Geomechanics of subsurface water withdrawal and injection

Land subsidence and uplift, ground ruptures, and induced seismicity are the principal geomechanic effects of groundwater withdrawal and injection. The major environmental consequence of groundwater pumping is anthropogenic land subsidence. The first observation concerning land settlement linked to subsurface processes was made in 1926 by the American geologists Pratt and Johnson, who wrote that \u2018\u2018the cause of subsidence is to be found in the extensive extraction of fluid from beneath the affected area.\u2019\u2019 Since then, impressive progress has been made in terms of: (a) recognizing the basic hydrologic and geomechanic principles underlying the occurrence; (b) measuring aquifer compaction and ground displacements, both vertical and horizontal; (c) modeling and predicting the past and future event; and (d) mitigating environmental impact through aquifer recharge and/or surface water injection. The first milestone in the theory of pumped aquifer consolidation was reached in 1923 by Terzaghi, who introduced the principle of \u2018\u2018effective intergranular stress.\u2019\u2019 In the early 1970s, the emerging computer technology facilitated development of the first mathematical model of the subsidence of Venice, made by Gambolati and Freeze. Since then, the comprehension, measuring, and simulation of the occurrence have improved dramatically. More challenging today are the issues of ground ruptures and induced/triggered seismicity, which call for a shift from the classical continuum approach to discontinuous mechanics. Although well known for decades, anthropogenic land subsidence is still threatening large urban centers and deltaic areas worldwide, such as Bangkok, Jakarta, and Mexico City, at rates in the order of 10 cm/yr

Simulazione numerica del flusso e trasporto di contaminanti in mezzi porosi a saturazione e densità variabile

La legislazione riguardante la salvaguardia e la tutela delle risorse idriche, e tra queste le acque sotterranee, è in continua crescita in tutti i paesi industrializzati. La protezione delle acque di falda dal sovrasfruttamento e dalla contaminazione di origine diversa (rifiuti urbani e industriali, pesticidi e fertilizzanti, scorie nucleari, ecc...) richiede la previsione degli effetti indotti dalle attività umane sulla quantità e qualità delle risorse sotterranee, previsione che si può conseguire solo attraverso l'impiego di idonei modelli matematico-numerici. Un problema di stringente attualità in tutti i paesi che si affacciano sul Mediterraneo è l'inquinamento degli acquiferi costieri per intrusione di acqua di mare. La simulazione della penetrazione del cuneo salino comporta lo sviluppo di modelli accoppiati di flusso e trasporto che possono essere accuratamente ed efficientemente risolti col metodo degli elementi finiti (FEM) che viene qui implementato in un mezzo poroso tridimensionale a saturazione variabile, e che è quindi in grado di simulare sia la zona insatura (suoli superficiali) che quella satura (falde in pressione). Le non linearità che scaturiscono dall'accoppiamento e dalle leggi costitutive della permeabilità e del coefficiente di immagazzinamento nella zona insatura sono risolte con le tecniche di Picard e di Newton parziale. I modelli discreti finali linearizzati sono trattati col metodo dei gradienti coniugati opportunamente precondizionati per le matrici simmetriche di flusso (PGC) e quelle non simmetriche di trasporto (GMRES, Bi-CGSTAB, TFQMR). Le procedure descritte sono implementate nel codice FEM CODESA-3D (COupled variable DEnsity and SAturation) di cui è offerto un esempio applicativo.In the industrialized countries subsurface water resources are increasingly subject to regulations for protection from over-exploitation and from contamination arising from urban, industrial, nuclear, military, and agricultural activities. Prediction of the effects of anthropogenic impacts on water quantity and quality is an important part of proper aquifer management, and can be achieved through the use of mathematical models. As an example, seawater intrusion in coastal aquifers represents a serious environmental problem, especially in the countries of the Mediterranean basin, and can be simulated using coupled models of water flow and solute transport. Sophisticated groundwater models such as these can be accurately and effciently solved numerically via finite element discretizations of the three-dimensional porous medium. Both saturated (groundwater) and unsaturated (soil water) zones can be represented, and nonlinearities arising from storage-pressure head and conductivity-pressure head dependencies in the unsaturated zone and from coupling of the two equations can be resolved using Picard, Newton, or partial Newton methods. The resulting linearized systems of equations can be solved using a variety of preconditioned conjugate gradient-like methods applicable to symmetric and non-symmetric systems. The mathematical formulation and numerical procedures to be described form the basis of the CODESA-3D (COupled variable DEnsity and SAturation) model

A Novel Factorized Sparse Approximate Inverse Preconditioner with Supernodes

AbstractKrylov methods preconditioned by Factorized Sparse Approximate Inverses (FSAI) are an efficient approach for the solution of symmetric positive definite linear systems on massively parallel computers. However, FSAI often suffers from a high set-up cost, especially in ill-conditioned problems. In this communication we propose a novel algorithm for the FSAI computation that makes use of the concept of supernode borrowed from sparse LU factorizations and direct methods

Nuclear Waste Repository Characterization: A Spatial Estimation/Identification Approach

