherein vaporization is taken place(in case of liquid fuel) or preheated(in case of gaseous fuel) before mixing with the combustion air followed by combustion within another porous medium at downstream. In a former version of the high performance flexible porous medium burner, the upstream porous medium is incorporated with a cooling system using the combustion air as a coolants to prevent thermal decomposition of fuels and thus the burner clogging caused by carbon deposit within the porous medium can be avoided. However, the cooling effect cannot be properly controlled such that the boiling point of the liquid fuel is maintained at suitable value irrespective of the volume flow rate of the combustion air,which is linearly varied with the firing rate of the burner. In particular at the lean burn condition, where high air flow rate is required with high cooling effect with porous medium. This can result in the porous medium temperature lower than the corresponding boiling point of the liquid fuel and thus evaporation of the fuel is failed and the combustion is ceased. Therefore, method of controlling the cooling air flow rate in the porous medium is proposed and studied in order to appropriately control the porous medium temperature and maintain it at above the boiling point irrespective of the combustion conditions. In this research, experimental and computation analysis are used to design the flexible porous burner(FPMB),with adjustable cooling effect. The result shows that, the new design of FPMB which has temperature in the upstream porous medium is higher than boiling point and lower than thermal decomposition temperature of fuel(kerosene) at all conditions and can be operated at a wide range of equivalence ratio without fuel decomposition and fuel non-vaporization problem.     

An investigation of hydraulic fracturing. Part II: two-phase flow model

In the previous work presented in Part I (Theoret. Appl. Fracture Mech. 18, 89–102 (1993)), hydraulic fracture in an infinitely large saturated porous medium is analyzed under an assumption of one-phase flow in the medium. The investigation is extended in this paper to the case of a two phase saturated immiscible flow of oil and water in the porous medium. The medium is initially saturated with oil. Flow in the medium is induced by diffusion of water injected into the fracture. The quasi-static growth of the fracture for a prescribed injection rate is analyzed based on the assumptions that the pressure in the fracture is uniform and that the permeating flow in the medium is unidirectional. The constant fracture toughness criterion for plane strain deformation is employed and the effect of capillary pressure is neglected. Empirical formulas are used for the permeabilities of the oil and water phases. It is seen that the distributions of water saturation and pore pressure in the medium are governed by two nonlinear partial differential equations. Numerical solutions are obtained by a finite difference scheme with iterations. It is found that the injected water is restricted within a layer near the surface of the fracture whose thickness is small compared with the length of the fracture. Thus the flow in the medium is governed essentially by the oil phase. To compare our problem with the corresponding problem of one-phase flow, we find that the difference in crack growth in these two problems is small for the ration of kinematic viscosities of the oil and water phases within the practical range. Hence our study confirms the validity of the one phase flow assumption used in the previous work for prediction of hydraulic fracture growth.     

Stable Propagation of Saturation Overshoots for Two-Phase Flow in Porous Media

Propagation of saturation overshoots for two-phase flow of immiscible and incompressible fluids in porous media is analyzed using different computational methods. In particular, it is investigated under which conditions a given saturation overshoot remains stable while moving through a porous medium. Two standard formulations are employed in this investigation, a fractional flow formulation and a pressure–saturation formulation. Neumann boundary conditions for pressure are shown to emulate flux boundary conditions in homogeneous media. Gravity driven flows with Dirichlet boundary conditions for pressure that model infiltration into heterogeneous media with position-dependent permeability are found to exhibit pronounced saturation overshoots very similar to those seen in experiment.     

