Interval Inversion Method Research Articles

Level of thermal maturity estimation in unconventional reservoirs using interval inversion and simulating annealing method

AbstractThis study presents a novel geophysical approach for estimating the level of thermal maturity (LOM) in unconventional hydrocarbon reservoirs using well log data. LOM is a crucial parameter for assessing the hydrocarbon generation potential of source rocks, but it traditionally relies on laboratory measurements of core samples, which can be time-consuming and costly. The proposed method combines two techniques: interval inversion for estimating total organic carbon (TOC) content from well logs and simulated annealing (SA) optimization for deriving LOM from the estimated TOC. The interval inversion method enables accurate TOC estimation by jointly interpreting multiple well logs over depth intervals, overcoming limitations of conventional point-by-point inversion. Using the estimated TOC, the SA algorithm optimizes an energy function related to Passey's empirical TOC-LOM relationship, iteratively finding the optimal LOM value that best fits the well log data. This approach provides a continuous in situ LOM profile along the borehole without requiring core measurements. The effectiveness of the method is demonstrated through case studies on datasets from the North Sea (Norway), the Pannonian Basin (Hungary), and the Kingak Formation (Alaska). The LOM estimates show good agreement with reported maturity levels and allow reliable reservoir characterization. Statistical analysis confirms the robustness and accuracy of the results. By reducing dependence on core data, this integrated inversion-optimization workflow streamlines the reservoir prospecting phase, enhancing operational efficiency. The method holds promising applications across diverse geological settings for cost-effective evaluation of unconventional hydrocarbon plays.

Integrated workflow incorporating the Hurst exponent and interval inversion for evaluating groundwater formations

A novel well-log-analysis approach is presented for an improved prediction of petrophysical properties in groundwater formations. Geophysical well logs are simultaneously processed for quantifying the lithology, storage capacity, and water flow parameters. A fully automated data processing workflow is proposed, the feasibility of which is assured by an appropriate starting model set by the joint application of factor analysis and the Hurst exponent, and a solution of a highly overdetermined inverse problem. The Hurst exponent is used for zone boundary detection, which assists the series expansion-based interval inversion method applied for estimation of the petrophysical parameters of clastic formations. The hydraulic conductivity as a well log is directly derived from the inversion results. The workflow is tested using both synthetic data contaminated with 5% Gaussian distributed noise and real data collected from a thermal water well in Baktalórántháza, eastern Hungary. At the test site, the Hurst exponent extracted from the wireline logs allows one to divide the processed interval into subzones around the Pleistocene-Miocene boundary. The observed wireline logs are inverted to estimate the volumetric parameters (porosity, shale content, water saturation, etc.) of the same zones. The predicted parameters, including hydraulic conductivity, reveal that Pleistocene sediments contain good aquifers with formation quality varying with depth. The shale volume and hydraulic conductivity logs show a proper match with the core data, which confirms the results of the comprehensive analysis. The suggested workflow is recommended for the evaluation of groundwater formations located in different depth domains, from unsaturated sediments to geothermal reservoirs.

Interval inversion of multiwell logging data for estimating laterally varying petrophysical parameters and formation boundaries

The present paper introduces a Legendre polynomials based interval inversion method for processing multi-borehole logging data. The method allows the determination of lateral changes of the layer-thicknesses together with the vertical and lateral variations of petrophysical parameters along a 2D cross-section of several boreholes. The method is assessed using noisy synthetic measurements of a petrophysical model made of two-layers structure related to hydrocarbon bearing formations. The numerical experiments aided to investigate the stability and convergence of the 2D interval inversion procedure. To ensure the accuracy and reliability of the inversion results, the misfit of data and model distance are tested, beside the calculation of estimation errors and correlation coefficients. A large amount of input data relative to the number of unknowns results in a high overdetermined ratio, consequently more precise estimates are obtained in stable and convergent procedure than in conventional local (1D) inversion schemes. The feasibility of the 2D interval inversion method is shown by analysing in-situ well logging data acquired in four wells situated in an Egyptian hydrocarbon field.

