Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media
Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media
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模拟离散裂缝多孔介质中温盐流和反应性溶质输运的耦合
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发表时间：
2006
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通讯作者：
T. Graf
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作者：
T. Graf
建立了裂隙多孔介质中石英-水化学体系与变密度、变粘度渗流耦合的三维数值模型。在岩石热膨胀可以忽略的假设下，新模型还解决了裂隙多孔介质中的热传递问题。计算了流体性质、密度和粘度以及化学常数(溶解速率常数、平衡常数和活度系数)作为主要离子浓度和温度的函数。反应和流动参数，如矿物表面积和渗透率，在每个时间步长结束时用显式计算的反应速率进行更新。忽略了孔隙率和孔径变化对比存储的影响。自适应时间步长用于加速和减慢模拟过程，以防止出现物理上不真实的结果。新的时间增量取决于基质孔隙度和/或裂缝孔径的最大变化。为了保证数值的稳定性，模型参数的更新采用了时间层L+1反应速率隐式时间加权格式。用裂隙多孔介质中变密度流动、反应溶质运移和热传递等现有的解析、数值和物理基准问题对该模型进行了验证。模型公式的复杂性使化学反应和变密度流动的研究比以前更接近实际。本研究首先研究了裂隙多孔介质中的变密度渗流和输运现象，在裂隙多孔介质中，可以发生任意倾斜的单个裂缝。导出了体力矢量的一般数学表达式，它考虑了任意方向裂缝中的变密度流动和输运。对埋藏在多孔介质中的单一裂隙进行了变密度渗流和溶质运移的模拟。模拟结果表明，裂缝中的密度驱动流在多孔介质中产生对流，而高渗透裂缝起到了对流的屏障作用。新模型被应用于模拟例证，例如热羽流在化学反应裂隙介质中的水平运动。温盐(双扩散)传输既影响浮力驱动的流动，也影响化学反应。自由对流取决于流体(热盐水或III冷盐水)和参考流体之间的密度对比度。在这个例子中，密度差通常很小，裂缝并不像优先路径那样起作用，但有助于羽流的横向扩散。热区相当于石英的溶解区域，而在较冷的区域，主要是进口二氧化硅的沉淀。在高盐度地区，二氧化硅浓度与盐度成反比，在低盐度地区与温度成正比。该系统对温度误差最敏感。这是因为温度既影响溶解动力学(Arrhenius方程)，也影响石英的溶解度。
A three-dimensional numerical model is developed that couples the quartz-water chemical system with variable-density, variable-viscosity flow in fractured porous media. The new model also solves for heat transfer in fractured porous media, under the assumption of negligible thermal expansion of the rock. The fluid properties density and viscosity as well as chemistry constants (dissolution rate constant, equilibrium constant and activity coefficient) are calculated as a function of the concentrations of major ions and of temperature. Reaction and flow parameters, such as mineral surface area and permeability, are updated at the end of each time step with explicitly calculated reaction rates. The impact of porosity and aperture changes on specific storage is neglected. Adaptive time stepping is used to accelerate and slow down the simulation process in order to prevent physically unrealistic results. New time increments depend on maximum changes in matrix porosity and/or fracture aperture. Reaction rates at time level L+1 (implicit time weighting scheme) are used to renew all model parameters to ensure numerical stability. The model is verified against existing analytical, numerical and physical benchmark problems of variable-density flow, reactive solute transport and heat transfer in fractured porous media. The complexity of the model formulation allows chemical reactions and variable-density flow to be studied in a more realistic way than previously possible. The present study first addresses the phenomenon of variable-density flow and transport in fractured porous media, where a single fracture of an arbitrary incline can occur. A general mathematical formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulations of variable-density flow and solute transport are conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the highpermeability fracture acts as a barrier for convection. The new model was applied to simulate illustrative examples, such as the horizontal movement of a hot plume in a chemically reactive fractured medium. Thermohaline (double-diffusive) transport impacts both buoyancy-driven flow and chemical reactions. Free convective flow depends on the density contrast between the fluid (hot brine or iii cool saltwater) and the reference fluid. In the example, density contrasts are generally small and fractures do not act like preferential pathways but contribute to transverse dispersion of the plume. Hot zones correspond to areas of quartz dissolution while in cooler zones, precipitation of imported silica prevails. The silica concentration is inversely proportional to salinity in high-salinity regions and directly proportional to temperature in low-salinity regions. The system is the most sensitive to temperature inaccuracy. This is because temperature impacts both the dissolution kinetics (Arrhenius equation) and the quartz solubility.