A multiscale method for subsurface inverse modeling: Single-phase transient flow

High-resolution geologic models that incorporate observed state data are expected to effectively enhance the reliability of reservoir performance prediction. One of the major challenges faced is how to solve the large-scale inverse modeling problem, i.e., to infer high-resolution models from the given observations of state variables that are related to the model parameters according to some known physical rules, e.g., the flow and transport partial differential equations. There are typically two difficulties, one is the high-dimensional problem and the other is the inverse problem. A multiscale inverse method is presented in this work to attack these problems with the aid of a gradient-based optimization algorithm. In this method, the model responses (i.e., the simulated state data) can be efficiently computed from the high-resolution model using the multiscale finite-volume method. The mismatch between the observations and the multiscale solutions is then used to define a proper objective function, and the fine-scale sensitivity coefficients (i.e., the derivatives of the objective function with respect to each node’s attribute) are computed by a multiscale adjoint method for subsequent optimization. The difficult high-dimensional optimization problem is reduced to a one-dimensional one using the gradient-based gradual deformation method. A synthetic single-phase transient flow example problem is employed to illustrate the proposed method. Results demonstrate that the multiscale framework presented is not only computationally efficient but also can generate geologically consistent models. By preserving spatial structure for inverse modeling, the method presented overcomes the artifacts introduced by the multiscale simulation and may enhance the prediction ability of the inverse-conditional realizations generated.     

Study of Al-substituted hematites, prepared from thermal treatment of lepidocrocite

A study of the characteristics of the Morin transition in aluminous hematites, α-(Fe_1?xAl_x)₂O₃, produced from thermally transformed lepidocrocites, is reported. Six compositions with Al contents between 0.2 and 10 at% have been considered. It is argued that these samples present the advantage that they contain smaller amounts of hydroxyl and water as compared to hematites obtained by other preparation methods. The samples were characterised by a variety of conventional techniques, including thermal analyses, X-ray diffraction, FTIR, TEM/EDX, BET surface-area measurements and diffuse reflectance spectroscopy. All results indicate that the Al is structurally incorporated in the hematite lattices. Transmission Mössbauer spectra were recorded at various temperatures between 80?K and room temperature in order to precisely determine the Morin-transition region and the spin structure in both the low-temperature antiferromagnetic and weakly ferromagnetic states. It was found that the Morin-transition temperatures are markedly higher as compared to similar hematites made from aluminous goethites and that a transition phenomenon persists to an Al substitution of up to at least 10 at%. This different behaviour is ascribed to lower concentrations of structural hydroxyl groups in these lepidocrocite-based hematites.     

Mössbauer effect study of the spin structure in natural hematites

Three natural hematites, α-Fe₂O₃, from the region of Elba have been investigated by means of ⁵⁷Fe Mössbauer spectroscopy at variable temperatures between 80 and 400K. The samples were selected on the basis of their different morphology as observed from powder X-ray diffraction and transmission electron microscopy. The mean crystallite diameters (MCD) along [104] are 1000, 280 and 40 nm respectively. Energy-dispersive analyses of X-rays revealed the presence of minor amounts of Si impurities in those two hematites having the largest MCD. All three hematites show the coexistence at low temperatures of antiferromagnetic-like (AF) and weakly-ferromagnetic-like (WF) spin states. The saturation values of the AF and WF magnetic hyperfine fields and quadrupole shifts have been determined, from which conclusions are drawn concerning the spin structure in relation to the crystallinity of the samples. The variations of the hyperfine parameters in the Morin-transition region indicate a gradual reorientation of both AF and WF spins towards the basal plane. As expected, the Morin transition itself is affected by the particle size. The two hematites exhibiting the largest particle dimensions still show an AF contribution for T>270K. It is suggested, and argued that this unusual behaviour is due to the presence of Si⁴⁺, and hence Fe²⁺, in the lattice. The characteristic Mössbauer temperatures and the intrinsic isomer shifts were evaluated from the temperature variation of the observed isomer shifts. Both parameters are not significantly affected by the morphology and are in excellent agreement with data obtained for synthetic hematites.     

Geochemical soil prospecting in Northwest Kalimantan, Indonesia

A target area in northwestern Kalimantan, Indonesia, already defined by a geochemical stream-sediment survey, has been further investigated by geochemical analysis of soils and samples of test pits. Overlapping geochemical anomalies in the soils were found for Cu, Mo, Au and Bi. Anomalies and high values of the other elements, Pb, Zn, Fe, Mn and As, can be explained by lithology and by scavenging and coprecipitation phenomena at the break of slopes.With the aid of detailed geochemical mapping and mineralogical and petrographic analysis the Cu-Mo-Au-Bi anomaly was explained by a porphyry-type mineralization consisting mainly of chalcopyrite and molybdenite within a quartz-enriched granodiorite. Hydrothermal alteration consists of a potassic zone, including the anomaly, and a broad propylitic zone. This type of mineralization is related to the plate-tectonic evolution of Sundaland. The possibility of a belt of porphyry-type mineralization in western Kalimantan is proposed.     

Characterisation of the magnetic iron phases in Clovis Class rocks in Gusev crater from the MER Spirit Mössbauer spectrometer

Mössbauer backscattering spectra of eight Martian rocks, acquired by the MIMOS II spectrometer of Rover Spirit (MER-A) and containing goethite in addition to other iron minerals, have been selected for in-depth numerical analysis. Where feasible, different temperature windows for a given rock were considered. A novel calibration/folding procedure, exclusively based on the fitted positions of the eight prominent absorption lines in the transmission spectra of the reference target and not relying on the error signal of the MIMOS II spectrometer, has been developed. It is demonstrated that this procedure yields reliable and reasonably accurate values for the adjusted Mössbauer parameters of the respective spectra of the rock targets. These spectra are all composed of magnetically split components arising from hematite, magnetite and goethite phases, in addition to a ferrous and a ferric doublet that can be ascribed to the presence of Fe silicates, possibly glasses. It is argued that the Fe³⁺ doublet has no significant contribution from superparamagnetic Fe-oxide particles. The hematite components reflect the coexistence of antiferromagnetic and weakly ferromagnetic spin states. In general the magnetite content in the selected rocks is low. The goethite subspectra are very broad and asymmetric and need to be described by a model-independent distribution of hyperfine fields. The as-such obtained parameter values indicate an average particle size of the order of 10 nm. For all examined rock spectra, the adjusted parameter values for the various Fe oxides are completely in line with those known for terrestrial (natural or synthetic) species.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Image transforms for determining fit-for-purpose complexity of geostatistical models in flow modeling

Increased diversity of water or energy resources has led to an increased complexity in models aimed at representing accurately dynamic behavior and geological variability in such systems. In terms of variability of properties at least, simple layered models have mostly been replaced with more complex geostatistical models. The newest trend is to replace covariance-based models with geologically more realistic models such as Boolean, multiple-point, surface-, or process-based models. In this paper, we address the following question: given some design purpose or a set of flow-based decision variables, does adding more complexity increase predictability and ultimately improve decisions based on such models? In this paper, we do not attempt to make any generalizing statements or answer this question with yes/no, but provide some initial ideas on practical workflows to discover the needed complexity. We do treat complexity only in the context of decision making under uncertainty. Two workflows are proposed: complexifying versus simplifying. In these workflows, we attempt to extract, using image transforms, relevant features of the variability between geostatistical realizations that are related to uncertainty in flow dynamics. A simple distance-based calibration between the static variability and dynamic variability provides a means to decide on what the relevant complexity of geostatistical models should be for the given purpose.