The Equations Archie Forgot: Anisotropy of the Rocks

2010 ◽  
Vol 13 (05) ◽  
pp. 823-836 ◽  
Author(s):  
Carlos F. Haro
Keyword(s):  
Ad Hoc ◽  
Water Saturation ◽  
Power Laws ◽  
Fluid Distribution ◽  
Data Sets ◽  
Solution Flow ◽  
Original Analysis ◽  
Particular Solution ◽  
Saturation Exponent ◽  
Complex Formations

Summary Archie's empirical equation is used extensively to estimate hydrocarbons in place. This power-laws combination has stood the test of time with few changes. However, it is still poorly understood and considered an ad hoc relation. Our original analysis will prove these laws rigorously, show how they must be amended, and introduce additional accompanying equations. This comprehensive model, which represents the electrical flow through the intricate conductive paths of the rock, is confirmed with Archie's and Hamada's core data sets. It corrects for Archie's inaccuracies. A thorough appreciation of the pore-scale physics behind the modified version of Archie's equation is presented. The principles can be applied in clean and complex formations (shaly sands, thin beds, and vuggy or fractured carbonates) to obtain enhanced values of water saturation. The theory sheds light on the role and quantification of anisotropy. Solving for the elaborate pore geometry, we use the Laplace differential equation (not Ohm's law), appropriate in the analysis of electrostatic fields in charge-free regions. Rock morphology dictates its boundary conditions (Jin 2007; Ghous 2005), characterized as corner angles. The corresponding particular solution (flow around a corner) and modeling tactic delineate the streamlines throughout the pores. The angles establish strong mathematical links among the exponents of Archie's equation, the geometry of the rock frame, and the spatial fluid distribution. This quantitative method is lacking in previous saturation models. The solution constitutes the basis to solve more-complicated rock layouts. It enables the calculation of equivalent resistivities (normalized resistances) to take advantage of well-established electrical relationships. The extra equations compute the variable exponents and coefficients of Archie's equation at every depth. They obtain the saturation exponent in clean rocks as a function of water saturation, crucial to the quality control of core electrical data and to the quantification of reservoirs under changing saturation (waterflooding). Therefore, improved calculations of original and remaining hydrocarbons are achieved.

scholarly journals Effects of Foam Microbubbles on Electrical Resistivity and Capillary Pressure of Partially Saturated Porous Media

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3385 ◽  
Author(s):  
Abdulrauf R. Adebayo ◽  
Abubakar Isah ◽  
Mohamed Mahmoud ◽  
Dhafer Al-Shehri
Keyword(s):  
Porous Media ◽  
Electrical Resistivity ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Water Saturation ◽  
Porous Plate ◽  
Fluid Distribution ◽  
Cross Sectional ◽  
Injection Process ◽  
Saturation Exponent

Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas–water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.

scholarly journals Experiments of Image Classification Using Dissimilarity Spaces Built with Siamese Networks

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1573
Author(s):  
Loris Nanni ◽  
Giovanni Minchio ◽  
Sheryl Brahnam ◽  
Gianluca Maguolo ◽  
Alessandra Lumini
Keyword(s):  
Vector Space ◽  
Image Classification ◽  
Ad Hoc ◽  
Feature Space ◽  
Medical Data ◽  
Training Data ◽  
Data Sets ◽  
Large Set ◽  
Clustering Methods ◽  
Siamese Networks

Traditionally, classifiers are trained to predict patterns within a feature space. The image classification system presented here trains classifiers to predict patterns within a vector space by combining the dissimilarity spaces generated by a large set of Siamese Neural Networks (SNNs). A set of centroids from the patterns in the training data sets is calculated with supervised k-means clustering. The centroids are used to generate the dissimilarity space via the Siamese networks. The vector space descriptors are extracted by projecting patterns onto the similarity spaces, and SVMs classify an image by its dissimilarity vector. The versatility of the proposed approach in image classification is demonstrated by evaluating the system on different types of images across two domains: two medical data sets and two animal audio data sets with vocalizations represented as images (spectrograms). Results show that the proposed system’s performance competes competitively against the best-performing methods in the literature, obtaining state-of-the-art performance on one of the medical data sets, and does so without ad-hoc optimization of the clustering methods on the tested data sets.

