A two-invariant pseudoelastic model for reservoir compaction
N. Spiezia, M. Ferronato, C. Janna, P. Teatini
Dept. of Civil, Environmental and Architectural Engineering,
University of Padova, Padova, Italy
ABSTRACT
Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is
a challenging task that could have important environmental, social, and economical
impacts. Finite element models, if endowed with an appropriate constitutive law,
represent a useful tool for computing the displacements, the deformations, and the
stress distributions in reservoir applications. Several studies show that hypoelastic
laws, based on a stress-dependent vertical compressibility, are able to provide accurate
results, confirmed by in situ and satellite measurements. On the other hand,
such laws present some weaknesses related to the numerical implementation, in particular
due to the nonsymmetry of the tangent operator. This paper presents a new
constitutive model based on 2 invariants (the mean normal and deviatoric stresses),
characterized by a variable pressure-dependent bulk modulus K. This constitutive
law allows for overcoming most shortcomings of the hypoelastic law, although preserving
the same accuracy, reliability, and ease of use and calibration. This paper
presents a procedure to identify the parameters of the new model, starting from the
typically available data on the vertical compressibility. Numerical results show a
good agreement between the 2 laws, suggesting the proposed approach as a valid
alternative in reservoir applications
