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

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Armand Abordán ◽  
Norbert Péter Szabó
Keyword(s):  
Inverse Problem ◽  
Factor Analysis ◽  
Water Saturation ◽  
Inversion Method ◽  
Model Parameters ◽  
Depth Range ◽  
Petrophysical Parameters ◽  
Shale Volume ◽  
Interval Inversion ◽  
The Impact

AbstractThis 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.

scholarly journals Interval inversion approach for an improved interpretation of well logs

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. D155-D167 ◽  
Author(s):  
Mihály Dobróka ◽  
Norbert Péter Szabó ◽  
József Tóth ◽  
Péter Vass
Keyword(s):  
Inverse Problem ◽  
Well Logging ◽  
Well Logs ◽  
Depth Interval ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Petrophysical Parameters ◽  
Inversion Procedure ◽  
Interval Inversion

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.

Joint seismic and petrophysical nonlinear inversion with Gaussian mixture-based adaptive regularization

Geophysics ◽  
2021 ◽  
pp. 1-57
Author(s):  
Qiang Guo ◽  
Jing Ba ◽  
Li-Yun Fu ◽  
Cong Luo
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Simulated Annealing Algorithm ◽  
Gaussian Mixture ◽  
Forward Model ◽  
Inversion Method ◽  
Model Parameters ◽  
Adaptive Regularization ◽  
Petrophysical Parameters ◽  
Highly Nonlinear

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating petrophysical properties of rocks to observed seismic data is highly nonlinear, and solving the relevant inverse problem is a challenging task. We present a novel inversion method for jointly estimating elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill-conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we introduce a regularization term based on the prior Gaussian mixture model under Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared to the sequential inversion and non-adaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.

Microseismic moment-tensor inversion and sensitivity analysis in VTI media

Geophysics ◽  
2020 ◽  
pp. 1-74
Author(s):  
Han Li ◽  
Xu Chang ◽  
Xiao-Bi Xie ◽  
Yibo Wang
Keyword(s):  
Hydraulic Fracturing ◽  
Focal Mechanism ◽  
Moment Tensor ◽  
Staggered Grid ◽  
Inversion Method ◽  
Model Parameters ◽  
Seismic Moment Tensor ◽  
Tensor Model ◽  
Double Couple ◽  
The Impact

Through the study of microseismic focal mechanisms, information such as fracture orientation, event magnitude, and in-situ stress status can be quantitatively obtained, thus, providing a reliable basis for unconventional oil and gas exploration. Most source inversion methods assume that the medium is isotropic. However, hydraulic fracturing is usually conducted in sedimentary rocks, which often exhibit strong anisotropy. Neglecting this anisotropy may cause errors in focal mechanism inversion results. We propose a microseismic focal mechanism inversion method that considers velocity anisotropy in a vertically transverse isotropic (VTI) medium. To generate synthetic data, we adopt the moment-tensor model to represent microearthquake sources. We use a staggered-grid finite-difference (SGFD) method to calculate synthetic seismograms in anisotropic media. We perform seismic moment-tensor (SMT) inversion with only P-waves by matching synthetic and observed waveforms. Both synthetic and field datasets are used to test the inversion method. For the field dataset, we investigate the inversion stability using randomly selected partial datasets in the calculation. We pay special attention to analyze the sensitivity of the inversion. We test and evaluate the impact of noise in the data and errors in the model parameters ( VP0, ε, and δ) on the SMT inversion using synthetic datasets. The results indicate that for a surface acquisition system, the proposed method can tolerate moderate noise in the data, and deviations in the anisotropy parameters can cause errors in the SMT inversion, especially for dip-slip events and the inverted percentages of non-double-couple components. According to our study, including anisotropy in the model is important to obtain reliable non-double-couple components of moment tensors for hydraulic fracturing induced microearthquakes.

scholarly journals Determination of Petrophysical Parameters of Reservoir Rock with a Special Look to Shale Effect (Case Study: One of the Gas Fields in Southern Iran)

2021 ◽  
Vol 5 (2) ◽  
pp. 1-10
Author(s):  
Taheri K
Keyword(s):  
Water Saturation ◽  
Accurate Determination ◽  
Reservoir Rock ◽  
Petrophysical Properties ◽  
Gas Reservoir ◽  
Reservoir Water ◽  
Petrophysical Parameters ◽  
Hydrocarbon Reservoir ◽  
Shale Volume

