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A 3-D hydrodynamic dispersion model for modeling tracer transport in Geothermal Reservoirs

A 3-D hydrodynamic dispersion model for modeling tracer transport in Geothermal Reservoirs

Date: January 26, 1998
Creator: Wu, Yu-Shu & Pruess, Karsten
Description: A 3-D hydrodynamic dispersion model for tracer transport is developed and implemented into the TOUGH2 EOS3 (T2R3D) module. The model formulation incorporates a full dispersion tensor, based on a 3-D velocity field with a 3-D, irregular grid in a heterogeneous geological system. Two different weighting schemes are proposed for spatial average of 3-D velocity fields and concentration gradients to evaluate the mass flux by dispersion and diffusion of a tracer or a radionuclide. This new module of the TOUGH2 code is designed to simulate processes of tracer/radionuclide transport using an irregular, 3-D integral finite difference grid in non-isothermal, three-dimensional, multiphase, porous/fractured subsurface systems. The numerical method for this transport module is based on the integral finite difference scheme, as in the TOUGH2 code. The major assumptions of the tracer transport module are: (a) a tracer or a radionuclide is present and transported only within the liquid phase, (b) transport mechanisms include molecular diffusion and hydrodynamic dispersion in the liquid phase in addition to advection, and (c) first order decay and linear adsorption on rock grains are taken into account. The tracer or radionuclide is introduced as an additional mass component into the standard TOUGH2 formulation, time is discretized fully implicitly, ...
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3-D Measurement of Deformation Microstructure of Al(0.2%)Mg Using Submicron Resolution White X-Ray Microbeams

3-D Measurement of Deformation Microstructure of Al(0.2%)Mg Using Submicron Resolution White X-Ray Microbeams

Date: November 29, 1999
Creator: Larson, B. C.; tamura, N.; Chung, J.-S.; Ice, G. E.; Budai, J. D.; Tischler, J. Z. et al.
Description: We have used submicron-resolution white x-ray microbeams on the MHATT-CAT beamline 7-ID at the Advanced Photon Source to develop techniques for three-dimensional investigation of the deformation microstructure in a 20% plane strain compressed Al(0.2%)Mg tri-crystal. Kirkpatrick-Baez mirrors were used to focus white radiation from an undulator to a 0.7 x 0.7 {micro}m{sup 2} beam that was scanned over bi- and tri-crystal regions near the triple-junction of the tri-crystal. Depth resolution along the x-ray microbeam of less than 5 microns was achieved by triangulation to the diffractibn source point using images taken at a series of CCD distances from the microbeam. Computer indexing of the deformation cell structure in the bi-crystal region provided orientations of individual subgrains to {approximately}0.01 degrees, making possible detailed measurements of the rotation axes between individual cells.
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A 3-D model of superfluid helium suitable for numerical analysis

A 3-D model of superfluid helium suitable for numerical analysis

Date: January 1, 2008
Creator: Darve, C.; U., /Fermilab /Northwestern; Patankar, N.A.; U., /Northwestern; Van Sciver, S.W. & Lab., /Natl. High Mag. Field
Description: The two-fluid description is a very successful phenomenological representation of the properties of Helium II. A 3-D model suitable for numerical analysis based on the Landau-Khalatnikov description of Helium II is proposed. In this paper we introduce a system of partial differential equations that is both complete and consistent as well as practical, to be used for a 3-D solution of the flow of Helium II. The development of a 3-D numerical model for Helium II is motivated by the need to validate experimental results obtained by observing the normal component velocity distribution in a Helium II thermal counter-flow using the Particle Image Velocimetry (PIV) technique.
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A 3-d modular gripper design tool

A 3-d modular gripper design tool

Date: January 1, 1997
Creator: Brown, R.G. & Brost, R.C.
Description: Modular fixturing kits are precisely machined sets of components used for flexible, short-turnaround construction of fixtures for a variety of manufacturing purposes. A modular vise is a parallel-jaw vise, where each jaw is a modular fixture plate with a regular grid of precisely positioned holes. A modular vise can be used to locate and hold parts for machining, assembly, and inspection tasks. To fixture a part, one places pins in some of the holes so that when the vise is closed, the part is reliably located and completely constrained. The modular vise concept can be adapted easily to the design of modular parallel-jaw grippers for robots. By attaching a grid plate to each jaw of a parallel-jaw gripper, the authors gain the ability to easily construct high-quality grasps for a wide variety of parts from a standard set of hardware. Wallack and Canny developed a previous algorithm for planning planar grasp configurations for the modular vise. In this paper, the authors expand this work to produce a 3-d fixture/gripper design tool. They describe several analyses added to the planar algorithm to improve its utility, including a three-dimensional grasp quality metric based on geometric and force information, three-dimensional geometric loading analysis, ...
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A 3-d modular gripper design tool

