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Mechanically-based numerical modeling is a powerful tool for investigating fundamental processes associated with the formation and evolution of both large and small-scale geologic structures. Such methods are complementary with traditional geometrically-based cross-section analysis tools, as they enable mechanical validation of geometric interpretations. A variety of numerical methods are now widely used, and readily accessible to both expert and novice. We provide an overview of the two main classes of methods used for geologic studies: continuum methods (finite element, finite difference, boundary element), which divide the model into elements to calculate a system of equations to solve for both stress and strain behavior; and particle dynamics methods, which rely on the interactions between discrete particles to define the aggregate behavior of the system. The complex constitutive behaviors, large displacements, and prevalence of discontinuities in geologic systems, pose unique challenges for the modeler. The two classes of methods address these issues differently; e.g., continuum methods allow the user to input prescribed constitutive laws for the modeled materials, whereas the constitutive behavior ‘emerges’ from particle dynamics methods. Sample rheologies, case studies and comparative models are presented to demonstrate the methodologies and opportunities for future modelers. 相似文献
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Conditioning complex subsurface flow models on nonlinear data is complicated by the need to preserve the expected geological connectivity patterns to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. The method has also been adopted for low-rank parameterization of complex geologic models to facilitate uncertainty quantification workflows. A difficulty in adopting these methods for subsurface flow modeling is the complexity associated with nonlinear flow data conditioning. While conditional GAN (CGAN) can condition simulated images on labels, application to subsurface problems requires efficient conditioning workflows for nonlinear data, which is far more complex. We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through conditional GAN, whereby a production response label is used as an auxiliary input during the training stage of GAN. The production label is derived from clustering of the flow responses of the prior model realizations (i.e., training data). The underlying assumption of this approach is that GAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method is to use a subset of samples from the training data that are within a certain distance from the observed flow responses and use them as training data within GAN to generate new model realizations. In this case, GAN is not required to learn the nonlinear relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns in the selected realizations that provide a close match to the observed data. The conditional low-dimensional parameterization for complex geologic models with diverse spatial features (i.e., when multiple geologic scenarios are plausible) performed by GAN allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making. We present and discuss the important properties of GAN for data conditioning using several examples with increasing complexity.
相似文献5.
John R. Nimmo Kaitlyn M. Creasey Kim S. Perkins Benjamin B. Mirus 《Hydrogeology Journal》2017,25(2):421-444
Layers of strong geologic contrast within the unsaturated zone can control recharge and contaminant transport to underlying aquifers. Slow diffuse flow in certain geologic layers, and rapid preferential flow in others, complicates the prediction of vertical and lateral fluxes. A simple model is presented, designed to use limited geological site information to predict these critical subsurface processes in response to a sustained infiltration source. The model is developed and tested using site-specific information from the Idaho National Laboratory in the Eastern Snake River Plain (ESRP), USA, where there are natural and anthropogenic sources of high-volume infiltration from floods, spills, leaks, wastewater disposal, retention ponds, and hydrologic field experiments. The thick unsaturated zone overlying the ESRP aquifer is a good example of a sharply stratified unsaturated zone. Sedimentary interbeds are interspersed between massive and fractured basalt units. The combination of surficial sediments, basalts, and interbeds determines the water fluxes through the variably saturated subsurface. Interbeds are generally less conductive, sometimes causing perched water to collect above them. The model successfully predicts the volume and extent of perching and approximates vertical travel times during events that generate high fluxes from the land surface. These developments are applicable to sites having a thick, geologically complex unsaturated zone of substantial thickness in which preferential and diffuse flow, and perching of percolated water, are important to contaminant transport or aquifer recharge. 相似文献
