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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.
Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.  相似文献   

3.
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   

4.
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   

5.
—?We study the filling of horizontal cracks with constant aperture driven by capillary forces. The physical model of the crack consists of a narrow gap between two flat glass plates (Hele-Shaw cell). The liquid enters the gap through a hole in the bottom plate. The flow is driven purely by the force acting on the contact lines between solid, liquid, and gas. We developed a theoretical model for this type of flow on the basis of Darcy's law; it allows for the consideration of different surface conditions.¶We run the experiment for two surface conditions: Surfaces boiled in hydrogen peroxide to remove initial contamination, and surfaces contaminated with 2-propanol after boiling in hydrogen peroxide. The flow rate depends on the gap aperture and on the interaction of the liquid with the air and the solid surfaces: The smaller the aperture, the lower the flow rate due to viscous resistance of the liquid. The flow rate is also reduced when the glass surfaces are contaminated with 2-propanol. The contact line force per unit length is approximately 60% higher on clean glass surfaces than it is on glass surfaces with the 2-propanol contamination. These experimental results are in agreement with our theoretical model and are confirmed by independent measurements of the liquid-solid interaction in capillary rise experiments under static conditions with the same Hele-Shaw cell.¶Another aspect of this study is the distribution of the liquid for the different surface conditions. The overall shape is a circular disk, as assumed in the theoretical model. However, a pronounced contact line roughness develops in case of the surfaces contaminated with 2-propanol, and air bubbles are trapped behind the contact line. A further analysis of the flow regime using the capillary number and the ratio of the viscosities of the involved fluids (water and air) reveals that the experiments take place in the transition zone between stable displacement and capillary fingering, i.e., neither viscous nor capillary fingers develop under the conditions of the experiment. The contact line roughness and the trapped air bubbles in the contaminated cell reflect local inhomogeneities of the surface wettability.  相似文献   

6.
To better understand the effect of fluid distribution on the electric response of rocks saturated with oil and brine, we conducted experimental studies on the complex electrical impedance in a Berea sandstone, together with in situ acquisitions of oil distribution images employing a high‐resolution medical X‐ray computed tomography. We performed two tests of brine displacement by oil under high (10 MPa) and low (5 MPa) pressures, which were accompanied by fingering and stable displacement patterns, respectively. The measured complex impedance data were fitted to the Cole model to obtain the resistance, capacitance, peak frequency of the imaginary impedance, and the exponent α of the rock–fluid system. With increasing oil saturation, the resistance showed an increasing trend, whereas the other three parameters decreased. The fingering displacement exhibited lower resistance and capacitance than the stable displacement. The analysis of the resistance changes using a simple parallel connection model indicates that there are more components of residual brine in parallel connections in the fingering pattern than in the stable displacement pattern at the same saturation. We also interpreted the normalised changes in the capacitance (or apparent dielectric constant) with respect to the oil saturation via an analysis of the shape factor of fluid distribution based on the Maxwell–Wagner–Brugermann–Hanai model. The changes in the shape factor suggest that the pinch‐off of the brine in parallel connection by the oil is a dominant mechanism reducing the capacitance. In the stable displacement, most of the connections in the brine phase are immediately pinched off by oil displacement front at a local oil saturation of 65%. Conversely, in the fingering displacement, there is a transition from the bulk or layered brine to the pinched‐off at a local oil saturation below 60%. The analyses indicate that the difference in the fluid distribution under different fluid conditions is responsible for the non‐Archie behaviour.  相似文献   

7.
Interplay between capillary, gravity and viscous forces in unsaturated porous media gives rise to a range of complex flow phenomena affecting morphology, stability and dynamics of wetting and drainage fronts. Similar average phase contents may result in significantly different fluid distribution and patterns affecting macroscopic transport properties of the unsaturated medium. The formulation of general force balance within simplified pore spaces yields scaling relationships for motion of liquid elements in which gravitational force in excess of capillary pinning force scales linearly with viscous force. Displacement fluid front morphology is described using dimensionless force ratios expressed as Bond and Capillary numbers. The concise representations of a wide range of flow regimes with scaling relations, and predictive capabilities of front morphology based on dimensionless numbers lend support to certain generalizations. Considering available experimental data, we are able to define conditions for onset of unstable and intermittent flows leading to enhanced liquid and gas entrapment. These results provide a basis for delineation of a tentative value of Bo ∼ 0.05 as an upper limit of applicability of the Richards equation (at pore to sample scales) and related continuum-based flow models.  相似文献   

