Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media     

Peter John Cleall 《国际地质力学数值与分析法杂志》2011,35(4):438-460

Analytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Diffusive mass exchange of non‐reactive substances in dual‐porosity porous systems – column experiments under saturated conditions          下载免费PDF全文

Bastian Knorr  Piotr Maloszewski  Florian Krämer  Christine Stumpp 《水文研究》2016,30(6):914-926

Diffusive mass exchange into immobile water regions within heterogeneous porous aquifers influences the fate of solutes. The percentage of immobile water is often unidentified in natural aquifers though. Hence, the mathematical prediction of solute transport in such heterogeneous aquifers remains challenging. The objective of this study was to find a simple analytical model approach that allows quantifying properties of mobile and immobile water regions and the portion of immobile water in a porous system. Therefore, the Single Fissure Dispersion Model (SFDM), which takes into account diffusive mass exchange between mobile and immobile water zones, was applied to model transport in well‐defined saturated dual‐porosity column experiments. Direct and indirect model validation was performed by running experiments at different flow velocities and using conservative tracer with different molecular diffusion coefficients. In another column setup, immobile water regions were randomly distributed to test the model applicability and to determine the portion of immobile water. In all setups, the tracer concentration curves showed differences in normalized maximum peak concentration, tailing and mass recovery according to their diffusion coefficients. These findings were more pronounced at lower flow rates (larger flow times) indicating the dependency of diffusive mass exchange into immobile water regions on tracers' molecular diffusion coefficients. The SFDM simulated all data with high model efficiency. Successful model validation supported the physical meaning of fitted model parameters. This study showed that the SFDM, developed for fissured aquifers, is applicable in porous media and can be used to determine porosity and volume of regions with immobile water. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

Controls on metamorphic equilibration: the importance of intergranular solubilities mediated by fluid composition          下载免费PDF全文

W. D. Carlson  J. D. Hixon  J. M. Garber  R. J. Bodnar 《Journal of Metamorphic Geology》2015,33(2):123-146

A dramatic demonstration of the role of intergranular solubility in promoting chemical equilibration during metamorphism is found in the unusual zoning of garnet in pelitic schist exposed at Harpswell Neck, Maine, USA. Many garnet crystals have irregular, patchy distributions of Mn, Cr, Fe and Mg in their inclusion‐rich interiors, transitioning to smooth, concentric zoning in their inclusion‐poor outer rims; in contrast, zoning of Ca and Y is comparatively smooth and concentric throughout. We re‐assess the disputed origin of these zoning features by examining garnet growth in the context of the thermal and structural history of the rocks, and by evaluating the record of fluid–rock interaction revealed in outcrop‐scale veining and fluid‐inclusion assemblages. The transition in the character of garnet zoning correlates with the onset of a synkinematic, simple‐shear‐dominated phase of garnet growth and with a shift in the composition of the intergranular fluid from CO₂‐rich to H₂O‐rich. Compositional variations in garnet are therefore best explained by a two‐stage growth history in which intergranular diffusive fluxes reflect differences in the concentration of dissolved species in these two contrasting fluids. Interiors of garnet crystals grew in the presence of a CO₂‐rich fluid, in which limited solubility for Mn and Cr (and perhaps Fe and Mg) produced patchy disequilibrium overprint zoning, while appreciable solubility for Ca and Y permitted their rock‐wide equilibration. Rims grew in the presence of an H₂O‐rich fluid, in which high intergranular concentrations for all elements except Cr enabled diffusion over length scales sufficient for rock‐wide equilibration. This striking example of partial chemical equilibrium during reaction and porphyroblast growth implies that thermal effects may commonly be subsidiary in importance to solubilities in the intergranular medium as determinants of length scales for metamorphic equilibration.  相似文献   

Grain‐scale pressure variations and chemical equilibrium in high‐grade metamorphic rocks     

L. Tajčmanová  Y. Podladchikov  R. Powell  E. Moulas  J.C. Vrijmoed  J.A.D. Connolly 《Journal of Metamorphic Geology》2014,32(2):195-207

In the classical view of metamorphic microstructures, fast viscous relaxation (and so constant pressure) is assumed, with diffusion being the limiting factor in equilibration. This contribution is focused on the only other possible scenario – fast diffusion and slow viscous relaxation – and brings an alternative interpretation of microstructures typical of high‐grade metamorphic rocks. In contrast to the pressure vessel mechanical model applied to pressure variation associated with coesite inclusions in various host minerals, a multi‐anvil mechanical model is proposed in which strong single crystals and weak grain boundaries can maintain pressure variation at geological time‐scales in a polycrystalline material. In such a mechanical context, exsolution lamellae in feldspar are used to show that feldspar can sustain large differential stresses (>10 kbar) at geological time‐scales. Furthermore, it is argued that the existence of grain‐scale pressure gradients combined with diffusional equilibrium may explain chemical zoning preserved in reaction rims. Assuming zero net flux across the microstructure, an equilibrium thermodynamic method is introduced for inferring pressure variation corresponding to the chemical zoning. This new barometric method is applied to plagioclase rims around kyanite in felsic granulite (Bohemian Massif, Czech Republic), yielding a grain‐scale pressure variation of 8 kbar. In this approach, kinetic factors are not invoked to account for mineral composition zoning preserved in rocks metamorphosed at high grade.  相似文献   

