纵向弥散作用与渗透介质非均质性定量关系的模拟研究

在地下水污染模拟预报中,弥散参数是很难确定的一个模型参数。因实验室小尺度弥散规律一般不能用于大尺度弥散过程,而野外示踪试验却耗资大、周期长,限制了其实用性。文中利用随机数值模拟手段、基于随机理论的蒙特卡罗方法及序贯高斯模拟技术来生成渗透系数随机场,并研究渗透系数对数场的方差、相关长度以及变异函数类型在不同尺度上对纵向弥散度的影响,进而建立纵向弥散度与随机分布渗透系数场的方差和相关长度的统计定量关系,并与Gelhar理论计算结果进行比较。数值模拟结果表明,经过一定迁移距离后纵向弥散度与随机分布渗透系数对数场的方差和相关长度具有良好的线性统计关系,与Gelhar理论公式表达的关系类型类似。但对于较大的方差,纵向弥散度模拟结果明显大于Gelhar理论计算值,而对于较大相关长度在迁移距离不很大时,纵向弥散度模拟结果明显小于Gelhar理论计算值。本研究可为野外大尺度地下水污染预报模型中水动力弥散参数的确定提供方法借鉴。

Investigation of the relation between longitudinal dispersion and heterogeneity using the numerical simulation approach

Since the laboratory experiments generally present groundwater flow and solute transport in a small scale while the field tracer tests are time-and cost-consuming,it is difficult to obtain practically the dispersion parameter for a solute transport model used for the simulation and prediction of groundwater contamination at large scales.In this study,the stochastic numerical simulations were performed by implementing the Monte Carlo approach and Gauss sequential simulations to generate multiple realizations of stochastic hydraulic conductivity fields for investigations of relation between heterogeneity and longitudinal dispersivity.The heterogeneity of the geologic media was described by a log hydraulic conductivity field with the specific characteristic parameters of the variances(σ2) and correlation lengths(λ).The effects of the variances and correlation lengths as well as the variogram models were examined on longitudinal dispersivity.The numerical simulation results indicate that the relation between the simulated longitudinal dispersivity and the specified variance as well as the correlation length may be characterized statistically with a linear model,and particularly that after the plume moved down gradient at a sufficient distance relatively to the specified corresponding correlation length under small variances,the heterogeneous flow fields exhibit the dispersion behavior with a longitudinal dispersivity value close to that calculated based on the Gelhar's theoretical stochastic model.However,for the large variances,the longitudinal dispersivity values computed based on the numerical simulations were obviously larger than those obtained from the Gelhar's model.Moreover,when the solute transferred without an adequate moving distance compared with the specified corresponding correlation lengths,the simulated longitudinal dispersivity was considerably smaller than that calculated based on the Gelhar's model.Practically,the investigation results achieved from this study may establish part of a basis for estimation of the representative hydraulic dispersion parameters in prediction of groundwater contamination at a large field scale.