共查询到20条相似文献，搜索用时 31 毫秒
1.
Motivated by a wide range of applications from enhanced oil recovery to carbon dioxide sequestration, we have developed a two-dimensional, pore-level model of immiscible drainage, incorporating viscous, capillary, and gravitational effects. This model has been validated quantitatively, in the very different limits of zero viscosity ratio and zero capillary number; flow patterns from modeling agree well with experiment. For a range of stable viscosity ratios (μinjected/μdisplaced ? 1), we have increased the capillary number, Nc, and studied the way in which the flows deviate from capillary fingering (the fractal flow of invasion percolation) and become compact for realistic capillary numbers. Results exhibiting this crossover from capillary fingering to compact invasion are presented for the average position of the injected fluid, the fluid–fluid interface, the saturation and fractional flow profiles, and the relative permeabilities. The agreement between our results and earlier theoretical predictions [Blunt M, King MJ, Scher H. Simulation and theory of two-phase flow in porous media. Phys Rev A 1992;46:7680–99; Lenormand R. Flow through porous media: limits of fractal patterns. Proc Roy Soc A 1989;423:159–68; Wilkinson D. Percolation effects in immiscible displacement. Phys Rev A 1986;34:1380–90; Xu B, Yortsos YC, Salin D. Invasion Percolation with viscous forces. Phys Rev E 1998;57:739–51] supports the validity of these general theoretical arguments, which were independent of the details of the porous media in both two and three dimensions. 相似文献
2.
The macroscopic modelling of two-phase flow processes in subsurface hydrosystems or industrial applications on the Darcy scale usually requires a constitutive relationship between capillary pressure and saturation, the Pc(Sw) relationship. Traditionally, it is assumed that a unique relation between Pc and Sw exists independently of the flow conditions as long as hysteretic effects can be neglected. Recently, this assumption has been questioned and alternative formulations have been suggested. For example, the extended Pc(Sw) relationship by Hassanizadeh and Gray [Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990;13(4):169–86] proposes that the difference between the phase pressures to the equilibrium capillary pressure is a linear function of the rate of change of saturation, thereby introducing a constant of proportionality, the coefficient τ. It is desirable to identify cases where the extended relationship needs to be considered. Consequently, a dimensional analysis is performed on the basis of the two-phase balance equations. In addition to the well-known capillary and gravitational number, the dimensional analysis yields a new dimensionless number. The dynamic number Dy quantifies the ratio of dynamic capillary to viscous forces. Relating the dynamic to the capillary as well as the gravitational number gives the new numbers DyC and DyG, respectively. For given sets of fluid and porous medium parameters, the dimensionless numbers Dy and DyC are interpreted as functions of the characteristic length and flow velocity. The simulation of an imbibition process provides insight into the interpretation of the characteristic length scale. The most promising choice for this length scale seems to be the front width. We conclude that consideration of the extended Pc(Sw) relationship may be important for porous media with high permeability, small entry pressure and high coefficient τ when systems with a small characteristic length (e.g. steep front) and small characteristic time scale are under investigation. 相似文献
3.
《Advances in water resources》1998,21(7):605-615
The interface of two immiscible fluids flowing in porous media may behave in an unstable fashion. This instability is governed by the pore distribution, differential viscosity and interface tension between the two immiscible fluids. This study investigates the factors that control the interface instability at the wetting front. The development of the flow equation is based on the mass balance principle, with boundary conditions such as the velocity continuity and capillary pressure balance at the interface. By assuming that the two-phase fluids in porous media are saturated, a covariance function of the wetting front position is derived by stochastic theory. According to those results, the unstable interface between two immiscible fluids is governed by the fluid velocity and properties such as viscosity and density. The fluid properties that affect the interface instability are expressed as dimensionless parameters, mobility ratio, capillary number and Bond number. If the fluid flow is driven by gravitational force, whether the interface undergoes upward displacement or downward displacement, the variance of the unstable interface decreases with an increasing mobility ratio, increases with increasing capillary number, and decreases with increasing Bond number. For a circumstance in which fluid flow is horizontal, our results demonstrate that the capillary number does not influence the generation of the unstable interface. 相似文献
4.
