A two-invariant pseudoelastic model for reservoir compaction

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.