Azimuthal Resistivity Research Articles

First LWD Co-Located Antenna Sensors for Real-Time Anisotropy and Dip Angle Determination, Yielding Better Look-Ahead Detection

Electromagnetic (EM) resistivity tools measure the electrical properties of downhole formations that are critical in determining the hydrocarbon saturation of a reservoir. In complex and heterogeneous reservoirs, both horizontal and vertical formation resistivities are required to obtain an accurate hydrocarbon saturation. For decades, wireline multicomponent induction type measurements have provided reliable determination of formation anisotropy, structural dip, and dip azimuth in wells with any orientation relative to the bedding planes. Logging-while-drilling (LWD) multi-array propagation resistivity tools have also demonstrated similar capability in deviated wells where the relative dip angle is between 45° and 90°. However, measuring anisotropy and dip in wells with a low relative dip angle still poses difficulties for LWD propagation resistivity systems because of the antenna structures employed. This paper describes the development of a new LWD EM sensor equipped with an innovative, co-located, tilted antenna structure. The tool, along with a unique processing scheme, enables the determination of horizontal and vertical resistivity as well as the dip angle and the azimuth of the formation based on an assumption of transversely isotropic (TI) formation models (Graciet and Shen, 1998) while drilling in real time. The co-located sensor design is capable of acquiring multicomponent signals that are sensitive to formation anisotropy and structural dip in wells at any orientation. Modeling studies and several field trials have proven that the design concept can detect these formation properties at any arbitrary wellbore deviation. This paper presents test results from the new technology, together with reference measurements from azimuthally compensated LWD and fully triaxial wireline resistivity measurements. A good comparison is observed in these trials, providing an independent verification of the tool performance. The azimuthal measurements of the new sensors allow for determining formation anisotropy and dip at any wellbore deviation (Bittar et al., 2011b; Bittar et al., 2012), as well as providing 360° azimuthal resistivity and geosignals and allowing a three-dimensional (3D) resistivity mapping technique for real-time decisions. Integrating the co-located antennas with deep-reading antennas in a near-bit collar further provides both anisotropy measurements and ultradeep signals very close to the bit and enhances look-ahead detection ranges for LWD applications.

Maximizing Net Pay in Penta-Lateral Well With Advanced Proactive Geosteering and 2D Structural Analysis Using Azimuthal Resistivity Measurements

A unique challenge for ongoing Schrader Bluff development is to increase field production with the drilling of a high-angle, multilateral producer. To address the challenge, a project was initiated with the primary goal to safely drill five laterals with a key emphasis on maximizing net sand exposure while balancing the short- and long-term value associated with selecting the appropriate technology. This paper focuses on the technical aspects of the proactive geosteering with azimuthal resistivity measurements and multilayered user-guided inversion used in this project. The prewell study based on multiple offset wells is discussed in detail, followed by presenting the highlights of the real-time drilling/geosteering operations, and concluded with the comprehensive post-well analysis study after all five laterals were drilled. The key effort before the drilling was thorough simulation of various scenarios for several target formations. It allowed the selection of the proper geosteering service level (tools and data inversion methods), providing required resolution capabilities but not exceeding the project budget. Value of inversion on real-time data is demonstrated with several examples accompanied by uncertainty analysis of inversion results. Post-well processing included quantification of the main fault amplitude, in-depth uncertainty analysis, and 3D visualization, as well as geological interpretation using an advanced 3D modeling application. The final position and orientation of the major fault were supported with the results of 2D inversion performed in the vicinity of the fault. The integration between advanced geosteering tools and an active team effort helped achieve this complex penta-lateral well, drilling all legs with excellent directional control with numerous steering adjustments and a final net pay of 20,455 ft out of 28,886 ft drilled, which exceeded the operator’s expectations.

