On the possible contribution of clayey inter-layers to delayed land subsidence above producing aquifers

Abstract. In recent years, measurements of land subsidence above pumped aquifers by permanent GPS and InSAR have exhibited some delay relative to drawdown ranging from months to years. The current modeling approaches accounting for water fluid dynamics and porous medium geomechanics may fail to predict such a delay and may underestimate the land settlement after the well shutdown. In the present communication, an investigation is made on the residual compaction of the intervening clayey formations as a possible contribution to retarded land subsidence. The pore pressure variation within the aquifer and its propagation in the clay are simulated by a finite element flow model, with the resulting pore pressure decline used as input data in a hypo-plastic geomechanical model. A proper sensitivity analysis on (i) aquifer depth, (ii) ratio between the sandy and the clayey layers thickness and hydraulic conductivity, (iii) oedometric compressibility in first and second loading cycles, is performed for a typical geology of a Quaternary sedimentary basin. The results show that a certain fraction, up to 20 % of the overall land subsidence, can take place after the shutdown of the producing wells depending on actual basin, litho-stratigraphy and parameter values

Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema of the spectrum. We use this preconditioned framework to solve a $3 \times 3$ block system arising in the simulation of fluid flow in large-size discrete fractured networks. We apply our polynomial preconditioner to a suitable Schur complement related with this system, which can not be explicitly computed because of its size and density. Numerical results confirm the excellent properties of the proposed preconditioner up to very high polynomial degrees. The parallel implementation achieves satisfactory scalability by taking advantage from the reduced number of scalar products and hence of global communications

An engineering approach to quantify geomechanical safety factors in UGS programs

Abstract. Underground Gas Storage (UGS) has become one of the most widely used practices to cope with seasonal peaks in energy consumption. The planning of any new UGS facility, or its upgrading to increase the working gas volume and reservoir performance, must be supported by an evaluation of possible induced effects on the environment. From a geomechanical point of view, storage activity results in a cyclic change in stress and deformation in the reservoir rock and the surrounding formations. The main environmental issues to be accounted for when natural fluid pore pressure is planned to be exceeded are the following: (a) the differential displacements at the land surface possibly mining the integrity of ground structure; (b) the integrity of the reservoir and caprock; (c) the possible reactivation of faults, if the target reservoir is located in a faulted basin; and (d) the vertical upheaval and land subsidence that can impact on the surface drainage network in low lying coastal areas. We present an original methodology for evaluating the geomechanical safety of UGS activities using an approach derived from what is traditionally applied in the structural design of buildings. A safety factor, a margin of security against risks, is defined for each of the geomechanical issues listed above. First, a 3D FE-IE numerical model is developed to reproduce the stress and displacement due to the UGS program under evaluation. Then the reservoir pressure is increased until the "failure" condition is reached allowing to evaluate how far the project designed condition is from the above limit. The proposed approach is applied to Romagna, a depleted gas reservoir in Northern Italy converted to UGS, with the aim of investigating the safety of the project to increase the reservoir pressure up to 120 % pi, where pi is the original reservoir pressure before the start of primary production. The 3D geomechanical model has been developed using recent 3D seismic data, land displacements by InSAR, lab tests on reservoir and caprock samples, in-situ Modular Formation Dynamic Tester (MDT) stress tests, and large background information acquired from other UGS reservoirs located in the same sedimentary basin. The analysis outcome has revealed that the investigated scenario is safe, with safety factor larger than 1, in the range from 1.2 to 4. The most critical condition (the smallest safety factor) has been obtained in relation to the mechanical integrity of the reservoir formation, under very conservative conditions (cohesion = 0, friction angle = 30∘)

