Influence of interfaces roughness on elastic properties of layered media

We present a numerical study of the effect of the interfaces’ roughness on layered media’s upscaled elastic parameters. First, we consider a layered model with two types of elastic materials, assuming that the interfaces are not flat but rough, and apply the numerical upscaling technique to estimate the effective elastic properties of such models. After that, we apply a downscaling technique to reconstruct a layered media with flat interfaces but with uncertainties in elastic moduli of the layers. Next, we compute the covariance of the elements of the reconstructed stiffness matrix and prove that the logarithm of this matrix is linearly related to the logarithms of the standard deviation and the correlation length of the interfaces of the original problem. Finally, we use generated dataset to estimate covariance matrices of the stiffness matrix for arbitrary interface roughnesses.     

REV Grid Technique for Reservoir Upscaling

Abstract

Lasseter et al. (Lasseter, T. J., Waggoner, J. R., Lake, L. W. (1986 Lasseter, T. J., Waggoner, J. R. and Lake, L. W. 1986. Reservoir Heterogeneities and Their Influence on Ultimate Recovery. Reservoir Characterization 545Orlando, FL: Academic Press Inc..  [Google Scholar]). Reservoir Heterogeneities and Their Influence on Ultimate Recovery. Reservior Characterization, Orlando, Florida: Academic Press Inc., 545.) proposed that scale-up of properties should be done from the scale of a representative elementary volume (REV), a volume for which the measured property does not change with an increase in scale over a given limit of scale. The notion of REV has been a quite argued concept owing to its definition is not unequivocal, and it did not address how to obtain it in real system, some people even argue if REV really exists. Qi et al. (Qi, D., Wong, P. M., Liu, K. (2001 Qi, D., Wong, P. M. and Liu, K. 2001. An improved global upscaling approach for reservoir simulation. Petroleum Science and Technology, 19(7–8): 779–795. [CROSSREF][Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). An improved global upscaling approach for reservoir simulation. Petroleum Science and Technology 19(7–8):779–795.) based on REV concept, proposed the new idea of REVG (representative elemental volume grid). This article further developed this idea, and based on it, proposed the REV grid upscaling technique. This new technique uses an algorithm, which is a combination of two-procedure-upgridding with reverse stepwise approach, it is a field-oriented 3D model. The new method concentrates on constructing a unique coarse grid, referred to as pseudo-REVG, which could best describe the heterogeneity of the original model at given scale. Mathematically, the variance of properties in REVG is the smallest within each block, and largest between the blocks. The proposed method is applied to two case studies, one of them is a 3D multiphase real reservoir, and the flow simulation results show that the consistency of the reservoir behavior before and after upscaling with REV grid technique is excellent. It is much better than that of the conventional upscaling methods.     

An assessment of photosynthetic light use efficiency from space: Modeling the atmospheric and directional impacts on PRI reflectance

Estimation of photosynthetic light use efficiency (ε) from satellite observations is an important component of climate change research. The photochemical reflectance index, a narrow waveband index based on the reflectance at 531 and 570 nm, allows sampling of the photosynthetic activity of leaves; upscaling of these measurements to landscape and global scales, however, remains challenging. Only a few studies have used spaceborne observations of PRI so far, and research has largely focused on the MODIS sensor. Its daily global coverage and the capacity to detect a narrow reflectance band at 531 nm make it the best available choice for sensing ε from space. Previous results however, have identified a number of key issues with MODIS-based observations of PRI. First, the differences between the footprint of eddy covariance (EC) measurements and the MODIS footprint, which is determined by the sensor's observation geometry make a direct comparison between both data sources challenging and second, the PRI reflectance bands are affected by atmospheric scattering effects confounding the existing physiological signal. In this study we introduce a new approach for upscaling EC based ε measurements to MODIS. First, EC-measured ε values were “translated” into a tower-level optical PRI signal using AMSPEC, an automated multi-angular, tower-based spectroradiometer instrument. AMSPEC enabled us to adjust tower-measured PRI values to the individual viewing geometry of each MODIS overpass. Second, MODIS data were atmospherically corrected using a Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm, which uses a time series approach and an image-based rather than pixel-based processing for simultaneous retrievals of atmospheric aerosol and surface bidirectional reflectance (BRDF). Using this approach, we found a strong relationship between tower-based and spaceborne reflectance measurements (r² = 0.74, p < 0.01) throughout the vegetation period of 2006. Swath (non-gridded) observations yielded stronger correlations than gridded data (r² = 0.58, p < 0.01) both of which included forward and backscatter observations. Spaceborne PRI values were strongly related to canopy shadow fractions and varied with different levels of ε. We conclude that MAIAC-corrected MODIS observations were able to track the site-level physiological changes from space throughout the observation period.     

Estimation of soil clay and calcium carbonate using laboratory, field and airborne hyperspectral measurements

This paper examines how reflectance spectrometry used in the laboratory to estimate clay and calcium carbonate (CaCO₃) soil contents can be applied to field and airborne measurements for soil property mapping. A continuum removal (CR) technique quantifying specific absorption features of clay (2206 nm) and CaCO₃ (2341 nm) was applied to laboratory, field and airborne HYMAP reflectance measurements collected in 2003 (33 sites) and 2005 (19 sites) over bare soil sites of a few meters within the La Peyne Valley area, southern France. Nine intermediate stages from the laboratory up to HYMAP sensor measurements were considered for separately evaluating the possible degradation of estimation performances when going across scales and sensors, e.g. radiometric calibration, spectral resolution, spatial variability, illumination conditions, and surface status including roughness, soil moisture and presence and nature of pebbles.Significant relationships were observed between clay and CaCO₃ contents and CR values computed respectively at 2206 nm and 2341 nm from reflectance measurements at the laboratory level with an ASD spectrophotometer up to the HYMAP spectro-imaging sensor. Performances of clay and CaCO₃ estimations decreased from the laboratory to airborne scales. The main factors inducing uncertainties in the estimates were radiometric and wavelength calibration uncertainties of the HYMAP sensor as well as possible residual atmospheric effects.     

