基于负表皮层影响的径向溶质运移模型构建与新求解方法

A New Analytical Method for Modeling Radially Divergent Solute Transport in Two-zone Confined Aquifers with Negative Skin Effects

对于模拟示踪试验的溶质运移,传统方法采用细网格离散小尺度表皮层,存在网格数量多和计算时间长等问题。由于表皮层外缘的参数变化剧烈,即使采用细网格,仍然存在显著误差。因此发展基于完整井的新示踪试验溶质运移模型,提出新的瞬态Robin边界条件反映表皮层吸附/解吸溶质的影响,实现表皮层的无网格。应用拉普拉斯变换导出模型的解析解,通过有限元法建立基于非完整井的数值解。结果显示新瞬态Robin边界条件精准反映负表皮层的影响。对于求解反演问题,表皮层宽度的估计范围由0.45~0.54 m缩至0.47~0.48 m,纵向弥散度由0.6~10.0 m缩至6.4~7.7 m,参数估计的可靠度显著提升。表皮层的无网格节省97%的数值解计算时间。

Various models have been developed for radially divergent tracer tests in two-zone confined aquifers of the skin and formation zones.However,existing numerical solutions require considerable computing time because of the fine spatial discretization of skins.The abrupt change in parameters near the skin-formation interface produces significant errors while predicting the spatiotemporal concentration near the interface,despite fine spatial discretization.In this study,a new model was developed for conducting radially divergent tracer tests in a partially penetrating well in a two-zone-confined aquifer.The skin was treated as a new transient Robin boundary condition specified at the skin-formation interface to reflect the effect of solute adsorption/release in the skin and achieve no skin discretization.A finite element solution for the model was developed.The analytical solution of the model modified for full penetration of the well was developed using the Laplace transform.These results suggest that the transient Robin boundary condition leads to accurate concentration predictions affected by negative skin.The analytical solution predicts reliable ranges of 0.47~0.48 m for the skin width w and 6.4~7.7 m for the longitudinal dispersivityα'_(l),whereas a traditional solution exhibits a range of 0.45 m≤w≤0.54 m and 0.6 m≤α'_(l)≤10 m.The finite element solution required only 3%of the computing time for obtaining a finite element solution based on fine skin discretization.In conclusion,this study provides implications not only for theoretical advances but also for useful numerical methods.