Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global (LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore, the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is, the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured grids.     

Coseismic responses and the mechanism behind MW 5.1 earthquake of March 14, 2005 in the Koyna–Warna region, India

An earthquake of M_w 5.1 occurred on March 14, 2005, in the seismically active Koyna–Warna region in western India, the site known for the largest reservoir triggered seismicity (RTS) in the world. For more than four decades, earthquakes with M  4.0 have occurred in this region at regular intervals. Impoundment of reservoirs and changes in lake levels can trigger earthquakes by two processes of stress modifications, namely direct loading effect of the reservoir and diffusion through various faults and fractures. In this paper we analysed the reservoir water level data at Koyna and Warna reservoirs prior to the occurrence of the March 14, 2005 earthquake, to explain the dominant mechanism behind its occurrence and its correlation with the observed coseismic changes. We conclude that the diffusion process, not the reservoir load effect, is the dominating mechanism triggering earthquakes in the region. The coseismic changes in deep well water levels sensitive to earth tides are found to be to the order of 1–12 cm.     

Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.     

Accurate local upscaling with variable compact multipoint transmissibility calculations

We propose a new single-phase local upscaling method that uses spatially varying multipoint transmissibility calculations. The method is demonstrated on two-dimensional Cartesian and adaptive Cartesian grids. For each cell face in the coarse upscaled grid, we create a local fine grid region surrounding the face on which we solve two generic local flow problems. The multipoint stencils used to calculate the fluxes across coarse grid cell faces involve the six neighboring pressure values. They are required to honor the two generic flow problems. The remaining degrees of freedom are used to maximize compactness and to ensure that the flux approximation is as close as possible to being two-point. The resulting multipoint flux approximations are spatially varying (a subset of the six neighbors is adaptively chosen) and reduce to two-point expressions in cases without full-tensor anisotropy. Numerical tests show that the method significantly improves upscaling accuracy as compared to commonly used local methods and also compares favorably with a local–global upscaling method.     

Geochemistry of amphibolitized eclogites and cross-cutting tonalitic–trondhjemitic dykes in the Metamorphic Kimi Complex in East Rhodope (N.E. Greece): implications for partial melting at the base of a thickened crust

In the ultra-high pressure Metamorphic Kimi Complex widespread tonalitic–trondhjemitic dykes, with an intrusion age ca. 65–63 Ma, cross-cut boudins and layers of amphibolitized eclogites. Geochemical investigation proclaims the tied genetic relationship of the amphibolitized eclogites and the associated tonalitic–trondhjemitic dykes. The major and trace element contents and rare earth element patterns of the amphibolitized eclogites indicate formation of their protoliths by fractional crystallization of tholeiitic magmas in a back-arc environment. The tonalites and trondhjemites are characterized by moderate to high Sr contents (>130 ppm), and low Y (<8.2 ppm) and heavy rare earth element contents (Yb content of 0.19–0.88 ppm). The chemical composition of the tonalitic and trondhjemitic dykes are best explained by partial melting of a tholeiitic source like the amphibolitized eclogites with residual garnet and amphibole, at the base of a thickened crust during Early Tertiary subduction/accretion at the southern margins of the European continent.     

Hydrogeologic assessment of escalating groundwater exploitation in the Indus Basin, Pakistan

Groundwater development has contributed significantly to food security and reduction in poverty in Pakistan. Due to rapid population growth there has been a dramatic increase in the intensity of groundwater exploitation leading to declining water tables and deteriorating groundwater quality. In such prevailing conditions, the hydrogeological appraisal of escalating groundwater exploitation has become of paramount importance. Keeping this in view, a surface water–groundwater quantity and quality model was developed to assess future groundwater trends in the Rechna Doab (RD), a sub-catchment of the Indus River Basin. Scenario analysis shows that if dry conditions persist, there will be an overall decline in groundwater levels of around 10 m for the whole of RD during the next 25 years. The lower parts of RD with limited surface water supplies will undergo the highest decline in groundwater levels (10 to 20 m), which will make groundwater pumping very expensive for farmers. There is a high risk of groundwater salinization due to vertical upconing and lateral movement of highly saline groundwater into the fresh shallow aquifers in the upper parts of RD. If groundwater pumping is allowed to increase at the current rate, there will be an overall decline in groundwater salinity for the lower and middle parts of RD because of enhanced river leakage.     

Surface water–groundwater interaction and chemistry in a mineral-armored hydrothermal outflow channel, Yellowstone National Park, USA

Small quantities of groundwater interact with hydrothermal surface water to drive in-stream geochemical processes in a silica-armored hot-spring outflow channel in Yellowstone National Park, USA. The objective of this study was to characterize the hydrology and geochemistry of this unique system in order to (1) learn more about the Yellowstone Plateau’s subsurface water mixing between meteoric and hydrothermal waters and (2) learn more about the chemical and physical processes that lead to accumulation of streambed cements, i.e., streambed armor. A combination of hydrological, geochemical, mineralogical, microscopic, and petrographic techniques were used to identify groundwater and surface-water exchange. Interaction could be identified in winter because of differences in surface water and groundwater composition but interaction at other times of the year cannot be ruled out. Dissolved constituents originating from groundwater (e.g., Fe(II) and Mg) were traced downstream until oxidation and/or subsequent precipitation with silica removed them, particularly where high affinity substrates like cyanobacterial surfaces were present. Because the stream lies in a relatively flat drainage basin and is fed mainly by a seasonally relatively stable hot spring, this system allowed study of the chemical processes along a stream without the obscuring effects of sedimentation.     

Field scale heterogeneity of redox conditions in till-upscaling to a catchment nitrate model

Point scale studies in different settings of glacial geology show a large local variation of redox conditions. There is a need to develop an upscaling methodology for catchment scale models. This paper describes a study of field-scale heterogeneity of redox-interfaces in a till aquitard within an area of 600?×?600 m. The results showed significant variation of the depths to the redox-interface and thickness of the aquitard. Nitrate was present above the redox-interface but reduced to non-detectable levels a few metres below the interface. An upscaling approach for an area of 92 km² is proposed. Two models are proposed to predict the depth to the redox-interface in the aquitard and the resulting nitrate recharge concentrations to an underlying aquifer. The first model assumes that the depth to the redox-interface reflects the hydraulic head in the aquitard, and the second model assumes that the depth of the redox-interface is randomly distributed according to a log-normal probability distribution function. The upscaling approach using the random redox model estimated recharge concentrations comparable to the observed concentration in the underlying aquifer. The presented upscaling approach is applicable in distributed catchment models where sub-grid variability cannot be represented by the large grids.