Two-phase imbibition behavior of immiscible fluids was studied in dry and prewetted porous media using a laser-induced fluorescence technique. Imbibition was first investigated in two-dimensional (2-D) systems under conditions comparable to those for a study of drainage [Ovdat H, Berkowitz B. Pore-scale study of drainage displacement under combined capillary and gravity effects in index-matched porous media. Water Resources Research 2006;42:W06411. doi:10.1029/2005WR004553] in the capillary-dominated regime. The effect of initial wetting saturation (IWS) was then explored in 2-D and 3-D porous media under the combined effect of gravity, capillary and viscous forces, within and outside the capillary-dominated regime. Parameters that describe maximum vertical advance, volumetric fraction, total surface area and specific surface area of the invading fluid were used to quantify the behavior. Comparison of 2-D drainage and imbibition patterns demonstrates significant qualitative differences under analogous viscosity ratio, buoyancy number, and capillary number values. However, quantitative analyses show strong pore-scale similarities between these patterns. Invasion structures in 3-D, prewetted (IWS ≈ 8% of the pore volume) porous media are ramified, with lateral branching and regions containing trapped residual fluid. These structures are qualitatively and quantitatively different from the compact, branchless structures that develop in dry (IWS = 0) porous media. 相似文献
5.
We have conducted a series of high-resolution numerical experiments using the Pair-Wise Force Smoothed Particle Hydrodynamics (PF-SPH) multiphase flow model. First, we derived analytical expressions relating parameters in the PF-SPH model to the surface tension and static contact angle. Next, we used the model to study viscous fingering, capillary fingering, and stable displacement of immiscible fluids in porous media for a wide range of capillary numbers and viscosity ratios. We demonstrated that the steady state saturation profiles and the boundaries of viscous fingering, capillary fingering, and stable displacement regions compare favorably with micromodel laboratory experimental results. For a displacing fluid with low viscosity, we observed that the displacement pattern changes from viscous fingering to stable displacement with increasing injection rate. When a high viscosity fluid is injected, transition behavior from capillary fingering to stable displacement occurred as the flow rate was increased. These observations are also in agreement with the results of the micromodel laboratory experiments. 相似文献
6.
Y. Bernabé 《Pure and Applied Geophysics》1997,149(3):489-506
—The "dynamic" permeability k(ω) of heterogeneous networks of cracks, tubes and spheres, was determined by numerically simulating the harmonic flow of an interstitial fluid for a wide range of frequencies. For comparison with previous works, this procedure was applied to the 100 network realizations used in Bernabé (1995). In most cases, the calculated frequency dependence of the real and imaginary parts of k(ω) was consistent with the JKD model (Johnson et al., 1987), showing a transition from "viscous", macroscopic flow at low frequencies to "inertial" flow at high frequencies. The viscous skin depth δ c at the transition was found to be proportional to the critical capillary radius r c from a capillary invasion (Katz and Thompson, 1986). A simple explanation is that these two length scales arise from the same percolation problem. On the other hand, δ c was not well correlated with the JKD parameter Λ. The conclusion is that Λ and δ c (or r c ?) are two independent parameters, derived from two unrelated approaches (i.e., weighted averaging and percolation theory). Finally, an attempt was made to relax the initial assumptions of a rigid solid matrix and an incompressible fluid. It was observed that the effect of the fluid compressibility could occasionally be very large, especially when networks with large amounts of storage pore space were considered. 相似文献
7.
When nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid–fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid–fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid–fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid–fluid displacement. 相似文献
8.