Interval inversion based well log analysis assisted by petrophysical laboratory measurements for evaluating tight gas formations in Derecske through, Pannonian basin, east Hungary

The evaluation of Hungarian tight gas formations requires the use of innovative interpretation technologies because of diverse geological environment, heterogeneous dataset including several variables measured with different accuracies, and reservoirs under varying petrophysical conditions. Conventional well logging methods based on the use of limited number of wireline logs make only a quick-look interpretation, in which a limited number of unknowns is determined, and there is a non-negligible risk for occurrence of ambiguity. In order to increase the overdetermination (data-to-unknowns) ratio and the estimation accuracy and reliability, all suitable well logs are to be jointly processed in a more effective manner. To estimate the total organic carbon content together with porosity, water saturation, shale content and rock matrix volumes with higher accuracy, a new inversion methodology is introduced that is tested in tight gas reservoirs. A differential evolution algorithm-based interval inversion method is developed that is combined by nano-permeability and high precision porosity laboratory measurements for the detection and evaluation of Hungarian tight gas reservoirs. Spectral gamma-ray, neutron-porosity and electric resistivity logs are jointly analyzed using the interval inversion approach. By solving a highly overdetermined inverse problem, the effective porosity, water- and gas saturation, shale and sand content, as well as the kerogen volume are estimated in a reliable inversion procedure. The silt and clay content of Miocene tight gas formations are separated and both determined by inversion, while the total organic carbon content is derived from the inversion results. The permeability log is directly derived from the inverted porosity values using the local porosity versus permeability relation established by multi-well core analysis. The combination of in situ wireline log data analysis and porosity and nano-permeability laboratory measurements is shown to be advantageous for a more reliable interpretation of unconventional hydrocarbon formations. An added advantage of the interval inversion method is the calculation of depth dependent errors of the estimated petrophysical quantities. It is shown that total organic carbon and other volumetric parameters can be determined with high accuracy in one interpretation procedure. In the Derecske basin, East Hungary, gas indications are confirmed by interval inversion, that were previously made it probable according to measurements made on poor core samples and rather noise-sensitive local well logging inversion procedure. The joint evaluation of new core data and original wireline logs using the proposed methodology may reveal further potential tight gas resources in the studied area. The Hungarian case study confirms that the suggested workflow may serve a new alternative for an improved evaluation of tight gas formations in different other hydrocarbon fields.

Uncertainty reduction of interval inversion estimation results using a factor analysis approach

This paper aims to investigate the impact of the overdetermination (data-to-unknowns) 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.

Interval inversion as innovative well log interpretation tool for evaluating organic-rich shale formations

The identification and detailed evaluation of unconventional hydrocarbon reservoirs require the application of advanced well logging data processing techniques. Since the number of the petrophysical properties such as porosity, water and hydrocarbon saturation, kerogen content, and fractional volumes of matrix components may exceed that of the observed wireline log types, currently used quick-look methods based on few well logs provide approximate solution to a part of the above petrophysical quantities. For instance, Passey's method basically utilizes two well logs for identifying the sweet spots and estimating the total organic content (TOC). Local inversion techniques estimating the petrophysical parameters in a given depth are also limited because of low overdetermination (data-to-unknowns) ratio and hence are very sensitive to data noises. Instead of using traditional empirical methods and to avoid ambiguous solutions by local inversion evaluations, data of all wireline logs measured in a longer depth interval are simultaneously inverted to give more accurate estimate to the petrophysical parameters in a highly overdetermined inverse problem. The suggested interval inversion approach allows the determination of the fractional volumes of rock constituents with their estimation errors in a joint inversion procedure. As part of the inversion process, the forward problem is improved by using kerogen and pyrite effects corrected probe response functions. Synthetic modeling tests are made to detect the noise sensitivity and outlier resistance of the proposed inversion algorithm, while a float-encoded genetic algorithm variant of the interval inversion method is applied to invert real data measured in an organic-rich shale reservoir in Alaska, USA. The feasibility is demonstrated by a well agreement between the inversion derived TOC values and those of measured on core samples. The interval inversion method not only works reliably in the presented shale gas formations, but it can be extended to evaluating other types of unconventional reservoirs.

