Uncertainty quantification of contaminant transport and risk assessment with conditional stochastic collocation method

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• 作者：Liangsheng Shi (1)
  Lingzao Zeng (2)
  Yunqing Tang (1)
  Cheng Chen (3)
  Jinzhong Yang (1)
  
• 关键词：Solute transport ; Conditional simulation ; Stochastic collocation method ; Random field
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：27
• 期：6
• 页码：1453-1464
• 全文大小：873KB
• 参考文献：1. Baalousha H, Kongeter J (2006) Stochastic modelling and risk analysis of groundwater pollution using FORM coupled with automatic differentiation. Adv Water Resour 29(12):1815-832 CrossRef
  2. Bellin A, Fiori A (2003) Non-ergodic solute transport in self-similar porous formations: the effect of conditioning. Adv Water Resour 26(7):759-71 CrossRef
  3. Bjerager P (1990) On computation methods for structural reliability analysis. Struct Saf 9:79-6 CrossRef
  4. Foo J, Karniadakis GE (2010) Multi-element probabilistic collocation method in high dimensions. J Comput Phys 229(5):1536-557 CrossRef
  5. Ganapathysubramanian B, Zabaras N (2007) Sparse grid collocation schemes for stochastic natural convection problems. J Comput Phys 225(1):652-85 CrossRef
  6. Ghanem R, Spanos P (1991) Stochastic finite elements: a spectral approach. Springer, New York CrossRef
  7. Harter T, Yeh TCJ (1996) Conditional stochastic analysis of solute transport in heterogeneous, variably saturated soils. Water Resour Res 32(6):1597-609 CrossRef
  8. Hernandez AF, Neuman SP, Guadagnini A, Carrera J (2003) Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion. Stoch Environ Res Risk Assess 17(5):329-38 CrossRef
  9. Hu BX, He C (2006) Using sequential self-calibration method to estimate a correlation length of a log-conductivity field conditioned upon a tracer test and limited measured data. Stoch Environ Res Risk Assess 21(1):89-6 CrossRef
  10. Li H, Zhang D (2007) Probabilistic collocation method for flow in porous media: comparisons with other stochastic method. Water Resour Res 43:44-8. doi:10.1029/2006WR005673
  11. Li W, Lu Z, Zhang D (2009) Stochastic analysis of unsaturated flow with probabilistic collocation method. Water Resour Res 45:W08425. doi:10.1029/2008WR007530
  12. Li J, Li J, Xiu D (2011) An efficient surrogate-based method for computing rare failure probability. J Comput Phys 230:8683-697 CrossRef
  13. Lin G, Tartakovsky AM (2009) An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media. Adv Water Resour 32(5):712-22. doi:10.1016/j.advwatres.2008.09.003 CrossRef
  14. Lin G, Tartakovsky AM, Tartakovsky DM (2010) Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids. J Comput Phys 229(19):6995-012 CrossRef
  15. Liou TS, Yeh HD (1997) Conditional expectation for evaluation of risk groundwater flow and solute transport: one-dimensional analysis. J Hydrol 199(3-):378-02 CrossRef
  16. Lu Z, Zhang D (2003) On importance sampling Monte Carlo approach to uncertainty analysis of flow and transport in porous media. Adv Water Resour 26(11):1177-188 CrossRef
  17. Lu Z, Zhang D (2004) Conditional simulations of flow in randomly heterogeneous porous media using a KL-based moment-equation approach. Adv Water Resour 27:859-74 CrossRef
  18. Morales-Casique E, Neuman SP, Guadagnini A (2006) Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: theoretical framework. Water Resour Res 2006(29):1238-255
  19. Müller F, Jenny P, Meyer DW (2011) Probabilistic collocation and Lagrangian sampling for advective tracer transport in randomly heterogeneous porous media. Adv Water Resour 34(12):1527-538 CrossRef
  20. Nobile F, Tempone R, Webster CG (2008) An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data. SISM J Numer Anal 46(5):2411-442 CrossRef
  21. Pan F, Ye M, Zhu J, Wu YS, Hu B, Yu Z (2009) Incorporating layer- and local scale heterogeneities in numerical simulation of unsaturated flow and tracer transport. J Contam Hydrol 103(3-):194-05 CrossRef
  22. Samuel H, Yeh TCJ (1997) Estimation of co-conditional moments of transmissivity, hydraulic head, and velocity fields. Adv Water Resour 22(1):87-5
  23. Shi L, Yang J (2009) Qualification of uncertainty for simulating solute transport in the heterogeneous media with sparse grid collocation method. J Hydrodyn 21(6):779-89 CrossRef
  24. Shi L, Yang J, Zhang D, Li H (2009) Probabilistic collocation method for unconfined flow in heterogeneous media. J Hydrol 365(1-):4-0 CrossRef
  25. Tong J, Hu BX, Yang J (2012) Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field. Stoch Environ Res Risk Assess 26(3):467-78 CrossRef
  26. Wasilkowski GW, Wozniakowski H (1995) Explicit cost bounds of algorithms for multivariate tensor product problems. J Complex 11:1-6 CrossRef
  27. Xiu D, Hesthaven JS (2005) High-order collocation methods for differential equations with random inputs. SIAM J Sci Comput 27(3):1118-139 CrossRef
  28. Zeng L, Shi L, Zhang D, Wu L (2012) A sparse grid based Bayesian method for contaminant source identification. Adv Water Resour 37:1- CrossRef
  29. Zhang D, Shi L, Chang H, Yang J (2010) A comparative study of numerical approaches to risk analysis of contaminant transport. Stoch Environ Res Risk Assess 24(7):971-84 CrossRef
  
• 作者单位：Liangsheng Shi (1)
  Lingzao Zeng (2)
  Yunqing Tang (1)
  Cheng Chen (3)
  Jinzhong Yang (1)
  
  1. National Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, People’s Republic of China
  2. Institute of Soil and Water Resources and Environmental Science, Zhejiang University, No. 866 Yuhangtang Road, Hangzhou, Zhejiang, 310058, People’s Republic of China
  3. Production Enhancement, Halliburton, Houston, TX, 77032, USA
  

文摘

Solute transport prediction is always subject to uncertainty due to the scarcity of observation data. The data worth of limited measurements can be explored by conditional simulation. This paper presents an efficient approach for the conditional simulation of solute transport in a randomly heterogeneous aquifer. The conditioning conductivity field is parameterized by the Karhunen–Loève (KL) expansion, and the concentration field is represented by Lagrange polynomials of random variables in the KL expansion. After employing the stochastic collocation method (SCM), stochastic governing advection–dispersion equations are reduced to a series of uncoupled deterministic equations. The concentration realizations can be obtained by sampling the established Lagrange polynomials instead of solving governing equations repeatedly. We assess the accuracy and computational efficiency of this method in comparison to the conditional Monte Carlo simulation. The influence of conditioning to hydraulic conductivity measurements on transport is analyzed. Numerical results demonstrate that the SCM can efficiently derive the conditional statistics of concentration as well as the probability of the aquifer to be contaminated. It is shown that the contamination risk is significantly influenced by measurements conditioning.