Predictive Assessment of Groundwater Flow Uncertainty in Multiscale Porous Media by Using Truncated Power Variogram Model

  • Liang Xue
  • Diao Li
  • Tongchao Nan
  • Jichun Wu


The spatial distribution of hydrogeological properties is essentially heterogeneous. Heterogeneity can be characterized quantitatively using geostatistics, which conventionally assumes that the stochastic process is stationary. However, growing evidence indicates that the spatial variability has the multiscale self-similarity characteristics and can be better characterized using non-stationary model but with statistically homogeneous increments. A general framework is developed in this work to conduct the uncertainty quantification analysis by using truncated power variogram model, which can explicitly account for measurement scale, observation scale, and window scale. The effect of the multiscale characteristics of the hydrogeological properties on the uncertainty and the consequential risk associated with the groundwater flow process is investigated. A synthetic two-dimensional saturated steady-state groundwater flow problem is used to evaluate the performance to predict the flow field distribution. For comparative purposes, the evaluation is based on both the truncated power and the traditional variogram models when the underlying porous medium is a random fractal field. The results show that the truncated power variogram model can perform the uncertainty quantification more accurately, and the adoption of traditional variogram model tends to result in a smoother estimation on the flow field and underestimate the uncertainty associated with the hydraulic head prediction. Upscaling is generally inevitable to avoid predictive uncertainty underestimation when the underlying random field exhibits multiscale characteristics.


Multiscale Random fractals Observation scale Truncated power variogram Geostatistics 



This work is funded by the Science Foundation of China University of Petroleum - Beijing (Grant No. 2462014YJRC038), the National Science and Technology Major Project (Grant No. 2016ZX05037003), National Natural Science Foundation of China (Grant No. 41602250) and China Geological Survey (Grant No. DD20160293).

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflicts of interest or financial disclosures to report.


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Authors and Affiliations

  1. 1.State Key Laboratory of Petroleum Resources and ProspectingChina University of PetroleumBeijingChina
  2. 2.Department of Oil-Gas Field Development, College of Petroleum EngineeringChina University of PetroleumBeijingChina
  3. 3.Department of Hydrosciences, School of Earth Sciences and EngineeringNanjing UniversityNanjingChina
  4. 4.State Key Laboratory of Pollution Control and Resources ReuseNanjingChina

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