On the construction of AMG prolongation through energy minimization

Algebraic Multigrid (AMG) is a very popular iterative method used in several applications. This wide diffusion is due to its effectiveness in solving linear systems arising from PDEs discretization. The key feature of AMG is its optimality, i.e., the ability to guarantee a convergence rate independent of the mesh size for different problems. This is obtained through a good interplay between the smoother and the interpolation. Unfortunately, for difficult problems, such as those arising from structural mechanics or diffusion problems with large jumps in the coefficients, standard smoothers and interpolation techniques are not enough to ensure fast convergence. In these cases, an improved prolongation operator is required to enhance the AMG effectiveness. In this work, we present an updated prolongation according to an energy minimization criterion and show how this minimization can be seen as a constrained minimization problem. In detail, we have that the constraint is twofold: the prolongation must be sparse, and its range must represent the operator near-kernel. Even though energy minimization is well-known in the AMG community, it has little application due to both its cost and difficult implementation. Here, we would like to make energy minimization feasible through suitable preconditioned and effective implementation. In particular, to solve this problem, we propose two strategies: a restricted Krylov subspace iterative procedure and the null-space method. Both approaches can be preconditioned to speed up the setup time. Finally, thanks to some numerical experiments, we demonstrate how the convergence rate can be significantly increased at a reasonable setup cost

Chronos: A general purpose classical amg solver for high performance computing

The numerical simulation of physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large-scale simulations are concerned, one of the most computationally expensive tasks is the solution of linear systems of equations arising from the discretization of the partial differential equations governing physical processes. This work presents Chronos, a collection of linear algebra functions specifically designed for the solution of large, sparse linear systems on massively parallel computers. Its emphasis is on modern, effective, and scalable Algebraic Multigrid (AMG) preconditioners for high performance computing (HPC). This work describes the numerical algorithms and the main structures of this software suite, especially from an implementation standpoint. Several numerical results arising from practical mechanics and fluid dynamics applications with hundreds of millions of unknowns are addressed and compared with other state-of-the-art linear solvers, proving Chronos's efficiency and robustness

A GPU-accelerated adaptive FSAI preconditioner for massively parallel simulations

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in the further development of scientific and technical software. For large scale simulations, nowadays accounting for several millions or even billions of unknowns, it is quite common to resort to preconditioned iterative solvers for exploiting their low memory requirements and, at least potential, parallelism. Approximate inverses have been shown to be robust and effective preconditioners in various contexts. In this work, we show how adaptive Factored Sparse Approximate Inverse (aFSAI), characterized by a very high degree of parallelism, can be successfully implemented on a distributed memory computer equipped with GPU accelerators. Taking advantage of GPUs in adaptive FSAI set-up is not a trivial task, nevertheless we show through an extensive numerical experimentation how the proposed approach outperforms more traditional preconditioners and results in a close-to-ideal behavior in challenging linear algebra problems

Gas storage in compartmentalized reservoirs: A numerical investigation on possible "unexpected'' fault activation

Underground gas storage (UGS) is a practice that is becoming widely implemented to cope with seasonal peaks of gas consumption. When the target reservoir is located in a faulted basin, a major safety issue concerns the reactivation of pre-existing faults, possibly inducing (micro-) seismicity. Faults are reactivated when the shear stress exceeds the limiting acceptable strength. It has been observed in The Netherlands that this occurrence can happen \u201cunexpectedly\u201d during the life of a UGS reservoir, i.e. when the actual stress regime is not expected to reach the failure condition. A numerical analysis by a 3D FE-IE elasto-plastic geomechanical simulator has been carried out to cast light in this respect, by investigating the mechanisms and the critical factors that can be responsible for a fault reactivation during the various stages of UGS in reservoirs located in the Rotliegend formation. The model outcomes show that the settings (in terms of reservoir and fault geometry, geomechanical parameters, and pressure change distribution) more prone to fault activation during primary production are also the most critical ones during cushion gas injection and UGS cycles

