Iglesias, Marco and McLaughlin, Dennis (2012) Data inversion in coupled subsurface flow and geomechanics models. Inverse Problems, Vol. 28 (No. 11). p. 115009. doi:10.1088/0266-5611/28/11/115009 ISSN 0266-5611.

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Abstract

We present an inverse modeling approach to estimate petrophysical and elastic properties of the subsurface. The aim is to use the fully coupled geomechanics-flow model of Girault et al (2011 Math. Models Methods Appl. Sci. 21 169–213) to jointly invert surface deformation and pressure data from wells. We use a functional-analytic framework to construct a forward operator (parameter-to-output map) that arises from the geomechanics-flow model of Girault et al. Then, we follow a deterministic approach to pose the inverse problem of finding parameter estimates from measurements of the output of the forward operator. We prove that this inverse problem is ill-posed in the sense of stability. The inverse problem is then regularized with the implementation of the Newton-conjugate gradient (CG) algorithm of Hanke (1997 Numer. Funct. Anal. Optim. 18 18–971). For a consistent application of the Newton-CG scheme, we establish the differentiability of the forward map and characterize the adjoint of its linearization. We provide assumptions under which the theory of Hanke ensures convergence and regularizing properties of the Newton-CG scheme. These properties are verified in our numerical experiments. In addition, our synthetic experiments display the capabilities of the proposed inverse approach to estimate parameters of the subsurface by means of data inversion. In particular, the added value of measurements of surface deformation in the estimation of absolute permeability is quantified with respect to the standard history matching approach of inverting production data with flow models. The proposed methodology can be potentially used to invert satellite geodetic data (e.g. InSAR and GPS) in combination with production data for optimal monitoring and characterization of the subsurface.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Inverse Problems
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0266-5611
Official Date:	2012
Dates:	Date Event 2012 Published
Volume:	Vol. 28
Number:	No. 11
Page Range:	p. 115009
DOI:	10.1088/0266-5611/28/11/115009
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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