Data Assimilation For Subsurface Flow Models

As a phenomenon of flow in porous media,subsurface flow is ubiquitous in nature and has significant impacts on human production and life.The research on subsurface flow is with theoretical and practical importance for soil water resources managements,environmental pollution prevention,and clean energy exploitation.As a complementary method for experimental research,the numerical modeling approach emphasizes on building mathematic models based on the inherent scientific laws,and is usually used for providing quantitative predictions.To obtain reliable predictions,we need to reduce the uncertainties in model parameters.However,the parameters like permeability and porosity in subsurface flow models are usually spatially heterogeneous,and their direct measurements are expensive and time-consuming to obtain.One recent popular research is to incorporate the indirect measurements,e.g.,the pressure and concentration which are relatively easier to obtain,to estimate the model parameters through the data assimilation methods.Nevertheless,the spatial heterogeneity of the parameters and the high computational cost of large-scale numerical models have posed great challenges to existing data assimilation methods.What's more,the numerical models are just the simplification of real-world processes.They may not precisely describe the entire processes when dealing with the complex real-world problems,which may lead to structural errors.Therefore,the over-reliance on a specific model would make potential threats to the accuracy of data assimilation.To address the issues above and motivated by the recent developments of data assimilation,uncertainty quantification and machine learning,in this dissertation,the surrogate models are employed in the classical data assimilation methods to improve computational efficiency,and new data assimilations schemes using machine learning techniques are proposed for complicated problems through strengthening the data utilization and reducing the dependence on specific numerical models.Thus,the effects caused by model errors may be alleviated.The main research contents are given below:(1)To improve the computational efficiency of iterative ensemble Kalman filter(IEn KF)in large-scale nonlinear problems,we proposed a probabilistic collocation based iterative Kalman filter(PCIKF).In PCIKF,the polynomial chaos expansion(PCE)was utilized to build surrogates for original numerical models,and the PCE coefficients were used to quantify the sensitivity between parameters and measurements.As a result,the efficiency could be greatly improved.For the relatively high-dimensional(i.e.,with a large number of unknown parameters)problems,we conducted analysis of variance for the outputs of original models,and only kept the zero-and first-order terms for PCE,which further reduced the computational cost.We applied PCIKF for data assimilation of landfill water-gas transport models and compared it with IEn KF.The results of numerical cases showed that with the same computational cost,PCIKF could achieve better estimation accuracy,and with the same accuracy,PCIKF was more computationally efficient.(2)To guarantee both the accuracy and efficiency of data assimilation,we combined the ensemble smoother with multiple data assimilation(ES-MDA)with multi-fidelity simulation,and proposed an adaptive multi-fidelity ensemble smoother(AMF-ES).The level of fidelity is a comprehensive measurement for the efficiency and accuracy of a model.Generally,the higher of the fidelity level,the more accurate and less efficient of the model,and vice versa.In AMF-ES,a small number of samples provided by the high-fidelity(HF)model and a large number of samples provided by the low-fidelity(LF)model were used to build a multi-fidelity Gaussian process(GP)surrogate for the original HF model,and the surrogate could simultaneously leverage the accuracy of HF model and the efficiency of LF model.During data assimilation,the adaptive selection of a certain number of samples enabled multi-fidelity GP to be refined around the posterior region with an affordable computational cost.We tested the performance of AMF-ES in a numerical case of unsaturated water flow and a real-world water-gas flow experiment in a large-scale bioreactor.The results demonstrated that AMF-ES was at least 15 times more efficient than ES-MDA using only the HF model,without sacrificing the accuracy of parameter estimation.(3)By considering the numerical models may not be accurate when coping with highly complicated real-world problems,we proposed to build a data-driven model while adhering the inherent physical constraints.We introduced the physics-informed generative adversarial networks(PI-GANs)into the data assimilation of subsurface flow models.We extended the original onedimensional PI-GANs to two-dimensional ones.The results showed that PI-GANs could effectively learn massive observation data collected at sparse locations to capture their distributions,and simultaneously satisfy the potential physical constraints.Eventually,the trained PI-GANs could accurately predict the distribution of parameters and states at the unmeasured locations,and each predicted sample could generally satisfy the given saturated flow equations.What's more,PI-GANs were built on neural networks,which endowed it the advantage to deal with highdimensional problems through adjusting the network architectures flexibly.However,it needs to mention that spatial variability can be better characterized by more data at the increasing monitoring cost.Therefore,the high demands for training data could be a limitation of PI-GANs in practical applications.(4)To address the limitation of PI-GANs in data requirement,we borrowed the idea from image processing,and utilized the image semantic inpainting methods to estimate the heterogeneous parameter field.Nevertheless,the original image semantic inpainting can only use the direct parameter measurements,which fails to utilize indirect measurements like pressure and concentration.Therefore,we proposed a physics-informed image semantic inpainting framework,aiming at utilizing both the direct and indirect measurements,and realizing data assimilation.The physicsinformed WGAN-GP is the key part of this framework,and it utilized convolutional neural networks to explore the local correlations of the heterogeneous field,and employed the convolutional kernel as a finite difference operator to represent the physical constraints,which would be added to the original loss function of WGAN-GP.The computation was split into two stages.In the first stage,a large number of prior samples that satisfy the potential numerical model were used to train the WGAN-GP,and in the second stage,the predictions at unmeasured locations were given by the trained WGAN-GP based on the sparse measurements.The performance of the proposed framework was evaluated in a groundwater flow case with heterogeneous parameter field.The results showed that the WGAN-GP could learn the potential physical laws and eventually predict the whole parameter field based on the sparse measurements.Meanwhile,it was also validated that the hydraulic head data could help improve the prediction performance of the hydraulic conductivity field.This method provided a new concept of data assimilation,and avoided the huge demands for observation data like PI-GANs,which endowed it advantages to get applied in real-world subsurface flow problems with sparse observation data.