A Fast ANN Trained Solver Enables Real-Time Radial Inversion of Dielectric Dispersion Data & Accurate Estimate of Reserves in Challenging Environments

Dielectric dispersion measurements are increasingly used by petrophysicists to reduce uncertainty in their hydrocarbon saturation analysis, and subsequent reserves estimation, especially when encountered with challenging environments. Some of these challenges are related to variable or unknown formation water salinity and/or a changing rock texture which is a common attribute of carbonate reservoirs found in the Middle East. A new multi-frequency, multi-spacing dielectric logging service, utilizes a sensor array scheme which provides wave attenuation and phase difference measurements at multiple depths of investigation up to 8 inches inside the formation. The improvement in depth of investigation provides a better measurement of true formation properties, however, also provides a higher likelihood of measuring radial heterogeneity due to spatially variable shallow mud-filtrate invasion. Meaningful petrophysical interpretation requires an accurate electromagnetic (EM) inversion, which accommodates this heterogeneity, while converting raw tool measurements to true formation dielectric properties. Forward modeling solvers are typically beset with a slow processing speed precluding use of complex, albeit representative, formation petrophysical models. An artificial neural network (ANN) has been trained to significantly speed up the forward solver, thus leading to implementation and real-time execution of a complex multi-layer radial inversion algorithm. The paper describes, in detail, the development, training and validation of both the ANN network and the inversion algorithm. The presented algorithm and ANN inversion has shown ability to accurately resolve mud filtrate invasion profile as well as the true formation properties of individual layers. Examples are presented which demonstrate that comprehensive, multi-frequency, multi-array, EM data sets are inverted efficiently for dis-similar dielectric properties of both invaded and non-invaded formation layers around the wellbore. The results are further utilized for accurate hydrocarbon quantification otherwise not achieved by conventional resistivity based saturation techniques. This paper presents the development of a new EM inversion algorithm and an artificial neural network (ANN) trained to significantly speed up the solution of this algorithm. This approach leads to a fast turnaround for an accurate petrophysical analysis, reserves estimate and completion decisions.

Assessment of Water Saturation Using Dielectric Permittivity Measurements in Formations with Complex Pore Structure: Application to the Core- and Log- Scale Domains

Broadband dielectric dispersion measurements are attractive options for assessment of water-filled pore volume, especially when quantifying salt concentration is challenging. However, conventional models for interpretation of dielectric measurements such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG) model require oversimplifying assumptions about pore structure and distribution of constituting fluids/minerals. Therefore, dielectric-based estimates of water saturation are often not reliable in the presence of complex pore structure, rock composition, and rock fabric (i.e., spatial distribution of solid/fluid components). The objectives of this paper are (a) to propose a simple workflow for interpretation of dielectric permittivity measurements in log-scale domain, which takes the impacts of complex pore geometry and distribution of minerals into account, (b) to experimentally verify the reliability of the introduced workflow in the core-scale domain, and (c) to apply the introduced workflow for well-log-based assessment of water saturation. The dielectric permittivity model includes tortuosity-dependent parameters to honor the complexity of the pore structure and rock fabric for interpretation of broadband dielectric dispersion measurements. We estimate tortuosity-dependent parameters for each rock type from dielectric permittivity measurements conducted on core samples. To verify the reliability of dielectric-based water saturation model, we conduct experimental measurements on core plugs taken from a carbonate formation with complex pore structures. We also introduce a workflow for applying the introduced model to dielectric dispersion well logs for depth-by-depth assessment of water saturation. The tortuosity-dependent parameters in log-scale domain can be estimated either via experimental core-scale calibration, well logs in fully water-saturated zones, or pore-scale evaluation in each rock type. The first approach is adopted in this paper. We successfully applied the introduced model on core samples and well logs from a pre-salt formation in Santos Basin. In the core-scale domain, the estimated water saturation using the introduced model resulted in an average relative error of less than 11% (compared to gravimetric measurements). The introduced workflow improved water saturation estimates by 91% compared to CRIM. Results confirmed the reliability of the new dielectric model. In application to well logs, we observed significant improvements in water saturation estimates compared to cases where a conventional effective medium model (i.e., CRIM) was used. The documented results from both core-scale and well-log-scale applications of the introduced method emphasize on the importance of honoring pore structure in the interpretation of dielectric measurements.