Experimental Study on the Saturation Model of Volcanic Rock Based on Fluid Distribution

2021 ◽  
Vol 62 (4) ◽  
pp. 422-433
Author(s):  
Baozhi Pan ◽  
◽  
Weiyi Zhou ◽  
Yuhang Guo ◽  
Zhaowei Si ◽  
...  
Keyword(s):  
Volcanic Rock ◽  
Oil And Gas ◽  
Water Saturation ◽  
Early Stage ◽  
Evaluation Model ◽  
Acoustic Velocity ◽  
Distribution Model ◽  
Fluid Distribution ◽  
Water Drainage ◽  
Gas Reservoirs

A saturation evaluation model suitable for Nanpu volcanic rock formation is established based on the experiment of acoustic velocity changing with saturation during the water drainage process of volcanic rock in the Nanpu area. The experimental data show that in the early stage of water drainage, the fluid distribution in the pores of rock samples satisfies the patchy formula. With the decrease of the sample saturation, the fluid distribution in the pores is more similar to the uniform fluid distribution model. In this paper, combined with the Gassmann-Brie and patchy formula, the calculation equation of Gassmann-Brie-Patchy (G-B-P) saturation is established, and the effect of contact softening is considered. The model can be used to calculate water saturation based on acoustic velocity, which provides a new idea for the quantitative evaluation of volcanic oil and gas reservoirs using seismic and acoustic logging data.

EFFICIENT PETROPHYSICAL UNCERTAINTY PROPAGATION VIA DATA-DRIVEN ANALYTICS

2021 ◽  
Author(s):  
Carlo Cristiano ◽  
◽  
Marco Pirrone ◽  
Keyword(s):  
Ad Hoc ◽  
Water Saturation ◽  
Mechanistic Model ◽  
Mitigation Strategies ◽  
Data Driven ◽  
Standard Approach ◽  
Reservoir Modeling ◽  
Parameter Uncertainties ◽  
Volume Porosity ◽  
Very High

Risk-mitigation strategies are most effective when the major sources of uncertainty are determined through dedicated and in-depth studies. In the context of reservoir characterization and modeling, petrophysical uncertainty plays a significant role in the risk assessment phase, for instance in the computation of volumetrics. The conventional workflow for the propagation of the petrophysical uncertainty consists of physics-based model embedded into a Monte Carlo (MC) template. In detail, open-hole logs and their inherent uncertainties are used to estimate the important petrophysical properties (e.g. shale volume, porosity, water saturation) with uncertainty through the mechanistic model and MC simulations. In turn, model parameter uncertainties can be also considered. This standard approach can be highly time-consuming in case the physics-based model is complex, unknown, difficult to reproduce (e.g. old/legacy wells) and/or the number of wells to be processed is very high. In this respect, the aim of this paper is to show how a data-driven methodology can be used to propagate the petrophysical uncertainty in a fast and efficient way, speeding-up the complete process but still remaining consistent with the main outcomes. In detail, a fit-for-purpose Random Forest (RF) algorithm learns through experience how log measurements are related to the important petrophysical parameters. Then, a MC framework is used to infer the petrophysical uncertainty starting from the uncertainty of the input logs, still with the RF model as a driver. The complete methodology, first validated with ad-hoc synthetic case studies, has been then applied to two real cases, where the petrophysical uncertainty has been required for reservoir modeling purposes. The first one includes legacy wells intercepting a very complex lithological environment. The second case comprises a sandstone reservoir with a very high number of wells, instead. For both scenarios, the standard approach would have taken too long (several months) to be completed, with no possibility to integrate the results into the reservoir models in time. Hence, for each well the RF regressor has been trained and tested on the whole dataset available, obtaining a valid data-driven analytics model for formation evaluation. Next, 1000 scenarios of input logs have been generated via MC simulations using multivariate normal distributions. Finally, the RF regressor predicts the associated 1000 petrophysical characterization scenarios. As final outcomes of the workflow, ad-hoc statistics (e.g. P10, P50, P90 quantiles) have been used to wrap up the main findings. The complete data-driven approach took few days for both scenarios with a critical impact on the subsequent reservoir modeling activities. This study opens the possibility to quickly process a high number of wells and, in particular, it can be also used to effectively propagate the petrophysical uncertainty to legacy well data for which conventional approaches are not an option, in terms of time-efficiency.

scholarly journals Ad hoc procedure for optimising agreement between observational records

2016 ◽  
Vol 32 (2) ◽  
pp. 589 ◽  
Author(s):  
Javier Arana ◽  
Daniel Lapresa ◽  
María Teresa Anguera ◽  
Belén Garzón
Keyword(s):  
Observational Studies ◽  
Order Parameter ◽  
Ad Hoc ◽  
Kappa Statistic ◽  
Data Sets ◽  
The Third ◽  
Complex Events

Observational studies in the field of sport are complicated by the added difficulty of having to analyse multiple, complex events or behaviours that may last just a fraction of a second. In this study, we analyse three aspects related to the reliability of data collected in such a study. The first aim was to analyse and compare the reliability of data sets assessed quantitatively (calculation of kappa statistic) and qualitatively (consensus agreement method). The second aim was to describe how, by ensuring the alignment of events, we calculated the kappa statistic for the order parameter using SDIS-GSEQ software (version 5.1) for data sets containing different numbers of sequences. The third objective was to describe a new consultative procedure designed to remove the confusion generated by discordant data sets and improve the reliability of the data. The procedure is called “consultative” because it involves the participation of a new observer who is responsible for consulting the existing observations and deciding on the definitive result.

