Sampling-based flood risk analysis for fluvial dike systems

A dike system of moderate size has a large number of potential system states, and the loading imposed on the system is inherently random. If the system should fail, in one of its many potential failure modes, the topography of UK floodplains is usually such that hydrodynamic modelling of flood inundation is required to generate realistic estimates of flood depth and hence damage. To do so for all possible failure states may require 1,000s of computationally expensive inundation simulations. A risk-based sampling technique is proposed in order to reduce the computational resources required to estimate flood risk. The approach is novel in that the loading and dike system states (obtained using a simplified reliability analysis) are sampled according to the contribution that a given region of the space of basic variables makes to risk. The methodology is demonstrated in a strategic flood risk assessment for the city of Burton-upon-Trent in the UK. 5,000 inundation model simulations were run although it was shown that the flood risk estimate converged adequately after approximately half this number. The case study demonstrates that, amongst other factors, risk is a complex function of loadings, dike resistance, floodplain topography and the spatial distribution of floodplain assets. The application of this approach allows flood risk managers to obtain an improved understanding of the flooding system, its vulnerabilities and the most efficient means of allocating resource to improve performance. It may also be used to test how the system may respond to future external perturbations.     

The impact of different clay minerals on the anisotropy of clay matrix in shale

Although clay is composed of disconnected anisotropic clay platelets, many rock physics models treat the clay platelets in shale as interconnected. However, the clay matrix in shales can be modelled as anisotropic clay platelets embedded within a soft isotropic interplatelet region, allowing the influence of disconnected clay platelets on the elastic properties of the clay matrix to be analysed. In this model, properties of the interplatelet region are governed by its effective bulk and shear moduli, whereas the effective properties of the clay platelets are governed by their volume fraction, aspect ratio and elastic stiffness tensor. Together, these parameters implicitly account for variations in clay and fluid properties, as well as fluid saturation. Elastic stiffnesses of clay platelets are obtained from the literature, including both experimental measurements and first-principles calculations of the full anisotropic (monoclinic or triclinic) elastic stiffness tensors of layered silicates. These published elastic stiffness tensors are used to compile a database of equivalent transverse isotropic elastic stiffness tensors, and other physical properties, for eight common varieties of layered silicates. Clay matrix anisotropy is then investigated by examining the influence of these different elastic stiffnesses, and of varying model parameters, upon the effective transverse isotropic elastic stiffness tensor of the clay matrix. The relationship between the different clay minerals and their associated anisotropy parameters is studied, and their impact on the resulting anisotropy of the clay matrix is analysed.     

Sensitivity of reflection seismic data to oil-column height in high-porosity sandstones

Tuning is the effect of interference between the reflections from the top and bottom of a thin layer on the amplitude of the composite reflection. For a homogeneous sandstone reservoir containing an oil column overlying brine, interference between the reflection from the top reservoir and the oil/water contact is a function of the height of the oil column. If the properties of the sandstone do not vary across the oil/water contact, the SS, PS and SP reflection coefficients from the oil/water contact are small in comparison to the PP reflection coefficient. This allows analytic expressions for the effective PP and PS reflection coefficients from the reservoir to be derived that include all P‐wave multiples within the oil column. For a given source/receiver offset, the component of the wavevector inside the oil column normal to the interface is larger for the PPPP reflection than for the PPPS reflection, due to the asymmetry in the raypath for the PPPS reflection. The PPPS reflection is therefore useful for determining oil‐column heights larger than that discriminated by the PPPP reflection, especially when used at wider offsets. A convenient classification of the AVO response of hydrocarbon‐bearing sandstone reservoirs overlain by shale is the scheme of Rutherford and Williams. Class 1 sands have higher acoustic impedance for normal incidence than the overlying shale, Class 2 sands have nearly the same acoustic impedance as the shale and Class 3 sands have lower acoustic impedance. Synthetic shot gathers calculated for these three classes as a function of oil‐column height show that a combination of the PPPP and the PPPS amplitudes can be plotted as a tuning trajectory, which can be used to determine the oil‐column height. This method is most sensitive for reservoirs that belong to AVO classes 1 and 2, and therefore may be useful in AVO analysis of Class 1 and 2 reservoirs where the traditional AVO indicators (developed for Class 3 reservoirs) do not work very well. These results demonstrate the usefulness of shear waves recorded in the marine environment at wide offsets.     

