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Probability perturbation method applied to the inversion of groundwater flow models using HydroGeoSphere
Hermans, Thomas; Scheidt, Céline; Caers, Jef et al.
20133rd HydroGeoSphere User Conference
 

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Keywords :
Probability Perturbation Method; Inverse Problems; HydroGeoSphere; Multiple-Point Statistics; SGems
Abstract :
[en] Solving spatial inverse problems in Earth Sciences remains a big challenge given the high number of parameters to invert for and the complexity of non-linear forward models. Techniques were developed to reduce the number of parameters to invert for or to produce geologically consistent simulations from an initial guess. These techniques ask for a prior model to constrain the spatial distribution of the solution. Geostatistical models contain, by nature, information to control the spatial features of the inverse solutions, but the integration of dynamic data into such models remains difficult. We adapted, the “probability perturbation algorithm” (PPM) using Matlab® to invert hydrogeological data using multiple-point geostatistics to build models of pre-defined hydrofacies. The algorithm uses HydroGeoSphere (HGS) to compute the forward response of the model and SGems to produce geostatistical realizations. The algorithm only needs the proper definition of all the parameters to be used by HydroGeoSphere (grid matching with SGems, position of the wells, pumping rate, facies properties, boundary conditions, etc.). The PPM algorithm will automatically seek solutions fitting both hydrogeological data and geostatistical constraints. Through the inversion process, the initial geostatistical realization is perturbed. Only geometrical features of the model are affected, i.e. we do not attempt to directly find the optimal value of hydrogeological parameters, but the optimal spatial distribution of facies whose prior distribution is quantified in a training image. The algorithm can be divided in three steps. In the first step, we use SGems to generate an initial facies model with the multiple-point geostatistical algorithm SNESIM (single normal equation simulation). The facies model is composed of several categories representing hydrological facies (e.g. gravel, sand and clay). It can be conditioned using hard data (borehole data) and/or soft data (e.g. geophysical data). We then run a first flow simulation with HydroGeoSphere. This requires defining hydrogeological parameters (porosity, hydraulic conductivity, etc.) for each category of the facies model to create a hydrogeological model. The response of the latter model is compared to the expected one through an objective function. In the second step, a perturbation to the facies model is computed using a single parameter called rD. This perturbation is used to generate a new facies model with SGems and calculate a new objective function value via HGS, as done in the first step. An inner loop optimizes the value of rD. In the third step, we verify if the objective function of the best fitting model is smaller than a predefined value. If it is the case, we stop the algorithm, otherwise we go back to step 2 until convergence. We illustrate the methodology with a synthetic example in an alluvial aquifer. The model is based on a training image depicting gravel channels and clay lenses in a coarse sand aquifer. We simulate a pumping test and inverse water level data recorded at 9 wells using our implementation of the PPM algorithm. Using this method, it is possible to generate multiple solutions and to derive a posterior probability of the facies distribution.
Disciplines :
Geological, petroleum & mining engineering
Author, co-author :
Hermans, Thomas ;  Université de Liège - ULiège > Département Argenco : Secteur GEO3 > Géophysique appliquée
Scheidt, Céline;  Stanford University > Energy Resource Engineering
Caers, Jef;  Stanford University > Energy Resource Engineering
Nguyen, Frédéric ;  Université de Liège - ULiège > Département Argenco : Secteur GEO3 > Géophysique appliquée
Language :
English
Title :
Probability perturbation method applied to the inversion of groundwater flow models using HydroGeoSphere
Publication date :
04 April 2013
Event name :
3rd HydroGeoSphere User Conference
Event organizer :
University of Neuchâtel
Event place :
Neuchâtel, Switzerland
Event date :
du 3 avril au 5 avril 2013
Audience :
International
References of the abstract :
3rd International HydroGeoSphere User Conference 2013 - Program with Abstracts
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 29 March 2013

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