8.
We report experiments on the flow of two fluids of contrasting viscosity through a pipe in which low-viscosity fluid occupies the center of the pipe. The volume flux of the low-viscosity fluid in the pipe increased during an experiment but did not reach 100% in most cases. The transition from high- to low-viscosity-dominated outflow involved a drop in pressure gradient and an increase in flow rate due to reduced viscous resistance in the pipe. Initially, the central flow was thin and parallel-sided, but as its diameter increased the flow became unstable. A sequence of instabilities was observed during the course of each experiment, both in time and as a function of height in the pipe. In the most commonly observed instability the central flow adopted a helical geometry. The transition from parallel-sided to unstable flow first appeared at the top of the pipe and propagated downwards against the flow. Axisymmetric instabilities originating at the pipe entrance were also observed. All forms of instability exhibited entrainment of viscous fluid into the faster moving central flow. Entrainment was extensive early in the existence of the central flow, but later on the volume flux of lower-viscosity fluid in the central flow rose more rapidly than the rate of entrainment and the proportion of lower-viscosity fluid increased with time. These compositional changes determined the viscosity of the central flow which was found to control its diameter and velocity. In banded pumice deposits, silicic pumice without mafic component is commonly erupted alongside banded pumice blocks. We infer that banded pumice may correspond to the central flow in our experiments, i. e., that viscous magma has been incorporated into less viscous melt, and that pure acid pumice is derived from the outer flow. Changes in eruption style may be caused by variations in pressure gradient and flow rate due to changes in the viscosity of the melt in the conduit. Varied mafic/silicic proportions and degree of mixing in magmatic associations are controlled by the bulk volume erupted, discharge rate, initial temperature difference and aspect ratio of the conduit.  相似文献   

9.
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   

10.
Laboratory experiments that combine thermal convection in a rapidly rotating shell with a sudden increase of the shell’s rotation rate (spin-up) enable us to study processes related to turbulent viscous coupling between planetary fluid cores and solid mantles. We experimentally measure the large-scale effective viscosity by determining how the synchronisation time between the fluid and the shell (called the spin-up time) is shortened when convective turbulence exists in the bulk of the fluid. Our experiments suggest that viscous core-mantle coupling in planets may be greater than has been previously estimated using molecular viscosity values.  相似文献   

11.
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   

12.
Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.  相似文献   

13.
The use of surfactant solutions for the in situ recovery of residual NAPL in aquifers is increasingly considered as a viable remediation technique. The injection of a few pore volumes of high concentration surfactant solutions can mobilize most of the residual NAPL contacted by the solutions. However, the washing solutions'physico-chemical properties (low density and high viscosity), combined with the natural porous media heterogeneity, can prevent a good sweep of the entire contaminated volume. From the petroleum industry, it is well-known that polymer solutions can be injected following a surfactant solution slug to act as a mobility buffer and increase the overall sweep efficiency. The objective of our laboratory study is first to select and characterize polymers that would be suitable for aquifer restoration. Our experiments showed that among several polymers, xanthan gum solution rheology was made in order to predict shear rates, xanthan gum concentrations, salinity, and temperature effects on solution viscosity. The second set of experiments were made with a sand box which was designed to reproduce a simple heterogeneous media consisting of layers of sand with different permeability. These tests illustrate the xanthan gum solution's ability to increase surfactant solution's sweep efficiency and limit viscous fingering. The tests established that: (1) the injection of xanthan solution behind a surfactant solution slug decreases fluid velocity in high permeability layers and increases it in low-permeability ones, thus increasing the sweep efficiency (2) xanthan solutions eliminate viscous fingering at the polymer/surfactant solution front; (3) a xanthan solution preflush is desirable to limit surfactant solution mobility and prevent surfactant adsorption on solids; and (4) depending on site heterogeneity injection strategies should be applied to limit overriding by low-density surfactant solution.  相似文献   

14.
Summary The problem of penetration of a fluid into a porous medium containing a more viscous liquid is investigated. It is known that the displacement front may become unstable in this case as it may break up into «fingers». The problem of inception of fingers has been treated previously in the literature by describing the displacement front in terms of its Fourier transform. In the present paper, we generalize earlier procedures by making allowance for an arbitrary elemental growth law. Furthermore, we assume that the phenomenon of fingering is not solely governed by the prevailing flow potentials, but also by the spectrum of heterogeneities in the porous medium. This is achieved by introducing a constant characteristic of the frequency of the heterogeneities in the porous medium. It then turns out that the maximum rate of growth as a function of wave length is considerably shifted from that predicted in the literature. At the same time it is also shown that the difficulty encountered by other workers which consists of small wave lengths growing at an infinitely high rate, is being avoided.Paper presented orally at the 1960 Meeting of the A.I.M.E. in Denver (as paper number 1551-G of the program).  相似文献   

15.
We present a model which accounts for the common, but paradoxical arrangement of composite intrusions (i.e. silicic core and mafic margins) on the basis of analogue experiments using gelatin and aqueous solutions. The present model involves simultaneous flow-out of the upper and lower magmas from a longitudinal crack along the chamber wall. Experimental results suggest that the mafic magma from the lower layer leaks from the side-wall of the chamber and travels faster than the silicic magma because of its lower viscosity, so that the mafic magma reaches the tip of the crack first. Once the mafic magma reaches the crack tip, then the rate of dyke propagation becomes determined by the viscosity of the less viscous mafic magma, and so it can advance rapidly. The viscous silicic magma can flow efficiently into the center of the dyke, being lubricated by the mafic magma margins. This model accounts for the common arrangement of composite intrusions and gives an efficient mechanism of flow of viscous silicic magmas.  相似文献   

