Structure and modeling of disorder in miserite from the Murun (Russia) and Dara-i-Pioz (Tajikistan) massifs

The structure, structural disorder and chemistry of miserite from the charoite-bearing rocks of the Murun massif (Russia) and from alkaline-syenite pegmatitic rocks of the Dara-i-Pioz massif (Tajikistan) were investigated employing a combination of electron microprobe, single crystal diffraction and micro-Fourier transform infrared spectroscopy analysis. Chemical analysis of the sample investigated by X-ray diffraction evidenced that Dara-i-Pioz miserite has a greater REE concentration than Murun miserite (~0.22 vs. 0.05 apfu, respectively) and also contains Y (0.14 apfu), which is absent in Murun miserite. The occurrence of a band at about 1,600 cm^?1 testified to the presence of H₂O in miserite at hand. Structural analyses yielded average cell parameters of a = 10.092, b = 16.016, c = 7.356 Å, α = 96.60°, β = 111.27° and γ = 76.34°. Anisotropic structural refinement in space group P $\bar{1}$ converged at similar values for the analyzed samples (R ~3.4, R _w ~3.8 %). An interesting feature shown by both the miserite specimen is the presence, revealed by difference Fourier analysis, of a disordered part of the structure. This turned out to be due to the flipping of the tetrahedra belonging to the isolated [Si₂O₇]^6? diorthogroups, one of the two radicals (the other is [Si₁₂O₃₀]^12?) characterizing the miserite structure. The sixfold and seven-vertex Ca polyhedra linked to the inverted diorthogroups show variation in coordination number with respect to those of the ordered structure.     

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.