Dual models of pore spaces

We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology.     

Gravimetric monitoring of the first field‐wide steam injection in a fractured carbonate field in Oman – a feasibility study

Gas‐Oil Gravity Drainage is to be enhanced by steam injection in a highly fractured, low permeability carbonate field in Oman. Following a successful pilot, field‐wide steam injection is being implemented, first of this type in the world. A dedicated monitoring program has been designed to track changes in the reservoir. Various observations are to be acquired, including, surface deformation, temperature measurements, microseismic, well logs, pressure and saturation measurements to monitor the reservoir. Because significant changes in the reservoir density are expected, time‐lapse gravimetry is also being considered. In this paper we investigate the feasibility of gravimetric monitoring of the thermally enhanced gravity drainage process at the carbonate field in Oman. For this purpose, forward gravity modelling is performed. Based on field groundwater measurements, the estimates of the hydrological signal are considered and it is investigated under what conditions the groundwater influences can be minimized. Using regularized inversion of synthetic gravity data, we analyse the achievable accuracy of heat‐front position estimates. In case of large groundwater variations at the field, the gravity observations can be significantly affected and, consequently, the accuracy of heat‐front monitoring can be deteriorated. We show that, by applying gravity corrections based on local observations of groundwater, the hydrological influences can to a large extent be reduced and the accuracy of estimates can be improved. We conclude that gravimetric monitoring of the heat‐front evolution has a great potential.     

Gravity field determination using boundary element methods

The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m² digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km² with an accuracy of the order 10^–3 to 10^–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques.     

Diatomeen-, pollen- und sedimentmikrostratigraphische Untersuchungen zur anthropogenen Beeinflussung des Höllerer Sees (Oberösterreich)

A profundal sediment core from Höllerer See frozen in situ was studied by means of diatom, microstratigraphical tape peel and pollen analyses. Varved sequences reflect eutrophication during mediaeval settlement and according to varve counts a recent eutrophic phase since the 1970's. Mesotrophication in-between coincides with regrowth of forests near the lake.

     

The mechanical state of the lithosphere in the Altiplano-Puna segment of the Andes

Information about topography, the shape of the geoid, seismicity, Neogene deformation and volcanism in the region of Altiplano-Puna of western South America is used to analyse the state of stress across the convergent plate margin in terms of the effects of topography and simple models of its compensation. An average elevation near 4 km is consistent with compensation by a yet unresolved combination of crustal root and hot uppermost mantle producing a geoid high of 22–27 meters, average horizontal compressive stress (in excess of a reference sea level lithostatic value) of 390 bars in a 150 km thick lithosphere, and an average shear stress of 170 bars along a 30° dipping interplate boundary. The basis for these estimates is evidence for a neutral to extensional stress regime within the high plateau contrasted with a compressional regime on the eastern slopes and along the interplate boundary itself. Comparison with other plateaus in a convergent plate tectonic setting suggests an evolutionary sequence from compressional to extensional tectonics as elevation of the plateau increases.     

Remote sensing of substances in water

Remote sensing of water colour and its application to the mapping of pigments, suspended matter and other substances by means of airborne and spaceborne sensors is discussed. After an introduction to the physical process involved, the methods for a quantitative interpretation especially of CZCS data are indicated. Applications towards the monitoring of coastal pollution, of algae blooms and of dynamic processes are shown by means of selected examples. Multispectral scanner and imaging spectrometer technologies are discussed with special reference to NASA's Earth Observation System and ESA's Earth Observation Programme.     

Reservoir Description with Integrated Multiwell Data Using Two-Dimensional Wavelets

Inferring reservoir data from dynamic production data has long been done through matching the production history. However, proper integration of available production history has always been a challenge. Different production history data such as well pressure and water cut often occur at different scales making their joint inversion difficult. Furthermore, production data obtained from the same well or even the same reservoir are often correlated making a significant portion of the dataset redundant. Thirdly, the massiveness of the data recorded from wells in a large reservoir over a long period of time makes the nonlinear inversion of such data computational demanding. In this paper, we propose the integration of multiwell production data using wavelet transform. The method involves the use of a two-dimensional wavelet transformation of the data space in order to integrate multiple production data and reduce the correlation between multiwell data. Multiple datasets from different wells, representing different production responses (pressure, water cut, etc.), were treated as a single matrix of data rather than separate vectors that assume no correlation amongst datasets. This enabled us to transform the multiwell production data into a two-dimensional wavelet domain and subsequently select the most important wavelets for history match. By minimizing the square of the Frobenius norm of the residual matrix we were able to match the calculated response to the observed response. We derived the relationship that allows us to replace a conventional minimization of the sum of squares of the l ₂ norms of multi-objective functions with the minimization of the square of the Frobenius norm of the integrated data. The usefulness of the approach is demonstrated using two examples. The approach proved very effective at reducing correlation between multiwell data. In addition, the method helped to reduce the cost of computing sensitivity coefficients. However, the method gave poor prediction of water cut when the datasets were not scaled before inverse modeling.