Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling

Abstract

[1] The ensemble Kalman filter (EnKF) is coupled with upscaling to build an aquifer model at a coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had been taken for the purpose of inverse modeling. Building an aquifer model at the support scale of observations is most often impractical since this would imply numerical models with many millions of cells. If, in addition, an uncertainty analysis is required involving some kind of Monte Carlo approach, the task becomes impossible. For this reason, a methodology has been developed that will use the conductivity data at the scale at which they were collected to build a model at a (much) coarser scale suitable for the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (1) Generate an ensemble of realizations of conductivities conditioned to the conductivity data at the same scale at which conductivities were collected. (2) Upscale each realization onto a coarse discretization; on these coarse realizations, conductivities will become tensorial in nature with arbitrary orientations of their principal components. (3) Apply the EnKF to the ensemble of coarse conductivity upscaled realizations in order to condition the realizations to the measured piezometric head data. The proposed approach addresses the problem of how to deal with tensorial parameters, at a coarse scale, in ensemble Kalman filtering while maintaining the conditioning to the fine-scale hydraulic conductivity measurements. We demonstrate our approach in the framework of a synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities, piezometric heads, or both is analyzed.

Simultaneous Estimation of Geologic and Reservoir State Variables Within an Ensemble-Based Multiple-Point Statistic Framework

“…In order to accomplish this, a flexible pattern search strategy is implemented without specifying template as in the traditional MPS method. Moreover, unlike the previous study (Zhou et al 2012) that only works on a categorical parameter field, here the proposed method is demonstrated both in the cases of categorical and continuous parameter fields.…”

“…Jafarpour and Khodabakhshi (2011) developed the probability conditioning method, in which the dynamic data are first conditioned by EnKF to derive the parameter mean values, and then used these as soft data to regenerate the parameter realizations using MPS. Zhou et al (2012) developed a pattern searching inverse method to estimate both static and state parameters within an MPS framework. They extend the Direct Sampling (DS) method by Mariethoz et al (2010b) for inverse modeling; for this purpose they work with an ensemble of realizations of conductivity and their associated heads as multiple training images, this allows them to take into account patterns in the spatial fields of measured heads and conductivities when sampling with the DS algorithm.…”

“…This is done in the EnKF method, which is able to simultaneously estimate the parameter and state variables using incremental observed dynamic data and thus renders possible real-time data assimilation. The EnKF is gaining popularity in various disciplines such as meteorology, petroleum engineering and hydrogeology (Hamill et al 2001;Wen and Chen 2006;Gu and Oliver 2006;Chen and Zhang 2006;Hendricks Franssen and Kinzelbach 2008;Li et al 2012). However, EnKF has an optimal solution only if the parameter follows a multiGaussian distribution and if the state transfer function is linear (Aanonsen et al 2009).…”

“…In this work, a novel inverse method: Ensemble PATtern searching method (En-PAT) is proposed, which is an extension of the pattern searching inverse method previously proposed by Zhou et al (2012). Unlike the previous work focusing only on the estimation of geologic parameter such as conductivity, in this study, both the geologic parameter and reservoir state variables such as piezometric head, at each conditioning time step, are explicitly estimated through a pattern searching scheme.…”

Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

“…The EnKF is increasingly studied in hydrogeology as well as in petroleum engineering (e.g. Wen and Chen, 2005;Chen and Zhang, 2006;Hendricks Franssen and Kinzelbach, 2008;Sun et al, 2009;Nowak, 2009;Nan and Wu, 2010;Li et al, 2012b). The attractive characteristics of the EnKF are: (i) the efficiency in computation (e.g.…”