LWD DATA INVERSION FOR STRUCTURE WITH ANGULAR UNCONFORMITY

Non-structural traps and reservoir flanks are characterized by angular unconformities. Angular unconformity between dipping formation and sub-horizontal oil-water contact is common in the North Sea fields. This paper presents an approach to real-time inversion of LWD resistivity data for the scenario with angular unconformity. The approach utilizes artificial neural networks (ANNs) for calculating the tool responses in parametric surface-based 2D resistivity models. We propose a parametric model with two non-parallel boundaries suitable for scenarios with angular unconformity and pinch-out. Training of ANNs for this parametric model is performed using a database containing samples with the model parameters and corresponding tool responses. ANNs are the kernel of 2D inversion based on the Levenberg-Marquardt optimization method. To demonstrate applicability of our approach and compare with the results of 1D inversion, we analyze Extra Deep Azimuthal Resistivity tool responses in a 2D synthetic model. It is shown that 1D inversion determines either the position of the oil-water contact or dipping layers structure. At the same time, 2D inversion makes it possible to correctly reconstruct the positions of non-parallel boundaries. Performance of 2D inversion based on ANNs is suitable for real-time applications.

Optimal Wellbore Placement of a Penta-Lateral Well in the Schrader Bluff Reservoir, North Slope, Alaska

Summary A significant oil resource exists within the Schrader Bluff and stratigraphic equivalent West Sak reservoirs located on the central North Slope of Alaska. The Schrader Bluff resource is under development in the Kuparuk River Unit, Milne Point, and within the Prudhoe Bay Unit. These areas have developed reservoirs with oil viscosities up to 200 cp under waterflood and viscosity-reducing miscible gas injection. A grass roots penta-lateral gas-lifted producer was drilled and completed to unlock untapped oil in the northern portion of the Polaris S-Pad Schrader Bluff viscous oil reservoir in Prudhoe Bay, Alaska. This producer was the first multilateral well drilled in the Orion and Polaris Schrader Bluff reservoirs in ≈8 years. The team worked to unlock surface and subsurface opportunities, delivering a substantially lower cost of access than planned. Production rate from Schrader Bluff reservoir wells has a positive correlation with contacted net sandstone. Optimal well placement in each of the five laterals was key to the delivery of a successful project. A novel approach to geosteering was used to maximize net sandstone exposure, utilizing deep azimuthal resistivity and real-time user-guided multilayered inversion modeling.

Mapping Complex Injectite Bodies With Multiwell Electromagnetic 3D Inversion Data

Electromagnetic (EM) inversion processing of ultradeep resistivity data has advanced from one dimensional (1D) to three dimensional (3D). These advances have helped improve the geological complexity that can be imaged and provide additional reservoir information. The large depth of investigation (DOI) of ultradeep LWD EM tools means that distant boundaries might not be detected by any other sensor in the tool string, making it difficult to verify the results. As inversion results represent a model of the subsurface resistivity distribution and not a direct measurement, it is important to have high confidence in the results. Directly comparing the component data measured by the tool to the modeled component data from the inversion across multiple frequencies provides confidence in the resultant model where the data have a close fit. However, as measurement sensitivities decrease with distance, there is potential for non-uniqueness, generating a model that is geologically unrealistic. Increased confidence can be achieved with independent verification of the model. This paper details results from a trilateral well in an injectite reservoir wherein the sand distribution was expected to be complex. The 1D inversions showed the vertical distribution of the sand, but the results were sometimes distorted by lateral resistivity variations. The 3D inversion of the data allowed the lateral resistivity variations to be resolved. These results can be corroborated by direct comparison with azimuthal resistivity images. Additionally, the laterals all diverged from the same main bore and remained close together initially in an area containing major sand injectites. The 3D inversions from two of the wells overlap and define similarly shaped structures, providing confidence in the 3D inversion model. In complex geobodies, such as the injectites described, significant lateral variation in the reservoir distribution is expected, which is not captured by 1D inversion. Understanding the shape of these structures and their potential connectivity using 3D inversion provides a major increase in reservoir understanding that is critical to completion design.