scholarly journals Sistema de observación para analizar la interacción en el juego de Boccia por equipos

2019 ◽  
Vol 20 (1) ◽  
pp. 37-47
Author(s):  
Daniel Lapresa Ajamil ◽  
Javier Pascual Laguna ◽  
Javier Arana ◽  
M. Teresa Anguera
Keyword(s):  
Ad Hoc ◽  
High Reliability ◽  
Observation System ◽  
Data Sets ◽  
Antisocial Behaviors ◽  
Observation Instrument ◽  
The Social ◽  
El Sistema ◽  
Disability Group ◽  
Generalizability Study

Se ha diseñado un instrumento de observación ad hoc, combinación de formato de campo y sistemas de categorías, que permite analizar la interacción social -conductas prosociales y antisociales- que tiene lugar en la competición por equipos en el juego de boccia. El registro y codificación de los datos se ha desarrollado mediante el software Lince. La validez de contenido del instrumento de observación ha quedado avalada por el equipo técnico de la Selección Española de boccia. Los resultados relativos a la concordancia entre los registros generados por tres observadores diferentes, calculada mediante el coeficiente Kappa de Cohen, indican una elevada fiabilidad de los datos obtenidos mediante el sistema de observación. En el seno de la teoría de la Generalizabilidad, mediante el software SAGT, se ha desarrollado el plan de medida [Jugador] [Categoría] / [Parcial], que ha permitido asegurar que, con el número de parciales analizados, se consigue una elevada fiabilidad de precisión de generalización. Además, se ha procedido a la optimización del plan de medida [Parciales] [Categorías] / [Jugador]. La operatividad del sistema de observación desarrollado ha quedado patente en los T-patterns detectados mediante el software Theme, versión 6. Edu. De los resultados obtenidos se desprende que el juego de boccia constituye un entorno favorable de elevado valor formativo para el colectivo de la discapacidad. The observation instrument was purpose-built and combines a field format with systems of categories. The observation instrument allows to analyze the social interaction -prosocial and antisocial behaviors- that takes place in team boccia competition. The content validity of the observation instrument has been guaranteed by the coaching staff of the Boccia Spanish Team. The data were coded with the Lince software programme. Cohen's Kappa coefficient obtained by comparing the data sets generated by three observers indicates a high reliability of the data. We also performed a generalizability study, [Player][Category]/[End], demonstrating the consistency of the data based on the Ends observed. The application of the optimization module for [End][Category]/[Player] facets showed us how many players would constitute an optimal sample in future studies. The practical application of the observation system was demonstrated by performing T-pattern analysis using Theme software programme. The results obtained show that boccia is a very favorable educational environment for the disability group. O instrumento de observação foi construído ad hoc e combina um formato de campo com sistemas de categorias. O instrumento de observação permite analisar a interação social - comportamentos anti-sociais e anti-sociais - que ocorre na competição de bocha em equipe. A validade de conteúdo do instrumento de observação foi garantida pela equipe técnica da Equipe Espanhola de Boccia. Os dados foram codificados com o programa de software Lince. Coeficiente Kappa de Cohen obtido pela comparação dos conjuntos de dados gerados por três observadores indica alta confiabilidade dos dados. Também realizamos um estudo de generalização [Jogador] [Categoria] / [Parcial], demonstrando a consistência dos dados com base nas extremidades observadas. A aplicação do módulo de otimização para as facetas [Parciales] [Categorias] / [Jogador] nos mostrou quantos jogadores seriam uma ótima amostra em estudos futuros. A aplicação prática do sistema de observação foi demonstrada através da análise do padrão T usando o programa de software Theme. Os resultados obtidos são desprezíveis que o jogo de bocha é constituído por um formulário de valor favorável para o colectivo da discapacidade.

Change within Continuity

2018 ◽  
Author(s):  
Jean C. Oi ◽  
Steven M. Goldstein
Keyword(s):  
Political Institutions ◽  
Ad Hoc ◽  
Economic Structure ◽  
Organizational Structures ◽  
The Political ◽  
Formal Organization ◽  
Political Consequences ◽  
Government Institutions ◽  
The Core ◽  
Original Analysis

