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

A Three-Dimensional B.I.E.M. Program

The program PECET (Boundary Element Program in Three-Dimensional Elasticity) is presented in this paper. This program, written in FORTRAN V and implemen ted on a UNIVAC 1100,has more than 10,000 sentences and 96 routines and has a lot of capabilities which will be explained in more detail. The object of the program is the analysis of 3-D piecewise heterogeneous elastic domains, using a subregionalization process and 3-D parabolic isopara, metric boundary elements. The program uses special data base management which will be described below, and the modularity followed to write it gives a great flexibility to the package. The Method of Analysis includes an adaptive integration process, an original treatment of boundary conditions, a complete treatment of body forces, the utilization of a Modified Conjugate Gradient Method of solution and an original process of storage which makes it possible to save a lot of memory

Flood Protection in Venice under Conditions of Sea-Level Rise: An Analysis of Institutional and Technical Measures

It is widely acknowledged that in times of climate change loss of coastal resources and risk for human life can be minimized by implementing adaptation strategies. Such strategies need to encompass a balanced mix of non-structural (institutional) and structural (technical) measures based on sound scientific knowledge. This article discusses measures carried out to protect the city of Venice, Italy from flooding (locally known as “high water”), and reflects on their ability to anticipate a possible acceleration of sea-level rise as induced by climate change. It is based on scientific literature, legislative and policy documents of key institutions, reports and documents of organizations working on Venice issues, newspaper articles, and interviews. Our analysis shows that the synergic action of the hydraulic defense infrastructure under construction is in principle adequate to withstand a broad range of sea-level rise scenarios for the next 100 years. However, when the goal is to use these investments effectively major changes in the existing institutional arrangements will be required in the years to come. The Venice findings point out the difficulties and yet the importance of identifying and implementing both non-structural and structural measures to adapt to climate change

Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

We present an inverse modeling procedure for the estimation of model parameters of sedi- mentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophys- ical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likeli- hood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quanti- fied through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approxi- mations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored