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1.
In porous media, the dynamics of the invading front between two immiscible fluids is often characterized by abrupt reconfigurations caused by local instabilities of the interface. As a prototype of these phenomena we consider the dynamics of a meniscus in a corner as it can be encountered in angular pores. We investigate this process in detail by means of direct numerical simulations that solve the Navier–Stokes equations in the pore space and employ the Volume of Fluid method (VOF) to track the evolution of the interface. We show that for a quasi-static displacement, the numerically calculated surface energy agrees well with the analytical solutions that we have derived for pores with circular and square cross sections. However, the spontaneous reconfigurations are irreversible and cannot be controlled by the injection rate: they are characterized by the amount of surface energy that is spontaneously released and transformed into kinetic energy. The resulting local velocities can be orders of magnitude larger than the injection velocity and they induce damped oscillations of the interface that possess their own time scales and depend only on fluid properties and pore geometry. In complex media (we consider a network of cubic pores) reconfigurations are so frequent and oscillations last long enough that increasing inertial effects leads to a different fluid distribution by influencing the selection of the next pore to be invaded. This calls into question simple pore-filling rules based only on capillary forces. Also, we demonstrate that inertial effects during irreversible reconfigurations can influence the work done by the external forces that is related to the pressure drop in Darcy’s law. This suggests that these phenomena have to be considered when upscaling multiphase flow because local oscillations of the menisci affect macroscopic quantities and modify the constitutive relationships to be used in macro-scale models. These results can be extrapolated to other interface instabilities that are at the origin of fast pore-scale events, such as Haines jumps, snap-off and coalescence.  相似文献   

2.
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   

3.
Abstract

This paper describes the source-sink driven flow in a two-layer fluid confined in a rotating annulus. Light fluid is injected at the inner wall, while denser fluid is withdrawn at the outer wall. The interface between the immiscible fluids intersects the bottom and thus produces a front. The net transport from the source to the sink is carried by Ekman layers at the bottom and at the interface, and by Stewartson layers at the side walls. A detached Stewartson layer arises at the front, leading to a pronounced upwelling circulation.  相似文献   

4.
The aim of seismic reservoir monitoring is to map the spatial and temporal distributions and contact interfaces of various hydrocarbon fluids and water within a reservoir rock. During the production of hydrocarbons, the fluids produced are generally displaced by an injection fluid. We discuss possible seismic effects which may occur when the pore volume contains two or more fluids. In particular, we investigate the effect of immiscible pore fluids, i.e. when the pore fluids occupy different parts of the pore volume. The modelling of seismic velocities is performed using a differential effective‐medium theory in which the various pore fluids are allowed to occupy the pore space in different ways. The P‐wave velocity is seen to depend strongly on the bulk modulus of the pore fluids in the most compliant (low aspect ratio) pores. Various scenarios of the microscopic fluid distribution across a gas–oil contact (GOC) zone have been designed, and the corresponding seismic properties modelled. Such GOC transition zones generally give diffuse reflection regions instead of the typical distinct GOC interface. Hence, such transition zones generally should be modelled by finite‐difference or finite‐element techniques. We have combined rock physics modelling and seismic modelling to simulate the seismic responses of some gas–oil zones, applying various fluid‐distribution models. The seismic responses may vary both in the reflection time, amplitude and phase characteristics. Our results indicate that when performing a reservoir monitoring experiment, erroneous conclusions about a GOC movement may be drawn if the microscopic fluid‐distribution effects are neglected.  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.
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   

7.
Borehole fluid injections are accompanied by microseismic activity not only during but also after termination of the fluid injection. Previously, this phenomenon has been analysed, assuming that the main triggering mechanism is governed by a linear pressure diffusion in a hydraulically isotropic medium. In this context the so‐called back front of seismicity has been introduced, which allows to characterize the hydraulic transport from the spatiotemporal distribution of post‐injection induced events. However, rocks are generally anisotropic, and in addition, fluid injections can strongly enhance permeability. In this case, permeability becomes a function of pressure. For such situations, we carry out a comprehensive study about the behaviour and parametrization of the back front. Based on a model of a factorized anisotropic pressure dependence of permeability, we present an approach to reconstruct the principal components of the diffusivity tensor. We apply this approach to real microseismic data and show that the back front characterizes the least hydraulic transport. To investigate the back front of non‐linear pore‐fluid pressure diffusion, we numerically consider a power‐law and an exponential‐dependent diffusivity. To account for a post‐injection enhanced hydraulic state of the rock, we introduce a model of a frozen (i.e., nearly unchanged after the stimulation) medium diffusivity and generate synthetic seismicity. We find that, for a weak non‐linearity and 3D exponential diffusion, the linear diffusion back front is still applicable. This finding is in agreement with microseismic data from Ogachi and Fenton Hill. However, for a strong non‐linear fluid–rock interaction such as hydraulic fracturing, the back front can significantly deviate from a time dependence of a linear diffusion back front. This is demonstrated for a data set from the Horn River Basin. Hence, the behaviour of the back front is a strong indicator of a non‐linear fluid–rock interaction.  相似文献   

