Ground surface dynamics is one of the processes influencing the future of the Wadden Sea area. Vertical land movement, both subsidence and heave, is a direct contributor to changes in the relative sea level. It is defined as the change of height of the Earth’s surface with respect to a vertical datum. In the Netherlands, the Normaal Amsterdams Peil (NAP) is the official height datum, but its realisation via reference benchmarks is not timedependent. Consequently, NAP benchmarks are not optimal for monitoring physical processes such as land subsidence. However, surface subsidence can be regarded as a differential signal: the vertical motion of one location relative to the vertical motion of another location. In this case, the actual geodetic height datum is superfluous. In the present paper, we highlight the processes that cause subsidence, with specific focus on the Wadden Sea area. The focus will be toward anthropogenic causes of subsidence, and how to understand them; how to measure and monitor and use these measurements for better characterisation and forecasting; with some details on the activities in the Wadden Sea that are relevant in this respect. This naturally leads to the identification of knowledge gaps and to the formulation of notions for future research.

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Subsidence in the Dutch Wadden Sea

Robust numerical implementation of a 3D rate‐dependent model for reservoir geomechanical simulations

Anthropogenic land subsidence can be evaluated and predicted by numerical models, which are often built over deterministic analyses. However, uncertainties and approximations are present, as in any other modeling activity of real-world phenomena. This study aims at combining data assimilation techniques with a physically-based numerical model of anthropogenic land subsidence in a novel and comprehensive workflow, to overcome the main limitations concerning the way traditional deterministic analyses use the available measurements. The proposed methodology allows to reduce uncertainties affecting the model, identify the most appropriate rock constitutive behavior and characterize the most significant governing geomechanical parameters. The proposed methodological approach has been applied in a synthetic test case representative of the Upper Adriatic basin, Italy. The integration of data assimilation techniques into geomechanical modeling appears to be a useful and effective tool for a more reliable study of anthropogenic land subsidence.

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A novel methodological approach for land subsidence prediction through data assimilation techniques

. From the analysis of GPS monitoring data collected above gas
fields in the Adriatic Sea, in a few cases subsidence responses have been
observed not to directly correlate with the production trend. Such behavior,
already described in the literature, may be due to several physical
phenomena, ranging from simple delayed aquifer depletion to a much more
complex time-dependent mechanical response of subsurface geomaterials to
fluid withdrawal. In order to accurately reproduce it and therefore to be
able to provide reliable forecasts, in the last years Eni has enriched its
3D finite element geomechanical modeling workflow by adopting an advanced
constitutive model (Vermeer and Neher, 1999), which also considers the
viscous component of the deformation. While the numerical implementation of
such methodology has already been validated at laboratory scale and tested
on synthetic hydrocarbon fields, the work herein presents its first
application to a real gas field in the Adriatic Sea where the phenomenon has
been observed. The results show that the model is capable to reproduce very
accurately both GPS data and other available measurements. It is worth
remarking that initial runs, characterized by the use of model parameter
values directly obtained from the interpretation of mechanical laboratory
tests, already provided very good results and only minor tuning operations
have been required to perfect the model outcomes. Ongoing R&D projects
are focused on a regional scale characterization of the Adriatic Sea basin
in the framework of the Vermeer and Neher model approach.

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Elasto-viscoplastic modeling of subsidence above gas fields in the Adriatic Sea

Evaluating the subsidence above gas reservoirs with an elasto-viscoplastic constitutive law. Laboratory evidences and case histories

Subsidence modeling is an important activity in the oil and gas industry, for the environmental and operational implications associated to this phenomenon. Abaqus/Standard has been used for many years in Eni as the main numerical simulator for studying the geomechanical behavior of reservoirs. The results of a large campaign of acquisition of subsidence monitoring data in conjunction with the advanced analysis of laboratory experiments have shown that, in some cases, an improved mechanical characterization can be tailored to better capture the complex behavior of the reservoir rock under the effect of underground fluid withdrawal. In this work we first present an implementation in Abaqus/Standard of an elasto-viscoplastic model - namely the Vermeer and Neher model - as user defined material by means of the UMAT subroutine. Next, we provide the results of various simulations of laboratory tests that were performed to investigate its capability to identify the main features of the behavior of reservoir sands, also including time dependency. Finally, we show a preliminary application to a synthetic, nonetheless realistic, reservoir model that has been performed to assess the capabilities of the elasto-viscoplastic model in the simulation of subsidence evolution

Implementation of an elasto-viscoplastic constitutive law in Abaqus/Standard for an improved characterization of rock materials

Advances in Geomechanical Subsidence Modeling: Effects of Elasto-Visco-Plastic Constitutive behavior.

In the oil and gas industry, subsidence modelling aims to predict the deformation of the ground surface induced by hydrocarbon withdrawal from underground reservoir rocks. In reason of environmental and operational implications associated to subsidence, energy companies make a firm commitment to providing accurate estimates and reliable forecasts. This goal can be achieved through numerical simulations with advanced constitutive models accounting for soil/rock plasticity and creep, such as the model proposed by Vermeer and Neher in 1999. Several different implementations of this model have been proposed in the literature, including explicit and semi-implicit time integrations, but a clean and consistent fully implicit formulation is still missing. In this work, in the line of the classical approach for the modified Cam-Clay model, a fully implicit backward-difference integration is proposed and validated. The derivation of the consistent stiffness matrix is also described in detail, together with its validation strategy. The model has also been implemented in a commercial code for finite element analysis through a user-defined material subroutine. We show the expected advantages of the implicit formulation in terms of stability with respect to the explicit formulation. The examples include studies at material point level and at field scale for a case study of subsidence above a synthetic gas reservoir.

Fabrizio Gemelli

Papers

Implementation of an elasto-viscoplastic constitutive law in Abaqus/Standard for an improved characterization of rock materials

Elasto-viscoplastic modeling of subsidence above gas fields in the Adriatic Sea

Evaluating the subsidence above gas reservoirs with an elasto-viscoplastic constitutive law. Laboratory evidences and case histories

Advances in Geomechanical Subsidence Modeling: Effects of Elasto-Visco-Plastic Constitutive behavior.

A Numerical Study on Explicit vs Implicit Time Integration of the Vermeer-Neher Constitutive Model