A dominant mechanism for residual trapping of a nonwetting fluid in porous media during imbibition is snap-off or the disconnection of a continuous stream of the nonwetting fluid when it passes through pore constrictions and when a criterion based on capillary pressure imbalance is met. While quasi-static criteria for Roof snap-off have been defined for pores based on the imbalance between capillary pressure across the front/tail meniscus and local capillary pressure at the pore throat, and expressed in terms of pore body to pore throat ratio for simplification, we extended the previous quasi-static snap-off criterion by considering the local capillary pressure imbalance between the pore body and the pore throat for both circular and noncircular pores when the wetting film exists. We then used the criterion to analyze results from computational fluid dynamics (CFD) simulations of multi-phase flow with supercritical CO2 as the nonwetting fluid and water as the wetting fluid. The extended criterion successfully described most situations we modeled. Furthermore, we compared fluid interface shape for a noncircular 3D pore predicted by the minimum surface energy (MSE) theory against 3D CFD simulations. While the fluid interface shape at the pore throat for 3D simulation was consistent with the shape predicted by MSE theory, the shape could not be successfully predicted by the MSE theory at the upstream and downstream pore body. Moreover, film flow existed for the noncircular pore at the downstream pore body. 相似文献
9.
Suspended sediment fluxes at an intertidal flat: The shifting influence of wave,wind, tidal,and freshwater forcing 总被引：1，自引：0，他引：1
Using in situ, continuous, high frequency (8–16 Hz) measurements of velocity, suspended sediment concentration (SSC), and salinity, we investigate the factors affecting near-bed sediment flux during and after a meteorological event (cold front) on an intertidal flat in central San Francisco Bay. Hydrodynamic forcing occurs over many frequency bands including wind wave, ocean swell, seiching (500–1000 s), tidal, and infra-tidal frequencies, and varies greatly over the time scale of hours and days. Sediment fluxes occur primarily due to variations in flow and SSC at three different scales: residual (tidally averaged), tidal, and seiching. During the meteorological event, sediment fluxes are dominated by increases in tidally averaged SSC and flow. Runoff and wind-induced circulation contribute to an order of magnitude increase in tidally averaged offshore flow, while waves and seiching motions from wind forcing cause an order of magnitude increase in tidally averaged SSC. Sediment fluxes during calm periods are dominated by asymmetries in SSC over a tidal cycle. Freshwater forcing produces sharp salinity fronts which trap sediment and sweep by the sensors over short (∼30 min) time scales, and occur primarily during the flood. The resulting flood dominance in SSC is magnified or reversed by variations in wind forcing between the flood and ebb. Long-term records show that more than half of wind events (sustained speeds of greater than 5 m/s) occur for 3 h or less, suggesting that asymmetric wind forcing over a tidal cycle commonly occurs. Seiching associated with wind and its variation produces onshore sediment transport. Overall, the changing hydrodynamic and meteorological forcing influence sediment flux at both short (minutes) and long (days) time scales. 相似文献
10.
The internal deformation within debris flows holds essential information on dynamics and flow resistance of such mass-wasting processes. Systematic measurements of velocity profiles in real-scale debris flows are not yet available. Additionally, data on basal stresses of the solid and the fluid phase are rare. Here, we present and analyse measurements of vertical velocity profiles in two debris flows naturally occurring in the Gadria Creek, Italy. The method is based on cross-correlation of paired conductivity signals from an array of sensors installed on a fin-shaped wall located in the middle of the channel. Additionally, we measure normal stress and pore fluid pressure by two force plates with integrated pressure transducers. We find internal deformation throughout the flows. Only at the very front was some en-bloc movement observed. Velocity profiles varied from front to tail and between flows. For one debris flow, pore fluid pressure close to normal stress was measured, whereas the other flow was less liquefied. The median shear rates were mostly less than 5 s−1 and Savage numbers at the basal layer ranged from 0.01 to 1. Our results highlight the variable nature of debris flows and provide quantitative data on shear rate and basal stress distribution to help guide model development for hazard assessment and landscape evolution. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd. 相似文献
11.
The characteristic functions relating relative permeabilities and capillary pressures to fluid saturations (kr–S–Pc models) are of great importance for the modelling of sub-surface multi-phase flow and transport. In order to test their performance and to identify their important parameters, four well-known three-phase kr–S–Pc models have been tested against published experimental data on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. Both homogenous systems and systems with embedded heterogeneities have been analysed. 相似文献
12.