Primary and Secondary Infiltration of Wetting Liquid Sessile Droplet into Porous Medium

The infiltration of a wetting droplet into the porous medium is a two-step process referred to as primary and secondary infiltration. In the primary infiltration there is a free liquid present at the porous medium surface, and when no fluid is left on the surface, the secondary infiltration is initiated. In both situations the driving force is the capillary pressure that is influenced by the local medium heterogeneities. A capillary network model based on the micro-force balance is developed with the same formulation applied to both infiltrations. The only difference between the two is that the net liquid flow into the porous medium in the secondary infiltration is equal to zero. The primary infiltration starts as a single-phase (fully saturated) flow and may proceed as a multiphase flow. The multiphase flow emerges as the interface (flow front) becomes irregular in shape. The immobile clusters of the originally present phase can be locally formed due to entrapment. Throughout the infiltration, it was found that portions of the liquid phase can be detached from the main body of the liquid phase forming some isolated liquid ganglia that increase in number and decrease in size. The termination of the secondary infiltration occurs once the ganglia become immobile due to their reduction in size. From the transient solution, the changes in the liquid saturation and capillary pressure during the droplet infiltration are determined. The solution developed in this study is used to investigate the droplet infiltration dynamics. However, the solution can be used to study the flow in fuel cell, nano-arrays, composites, and printing.     

高温高压气体在低含水率介质中迁移的数值模拟

针对气液两相非等温渗流模型高度非线性的特点,发展了适宜的数值离散方法。根据相态转换准则和控制方程的性质,采用最低饱和度法简化算法。空间离散方面,使用有限体积法;时间离散方面,设计了一套包含合理求解顺序的Picard迭代法,解决了方程组强耦合的问题。利用上述数值方法对高温高压气体的迁移行为进行数值模拟,证明了气体在低含水率介质和等效孔隙度的干燥介质内的运动基本一致,并分析了空腔内的气液相态转变过程。在此基础上,研究了多孔介质孔隙度和渗透率对气体压强演化和示踪气体迁移的影响。研究表明,孔隙度越小（相同渗透率）、渗透率越高（相同孔隙度）,示踪气体的迁移距离越远,并给出了估算不同孔隙度和渗透率下迁移距离的半经验公式。     

A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media

The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.     

Dynamic Relative Permeability and Simulation of WAG Injection Processes

In this work, we investigate the impact of mobility changes due to flow reversals from co-current to counter-current flow on the displacement performance of water alternating gas (WAG) injection processes. In WAG processes, the injected gas will migrate toward the top of the formation while the injected water will migrate toward the bottom of the formation. The segregation of gas, oil and water phases will result in counter-current flow occurring in the vertical direction in some portions of the reservoir during the displacement process. Previous experimental and theoretical studies of counter-current flow have shown that the relative mobility of each of the phases in a porous medium is considerably less when counter-current flow prevails as compared to co-current flow settings. A reduction of the relative permeability in the vertical direction results in a dynamic anisotropy in phase mobilities. This effect has, to the best of our knowledge, not previously been considered in the modeling and simulation of WAG processes. A new flow model that accounts for flow reversals in the vertical direction has been implemented and tested in a three-phase compositional reservoir simulator. In order to investigate the impact of flow reversals, results from the new flow model are compared to cases where counter-current flow effects on the phase mobilities are ignored. A range of displacement settings, covering relevant slug sizes, have been investigated to gauge the impact of mobility reductions due to flow reversals. Significant differences, in terms of saturation distribution, producing GOR and oil recovery, are observed between the conventional flow model (ignoring mobility reductions due to counter-current flow) and the proposed new model that accounts for reductions in phase mobility during counter-current flow. Accordingly, we recommend that an explicit representation of flow transitions between co-current and counter-current flow (and the related impact on phase mobilities) should be considered to ensure accurate and optimal design of WAG injection processes.     

Mathematical model of two-phase fluid nonlinear flow in low-permeability porous media with applications

IntroductionItisasuccessfulexampleinadevelopmentstoryofscienceandtechnologyformechanicsoffluidsinporousmediatocombinewithengineeringtechnology .Fieldsinfluencedbythemechanicsinvolveddevelopmentofoil_gasandgroundwaterresources,controlonseawaterintrusionandsubsidenceandgeologichazards,geotechnicalengineeringandbioengineering ,andairlineindustry[1～ 7].Aproblemonnonlinearflowinlow_permeabilityporousmediaisbutonlyabasiconeindifferentkindsofengineeringfields,butalsooneoffrontlineresearchfieldsofmod…     