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Stochastic continuum modeling of flow and transport in a crystalline rock mass: Fanay-Augères,France, revisited 总被引：1，自引：0，他引：1
A stochastic discrete-fracture model was used by Cacas et al.a,b to interpret flow measurements and transport experiments in a fractured crystalline rock mass at Fanay-Augères. They considered continuum models to be incapable of properly interpreting small-scale measurements or tracer tests in fractured systems, which, in their view, require three-dimensional modeling of numerous discrete channels; in their opinion, continuum modeling applies only to average flow on a relatively large scale. Cacas et al. considered their discrete fracture model to have been validated by its demonstrated ability to reproduce selected experimental results. In this paper, flow and transport at Fanay-Augères are modeled by viewing the fractured rock as a stochastic continuum in a manner originally proposed by Neumanc,d. The stochastic continuum approach obviates the need for detailed information about fracture geometry or assumptions about how individual fractures control flow and transport. All it requires is the delineation of a few dominant features, which can be embedded into the stochastic continuum model as heterogeneous porous slabs. Though a fault zone has been identified at the Fanay-Augères experimental site, it has been modeled neither by Cacas et al. nor in this paper. In fact, in this paper, a larger selection of experimental results than those considered by Cacas et al. are reproduced merely by modeling the rock as a statistically homogeneous continuum in two dimensions. These results demonstrate that a continuum approach may be well suited for the analysis of flow and transport in fractured rock. This does not constitute a validation of the continuum approach, just as the results of Cacas et al. fall short of validating the discrete fracture approach. Instead, the two sets of results illustrate jointly the well-established principle that an open system, especially one as complex as fractured hydrogeologic environments tend to be, cannot be described uniquely on the basis of sparse data and need not be described in great detail to capture its salient behavior by a model.a Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990a) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 1. The flow model. Water Resour Res 26(3):479–489b Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990b) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 2. The transport model. Water Resour Res 26(3):491–500c Neuman SP (1987) Stochastic continuum representation of fractured rock permeability as an alternative to the REV and fracture network concepts, in Rock Mechanics. In: Farmer IW, Daemen JJK, Desai CS, Glass CE, Neuman SP (eds) Proceedings of the 28th U.S. Symposium, Tucson, Arizona. Balkema, Rotterdam, pp 533–561d Neuman SP (1988) A proposed conceptual framework and methodology for investigating flow and transport in Swedish crystalline rocks. SKB Swedish Nuclear Fuel and Waste Management Co., Stockholm, September, Arbetsrapport 88–37, 39 pp 相似文献
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Development of a coupled surface-groundwater-pipe network model for the sustainable management of karstic groundwater 总被引：1，自引：0，他引：1
This paper considers the hydrogeological simulation of groundwater movement in karstic regions using a hydrological modelling system (SHETRAN) which has been adapted for modelling flow in karstic aquifers. Flow and transport through karstic aquifers remains poorly understood, yet quantitative hydrogeological models are essential for developing and implementing groundwater protection policies. The new model has been developed and used within the STALAGMITE (Sustainable Management of Groundwater in Karstic Environments) project, funded by the European Commission. The SHETRAN model is physically based insofar as most of the parameters have some physical meaning. The SHETRAN model represents all of the key processes in the hydrological cycle, including subsurface flow in the saturated and unsaturated zones, surface flow over the ground surface and in channels, rainfall interception by vegetation canopies, evapotranspiration, snow-pack development and snowmelt. The modifications made to SHETRAN to simulate karstic aquifers are (1) the coupling of a pipe network model to a variably saturated, three-dimensional groundwater component (the VSS-NET component), to simulate flow under pressure in saturated conduits; (2) the coupling of surface water features (e.g. sinking streams or "ponors", and spring discharges) to the conduit system; (3) the addition of a preferential "bypass" flow mechanism to represent vertical infiltration through a high-conductivity epikarst zone. Lastly, a forward particle tracking routine has been developed to trace the path of hypothetical particles with matrix and pipe flow to springs or other discharge points. This component allows the definition of groundwater protection zones around a source for areas of the catchment (watershed) which are vulnerable to pollution from non-point sources (agriculture and forestry). 相似文献