This chapter introduces the volume and offers an in-depth analyzes of the changes that have taken place in Zouping’s political economy over the last 15 years. It poses the core question of whether China’s political institutions have somehow managed to cope despite remaining basically unreformed, or have there been more subtle and profound changes in the way that the old organizational structures actually operate. Ad hoc bureaucratic adaptations and accommodations change the operation, if not the organizational form, of local government institutions, where existing agencies play new and unexpected roles. It is institutional agility, with on-going political change masked by outward continuity in formal organization. The sections on the county’s economic development include original analysis of the county’s changing economic structure, the shift from public to private enterprise, and the political consequences of economic change. The chapter ends with a summary of the different chapters in the volume.

scholarly journals PLANE-SYMMETRIC INHOMOGENEOUS BULK VISCOUS COSMOLOGICAL MODELS WITH VARIABLE Λ

2003 ◽  
Vol 12 (05) ◽  
pp. 941-951 ◽  
Author(s):  
ANIRUDH PRADHAN ◽  
HARE RAM PANDEY
Keyword(s):  
Cosmological Model ◽  
Viscous Fluid ◽  
Cosmological Constant ◽  
Ad Hoc ◽  
Fluid Distribution ◽  
Geometric Features ◽  
Plane Symmetric ◽  
Bulk Viscous Fluid ◽  
Variable Λ ◽  
Bulk Viscous

A plane-symmetric non-static cosmological model representing a bulk viscous fluid distribution has been obtained which is inhomogeneous and anisotropic and a particular case of which is gravitationally radiative. Without assuming any ad hoc law, we obtain a cosmological constant as a decreasing function of time. The physical and geometric features of the models are also discussed.

Direct elastic properties to resistivity transforms

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. IM109-IM118
Author(s):  
Dimitrios Economou ◽  
Behzad Alaei
Keyword(s):  
Water Saturation ◽  
Data Sets ◽  
Seismic Velocities ◽  
Even Start ◽  
Novel Approach ◽  
Multivariate Nonlinear Regression ◽  
Subsurface Resistivity ◽  
Relationship Of ◽  
Norwegian Continental Shelf ◽  
Good Agreement

Numerous publications have dealt with estimations of resistivity from elastic parameters and vice versa. Attempts have been made in the cross-property relationship of elastic and electric properties, in particular, velocity to resistivity using different parameters, such as porosity and water saturation. These types of transforms are currently used to predict background seismic velocities and resistivities, or even start models for seismic or controlled source electromagnetic (CSEM) inversions. However, they are not reliable predictors because they depict the regional elastic or electric variations with limited accuracy. We present a novel approach for the development of models capable of estimating the regional subsurface resistivity based on information from regional wells and seismic inversions. We apply multivariate nonlinear regression on data derived from regional wells and seismic inversions and subsequently produced an estimation of subsurface horizontal resistivity that could be either used as a direct hydrocarbon indicator or provide a constraint on the horizontal resistivity in anisotropic CSEM inversions. We have verified the validity of the approach using two data sets from the Norwegian continental shelf. We found very good agreement between the borehole-measured and predicted resistivity.

scholarly journals Improved retrieval of nitrogen dioxide (NO<sub>2</sub>) column densities by means of MKIV Brewer spectrophotometers

2014 ◽  
Vol 7 (11) ◽  
pp. 4009-4022 ◽  
Author(s):  
H. Diémoz ◽  
A. M. Siani ◽  
A. Redondas ◽  
V. Savastiouk ◽  
C. T. McElroy ◽  
...  
Keyword(s):  
Nitrogen Dioxide ◽  
Ad Hoc ◽  
Absorption Spectrometry ◽  
Atmospheric Composition ◽  
Data Sets ◽  
Data Set ◽  
Noise Interference ◽  
Atmospheric Species ◽  
Mass Factor

Abstract. A new algorithm to retrieve nitrogen dioxide (NO2) column densities using MKIV ("Mark IV") Brewer spectrophotometers is described. The method includes several improvements, such as a more recent spectroscopic data set, the reduction of measurement noise, interference by other atmospheric species and instrumental settings, and a better determination of the zenith sky air mass factor. The technique was tested during an ad hoc calibration campaign at the high-altitude site of Izaña (Tenerife, Spain) and the results of the direct sun and zenith sky geometries were compared to those obtained by two reference instruments from the Network for the Detection of Atmospheric Composition Change (NDACC): a Fourier Transform Infrared Radiometer (FTIR) and an advanced visible spectrograph (RASAS-II) based on the differential optical absorption spectrometry (DOAS) technique. To determine the extraterrestrial constant, an easily implementable extension of the standard Langley technique for very clean sites without tropospheric NO2 was developed which takes into account the daytime linear drift of stratospheric nitrogen dioxide due to photochemistry. The measurement uncertainty was thoroughly determined by using a Monte Carlo technique. Poisson noise and wavelength misalignments were found to be the most influential contributors to the overall uncertainty, and possible solutions are proposed for future improvements. The new algorithm is backward-compatible, thus allowing for the reprocessing of historical data sets.

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