Transport of reactive tracers in rock fractures
Transport of reactive tracers in rock fractures
复制标题
岩石裂缝中反应示踪剂的传输
DOI：
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发表时间：
1999
影响因子：
3.7
通讯作者：
H. Cheng
中科院分区：
文献类型：
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作者：
V. Cvetkovic;J. Selroos;H. Cheng
本文研究了示踪剂在单裂隙中的传质反应。一个拉格朗日概率模型的开发，传质反应扩散到岩石基质和随后的吸附在基质中，和吸附在断裂表面上，以及在计量（填充）材料在断裂。吸附反应被假定为线性的，在一般情况下，动力学控制。两个主要的简化假设是，在岩石基质中的扩散是一维的，垂直于断裂面，和示踪剂在断裂面内仅通过平流位移。所提出的模型的主要特点是，平流输送和扩散传质相关的动态方式通过流动方程。我们确定了两个拉格朗日随机变量τ和β作为控制对流和扩散传质的关键参数，并由流场决定。运输问题的概率解是基于（τ，β）的统计数据，我们使用一阶展开进行分析，并使用Monte Carlo模拟进行数值计算。为了研究（τ，β）-统计量，我们假设“立方定律”在局部适用，从而用雷诺润滑方程描述压力场。我们发现τ和β之间有很强的相关性，这表明β <$τ3/2是确定性的关系;指数3/2是“立方定律”的伪像。结果表明，裂缝中的流体动力学对τ和β的变化有很大的影响，但对τ和β之间的关系影响相对较小。（衰减）示踪剂质量回收的概率分布分散在参数空间中，由于裂缝孔径的变化。
Transport of tracers subject to mass transfer reactions in single rock fractures is investigated. A Lagrangian probabilistic model is developed where the mass transfer reactions are diffusion into the rock matrix and subsequent sorption in the matrix, and sorption on the fracture surface as well as on gauge (infill) material in the fracture. Sorption reactions are assumed to be linear, and in the general case kinetically controlled. The two main simplifying assumptions are that diffusion in the rock matrix is one-dimensional, perpendicular to the fracture plane, and the tracer is displaced within the fracture plane by advection only. The key feature of the proposed model is that advective transport and diffusive mass transfer are related in a dynamic manner through the flow equation. We have identified two Lagrangian random variables τ and β as key parameters which control advection and diffusive mass transfer, and are determined by the flow field. The probabilistic solution of the transport problem is based on the statistics of (τ, β), which we evaluated analytically using first-order expansions, and numerically using Monte Carlo simulations. To study (τ, β)-statistics, we assumed the ‘cubic law’ to be applicable locally, whereby the pressure field is described with the Reynolds lubrication equation. We found a strong correlation between τ and β which suggests a deterministic relationship β∼τ3/2; the exponent 3/2 is an artifact of the ‘cubic law’. It is shown that flow dynamics in fractures has a strong influence on the variability of τ and β, but a comparatively small impact on the relationship between τ and β. The probability distribution for the (decaying) tracer mass recovery is dispersed in the parameter space due to fracture aperture variability.