Transdimensional inversion of flow data in geomodeling: a first example on a two-dimensional layered porous medium

Julien Herrero and Thomas Bodin and Mustapha Zakari and Capucine Legentil and Guillaume Caumon. ( 2022 )
in: 2022 {RING} {Meeting}, pages 25, ASGA

Abstract

Evaluation of georesources involves to appropriately manage the level of detail needed in geomodels for subsurface porous flow and transport problems. The non-uniqueness of the problems considered in aquifer or reservoir modeling calls for using methods such as stochastic Bayesian inversion to appropriately estimate rock property parameters and quantify uncertainty. These approaches often consider a fixed number of model parameters. In geomodeling, however, some model components are discrete at the scale of concern (e.g., minerals, facies, fractures, layers), hence lead to unknown number of parameters in the inverse problem. To address this issue, we propose to use transdimensional Monte Carlo methods (also known as reversible jump Markov chain Monte Carlo) which are a way to solve the inverse problem with a suitable geological parameterization when the number of model parameters is an unknown. We consider as a first application example the 2D case of implicit layer interfaces defined by a level-set in a porous reservoir model. Using a Voronoi diagram parameterization, the number of discrete layers becomes an unknown parameter. Rather than randomly perturbing the petrophysical field of interest, we build the prior model by an averaging process of log data located inside layers. Hence, each layer is defined by thickness and interface depth information, and a constant petrophysical value. Through a history matching problem, a set of flow simulations is performed to generate production data used in the Markov chain as an acceptance criterion. These numerical simulations can only be solved on a model discretization conformal to discontinuities. To address this challenge, we capitalize on the local mesh updating strategy presented by Legentil et al. (2022). First results on a set of horizontal layers demonstrate that the algorithm is capable to capture the main geological discontinuities from a prior permeability model and flow data, suggesting that this transdimensional tool could be applied for more complex geometries such as anticlines or faulted reservoir models.

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BibTeX Reference

@INPROCEEDINGS{herrero_transdimensional_2022,
    author = { Herrero, Julien and Bodin, Thomas and Zakari, Mustapha and Legentil, Capucine and Caumon, Guillaume },
     title = { Transdimensional inversion of flow data in geomodeling: a first example on a two-dimensional layered porous medium },
 booktitle = { 2022 {RING} {Meeting} },
      year = { 2022 },
     pages = { 25 },
 publisher = { ASGA },
  abstract = { Evaluation of georesources involves to appropriately manage the level of detail needed in geomodels for subsurface porous flow and transport problems. The non-uniqueness of the problems considered in aquifer or reservoir modeling calls for using methods such as stochastic Bayesian inversion to appropriately estimate rock property parameters and quantify uncertainty. These approaches often consider a fixed number of model parameters. In geomodeling, however, some model components are discrete at the scale of concern (e.g., minerals, facies, fractures, layers), hence lead to unknown number of parameters in the inverse problem. To address this issue, we propose to use transdimensional Monte Carlo methods (also known as reversible jump Markov chain Monte Carlo) which are a way to solve the inverse problem with a suitable geological parameterization when the number of model parameters is an unknown. We consider as a first application example the 2D case of implicit layer interfaces defined by a level-set in a porous reservoir model. Using a Voronoi diagram parameterization, the number of discrete layers becomes an unknown parameter. Rather than randomly perturbing the petrophysical field of interest, we build the prior model by an averaging process of log data located inside layers. Hence, each layer is defined by thickness and interface depth information, and a constant petrophysical value. Through a history matching problem, a set of flow simulations is performed to generate production data used in the Markov chain as an acceptance criterion. These numerical simulations can only be solved on a model discretization conformal to discontinuities. To address this challenge, we capitalize on the local mesh updating strategy presented by Legentil et al. (2022). First results on a set of horizontal layers demonstrate that the algorithm is capable to capture the main geological discontinuities from a prior permeability model and flow data, suggesting that this transdimensional tool could be applied for more complex geometries such as anticlines or faulted reservoir models. }
}