8.
In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave-induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave-induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two-time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi-static equation in frequency domain. Moreover, the effects of change in saturation of three-phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three-phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub-seismic and seismic frequencies.  相似文献   

9.
Quantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.  相似文献   

10.
It is evident from the laboratory experiments that shear moduli of different porous isotropic rocks may show softening behaviour upon saturation. The shear softening means that the shear modulus of dry samples is higher than of saturated samples. Shear softening was observed both at low (seismic) frequencies and high (ultrasonic) frequencies. Shear softening is stronger at seismic frequencies than at ultrasonic frequencies, where the softening is compensated by hardening due to unrelaxed squirt flow. It contradicts to Gassmann's theory suggesting that the relaxed shear modulus of isotropic rock should not depend upon fluid saturation, provided that no chemical reaction between the solid frame and the pore fluid. Several researchers demonstrated that the shear softening effect is reversible during re-saturation of rock samples, suggesting no permanent chemical reaction between the solid frame and the pore fluid. Therefore, it is extremely difficult to explain this fluid–rock interaction mechanism theoretically, because it does not contradict to the assumptions of Gassmann's theory, but contradicts to its conclusions. We argue that the observed shear softening of partially saturated rocks by different pore fluids is related to pore-scale interfacial phenomena effects, typically neglected by the rock physics models. These interface phenomena effects are dependent on surface tension between immiscible fluids, rock wettability, aperture distribution of microcracks, compressibility of microcracks, porosity of microcracks, elastic properties of rock mineral, fluid saturation, effective stress and wave amplitude. Derived equations allow to estimate effects of pore fluids and saturation on the shear modulus and mechanical strength of rocks.  相似文献   

11.
In a phreatic aquifer, fresh water is withdrawn by pumping from a recovery well. As is the case here, the interfacial surface (air/water) is typically assumed to be a sharp boundary between the regions occupied by each fluid. The pumping efficiency depends on the method by which the fluid is withdrawn. We consider the efficiency of both continuous and pulsed pumping. The maximum steady pumping rate, above which the undesired fluid will break through into the well, is defined as critical pumping rate. This critical rate can be determined analytically using an existing solution based on the hodograph method, while a Boundary Element Method is applied to examine a high flow rate, pulsed pumping strategy in an attempt to achieve more rapid withdrawal. A modified kinematic interface condition, which incorporates the effect of capillarity, is used to simulate the fluid response of pumping. It is found that capillarity influences significantly the relationship between the pumping frequency and the fluid response. A Hele-Shaw model is set up for experimental verification of the analytical and numerical solutions in steady and unsteady cases for pumping of a phreatic aquifer. When capillarity is included in the numerical model, close agreement is found in the computed and observed phreatic surfaces. The same model without capillarity predicts the magnitude of the free surface fluctuation induced by the pulsed pumping, although the phase of the fluctuation is incorrect.  相似文献   

12.
During geologic storage of carbon dioxide (CO2), trapping of the buoyant CO2 after injection is essential in order to minimize the risk of leakage into shallower formations through a fracture or abandoned well. Models for the subsurface behavior of the CO2 are useful for the design, implementation, and long-term monitoring of injection sites, but traditional reservoir-simulation tools are currently unable to resolve the impact of small-scale trapping processes on fluid flow at the scale of a geologic basin. Here, we study the impact of solubility trapping from convective dissolution on the up-dip migration of a buoyant gravity current in a sloping aquifer. To do so, we conduct high-resolution numerical simulations of the gravity current that forms from a pair of miscible analogue fluids. Our simulations fully resolve the dense, sinking fingers that drive the convective dissolution process. We analyze the dynamics of the dissolution flux along the moving CO2–brine interface, including its decay as dissolved buoyant fluid accumulates beneath the buoyant current. We show that the dynamics of the dissolution flux and the macroscopic features of the migrating current can be captured with an upscaled sharp-interface model.  相似文献   

13.
We used hydrogeologic models to assess how fault-zone properties promote or inhibit the downward propagation of fluid overpressures from a basal reservoir injection well (150 m from fault zone, Q = 5000 m3/day) into the underlying crystalline basement rocks. We varied the permeability of the fault-zone architectural components and a crystalline basement weathered layer as part of a numerical sensitivity study. Realistic conduit-barrier style fault zones effectively transmit elevated pore pressures associated with 4 years of continuous injection to depths of approximately 2.5 km within the crystalline basement while compartmentalizing fluid flow within the injection reservoir. The presence of a laterally continuous, relatively low-permeability altered/weathered basement horizon (kaltered layer = 0.1 × kbasement) can limit the penetration depth of the pressure front to approximately 500 m. On the other hand, the presence of a discontinuous altered/weathered horizon that partially confines the injection reservoir without blocking the fault fluid conduit promotes downward propagation of pressures. Permeability enhancement via hydromechanical failure was found to increase the depth of early-time pressure front migration by a factor of 1.3 to 1.85. Dynamic permeability models may help explain seismicity at depths of greater than 10 km such as is observed within the Permian Basin, NM.  相似文献   