Numerical solution of the integral equations of the electromagnetic field in geosteering problems

Extra-deep azimuthal resistivity measurements improve the depth of investigation up to 30 m from the wellbore. Interpretation of electromagnetic logging data in the neighbourhood of a well becomes an important technical problem. We present an efficient parallel method for computation of induction tool responses with multiple transmitter–receiver configurations in 2D pixel-based anisotropic model crossed by an arbitrary well trajectory. The cornerstone of the approach is volume integral equation method. We consider the conductivity distribution as a sum of background and anomalous conductivities. Background conductivity is 1D-layered. Anomalous conductivity has arbitrary 2D distribution. Electromagnetic fields are the superposition of background and anomalous fields. Background fields are calculated exactly using rigorous analytical solution for 1D-layered background model. With this approach, the 2D pixel-based model is treated as an extension of the 1D-layered model. The anomalous fields are required only in pixels with conductivity different from the conductivity of the 1D-layered model. Anomalous fields are calculated using convergent series of integral operators [1]. The approach takes into account conductivity anisotropy and allows obtaining both the exact solution and the fast approximate one. The convergence of approximate solution is investigated on some synthetic examples.

Study of the Quaternary Deposits at the East and West Shoulders of Mosul Dam Using Azimuthal 2D Resistivity Imaging

The field survey included three geoelectric traverses on the eastern side of the Tigris River parallel and perpendicular on the axis of the Tairah anticline consisting of seven sites of ( Azimuthal Resistivity Tomography; ART) located above the Quaternary depositions in the southern flank. Two traverses were also conducted in the western side of the river parallel and perpendicular on the east Butmah anticline consisting of four sites located above the recent sediments in the southern flank of it. The sites are chosen taking into account the consideration of the geological, tectonic and topographic data of previous studies and current field reconnaissance trips. A sympathetic analysis of the resistivity tomography is performed in nine azimuths of the above mentioned locations using fifteen repetitive processing attempts and the mean root squares ranged between 5.8% -11.7%. The eastern side of the study area with different directions indicates electrical horizons, the first reflects a variable resistivity which represents accumulations of top soil, the second band of high resistivity which reflects the river terraces constitutes, while the third horizon represents the clear extension of the mud and limestone deposits of Fatha Formation with a vertical conductive zones in the rock layers at some traverses. As well as the ART on the western side of the study region identified three electric horizons: the first with high resistivity reflecting the surface soil layer, and the second domain of low resistivity representing the sediments of the valley slopes and concentrating on the southern limb of Butmah anticline. The third of heterogeneous resistivity values reflects Fatha Formation deposits covering its exposures at the core of the two anticlines and locating beneath the research traverses. Using the technology of 2D resistivity imaging reveals that the nine orientations around a central point in eleven locations above recent sediments are represented by river terraces and alluvial deposits on the shoulders of the Mosul Dam. The current study concludes the ability to capture fractures, which is of great importance due to their effect on the displacements of the dam's body and Fatha sediments surrounding it.

On the depth of detection of logging-while-drilling resistivity measurements for looking-around and looking-ahead applications

The depth of detection (DOD), which is an important concept in logging data interpretation, describes the detection capability of the borehole measurements. We have extended the definition of DOD for azimuthal information, namely, the geosignal delivered by azimuthal resistivity tools, to resistivity logs in logging-while-drilling (LWD) applications. Instead of using the radial geometric factor, the detection thresholds in predicting a geologic boundary are used to describe the DOD of a measurement. This definition unifies the criteria to evaluate the detectability of different borehole measurements, such as LWD resistivity measurements and geosignals. It also can be generalized to other kinds of well logging methods in LWD applications. Using the proposed definition, we analyze the detection capability of the LWD resistivity measurements in looking-around and looking-ahead applications; they provide more tangible descriptions. In vertical or near-vertical wells, the definition provides an indicator to evaluate the capability and reliability of looking ahead of deep/ultradeep LWD resistivity tools. The investigations on the influence of the DOD on the distance-to-boundary inversion, which can help in developing a robust and accurate inversion scheme, also are presented and discussed.

