History Matching of Channelized Reservoirs With Vector-Based Level-Set Parameterization

SPE Journal ◽  
2014 ◽  
Vol 19 (03) ◽  
pp. 514-529 ◽  
Author(s):  
Jing Ping ◽  
Dongxiao Zhang
Keyword(s):  
Level Set ◽  
History Matching ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Matching Problem ◽  
Level Set Function ◽  
Level Function ◽  
Set Up ◽  
Non Gaussian ◽  
Channelized Reservoirs

Summary For channelized reservoirs with unknown channel distributions, identifying the continuous and sinuous features of channel distributions is crucial for determining their production behaviors. However, traditional history-matching methods are not appropriate because the pixel-based rock-property fields are usually highly non-Gaussian. In this work, a vector-based level-set parameterization technique for channelized reservoirs is presented. We also propose a combination of this parameterization method and a frequently used history-matching approach, the ensemble Kalman filter (EnKF). To properly represent the continuity and sinuosity of its embedded features, the channelized reservoir is parameterized with a vector that consists of level-set function, real radius, and virtual radius on a representing node system. The level-function value indicates the existence of the particular facies; the real radius of a circle in two dimensions or a sphere in three dimensions signifies the size of the facies; and the virtual radius is used to ensure the continuity of the channelized facies. The 2D and 3D examples of channelized reservoirs are set up to demonstrate the capability of the proposed method. It is found that this method is effective to deal with the history-matching problem of channelized reservoirs.

scholarly journals Integration of an Iterative Update of Sparse Geologic Dictionaries with ES-MDA for History Matching of Channelized Reservoirs

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Sungil Kim ◽  
Baehyun Min ◽  
Kyungbook Lee ◽  
Hoonyoung Jeong
Keyword(s):  
History Matching ◽  
Gas Reservoirs ◽  
Dynamic Data ◽  
Multiple Data ◽  
Ensemble Smoother ◽  
Water Rate ◽  
Non Gaussian ◽  
Value Decomposition ◽  
Channelized Reservoirs ◽  
Channel Properties

This study couples an iterative sparse coding in a transformed space with an ensemble smoother with multiple data assimilation (ES-MDA) for providing a set of geologically plausible models that preserve the non-Gaussian distribution of lithofacies in a channelized reservoir. Discrete cosine transform (DCT) of sand-shale facies is followed by the repetition of K-singular value decomposition (K-SVD) in order to construct sparse geologic dictionaries that archive geologic features of the channelized reservoir such as pattern and continuity. Integration of ES-MDA, DCT, and K-SVD is conducted in a complementary way as the initially static dictionaries are updated with dynamic data in each assimilation of ES-MDA. This update of dictionaries allows the coupled algorithm to yield an ensemble well conditioned to static and dynamic data at affordable computational costs. Applications of the proposed algorithm to history matching of two channelized gas reservoirs show that the hybridization of DCT and iterative K-SVD enhances the matching performance of gas rate, water rate, bottomhole pressure, and channel properties with geological plausibility.

scholarly journals 3D Modelling of Doped and Multi-Materials during Sintering of a Granular Packing

2013 ◽  
Vol 554-557 ◽  
pp. 724-731
Author(s):  
Howatchinou Tossoukpe ◽  
François Valdivieso ◽  
Julien Bruchon ◽  
Sylvain Drapier
Keyword(s):  
Level Set ◽  
Adaptive Mesh ◽  
Three Dimensions ◽  
Granular Packing ◽  
Level Set Function ◽  
Chemical Potentials ◽  
Molecular Flux ◽  
Grain Surface ◽  
Set Function ◽  
Level Set Framework

This paper presents a level set framework for the modelling of doping effect during surfacediffusion phenomena in a granular packing. The molecular flux of the doped compound is related tothe chemical potentials of all the diffusion species. The evolution of the grain compact is simulatedin three dimensions, based on the resulting kinetic law relating the surface diffusion velocity to thethermodynamic driving force. An anisotropic adaptive mesh, based on the level set function propertiesis used to refine the mesh in the surroundings of the grain surface. The simulations have been perfomedby using parallel computing strategy.

