Optimal Design And Uncertainty Analysis Of DNAPLs-Contaminated Aquifer Remediation Based On Surrogate Model

During oil exploitation,processing,storage and transportation,oil organic pollutants often enter the aquifer due to leakage and accidents,causing serious pollution to the groundwater and endangering the ecological environment and the safety of drinking water.After the petroleum pollutants flow into the underground aquifer,they usually exist in the form of non-aqueous phase liquids(NAPLs),including LNAPLs with a density lower than water and DNAPLs with a density higher than water.DNAPLs have characteristics of low solubility,low mobility and high density,and therefore they will stay in underground aquifers for a long time,thus causing long-term groundwater pollution.It is more difficult to clear them than to clear LNAPLs,and the traditional Pump and Treat(P&T)technology usually cannot achieve the desired clearing goals.Surfactant Enhanced Aquifer Remediation(SEAR),as an improvement of the P&T technology,injects water containing surfactants into the aquifers,thus greatly improving the effect of the P&T technology on the clearance of DNAPLs in aquifers via the solubilization and flow enhancement of surfactants for DNAPLs.However,the cost of SEAR is quite high,and there are many factors affecting its cost and efficiency,such as the number and the location of extraction and injection wells,the amount of extraction and injection and the repair time.It is a very challenging task to develop a cost-effective remediation design on the premise of ensuring the repair effect and money saving and considering the affecting factors mentioned above.The simulation-optimization approach is an effective method to solve the optimization design of SEAR.In order to reduce the computational time of the simulation-optimization approach,a surrogate model is needed to take place of the simulation model for calculation.The accuracy of the surrogate model is highly dependent on the sampling method and the modeling method.Therefore,it is essential to explore an optimal sampling method and a modeling method for the surrogate model.However,due to the adoption of a surrogate instead of the simulation model for optimization,the optimization design obtained is affected to some extent due to the error between them.Moreover,in the modeling the simulation model,there are also a large number of uncertain factors,such as the uncertainty of the parameters of the simulation model.Therefore,these uncertainties must be considered and handled.In this paper,the optimal remediation designs under different confidence levels in terms of the remediation design optimization of nitrobenzene(which belongs to DNAPLs)contaminating groundwater in a chemical plant were obtained using the multi-phase flow simulation technology,the surrogate model,simulation-optimization method and uncertainty analysis.Firstly,a multi-phase flow numerical simulation model simulating the migration of DNAPLs was established based on the collected data,and the UTCHEM was used to solve this model.After the simulation model was established,the initial training samples used to establish the surrogate model were obtained using the Latin hypercube sampling method.Based on the training samples,the corresponding surrogate models were established using MGGP(Multi-Gene Genetic Programming),SVR(Support Vector Regression)and KRG(Kriging),respectively.Then,the three stand-alone surrogate models were combined to establish four ensemble surrogate models,including KRG-SVR,MGGP-KRG,MGGP-SVR and MGGP-KRG-SVR.The accuracy of the surrogate models was evaluated by appropriate indicators,and the most accurate surrogate model(i.e.the MGGP-KRG model)was selected.Then,in order to further improve the accuracy of the surrogate model,an adaptive sampling algorithm was adopted to search for new sample points around the original samples which have big errors and add them to the initial training samples.Based on the updated training samples,the most accurate surrogate model was updated to improve its overall approximation degree to the simulation model.Then,the minimization of the cost of the DNAPLs contaminated aquifer remediation design was used as the objective function,the number of the extraction and injection wells,the location of the extration and injection wells,the amount of water extraction and injection of each well and the repair time were used as the decision variables,and the removal rate of nitrobenzene should reach the remediation goal was used as an inequality constraint,the surrogate of the simulation model which describes the transport of the pollutant was used as an equality constraint,and other related constraints,so as to establish the 0-1 mixed integer nonlinear programming optimization model.The genetic algorithm was adopted to solve this optimization model.Afterwards,the uncertainty of the surrogate model was handled by the "conservative surrogate" method,which reduces the impact of the error between the surrogate and the simulation model on the optimization results.Finally,with regard to the uncertainty of the model parameters,Monte Carlo simulation was firstly used to analyze its uncertainty,and then a stochastic optimization model was established and solved by the chance constrained programming method to obtain the optimal remediation designs under different confidence levels.Based on the above researches,the following six conclusions can be obtained:(1)Compared with Kriging(KRG)and Support Vector Regression(SVR),the surrogate model established by multi-gene genetic programming(MGGP)is more accurate,indicating that MGGP has advantages in surrogate modeling.(2)Compared with the stand-alone surrogate models,the ensemble surrogate models have higher accuracy,indicating that ensemble surrogate model is a promising modeling method.Among all the ensemble surrogate models that were established,the most accurate one is the MGGP-KRG instead of the MGGP-KRG-SVR,indicating that the ensemble surrogate model is not better in case of being combined by more stand-alone surrogate models.Instead,only the combination of stand-alone surrogate models with complementary properties can exert their largest advantages.(3)The adaptive sampling by adding new samples around the original samples which have big errors effectively improves the overall quality of sampling,thus improving the overall approximation degree of the surrogate model to the simulation model,indicating that this adaptive sampling method is conducive to improving the accuracy of the surrogate model.(4)Not only treat the locations of the extraction and water injection wells,the amount of extraction and injection and the repair time as the decision variables,but also treat the number of the extraction and water injection wells as the decision variables,establishing the 0-1 mixed integer nonlinear programming optimization model.Thus,realizing the overall consideration of these decision variables,obtaining the overall optimal remediation design.(5)By analysis of the uncertainties in the process of finding optimal groundwater remediation design,optimal groundwater remediation designs under different confidence levels are obtained,providing different decision scheme for the decision makers.