We investigate a novel application of Fŕechet derivatives for time-lapse mapping of deep, electrically-enhanced fracture systems with a borehole to surface DC resistivity array. The simulations are evaluated for a cased horizontal wellbore embedded in a homogeneous halfspace, where measurements are evaluated near, mid-range, and far from the well head. We show that, in all cases, measurements are sensitive to perturbations centered on the borehole axis and that the sensitivity volume decreases as a function of increased measurement offset from the well head. The sensitivity analysis also illustrates that careful consideration must be taken when developing an electrical survey design for these scenarios. Specifically, we show that positive perturbations in earth conductivity near the wellbore can manifest as both positive and negative measurement perturbations, depending on where the measurement is taken. Furthermore, we show that the transition between the regions along the wellbore of positive and negative contribution results in a "pinch point", representing a region along the wellbore where a given surface measurement is blind to any changes or enhancement of electrical conductivity.
In this paper we explore simulated responses of electromagnetic (EM) signals relative to in situ field surveys and quantify the effects that different values of conductivity in sea ice have on the EM fields. We compute EM responses of ice types with a three-dimensional (3-D) finite-volume discretization of Maxwell's equations and present 2-D sliced visualizations of their associated EM fields at discrete frequencies. Several interesting observations result: First, since the simulator computes the fields everywhere, each gridcell acts as a receiver within the model volume, and captures the complete, coupled interactions between air, snow, sea ice and sea water as a function of their conductivity; second, visualizations demonstrate how 1-D approximations near deformed ice features are violated. But the most important new finding is that changes in conductivity affect EM field response by modifying the magnitude and spatial patterns (i.e. footprint size and shape) of current density and magnetic fields. These effects are demonstrated through a visual feature we define as 'null lines'. Null line shape is affected by changes in conductivity near material boundaries as well as transmitter location. Our results encourage the use of null lines as a planning tool for better ground-truth field measurements near deformed ice types.
We investigate through numerical simulation the usefulness of DC resistivity data for characterizing subsurface fractures with elevated electrical conductivity by considering a geophysical experiment consisting of a grounded current source deployed in a steel cased borehole. In doing so, the borehole casing behaves electrically as a spatially extended line source, efficiently energizing the fractures with a steady current. Finite element simulations of this experiment for a horizontal well intersecting a small set of vertical fractures indicate that the fractures manifest electrically in (at least) two ways: a local perturbation in the electric potential proximal the fracture set, with limited far-field expression; and, an overall reduction in the electric potential along the entire length of borehole casing due to enhanced current flow through the fractures into the surrounding formation. The change in casing potential results in a measureable effect that can be observed far from fractures themselves, at distances where the local perturbations in the electric potential around the fractures are imperceptible. Under these conditions, our results suggest that far-field, time-lapse measurements of DC potentials surrounding a borehole casing can be reasonably interpreted by simple, linear inversion for a Coulomb charge distribution along the borehole path, including a local charge perturbation due to the fractures. Such an approach offers an inexpensive method for detecting and monitoring the time-evolution of electrically conducting fractures while ultimately providing an estimate of their effective conductivity - the latter providing an important measure independent of seismic methods on fracture shape, size, and hydraulic connectivity.
The project objective was to detail better ways to assess and exploit intelligent oil and gas field information through improved modeling, sensor technology, and process control to increase ultimate recovery of domestic hydrocarbons. To meet this objective we investigated the use of permanent downhole sensors systems (Smart Wells) whose data is fed real-time into computational reservoir models that are integrated with optimized production control systems. The project utilized a three-pronged approach (1) a value of information analysis to address the economic advantages, (2) reservoir simulation modeling and control optimization to prove the capability, and (3) evaluation of new generation sensor packaging to survive the borehole environment for long periods of time. The Value of Information (VOI) decision tree method was developed and used to assess the economic advantage of using the proposed technology; the VOI demonstrated the increased subsurface resolution through additional sensor data. Our findings show that the VOI studies are a practical means of ascertaining the value associated with a technology, in this case application of sensors to production. The procedure acknowledges the uncertainty in predictions but nevertheless assigns monetary value to the predictions. The best aspect of the procedure is that it builds consensus within interdisciplinary teams The reservoir simulation and modeling aspect of the project was developed to show the capability of exploiting sensor information both for reservoir characterization and to optimize control of the production system. Our findings indicate history matching is improved as more information is added to the objective function, clearly indicating that sensor information can help in reducing the uncertainty associated with reservoir characterization. Additional findings and approaches used are described in detail within the report. The next generation sensors aspect of the project evaluated sensors and packaging survivability issues. Our findings indicate that packaging represents the most significant technical challenge associated with application of sensors in the downhole environment for long periods (5+ years) of time. These issues are described in detail within the report. The impact of successful reservoir monitoring programs and coincident improved reservoir management is measured by the production of additional oil and gas volumes from existing reservoirs, revitalization of nearly depleted reservoirs, possible re-establishment of already abandoned reservoirs, and improved economics for all cases. Smart Well monitoring provides the means to understand how a reservoir process is developing and to provide active reservoir management. At the same time it also provides data for developing high-fidelity simulation models. This work has been a joint effort with Sandia National Laboratories and UT-Austin's Bureau of Economic Geology, Department of Petroleum and Geosystems Engineering, and the Institute of Computational and Engineering Mathematics.