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Anthony C. Runkel Robert G. Tipping Jessica R. Meyer Julia R. Steenberg Andrew J. Retzler Beth L. Parker Jeff A. Green John D. Barry Perry M. Jones 《Hydrogeology Journal》2018,26(7):2133-2159
A hydrogeologic conceptual model that improves understanding of variability in aquitard integrity is presented for a fractured sedimentary bedrock unit in the Cambrian-Ordovician aquifer system of midcontinent North America. The model is derived from multiple studies on the siliciclastic St. Lawrence Formation and adjacent strata across a range of scales and geologic conditions. These studies employed multidisciplinary techniques including borehole flowmeter logging, high-resolution depth-discrete multilevel well monitoring, fracture stratigraphy, fluorescent dye tracing, and three-dimensional (3D) distribution of anthropogenic tracers regionally. The paper documents a bulk aquitard that is highly anisotropic because of poor connectivity of vertical fractures across matrix with low permeability, but with ubiquitous bed parallel partings. The partings provide high bulk horizontal hydraulic conductivity, analogous to aquifers in the system, while multiple preferential termination horizons of vertical fractures serve as discrete low vertical hydraulic conductivity intervals inhibiting vertical flow. The aquitard has substantial variability in its ability to protect underlying groundwater from contamination. Across widespread areas where the aquitard is deeply buried by younger bedrock, preferential termination horizons provide for high aquitard integrity (i.e. protection). Protection is diminished close to incised valleys where stress release and weathering has enhanced secondary pore development, including better connection of fractures across these horizons. These conditions, along with higher hydraulic head gradients in the same areas and more complex 3D flow where the aquitard is variably incised, allow for more substantial transport to deeper aquifers. The conceptual model likely applies to other fractured sedimentary bedrock aquitards within and outside of this region. 相似文献
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Mechanics-based restoration has been seen by some in the structural geology community as a panacea – a new technology that melds the retrodeformational merits of kinematic balancing with principles of continuum mechanics. The method has been touted for its ability to simulate complex 3D systems without assumptions of plane strain, allowing for heterogeneous fault slip distributions and mechanical interaction of fault segments. It has been suggested as a means to predict distributions of geologic strain and associated small-scale structures; however, we demonstrate that the kinematics of restoration models may differ significantly from forward deformation. Restoration models are governed by boundary conditions that are different from the forces driving forward geologic deformation. Models may be improved by supplementing restoration boundary conditions with loads that attempt to reverse tectonic strain, but unphysical artifacts persist. Mechanics-based restoration may be an appropriate tool for traditional applications of kinematic models including validation of structural interpretation and modeling geometric evolution; however, more subtle features, particularly strain distribution, should be treated with skepticism. Restoration models may provide insights to the initial configuration of forward mechanical models with physically appropriate boundary conditions and non-linear material behavior. Forward models provide the best means for simulating deformation and predicting subsidiary structures. 相似文献
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Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion 总被引：1，自引：0，他引：1
Christopher I. McDermott Robert Walsh Ralph Mettier Georg Kosakowski Olaf Kolditz 《Computational Geosciences》2009,13(3):349-361
Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage
and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the
characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between
flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced
to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale
at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability
criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport
modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous
fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods
can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and
