Efficient Conditioning of 3D Fine-Scale Reservoir Model To Multiphase Production Data Using Streamline-Based Coarse-Scale Inversion and Geostatistical Downscaling

1999 ◽  
Author(s):  
Thomas T. Tran ◽  
Xian-Huan Wen ◽  
Ronald A. Behrens
Keyword(s):  
Production Data ◽  
Fine Scale ◽  
Reservoir Model ◽  
Coarse Scale

Multiscale Data Integration Using Markov Random Fields

2002 ◽  
Vol 5 (01) ◽  
pp. 68-78 ◽  
Author(s):  
Sang Heon Lee ◽  
Adel Malallah ◽  
Akhil Datta-Gupta ◽  
David Higdon
Keyword(s):  
Data Integration ◽  
Posterior Distribution ◽  
Random Fields ◽  
Spatial Modeling ◽  
Data Sources ◽  
Production Data ◽  
Fine Scale ◽  
Reservoir Model ◽  
Coarse Scale ◽  
Well Data

Summary We propose a hierarchical approach to spatial modeling based on Markov Random Fields (MRF) and multiresolution algorithms in image analysis. Unlike their geostatistical counterparts, which simultaneously specify distributions across the entire field, MRFs are based on a collection of full conditional distributions that rely on the local neighborhoods of each element. This critical focus on local specification provides several advantages:MRFs are computationally tractable and are ideally suited to simulation based computation, such as Markov Chain Monte Carlo (MCMC) methods, andmodel extensions to account for nonstationarity, discontinuity, and varying spatial properties at various scales of resolution are easily accessible in the MRF framework. Our proposed method is computationally efficient and well suited to reconstruct fine-scale spatial fields from coarser, multiscale samples (based on seismic and production data) and sparse fine-scale conditioning data (e.g., well data). It is easy to implement, and it can account for the complex, nonlinear interactions between different scales, as well as the precision of the data at various scales, in a consistent fashion. We illustrate our method with a variety of examples that demonstrate the power and versatility of the proposed approach. Finally, a comparison with Sequential Gaussian Simulation with Block Kriging (SGSBK) indicates similar performance with less restrictive assumptions. Introduction A persistent problem in petroleum reservoir characterization is to build a model for flow simulations based on incomplete information. Because of the limited spatial information, any conceptual reservoir model used to describe heterogeneities will, necessarily, have large uncertainty. Such uncertainties can be significantly reduced by integrating multiple data sources into the reservoir model.1 In general, we have hard data, such as well logs and cores, and soft data, such as seismic traces, production history, conceptual depositional models, and regional geological analyses. Integrating information from this wide variety of sources into the reservoir model is not a trivial task. This is because different data sources scan different length scales of heterogeneity and can have different degrees of precision.2 Reconciling multiscale data for spatial modeling of reservoir properties is important because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as seismic and production data. A hierarchical model is particularly well suited to address the multiscaled nature of spatial fields, match available data at various levels of resolution, and account for uncertainties inherent in the information.1–3 Several methods to combine multiscale data have been introduced in the literature, with a primary focus on integrating seismic and well data.3–9 These include conventional techniques such as cokriging and its variations,3–6 SGSBK,7 and Bayesian updating of point kriging.8,9 Most kriging-based methods are restricted to multi-Gaussian and stationary random fields.3–9 Therefore, they require data transformation and variogram construction. In practice, variogram modeling with a limited data set can be difficult and strongly user-dependent. Improper variograms can lead to errors and inaccuracies in the estimation. Thus, one might also need to consider the uncertainty in variogram models during estimation. 10 However, conventional geostatistical methods do not provide an effective framework to account for the uncertainty of the variogram. Furthermore, most of the multiscale integration algorithms assume a linear relationship between the scales. The objective of this paper is to introduce a novel multiscale data-integration technique that provides a flexible and sound mathematical framework to overcome some of the limitations of conventional geostatistical techniques. Our approach is based on multiscale MRFs11–14 that can effectively integrate multiple data sources into high-resolution reservoir models for reliable reservoir forecasting. This proposed approach is also ideally suited to simulation- based computations, such as MCMC.15,16 Methodology Our problem of interest is to generate fine-scale random fields based on sparse fine-scale samples and coarse-scale data. Such situations arise when we have limited point measurements, such as well data, and coarse-scale information based on seismic and/or production data. Our proposed method is a Bayesian approach to spatial modeling based on MRF and multiresolution algorithms in image analysis. Broadly, the method consists of two major parts:construction of a posterior distribution for multiscale data integration using a hierarchical model andimplementing MCMC to explore the posterior distribution. Construction of a Posterior Distribution for Multiscale Data Integration. A multiresolution MRF provides an efficient framework to integrate different scales of data hierarchically, provided that the coarse-scale resolution is dependent on the next finescale resolution.11 In general, a hierarchical conditional model over scales 1,. . ., N (from fine to coarse) can be expressed in terms of the product of conditional distributions,Equation 1 where p(xn), n=1, . . ., N, are MRF models at each scale, and the terms p(xn|xn-1) express the statistical interactions between different scales. This approach links the various scales stochastically in a direct Bayesian hierarchical modeling framework (Fig. 1). Knowing the fine-scale field xn does not completely determine the field at a coarser scale xn+1, but depending on the extent of the dependence structure modeled and estimated, it influences the distribution at the coarser scales to a greater or lesser extent. This enables us to address multiscale problems accounting for the scale and precision of the data at various levels. For clarity of exposition, a hierarchical model for reconciling two different scales of data will be considered below.Equation 2 From this equation, the posterior distribution of the fine-scale random field indexed by 1 given a coarse-scale random field indexed by 2 can be derived as follows.

