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1.
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   

2.
This study aims at modeling the transport of a conservative tracer in two dimensions, as experimentally observed in a strongly heterogeneous medium under conditions of variable water saturation during drainage and imbibition. Solute transport experiments were conducted in a sand tank containing an artificial packing of three quartz sands of different particle sizes. The packing was characterized by the presence of numerous homogeneous layers (0.5 × 5 × 5 cm) inclined at 45° and randomly distributed in a tank. Six different stationary flow conditions were sequentially established during imbibition and drainage. When a stationary flow regime was reached, several solute pulses were applied at different positions at the upper surface of the sand structure. The transport regime was studied by monitoring the tracer plumes injected as point-like pulses at the surface, as they travelled through the sand bedding.  相似文献   

3.
After the initiation of gravity drainage, water is often assumed to be either (a) draining under unit gradient, or (b) at capillary/gravity equilibrium. Both of these simplifications can be useful, but the regimes of validity of each assumption must be delineated. Water pressures are measured versus time and distance as water drains out of a 1.6 m long sand column to determine the relative effects of capillary and gravitational forces during drainage. For medium sized sands (0.15–0.3 mm in diameter), the capillary pressure is constant in space in a large region of the column for over 12 days, and the water continues to flow under unit gradient for relatively long time scales. Similar results are seen for finer sands, but with a much faster approach to equilibrium. Numerical simulations and analytical estimates are presented and compare favorably to the measurements. Together, the experimental, theoretical and analytical results are used to calculate when capillary/gravity equilibrium is reached as a function of porous media properties and length of the unsaturated zone. The ratio of the length of the unsaturated zone to the bubbling pressure is a key parameter in determining the drainage regime, and that even for relatively short unsaturated zones the equilibrium time scale can be on the order of years.  相似文献   

4.
In this study we performed three categories of steady- and unsteady-state core-flooding experiments to investigate capillary trapping, relative permeability, and capillary pressure, in a scCO2 + SO2/brine/limestone system at elevated temperature and pressure conditions, i.e., 60 °C and 19.16 MPa. We used a Madison limestone core sample acquired from the Rock Springs Uplift in southwest Wyoming. We carried out two sets of steady-state drainage-imbibition relative permeability experiments with different initial brine saturations to study hysteresis. We found that the final scCO2 + SO2 drainage relative permeability was very low, i.e., 0.04. We also observed a rapid reduction in the scCO2-rich phase imbibition relative permeability curve, which resulted in a high residual trapping. The results showed that between 62.8% and more than 76% of the initial scCO2 + SO2 at the end of drainage was trapped by capillary trapping mechanism (trapping efficiency). We found that at higher initial brine saturations, the trapping efficiency was higher. The maximum initial and residual scCO2-rich phase saturations at the end of primary drainage and imbibition were 0.525 and 0.329, respectively. Each drainage-imbibition cycle was followed by a dissolution process to re-establish Sw = 1. The dissolution brine relative permeabilities for both cycles were also obtained. We characterized the scCO2 + SO2/brine capillary pressure hysteresis behavior through unsteady-state primary drainage, imbibition, and secondary drainage experiments. We observed negative imbibition capillary pressure curve indicative of possible wettability alteration throughout the experiments due to contact with scCO2 + SO2/brine fluid system. The trapping results were compared to those reported in literature for other carbonate core samples. We noticed slightly more residual trapping in our sample, which might be attributed to heterogeneity, different viscosity ratio, and pore-space topologies. The impact of dynamic effects, i.e., high brine flow rate imbibition tests, on trapping of the scCO2-rich phase was also explored. We performed two imbibition experiments with relatively high brine flow rates. The residual scCO2 saturation dropped to 0.291 and 0.262 at the end of the first and second imbibition tests, i.e., 11.5% and 20.4%, respectively, compared to 0.329 under capillary-dominated regime.  相似文献   

5.
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   

6.
Processes in porous media governed by capillary forces, such as drainage or imbibition of wetting phase, are of great importance in different branches of soil science, petroleum engineering and hydrology. In this work we describe a new way of modeling imbibition by considering the movement and merger of interfaces at the pore level. The model is based upon a physically consistent dynamic criterion for the imbibition of a single pore originally proposed by Melrose.  相似文献   

7.
Accurate modeling of storage of carbon dioxide (CO2) in heterogeneous aquifers requires experiments of the capillary pressure as function of temperature and pressure. We present a method with which static drainage and imbibition capillary pressures can be measured continuously as a function of saturation at various temperature (T) and pressure (P) conditions. The measurements are carried out at (TP) conditions of practical interest. Static conditions can be assumed as small injection rates are applied. The capillary pressure curves are obtained for the unconsolidated sand–distilled water–CO2 system. The experimental results show a decrease of drainage and imbibition capillary pressure for increasing CO2 pressures and pronounced dissolution rate effects for gaseous CO2. Significant capillary pressure fluctuations and negative values during imbibition are observed at near critical conditions. The measurement procedure is validated by a numerical model that simulates the experiments.  相似文献   