Determination of petrophysical parameters is necessary for modeling hydrocarbon reservoir rock. The petrophysical properties of rocks influenced mainly by the presence of clay in sedimentary environments. Accurate determination of reservoir quality and other petrophysical parameters such as porosity, type, and distribution of reservoir fluid, and lithology are based on evaluation and determination of shale volume. If the effect of shale volume in the formation not calculated and considered, it will have an apparent impact on the results of calculating the porosity and saturation of the reservoir water. This study performed due to the importance of shale in petrophysical calculations of this gas reservoir. The shale volume and its effect on determining the petrophysical properties and ignoring it studied in gas well P19. This evaluation was performed in Formations A and B at depths of 3363.77 to 3738.98 m with a thickness of 375 m using a probabilistic calculation method. The results of evaluations of this well without considering shale showed that the total porosity was 0.1 percent, the complete water saturation was 31 percent, and the active water saturation was 29 percent, which led to a 1 percent increase in effective porosity. The difference between water saturation values in Archie and Indonesia methods and 3.3 percent shale volume in the zones show that despite the low shale volume in Formations A and B, its effect on petrophysical parameters has been significant. The results showed that if the shale effect not seen in the evaluation of this gas reservoir, it can lead to significant errors in calculations and correct determination of petrophysical parameters.

scholarly journals Fast probabilistic petrophysical mapping of reservoirs from 3D seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. O1-O19 ◽  
Author(s):  
Mohammad S. Shahraeeni ◽  
Andrew Curtis ◽  
Gabriel Chao
Keyword(s):  
Seismic Data ◽  
Water Saturation ◽  
Random Noise ◽  
Clay Content ◽  
Inversion Method ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Desktop Computer ◽  
Data Set ◽  
Mixture Density

A fast probabilistic inversion method for 3D petrophysical property prediction from inverted prestack seismic data has been developed and tested on a real data set. The inversion objective is to estimate the joint probability density function (PDF) of model vectors consisting of porosity, clay content, and water saturation components at each point in the reservoir, from data vectors with compressional- and shear-wave-impedance components that are obtained from the inversion of seismic data. The proposed inversion method is based on mixture density network (MDN), which is trained by a given set of training samples, and provides an estimate of the joint posterior PDF’s of the model parameters for any given data point. This method is much more time and memory efficient than conventional nonlinear inversion methods. The training data set is constructed using nonlinear petrophysical forward relations and includes different sources of uncertainty in the inverse problem such as variations in effective pressure, bulk modulus and density of hydrocarbon, and random noise in recorded data. Results showed that the standard deviations of all model parameters were reduced after inversion, which shows that the inversion process provides information about all parameters. The reduction of uncertainty in water saturation was smaller than that for porosity or clay content; nevertheless the maximum of the a posteriori (MAP) of model PDF clearly showed the boundary between brine saturated and oil saturated rocks at wellbores. The MAP estimates of different model parameters show the lateral and vertical continuity of these boundaries. Errors in the MAP estimate of different model parameters can be reduced using more accurate petrophysical forward relations. This fast, probabilistic, nonlinear inversion method can be applied to invert large seismic cubes for petrophysical parameters on a standard desktop computer.

scholarly journals Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3082
Author(s):  
Rafał Brociek ◽  
Agata Wajda ◽  
Damian Słota
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Model Parameters ◽  
Two Dimensional ◽  
Ant Colony Optimization Algorithm ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
The Impact

The article presents a method for solving the inverse problem of a two-dimensional anomalous diffusion equation with a Riemann–Liouville fractional-order derivative. In the first part of the present study, the authors present a numerical solution of the direct problem. For this purpose, a differential scheme was developed based on the alternating direction implicit method. The presented method was accompanied by examples illustrating its accuracy. The second part of the study concerned the inverse problem of recreating the model parameters, including the orders of the fractional derivative, in the anomalous diffusion equation. Equations of this type can be used to describe, inter alia, the heat conductivity in porous materials. The ant colony optimization algorithm was used to solve this problem. The authors investigated the impact of the distribution of measurement points, the use of different mesh sizes, and the input data errors on the obtained results.