A 3-d modular gripper design tool

Date: February 1, 1997
Creator: Brown, R.G. & Brost, R.C.
Description: Modular fixturing kits are sets of components used for flexible, rapid construction of fixtures. A modular vise is a parallel-jaw vise, each jaw of which is a modular fixture plate with a regular grid of precisely positioned holes. To fixture a part, one places pins in some of the holes so that when the vise is closed, the part is reliably located and completely constrained. The modular vise concept can be adapted easily to the design of modular parallel-jaw grippers for robots. By attaching a grid-plate to each jaw of a parallel-jaw gripper, one gains the ability to easily construct high-quality grasps for a wide variety of parts from a standard set of hardware. Wallack and Canny developed an algorithm for planning planar grasp configurations for the modular vise. In this paper, the authors expand this work to produce a 3-d fixture/gripper design tool. They describe several analyses they have added to the planar algorithm, including a 3-d grasp quality metric based on force information, 3-d geometric loading analysis, and inter-gripper interference analysis. Finally, the authors describe two applications of their code. One of these is an internal application at Sandia, while the other shows a potential use of the ...
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3-D Numerical Modeling of a Complex Salt Structure

3-D Numerical Modeling of a Complex Salt Structure

Date: February 17, 2000
Creator: House, L.; Larsen, S. & Bednar, J. B.
Description: Reliably processing, imaging, and interpreting seismic data from areas with complicated structures, such as sub-salt, requires a thorough understanding of elastic as well as acoustic wave propagation. Elastic numerical modeling is an essential tool to develop that understanding. While 2-D elastic modeling is in common use, 3-D elastic modeling has been too computationally intensive to be used routinely. Recent advances in computing hardware, including commodity-based hardware, have substantially reduced computing costs. These advances are making 3-D elastic numerical modeling more feasible. A series of example 3-D elastic calculations were performed using a complicated structure, the SEG/EAGE salt structure. The synthetic traces show that the effects of shear wave propagation can be important for imaging and interpretation of images, and also for AVO and other applications that rely on trace amplitudes. Additional calculations are needed to better identify and understand the complex wave propagation effects produced in complicated structures, such as the SEG/EAGE salt structure.
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A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry

A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry

Date: December 1, 1995
Creator: Goldberg, K.A.; Tejnil, E. & Bokor, J.
Description: A 3-D electromagnetic field simulation is used to model the propagation of extreme ultraviolet (EUV), 13-nm, light through sub-1500 {Angstrom} dia pinholes in a highly absorptive medium. Deviations of the diffracted wavefront phase from an ideal sphere are studied within 0.1 numerical aperture, to predict the accuracy of EUV point diffraction interferometersused in at-wavelength testing of nearly diffraction-limited EUV optical systems. Aberration magnitudes are studied for various 3-D pinhole models, including cylindrical and conical pinhole bores.
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3-D Ray-tracing and 2-D Fokker-Planck Simulations of Radiofrequency Application to Tokamak Plasmas

3-D Ray-tracing and 2-D Fokker-Planck Simulations of Radiofrequency Application to Tokamak Plasmas

Date: May 1, 1999
Creator: Cardinali, A.; Paoletti, F. & Bernabei, S.
Description: A state of the art numerical tool has been developed to simulate the propagation and the absorption of coexisting different types of waves in a tokamak geometry. The code includes a numerical solution of the three-dimensional (R, Z, {Phi}) toroidal wave equation for the electric field of the different waves in the WKBJ approximation. At each step of integration, the two-dimensional (v{sub {parallel}}, v{sub {perpendicular}}) Fokker-Planck equation is solved in the presence of quasilinear diffusion coefficients. The electron Landau damping of the waves is modeled taking into account the interaction of the wave electric fields with the quasilinearly modified distribution function. Consistently, the code calculates the radial profiles of non-inductively generated current densities, the transmitted power traces and the total power damping curves. Synergistic effects among the different type of waves (e.g., lower hybrid and ion Bernstein waves) are studied through the separation of the contributions of the single wave from the effects due to their coexistence.
Contributing Partner: UNT Libraries Government Documents Department
3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