Electromagnetic induction is a classic geophysical exploration method designed for subsurface characterization--in particular, sensing the presence of geologic heterogeneities and fluids such as groundwater and hydrocarbons. Several approaches to the computational problems associated with predicting and interpreting electromagnetic phenomena in and around the earth are addressed herein. Publications resulting from the project include [31]. To obtain accurate and physically meaningful numerical simulations of natural phenomena, computational algorithms should operate in discrete settings that reflect the structure of governing mathematical models. In section 2, the extension of algebraic multigrid methods for the time domain eddy current equations to the frequency domain problem is discussed. Software was developed and is available in Trilinos ML package. In section 3 we consider finite element approximations of De Rham's complex. We describe how to develop a family of finite element spaces that forms an exact sequence on hexahedral grids. The ensuing family of non-affine finite elements is called a van Welij complex, after the work [37] of van Welij who first proposed a general method for developing tangentially and normally continuous vector fields on hexahedral elements. The use of this complex is illustrated for the eddy current equations and a conservation law problem. Software was developed and is available in the Ptenos finite element package. The more popular methods of geophysical inversion seek solutions to an unconstrained optimization problem by imposing stabilizing constraints in the form of smoothing operators on some enormous set of model parameters (i.e. ''over-parametrize and regularize''). In contrast we investigate an alternative approach whereby sharp jumps in material properties are preserved in the solution by choosing as model parameters a modest set of variables which describe an interface between adjacent regions in physical space. While still over-parametrized, this choice of model space contains far fewer parameters than before, thus easing the computational burden, in some cases, of the optimization problem. And most importantly, the associated finite element discretization is aligned with the abrupt changes in material properties associated with lithologic boundaries as well as the interface between buried cultural artifacts and the surrounding Earth. In section 4, algorithms and tools are described that associate a smooth interface surface to a given triangulation. In particular, the tools support surface refinement and coarsening. Section 5 describes some preliminary results on the application of interface identification methods to some model problems in geophysical inversion. Due to time constraints, the results described here use the GNU Triangulated Surface Library for the manipulation of surface meshes and the TetGen software library for the generation of tetrahedral meshes.
We address the electromagnetic induction problem for fully 3D geologic media and present a solution to the governing Maxwell equations based on a power series expansion. The coefficients in the series are computed using the adjoint method assuming an underlying homogeneous reference model. These solutions are available analytically for point dipole source terms and lead to rapid calculation of the expansion coefficients. First order solutions are presented for a model study in petroleum geophysics composed of a multi-component induction sonde proximal to a fault within a compartmentalized hydrocarbon reservoir.
Borehole radar systems can provide essential subsurface structural information for environmental evaluation, geotechnical analysis, or energy exploration. Sandia developed a prototype continuous-wave Borehole Radar (BHR) in 1996, and development of a practical tool has been continuing at a Russian institute under a Sandia contract. The BHR field experiments, which were planned for the summer of 2001 in Russia, provided a unique opportunity to evaluate the latest Sandia algorithms with actual field data. A new three-dimensional code was developed to enable the analysis of BHR data on modest-sized desktop workstations. The code is based on the staggered grid, finite difference technique, and eliminates 55% of the massive storage associated with solving the system of finite-difference linear equations. The code was used to forward-model the Russian site geometry and placement of artificial targets to anticipate any problems that might arise when the data was received. Technical software and equipment problems in the Russian field tests, conducted in August 2001, invalidated all but one of the data sets. However, more field tests with improved equipment and software are planned for 2002, and analysis of that data will be presented in a future report.
IEEE Transactions on Geoscience and Remote Sensing
Everett, Mark E.; Badea, Eugene A.; Shen, Liang C.; Merchant, Gulamabbas A.; Weiss, Chester J.
Electromagnetic induction (EMI) by a magnetic dipole located above a dipping interface is of relevance to the petroleum well-logging industry. The problem is fully three-dimensional (3-D) when formulated as above, but reduces to an analytically tractable one-dimensional (1-D) problem when cast as a small tilted coil above a horizontal interface. The two problems are related by a simple coordinate rotation. An examination of the induced eddy currents and the electric charge accumulation at the interface help to explain the inductive and polarization effects commonly observed in induction logs from dipping geological formations. The equivalence between the 1-D and 3-D formulations of the problem enables the validation of a previously published finite element solver for 3-D controlled-source EMI.