A Velocity-Based Approach to Visco-Elastic Flow of Rock

In structural geology, viscous creep is generally recognized as the major deformation mechanism in the folding of rock layers through geological time scales of hundreds of thousands of years. Moreover, since deformation of rock salt by creep takes already place on relatively small time scales—weeks to months, say—creep is a relevant phenomenon when studying salt mining, notably the convergence of mine cavities and the land subsidence caused by it. While creep is the dominant process on relatively long time scales, elasticity plays a dominant role in processes that take place on relatively short time scales. The elastic response to a stress is a displacement; the shape of the rock is deformed instantaneously with respect to its initial shape. However, the viscous response of a rock to a stress is a relatively low velocity in the order of millimeters per months or years, say. In this paper we consider the two deformation phenomena creep and elasticity. In general, elasticity is a compressible phenomenon, while creep is incompressible. Here we approximate creep by the introduction of a negligibly small amount of compressibility, which makes creep velocity calculations similar to conventional elastic displacement calculations. Using this procedure, a standard finite element package for elasticity can be applied to viscous problems, also in combination with elasticity. The method has been demonstrated to upscaling of creep viscosities.     

A Direct Inverse Model to Determine Permeability Fields from Pressure and Flow Rate Measurements

The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard block-centered finite difference method. With an a priori grid block permeability field as input, two forward runs are made: the first is constrained with the measured pressures; the second is constrained with the measured flow rates. We calculate the pressures in the grid block centers from the first run, while from the second run we calculate the fluxes through the faces between the grid blocks. Substitution of these pressures and fluxes into Darcy’s law then yields the transmissibilities at the faces and hence the permeabilities in the grid blocks. In this way the “hard” data (measured pressures and flow rates) are always honored while the “soft”, geological data can be incorporated at the discretion of the geologist. Using a synthetic example, we demonstrate the method and compare the results with another method: Ensemble Kalman Filtering. The two methods agree within the scope of their applicability. The Double Constraint method focuses initially on determining spatial distributions of the permeability field for single-phase, steady state flow. For history matching an extension is required to non-steady state, two-phase flow conditions, which is already possible with EnKF. We are currently investigating the possibility of combining the two methods, whereby the strengths of the two methods could be fully exploited.     

Strengthening bottom-up and top-down climate governance

Although the UN and EU focus their climate policies on the prevention of a 2 °C global mean temperature rise, it has been estimated that a rise of at least 4?°C is more likely. Given the political climate of inaction, there is a need to instigate a bottom-up approach so as to build domestic support for future climate treaties, empower citizens, and motivate leaders to take action. A review is provided of the predominant top-down cap-and-trade policies in place – the Kyoto Protocol and EU Emissions Trading Scheme (EU ETS) – with a focus on the grandfathering of emissions entitlements and the possibility of offsetting emissions. These policies are evaluated according to two criteria of justice and it is concluded that they fail to satisfy them. Some suggestions as to how the EU ETS can be improved so as to enable robust climate action are also offered.

Policy relevance

The current supranational climate policy has not been successful and global leaders have postponed the adoption of a meaningful successor to the Kyoto Protocol. In view of this inaction, bottom-up approaches with regard to climate policy should be further developed. It is argued that two of the main top-down policies, grandfathering and offsetting, impede the avowed goals of EU climate policy and pose significant ethical dilemmas with regard to participatory and intergenerational justice. In order to provide a more robust EU climate policy, the EU should inter alia provide a long-term perspective for investors, reduce the volatility of the carbon price, and prepare for the possibility of carbon leakage.     

Addressing sources of uncertainty in runoff projections for a data scarce catchment in the Ecuadorian Andes

Future climate projections from general circulation models (GCMs) predict an acceleration of the global hydrological cycle throughout the 21st century in response to human-induced rise in temperatures. However, projections of GCMs are too coarse in resolution to be used in local studies of climate change impacts. To cope with this problem, downscaling methods have been developed that transform climate projections into high resolution datasets to drive impact models such as rainfall-runoff models. Generally, the range of changes simulated by different GCMs is considered to be the major source of variability in the results of such studies. However, the cascade of uncertainty in runoff projections is further elongated by differences between impact models, especially where robust calibration is hampered by the scarcity of data. Here, we address the relative importance of these different sources of uncertainty in a poorly monitored headwater catchment of the Ecuadorian Andes. Therefore, we force 7 hydrological models with downscaled outputs of 8 GCMs driven by the A1B and A2 emission scenarios over the 21st century. Results indicate a likely increase in annual runoff by 2100 with a large variability between the different combinations of a climate model with a hydrological model. Differences between GCM projections introduce a gradually increasing relative uncertainty throughout the 21st century. Meanwhile, structural differences between applied hydrological models still contribute to a third of the total uncertainty in late 21st century runoff projections and differences between the two emission scenarios are marginal.