Margot Gerritsen

A Coupled Local-Global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations

A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local-global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for dierent global boundary conditions is also considered.

Algorithms for Large, Sparse Network Alignment Problems

We propose a new distributed algorithm for sparse variants of the network alignment problem, which occurs in a variety of data mining areas including systems biology, database matching, and computer vision. Our algorithm uses a belief propagation heuristic and provides near optimal solutions for this NP-hard combinatorial optimization problem. We show that our algorithm is faster and outperforms or ties existing algorithms on synthetic problems, a problem in bioinformatics, and a problem in ontology matching. We also provide a unified framework for studying and comparing all network alignment solvers.

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.

Improved Predictability of In-Situ-Combustion Enhanced Oil Recovery

In-situ combustion (ISC) possesses advantages over surface-generated steam injection for deep reservoirs in terms of wellbore heat losses and generation of heat above the critical point of water. Additionally, ISC has drastically lower requirements for water and natural gas, and potentially a smaller surface footprint in comparison to steam. In spite of its apparent advantages, prediction of the likelihood of successful ISC is unclear. Conventionally, combustion tube tests of a crude-oil and rock are used to infer that ISC works at reservoir scale and estimate the oxygen requirements. Combustion tube test results may lead to field-scale simulation on a coarse grid with upscaled Arrhenius reaction kinetics. As an alternative, we suggest a comprehensive workflow to predict successful combustion at the reservoir scale. The method is based on experimental laboratory data and simulation models at all scales. In our workflow, a sample of crushed reservoir rock or an equivalent synthetic sample is mixed with water/brine and the crude-oil sample. The mixture is placed in a kinetics cell reactor and oxidized at different heating rates. An isoconversional method is used to estimate kinetic parameters versus temperature and combustion characteristics of the sample. Results from the isoconversional interpretation provide a first screen of the likelihood that a combustion front is propagated successfully. Then, a full-physics simulation of the kinetics cell experiment is used to predict the flue gas composition. The model combines a detailed PVT analysis of the multiphase system and a multistep reaction model. A mixture identical to that tested in the kinetics cell is also burned in a combustion tube experiment. Temperature profiles along the tube and also the flue gas compositions are measured during the experiment. A highresolution simulation model of the combustion tube test is developed and validated. Finally, the high-resolution model is used as a basis for upscaling the reaction model to field dimensions. Fieldscale simulations do not employ Arrhenius kinetics. As a result, significant stiffness is removed from the finite difference simulation of the governing equations. Preliminary field-scale simulation shows little sensitivity to grid-block size and the computational work per time step is much reduced.

Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrödinger Equation

In this paper we extend the results from our earlier work on stable boundary closures for the Schrödinger equation using the summation-by-parts-simultaneous approximation term (SBP–SAT) method to include stability and accuracy at nonconforming grid interfaces. Stability at the grid interface is shown by the energy method, and the estimates are generalized to multiple dimensions. The accuracy of the grid interface coupling is investigated using normal mode analysis for operators of 2nd and 4th order formal interior accuracy. We show that full accuracy is retained for the 2nd and 4th order operators. The accuracy results are extended to 6th and 8th order operators by numerical simulations, in which case two orders of accuracy is gained with respect to the lower order approximation close to the interface.

High Order Stable Finite Difference Methods for the Schrödinger Equation

In this paper we extend the Summation-by-parts-simultaneous approximation term (SBP-SAT) technique to the Schrödinger equation. Stability estimates are derived and the accuracy of numerical approximations of interior order 2m, m=1,2,3, are analyzed in the case of Dirichlet boundary conditions. We show that a boundary closure of the numerical approximations of order m lead to global accuracy of order m+2. The results are supported by numerical simulations.

A Framework for Quantitative Assessment of Impacts Related to Energy and Mineral Resource Development

Natural resource planning at all scales demands methods for assessing the impacts of resource development and use, and in particular it requires standardized methods that yield robust and unbiased results. Building from existing probabilistic methods for assessing the volumes of energy and mineral resources, we provide an algorithm for consistent, reproducible, quantitative assessment of resource development impacts. The approach combines probabilistic input data with Monte Carlo statistical methods to determine probabilistic outputs that convey the uncertainties inherent in the data. For example, one can utilize our algorithm to combine data from a natural gas resource assessment with maps of sage grouse leks and piñon-juniper woodlands in the same area to estimate possible future habitat impacts due to possible future gas development. As another example: one could combine geochemical data and maps of lynx habitat with data from a mineral deposit assessment in the same area to determine possible future mining impacts on water resources and lynx habitat. The approach can be applied to a broad range of positive and negative resource development impacts, such as water quantity or quality, economic benefits, or air quality, limited only by the availability of necessary input data and quantified relationships among geologic resources, development alternatives, and impacts. The framework enables quantitative evaluation of the trade-offs inherent in resource management decision-making, including cumulative impacts, to address societal concerns and policy aspects of resource development.

Efficient flight of pterosaurs - an unsteady aerodynamic approach

apping gait is a complex combination of motions that sustains an animal in the air and propels it forward at a sustainable energy cost. In this aerodynamic study, we identify the main motions of the wings of a well-preserved specimen of Anhanguera piscator. We describe a methodology designed to handle the complex wing kinematics. Because the detailed wing shape can not be inferred from fossils, simplifying assumptions are made to dene

An Energy-Stable High-Order Central Difference Scheme for the Two-Dimensional Shallow Water Equations

An energy-stable high-order central finite difference scheme is derived for the two-dimensional shallow water equations. The scheme is mathematically formulated using the semi-discrete energy method for initial boundary value problems described in Olsson (1995, Math. Comput. 64, 1035–1065): after symmetrizing the equations via a change to entropy variables, the flux derivatives are entropy-split enabling the formulation of a semi-discrete energy estimate. We show experimentally that the entropy-splitting improves the stability properties of the fully discretized equations. Thus, the dependence on numerical dissipation to keep the scheme stable for long term time integrations is reduced relative to the original unsplit form, thereby decreasing non-physical damping of solutions. The numerical dissipation term used with the entropy-split equations is in a form which preserves the semi-discrete energy estimate. A random one-dimensional dam break calculation is performed showing that the shock speed is computed correctly for this particular case, however it is an open question whether the correct shock speed will be computed in general

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

Abstract The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k ( p ) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k ( p ) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.