Long-wave seismic anisotropy of heterogeneous reservoirs

Borehole logs often show considerable variation over small lengths, consistent with fine layering of the formation. Elastic upscaling allows layering on a fine length scale to be replaced by thicker, homogeneous equivalent transversely isotropic layers, thus creating a model with far fewer layers. In this paper, the effect of inclusions of finite lateral extent on elastic upscaling is examined. For inclusions with a small thickness to width ratio, Backus averaging gives a good approximation to the long-wavelength elastic properties of the medium. However, for larger thickness to width ratios, the anisotropy of the medium can be significantly reduced. For inclusions that are long in comparison to their width, azimuthal anisotropy may result if the inclusions show a preferential orientation. This could result from the presence of flow during deposition. The azimuthal anisotropy increases with increasing thickness to width ratio of the inclusions, and vanishes when this ratio is zero. For larger thickness to width ratios, the magnitude of the azimuthal anisotropy may be of similar magnitude to that commonly seen in sedimentary basins. Azimuthal anisotropy is usually attributed to the presence of aligned fractures within the formation. The present results suggest a further source of azimuthal anisotropy that may be significant.     

The effect of mineralization on the ratio of normal to tangential compliance of fractures

The effect of a fracture on the propagation of seismic waves can be represented in terms of the normal compliance B_N and tangential compliance B_T of the fracture. If   B_N / B_T = 1  for all fractures, the effective elastic stiffness tensor of an isotropic background containing an arbitrary orientation distribution of fractures is orthotropic (i.e., has three orthogonal planes of mirror symmetry) in the long-wave limit. However, deviations from orthotropy may occur if   B_N / B_T   differs significantly from unity and this can cause the principal axes of the P -wave NMO ellipse and of the variation in the PP -reflection amplitude as a function of azimuth, to deviate from the fast and slow polarization direction of a vertically propagating S -wave. Simple models of a fracture in terms of a planar distribution of cracks suggest that   B_N / B_T ≈ 1  for dry fractures. However, naturally occurring fractures often exhibit mineralization in the form of bridges between opposing faces of the fracture. The presence of such bridges leads to significant departures of   B_N / B_T   from unity.     

Characterizing production‐induced anisotropy of fractured reservoirs having multiple fracture sets

Since natural fractures in petroleum reservoirs play an important role in determining fluid flow during production, knowledge of the orientation and density of fractures is required to optimize production. This paper outlines the underlying theory and implementation of a fast and efficient algorithm for upscaling a Discrete Fracture Network (DFN) to predict the fluid flow, elastic and seismic properties of fractured rocks. Potential applications for this approach are numerous and include the prediction of fluid flow, elastic and seismic properties for fractured reservoirs, model‐based inversion of seismic Amplitude Versus Offset and Azimuth (AVOA) data and the optimal placement and orientation of infill wells to maximize production. Given that a single fracture network may comprise hundreds of thousands of individual fractures, the sheer size of typical DFNs has tended to limit their practical applications. This paper demonstrates that with efficient algorithms, the utility of Discrete Fracture Networks can be extended far beyond mere visualization.     

National-scale Assessment of Current and Future Flood Risk in England and Wales

In recent years, through the availability of remotely sensed data and other national datasets, it has become possible to conduct national-scale flood risk assessment in England and Wales. The results of this type of risk analysis can be used to inform policy-making and prioritisation of resources for flood management. It can form the starting point for more detailed strategic and local-scale flood risk assessments. The national-scale risk assessment methodology outlined in this paper makes use of information on the location, standard of protection and condition of flood defences in England and Wales, together with datasets of floodplain extent, topography, occupancy and asset values. The flood risk assessment was applied to all of England and Wales in 2002 at which point the expected annual damage from flooding was estimated to be approximately £1 billion. This figure is comparable with records of recent flood damage. The methodology has subsequently been applied to examine the effects of climate and socio-economic change 50 and 80 years in the future. The analysis predicts increasing flood risk unless current flood management policies, practices and investment levels are changed – up to 20-fold increase in real terms economic risk by the 2080s in the scenario with highest economic growth. The increase is attributable primarily to a combination of climate change (in particular sea level rise and increasing precipitation in parts of the UK) and increasing economic vulnerability.