Bridging rigorous assessment of water availability from field to catchment scale with a parsimonious agro-hydrological model

While simple crop and hydrological models are limited with respect to the number and accuracy of the processes they incorporate, complex models have high demand for data. Due to the limitations of both categories of models, there is a need for new agro-hydrological models that simulate both crop productivity and water availability in agricultural catchments, with low data and calibration requirements. This study aimed at developing a widely applicable parsimonious agro-hydrological model, AquaCrop-Hydro, which couples the AquaCrop crop water productivity model with a conceptual hydrological model. AquaCrop-Hydro, simulating crop productivity, the daily soil water balance and discharge at the catchment outlet, performed well for an agricultural catchment in Belgium. The model can be used to investigate the effect of agricultural management and environmental changes from field to catchment scale in support of sustainable water management in agricultural areas.     

A REDUCED-BOUNDARY-FUNCTION METHOD FOR LONGITUDINAL SOLUTION DISPERSION IN SYMMETRIC CONFINED FLOWS

We present a reduced-boundary-function method for longitudinal solute transport in symmetric laminar flows. Flow is confined by two flat plates separated by a distance of 2a or by a tube with a radius of a (Figure 1). The standard advection-diffusion equation is mapped onto the boundary (r = a and r = 0, where r is the distance from the centerline shown in Figure 1). The original problem of solving c(x,r,t) is reduced to solve the solutions of c at the boundary, and the problem dimensionality is reduced from 3 to 2. Final results show that the boundary concentration c_a(x,t) = c(x, r = a,t) is advected at the mean velocity with a dispersion equal to the molecular diffusion. The centerline concentration c₀(x,t) = c(x,r = 0,t) is also advected at the mean velocity, but with a dispersion much larger than the Taylor dispersion. The cross-sectional average concentration is in agreement with the classical Taylor dispersion by neglecting higher order contributions. This study is relevant to the upscaling of solute transport.     

New dynamic permeability upscaling method for flow simulation under depletion drive and no-crossflow conditions

The main purpose of upscaling in reservoir simulation is to capture the dynamic behavior of fine scale models at the coarse scale.Traditional static or dynamic methods use assumptions about the boundary conditions to determine the upscaled properties.In this paper,we show that the upscaled properties are strongly dependent on the flow process observed at the fine scale.We use a simple no-crossflow depletion drive process and demonstrate that an upscaled property is not a constant value.Instead,if the goal is to match the performance of the fine scale model,the upscaled permeability changes with time.We provide an analytical solution to determine the upscaled permeability and present the value of upscaled permeability under limiting conditions.Our equation suggests that it is possible that upscaled value can fall outside the range of fine scale values under certain conditions.We show that for pseudo steady state flow,using common averaging methods like arithmetic or even geometric averaging methods can lead to optimistic results.We also show that the no-crossflow solution is significantly different than crossflow solution at late times.We validate our method by comparing the results of the method with flow simulation results in two and multi-layered models.     

Erratum to "Structural and physiological responses to ozone in Manna ash (Fraxinus ornus L.) leaves of seedlings and mature trees under controlled and ambient conditions"

Leaf-level microscopical symptom structure and physiological responses were investigated in seedlings experimentally exposed to ozone (O₃) in indoor chambers (150 ppb, 8 h d^− 1 per 7 weeks), and field trees of Manna ash (Fraxinus ornus) exposed to ambient O₃ (max 93 ppb per one growing season). Ozone-induced leaf injury, including leaf reddening and stippling, was observed in both seedlings and mature trees, but the morphology of injury in the stipples differed, being hypersensitive-like (HR-like) in the chamber seedlings and accelerated cell senescence (ACS) in the field trees. In both exposure conditions, the main structural impact of O₃ was on the mesophyll and especially the upper assimilating cell layers. The main physiological impact was on carbon assimilation and on stomatal sluggishness. These effects were not due to stomatal structural injury and were more severe in juvenile compared to mature trees because of environmental (water availability, light) and constitutional (gas exchange capacity) factors and differences in the cell physiology processes (HR-like vs. ACS) triggered by ozone stress. Given the plasticity of plant responses to ozone stress, dose/response relationships for tree seedlings in the indoor chambers cannot be extrapolated to mature trees unless ambient conditions are closely simulated.     

Sensitivity-based upscaling for history matching of reservoir models

Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical. Consequently, upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs. This is because as the number of grid blocks increases, the number of flow equations increases and this increases, in large proportion, the time required for solving flow problems. Although we can adopt parallel computation to share the load, a large number of grid blocks still pose significant computational challenges. Thus, upscaling acts as a bridge between the reservoir scale and the simulation scale. However as the upscaling ratio is increased, the accuracy of the numerical simulation is reduced; hence, there is a need to keep a balance between the two. In this work, we present a sensitivity-based upscaling technique that is applicable during history matching. This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix. The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp–wk approach. In the 2Dwp–wk approach, a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression. The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix. The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled. In essence, neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model, thus integrating upscaling with wavelet multiscale inverse modeling. We apply the method to estimate the parameters of two synthetic reservoirs. The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis. The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results. The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.