Lunati Ivan, Kinzelbach Wolfgang, Sørensen Ivan
Institute for Hydromechanics and Water Resources Management, ETH Zürich, HIL G34.2, ETH Hönggerberg, CH-8093, Zurich, Switzerland.
J Contam Hydrol. 2003 Dec;67(1-4):195-217. doi: 10.1016/S0169-7722(03)00065-2.
The relevant velocity that describes transport phenomena in a porous medium is the pore velocity. For this reason, one needs not only to describe the variability of transmissivity, which fully determines the Darcy velocity field for given source terms and boundary conditions, but also any variability of the pore volume. We demonstrate that hydraulically equivalent media with exactly the same transmissivity field can produce dramatic differences in the displacement of a solute if they have different pore volume distributions. In particular, we demonstrate that correlation between pore volume and transmissivity leads to a much smoother and more homogeneous solute distribution. This was observed in a laboratory experiment performed in artificial fractures made of two plexiglass plates into which a space-dependent aperture distribution was milled. Using visualization by a light transmission technique, we observe that the solute behaviour is much smoother and more regular after the fractures are filled with glass powder, which plays the role of a homogeneous fault gouge material. This is due to a perfect correlation between pore volume and transmissivity that causes pore velocity to be not directly dependent on the transmissivity, but only indirectly through the hydraulic gradient, which is a much smoother function due to the diffusive behaviour of the flow equation acting as a filter. This smoothing property of the pore volume-transmissivity correlation is also supported by numerical simulations of tracer tests in a dipole flow field. Three different conceptual models are used: an empty fracture, a rough-walled fracture filled with a homogeneous material and a parallel-plate fracture with a heterogeneous fault gouge. All three models are hydraulically equivalent, yet they have a different pore volume distribution. Even if piezometric heads and specific flow rates are exactly the same at any point of the domain, the transport process differs dramatically. These differences make it important to discriminate in situ among different conceptual models in order to simulate correctly the transport phenomena. For this reason, we study the solute breakthrough and recovery curves at the extraction wells. Our numerical case studies show that discrimination on the basis of such data might be impossible except under very favourable conditions, i.e. the integral scale of the transmissivity field has to be known and small compared to the dipole size. If the latter conditions are satisfied, discrimination between the rough-walled fracture filled with a homogeneous material and the other two models becomes possible, whereas the parallel-plate fracture with a heterogeneous fault gouge and the empty fracture still show identifiability problems. The latter may be solved by inspection of aperture and pressure testing.
描述多孔介质中输运现象的相关速度是孔隙速度。因此，人们不仅需要描述导水率的变异性（它在给定源项和边界条件下完全决定达西速度场），还需要描述孔隙体积的任何变异性。我们证明，具有完全相同导水率场的水力等效介质，如果它们具有不同的孔隙体积分布，在溶质运移方面会产生显著差异。特别是，我们证明孔隙体积与导水率之间的相关性会导致溶质分布更加平滑和均匀。这在一个实验室实验中得到了观察，该实验在由两块有机玻璃板制成的人工裂缝中进行，在其中铣出了与空间相关的孔径分布。通过光透射技术进行可视化观察，我们发现当裂缝填充玻璃粉末（其起到均匀断层泥材料的作用）后，溶质行为更加平滑和规则。这是由于孔隙体积与导水率之间存在完美的相关性，导致孔隙速度并非直接取决于导水率，而是仅通过水力梯度间接相关，由于作为过滤器的流动方程的扩散行为，水力梯度是一个更加平滑的函数。孔隙体积 - 导水率相关性的这种平滑特性也得到了偶极流场中示踪剂测试数值模拟的支持。使用了三种不同的概念模型：一个空裂缝、一个填充有均匀材料的粗糙壁裂缝和一个具有非均匀断层泥的平行板裂缝。所有这三种模型在水力上是等效的，但它们具有不同的孔隙体积分布。即使在区域的任何点处测压水头和比流量完全相同，输运过程也会有显著差异。这些差异使得在原位区分不同的概念模型对于正确模拟输运现象变得很重要。因此，我们研究了抽水井处的溶质突破和恢复曲线。我们的数值案例研究表明，除了在非常有利的条件下，即导水率场的积分尺度必须已知且与偶极尺寸相比很小，基于此类数据进行区分可能是不可能的。如果满足后一个条件，则可以区分填充有均匀材料的粗糙壁裂缝与其他两种模型，而具有非均匀断层泥的平行板裂缝和空裂缝仍然存在可识别性问题。后者可以通过检查孔径和压力测试来解决。