Date: September 9, 2002
Creator: La Pointe, Paul; Parney, Robert; Eiben, Thorsten; Dunleavy, Mike; Whitney, John & Eubanks, Darrel
Description: The goal of this project is to improve the recovery of oil from the Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models.
Contributing Partner: UNT Libraries Government Documents Department
3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

Date: September 9, 2002
Creator: Pointe, La; Paul; Parney, Robert; Eiben, Thorsten; Dunleavy, Mike & Whitney, John
Description: The goal of this project is to improve the recovery of oil from the Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models.
Contributing Partner: UNT Libraries Government Documents Department
3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

Date: September 9, 2002
Creator: La Pointe, Paul R. & Hermanson, Jan
Description: The goal of this project is to improve the recovery of oil from the Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models.
Contributing Partner: UNT Libraries Government Documents Department
3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

Date: September 9, 2002
Creator: La Pointe, Paul R.; Hermanson, Jan & Eiben, Thorsten
Description: The goal of this project is to improve the recovery of oil from the Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models.
Contributing Partner: UNT Libraries Government Documents Department
3-D RESERVOIR AND STOCHASTIC FRACTURE NETWORK MODELING FOR ENHANCED OIL RECOVERY, CIRCLE RIDGE PHOSPHORIA/TENSLEEP RESERVOIR, WIND RIVER RESERVATION, ARAPAHO AND SHOSHONE TRIBES, WYOMING

3-D RESERVOIR AND STOCHASTIC FRACTURE NETWORK MODELING FOR ENHANCED OIL RECOVERY, CIRCLE RIDGE PHOSPHORIA/TENSLEEP RESERVOIR, WIND RIVER RESERVATION, ARAPAHO AND SHOSHONE TRIBES, WYOMING

Date: November 18, 2002
Creator: Pointe, Paul La; Hermanson, Jan; Parney, Robert; Eiben, Thorsten; Dunleavy, Mike; Steele, Ken et al.
Description: This report describes the results made in fulfillment of contract DE-FG26-00BC15190, ''3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, Wind River Reservation, Arapaho and Shoshone Tribes, Wyoming''. The goal of this project is to improve the recovery of oil from the Tensleep and Phosphoria Formations in Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models. Fields in which natural fractures dominate reservoir permeability, such as the Circle Ridge Field, often experience sub-optimal recovery when recovery processes are designed and implemented that do not take advantage of the fracture systems. For example, a conventional waterflood in a main structural block of the Field was implemented and later suspended due to unattractive results. It is estimated that somewhere less than 20% of the OOIP in the Circle Ridge Field have been recovered after more than 50 years' production. Marathon Oil Company identified the Circle Ridge Field as an attractive candidate for several advanced IOR processes that explicitly take advantage of the natural fracture system. These processes require ...
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A 3-D SAR approach to IFSAR processing

A 3-D SAR approach to IFSAR processing

Date: March 1, 2000
Creator: DOERRY,ARMIN W. & BICKEL,DOUGLAS L.
Description: Interferometric SAR (IFSAR) can be shown to be a special case of 3-D SAR image formation. In fact, traditional IFSAR processing results in the equivalent of merely a super-resolved, under-sampled, 3-D SAR image. However, when approached as a 3-D SAR problem, a number of IFSAR properties and anomalies are easily explained. For example, IFSAR decorrelation with height is merely ordinary migration in 3-D SAR. Consequently, treating IFSAR as a 3-D SAR problem allows insight and development of proper motion compensation techniques and image formation operations to facilitate optimal height estimation. Furthermore, multiple antenna phase centers and baselines are easily incorporated into this formulation, providing essentially a sparse array in the elevation dimension. This paper shows the Polar Format image formation algorithm extended to 3 dimensions, and then proceeds to apply it to the IFSAR collection geometry. This suggests a more optimal reordering of the traditional IFSAR processing steps.
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3-D Seismic Experimentation and Advanced Processing/Inversion Development for Investigations of the Shallow Subsurface

3-D Seismic Experimentation and Advanced Processing/Inversion Development for Investigations of the Shallow Subsurface

Date: December 1, 2004
Creator: Levander, Alan R.
Description: Under ER63662, 3-D Seismic Experimentation and Advanced Processing/Inversion Development for Investigations of the Shallow Subsurface, we have completed a number of subprojects associated with the Hill Air Force Base (HAFB) high resolution 3-D reflection/tomography dataset.
Contributing Partner: UNT Libraries Government Documents Department
3-D Seismic Exploration Project, Ute Indian Tribe, Uintah and Ouray Reservation, Uintah County, Utah