This paper considers the application of spatial estimation techniques to a groundwater aquifer and geological borehole data. It investigates the adequacy of these techniques to reliably develop contour maps from various data sets. The practice of spatial estimation is discussed and the estimator is then applied to a groundwater aquifer system and a deep geological formation. It is shown that the various statistical models must first be identified from the data and evaluated before reasonable results can be expected

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

On the equivalence of total stress and pressure gradient formulations for predicting land subsidence above compacting gas/oil fields

The solution of the poroelastic equations for predicting land subsidence above productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressure gradient regarded as a distributed body force, or the total stress incorporating the pore pressure. In the finite element (FE) method both approaches prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source related to the pore pressure seems to generate different local forces on the element nodes. The two formulations are briey reviewed and discussed for triangular and tetrahedral finite elements. They are shown to yield different results at the global level as well in a three-dimensional axisymmetric porous medium if the FE integration is performed using the average element-wise radius. A modification to both formulations is suggested which allows to correctly solve the problem of a finite reservoir with an infinite pressure gradient, i.e. with a pore pressure discontinuity on its boundary

Estimate of a spatially variable reservoir compressibility by assimilation of ground surface displacement data

Abstract. Fluid extraction from producing hydrocarbon reservoirs can cause anthropogenic land subsidence. In this work, a 3-D finite-element (FE) geomechanical model is used to predict the land surface displacements above a gas field where displacement observations are available. An ensemble-based data assimilation (DA) algorithm is implemented that incorporates these observations into the response of the FE geomechanical model, thus re- ducing the uncertainty on the geomechanical parameters of the sedimentary basin embedding the reservoir. The calibration focuses on the uniaxial vertical compressibility c M , which is often the geomechanical parameter to which the model response is most sensitive. The partition of the reservoir into blocks delimited by faults moti- vates the assumption of a heterogeneous spatial distribution of c M within the reservoir. A preliminary synthetic test case is here used to evaluate the effectiveness of the DA algorithm in reducing the parameter uncertainty associated with a heterogeneous c M distribution. A significant improvement in matching the observed data is obtained with respect to the case in which a homogeneous c M is hypothesized. These preliminary results are quite encouraging and call for the application of the procedure to real gas fields

Modelling ground rupture due to groundwater withdrawal: applications to test cases in China and Mexico

Abstract. The stress variation induced by aquifer overdraft in sedimentary basins with shallow bedrock may cause rupture in the form of pre-existing fault activation or earth fissure generation. The process is causing major detrimental effects on a many areas in China and Mexico. Ruptures yield discontinuity in both displacement and stress field that classic continuous finite element (FE) models cannot address. Interface finite elements (IE), typically used in contact mechanics, may be of great help and are implemented herein to simulate the fault geomechanical behaviour. Two main approaches, i.e. Penalty and Lagrangian, are developed to enforce the contact condition on the element interface. The incorporation of IE incorporation into a three-dimensional (3-D) FE geomechanical simulator shows that the Lagrangian approach is numerically more robust and stable than the Penalty, thus providing more reliable solutions. Furthermore, the use of a Newton-Raphson scheme to deal with the non-linear elasto-plastic fault behaviour allows for quadratic convergence. The FE – IE model is applied to investigate the likely ground rupture in realistic 3-D geologic settings. The case studies are representative of the City of Wuxi in the Jiangsu Province (China), and of the City of Queretaro, Mexico, where significant land subsidence has been accompanied by the generation of several earth fissures jeopardizing the stability and integrity of the overland structures and infrastructure.</p

On the importance of the heterogeneity assumption in the characterization of reservoir geomechanical properties

The geomechanical analysis of a highly compartmentalized reservoir is performed to simulate the seafloor subsidence due to gas production. The available observations over the hydrocarbon reservoir consist of bathymetric surveys carried out before and at the end of a 10-yr production life. The main goal is the calibration of the reservoir compressibility cM, that is, the main geomechanical parameter controlling the surface response. Two conceptual models are considered: in one (i) cM varies only with the depth and the vertical effective stress (heterogeneity due to lithostratigraphic variability); in another (ii) cM varies also in the horizontal plane, that is, it is spatially distributed within the reservoir stratigraphic units. The latter hypothesis accounts for a possible partitioning of the reservoir due to the presence of sealing faults and thrusts that suggests the idea of a block heterogeneous system with the number of reservoir blocks equal to the number of uncertain parameters. The method applied here relies on an ensemble-based data assimilation (DA) algorithm (i.e. the ensemble smoother, ES), which incorporates the information from the bathymetric measurements into the geomechanical model response to infer and reduce the uncertainty of the parameter cM. The outcome from conceptual model (i) indicates that DA is effective in reducing the cM uncertainty. However, the maximum settlement still remains underestimated, while the areal extent of the subsidence bowl is overestimated. We demonstrate that the selection of the heterogeneous conceptual model (ii) allows to reproduce much better the observations thus removing a clear bias of the model structure. DA allows significantly reducing the cM uncertainty in the five blocks (out of the seven) characterized by large volume and large pressure decline. Conversely, the assimilation of land displacements only partially constrains the prior cM uncertainty in the reservoir blocks marginally contributing to the cumulative seafloor subsidence, that is, blocks with low pressure