Inversion and uncertainty assessment of ultra-deep azimuthal resistivity logging-while-drilling measurements using particle swarm optimization

As the depth of detection of logging-while-drilling azimuthal resistivity tools increases, more details about formation structure fall into the detection zone. The complicated measurement responses make it impractical to directly interpret the formation from measurements. An inversion process is indispensable to reconstruct the multi-layer formation. Geological inverse problem is known to be non-convex, i.e. the global optimum is surrounded by multiple local optima. Gradient methods are prone to be trapped in local optimum without a good initial model; therefore, in this paper, particle swarm optimization (PSO), a global searching approach, is implemented for the interpretation of ultra-deep azimuthal resistivity measurements. This paper investigates the performance of PSO algorithm through parameter analysis and parallelization study. Also, a gradient method is applied to accelerate the convergence rate. Additionally, to evaluate the risk of solutions, a separate uncertainty assessment procedure is employed. The ability of PSO algorithm is demonstrated by several synthetic examples. Moreover, to justify the capacity of this method, one case study based on field measurements is performed.

Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation.

We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lüst differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lüst equation and derive a comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow.

Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications

In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).

Numerical and experimental simulations of multiarray azimuthal laterolog sonde responses in fractured reservoirs

The occurrence, orientation, and development of fractures are key parameters in the evaluation of carbonate and volcanic reservoirs. We have used a 3D finite-element method to numerically simulate the logging responses of a newly proposed multiarray azimuthal laterolog sonde (MALS) in a fractured formation. More importantly, a physical simulation performed with a scaled-down 3D resistivity apparatus was developed to verify the numerical simulation results. Comparative analysis indicated that the laterolog resistivity curves are controlled by the fracture dip angles. High-angle fractures normally correspond to positive differences in the array laterolog curves, whereas fractures with low dip angles consistently result in a negative difference. The MALS tool also provides an azimuthal resistivity measurement that can be used to determine the fracture dipping direction. The sine-wave trend in the 2D imaging of azimuthal resistivity displays the fracture occurrence. In addition, MALS can be used to identify vertical fractures around a borehole within a certain distance. In addition, combined with laterolog data, the fracture occurrence and extension length can be evaluated.

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

We present systematic investigations on the physics, detection performance and inversion of logging-while-drilling extra-deep azimuthal resistivity measurements (EDARM). First, the definitions of EDRAM measurements are discussed, followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals. Then, a new definition of detection depth, which considers the uncertainty of inversion results caused by the data noise, is proposed to quantify the detection capability of EDARM. Finally, the Bayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data. Numerical results show that EDARM is capable of detecting the azimuth and distance of remote bed boundaries, and the detection capability increases with increasing spacing and resistivity contrast. The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles. In addition, multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.

Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo‐analytic formulas

ABSTRACTDownhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo‐analytic solution for eccentric coaxial and tilted‐coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging‐while‐drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well‐established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging‐while‐drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.

Resistivity Isotropicity and Homogeneity for Sub-base Layer of Selected Roads in Ninevah Governorate, Northern Iraq

Field surveys of electrical resistance are achieved in order to study the sub-base layer of the under constructive roads where the present study is conducted in six locations (Bardarash, Rovya, Mahalabyia 1 and 2, Al-Gwair and Bashiqa) based on the existence of projects for roads under construction by the Directorate of Roads and Bridges. Furthermore, Azimuthal resistivity survey is applied using Parker-Watson array with an electrode spacing and azimuth depending on road directions. Also a reverse surveys are performed on the same points of sounding. The resistance ratios (Rd1, Rd2) are then calculated and represented as polar diagrams and cartesian curves. Moreover, analysis relationships are done between the phases, amplitudes, frequencies and their reflections. It is observed from the polar diagrams of the mean resistance values, there is a resistivity variation with the depths and directions of the spread. It is also noticed that there are changes of the Anisotropy Coefficient (AC) values reflecting the effect of the lithofacies contrasts of the sub-base layer belonging to the paving and compacting mechanism underneath the central point of the azimuthal survey. A comparison between AC and Homogeneity Indices (HI) are determined, and the latest values are detected using the standard deviation approach which is thought to reflect the dispersion of measured resistances due to the heterogeneity constitutes.