scholarly journals Factorial invariance of the Adult State Hope Scale

2014 ◽  
Vol 40 (1) ◽  
Author(s):  
Petrus Nel ◽  
Adré Boshoff
Keyword(s):  
Factor Analysis ◽  
Positive Psychology ◽  
Exploratory Factor Analysis ◽  
Quantitative Research ◽  
Factorial Invariance ◽  
Measuring Instruments ◽  
Model Parameters ◽  
Cross Sectional ◽  
And Gender ◽  
The Impact

Orientation: Given the interest in the impact of positive psychology on employees, it is imperative to use reliable and valid instruments to operationalise positive-psychology constructs. One such construct is hope.Research purpose: The purpose of the study was to assess the degree of factorial invariance across race and gender by using a sample of aspiring chartered accountants.Motivation for the study: Previous research on the hope construct and associated measuring instruments have been conducted, using homogenous samples from Westernised cultures. Researchers need to be careful to assume that hope looks and behaves in exactly the same manner across cultures and groups.Research approach, design and method: A cross-sectional quantitative research design was used. A sample of 295 aspiring chartered accountants participated in the study. Exploratory factor analysis was used to determine the degree of factor similarity across groups, utilising Tucker’s coefficient of congruence. To supplement the exploratory factor analysis, a series of increasingly restrictive multi-group analyses were conducted to test the invariance of model parameters across the groups.Main findings: No significant differences were found in the factor patterns for the agency and pathways factors for (1) the white and designated groups and (2) females and males.Practical/managerial implications: Evidence related to factorial invariance was found. This should inform researchers and practitioners that both pathways and agency look similar across racial and gender groups.Contribution/value-add: Researchers are urged to use various statistical techniques, in combination, to determine the degree of factorial invariance across groups.

scholarly journals Log based petrophysical analysis of mio-pliocene sandstone reservoir encountered in well Rashidpur 4 of Bengal Basin in Bangladesh

2016 ◽  
Vol 51 (1) ◽  
pp. 23-34
Author(s):  
M Farhaduzzaman ◽  
MA Islam ◽  
WH Abdullah ◽  
J Dutta
Keyword(s):  
Gamma Ray ◽  
Water Saturation ◽  
Xrd Analysis ◽  
Bengal Basin ◽  
Petrophysical Parameters ◽  
Shale Volume ◽  
Quantitative Measurements ◽  
Volume Porosity ◽  
Bulk Volume ◽  
Hydrocarbon Saturation

Rashidpur is located in the northeastern part of Bangladesh which is surrounded on three sides by India and on a small portion by Myanmar. Gamma-ray, spontaneous potential, density, neutron, resistivity, caliper, temperature and sonic logs are used to analyze petrophysical parameters of the well Rashidpur 4, Bangladesh. Quantitative measurements of different factors such as shale volume, porosity, permeability, water saturation, hydrocarbon saturation and bulk volume of water are carried out using well logs. Petrographic and XRD results based on several core samples are also compared with log-derived parameters. Twenty permeable zones are identified whereby four are hydrocarbon bearing in the studied Mio-Pliocene reservoir sandstones. Measured shale volume ranges from 11% to 38% and porosity is 19% to 28%. However, log-derived porosity is slightly higher than the thin section porosity. Water saturation of the interested zones varies from 14% to 38%, 13% to 39% and 16% to 41% measured from Schlumberger, Fertl and Simandoux formula respectively. Conversely, hydrocarbon saturation of the examined hydrocarbon zones ranges from 62% to 86%, 61% to 83% and 59% to 84% respectively. In the analyzed zones, the permeability values are calculated as 28-305 mD. Good to very good quality hydrocarbon reservoirs are appraised for the studied four zones based on the petrophysical parameters, petrographic observation and XRD analysis. Among these, Zone 4 is the best quality reservoir for hydrocarbon.Bangladesh J. Sci. Ind. Res. 51(1), 23-34, 2016

scholarly journals Geophysical and hydrocarbon prospect evaluation of Nukhul Formation at Rabeh East oil field, Southern Gulf of Suez Basin, Egypt