applied to fractures representing experimental field conditions in the Grimsel rock laboratory. 相似文献
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《Applied Geochemistry》2004,19(3):359-377
The Dakota aquifer of the central and eastern Great Plains of the United States is an important source of water for municipal supplies, irrigation and industrial use. Although the regional flow system can be characterized generally as east to northeasterly from the Rocky Mountains towards the Missouri River, locally the flow systems are hydrologically complex. This study uses Sr isotopic data from groundwater and leached aquifer samples to document the complex subsystems within the Dakota aquifer in Nebraska and Kansas. The interaction of groundwater with the geologic material through which it flows has created spatial patterns in the isotopic measurements that are related to: long-term water–rock interaction, during which varying degrees of isotopic equilibrium between water and rock has been achieved; and the alteration of NaCl fluids by water-rock interaction. Specifically, Sr isotopic data distinguish brines from Kansas and western Nebraska from those in eastern Nebraska: the former are interpreted to reflect interaction with Permian rocks, whereas the latter record interaction with Pennsylvanian rocks. The Sr isotopic composition of groundwater from other parts of Nebraska and Kansas are a function of the dynamic interaction between groundwater and unlithified sediments (e.g., glacial till and loess), followed by interaction with oxidized and unoxidized sediments within the Dakota Formation. This study illustrates the power of combining Sr chemistry with more conventional geochemical data to obtain a more complete understanding of groundwater flow systems within regional aquifer systems where extensive monitoring networks do not exist. 相似文献
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A modeling study was carried out to evaluate the influence of aquifer heterogeneity, as represented by geologic layering, on heat transport and storage in an aquifer thermal energy storage (ATES) system in Agassiz, British Columbia, Canada. Two 3D heat transport models were developed and calibrated using the flow and heat transport code FEFLOW including: a “non-layered” model domain with homogeneous hydraulic and thermal properties; and, a “layered” model domain with variable hydraulic and thermal properties assigned to discrete geological units to represent aquifer heterogeneity. The base model (non-layered) shows limited sensitivity for the ranges of all thermal and hydraulic properties expected at the site; the model is most sensitive to vertical anisotropy and hydraulic gradient. Simulated and observed temperatures within the wells reflect a combination of screen placement and layering, with inconsistencies largely explained by the lateral continuity of high permeability layers represented in the model. Simulation of heat injection, storage and recovery show preferential transport along high permeability layers, resulting in longitudinal plume distortion, and overall higher short-term storage efficiencies. 相似文献
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模拟裂隙多孔介质中变饱和渗流的广义等效连续体方法 总被引：2，自引：0，他引：2
描述了一种计算裂隙多孔介质中变饱和渗流的广义等效连续体方法。这种方法忽略裂隙的毛细作用,设定一个与某孔隙饱和度相对应的综合饱和度极限值,并假定：（1）如果裂隙多孔介质的综合饱和度小于该极限值,水只在孔隙中存在并流动,而裂隙中则没有水的流动;（2）如果综合饱和度等于或大于该极限值,水将进入裂隙,并在裂隙内运动。分析比较了等效连续体模型的不同计算方法,并给出了一个模拟裂隙岩体中变饱和渗流与传热耦合问题的应用算例。结果表明,所述方法具有一般性,可以有效地模拟裂隙多孔介质中变饱和渗流的基本特征。 相似文献
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Witherspoon, P.A. and Gale, J.E., 1977. Mechanical and hydraulic properties of rocks related to induced seismicity. Eng. Geol., 11(1): 23–55.The mechanical and hydraulic properties of fractured rocks are considered with regard to the role they play in induced seismicity. In many cases, the mechanical properties of fractures determine the stability of a rock mass. The problems of sampling and testing these rock discontinuities and interpreting their non-linear behavior are reviewed. Stick slip has been proposed as the failure mechanism in earthquake events. Because of the complex interactions that are inherent in the mechanical behavior of fractured rocks, there seems to be no simple way to combine the deformation characteristics of several sets of fractures when there are significant perturbations of existing conditions. Thus, the more important fractures must be treated as individual components in the rock mass.In considering the hydraulic properties, it has been customary to treat a fracture as a parallel-plate conduit and a number of mathematical models of fracture systems have adopted this approach. Non-steady flow in fractured systems has usually been based on a two-porosity model, which assumes the primary (intergranular) porosity contributes only to storage and the secondary (fracture) porosity contributes only to the overall conductivity. Using such a model, it has been found that