Uncertainty Analysis Of Surrogate-based Optimization For Remediation Strategy Of DNAPLs-contaminated Aquifer

Petroleum products have been the critical materials for industrial production since the beginning of 20th century.But leakage,underlying discharge and spill of them result in environmental contamination,which seriously threaten human health.These water-immiscible liquid organic contaminants enter underground and generally exist in the form of non-aqueous phase liquids(NAPLs).NAPLs can be classified into two types according to the density:light non-aqueous phase liquids and dense non-aqueous phase liquids.Dense NAPLs(DNAPLs),with densities greater than water,have the characteristics of low solubility,high toxicity and interfacial tension.Conventional remediation techniques(e.g.,pump and treat,vapor extraction,and in situ bioremediation)are commonly unsuccessful or have limited effects in treating DNAPL-contaminated soils/groundwater systems.Surfactant flushing technology,which is also known as surfactant enhanced aquifer remediation(SEAR),is a form of chemical enhancement for pump and treats technology.It is capable of increasing the remediation efficiency of the pump and treats technique significantly by enhancing the solubility and mobility of DNAPLs in aqueous phase.However,surfactants are high priced which immediately leads to the high cost of SEAR.Thus,the selection of an optimal strategy which increases the remediation efficiency and reduces the remediation cost simultaneously is critical.Simulation-optimization techniques,which increasingly draw an extensive attention,have been effective tools for solving such type of problems.To reduce the high computational burden results from invoking numerical simulation model repeatedly in the process of resolving,a method is replacing the numerical model with an efficient surrogate model.This effectively increases the applicability of simulation optimization modeling of SEAR at DNAPL-contaminated sites.Although surrogate model contributes to realize the coupling of simulation model and optimization model technology,there are many uncertain factors in the process of simulation modeling,surrogate modeling and optimization model resolving.If these uncertain factors,which affect the optimization results to a great extent,are not taken into consideration,the obtained optimal strategy is likely to fail in achieving expected effect in the process of practical application and result in wasting a great deal of manpower and material resources.Therefore,it is an urgent as well as theoretically and practically important scientific problem to analyze the uncertainty of simulation model and surrogate model in the process of simulation-optimization,which can improve the reliability of optimal remediation strategy.This goal can be achieved through comprehensively applying uncertainty analysis,multi-phase flow simulation model,surrogate model,and nonlinear programming model based on field investigation.In this paper,aiming at nitrobenzene contaminated aquifer remediation problem,a DNAPL-contaminated aquifer multi-phase flow numerical simulation model was firstly built.Injection/extraction rates and surfactant flush duration were set as input variables.Latin hypercube sampling method was adopted to collect input data in the feasible region for input variables,and output data were obtained through running of multi-phase flow simulation model.Radial basis function artificial neural network(RBFANN),support vector regression(SVR)and Kriging methods were used to build surrogate models of multi-phase flow simulation model simultaneously.In addition,genetic algorithm(GA),self-adaptive particle swarm optimization(self-adaptive PSO)and Self-adaptive PSO based on simulated annealing(SA)were used to optimize the parameters of surrogate model.The accuracy of three surrogate models and optimizing effects of three parameter optimization algorithms were then compared,and the optimal surrogate modeling technique and parameter optimization algorithm were selected for further use.On the basis of above research,a set pair weighted multi-surrogate was built to further improve the approximation accuracy and reduce the residuals distribution range.Residuals probability distribution was analyzed for representing the uncertainty of surrogate model.Surrogate model uncertainty analysis was followed by simulation model uncertainty analysis:Injection/extraction rates and surfactant flush duration were set as input variables,contaminants removal rate was set as output variable to build surrogate model of simulation model.Sobol’ global sensitivity analysis method based on surrogate model was used to identify the aquifer parameters that obviously influence the remediation efficiency to reduce the input dimension of surrogate model and increase the approximation accuracy.Then uncertainty analysis on simulation model was carried out.At last,a certain nonlinear programming model and a stochastic nonlinear programming model,in which the uncertainty analysis results were taken into account,were constructed with the remediation cost minimization as the objective function in conjunction with constraint conditions.The developed set pair weighted multi-surrogate was embedded in the optimization model for replacing the input output relationship of the simulation model.The function of uncertainty analysis was showed through the comparison of the optimal strategies obtained by solving two optimization models.General conclusions drawn from this study are the following:(1)RBFANN model,SVR model and Kriging model are all with high approximation accuracy for simulation model,while Kriging model is significantly better than others;Self-adaptive PSO based on SA rapidly searched the global optimum and avoided trapping in local minimal solution,and its optimization,and its optimization capability is better than GA and self-adaptive PSO.In conclusion,the optimal surrogate model is Kriging model with the parameters obtained by Self-adaptive PSO based on S A.(2)Kriging models were respectively built with several sets of training samples,and set pair weighted multi-surrogate was then built through set pair analysis.Compared with Kriging model,set pair weighted multi-surrogate significantly improved the approximation accuracy for simulation model.The maximum and average of residuals(absolute value)of the removal rates between Kriging model and simulation model were about 3%and 0.6%using 100 testing samples,while the maximum and average of residuals(absolute value)of the removal rates between set pair weighted multi-surrogate and simulation model were only 1.5%and 0.4%.(3)Sobol’ global sensitivity analysis results showed that when the six parameters change in the feasible region,porosity is the most important variable influencing remediation efficiency,followed by oleic phase dispersity.While the influence of permeability,aqueous phase dispersity,microemulsion phase dispersity and boundary condition can be neglected.Therefore,in the subsequent uncertainty analysis of simulation model,porosity and oleic phase dispersity were set as input variables to build the surrogate model of simulation model,while the other four parameters were treated as constants.By these efforts,the computation accuracy of uncertainty analysis can be improved.On the other hand,sensitivity analysis results have guiding significance for contaminated site investigation.The measurement precision of sensitive parameters should be improve.(4)The results simulation model uncertainty analysis demonstrate that:aquifer parameters change in the feasible region may results in obvious variation of simulation model output(contaminants removal rate).Output fluctuations from the average was nearly 2.5%.It is quite essential to carry out the uncertainty analysis of simulation model,and take it into consideration in the process of SEAR strategy optimization.(5)In the simulation optimization problem solving process,using surrogate model to replace the simulation can considerably reduce the computational burden,and keep a high accuracy.Carrying out the uncertainty analysis of simulation model and surrogate model,the confidence level of a given remediation strategy achieving one contaminants removal rate can be definated according to the uncertainty analysis results.Meanwhile,building a stochastic nonlinear programming model,and computing the optimal remediation strategies under different confident levels is of great significance for enriching research results.Decision maker can make a more reasonable and effective judgement by balancing the reliability and cost of remediation strategy according to the actual conditions such as the project requirement,the use of groundwater,and the location of contaminated site.