Study Of Heterogeneous Aquifer Parameter Calibration And Numerical Solution Of Fractional Advection-Dispersion Equation

Water resources in China are relatively scarce.Groundwater resources,as an important part of freshwater resources,play a vital role in the economy and human life.With the development and utilization of groundwater resources in China and the increase of industrial activities,the pollution of groundwater has attracted more and more attentions.As a general method,groundwater numerical simulation has been widely used in the evaluation of groundwater resources,prediction of groundwater pollutant transport,and guidance on groundwater remediation technology.The aquifer in nature,influenced by sedimentary conditions and different geological processes,has a strong heterogeneity,which causes anomalous transport in the migration of groundwater pollutants,such as the heavy-trail and early arrival in breakthrough curves.How to characterize the heterogeneity of aquifers and develop a method that can accurately simulate the transport and transformation of pollutants in heterogeneous aquifers,and apply to practical cases to provide guidance for the development,utilization and remediation of groundwater,have being a hot spot in the studies of groundwater solute transport simulation.There are two main methods for the simulation of groundwater solute transport in heterogeneous aquifer.The one is refine the aquifer model at the Representative Elementary Volume scale,accurately assign the parameters of each grid,and then simulate using the traditional advection-dispersion equations based on Fick's law.The other is modifying the traditional Fick's law to obtain fractional advection-dispersion equations that can be used to describe the anomalous diffusion of groundwater solute transport.For the method one,the Localized Ensemble Kalman Filter(EnKF)is an effective method,which can assimilate the observation data from real model,correct model parameter estimation,and then accurately characterize the parameters.In this paper,we first use the localized EnKF to assimilate the hydraulic head and solute transport observations to identify the logarithmic hydraulic conductivity field.In addition,explore the improvement of the identification of the hydraulic conductivity field by assimilating the two type of observation data than the result by assimilating one single type of observation data.Then assimilating solute transport observations to investigate the effect of localized EnKF in identifying logarithmic dispersivity in the model that solute transport only with advection and dispersion.Moreover,explore the influence of the ensemble size,initial guesses,number of observations,spatial distribution of observations,observe frequency,and observations errors on the calibration results.Finally,the effect of the localized EnKF on the assimilation of the solute transport data to identify the logarithmic dispersion field and the adsorption parameter field was explored.The main conclusions were as follows.?When hydraulic head and solute transport observations are assimilated by localized EnKF to calibrate the logarithmic hydraulic conductivity,the estimated parameter field is more similar to the real one than the result by assimilating only one single type of data,indicating that a variety of data can be used for parameter calibration.If the model runs for a short time,the solute transport scope is limited,and that only get a good estimation of parameter within the plume.?The dispersivity field can be well estimated by assimilating solute transport observations using the localized EnKF,and the influences of each influencing factor on the parameter estimation result are as follows:Within a certain range,increasing the number of realizations can improve the results of parameter estimation.Excessive observe points may make the parameter estimation results to worse,therefore,determining a reasonable number of observations has a great influence on improving the estimation result.If the initial guess is closer to the real ones,the estimated parameter fields are better.The observations with largr error,the information provided for the localized EnKF system is limited,and the dispersivity field cannot be well estimated;the observation location and observe frequency have a greater influence on the parameter identification result.Observe at specific points and specific time,can get the best parameter identification result.? Using the localized EnKF to assimilate solute transport data from an ideal two-dimensional confined aquifer(solute transport with advection-dispersion and adsorption),the logarithmic dispersivity field and the logarithmic distribution coefficient field can be estimated effectively,demonstrating the localized EnKF can be used to estimates two kind of parameters effectively at the same time.The number of realizations has an effect on the simultaneous estimation of multiple parameters:for a certain realizations number,it may be best for one kind of parameter estimation,but not for the other parameter.Therefore,a balance should be made between the computation and the accuracy of the calibration result.At the same time,considering its influence on the estimation results of different types of parameters,the number of optimal realizations is selected comprehensively.The choice of spatial and temporal distribution of the observation also has a great influence on the parameter estimation results:on the overall trend,the more observation data the parameter estimation results are,the better.Observing at some specific time can get the best parameter estimation result.For the method two,the numerical solution of the fractional convection dispersion equation is a hotspot in current research because the accuracy and efficiency of the method directly limit its application.This paper proposes a variable Weight particle tracking method(VWPTM)based on traditional particle tracking method to approximate the solution of fractional advection-dispersion equations for particle.In this method,each particle is assigned a variable walking probability and weight.After each jump,the number and weight of particles will be adjusted according to the ratio of the probability of reaching the point,the original weight of the particles and the walking probability.This method can help to improve the accuracy of the solution.The results of one-dimensional and two-dimensional examples are illustrated.Compared with traditional particle tracking method,variable weight particle tracking method can effectively improve the accuracy of solution.While improving the accuracy of the results,variable weight particle tracking will not increase the computations,which avoiding additional computational burden.For the space fractional advection-dispersion equations,it is not suitable,because the jump step is generate by a stable distribution random,which randomly walk with large variations.