the time required to achieve quasi-steady state flow in a fractured reservoir is one or two orders of magnitude greater than it is in a homogeneous system. In essentially all of this work, the assumption has generally been made that the fractures are rigid.However, it is clear from a review of the mechanical and hydraulic properties that not only are fractures easily deformed but they constitute the main flow paths in many rock masses. This means that one must consider the interaction of mechanical and hydraulic effects. A considerable amount of laboratory and field data is now available that clearly demonstrates this stress-flow behavior. Two approaches have been used in attempting to numerically model such behavior: (1) continuum models, and (2) discrete models. The continuum approach only needs information as to average values of fracture spacing and material properties. But because of the inherent complexity of fractured rock masses and the corresponding decrease in symmetry, it is difficult to develop an equivalent continuum that will simulate the behavior of the entire system. The discrete approach, on the other hand, requires details of the fracture geometry and material properties of both fractures and rock matrix. The difficulty in obtaining such information has been considered a serious limitation of discrete models, but improved borehole techniques can enable one to obtain the necessary data, at least in shallow systems. The possibility of extending these methods to deeper fracture systems needs more investigation. Such data must be considered when deciding whether to use a continuum or discrete model to represent the interaction of rock and fluid forces in a fractured rock system, especially with regard to the problem of induced seismicity. When one is attempting to alter the pressure distribution in a fault zone by injection or withdrawal of fluids, the extent to which this can be achieved will be controlled in large measure by the behavior of the fractures that communicate with the borehole. Since this is essentially a point phenomenon, i.e., the changes will propagate from a relatively small region around the borehole, the use of a discrete model would appear to be preferable. 相似文献
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Shale gas production has gradually achieved high and stable output, which makes it possible to make up for the shortage of oil and gas energy as an alternative energy source. Shale reservoir is compact, with well-developed nano-pore, and has the characteristics of adsorption and desorption, diffusion and slippage. At the same time, there are a large number of natural cracks, bedding and foliation. Hydraulic fractures expand irregularly after volume fracturing in horizontal wells. The whole system has multi-field coupling and cross-scale flow effects. Productivity prediction of shale gas is difficult and uncertain, which restricts the efficient development and evaluation of shale reservoirs. In this paper, the development status of productivity numerical models for shale gas horizontal wells is reviewed in consideration of the multi-scale transport characteristics of shale gas. These models include dual media capacity models, multiple media capacity models, and complex seam productivity models. It is considered that the dual medium and multi-media productivity models weaken the large permeable flow area and channel provided by the complex seam network system after shale reservoir lamination, and cannot comprehensively characterize the full-scale coupled transport characteristics of shale gas. The numerical model for productivity prediction of shale gas horizontal wells based on complex fracture network provides a multi-scale flow embedded fracture network system, which solves the problem of systematic flow without losing the ability to accurately characterize each scale flow. It is necessary to obtain the complex fracture network morphological characterization which conforms to reservoir geological characteristics, rock mechanical behavior and fluid-solid coupling mechanism. Fracture network characterization is the key to the productivity prediction of shale gas horizontal wells. 相似文献
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河北省地质环境条件复杂,灾害种类多,分布广,危害大。泥石流灾害以其数量大,爆发集中,成为危害最为严重的山区灾害之一。本文依据山区县市地质灾害调查与区划统计数据,对危害较重泥石流灾害发育特征和分布规律进行了初步分析,阐明了泥石流灾害与自然背景地质环境以及人为因素之间的关系,并据此提出了防治对策建议。 相似文献
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裂隙岩体中非饱和渗流与运移的概念模型及数值模拟 总被引：12，自引：2，他引：12
探讨了裂隙岩体中非饱和地下水渗流与溶质运移的几种概念模型的构造及数值模拟问题 ,如裂隙网络模型、连续体模型、等效连续体模型、双孔隙度 (单渗透率 )模型、双渗透率模型、多组份连续体模型等。在裂隙岩体中 ,非饱和地下水的渗流可能只局限于岩体中的岩石组份、或裂隙网络 ,也可能在裂隙和岩石中同时发生 ;对前一种情形只需考虑单一连续体中的流动 ,而后一种情况则需要包括地下水在岩石和裂隙之间的交换。岩体中的裂隙网络往往是溶质运移的主要通道 ;但当溶质在裂隙与岩石之间的渗透和扩散是重要的运移机制时 ,就需要考虑岩石与裂隙界面处的溶质交换。为了模拟岩石与裂隙之间地下水和溶质的交换 ,就需要了解岩石与裂隙之间相互作用的模式和范围 ,使得这类问题的概念模型较单一连续体模型多了一层不确定性、其数值模拟也变得更为困难。因为在实际问题中不易、甚至根本不能判别非饱和渗流的实际形态 ,具体采用哪种模型主要取决于分析的目的和对现场数据的掌握程度。不论哪种模型都会受到模型及参数不确定性的影响 ,因此必须考虑与其他辅助模型的比较. 相似文献
18.
