Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

This paper shows a history matching workflow with both production and 4D seismic data where the uncertainty of seismic data for history matching comes from Bayesian seismic waveform inversion. We use a synthetic model and perform two seismic surveys, one before start of production and the second after 1 year of production. From the first seismic survey, we estimate the contrast in slowness squared (with uncertainty) and use this estimate to generate an initial estimate of porosity and permeability fields. This ensemble is then updated using the second seismic survey (after inversion to contrasts) and production data with an iterative ensemble smoother. The impact on history matching results from using different uncertainty estimates for the seismic data is investigated. From the Bayesian seismic inversion, we get a covariance matrix for the uncertainty and we compare using the full covariance matrix with using only the diagonal. We also compare with using a simplified uncertainty estimate that does not come from the seismic inversion. The results indicate that it is important not to underestimate the noise in seismic data and that having information about the correlation in the error in seismic data can in some cases improve the results.     

Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe

Geological carbon storage represents a new and substantial challenge for the subsurface geosciences. To increase understanding and make good engineering decisions, containment processes and large-scale storage operations must be simulated in a thousand year perspective. A hierarchy of models of increasing computational complexity for analysis and simulation of large-scale CO₂ storage has been implemented as a separate module of the open-source Matlab Reservoir Simulation Toolbox (MRST). This paper describes a general family of two-scale models available in this module. The models consist of two-dimensional flow equations formulated in terms of effective quantities obtained from hydrostatic reconstructions of vertical pressure and saturation distributions. The corresponding formulation is fully implicit and is the first to give a mass-conservative treatment and include general (non-linearized) CO₂ properties. In particular, the models account for compressibility, dissolution, and hysteresis effects in the fine-scale capillary and relative permeability functions and can be used to accurately and efficiently study the combined large-scale and long-term effects of structural, residual, and solubility trapping.     

Reference points for optimal fish stock management: A lesson to be learned from the Northeast Arctic cod stock

In the North Atlantic the Icelandic, the North Sea, and the Newfoundland cod stocks are currently overexploited. Overexploitation also characterised the Northeast Arctic cod stock, but effective management measures introduced in 1990 and the years thereafter have brought this stock within safe biological limits. The Northeast Arctic cod stock is transboundary and shared between Norway and Russia. As guidelines for a sound management strategy of this cod stock in the future, reference points for management are discussed. As a point of departure, a management strategy which fulfils the objectives for fishery policy stated by Norway is analysed. These objectives, focusing on sustainable harvesting, increased profitability and the role of the fishery as employer of labour in rural districts are fundamental in most of the world's fishery nations.The “optimal” strategy is defined as the one which fulfils these in the best way possible. The natural variations are discussed and the biological and economic yield's dependence upon the rate of exploitation are analysed. The analysis shows that the size of the spawning stock should be no less than 500 000 tonnes and that highest yield is obtained through a rate of exploitation of around 17–30% (equivalent to a fishing mortality of about 0.20–0.40). A spawning stock size of 500 000 tonnes should therefore serve as a “limit reference point” and a fishing mortality of about 0.20–0.40 should serve as a “target reference point” in the management of Northeast Arctic cod.The method described may be applied to other demersal stocks to help establish target and limit reference points in order to conduct a sound management.     

Modelling of run up of steep non-breaking waves

A Navier–Stokes solver is used to examine steep waves as they run up a steep beach (10.54°). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results shows reasonable overall agreement in the prediction of the free-surface, velocities and accelerations within the flow. A spurious feature at the free-surface was found which does reduce the quality of the results. For a steep wave we see the transition from a steep wave front to a smooth run-up tongue at the beach that is in qualitative agreement with experiment.     

Food webs and carbon flux in the Barents Sea

Within the framework of the physical forcing, we describe and quantify the key ecosystem components and basic food web structure of the Barents Sea. Emphasis is given to the energy flow through the ecosystem from an end-to-end perspective, i.e. from bacteria, through phytoplankton and zooplankton to fish, mammals and birds. Primary production in the Barents is on average 93 g C m⁻² y⁻¹, but interannually highly variable (±19%), responding to climate variability and change (e.g. variations in Atlantic Water inflow, the position of the ice edge and low-pressure pathways). The traditional focus upon large phytoplankton cells in polar regions seems less adequate in the Barents, as the cell carbon in the pelagic is most often dominated by small cells that are entangled in an efficient microbial loop that appears to be well coupled to the grazing food web. Primary production in the ice-covered waters of the Barents is clearly dominated by planktonic algae and the supply of ice biota by local production or advection is small. The pelagic–benthic coupling is strong, in particular in the marginal ice zone. In total 80% of the harvestable production is channelled through the deep-water communities and benthos. 19% of the harvestable production is grazed by the dominating copepods Calanus finmarchicus and C. glacialis in Atlantic or Arctic Water, respectively. These two species, in addition to capelin (Mallotus villosus) and herring (Clupea harengus), are the keystone organisms in the Barents that create the basis for the rich assemblage of higher trophic level organisms, facilitating one of the worlds largest fisheries (capelin, cod, shrimps, seals and whales). Less than 1% of the harvestable production is channelled through the most dominating higher trophic levels such as cod, harp seals, minke whales and sea birds. Atlantic cod, seals, whales, birds and man compete for harvestable energy with similar shares. Climate variability and change, differences in recruitment, variable resource availability, harvesting restrictions and management schemes will influence the resource exploitation between these competitors, that basically depend upon the efficient energy transfer from primary production to highly successful, lipid-rich zooplankton and pelagic fishes.     

Prevention of oil spill from shipping by modelling of dynamic risk

This paper presents a new dynamic environmental risk model, with intended use within a new, dynamical approach for risk based ship traffic prioritisation. The philosophy behind this newly developed approach is that shipping risk can be reduced by directing efforts towards ships and areas that have been identified as high priority (high risk), prior to a potential accident. The risk model proposed in this paper separates itself from previous models by drawing on available information on dynamic factors and by focusing on the ship's surroundings. The model estimates the environmental risk of drift grounding accidents for oil tankers in real time and in forecast mode, combining the probability of grounding with oil spill impact on the coastline. Results show that the inherent dynamic risk introduced by an oil tanker sailing along the North Norwegian coast depends, not surprisingly, significantly upon wind and ocean currents, as well as tug position and cargo oil type. Results of this study indicate that the risk model is well suited for real time risk assessment, and effectively separates low risk and high risk situations. The model is well suited as a tool to prioritise oil tankers and coastal segments. This enables dynamic risk based positioning of tugs, using both real-time and projected risk, for effective support in case of a drifting ship situation.     

Homotopy scattering series for seismic forward modelling with variable density and velocity

We have derived a convergent scattering series solution for the frequency-domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann–Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann–Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann–Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like $N^3$, where $N$ is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann–Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so-called homotopy analysis method to derive an iterative solution for the vectorial Lippmann–Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as $N^2$. Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three-layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.