水动力条件对沉积物-水界面氧通量的影响   总被引：2，自引：0，他引：2  

郑阳华  邹浩东  何强  李宏  张青  陈德敏  艾海男 《湖泊科学》2018,30(6):1552-1559

氧环境决定了水体沉积物中各种生命所需元素的最终归趋，沉积物-水界面是水相与沉积物相氧传递的重要场所，而水动力条件是影响沉积物-水界面氧传递的重要因素.选择三峡库区一级支流御临河为研究对象，根据长年监测数据建立实验室模型，采用声学多普勒流速测试仪及微电极测试系统构建了非侵入式涡度相关测试系统，探究了不同水动力条件对沉积物-水界面氧通量的影响.结果表明：水体静止状态下沉积物-水界面溶解氧浓度随时间的增加而减少，非静止状态下随时间的增加而增加；沉积物-水界面氧通量随水体流速的增加而增加.根据氧通量求解对应流速下垂直涡动扩散系数并进行线性拟合，当水体流速为0.01~0.14 m/s时，垂直涡动扩散系数与水体流速的相关性最好，此时沉积物-水界面氧通量的传递以涡动扩散为主导.  相似文献   

The duration of near‐peak metamorphism from diffusion modelling of garnet zoning     

F. S. Spear 《Journal of Metamorphic Geology》2014,32(8):903-914

Garnet in a staurolite–kyanite zone sample from central Vermont displays a bell‐shaped Mn growth zoning with diffusional modification over the outer 100 μm. The diffusion is driven by the prograde net transfer reaction garnet + chlorite = kyanite + biotite as is evidenced by a well‐defined resorption zone on the rim. Analysis of the reaction history and resorbed garnet composition suggests that the peak temperature attained was 620–660 °C. Diffusional modelling of the rim diffusion provides an estimate of the duration of the metamorphic episode over which significant garnet diffusion occurs. The duration is a function of the assumed peak temperature and garnet diffusivities and range from a few hundred thousand years to a few million years. Such short durations require rapid tectonic burial and exhumation of relatively thin tectonic slices.  相似文献   

A helium stratified and ingassed lower mantle: resolving the helium paradoxes     

Honggang Zhu  Xuefang Li  Yingkui Xu 《Acta Geochimica》2020,(1):4-10

It is generally believed a variation of 3He/4He isotopic ratios in the mantle is due to only the decay of U and Th,which produces4 He as well as heat.Here we show that not only3He/4He isotopic ratios but also helium contents can be fractionated by thermal diffusion in the lower mantle.The driving force for that fractionation is the adiabatic or convective temperature gradient,which always produces elemental and isotopic fractionation along temperature gradient by thermal diffusion with higher light/heavy isotopic ratio in the hot end.Our theoretical model and calculations indicate that the lower mantle is helium stratified,caused by thermal diffusion due to*400℃temperature contrast across the lower mantle.The highest3He/4He isotopic ratios and lowest He contents are in the lowermost mantle,which is a consequence of thermaldiffusion fractionation rather than the lower mantle is a primordial and undegassed reservoir.Therefore,oceanicisland basalts derived from the deepest lower mantle with high3He/4He isotopic ratios and less He contents—the long-standing helium paradox,is solved by our model.Because vigorous convection in the upper mantle had resulted in disordered or disorganized thermal-diffusion effects in He,Mid-ocean ridge basalts unaffected by mantle plume have a relatively homogenous and lower!3He/4He isotopic compositions.Our model also predicts that 3He/4He isotopic ratios in the deepest lower mantle of early Earth could be even higher than that of Jupiter,the initial He isotopic ratio in our solar system,because the temperature contrast across the lower mantle in the early Earth is the largest and less4 He had been produced by the decay of U and Th.Moreover,the early helium-stratified lower mantle owned the lowest He contents due to over-degassing caused by the largest temperature contrast.Consequently,succeeding evolution of the lower mantle is a He ingassed process due to secular cooling of the deepest mantle.This explains why significant amount of He produced by the decay of U and Th in the lower mantle were not released,another long-standing heat–helium paradox.  相似文献   