Hydromechanical coupling in geologic processes 总被引：6，自引：2，他引：4
Earth's porous crust and the fluids within it are intimately linked through their mechanical effects on each other. This paper
presents an overview of such "hydromechanical" coupling and examines current understanding of its role in geologic processes.
An outline of the theory of hydromechanics and rheological models for geologic deformation is included to place various analytical
approaches in proper context and to provide an introduction to this broad topic for nonspecialists.
Effects of hydromechanical coupling are ubiquitous in geology, and can be local and short-lived or regional and very long-lived.
Phenomena such as deposition and erosion, tectonism, seismicity, earth tides, and barometric loading produce strains that
tend to alter fluid pressure. Resulting pressure perturbations can be dramatic, and many so-called "anomalous" pressures appear
to have been created in this manner. The effects of fluid pressure on crustal mechanics are also profound. Geologic media
deform and fail largely in response to effective stress, or total stress minus fluid pressure. As a result, fluid pressures
control compaction, decompaction, and other types of deformation, as well as jointing, shear failure, and shear slippage,
including events that generate earthquakes. By controlling deformation and failure, fluid pressures also regulate states of
stress in the upper crust.
Advances in the last 80 years, including theories of consolidation, transient groundwater flow, and poroelasticity, have been
synthesized into a reasonably complete conceptual framework for understanding and describing hydromechanical coupling. Full
coupling in two or three dimensions is described using force balance equations for deformation coupled with a mass conservation
equation for fluid flow. Fully coupled analyses allow hypothesis testing and conceptual model development. However, rigorous
application of full coupling is often difficult because (1) the rheological behavior of geologic media is complex and poorly
understood and (2) the architecture, mechanical properties and boundary conditions, and deformation history of most geologic
systems are not well known. Much of what is known about hydromechanical processes in geologic systems is derived from simpler
analyses that ignore certain aspects of solid-fluid coupling. The simplifications introduce error, but more complete analyses
usually are not warranted. Hydromechanical analyses should thus be interpreted judiciously, with an appreciation for their
limitations. Innovative approaches to hydromechanical modeling and obtaining critical data may circumvent some current limitations
and provide answers to remaining questions about crustal processes and fluid behavior in the crust.
Electronic Publication 相似文献
19.
Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes 总被引：2，自引：0，他引：2
The kinetics of chemical reactions at mineral surfaces and the rates of diffusion of species in an aqueous phase are coupled in many geochemical systems. Analytical solutions to equations describing coupled mineral dissolution/growth and solute transport in both transient and steady-state systems are used to delimit regimes of pure reaction control, pure transport control and mixed kinetic control of mass-transfer rates. The relative significance of the two processes depends on the magnitudes of the diffusion coefficients and rate constants as functions of temperature, and the degree of disequilibrium in the system. In addition, the system geometry, the ratio of mineral surface area to diffusion cross-section, and the porosity and tortuosity of the medium through which aqueous species diffuse affect reaction vs. diffusion control. In general, diffusion control increases with increasing temperature and increasing distance over which diffusion occurs. Calculations for the mixed kinetic regime in transient systems demonstrate that the relative significance of diffusion and surface reaction varies with reaction progress, and approaches a limiting value as equilibrium is approached. This limiting value may be appropriate to natural water-rock interactions that occur at conditions that are close to equilibrium. This result permits extension of simple models for irreversible mass transfer in homogeneous systems to systems in which mass-transfer kinetics are controlled by coupled surface reactions and mass transport. Criteria are established for time and length scales and fluid velocity limits on the validity of the continuum hypothesis and the local equilibrium assumption in mass-transport modeling. 相似文献