Surface deformation Inversion: Probing Pressure Dynamics and Fronts in Underground Storage
Authors: Abdollahi R. , Movassagh A. , Kasperczyk D. , Haghighi M. 
Published: October 2024

Abstract
The manipulation of reservoirs in different energy sectors, encompassing geothermal production, gas extraction, and the storage of gases like carbon dioxide, air, and hydrogen, frequently leads to seismic events and surface deformations as prominent consequences. The deformations on the surface offer vital insights and serve as an indirect diagnostic method, providing information about the nature and intensity of subsurface activities. Various methods with differing accuracies exist for measuring surface deformation, with tiltmeters being the most accurate. Tiltmeters possess the capability to detect deformations caused by activities like fluid injection, production, or hydraulic fracturing, making them particularly valuable in comprehensively understanding and monitoring subsurface dynamics. The objective of this study is to employ surface deformation data obtained from underground storage or production sites for the estimation of reservoir pressure values and their spatial fronts throughout the injection and production phases. Existing methods rely on analytical and semi-analytical forward models that employ the displacement solution for a thermoelastic strain nucleus within a half-space having a traction-free surface and an inversion model for estimating the pressure from deformation. Additionally, an inversion model is applied for the estimation of pressure based on deformation. The advanced semi-analytical forward models segment the reservoir into smaller elements resembling those used in reservoir simulations and calculate the resulting deformation caused by pressure alterations by aggregating the results from each individual block under constant pressure conditions. Nevertheless, these models come with diverse limitations, including but not limited to initial and boundary conditions, the number of layers, the shape of the reservoir, and the tilt of layers. In this study, the forward analytical model will be substituted with a numerical approach that possesses the capability to account for various complexities in reservoir and layering. Applying the accurate numerical forward model to convert subsurface pressure variations into surface deformation, optimization methods were employed to invert the surface deformation data and derive the pressure distribution within the reservoir. The model's proficiency was demonstrated by utilizing synthetic deformations generated by the numerical forward model to show the efficacy of the inversion technique. This demonstration emphasized the accuracy of the outcomes, demonstrating an error rate lower than 10% even in the worst-case scenario. A primary application of this method lies in assessing reservoir integrity, particularly in the context of underground gas storage, notably hydrogen due to its distinct properties. The integrity of these storage sites is paramount, necessitating comprehensive comprehension and precise control during injections and extractions to ensure operational success. The scrutiny of pressure values’ behavior and distribution within the reservoir assumes a pivotal role, acting as a critical gauge to distinguish between successful storage and potential issues such as leakage or loss within the system.