14.
Approximately 190 kg of 2 μm‐diameter zero‐valent iron (ZVI) particles were injected into a test zone in the top 2 m of an unconfined aquifer within a trichloroethene (TCE) source area. A shear‐thinning fluid was used to enhance ZVI delivery in the subsurface to a radial distance of up to 4 m from a single injection well. The ZVI particles were mixed in‐line with the injection water, shear‐thinning fluid, and a low concentration of surfactant. ZVI was observed at each of the seven monitoring wells within the targeted radius of influence during injection. Additionally, all wells within the targeted zone showed low TCE concentrations and primarily dechlorination products present 44 d after injection. These results suggest that ZVI can be directly injected into an aquifer with shear‐thinning fluids to induce dechlorination and extends the applicability of ZVI to situations where other emplacement methods may not be viable.  相似文献   

15.
Although there is no assumption of pore geometry in derivation of Gassmann's equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann's equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T2 data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann's equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore‐throat radius or nuclear magnetic resonance T2 could be set up, Gassmann's equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity.  相似文献   

16.
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   

17.
Deep saline aquifers are commonly used for disposal and storage of various surface fluids. The target injection zone must be hydraulically isolated from overlying zones in order to ensure containment of the injected fluids. Improperly plugged nonoperational abandoned wells that penetrate the injection zone are the main potential leakage pathways. Leakage through such wells may cause an observable pressure signal in a zone overlying the injection zone; such a signal can be used to detect the leakage. In this paper we develop an analytical model to evaluate the pressure change induced by leakage through a well in a multilayer system. Unlike previous analytical models on the topic, our model uses a closed system, which may significantly affect the strength and behavior of the pressure signal induced by leakage. The analytical model is first presented for a two-layer system centered at the leaky well location. We evaluate the leakage-induced pressure change using the Laplace transform of Duhamel’s superposition integral, yielding the solution in the Laplace domain. We then derive a late-time asymptotic solution using the final value theorem, which suggests that the leakage rate becomes constant after sufficient time. We then obtain the multilayer solution by extending the two-layer solution and presenting it in matrix form in the Laplace domain. We apply the solution to three examples. In the first example, we apply the analytical model to a two-layer system, investigating its behavior and comparing the results with a numerical solution. In order to demonstrate behavior and potential applications of the multilayer analytical model, we present two multilayer examples: one with identical layers and another, replicating a CO2 storage site, with dissimilar layers. The leakage-induced pressure change does not necessarily decrease as the distance increases from the injection zone toward the surface.  相似文献   

18.
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   

19.
注聚合物井井下温度分布数值模拟研究   总被引:3,自引:1,他引:2       下载免费PDF全文
本文提出了一种计算注聚合物井井下温度分布的方法,该方法视井筒内的聚合物溶液为非牛顿幂律流体,考虑注入流体在井筒中同一截面上的速度变化,根据聚合物溶液在多孔介质中的流变性,依据广义达西定律求取渗流速度,基于能量守恒方程建立柱坐标系下注聚合物井井筒内流体、注入层及围岩的二维温度场模型.通过合理的边界条件,将三部分模型耦合起来,采用交替方向半隐式有限差分法求解建立的井下温度场模型.考查了注入量、注入时间、幂律指数和稠度系数、注入液温度等因素对井下温度场分布的影响,结果表明,当注入的聚合物溶液温度低于注入层的原始温度时,随注入量和注入时间的增大以及粘度的减小,注入层的温度降低;注入聚合物溶液温度与注入层原始温度差越大,注入层处的温度剖面异常越明显.本文数值计算结果可用于指导注聚合物井的井温测井应用.  相似文献   

20.
We present a detailed analysis of the source properties of Long-Period (LP) signals recorded at Campi Flegrei Caldera (Italy) during the last (2005–2006) mini-uplift episode. Moment Tensor inversion via full-waveform modelling of broad-band seismograms indicates a crack-like source with a significant volumetric component. From auto-regressive modelling of the signal's tail we evaluate the dominant frequency and the attenuation factor of the oscillating source. Considering the acoustic properties of a fluid-filled crack, these values are consistent with the resonant oscillations of a crack filled by a water–gas mixture at variable gas–volume fraction. For these fluids, the crack size would be on the order of 40–420 m, a size range which is consistent with the spatial spreading of LP hypocenters. Analysis of temporally-correlated time series of seismological and geochemical data indicates that climaxing of LP activity was preceded by swarms of volcano-tectonic (VT) events and rapidly followed by a consistent increase of both thermal emissions and gas fluxes recorded at the surface (1 month — 2/3 days, respectively). Following these observations, we propose a conceptual model where VT activity increases permeability of the medium, thus favouring fluid mobility. As a consequence, the hydrothermal system experiences pressure perturbations able to trigger its resonant, LP oscillations.  相似文献   

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