Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Constructal Design of Energy Systems

This dissertation shows the use of Constructal law to find the relation between the morphing of the system configuration and the improvements in the global performance of the complex flow system. It shows that the better features of both flow and heat transfer architecture can be found and predicted by using the constructal law in energy systems. Chapter 2 shows the effect of flow configuration on the heat transfer performance of a spiral shaped pipe embedded in a cylindrical conducting volume. Several configurations were considered. The optimal spacings between the spiral turns and spire planes exist, such that the volumetric heat transfer rate is maximal. The optimized features of the heat transfer architecture are robust. Chapter 3 shows the heat transfer performance of a helically shaped pipe embedded in a cylindrical conducting volume. It shows that the optimized features of the heat transfer architecture are robust with respect to changes in several physical parameters. Chapter 4 reports analytically the formulas for effective permeability in several configurations of fissured systems, using the closed-form description of tree networks designed to provide flow access. The permeability formulas do not vary much from one tree design to the next, suggesting that similar formulas may apply to naturally fissured porous media with unknown precise details, which occur in natural reservoirs. Chapter 5 illustrates a counterflow heat exchanger consists of two plenums with a core. The results show that the overall flow and thermal resistance are lowest when the core is absent. Overall, the constructal design governs the evolution of flow configuration in nature and energy systems.

Radiation Dose to the Lens of the Eye from Computed Tomography Scans of the Head

While it is well known that exposure to radiation can result in cataract formation, questions still remain about the presence of a dose threshold in radiation cataractogenesis. Since the exposure history from diagnostic CT exams is well documented in a patient’s medical record, the population of patients chronically exposed to radiation from head CT exams may be an interesting area to explore for further research in this area. However, there are some challenges in estimating lens dose from head CT exams. An accurate lens dosimetry model would have to account for differences in imaging protocols, differences in head size, and the use of any dose reduction methods.

The overall objective of this dissertation was to develop a comprehensive method to estimate radiation dose to the lens of the eye for patients receiving CT scans of the head. This research is comprised of a physics component, in which a lens dosimetry model was derived for head CT, and a clinical component, which involved the application of that dosimetry model to patient data.

The physics component includes experiments related to the physical measurement of the radiation dose to the lens by various types of dosimeters placed within anthropomorphic phantoms. These dosimeters include high-sensitivity MOSFETs, TLDs, and radiochromic film. The six anthropomorphic phantoms used in these experiments range in age from newborn to adult.

First, the lens dose from five clinically relevant head CT protocols was measured in the anthropomorphic phantoms with MOSFET dosimeters on two state-of-the-art CT scanners. The volume CT dose index (CTDIvol), which is a standard CT output index, was compared to the measured lens doses. Phantom age-specific CTDIvol-to-lens dose conversion factors were derived using linear regression analysis. Since head size can vary among individuals of the same age, a method was derived to estimate the CTDIvol-to-lens dose conversion factor using the effective head diameter. These conversion factors were derived for each scanner individually, but also were derived with the combined data from the two scanners as a means to investigate the feasibility of a scanner-independent method. Using the scanner-independent method to derive the CTDIvol-to-lens dose conversion factor from the effective head diameter, most of the fitted lens dose values fell within 10-15% of the measured values from the phantom study, suggesting that this is a fairly accurate method of estimating lens dose from the CTDIvol with knowledge of the patient’s head size.

Second, the dose reduction potential of organ-based tube current modulation (OB-TCM) and its effect on the CTDIvol-to-lens dose estimation method was investigated. The lens dose was measured with MOSFET dosimeters placed within the same six anthropomorphic phantoms. The phantoms were scanned with the five clinical head CT protocols with OB-TCM enabled on the one scanner model at our institution equipped with this software. The average decrease in lens dose with OB-TCM ranged from 13.5 to 26.0%. Using the size-specific method to derive the CTDIvol-to-lens dose conversion factor from the effective head diameter for protocols with OB-TCM, the majority of the fitted lens dose values fell within 15-18% of the measured values from the phantom study.

Third, the effect of gantry angulation on lens dose was investigated by measuring the lens dose with TLDs placed within the six anthropomorphic phantoms. The 2-dimensional spatial distribution of dose within the areas of the phantoms containing the orbit was measured with radiochromic film. A method was derived to determine the CTDIvol-to-lens dose conversion factor based upon distance from the primary beam scan range to the lens. The average dose to the lens region decreased substantially for almost all the phantoms (ranging from 67 to 92%) when the orbit was exposed to scattered radiation compared to the primary beam. The effectiveness of this method to reduce lens dose is highly dependent upon the shape and size of the head, which influences whether or not the angled scan range coverage can include the entire brain volume and still avoid the orbit.

The clinical component of this dissertation involved performing retrospective patient studies in the pediatric and adult populations, and reconstructing the lens doses from head CT examinations with the methods derived in the physics component. The cumulative lens doses in the patients selected for the retrospective study ranged from 40 to 1020 mGy in the pediatric group, and 53 to 2900 mGy in the adult group.

This dissertation represents a comprehensive approach to lens of the eye dosimetry in CT imaging of the head. The collected data and derived formulas can be used in future studies on radiation-induced cataracts from repeated CT imaging of the head. Additionally, it can be used in the areas of personalized patient dose management, and protocol optimization and clinician training.