16.
We present the results of a pore-scale experimental study of residual trapping in consolidated sandstone and carbonate rock samples under confining stress. We investigate how the changes in wetting phase flow rate impacts pore-scale distribution of fluids during imbibition in natural, water-wet porous media. We systematically study pore-scale trapping of the nonwetting phase as well as size and distribution of its disconnected globules. Seven sets of drainage-imbibition experiments were performed with brine and oil as the wetting and nonwetting phases, respectively. We utilized a two-phase miniature core-flooding apparatus integrated with an X-ray microtomography system to examine pore-scale fluid distributions in small Bentheimer sandstone (D = 4.9 mm and L = 13 mm) and Gambier limestone (D = 4.4 mm and L = 75 mm) core samples. The results show that with increase in capillary number, the residual oil saturation at the end of the imbibition reduces from 0.46 to 0.20 in Bemtheimer sandstone and from 0.46 to 0.28 in Gambier limestone. We use pore-scale displacement mechanisms, in-situ wettability characteristics, and pore size distribution information to explain the observed capillary desaturation trends. The reduction was believed to be caused by alteration of the order in which pore-scale displacements took place during imbibition. Furthermore, increase in capillary number produced significantly different pore-scale fluid distributions during imbibition. We explored the pore fluid occupancies and studied size and distribution of the trapped oil clusters during different imbibition experiments. The results clearly show that as the capillary number increases, imbibition produces smaller trapped oil globules. In other words, the volume of individual trapped oil globules decreased at higher brine flow rates. Finally, we observed that the pore space in the limestone sample was considerably altered through matrix dissolution at extremely high brine flow rates. This increased the sample porosity from 44% to 62% and permeability from 7.3 D to 80 D. Imbibition in the altered pore space produced lower residual oil saturation (from 0.28 to 0.22) and significantly different distribution of trapped oil globules.  相似文献   

17.
Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.  相似文献   

18.
Injection of Newtonian crystal-free magmas into a partially crystallised host which may exhibit non-Newtonian properties produces magmatic structures such as pipes, syn-plutonic dikes or dendritic structures. Field relationships between the structure and the host rock commonly indicate what the rheological contrasts during the injection were. The manner in which a magma deforms in response to injection is mainly linked to crystal content and strain rate (i.e., injection rate). Three kinds of behaviour can be distinguished: (1) Newtonian at low crystal contents; (2) Non-Newtonian at intermediate (40–60%) crystal contents, or at high crystal contents if the strain rate is small; and (3) brittle failure at high crystal content or strain rates.Petrologic observations indicate that injection can take place when the host magma still behaves as a fluid. To investigate the physics of the injection process we review the results of injection experiments in non-Newtonian fluids. These experiments were performed to study viscous fingering in 2-D Hele Shaw cells. They provide the first step to establishing the main non-Newtonian effects during the formation of interfacial instabilities arising when a Newtonian fluid is injected into a more viscous fluid or paste. The qualitative comparison of the morphological features of the interfaces between the fluids in the experiments with those in nature suggests that, in magmas, irregularities of the interfaces (dikes and dendrites) result from non-Newtonian properties of the host. We conclude that fluid-like deformation, rather than brittle behaviour of the host, during injection is likely to produce the general features observed on the field. Cooling effects might be responsible for the widespread phenomenon of fragmentation. We emphasise that the main effect of non-Newtonian properties in partially crystallised magmas is to generate strongly heterogeneous media producing discontinuities which could explain the main morphological features of syn-plutonic injection structures.  相似文献   

19.
An alternative laboratory technique to measure the elastic constants of solid samples, based on the analysis of the cross‐correlation spectra of the vibratory response of randomly excited short solid cylinders, has been recently proposed. The aim of this paper is to check the ability of the technique called passive ultrasonic interferometry to monitor fluid substitution in different rock samples. Velocity variations due to fluid substitution are easily measured if the wave attenuation in the fluid‐saturated rock is not too large (typically in rocks with few cracks or microfractures). The experimental results are in agreement with the predictions of Biot–Gassmann poroelastic theory. The effect of substituting water with a stiffer saturating fluid, such as ethylene glycol, is to increase the overall bulk modulus of the rock, without any substantial effect on shear modulus. Furthermore, the experimental results compare well with those obtained independently with conventional pulse‐transmission technique using ultrasonic transducers. However, the measured pulse‐transmission bulk moduli are slightly larger than the corresponding measured ultrasonic interferometry moduli, with the deviation increasing with increasing fluid viscosity. This can be explained by dispersion due to wave‐induced flow of the viscous fluid since pulse‐transmission experiments involve higher frequencies than ultrasonic interferometry experiments.  相似文献   

20.
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