Evaluation of resistivity anisotropy parameters in the Eastern Mitidja basin, Algeria, using azimuthal electrical resistivity tomography

ABSTRACTWe study electrical anisotropy using azimuthal electrical resistivity tomography (A‐ERT) for identifying geological layers and determining the preferential aquifer flow direction. The work presented in this paper aims at calculating the anisotropy coefficient from the inverted resistivity measurements, relating the geophysical results to the site geology and water flow direction, and comparing the results with those obtained from prior studies using hydrogeological approaches. The study area is located in the Eastern Mitidja basin, about 15 km east of Algiers. The work carried out includes three measurement points, totalling 24 ERT profiles. For each point, eight A‐ERT profiles, using Wenner–Schlumberger array configuration, were performed every 22.5° around a fixed central point. The data processing includes two‐dimensional inversion of each profile, representation of the inverted resistivities at the central points as a function of the azimuth in polar diagrams, and implementation of an inversion program to determine the best fitting azimuthal anisotropy parameters. The origin of electrical anisotropy is probably due to grain alignment, which is often observed in fine‐grained sediments such as clays and some sands. This alignment creates a higher electrical resistivity perpendicular to the alignment than parallel to it, which is an indicator for higher hydraulic permeability in the minimum resistivity direction, which corresponds to the preferential groundwater flow direction.

A comparative evaluation of vertical fractures using different azimuthal electrical resistivity survey arrays

ABSTRACTThe identification of geological discontinuities such as fractures and faults is fundamental to geotechnical and hydrogeological characterization of rock masses. It is difficult to characterize these discontinuities, even by means of drill cores. Electrical resistivity has been historically employed as an alternative tool for the characterization of discontinuities, and new equipment for data acquisition and modern interpretation techniques have increased this possibility. However, when the characterization of vertical discontinuities is to be carried out in small areas, such as urban zones or for engineering works, traditional surveying may be impracticable, because it requires larger areas for proper acquisition. In these situations, azimuthal electrical resistivity surveying can be a good option, thanks to faster data acquisition and the possibility of reaching greater depths of investigation. There are several types of azimuthal arrays, but comparative analyses of their efficiency are still scarce. The objective of this study is to compare the applicability of several types of azimuthal resistivity surveys to identify vertical discontinuities in rock masses. The study was carried out in the laboratory using a scale model (tank), where boundary conditions could be well‐defined. We tried to replicate the natural conditions of a karstic area in Brazil, known to have hydrogeological and geotechnical problems associated with subvertical discontinuities. The simulations involved a limestone rock mass crosscut by a set of discontinuities with varied apertures. The selected arrays (square, equatorial dipole–dipole, Wenner and Schlumberger) encompassed varied inter‐electrode spacings and three different thicknesses of a saturated isotropic overburden, so as to represent field conditions. The azimuthal resistivity surveys, especially the Wenner array, proved to be promising in order to detect vertical discontinuities. The non‐collinear arrays are preferable when it comes to discerning the depth of investigation (square) and detecting electric anisotropy (equatorial dipole–dipole), despite small azimuthal distortions that were observed in relation to the strike of the discontinuities.

