Currently microseismic monitoring is widely used for fracture diagnosis. Since the method monitors the propagation of shear failure events, it is an indirect measure of the propped fracture geometry. Our primary interest is in estimating the orientation and length of the ‘propped’ fractures (not the created fractures), as that is the primary driver for well productivity. This thesis presents a new Low Frequency Electromagnetic Induction (LFEI) method that has the potential to estimate the propped length, height, orientation of hydraulic fractures, and vertical distribution of proppant within the fracture. The proposed technique involves pumping electrically conductive proppant (which is currently available) into the fracture and then using a specially built logging tool to measure the electromagnetic response of the formation. Results are presented for a proposed logging tool that consists of three sets of tri-directional transmitters and receivers at 6, 30 and 60 feet spacing respectively. The solution of Maxwell’s equations shows that it is possible to use the tool to determine both the orientation and the length of the fracture by detecting the location of these particles in the formation after hydraulic fracturing. Results for extensive sensitivity analysis are presented in this thesis to show the effect of different propped lengths, height and orientation of planar fractures in a shale environment. Multiple numerical simulations, using a state-of-the-art electromagnetic simulator (FEKO) indicate, as this work show, that we can detect and map fractures up to 250 feet in length, 0.2 inches wide, and with a 0 to 45 degree of inclination with respect to the wellbore. Special cases such as proppant banking, non-symmetrical bi-wing fractures, and wells with steel casing in place were studied. / text

<p>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.</p><p>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.</p><p>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.</p> / Dissertation