Estimation of permeability of shaly sand from Induced Polarization relaxation time spectra

The Singular Value Decomposition (SVD) method is used to invert induced polarization (IP) decay curve for the IP relaxation time spectrum. A nonnegative restriction is added during inversion for meaningful solution of the amplitude of the relaxation spectrum. The analysis of the experiment design, by comparing results in different range, shows that the appropriate number of relaxation arrangement points in data inversion lies with 32 to 64. The attenuation of noise in this range is better and resolution is good. IP relaxation spectrum indicates the pore size distribution that in turn indicates the permeability of shaly sand reservoir. Combining the average relaxation time (geometric average time) with the porosity can improve the accuracy of estimation of the permeability in comparison to that obtained using total porosity from core measurements

Opća jednadžba za neposrednu inverznu shemu podataka vertikalnog električnog sondiranja

A unified apparent resistivity equation is derived encompassing eight electrode configurations for Straightforward Inversion Scheme (SIS) on Vertical Electrical Sounding (VES) data. Suitable parameters are worked out to convert unified equation to a particular configuration viz. Wenner, Pole-Pole, Schlumberger, Pole-Dipole, Radial Dipole, Perpendicular Dipole, Parallel Dipole and Azimuthal Dipole. The derived equation is validated by forward computations of VES data for a 5-layer earth model that compares well with that of VES data obtained using existing individual equations for a particular configuration. SIS scheme is briefly described and a Schlumberger synthetic sounding data is generated using the unified equation over model riddled with equivalence /suppression and subsequently inverted using SIS to show the resolving power of the scheme via-a-vis low resistivity contrast between the layers. Two examples of field Schlumberger soundings from known lithology on a paleochannel in Mario Island in Northern Brazil are also included and the inverted continuous resistivity variation is presented to show the efficacy of the scheme.Izvedena je opća jednadžba za prividnu otpornost koja uključuje osam konfiguracija elektroda primjenjenih za neposrednu inverznu shemu (Straightforward Inversion Scheme (SIS)) podataka vertikalnog električnog sondiranja (VES). Nađeni su odgovarajući parametri koji omogućuju primjenu opće jednadžbe za određenu konfiguraciju (Wenner, pol-pol, Schlumberger, pol-dipol, radijalan dipol, okomit dipol, paralelni dipol i azimutalni dipol). Izračun za VES podatke za 5-slojni model podzemlja, dobro se slaže s podacima dobivenim upotrebom postojećih individualnih jednadžbi za određenu konfiguraciju, čime potvrđuje dobivenu jednadžbu. Opisana su dva primjera Schlumbergerovog sondiranja polja poznate litologije na paleo-kanalu na Mario otoku u sjevernom Brazilu i prikazana je varijacija invertiranog kontinuiranog otpora kako bi se pokazala efikasnost sheme

Efficient two-dimensional magnetotellurics modelling using implicitly restarted Lanczos method

This paper presents an efficient algorithm, FDA2DMT (Free Decay Analysis for 2D Magnetotellurics (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward computation of two-dimensional (2D) responses. The main advantage of this approach lies in the fact that only a small subset of eigenvalues and corresponding eigenvectors are required for satisfactory results. This small subset (pre-specified number) of eigenmodes are obtained using shift and invert implementation of Implicitly Restarted Lanczos Method (IRLM). It has been established by experimentation that only 15-20% smallest eigenvalue and corresponding eigenvectors are sufficient to secure the acceptable accuracy. Once the single frequency response is computed using eigenmode approach, the responses for subsequent frequencies can be obtained in negligible time. Experiment design results for validation of FDA2DMT are presented by considering two synthetic models from COMMEMI report, Brewitt-Taylor and Weaver (1976) model and a field data based model from Garhwal Himalaya

Unified equation for straightforward inversion scheme on vertical electrical sounding data

A unified apparent resistivity equation is derived encompassing eight electrode configurations for Straightforward Inversion Scheme (SIS) on Vertical Electrical Sounding (VES) data. Suitable parameters are worked out to convert unified equation to a particular configuration viz. Wenner, Pole-Pole, Schlumberger, Pole-Dipole, Radial Dipole, Perpendicular Dipole, Parallel Dipole and Azimuthal Dipole. The derived equation is validated by forward computations of VES data for a 5-layer earth model that compares well with that of VES data obtained using existing individual equations for a particular configuration. SIS scheme is briefly described and a Schlumberger synthetic sounding data is generated using the unified equation over model riddled with equivalence /suppression and subsequently inverted using SIS to show the resolving power of the scheme via-a-vis low resistivity contrast between the layers. Two examples of field Schlumberger soundings from known lithology on a paleochannel in Mario Island in Northern Brazil are also included and the inverted continuous resistivity variation is presented to show the efficacy of the scheme

Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

The computation of electromagnetic (EM)fields,for 1-D layered earth model,requires evaluation of Hankel Transform (HT)of the EM kernel function.The digital filtering is the most widely used technique to evaluate HT integrals.However,it has some obvious shortcomings. We present an alternative scheme,based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature.This expansion reduces the integral to a simple algebraic sum.The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters.The field curves for four types (A-,K-,H-and Q-type)of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson scheme. It is concluded that the present scheme is more accurate than the Anderson scheme

An Optimization-Based Topology Error Detection Method for Power System State Estimation

The paper presents an optimization-based method for topology error detection in power systems. The method utilizes the\ua0residual analysis\ua0in state estimation and minimization of normalized measurement residual, with the application of matrix inverse lemma. The work considers a hybrid measurement configuration, i.e., both SCADA and PMU measurements, for the test systems studied. The proposed method is implemented on the TOMLAB optimization platform under the mixed integer nonlinear programming category. The proposed method has been applied and tested on standard IEEE 14-bus and IEEE 118-bus test systems. The method is designed to be computationally efficient and produces accurate results for single topology error detection. The results from the IEEE 14-bus and IEEE 118-bus test systems have shown that the proposed method produces 100% and 94% accurate results for single topology error detection, respectively. The proposed method performs robustly with the increased measurement uncertainties and inclusion of bad data or gross errors in the measurements. The method has superiority in practical implementation over the meta-heuristics-based optimization methods. The proposed method can be easily implemented and could have potential application in the\ua0energy management systems\ua0of the power system control center