A Functional Data Analysis Approach to Surrogate Modeling in Reservoir and Geomechanics Uncertainty Quantification

Uncertainty quantification for geomechanical and reservoir predictions is in general a computationally intensive problem, especially if a direct Monte Carlo approach with large numbers of full-physics simulations is used. A common solution to this problem, well-known for the fluid flow simulations, is the adoption of surrogate modeling approximating the physical behavior with respect to variations in uncertain parameters. The objective of this work is the quantification of such uncertainty both within geomechanical predictions and fluid-flow predictions using a specific surrogate modeling technique, which is based on a functional approach. The methodology realizes an approximation of full-physics simulated outputs that are varying in time and space when uncertainty parameters are changed, particularly important for the prediction of uncertainty in vertical displacement resulting from geomechanical modeling. The developed methodology has been applied both to a subsidence uncertainty quantification example and to a real reservoir forecast risk assessment. The surrogate quality obtained with these applications confirms that the proposed method makes it possible to perform reliable time–space varying dependent risk assessment with a low computational cost, provided the uncertainty space is low-dimensional.     

Multimodal ensemble Kalman filtering using Gaussian mixture models

In this paper we present an extension of the ensemble Kalman filter (EnKF) specifically designed for multimodal systems. EnKF data assimilation scheme is less accurate when it is used to approximate systems with multimodal distribution such as reservoir facies models. The algorithm is based on the assumption that both prior and posterior distribution can be approximated by Gaussian mixture and it is validated by the introduction of the concept of finite ensemble representation. The effectiveness of the approach is shown with two applications. The first example is based on Lorenz model. In the second example, the proposed methodology combined with a localization technique is used to update a 2D reservoir facies models. Both applications give evidence of an improved performance of the proposed method respect to the EnKF.     

Quantitative analysis of H2O and CO2 in cordierite using polarized FTIR spectroscopy

We report a FTIR (Fourier transform infrared) study of a set of cordierite samples from different occurrence and with different H₂O/CO₂ content. The specimens were fully characterized by a combination of techniques including optical microscopy, single-crystal X-ray diffraction, EMPA (electron microprobe analysis), SIMS (secondary ion mass spectrometry), and FTIR spectroscopy. All cordierites are orthorhombic Ccmm. According to the EMPA data, the Si/Al ratio is always close to 5:4; X _Mg ranges from 76.31 to 96.63, and additional octahedral constituents occur in very small amounts. Extraframework K and Ca are negligible, while Na reaches the values up to 0.84 apfu. SIMS shows H₂O up to 1.52 and CO₂ up to 1.11 wt%. Optically transparent single crystals were oriented using the spindle stage and examined by FTIR micro-spectroscopy under polarized light. On the basis of the polarizing behaviour, the observed bands were assigned to water molecules in two different orientations and to CO₂ molecules in the structural channels. The IR spectra also show the presence of small amounts of CO in the samples. Refined integrated molar absorption coefficients were calibrated for the quantitative microanalysis of both H₂O and CO₂ in cordierite based on single-crystal polarized-light FTIR spectroscopy. For H₂O the integrated molar coefficients for type I and type II water molecules (ν₃ modes) were calculated separately and are ^[I]ε?=?5,200?±?700?l?mol^?1?cm^?2 and ^[II]ε?=?13,000?±?3,000?l?mol^?1?cm^?2, respectively. For CO₂ the integrated coefficient is $ \varepsilon_{{{\text{CO}}_{ 2} }} $ ?=?19,000?±?2,000?l?mol^?1?cm^?2.     

Geology of the Murcia Valley and Flood Plain Modifications in the Construction of the Circus Maximus,Rome, Italy

This paper presents a morphological and hydrogeological reconstruction of the Murcia Valley at the location of the great Roman stadium Circus Maximus in Rome. We reconstruct a valley segment using ERT (electrical resistivity tomography) and geoarchaeological drilling data that identified three main layers. The basal layer, with high resistivity values and convex shapes, is correlated to alluvial gravel and lithified silt‐clay sediments. The middle layer shows low‐to‐medium resistivity values extending to concavities between the basal convex shapes. The very low resistivity values of this middle layer characterize elliptical to circular morphologies and have been ascribed to the presence of water‐saturated clay‐silt and peaty sediments. The surface layer is characterized by widespread lateral inhomogeneity interpreted as anthropogenic fill. The data indicate a pre‐Roman anastomosed alluvial plain subsequently modified by human intervention. In an effort to reclaim the valley for construction of the Circus, the Romans utilized the natural topography and created a central embankment, later becoming the Spina, by filling depressions with sand taken from adjacent bars. Our study contributes to (1) knowledge of the pre‐Roman landscape, (2) understanding anthropogenic modification of the Murcia Valley flood plain, and (3) archaeological interpretation of the monument.