Richard Liu

Computation of Triaxial Induction Logging Tools in Layered Anisotropic Dipping Formations

In order to interpret the logging data from triaxial induction tools, inversion technology has been adopted. To make the inversion process reasonably fast, a fast forward method must be developed. Numerical methods, such as the finite element method and finite difference method, are flexible but slow for inversion purposes. In this paper, an analytic method is developed to simulate induction tools in deviated wells drilled in anisotropic formations. This method can be applied to the triaxial induction tools with transmitting and receiving coils oriented in three mutually perpendicular directions. The axis of the tool may intercept a formation with dip, azimuthal, and orientation angles. Formulations of the electromagnetic fields generated by these three transmitting coils are derived. The derivation uses the coefficient propagator method with the assumption of negligible borehole effect and invasion zones. This method overcomes the problem of numerical overflow without compromising the accuracy of the solution. Because the new induction tool has three transmitting and three receiving coils, a total of nine logs are obtained at each logging depth compared with one or two logs in regular induction or logging while drilling tools.

Simulation of full responses of a triaxial induction tool in a homogeneous biaxial anisotropic formation

Triaxial induction tools are used to evaluate fractured and lowresistivity reservoirs composed of thinly laminated sand-shale sequences. Thinly laminated and fractured reservoirs demonstrate transversely isotropic or fully anisotropic biaxial anisotropic electrical properties. Compared to the number of studies on transverse isotropy, relatively little work covers biaxial anisotropy because of the mathematical complexity. We have developed a theoretical analysis for the full response of a triaxial induction tool in a homogeneous biaxial anisotropic formation. The triaxial tool is composed of three mutually orthogonal transmitters and three mutually orthogonal receivers. The bucking coils are also oriented at three mutually orthogonal directions to remove direct coupling. Starting from the space-domain Maxwell’s equations, which the electromagnetic EM fields satisfied, we obtain the spectral-domain Maxwell’s equations by defining a Fourier transform pair. Solving the resultant spectraldomain vector equation, we can find the spectral-domain solution for the electric field. Then, the magnetic fields can be determined from a homogeneous form of Maxwell’s equations. The solution for the EM fields in the space domain can be expressed in terms of inverse Fourier transforms of their spectral-domain counterparts. We use modified Gauss-Laguerre quadrature and contour integration methods to evaluate the inverse Fourier transform efficiently. Our formulations are based on arbitrary relative dipping and azimuthal and tool angles; thus, we obtain the full coupling matrix connecting source excitations to magnetic field response. We have validated our formulas and investigated the effects of logging responses on factors such as relative dipping, azimuthal and tool angles, and frequency using our code. We only consider conductivity anisotropy, not anisotropy in dielectric permittivity and magnetic permeability. However, our method and formulas are straightforward enough to consider anisotropy in dielectric permittivity.

Design and Analysis of UWB TEM Horn Antenna for Ground Penetrating Radar Applications

A TEM horn antenna is usually applied to the air-launching GPR system. Traditionally, the variation of characteristic impedance of a TEM horn antenna is usually set to range from 50 Omega (characteristic impedance of a coaxial cable) to 376.7 Omega (free space wave impedance). However, a difference regularly exists between transmission-line wave characteristic impedance and free space wave impedance. In this paper, we demonstrate that there is no significant difference of performance with the different aperture impedance of the antenna. In addition, the simulated and experimental results both show that the performance of the designed TEM horn antenna matching with impedance of 200 Omega is better than that with free space impedance of 376.7 Omega. For fully understandings, a discussion is provided to explain the possible reasons. At the final aspects of this research, the other components, such as transmitter, receiver, and control units, would work with the TEM horn antennas to complete an air-launching GPR system.

A Borehole Imaging Method Using Electromagnetic Short Pulse in Oil-Based Mud

A borehole imaging method for nonconductive fluid application using a high-frequency electromagnetic (EM) short pulse is introduced in this letter. The pulsed borehole imaging system offers more advantages when compared with conventional dielectric or resistivity imaging tools. The continuous measurement in a wideband spectrum improves accuracy and provides comprehensive well-bore formation analysis information. A high resolution in both vertical and horizontal directions for well-bore cracks, rugosity, and dielectric dispersion of formations can be obtained by radiating an EM pulse signal with a center frequency of 1.2 GHz into a well-bore via a wideband antenna system. This design has been proven to work effectively in oil-based mud and may be used as an alternative tool for logging while drilling imaging applications. By using the transmission line matrix method, numerical simulation results are presented to verify the performance of the proposed EM pulse imaging system. An improved wideband bow-tie antenna is designed for a proposed multispacing EM pulsed imaging system as well.