Thermodynamics and Densification Kinetics in Solid-state Sintering of Ceramics

1999 ◽  
Vol 14 (4) ◽  
pp. 1398-1408 ◽  
Author(s):  
J. L. Shi
Keyword(s):  
Pore Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Rate Equations ◽  
Densification Rate ◽  
Interface Tension ◽  
Spherical Pore ◽  
Pore Model ◽  
Set Up ◽  
The Stability

Based on the stability analysis of the closed pores in two dimensions which was determined mathematically with their particle coordination number and dihedral angle, the stability of those in three dimensions was determined with a spherical pore model. The model is set up by first excluding the effect of interface tension, so the pore was supposed to be spherical, and then the tensile stress arisen from the interface tension was supposed to act on this hypothesized spherical pore. On the basis of the spherical pore model, microstructure models based on pores, not grains, for the real powder compacts were first established. Densification kinetics were then determined from the models by the densification rate equations, which were derived by relating density to pore size to grain size ratio, for the intermediate and final stages of sintering. The criteria for pore shrinkage were discussed quantitatively. The derived equations can be used to simulate the relation between densification rate and density during heating with a constant rate and for the explanation of the effects of pore size distribution, agglomerates, and green density on sintering.

Enhanced History Matching of Gas Reservoirs With an Aquifer Using the Combination of Discrete Cosine Transform and Level Set Method in ES-MDA

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Sungil Kim ◽  
Hyungsik Jung ◽  
Jonggeun Choe
Keyword(s):  
Discrete Cosine Transform ◽  
Level Set Method ◽  
Level Set ◽  
Measurement Errors ◽  
History Matching ◽  
Reservoir Characterization ◽  
Gas Reservoirs ◽  
Cosine Transform ◽  
Ensemble Smoother ◽  
Non Gaussian

Reservoir characterization is a process to make dependable reservoir models using available reservoir information. There are promising ensemble-based methods such as ensemble Kalman filter (EnKF), ensemble smoother (ES), and ensemble smoother with multiple data assimilation (ES-MDA). ES-MDA is an iterative version of ES with inflated covariance matrix of measurement errors. It provides efficient and consistent global updates compared to EnKF and ES. Ensemble-based method might not work properly for channel reservoirs because its parameters are highly non-Gaussian. Thus, various parameterization methods are suggested in previous studies to handle nonlinear and non-Gaussian parameters. Discrete cosine transform (DCT) can figure out essential channel information, whereas level set method (LSM) has advantages on detailed channel border analysis in grid scale transforming parameters into Gaussianity. However, DCT and LSM have weaknesses when they are applied separately on channel reservoirs. Therefore, we propose a properly designed combination algorithm using DCT and LSM in ES-MDA. When DCT and LSM agree with each other on facies update results, a grid has relevant facies naturally. If not, facies is assigned depending on the average facies probability map from DCT and LSM. By doing so, they work in supplementary way preventing from wrong or biased decision on facies. Consequently, the proposed method presents not only stable channel properties such as connectivity and continuity but also similar pattern with the true. It also gives trustworthy future predictions of gas and water productions due to well-matched facies distribution according to the reference.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Formulating the history matching problem with consistent error statistics

2021 ◽  
Author(s):  
Geir Evensen
Keyword(s):  
Simulation Model ◽  
Measurement Errors ◽  
History Matching ◽  
Critical Role ◽  
Bayes Theorem ◽  
Conditional Probability Density ◽  
Model Parameters ◽  
Rate Data ◽  
Matching Problem ◽  
Reservoir Prediction

AbstractIt is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, the conditional probability density function (pdf) of the uncertain model parameters is proportional to the prior pdf of the model parameters, multiplied by the likelihood of the measurements. The static model parameters are random variables characterizing the reservoir model while the observations include, e.g., historical rates of oil, gas, and water produced from the wells. The reservoir prediction model is assumed perfect, and there are no errors besides those in the static parameters. However, this formulation is flawed. The historical rate data only approximately represent the real production of the reservoir and contain errors. History-matching methods usually take these errors into account in the conditioning but neglect them when forcing the simulation model by the observed rates during the historical integration. Thus, the model prediction depends on some of the same data used in the conditioning. The paper presents a formulation of Bayes’ theorem that considers the data dependency of the simulation model. In the new formulation, one must update both the poorly known model parameters and the rate-data errors. The result is an improved posterior ensemble of prediction models that better cover the observations with more substantial and realistic uncertainty. The implementation accounts correctly for correlated measurement errors and demonstrates the critical role of these correlations in reducing the update’s magnitude. The paper also shows the consistency of the subspace inversion scheme by Evensen (Ocean Dyn. 54, 539–560 2004) in the case with correlated measurement errors and demonstrates its accuracy when using a “larger” ensemble of perturbations to represent the measurement error covariance matrix.

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