The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier–Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid–fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters. 相似文献
13.
Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well. 相似文献
14.
The partitioning of volatile non-aqueous phase liquid (NAPL) compounds to a discontinuous gas phase can result in the expansion of that gas phase, and the resulting gas flow can significantly affect the mass transfer from NAPL source zones. This recently reported gas flow generated by the spontaneous expansion of a discontinuous gas phase has not been extensively characterized in the literature. This study measured the expansion rate of a single gas cluster in a 1.1 mm sand above a pool of trans-1,2-dichloroethene (tDCE) in small-scale flow cell experiments. To characterize the gas flow, gas injection experiments in three sizes of sand were conducted at very slow injection rates typical of gas flow rates produced by gas expansion due to NAPL partitioning. Gas cluster spontaneous expansion rates above a tDCE pool were found to be 0.34 ± 0.02 and 0.29 ± 0.01 mL/day in duplicate experiments, which is sufficiently slow to result in discontinuous gas flow in porous media with a grain size diameter greater than 0.02 mm. Measured capillary pressures during gas injection showed patterns consistent with discontinuous gas flow, and identified multiple fragmentation events and expansion by coalescence with trapped clusters. The combination of pressure data and light transmission images were used to identify fragmentation and obtain direct measurements of the critical cluster length (i.e. the length at which withdrawal of the gas phase from a pore space occurs) in quasi-two-dimensional porous media for the first time. The measured critical cluster lengths were 1.4–3.6, 3.2–6.0 and 2.8–6.5 cm in 1.1, 0.7 and 0.5 mm sands, respectively. These values agreed well with estimates of the critical cluster length made using previously reported equations, and parameters derived from the medium’s capillary pressure-saturation relationship. 相似文献
15.
Harry Pavlopoulos 《Advances in water resources》2011,34(8):990-1011
Spectral multi-scaling postulates a power-law type of scaling of spectral distribution functions of stationary processes of spatial averages, over nested and geometrically similar sub-regions of the spatial parameter space of a given spatio-temporal random field. Presently a new framework is formulated for down-scaling processes of spatial averages, following naturally from the postulate of spectral multi-scaling, and key ingredients required for its implementation are described. Moreover, results from an extensive diagnostic study are presented, seeking statistical evidence supportive of spectral multi-scaling. Such evidence emerges from two sources of data. One is a 13 year long historical record of radar observations of rainfall in southeastern UK (Chenies radar), with high spatial (2 km) and temporal (5 min) resolution. The other is an ensemble of rain rate fields simulated by a spatio-temporal random pulse model fitted to the historical data. The results are consistent between historical and simulated rainfall data, indicating frequency-dependent scaling relationships interpreted as evidence of spectral multi-scaling across a range of spatial scales. 相似文献
16.
The water krw and oil kro relative permeability curves of a glass-etched planar pore network are estimated with history matching from transient displacement experiments performed at varying values of the capillary number, Ca , for two fluid systems: one of intermediate and one of strong wettability. The transient krw,kro are compared to corresponding ones measured with the steady-state method on the same porous medium [Avraam DG, Payatakes AC. Flow regimes and relative permeabilities during steady-state two-phase flow in porous media. J Fluid Mech 1995;293:207–36; Avraam DG, Payatakes AC. Generalized relative permeability coefficients during steady-state two-phase flow in porous media and correlation with the flow mechanisms. Transport Porous Med 1995;20:135–68; Avraam DG, Payatakes AC. Flow mechanisms, relative permeabilities, and coupling effects in steady-state two-phase flow through porous media. The case of strong wettability. Ind Eng Chem Res 1999;38:778–86.], and potential differences from them are interpreted in the light of the differences between the transient growth pattern, and the steady-state two-phase flow regime. For intermediate wettability, the transient kro and krw exceed the corresponding steady-state functions at low Ca values and have the tendency to become smaller than the steady-state ones at high Ca values. For strong wettability, the transient kro and krw are increasing functions of Ca, the transient kro is higher than the steady-state one, whereas the transient krw decreases substantially and becomes lower than the steady-state one at low Ca values. The dynamic capillary pressure estimated from transient experiments is a decreasing function of Ca in agreement with previous theoretical and experimental studies. 相似文献
17.