8.
In this paper, we extend pore-morphology-based methods proposed by Hazlett (1995) and Hilpert and Miller (2001) to simulate drainage and imbibition in uniformly wetting porous media and add an (optional) entrapment of the (non-)wetting phase. By improving implementation, this method allows us to identify the statistical representative elementary volume and estimate uncertainty by computing fluid flow properties and saturation distributions of hundreds of subsamples within a reasonable time-frame. The method was utilized to study three different porous medium systems and results demonstrate that morphology-based pore-scale modeling is a viable approach to assess the representative elementary volume with respect to capillary dominated two-phase flow. The focus of this paper is the determination of the representative elementary volume for multiphase-flow properties for a digital representation of a rock.  相似文献   

9.
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   

10.
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   

11.
Air injection into porous media is investigated by laboratory experiments and numerical modelling. Typical applications of air injection into a granular bed are aerated bio-filters and air sparging of aquifers. The first stage of the dynamic process consists of air injection into a fixed or a quasi-fixed water-saturated granular bed. Later stages could include stages of movable beds as well, but are not further investigated here. A series of laboratory experiments were conducted in a two-dimensional box of the size 60 cm × 38 cm × 0.55 cm consisting of glass walls and using glass beads of diameter 0.4–0.6 mm as granular material. The development of the air flow pattern was optically observed and registered using a digital video camera. The resulting transient air flow pattern can be characterized as channelled flow in a fixed porous medium with dynamic tree-like evolution behaviour. Attempts are undertaken to model the air injection process. Multiphase pore-scale modelling is currently disregarded since it is restricted to very small scales. Invasion percolation models taking into account gravity effects are usually restricted to slow processes. On the other hand a continuum-type two-phase flow modelling approach is not able to simulate the observed air flow pattern. Instead a stochastic continuum-type approach is discussed here, which incorporates pore-scale features on a subscale, relevant for the immiscible processes involved. Consequently, the physical process can be modelled in a stochastic manner only, where the single experiment represents one of many possible realizations. However, the present procedure retains realistic water and air saturation patterns and therefore produces similar finger lengths and widths as observed in the experiments. Monte Carlo type modelling leads to ensemble mean water saturation and the related variance.  相似文献   

12.
The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated porous media is important in a variety of engineering and geological contexts. However, surprisingly few studies have investigated this phenomenon. We present a theoretical framework for predicting the 1-dimensional movement of water into air-filled fractures within a porous medium based on early-time capillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimation of sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifies the extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water in unsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with different permeability classes ranging from 50 to 500 mD and were fractured using the Brazilian method. Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at the Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Water uptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrix sorptivities ranged from 2.9 to 4.6 mm s−0.5, and increased linearly as the permeability class increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 mm s−0.5, and increased linearly with increasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7 mm2 s−1 and increased linearly with increasing fracture aperture width and damage zone width. Both theory and observations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sedimentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increase the dispersion of the wetting front. Further research is needed to investigate this phenomenon in other natural and engineered porous media.  相似文献   

13.
A ground gravity survey over the Bondy gneiss complex and its mineralized iron oxide- and copper-rich hydrothermal system(s) in the Grenville Province of SW Quebec was undertaken to aid mineral exploration in mapping subsurface intrusions. Several kilometric-scale positive Bouguer anomalies were identified that coincide with outcropping mafic and intermediate intrusive rocks of the post peak-metamorphic, 1.17-1.16 Ga mafic to intermediate Chevreuil suite intrusions and a 1.09-1.07 Ga Rolleau ultramafic stock. An additional 4 × 3 kilometre positive gravity anomaly indicates a mafic body underlies part of the metamorphosed hydrothermal system in the area of magnetite, pyrite, pyrrhotite, and chalcopyrite mineralization. Advanced argilic alteration associated with sulphide enrichment here is however indicative of an epithermal system with a felsic intrusion fluid source. As a felsic intrusion cannot explain the positive Bouguer gravity anomaly both felsic and mafic bodies must be present beneath the mineralized zone. Our preferred interpretation based on integrating gravity data and 2D forward gravity modelling with the results of field and geochemical studies is that this anomaly corresponds to a ca. 500 m deep mafic 1.17-1.16 Ga Chevreuil suite pluton that may have provided the source for hydrothermal fluids associated with late ductile shear- and fault-related mineralization or remobilization of early mineralization associated with a felsic pluton into late structures. This interpretation is compatible with gabbro xenoliths in the 1.07 Ga Rivard lamprophyre dyke on the NW margin of the gravity anomaly that bear significant similarities with those of the Chevreuil intrusive suite. The presence of both early felsic and late mafic intrusions beneath a group of three mineral occurrences in the Bondy gneiss complex strengthens their prospectivity in comparison to other mineral occurrences in the area. That early, pre-metamorphic mineralization was upgraded late in the tectonothermal evolution during a subsequent igneous and deformation event agrees with interpretations of other IOCG-style deposits in the Lac Manitou area of the eastern Grenville Province.  相似文献   