Analysis and comparison of azimuthal resistivity measurement modes for laterolog tool

Though proposed previously, the azimuthal focusing modes applied to laterolog tool still need to be researched. A three-dimensional numerical simulation process is first applied to analyze the azimuthal resistivity measurement of deep measurement of dual laterolog tool adopting four modes, i.e., independent current-emitting mode, passive equipotential mode, independent current-adjusting mode and potential-measuring mode. Afterwards, three typical formation models, i.e., a formation model with a resistivity anomaly contacting the borehole wall, a formation model with a resistivity anomaly non-contacting the borehole wall and a formation model with asymmetrical horizontal or downward mud invasion in horizontal well, are developed to test the four modes and the integrated performances of the four modes are revealed. Two tests are carried out to test the independent current-adjusting mode. It has been demonstrated that overall the potential-measuring mode manifests the least ideal measured results, and it only possesses slightly qualitative measurement in the formation model with a resistivity anomaly non-contacting the borehole wall. The independent current-emitting mode can realize qualitative measurement in all the three formation models, but the measured azimuthal difference is indistinctive especially in the case of asymmetrical mud invasion in horizontal well. The passive equipotential mode exhibits an indigent effect, nevertheless it can quantitatively characterize the electrical difference in the formation model with a resistivity anomaly contacting borehole wall. The independent adjustable current mode is the optimum choice because it possesses the relatively perfect performance in all the three cases, especially in the extremely common asymmetrical mud invasion occurring in horizontal well. It has a relative measured error changing from 0.10% to 4.09% and can be adopted to uncover formation characteristics, and it should be the best azimuthal focusing mode employed by the laterolog tool for the azimuthal resistivity measurement.

Possible causes of electrical resistivity distribution inhomogeneity in Czochralski grown single crystal silicon

Electrical resistivity distribution maps have been constructed for single crystal silicon wafers cut out of different parts of Czochralski grown ingots. The general inhomogeneity of the wafers has proven to be relatively high, the resistivity scatter reaching 1–3 %. Two electrical resistivity distribution inhomogeneity types have been revealed: azimuthal and radial. Experiments have been carried out for crystal growth from transparent simulating fluids with hydrodynamic and thermophysical parameters close to those for Czochralski growth of silicon single crystals. We show that a possible cause of azimuthal electrical resistivity distribution inhomogeneity is the swirl-like structure of the melt under the crystallization front (CF), while a possible cause of radial electrical resistivity distribution inhomogeneity is the CF curvature. In a specific range of the Grashof, Marangoni and Reynolds numbers which depend on the ratio of melt height and growing crystal radius, a system of well-developed radially oriented swirls may emerge under the rotating CF. In the absence of such swirls the melt is displaced from under the crystallization front in a homogeneous manner to form thermal and concentration boundary layers which are homogeneous in azimuthal direction but have clear radial inhomogeneity. Once swirls emerge the melt is displaced from the center to the periphery, and simultaneous fluid motion in azimuthal direction occurs. The overall melt motion becomes helical as a result. The number of swirls (two to ten) agrees with the number of azimuthally directed electrical resistivity distribution inhomogeneities observed in the experiments. Comparison of numerical simulation results in a wide range of Prandtl numbers with the experimental data suggests that the phenomena observed in transparent fluids are universal and can be used for theoretical interpretation of imperfections in silicon single crystals.

Fast inversion of logging-while-drilling azimuthal resistivity measurements for geosteering and formation evaluation

We developed an efficient parametric inversion method for the determination of the distances to boundaries (DTBs), dip angle, and formation anisotropic resistivities from logging-while-drilling (LWD) azimuthal resistivity measurements (ARM) in real time. To increase the efficiency, the development employed a depth window, which will slide along the well trajectory during data processing. The local structure inside the depth window can be regarded as one-dimensional (1D) layered formation. A three-layer model (one transverse isotropic (TI) layer embedded between two isotropic shoulder layers) is assumed in the inversion to rebuild the formation structure. Then, the inversion problem is solved using a regularized Levenberg-Marquardt minimization approach. Multiple initial guesses are employed in order to avoid local minima and to find the global solution. Synthetic experiments show that the developed algorithm, which is capable of handling a large subset of the complex 3D conditions and arbitrary well trajectory, is robust and efficient. Discussions are also made to further demonstrate the advantages and limitations of ARM and the inversion processing in geosteering and formation evaluation.