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Laboratoire de mathématiques et de leurs applications (LMAP)


Directeur du LMAP


jacques.giacomoni@univ-pau.fr (jacques.giacomoni @ univ-pau.fr)


Directrice Adjointe du LMAP


sophie.mercier@univ-pau.fr (sophie.mercier @ univ-pau.fr)


Gestion administrative

gestion-lmap@univ-pau.fr (gestion-lmap @ univ-pau.fr)



secretariat-lmap@univ-pau.fr (secretariat-lmap @ univ-pau.fr)

Tél : 05 59 40 75 13
05 59 40 74 32

Fax : 05 59 40 75 55


Administrateurs Web

web-lma@univ-pau.fr (web-lma @ univ-pau.fr)

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Post-doctorat de 24 moisInverse problem for random field conditioning under connectivity constraints


Competences and keywords: Graph manipulation, optimization, stochastic methods, scoring or data mining, applied mathematics, reservoir simulation.

It becomes a common practice nowadays to take into account numerous uncertain parameters while petroleum
reservoir numerical representation. The multiple realizations are constructed by sampling the uncertainty domain
of parameters defining the structure, the geology and dynamic properties of the reservoir. By simulating the
dynamic response of multiple realizations, the uncertainties on reserves and the production profiles can be
evaluated. Such approach is mainly valuable for the green fields when there is no yet dynamic data.
When the dynamic response of field is available, the multiples realizations sampled from prior assumptions
might not fit the dynamic observations, hence the so the called “history matching” is applied. A history matching is
an inverse problem (Tarantola and Valette 1982) where the combination of uncertain input parameters of the
model is to be found in order to fit the observed data. Since, many techniques of assisted history matching are
appeared (see an exhaustive state of art in Linde et al. 2015). All these techniques can be symbolically split into two
groups, probabilistic and optimization approaches:

  • In the Probabilistic approaches we find the techniques such Forward modeling with rejection, Analytical Bayesian approach (mainly developed for multigaussian space), Experimental Bayesian (mainly proposed through parameterization).
  • The Optimization approaches in their turn are focused on the minimization of the objective function whether in the global input parameters’ space (mono-parameter sensitivity, experimental design, multi objective minimization) or are trying to capture local heterogeneities impacts (Iterative re-sampling, Gradual deformation, local PDF perturbation, Ensemble Kalman Filter, Ensemble Smoother).

Probabilistic approaches can be considered unbiased and robust by construction. But in practice, the high
dimension of the inverse problem requires a tremendous amount of a priori realizations in order to obtain a
representative ensemble of a posteriori ones. The optimization approaches in their turn do not guaranty that the
entire ensemble of potentially matching models is found. Although the optimization approaches are widely used in
the petroleum reservoir modeling, this is a serious limitation.
A common problem in practice is that even when providing an important number of a priori realizations
sampling into the wide uncertainty ranges on the input parameters, the dynamic responses interval does not always
cover the observed data. It induces a void a posteriori ensemble for probabilistic approaches, or an initial ensemble
very far from possible solutions for optimization methods. This practical bottleneck demonstrates the limitations
of the existing approaches proposed for the inverse problem with high number of parameters where the limited
number of the realizations does not cover representatively the uncertainty domain of the prior.

Post-doctoral study objectives:
The goal of this post-doctoral study is to propose another solution for the inverse problem in reservoir
modeling. It has been demonstrated in many applications and data acquisition (e.g. Canas et al. 1994, McLennan
and Deutsch 2005), that the dynamic response is mainly sensitive to the connected trajectories and related
capacities. Hence, instead of sampling the direct input parameters defining a prior with no guaranty that it will
represent a variability of possible dynamic responses, it is proposed to sample the indirect parameters impacting
the dynamic responses.
The post-doctoral fellow will be based at Total research center CSTJF (Centre Scientifique et Technique Jean
Géger). The supervising staff will be Dr Tatiana Chugunova from Total geostatistics team for problem definition,
reservoir simulation, field generators, database management and exploitation, and Pr Philippe Poncet from LMAP
(Lab. Mathematics and their Applications, UMR UPPA-CNRS 5142) for optimization and dedicated numerical
aspects. The salary will be around 2392 €/month (Index INM 619).

Contact: CV + motivation letter to be sent to philippe.poncet @ univ-pau.fr