地下水污染物迁移数值模拟分析.ppt

Dispersion Coefficient (D) D = D + Dd Dxx Dxy Dxz Dyx Dyy Dyz Dzx Dzy Dzz D = In general: D Dd D represents dispersion Dd represents molecular diffusion In a 3D flow field it is not possible to simplify the dispersion tensor to three principal components. In a 3D flow field, we must consider all 9 components of the dispersion tensor. The definition of the dispersion coefficient is more complicated for 2D or 3D flow. See Zheng and Bennett, eqns. 3.37-3.42. Dx = ?xvx + Dd Dy = ?yvx + Dd Dz = ?zvx + Dd Recall, that for 1D uniform flow: General form of the ADE: Expands to 9 terms Expands to 3 terms (See eqn. 3.48 in ZB) Effect of longitudinal and transverse dispersivities on the plume configuration Figure 3.24. from Zheng Bennett Dispersive Transport Advection-dispersion Equation (ADE) C0 C0 Advection only Advection Dispersion v = q/θ Assuming particles travel at same average linear velocity v=q/θ In fact, particles travel at different velocities vq/θ or vq/θ Derivation（推导） of the Advection-Dispersion Equation (ADE) Assumptions Equivalent（当量） porous medium (epm) (i.e., a medium with connected pore space or a densely fractured medium with a single network of connected fractures) Miscible flow（混相流动） (i.e., solutes dissolve in water; DNAPL’s（重非轻亲 水相液体） and LNAPL’s （轻非轻亲水相液体） require a different governing equation. See p. 472, note 15.5, in Zheng and Bennett.) 3. No density effects Density-dependent flow requires a different governing equation. See Zheng and Bennett, Chapter 15. Figures from Freeze Cherry (1979) Darcy’s law: ?s h1 h2 q = Q/A advective flux fA = q c ?s h1 h2 f = F/A Adective flux ?x h1 h2 fA = advective flux = qc f = fA + fD How to quantify the dispersive flux? How about Fick’s law （见下一张PPT） of diffusion? where Dd is the effective diffusion coefficient. Fick’s law describes diffusion of ions on a molecular scale as ions diffuse from areas of higher to lower concentrations. (Zheng Bennett, Fig. 3.8.)