Series Expansion-Based Genetic Inversion of Wireline Logging Data

An evolutionary approach is applied to solve the nonlinear well logging inverse problem. In the framework of the proposed interval inversion method, nuclear, sonic, and laterolog resistivity data measured at an arbitrary depth interval are jointly inverted, where the depth variation of porosity, water saturation, and shale volume is expanded into series using Legendre polynomials as basis functions. In the interval inversion procedure, the series expansion coefficients are estimated by using an adaptive float-encoded genetic algorithm. Since the solution of the inverse problem using traditional linear optimization tools highly depends on the selection of the initial model, a heuristic search is necessary to reduce the initial model dependence of the interval inversion procedure. The genetic inversion strategy used in interval inversion seeks the global extreme of the objective function and provides an estimate of the vertical distribution of petrophysical parameters, even starting the inversion procedure from extremely high distances from the optimum. For a faster computational process, after a couple of thousand generations, the genetic algorithm is replaced by some linear optimization steps. The added advantage of using the Marquardt algorithm is the possibility to characterize the accuracy of the series expansion coefficients and derived petrophysical properties. A Hungarian oil field example demonstrates the feasibility and stability of the improved interval inversion method. As a significance, the genetic inversion method does not require prior knowledge or strong restrictions on the values of petrophysical properties and gives highly reliable estimation results practically independent of the initial model and core information.

Interval inversion approach for an improved interpretation of well logs

The quality analysis of well-logging inversion results has always been an important part of formation evaluation. The precise calculation of hydrocarbon reserves requires the most accurate possible estimation of porosity, water saturation, and shale and rock-matrix volumes. The local inversion method conventionally used to predict the above model parameters depth by depth represents a marginally overdetermined inverse problem, which is rather sensitive to the uncertainty of observed data and limited in estimation accuracy. To reduce the harmful effect of data noise on the estimated model, we have suggested the interval inversion method, in which an increase of the overdetermination ratio allows a more accurate solution of the well-logging inverse problem. The interval inversion method inverts the data set of a longer depth interval to predict the vertical distributions of petrophysical parameters in a joint inversion procedure. In formulating the forward problem, we have extended the validity of probe response functions to a greater depth interval assuming the petrophysical parameters are depth dependent, and then we expanded the model parameters into a series using the Legendre polynomials as basis functions for modeling inhomogeneous formations. We solved the inverse problem for a much smaller number of expansion coefficients than data to derive the petrophysical parameters in a stable overdetermined inversion procedure. The added advantage of the interval inversion method is that the layer thicknesses and suitably chosen zone parameters can be estimated automatically by the inversion procedure to refine the results of inverse and forward modeling. We have defined depth-dependent model covariance and correlation matrices to compare the quality of the local and interval inversion results. A detailed study using well logs measured from a Hungarian gas-bearing unconsolidated formation revealed that the greatly overdetermined interval inversion procedure can be effectively used in reducing the estimation errors in shaly sand formations, which may refine significantly the results of reserve calculation.

Cluster Analysis Assisted Float-Encoded Genetic Algorithm for a More Automated Characterization of Hydrocarbon Reservoirs

A genetic algorithm-based joint inversion method is presented for evaluating hydrocarbon-bearing geological formations. Conventional inversion procedures routinely used in the oil industry perform the inversion processing of borehole geophysical data locally. As having barely more types of data than unknowns in a depth, a set of marginally over-determined inverse problems has to be solved along a borehole, which is a rather noise sensitive procedure. For the reduction of noise effect, the amount of overdetermination must be increased. To fulfill this requirement, we suggest the use of our interval inversion method, which inverts simultaneously all data from a greater depth interval to estimate petrophysical parameters of reservoirs to the same interval. A series expansion based discretization scheme ensures much more data against unknowns that significantly reduces the estimation error of model parameters. The knowledge of reservoir boundaries is also required for reserve calculation. Well logs contain information about layer-thicknesses, but they cannot be extracted by the local inversion approach. We showed earlier that the depth coordinates of layerboundaries can be determined within the interval inversion procedure. The weakness of method is that the output of inversion is highly influenced by arbitrary assumptions made for layer-thicknesses when creating a starting model (i.e. number of layers, search domain of thicknesses). In this study, we apply an automated procedure for the determination of rock interfaces. We perform multidimensional hierarchical cluster analysis on well-logging data before inversion that separates the measuring points of different layers on a lithological basis. As a result, the vertical distribution of clusters furnishes the coordinates of layer-boundaries, which are then used as initial model parameters for the interval inversion procedure. The improved inversion method gives a fast, automatic and objective estimation to layer-boundaries and petrophysical parameters, which is demonstrated by a hydrocarbon field example.