Effect of Vibrations on Pore Fluid Distribution in Porous Media

Understanding the role of shuttle vibrations in pore fluid distribution is an essential task in the exploration of plant growth in root modules aboard space flights. Results from experimental investigations are reported in this paper on the distribution of immiscible fluid phases in glass beads under vibrations. Hexadecane, a petroleum compound immiscible with and lighter than water, was used in the experiments. The higher freezing point of Hexadecane (18 °C) allowed the solidification of the entrapped blobs in the presence of water in porous media, so that their size distribution can be obtained. van Genuchten function, commonly used to express moisture retention curves, is found to be an adequate fit for blob size distribution at residual saturation. The effect of vibrations on the fate (mobilization, stranding, or breakup) of a solitary ganglion in porous media was studied using a network model. A mobility criterion considering viscous, gravity, and capillary forces was developed to determine the fate of a solitary ganglion in a porous medium. It is concluded that the effect of vibrations is to increase the likelihood of breakup and mobilization of blobs entrapped in porous media at residual saturation. The pore fluid distributions after vibrations are less uniform than those before vibrations.     

Effects of an impermeable wall in dissipative dynamics of saturated porous media

A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing on fluid content inside the porous medium under static load. Considering pure Darcy dissipation, the dynamics is described by a Cahn–Hilliard-like system of partial differential equations (PDE). The goal is to study the dynamics of the formation of stationary fluid-rich bubbles. The evolution of the strain and fluid density profiles of the porous medium is analysed in two physical situations: fluid free to flow through the boundaries of the medium and fluid flow prevented at one of the two boundaries. Moreover, an analytic result on the position of the interface between the two phases is provided.     

On the stability of Taylor bubbles inside a confined highly porous medium

This work focuses on the local hydrodynamics of a multiphase gas–liquid flow forced into an innovative medium of high porosity (96%): an open cell solid foam. The gas (nitrogen) and liquid (ethanol) phases are injected at constant flow-rates in a millichannel to form a well-controlled Taylor flow which enters the porous medium. Based on a fluorescence technique, the apparent liquid holdup in the porous medium is quantified, and its evolution in time and along the porous medium extracted from spatiotemporal diagrams. The analysis of the main frequency, when varying the gas–liquid flow-rate ratio, leads to the identification of two hydrodynamic regimes. A model based on a scaling analysis is proposed to quantify the dimensionless numbers describing the transition between both regimes. It points out that the bubble length fixed by the Taylor flow is the control parameter. The model prediction of the critical bubble length at which the transition occurs is in good agreement with the experimental observations.     

Measurement of 3D pore-scale flow in index-matched porous media

We present the experimental analysis of fluid flow at the pore-scale of a transparent porous medium with matched refractive indices of the solid and liquid phases. The planar laser-induced fluorescence (PLIF) technique described is the first to simultaneously visualize the 3D pore-scale flow of two immiscible liquid phases in porous media. Through the application of a highly precise index matching method and the employment of up-to-date CCD imaging hardware, the system features a high spatial resolution and sampling rate. The method was used to study the dispersion of a tracer dye in single-phase flow and the displacement of oil by water in an imbibition process.     

Electromagnetic Sounding of Oil and Gas Formations

A mathematical model is proposed that describes electrical conductivity variation in the near-well zone during drilling formations containing three immiscible phases: oil, gas, and a small amount of native salt water. It is assumed that borehole drilling is performed using a clay–water solution, the mass-exchange process between the moving mud filtrate and immovable native water is infinitely fast, and displacement of the gas phase occurs by piston flow. The redistribution of the immiscible phases is described by the conventional Buckley–Leverett equations. The electromagnetic response of the medium is interpreted using the earlier proposed method of probabilistic convolutions.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

Two-phase jet flows in porous media

An analytical model describing the development of the filtration instability of the displacement front of fluids with different viscosities in a porous medium with account for capillary forces is proposed. A set of laboratory experiments on viscous fluid displacement from a porous medium is carried out. To describe the observable flows the model deals with the characteristic profile of the mean water saturation along the flow rather than with the curves of relative phase permeabilities of the fluids. The analytical model developed well describes the results of the laboratory modeling and the data of an actual oil field operation.