Imaging of a fluid injection process using geophysical data - A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts

Massively parallel electrical conductivity imaging of the subsurface: Applications to hydrocarbon exploration

Three-dimensional (3D) geophysical imaging is now receiving considerable attention for electrical conductivity mapping of potential offshore oil and gas reservoirs. The imaging technology employs controlled source electromagnetic (CSEM) and magnetotelluric (MT) fields and treats geological media exhibiting transverse anisotropy. Moreover when combined with established seismic methods, direct imaging of reservoir fluids is possible. Because of the size of the 3D conductivity imaging problem, strategies are required exploiting computational parallelism and optimal meshing. The algorithm thus developed has been shown to scale to tens of thousands of processors. In one imaging experiment, 32,768 tasks/processors on the IBM Watson Research Blue Gene/L supercomputer were successfully utilized. Over a 24 hour period we were able to image a large scale field data set that previously required over four months of processing time on distributed clusters based on Intel or AMD processors utilizing 1024 tasks on an InfiniBand fabric. Electrical conductivity imaging using massively parallel computational resources produces results that cannot be obtained otherwise and are consistent with timeframes required for practical exploration problems

Massively-parallel electrical-conductivity imaging of hydrocarbonsusing the Blue Gene/L supercomputer

Large-scale controlled source electromagnetic (CSEM)three-dimensional (3D) geophysical imaging is now receiving considerableattention for electrical conductivity mapping of potential offshore oiland gas reservoirs. To cope with the typically large computationalrequirements of the 3D CSEM imaging problem, our strategies exploitcomputational parallelism and optimized finite-difference meshing. Wereport on an imaging experiment, utilizing 32,768 tasks/processors on theIBM Watson Research Blue Gene/L (BG/L) supercomputer. Over a 24-hourperiod, we were able to image a large scale marine CSEM field data setthat previously required over four months of computing time ondistributed clusters utilizing 1024 tasks on an Infiniband fabric. Thetotal initial data misfit could be decreased by 67 percent within 72completed inversion iterations, indicating an electrically resistiveregion in the southern survey area below a depth of 1500 m below theseafloor. The major part of the residual misfit stems from transmitterparallel receiver components that have an offset from the transmittersail line (broadside configuration). Modeling confirms that improvedbroadside data fits can be achieved by considering anisotropic electricalconductivities. While delivering a satisfactory gross scale image for thedepths of interest, the experiment provides important evidence for thenecessity of discriminating between horizontal and verticalconductivities for maximally consistent 3D CSEM inversions

On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)

In a previous paper, we showed how one can obtain from the action of a locally compact quantum group on a type I-factor a possibly new locally compact quantum group. In another paper, we applied this construction method to the action of quantum SU(2) on the standard Podles sphere to obtain Woronowicz' quantum E(2). In this paper, we will apply this technique to the action of quantum SU(2) on the quantum projective plane (whose associated von Neumann algebra is indeed a type I-factor). The locally compact quantum group which then comes out at the other side turns out to be the extended SU(1,1) quantum group, as constructed by Koelink and Kustermans. We also show that there exists a (non-trivial) quantum groupoid which has at its corners (the duals of) the three quantum groups mentioned above.Comment: 35 page

Three-dimensional gravity modeling and focusing inversion using rectangular meshes.

Rectangular grid cells are commonly used for the geophysical modeling of gravity anomalies, owing to their flexibility in constructing complex models. The straightforward handling of cubic cells in gravity inversion algorithms allows for a flexible imposition of model regularization constraints, which are generally essential in the inversion of static potential field data. The first part of this paper provides a review of commonly used expressions for calculating the gravity of a right polygonal prism, both for gravity and gradiometry, where the formulas of Plouff and Forsberg are adapted. The formulas can be cast into general forms practical for implementation. In the second part, a weighting scheme for resolution enhancement at depth is presented. Modelling the earth using highly digitized meshes, depth weighting schemes are typically applied to the model objective functional, subject to minimizing the data misfit. The scheme proposed here involves a non-linear conjugate gradient inversion scheme with a weighting function applied to the non-linear conjugate gradient scheme's gradient vector of the objective functional. The low depth resolution due to the quick decay of the gravity kernel functions is counteracted by suppressing the search directions in the parameter space that would lead to near-surface concentrations of gravity anomalies. Further, a density parameter transformation function enabling the imposition of lower and upper bounding constraints is employed. Using synthetic data from models of varying complexity and a field data set, it is demonstrated that, given an adequate depth weighting function, the gravity inversion in the transform space can recover geologically meaningful models requiring a minimum of prior information and user interaction

Enhancing proton mobility in polymer electrolyte membranes : lessons from molecular dynamic simulation

Typical proton-conducting polymer electrolyte membranes (PEM) for fuel cell applications consist of a perfluorinated polymeric backbone and side chains with SO3H groups. The latter dissociate upon sufficient water uptake into SO3- groups on the chains and protons in the aqueous subphase, which percolates through the membrane. We report here systematic molecular dynamics simulations of proton transport through the aqueous subphase of wet PEMs. The simulations utilize a recently developed simplified version (Walbran, A.; Kornyshev, A. A. J. Chem. Phys. 2001, 114, 10039) of an empirical valence bond (EVB) model, which is designed to describe the structural diffusion during proton transfer in a multiproton environment. The polymer subphase is described as an excluded volume for water, in which pores of a fixed slab-shaped geometry are considered. We study the effects on proton mobility of the charge delocalization inside the SO3- groups, of the headgroup density (PPM "equivalent weight"), and of the motion of headgroups and side chains. We analyze the correlation between the proton mobility and the degree of proton confinement in proton-carrying clusters near SO3- parent groups. We have found and rationalized the following factors that facilitate the proton transfer: (i) charge delocalization within the SO3- groups, (ii) fluctuational motions of the headgroups and side chains, and (iii) water content