3-D Seismic Exploration Project, Ute Indian Tribe, Uintah and Ouray Reservation, Uintah County, Utah

Date: September 9, 2002
Creator: Eckels, Marc T.
Description: The objectives of this North Hill Creek 3-D seismic survey were to: (1) cover as large an area as possible with available budget; (2) obtain high quality data throughout the depth range of the prospective geologic formations of 2,000' to 12,000' to image both gross structures and more subtle structural and stratigraphic elements; (3) overcome the challenges posed by a hard, reflective sandstone that cropped out or was buried just a few feet below the surface under most of the survey area; and (4) run a safe survey.
Contributing Partner: UNT Libraries Government Documents Department
3-D Seismic Methods for Geothermal Reservoir Exploration and Assessment--Summary

3-D Seismic Methods for Geothermal Reservoir Exploration and Assessment--Summary

Date: July 14, 2003
Creator: Majer, E.L.
Description: A wide variety of seismic methods covering the spectrum from DC to kilohertz have been employed at one time or the other in geothermal environments. The reasons have varied from exploration for a heat source to attempting to find individual fractures producing hot fluids. For the purposes here we will assume that overall objective of seismic imaging is for siting wells for successful location of permeable pathways (often fracture permeability) that are controlling flow and transport in naturally fractured reservoirs. The application could be for exploration of new resources or for in-fill/step-out drilling in existing fields. In most geothermal environments the challenge has been to separate the ''background'' natural complexity and heterogeneity of the matrix from the fracture/fault heterogeneity controlling the fluid flow. Ideally one not only wants to find the fractures, but the fractures that are controlling the flow of the fluids. Evaluated in this work is current state-of-the-art surface (seismic reflection) and borehole seismic methods (Vertical Seismic Profiling (VSP), Crosswell and Single Well) to locate and quantify geothermal reservoir characteristics. The focus is on active methods; the assumption being that accuracy is needed for successful well siting. Passive methods are useful for exploration and detailed monitoring for in-fill ...
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3-D Silicon Photonic Lattices- Cornerstone of an Emerging Photonics Revolution

3-D Silicon Photonic Lattices- Cornerstone of an Emerging Photonics Revolution

Date: July 8, 1999
Creator: Fleming, J.G. & Lin, Shawn-Yu
Description: Three-dimensional photonic lattices are engineered materials which are the photonic analogues of semiconductors. These structures were first proposed and demonstrated in the mid-to-late 1980's. However, due to fabrication difficulties, lattices active in the infrared are only just emerging. Wide ranges of structures and fabrication approaches have been investigated. The most promising approach for many potential applications is a diamond-like structure fabricated using silicon microprocessing techniques. This approach has enabled the fabrication of 3-D silicon photonic lattices active in the infrared. The structures display band gaps centered from 12{micro} down to 1.55{micro}.
Contributing Partner: UNT Libraries Government Documents Department
3-D SIMULATION FOR ASSESSMENT OF TRANSPARENT WEAPON DISASSEMBLY OPERATIONS

3-D SIMULATION FOR ASSESSMENT OF TRANSPARENT WEAPON DISASSEMBLY OPERATIONS

Date: September 1, 2000
Creator: JACKSON, J. W.
Description: No abstract prepared.
Contributing Partner: UNT Libraries Government Documents Department
3-D Spectral Induced Polarization (IP) Imaging: Non-Invasive Characterization Of Contaminant Plumes

3-D Spectral Induced Polarization (IP) Imaging: Non-Invasive Characterization Of Contaminant Plumes

Date: June 1, 1997
Creator: Morgan, Dale F.; Lesmes, David P.; Rodi, William; Shi, Weiqun; Frye, Kevin, M. & Sturrock, John
Description: The overall objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth's subsurface using field measurements of induced polarization (IP) effects. Three specific objectives towards this end are 1. 2. 3. Understanding IP at the laboratory level through measurements of complex resistivity as a function of frequency in rock and soil samples with varying pore geometries, pore fluid conductivities and saturations, and contaminant chemistries and concentrations. Developing effective data acquisition techniques for measuring the critical IP responses (time domain or frequency domain) in the field. Developing modeling and inversion algorithms that permit the interpretation of field IP data in terms of subsurface geology and contaminant plume properties.
Contributing Partner: UNT Libraries Government Documents Department
3-D Spectral IP Imaging: Non-Invasive Characterization DE FG02 96ER 14714