Interval inversion of borehole data for petrophysical characterization of complex reservoirs

Wireline logging surveys are routinely used for the reconnaissance and quantitative characterization of multi-mineral hydrocarbon structures. The interpretation of well-logging data, however, is quite a challenging task, because the conventionally used local inversion procedure becomes either an underdetermined or a slightly overdetermined problem that may result in poor parameter estimation. In order to determine the petrophysical model composed of several parameters, such as specific volumes of matrix components, water saturation, primary and secondary porosity and numerous zone-parameters, in a more reliable way a new inversion methodology is required. We suggest a joint inversion technique for the estimation of model parameters of multi-mineral rocks that inverts data acquired from a larger depth interval (hydrocarbon zone). The inverse problem is formulated assuming homogeneous intervals within the zone to get a highly overdetermined inversion procedure. The interval inversion method has been applied to shaly sandy hydrocarbon reservoirs, in this study, that is used for the estimation of petrophysical parameters of complex reservoirs. Numerical results with synthetic and field data demonstrate the feasibility of the inversion method in investigating carbonate and metamorphic structures.

Interval inversion of well-logging data for automatic determination of formation boundaries by using a float-encoded genetic algorithm

In the paper a real-valued genetic algorithm is presented for solving the non-linear well-logging inverse problem. The conventional way followed in the interpretation of well-logging data is the formulation of the inverse problem in each measuring point separately. Since barely less number of unknowns than data are estimated to one point, a set of marginally overdetermined inverse problems have to be solved, which sets a limit to the accuracy of estimation. Describing the petrophysical (reservoir) parameters in the form of series expansion, we extend the validity of probe response functions used in local forward modeling to a greater depth interval (hydrocarbon zone) and formulate the so-called interval inversion method, which inverts all data of the measured interval jointly. Assuming an interval-wise homogeneous petrophysical parameter distribution, significantly smaller number of unknowns than data have to be determined. The highly overdetermined inverse problem results in accurate and reliable estimation of petrophysical parameters given for the whole interval instead of separate measuring points. For measuring the storage capacity of the reservoir, the formation thickness is also required to be estimated. As a new feature in well logging inversion methodology, the boundary coordinates of formations are treated as new inversion unknowns and determined by the interval inversion method automatically. Instead of using traditional linear inversion techniques, global optimization is used to avoid problems of linearization related to the determination of formation thicknesses. In the paper, synthetic and field examples are shown to demonstrate the feasibility of the interval inversion method.

2D inversion of borehole logging data for simultaneous determination of rock interfaces and petrophysical parameters

In the paper a 2D joint inversion method is presented, which is applicable for the simultaneous determination of layer thickness variation and petrophysical parameters by processing well-logging data acquired in several boreholes along the profile. The so-called interval inversion method is tested on noisy synthetic data sets generated on hydrocarbon-bearing reservoir models. Numerical experiments are performed to study the convergence and stability of the inversion procedure. Data and model misfit, function distance related to layer thickness fitting are measured as well as estimation errors and correlation coefficients are computed to check the accuracy and reliability of inversion results. It is shown that the actual inversion procedure is stable and highly accurate, which arises from the great over-determination feature of the inverse problem. Even a case study is attached to the paper in which interval inversion procedure is applied for processing of multi-borehole logging data acquired in Hungarian hydrocarbon exploratory wells in order to determine petrophysical parameters and lateral changes of layer thicknesses.

Combined global/linear inversion of well-logging data in layer-wise homogeneous and inhomogeneous media

In the paper a combined inversion algorithm solving the nonlinear geophysical well-logging inverse problem is presented. We apply a successive combination of a float-encoded Genetic Algorithm as a global optimization method and the well-known linearized Marquardt algorithm forming a fast inversion procedure. The technique is able to decrease the CPU run time at least one order of magnitude compared to the Genetic Algorithm and gives the parameter estimation errors having a few linearized optimization steps at the end of the iteration process. We use depth-dependent tool response equations to invert all the data of a greater depth-interval jointly in order to determine petrophysical parameters of homogeneous or inhomogeneous layers in one inversion procedure. The so-called interval inversion method gives more accurate and reliable estimation for the petrophysical model parameters than the conventional point by point inversion methods. It also enables us to determine the layer-thicknesses that can not be extracted from the data set by means of conventional inversion techniques. We test the combined interval inversion method on synthetic data, and employ it to the interpretation of well logs measured in a Hungarian hydrocarbon exploratory borehole.