A 900MHz shielded bow-tie antenna system for ground penetrating radar

A back-cavity shielded bow-tie antenna system working at 900MHz center frequency for ground-coupled GPR application is investigated numerically and experimentally in this paper. Bow-tie geometrical structure is modified for a compact design and back-cavity assembly. A layer of absorber is employed to overcome the back reflection by omni-directional radiation pattern of a bow-tie antenna in H-plane, thus increasing the SNR and improve the isolation between T and R antennas as well. The designed antenna system is applied to a prototype GPR system. Tested data shows that the back-cavity shielded antenna works satisfactorily in the 900MHz GPR system.

Application of Complex Image Theory in Geosteering

With the development of horizontal drilling technology and application of the logging while drilling tool, geosteering systems have been widely applied in precision and adaptive drilling. The geosteering system controls the direction, in real time, of the drilling bit in horizontal or deviated well. The position information of both drilling bit and bed boundary is provided to the system for the determination of drilling directions in real time. In this paper, the complex image method (CIM) is applied to speed up the boundary detection process. The proposed method reduces the simulation time and improves the real-time performance of the control system. This method is implemented in both two-layer and three-layer cases. The accuracy of the proposed method is tested in different frequencies and conductivity contrasts. The simulation results show that the complex image theory works well in most geosteering situations. Compared with the results from the full solution, the complex image theory has satisfactory accuracy. Error only exists in areas within 2 ft away from boundaries. When there are 600 000 logging points, the CIM method is 160 times faster than a full solution.

Evaluation of electrical properties for complex mixtures with a low-frequency periodic technique

This paper presents an efficient numerical technique in evaluating the homogenized anisotropic electrical properties of mixtures with arbitrary inclusions at low-frequency region. The method is based on a low-frequency finite-different method in conjuncture with periodic boundary conditions. Using the developed method, the relationship between micro-scale inclusions and macro-level mixture electrical properties are explored. It is observed that in addition to inclusion volume, inclusion shape and spacing among inclusion objects can also significantly change the homogenized mixture electrical properties.

2.4GHz On-Board Parallel Plate Soil Moisture Sensor System

Moisture content measurements are very important to the evaluation and maintenance of highway pavements. Such applications require sensors can provide relative long time, continuous, and accurate measurements in hostile pavement environments. And sensors should be in contact with soils, concrete, asphalt or other pavement material In this paper, a 2.4GHz integrated parallel-plate soil moisture sensor system is presented. The moisture sensor is based on the principle that the phase shift in the transmission line is the function of medium dielectric constant, which is related to the moisture content. Compared with other methods like TDR and microstrip resonator, the phase shift detection method has better performance for these applications. Detailed sensor head design is based on the consideration of sensitivity, linearity, impedance match, dynamic range and power plane requirement. The solution is fully digital with integrated RF synthesizer, micro-controller, phase detection circuitry, baseband signal processing circuits, and digital communication protocol. The system calibration is built in the software program. The power management system reduces power consumption. The sensor network is able to handle as much as 256 sensors with single pair RS485 interface

High power variable nanosecond differential pulses generator design for GPR system

High power variable nanosecond differential pulses generators based on avalanche transistor and Marx Bank are investigated theoretically and experimentally. The circuit employs six avalanche transistors with charging and discharging circuitry for differential pulses generation and step recovery diode, Schottky diode for pulse shaping. The pulse width can be varied from 1ns to 4ns. The pulses amplitude varies from ±30V@1ns pulse width to ±58V@2ns pulse width. The repetition frequency can reach as high as 500kHz. This variable nanosecond differential pulses generator can be used in pulsed GPR system as transmitter and strobe generator in sequential sampling receiver circuit.

Design of a shielded antenna system for ground penetrating radar applications

A practical design guidance of a wide band shielded GPR antenna is discussed. The designed antenna is used in a GPR system working at 400MHz center frequency. Measured data show that with properly designed shielding and absorbing materials, the bow-tie antenna with shield performs as desired. Besides antenna design, the key issues in a shielded GPR antenna design are the depth of the shield box and the absorbing material insertion.