3-D Spectral IP Imaging: Non-Invasive Characterization DE FG02 96ER 14714

Date: June 1, 2000
Creator: Morgan, F. Dale; Rodi, William & Lesmes, David
Description: The Earth Resources Laboratory (ERL) performed a broad foundational study of spectral induced polarization (SIP) for site characterization. The project encompassed laboratory studies of microgeometry and chemistry effects on Induced Polarization (IP), an investigation of electromagnetic coupling (emc) noise, and development of 3D modeling and inversion codes. The major finding of the project is that emc noise presents a critical limitation for field implementation of SIP and conventional correction methods are inadequate. The project developed a frequency domain 3D complex resistivity modeling and inversion code Laboratory experiments were conducted to study the effects of solution chemistry and microgeometry on the SIP response of sandstone. Results indicate that changes in chemistry affect the magnitude of the spectral IP response and changes in microgeometry affect the shape of the spectral IP response. The developed physiochemical IP model can be used to invert spectral IP data for an apparent grain size distribution. Laboratory studies over the last twenty years have shown that SIP data must be acquired over several decades of frequency and include frequencies greater than 1kHz. A model of the components of emc noise has been developed and investigation with this model showed that inductive coupling is the most significant component. ...
Contributing Partner: UNT Libraries Government Documents Department
3-D Spectral IP Imaging: Non-Invasive Characterization of Contaminant Plumes

3-D Spectral IP Imaging: Non-Invasive Characterization of Contaminant Plumes

Date: June 1, 1998
Creator: Morgan, F. Dale; Rodi, William & Lesmes, David
Description: The overall objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth's subsurface using field measurements of induced polarization (IP) effects. Three specific objectives towards this end are: (1) Understanding IP at the laboratory level through measurements of complex resistivity as a function of frequency in rock and soil samples with varying pore geometries, pore fluid conductivities and saturations, and contaminant chemistries and concentrations. (2) Developing effective data acquisition techniques for measuring the critical IP responses (time domain or frequency domain) in the field. (3) Developing modeling and inversion algorithms that permit the interpretation of field IP data in terms of subsurface geology and contaminant plume properties.
Contributing Partner: UNT Libraries Government Documents Department
3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. 1998 annual progress report

3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. 1998 annual progress report

Date: June 1, 1998
Creator: Morgan, F. D.; Rodi, W. & Lesmes, D.
Description: 'The overall objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth''s subsurface using field measurements of induced polarization (IP) effects. Three specific objectives towards this end are: (1) understanding IP at the laboratory level through measurements of complex resistivity as a function of frequency in rock and soil samples with varying pore geometries, pore fluid conductivities and saturations, and contaminant chemistries and concentrations; (2) developing effective data acquisition techniques for measuring the critical IP responses (time domain or frequency domain) in the field; (3) developing modeling and inversion algorithms that permit the interpretation of field IP data in terms of subsurface geology and contaminant plume properties. The authors laboratory experiments to date are described in Appendices A and B, which consist of two papers submitted to the annual SAGEEP conference (Frye et al., 1998; Sturrock et al., 1998). The experiments involved measurements of complex resistivity vs. frequency on a suite of brine saturated sandstone samples. In one set of experiments, the fluid chemistry (pH, ionic strength, and cation type) was varied. In a second set of experiments, the microgeometry of the rock matrix was varied. The experiments showed that spectral IP responses ...
Contributing Partner: UNT Libraries Government Documents Department
3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. Annual progress report, September 15, 1996--September 14, 1997

3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. Annual progress report, September 15, 1996--September 14, 1997

Date: December 1, 1997
Creator: Frye, K.M.; Lesmes, D.P.; Morgan, F.D.; Rodi, W.; Shi, W. & Sturrock, J.
Description: 'The objective of this project is to develop the scientific basis for characterizing contaminant plumes in the earth''s subsurface using field measurements of induced polarization (IP) effects. The first-year accomplishments are (1) laboratory experiments on fluid-saturated sandstones quantifying the dependence of spectral IP responses on solution chemistry and rock micro-geometry; (2) library research on the current understanding of electromagnetic coupling effects on IP data acquired in the field: and (3) development of prototype forward modeling and inversion algorithms for interpreting IP data in terms of 3-D models of complex resistivity.'
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