热扩散驱动的元素分异和同位素分馏:一种不容忽视的硅酸盐成分分异机制     

常翱飞  丁兴 《岩石学报》2020,36(1):99-112

热扩散在地质过程中是否发挥重要作用一直存有争议。本文回顾了热扩散的研究历史和现状,重点总结了热扩散驱动的元素和同位素行为规律,并探讨了温度、硅酸盐组分、压力和氧逸度等因素对热扩散行为的影响。已有的研究表明,稳定热梯度下的硅酸盐热扩散效应类似于结晶分异或AFC过程,可以造成轻、重同位素分别在高温端和低温端富集,而主、微量元素的扩散方向则取决于两端化学势的高低和熔体中的电价平衡。从基性岩浆到酸性岩浆,熔体聚合度增大,黏度增加,热扩散速率明显降低,成网元素的热扩散效应减弱,变网元素则反之;水、氟、氯和硫化氢等挥发组分能增加熔体的非桥氧比例,降低熔体聚合度,因而能显著增强硅酸盐熔体中元素和同位素的热扩散效应。在此基础上,本文提出了当前硅酸盐体系热扩散研究中存在的五个亟需解决的问题,即:1)对不同硅酸盐体系的热扩散规律的研究还不够全面;2)对微量元素的热扩散行为认识不足;3)硅酸盐体系热扩散作用的影响因素及尺度还不够明确;4)热扩散作用的地质与地球化学关键识别标志有待确立;5)硅酸盐体系热扩散作用的理论模型有待建立。尽管硅酸盐体系热扩散的研究还存在诸多不足,但越来越多的证据表明,热扩散是地质过程中不容忽视的一种成分分异机制。这种机制会造成岩浆房或岩浆通道中的元素分异和同位素分馏,可能对于一些成分分异的岩石和矿床的形成具有重要的意义。  相似文献   

Interpreting zirconium‐in‐rutile thermometric results          下载免费PDF全文

K. Taylor‐Jones  R. Powell 《Journal of Metamorphic Geology》2015,33(2):115-122

At first sight, experimental results and observations on rocks suggest that the Zr content in rutile, where equilibrated with quartz and zircon, should be a useful thermometer for metamorphic rocks. However, diffusion data for Zr in rutile imply that thermometry should not, for plausible rates of cooling, give the high temperatures commonly observed in high‐grade metamorphic rocks. It is suggested here that such observations can be accounted for by high‐T diffusive closure of Si in rutile, causing the interior of rutile grains to become insensitive to the thermometer equilibrium well above the temperature of Zr diffusive closure. Paired with comparatively slow grain boundary diffusion and problematic zircon nucleation, this allows for cases of Zr retention in rutile through temperatures where Zr is still diffusively mobile within rutile grains. Other observations that may be accounted for in this context are large inter‐grain ranges of rutile Zr contents uncorrelated with rutile grain size, and flat Zr profiles across individual rutile grains, counter to what would be expected from diffusive closure. A consequence is that it is unlikely that Zr‐in‐rutile thermometry will be useful for estimating rock cooling rates.  相似文献   

Intergranular diffusion rates from the analysis of garnet surfaces: Implications for metamorphic equilibration          下载免费PDF全文

Tim J. Dempster  Shona Symon  Peter Chung 《Journal of Metamorphic Geology》2017,35(6):585-600

Novel approaches to garnet analysis have been used to assess rates of intergranular diffusion between different matrix phases and garnet porphyroblasts in a regionally metamorphosed staurolite‐mica‐schist from the Barrovian‐type area in Scotland. X‐ray maps and chemical traverses of planar porphyroblast surfaces reveal chemical heterogeneity of the garnet grain boundary linked to the nature of the adjacent matrix phase. The garnet preserves evidence of low temperature retrograde exchange with matrix minerals and diffusion profiles documenting cation movement along the garnet boundaries. Garnet–quartz and garnet–plagioclase boundaries preserve evidence of sluggish Mg, Mn and Fe diffusion at comparable rates to volume diffusion in garnet, whereas diffusion along garnet–biotite interfaces is much more effective. Evidence of particularly slow Al transport, probably coupled to Fe³⁺ exchange, is locally preserved on garnet surfaces adjacent to Fe‐oxide phases. The Ca distribution on the garnet surface shows the most complex behaviour, with long‐wavelength heterogeneities apparently unrelated to the matrix grain boundaries. This implies that the Ca content of garnet is controlled by local availability and is thought likely to reflect disequilibrium established during garnet growth. Geochemical anomalies on the garnet surfaces are also linked to the location of triple junctions between the porphyroblasts and the matrix phases, and imply enhanced transport along these channels. The slow rates of intergranular diffusion and the characteristics of different boundary types may explain many features associated with the prograde growth of garnet porphyroblasts. Thus, minerals such as quartz, Fe‐oxides and plagioclase whose boundaries with garnet are characterized by slow intergranular diffusion rates appear to be preferentially trapped as inclusions within porphyroblasts. As such grain boundary diffusion rates may be a significant kinetic impediment to metamorphic equilibrium and garnet may struggle to maintain chemical and textural equilibrium during growth in pelites.  相似文献