Lossy Titanite-Based Ceramics with Nominal Compositions CaTi1-xMySiO 5 (0 ≦ X, Y ≦ 1, M = Mn, Sn, Zr, Nb) Applicable to Millimeter Electromagnetic Wave Absorber

The titanite-based ceramics with nominal composition CaTi1-xMySiO5 (0≦x≦1, M = Mn, Sn, Zr (y = x), and M = Nb (y = 4x/5)) in which part x of Ti sites are replaced by several kinds of atoms had remarkable increase in both the real and imaginary parts of complex relative permittivity around x = 0.0125~0.1 compared with those of pure titanite CaTiSiO5 ( x = 0) at 70 GHz. Real part varied from 3 to 43, and the imaginary part from 0 to 12 (tangent delta from 0 to 0.28). No reflection condition is fulfilled for M = Zr when x = 0.05, d/λ0 =0.042, and for M = Nb in both cases when 0 < x < 0.0125, d/λ0 = 0.05 and 0.1 <x < 0.2, d/λ0 =0.042, where d is thickness of the plate sample and λ0 is the wavelength of incident electromagnetic wave. The dominant dielectric dispersion may occur due to difference of ionic polarization between Ti4+ ions and Mn4+, Sn4+, Zr4+, or Nb5+ ions relative to O2- ions, which becomes inactive and saturates around x = 0.0125~0.05. From the measurement of the lattice parameters, a, b, c, and the angle β, characterizing monoclinic crystal structure, this saturation may have close correlation with some structural rearrangement of constituting atoms, Ti and substituted M atoms in CaTi1-xMySiO5

Structural, Electrical and Magnetic Study in Nanocrystallite La2CuMnO6 Ceramics

Structural, dielectric and magnetic properties of nano-size polycrystalline, La2CuMnO6 (LCM) samples were studied in the temperature range 80 K to 300 K. Orthorhombic single phase with space group 'Pnma' was confirmed by Rietveld refinement of XRD peaks. The small-polaron driven dielectric dispersion showed relaxation peaks in the vicinity of low-temperatures. The X-ray absorption spectroscopy (XAS) confirmed the charge states of Cu (2+) and Mn (4+) ions. DC-resistivity analysis supported the thermally activated conduction for high temperature and the variable range hoping (VRH) mechanism of conduction at low-temperature. The deviation of super-exchange angles between B-site cations from an ideal 180º value produced non-collinearity in the antiferromagnetic response of this ceramic and was confirmed canted antiferromagnetic behaviour. Positive Curie temperature along with finite coercivity indicated that the super-exchange interaction between Cu2+ and Mn4+ ions influenced the magnetic behaviour of this ceramics and showed a heterogenous magnetic response.

INTERPRETATION OF MULTI-FREQUENCY DIELECTRIC PERMITTIVITY MEASUREMENTS FOR ASSESSMENT OF WATER SATURATION IN CARBONATE FORMATIONS WITH COMPLEX PORE STRUCTURE

Broadband relative dielectric dispersion measurements are considered interesting options for assessment of water-filled pore volume. Conventional models such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG), often overlook or oversimplify the complexity of pore structure, geometrical distribution of the constituting fluids, and spatial distribution of minerals. This yields to significant errors in assessment of water saturation especially in rocks with complex pore structure. Therefore, it becomes important to quantify the impacts of pore structure and spatial distribution of minerals on broadband relative dielectric dispersion measurements to be able to make decisions about reliability of water saturation estimates from these measurements in a given formation. The objectives of this paper are (a) to quantify the impacts of pore structure and spatial distribution of minerals on relative dielectric permittivity measurements in a wide range of frequencies, (b) to propose a new simple and physically meaningful workflow, which honors pore geometry and spatial distribution of minerals to enhance fluid saturation assessment using relative dielectric permittivity measurements, (c) to verify the reliability of the introduced model in the pore-scale domain. First, we perform numerical simulations of relative dielectric dispersion measurements in the frequency range of 20 MHz to 1 GHz in the pore-scale domain. The input to the numerical simulator includes pore-scale images of actual complex carbonate rock samples. We use a physically meaningful model which honors spatial distribution of the rock constituents for the multi-frequency interpretation of relative dielectric response. To verify the reliability of the model in multiple frequencies, we apply the model to the results of relative dielectric simulations in the pore-scale domain on 3D computed tomography scan (CT-scan) images of carbonate rock samples, which are synthetically saturated to obtain a wide range of water saturation. We successfully verified the reliability of the introduced model in the pore-scale domain using carbonate rock samples with multi-modal pore-size distribution. Estimated water saturations from the results of simulations at 1 GHz resulted in an average relative error of less than 4%. We observed measurable improvements in fluid saturation estimates compared to the cases which CRIM or MG models are used. Results demonstrated that application of conventional models to estimate water saturation from relative dielectric response is not reliable in frequencies below 1 GHz.