May 22 – 25, 2023
Europe/London timezone

Simulation of the inelastic deformations of porous reservoirs under cyclic loading relevant for underground hydrogen storage

May 25, 2023, 9:15 AM
Oral Presentation (MS12) Advances in computational and experimental poromechanics MS12


Mr Kishan Ramesh Kumar (TU Delft)


Subsurface geological formations can be utilized to safely store large-scale (TWh) renewable energy in the form of green gases such as hydrogen. Successful implementation of this technology involves estimating feasible storage sites, including rigorous mechanical safety analyses. Geological formations are often highly heterogeneous and entail complex nonlinear inelastic rock deformation physics when utilized for cyclic energy storage. One of the major concerns of energy storage in the subsurface is the consequent ground surface subsidence or uplift. Several researchers in the past have reported subsidence in the carboniferous sandstone fields across the world which are used to produce hydrocarbons (Hettema et al., 2002; Teatini et al., 2011). When these reservoirs are used to store hydrogen, this results in seasonal cyclic loading on the reservoir that could cause permanent subsidence or uplift depending on the operating conditions and the rock characteristics. This calls for accurate modeling of subsidence for understanding the grain scale physics of the rocks in the subsurface. In this work, we present a novel scalable computational framework to analyze the impact of nonlinear deformation of porous reservoirs under cyclic loading. The proposed methodology includes three different time-dependent nonlinear constitutive models to appropriately describe the behavior of sandstone, shale rock and salt rock. Inelastic deformations such as plasticity observed in sandstone (Pijnenburg et al., 2019), viscoplasticity observed in shale (Haghighat et al., 2020) and creep in rock-salt (Spiers et al., 1990) are commonly observed in underground formations by these rocks.

To model creep, a power law formulation, where strain rate is a function of stress, was employed for brittle rocks (Bérest et al., 2019; Xu et al., 2012). To model plasticity of sandstone, cyclic modified cam clay model (MCC) (Carter et al., 1979) is further extended to account for viscoplasticity of shale rocks using a Perzyna based formulation (Haghighat et al., 2020). An implicit time-integration scheme is developed to preserve the stability of the simulation. Firstly, these models are implemented and compared with the existing literature. In order to ensure its scalability, the numerical strategy adopts a multiscale finite element (Ramesh Kumar & Hajibeygi, 2021) formulation, in which coarse scale systems with locally-computed basis functions are constructed and solved. Further, the effect of heterogeneity on the results and estimation of deformation is analyzed. Lastly, the Bergermeer test case --an active Dutch natural gas storage field comprising predominantly of sandstone-- is studied to investigate the influence of inelastic deformation on the uplift caused by cyclic injection and production of gas. The constitutive laws are calibrated based on the uplift recorded by GPS stations for 1.75 years and then the uplift is compared with the GPS recorded stations for the remaining 2 years. The present study shows acceptable subsidence predictions in this field-scale test, once the properties of the finite element representative elementary volumes (REV) are tuned with the experimental data.


Bérest, P., Gharbi, H., Brouard, B., Brückner, D., DeVries, K., Hévin, G., Hofer, G., Spiers, C., & Urai, J. (2019). Very Slow Creep Tests on Salt Samples. Rock Mechanics and Rock Engineering, 52(9), 2917–2934.

Carter, J. P., Wroth, C. P., & Booker, J. R. (John R. . (1979). A critical state soil model for cyclic loading. In Soil Mechanics - Transient and Cyclic Loads (pp. 219–252). John Wiley & Sons Ltd.

Haghighat, E., Rassouli, F. S., Zoback, M. D., & Juanes, R. (2020). A viscoplastic model of creep in shale. GEOPHYSICS, 85(3), 155–166.

Hettema, M., Papamichos, E., & Schutjens, P. (2002). Subsidence delay: Field observations and analysis. Oil and Gas Science and Technology, 57(5), 443–458.

Pijnenburg, R. P. J., Verberne, B. A., Hangx, S. J. T., & Spiers, C. J. (2019). Inelastic Deformation of the Slochteren Sandstone: Stress-Strain Relations and Implications for Induced Seismicity in the Groningen Gas Field. Journal of Geophysical Research: Solid Earth, 124(5), 5254–5282.

Ramesh Kumar, K., & Hajibeygi, H. (2021). Multiscale simulation of inelastic creep deformation for geological rocks. Journal of Computational Physics, 440, 110439.

Spiers, C. J., Schutjens, P. M. T. M., Brzesowsky, R. H., Peach, C. J., Liezenberg, J. L., & Zwart, H. J. (1990). Experimental determination of constitutive parameters governing creep of rocksalt by pressure solution. Geological Society Special Publication, 54(1), 215–227.

Teatini, P., Castelletto, N., Ferronato, M., Gambolati, G., Janna, C., Cairo, E., Marzorati, D., Colombo, D., Ferretti, A., Bagliani, A., & Bottazzi, F. (2011). Geomechanical response to seasonal gas storage in depleted reservoirs: A case study in the Po River basin, Italy. Journal of Geophysical Research: Earth Surface, 116(F2).

Xu, T., Tang, C.-A., Zhao, J., Li, L., & Heap, M. J. (2012). Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys. J. Int.

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Country Netherlands
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Primary authors

Mr Kishan Ramesh Kumar (TU Delft) Dr Herminio Tasinafo Honorio (TU Delft) Dr Hadi Hajibeygi (TU Delft)

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