2021 ◽  
Vol 11 (7) ◽  
pp. 2877-2890
Author(s):  
Mohammad Abdelfattah Sarhan
Keyword(s):  
Water Saturation ◽  
Total Porosity ◽  
Effective Porosity ◽  
Oil Field ◽  
Normal Faults ◽  
Gulf Of Suez ◽  
Petrophysical Parameters ◽  
Shale Volume ◽  
Bulk Volume ◽  
Zone Ii

AbstractNukhul Formation is one of the primary oil reservoirs in the Gulf of Suez Basin. Rabeh East is an oil producer field located at the southern border of the Gulf of Suez. The present work deals with the geophysical investigation of Nukhul Formation in Rabeh East field using seismic lines and well log data of four wells, namely RE-8, RE-22, RE-25 and Nageh-1. The interpreted seismic profiles display that the RE-8 Well is the only well drilled within the up-thrown side of a significant horst fault block bounded by two normal faults. However, the other wells penetrated the downthrown side. The qualitative interpretation of the well logging data for RE-8 Well delineated two intervals have good petrophysical parameters and ability to store and produce oil. These zones locate between depths 5411.5 and 5424 ft (zone I) and between 5451 and 5459.5 ft (zone II). The calculated petrophysical parameters for zone I display water saturation (22–44%), shale volume (10–23%), total porosity (18–23%), effective porosity (12–20%) and bulk volume of water (0.04–0.06). Zone II exhibits water saturation (13–45%), shale volume (10–30%), total porosity (18–24%), effective porosity (11–20%) and bulk volume of water (0.03–0.05). This analysis reflects excellent petrophysical characteristics for the sandstones of Nukhul Formation in Rabeh East oil field for producing oil if the wells drilled in a suitable structural closure.

scholarly journals Petrophysical Reservoir Characterization of Habiganj Gas Field, Surma Basin, Bangladesh

2021 ◽  
Vol 10 (1) ◽  
pp. 1-10
Author(s):  
Shamiha Shafinaz Shreya ◽  
Md Anwar Hossain Bhuiyan ◽  
Shakhawat Hossain ◽  
Tania Sultana
Keyword(s):  
Reservoir Characterization ◽  
Water Saturation ◽  
Volumetric Analysis ◽  
Reservoir Quality ◽  
Gas Field ◽  
Hydrocarbon Production ◽  
Petrophysical Parameters ◽  
Shale Volume ◽  
Lower Reservoir ◽  
Surma Basin

The previous studies on the petrophysical and volumetric analysis of Habiganj gas field were based on limited well data. As the accuracy of volumetric analysis relies greatly on petrophysical parameters, it is important to estimate them accurately. In this study we analyzed all eleven wells drilled in the Habiganj field to determine the petrophysical parameters. Analysis of the well logs revealed two distinct reservoir zones in this field termed as upper reservoir zone and lower reservoir zone. Stratigraphically, these two reservoir zones are in the Bokabil and Bhuban Formation of Surma Group. Petrophysical analysis shows significant differences between the two zones in terms of petrophysical parameters. Porosity in the upper reservoir zone ranges from 12% to 36%, with an average of 28%. This zone is highly permeable, as indicated by the average permeability of 500 mili Darcy (mD). The average water saturation in this zone is around 18% suggesting high gas saturation. The lower reservoir zone has an average porosity, permeability, and water saturation of 12%, 60mD, and 43%, respectively, indicating poor reservoir quality. An analysis of log motifs indicates that the upper reservoir zone is composed of stacked sands of blocky pattern. The sands in this interval are clean, as indicated by the lower shale volume of 12-15%. The average thickness of this zone is 230m, and the presence of this zone in all the drilled wells suggests high lateral continuity. The lower reservoir zone consists of sand bodies of serrated pattern. The sands have high shale volume and are laterally discontinuous. Overall, the upper reservoir zone has superior petrophysical properties to the lower reservoir zone. Although the reservoir quality of the lower reservoir zone is poorer than that of the upper zone, this zone can be considered as the secondary target for hydrocarbon production. Petrophysical parameters of this study were estimated from all the eleven wells drilled in this field; hence the values are more accurate. The reported values of the petrophysical parameters in this study are recommended to use to re-estimate the reserves in Habiganj field. The Dhaka University Journal of Earth and Environmental Sciences, Vol. 10(1), 2021, P 1-10

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