This paper aims to investigate the impact of the overdetermination (data-tounknowns) ratio on the global inversion of wireline logging data. In the course of the so-called interval inversion method, geophysical data measured in a borehole over a longer depth range is jointly inverted and the depth variation of the investigated petrophysical parameters are expanded into series using Legendre polynomials as basis functions resulting in a highly overdetermined inverse problem. A metaheuristic Particle Swarm Optimization (PSO) approach is applied as a first phase of inversion for decreasing the starting model dependence of the interval inversion procedure. In the subsequent linear inversion steps, by using the measurement error of logging tools and the covariance matrix of the estimated petrophysical parameters, we can quantify the accuracy of the model parameters.The dataset used in this study consists of nuclear, resistivity and sonic logs which are inverted to compute porosity, shale volume and water saturation along the investigated interval. For increasing the data-to-unknowns ratio of the inverse problem, shale volume is estimated separately by a PSO-based factor analysis and fixed as known parameter for the interval inversion process. Since the shale volume has been described as high degree Legendre polynomial, a significant increase of the overdetermination ratio considerably decreases the uncertainty of the remaining model parameters allowing for a more reliable calculation of hydrocarbon content.

In this paper, we present an innovative factor analysis algorithm for hydrocarbon exploration to estimate the intrinsic permeability of reservoir rocks from well logs. Unlike conventional evaluation methods that employ a single or a limited number of data types, we process simultaneously all available data to derive the first statistical factor and relate it to permeability by regression analysis. For solving the problem of factor analysis, we introduce an improved particle swarm optimization method, which searches for the global minimum of the distance between the observed and calculated data and gives a quick estimation for the factor scores. The learning factors of the intelligent computational technique such as the cognitive and social constants are specified as hyperparameters and calculated by using simulated annealing algorithm as heuristic hyperparameter estimator. Instead of the arbitrary fixation of these hyperparameters, we refine them in an iterative process to give reliable estimation both for the statistical factors and formation permeability. The estimated learning parameters are consistent with literature recommendations. We demonstrate the feasibility of the proposed well-log analysis method by a Hungarian oilfield study involving open-hole wireline logs and core data. We determine the spatial distribution of permeability both along a borehole and between more wells using the factor analysis approach, which serves as efficient and reliable multivariate statistical tool for advanced formation evaluation and reservoir modeling.

In this paper, a set of machine learning (ML) tools is applied to estimate the water saturation of shallow unconsolidated sediments at the Bátaapáti site in Hungary. Water saturation is directly calculated from the first factor extracted from a set of direct push logs by factor analysis. The dataset observed by engineering geophysical sounding tools as special variants of direct-push probes contains data from a total of 12 shallow penetration holes. Both one- and two-dimensional applications of the suggested method are presented. To improve the performance of factor analysis, particle swarm optimization (PSO) is applied to give a globally optimized estimate for the factor scores. Furthermore, by a hyperparameter estimation approach, some control parameters of the utilized PSO algorithm are automatically estimated by simulated annealing (SA) to ensure the convergence of the procedure. The result of the suggested ML-based log analysis method is compared and verified by an independent inversion estimate. The study shows that the PSO-based factor analysis aided by hyperparameter estimation provides reliable in situ estimates of water saturation, which may improve the solution of environmental end engineering problems in shallow unconsolidated heterogeneous formations.

Factor analysis of well logging data can be effectively applied to calculate shale volume in hydrocarbon formations. A global optimization approach is developed to improve the result of traditional factor analysis by reducing the misfit between the observed well logs and theoretical data calculated by the factor model. Formation shaliness is directly calculated from the factor scores by a nonlinear regression relation, which is consistent in the studied area in Alaska, USA. The added advantage of the implementation of the Simulated Annealing method is the estimation of the theoretical values of nuclear, sonic, electrical as well as caliper well-logging data. The results of globally optimized factor analysis are compared and verified by independent estimates of self-potential logbased deterministic modeling. The suggested method is tested in two different shaly-sand formations in the North Aleutian Basin of Alaska and the comparative study shows that the assumed nonlinear connection between the factor scores and shale volume is applicable with the same regression constants in different burial depths. The study shows that factor analysis solved by the random search technique provides an independent in situ estimate to shale content along arbitrary depth intervals of a borehole, which may improve the geological model of the hydrocarbon structure in the investigated area.

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