14.
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   

15.
A quasi-static scheme based on pore space spatial statistics is presented to simulate pore-scale two-phase capillary-dominant displacement processes. The algorithm is coupled with computational fluid dynamics in order to evaluate saturation functions. Wettability heterogeneity in partial and fractional/mixed-wet media is implemented using a contact angle map. The simulation process is pixel-wised and performed directly on binary images. Bypassing and snap-off are tackled as non-wetting phase trapping mechanisms. Post-processing results include residual saturations, effective permeability and capillary pressure curves for drainage and imbibition scenarios. The primary advantages of the proposed workflow are eliminating pore space skeletisation/ discretization, superior time efficiency and minimal numerical drawbacks when compared to other direct or network-based simulation techniques.  相似文献   

16.
Grid convergence in space and time of variable-density flow in fractured-porous rock is systematically assessed. Convergence of the flow simulation is attained using both uniform and adaptive time-stepping. This contrasts to variable-density flow in unfractured porous media where grid convergence variable-density flow problems is almost never achieved. At high discretization levels, the number of fingers in fractured-porous rock is no longer influenced by spatial-temporal grid discretization, which is not the case in unfractured porous media. However, similar to unfractured porous media, the number of fingers in fractured-porous media varies at low discretization levels. Simulated convective pattern and penetration depth of the dense plume in fractured rock depend more on spatial discretization than on temporal discretization. The appropriate spatial-temporal grid is then used to examine some aspects of mixed convection in fractured-porous rock, characterized by the mixed convection number M. The critical mixed convection number Mc = 46 represents the transition between forced and free convection in fractured porous media, which is much higher than Mc = 1 in unfractured porous media. Thus, for mixed convective flow problems, the value of Mc is not a sufficient indicator to predict the convective mode (free convection-forced convection), and the presence of vertical fractures must be included in the prediction of convective flow modes.  相似文献   

17.
In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems.  相似文献   

18.
A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions.  相似文献   

19.
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   

20.
Impure reworked evaporitic sandstones, preserved on Meridiani Planum, Mars, are mixtures of roughly equal amounts of altered siliciclastic debris, of basaltic provenance (40 ± 10% by mass), and chemical constituents, dominated by evaporitic minerals (jarosite, Mg-, Ca-sulfates ± chlorides ± Fe-, Na-sulfates), hematite and possibly secondary silica (60 ± 10%). These chemical constituents and their relative abundances are not an equilibrium evaporite assemblage and to a substantial degree have been reworked by aeolian and subaqueous transport. Ultimately they formed by evaporation of acidic waters derived from interaction with olivine-bearing basalts and subsequent diagenetic alteration. The rocks experienced an extended diagenetic history, with at least two and up to four distinct episodes of cementation, including stratigraphically restricted zones of recrystallization and secondary porosity, non-randomly distributed, highly spherical millimeter-scale hematitic concretions, millimeter-scale crystal molds, interpreted to have resulted from dissolution of a highly soluble evaporite mineral, elongate to sheet-like vugs and evidence for minor synsedimentary deformation (convolute and contorted bedding, possible teepee structures or salt ridge features). Other features that may be diagenetic, but more likely are associated with relatively recent meteorite impact, are meter-scale fracture patterns, veins and polygonal fractures on rock surfaces that cut across bedding. Crystallization of minerals that originally filled the molds, early cement and sediment deformation occurred syndepositionally or during early diagenesis. All other diagenetic features are consistent with formation during later diagenesis in the phreatic (fluid saturated) zone or capillary fringe of a groundwater table under near isotropic hydrological conditions such as those expected during periodic groundwater recharge. Textural evidence suggests that rapidly formed hematitic concretions post-date the primary mineral now represented by crystal molds and early pore-filling cements but pre-date secondary moldic and vug porosity. The second generation of cements followed formation of secondary porosity. This paragenetic sequence is consistent with an extended history of syndepositional through post-depositional diagenesis in the presence of a slowly fluctuating, chemically evolving, but persistently high ionic strength groundwater system.  相似文献   

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