Heat transfer coefficients used in numerical simulations of volcanic eruptions are typically borrowed from industrial settings where the coefficients are well determined for non-permeable, machined (spherical) materials. Volcanic clasts, in contrast, are permeable and have irregular shapes. We performed a series of laboratory experiments to determine heat transfer coefficients for natural volcanic particles. We measured the surface and interior temperatures during cooling at wind speeds ranging from 0 to 10 m/s. We also measured the permeability and density of the particles. We find that the permeability of the particles has little effect on clast cooling. In the absence of any wind, heat loss occurs by free convection, and we find no relationship between the heat transfer coefficient and particle density. However, for non-zero Reynolds numbers (finite wind speed), the heat transfer coefficient decreases with increasing porosity. We obtain a correlation for the dimensionless heat loss, or Nusselt number, of the form Nu = 2 + aRe1/2Pr1/3 where a is a density dependent coefficient given by a = 0.00022ρ + 0.31, with ρ in kg/m3, and Re and Pr are the Reynolds number and Prandtl number, respectively. Compared with non-porous particles, heat transfer coefficients for natural pumice clasts are reduced by a factor of 2–3 for particles with similar Re. Numerical simulations show that this leads to an increase in depositional temperature by 50–90 °C. 相似文献
18.
The emplacement conditions for 39 igneous dikes cutting basalts in northwestern Ethiopia are evaluated by analyzing their displacement–length scaling relations. Maximum opening displacements and lengths of the dikes demonstrate displacement–length scaling of the form Dmax = 0.088L0.48, consistent with other populations of dikes and veins and different than the power-law scaling relation typically found for faults. The dikes propagated through the thin Trap basalt sequence under conditions of constant fracture toughness, with values corrected for three-dimensional dike geometry of ~ 77–273 MPa m1/2. The large values of fracture toughness are likely associated with (1) the toughening effects of near-tip damage, (2) mixed-mode dike propagation, as shown by magma flow fabric analysis through anisotropy of magnetic susceptibility (AMS) and image analysis of thin sections, and (3) elevated temperature within the blocky and ductile basaltic host rock, evidence of which has been found in the field. 相似文献
19.
A rectangular flume with dimensions of length 180 cm, height 60 cm and width 20 cm was used to observe the entry angle (i.e. angle between the interface and the centerline of the slot) of a two-layer flow withdrawal by a line sink. Saline water was used to form a bottom density current and red dye was applied. Based on the experimental data, one could see that the dimensionless discharge is more influential on the entry angle than the depth-averaged concentration of the lower-layer flow. Thus, the influence of concentration on experimental conditions is negligible for evaluation of the entry angle. The absolute values of entry angles increase with the absolute values of the dimensionless discharge. Almost all absolute values of the theoretical angle are bigger than that of the measured angle with a deviation bounded within 0.15 rad. The influence on the entry angle from the dimensionless discharge is symmetrical between the drawdown curve (interface above the slot) and the suck-up curve (interface below the slot). This phenomenon can be seen from a simplified form of a theoretical formula. 相似文献
20.
Peter F. Germann 《水文研究》2018,32(9):1166-1172
Preferential flow, a term that includes macropore flow, non‐equilibrium flow, and finger flow, stands in well known conflict with Richards' ( 1931 ) capillary flow. Acoustic velocity experiments demonstrate that preferential flow moves independently from, faster than, and before capillary flow during gravity‐driven infiltration. Viscous flow in permeable media is briefly introduced to the point where Richards' ( 1931 ) particular treatment of viscosity turns out as the hydro‐mechanical bifurcation from general laminar flow. Preferential flow is expected during significant infiltration, however, spatio‐temporarily limited according to the viscous‐flow regime. Two ways of delineating capillary flow from viscous flow reveal minimum path widths of preferential flow in the range of about 20 μm. 相似文献