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

A 3D elasto-plastic rate-dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium \u201cBeyond 2000 in Computational Geotechnics,\u201d pages 249-261, 1999). An original strain-driven algorithm with an Inexact Newton iterative scheme is used to compute the state variables for a given strain increment.The model is validated against laboratory measurements, checked on a simplified test case, and used to simulate land subsidence due to groundwater and hydrocarbon production. The numerical results prove computationally effective and robust, thus allowing for the use of the model on real complex geological settings

Sequence stratigraphy after the demise of a high-relief carbonate platform (Carnian of the Dolomites): Sea-level and climate disentangled

Sedimentary facies analysis aided by quantitative 3D georeferenced field data are applied to constrain the sequence stratigraphy of a complex stratigraphic interval in the Late Triassic of the Dolomites. This multidisciplinary approach was the key to disentangle the timing of climatic change vs. sea-level fluctuation and their effects on shallow water carbonate depositional systems. The “Carnian Pluvial Event”, a global episode of climate change worldwide documented at low latitudes, involved increased rainfall and possibly global warming. This climatic event begins before a drop of sea-level and caused the demise of microbial-dominated high-relief carbonate platforms that dominated the Dolomites region, and was followed by a period of coexistence of small microbial carbonate mounds and arenaceous skeletal-oolitic grainstones. A subsequent sealevel fall brought to the definitive disappearance of microbialites and shallow water carbonates switched to ramps dominated by oolitic-bioclastic grainstones. The crisis of early Carnian shallow water carbonate systems of the Dolomites generated a geological surface similar to a drowning unconformity, although no transgression occurred. As the high-relief microbial carbonate systems characterized by steep slopes switched to gently inclined oolitic-skeletal-siliciclastic ramps, basins were rapidly filled. The change of carbonate depositional systems was associated with an increase in siliciclastic input, in turn triggered by the onset of a humid climatic event and only later to a sealevel drop. This evolution of carbonate systems cannot be interpreted in the light of sea-level changes only: climate change, and consequent ecological changes in the main carbonate producing biotas, induced significant modifications in depositional geometries. This case study may serve as a conceptual model for the sedimentary evolution of carbonate systems subject to ecological crisis that do not evolve in platform drowning because, despite a drop in shallow water carbonate production, a combination of low subsidence and/or sea level drop maintains the platform top at shallow depth.Sedimentary facies analysis aided by quantitative 3D georeferenced field data is applied to constrain the sequence stratigraphy of a complex stratigraphic interval in the Late Triassic of the Dolomites. This multidisciplinary approach was the key to disentangle the timing of climatic change vs. sea-level fluctuation and their effects on shallow water carbonate depositional systems. The "Carnian Pluvial Event", a global episode of climate change worldwide documented at low latitudes, involved increased rainfall and possibly global warming. This climatic event begins before a drop of sea-level and caused the demise of microbial-dominated high-relief carbonate platforms that dominated the Dolomites region, and was followed by a period of coexistence of small microbial carbonate mounds and arenaceous skeletal-oolitic grainstones. A subsequent sea-level fall brought to the definitive disappearance of microbialites and shallow water carbonates switched to ramps dominated by oolitic-bioclastic grainstones. The crisis of early Carnian shallow water carbonate systems of the Dolomites generated a geological surface similar to a drowning unconformity, although no transgression occurred. As the high-relief microbial carbonate systems characterized by steep slopes switched to gently inclined oolitic-skeletal-siliciclastic ramps, basins were rapidly filled. The change of carbonate depositional systems was associated with an increase in siliciclastic input, in turn triggered by the onset of a humid climatic event and only later to a sea-level drop. This evolution of carbonate systems cannot be interpreted in the light of sea-level changes only: climate change, and consequent ecological changes in the main carbonate producing biotas, induced significant modifications in depositional geometries. This case study may serve as a conceptual model for the sedimentary evolution of carbonate systems subject to ecological crisis that do not evolve in platform drowning because, despite a drop in shallow water carbonate production, a combination of low subsidence and/or sea level drop maintains the platform top at shallow depth