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A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

Hermínio T. Honório, Maartje Houben, Kevin Bisdom, Arjan van der Linden, Karin de Borst, Lambertus J. Sluys, Hadi Hajibeygi

Abstract

Renewable hydrogen storage in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. Such operational conditions raise concerns about the mechanical stability of salt caverns. Choosing an appropriate constitutive model for salt mechanics is an important step in investigating this issue, and many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and which parameter set represent the given rock, based on stress-strain data, remains an unsolved challenge. For the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation datasets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is achieved by framing the calibration process as an optimization problem, for which the global PSO algorithm is employed. Dynamic data integration is achieved by a multi-step calibration strategy for a situation where experiments are included one at a time, as they become available. Additionally, our calibration strategy is made flexible to account for mild heterogeneity between rock samples, resulting in a single set of parameters that is representative of the deformation datasets. As a rigorous mathematical analysis and the lack of relevant experimental datasets, we consider a wide range of synthetic experimental data, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust and accuracy is improved as more experiments are included for calibration.

A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

Abstract

Renewable hydrogen storage in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. Such operational conditions raise concerns about the mechanical stability of salt caverns. Choosing an appropriate constitutive model for salt mechanics is an important step in investigating this issue, and many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and which parameter set represent the given rock, based on stress-strain data, remains an unsolved challenge. For the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation datasets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is achieved by framing the calibration process as an optimization problem, for which the global PSO algorithm is employed. Dynamic data integration is achieved by a multi-step calibration strategy for a situation where experiments are included one at a time, as they become available. Additionally, our calibration strategy is made flexible to account for mild heterogeneity between rock samples, resulting in a single set of parameters that is representative of the deformation datasets. As a rigorous mathematical analysis and the lack of relevant experimental datasets, we consider a wide range of synthetic experimental data, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust and accuracy is improved as more experiments are included for calibration.
Paper Structure (23 sections, 24 equations, 23 figures, 9 tables, 1 algorithm)

This paper contains 23 sections, 24 equations, 23 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Experimental methodology and results
  3. Model formulation
  4. Elastic strain
  5. Viscoelastic strain
  6. Viscoplastic strain
  7. Dislocation creep strain
  8. The model calibration strategy based on ensemble of data sets
  9. Group 1: Dislocation creep model
  10. Group 2: Elastic and viscoelastic models
  11. Group 3: Viscoplastic model
  12. Optimization strategy
  13. Optimization algorithm
  14. Multi-objective function optimization
  15. Results
  16. ...and 8 more sections

Figures (23)

  • Figure 1: Experimental results obtained from a triaxial test performed on the Z3 Leine salt rock sample.
  • Figure 2: Zoomed-in view of a reloading step of the experiment that allows for identification of both viscoplastic and viscoelastic deformations.
  • Figure 3: Discrete stress path in time.
  • Figure 4: Yield function for the viscoplastic model for different hardening parameters.
  • Figure 5: Steady state creep rates (slopes) represented by the magenta lines.
  • ...and 18 more figures