scholarly journals Spatial Downscaling of TRMM Precipitation Using Geostatistics and Fine Scale Environmental Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
No-Wook Park
Keyword(s):  
Environmental Variables ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Tropical Rainfall Measuring Mission ◽  
Predictive Performance ◽  
Environmental Modeling ◽  
Fine Scale ◽  
Coarse Scale ◽  
Uncertainty Measures ◽  
Trmm Precipitation

A geostatistical downscaling scheme is presented and can generate fine scale precipitation information from coarse scale Tropical Rainfall Measuring Mission (TRMM) data by incorporating auxiliary fine scale environmental variables. Within the geostatistical framework, the TRMM precipitation data are first decomposed into trend and residual components. Quantitative relationships between coarse scale TRMM data and environmental variables are then estimated via regression analysis and used to derive trend components at a fine scale. Next, the residual components, which are the differences between the trend components and the original TRMM data, are then downscaled at a target fine scale via area-to-point kriging. The trend and residual components are finally added to generate fine scale precipitation estimates. Stochastic simulation is also applied to the residual components in order to generate multiple alternative realizations and to compute uncertainty measures. From an experiment using a digital elevation model (DEM) and normalized difference vegetation index (NDVI), the geostatistical downscaling scheme generated the downscaling results that reflected detailed characteristics with better predictive performance, when compared with downscaling without the environmental variables. Multiple realizations and uncertainty measures from simulation also provided useful information for interpretations and further environmental modeling.

Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

2011 ◽  
Vol 9 (1) ◽  
pp. 180-204 ◽  
Author(s):  
Zhaoqin Huang ◽  
Jun Yao ◽  
Yajun Li ◽  
Chenchen Wang ◽  
Xinrui Lv
Keyword(s):  
Porous Media ◽  
Network Model ◽  
Darcy's Law ◽  
Permeability Tensor ◽  
Homogenization Theory ◽  
Fine Scale ◽  
Porous Rock ◽  
Coarse Scale ◽  
Equivalent Permeability ◽  
Discrete Fracture

AbstractA numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented. At first we proposed a new conceptual model, i.e., discrete fracture-vug network model, to model the realistic fluid flow in fractured vuggy porous medium on fine scale. This new model consists of three systems: rock matrix system, fractures system, and vugs system. The fractures and vugs are embedded in porous rock, and the isolated vugs could be connected via discrete fracture network. The flow in porous rock and fractures follows Darcy’s law, and the vugs system is free fluid region. Based on two-scale homogenization theory, we obtained an equivalent macroscopic Darcy’s law on coarse scale from fine-scale discrete fracture-vug network model. A finite element numerical formulation for homogenization equations is developed. The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks. The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.

Survival analysis at multiple scales for the modeling of track geometry deterioration

2017 ◽  
Vol 232 (3) ◽  
pp. 842-850 ◽  
Author(s):  
Negin Alemazkoor ◽  
Conrad J Ruppert ◽  
Hadi Meidani
Keyword(s):  
Survival Analysis ◽  
Multiple Scales ◽  
Fine Scale ◽  
Coarse Scale ◽  
Track Geometry ◽  
Time Period ◽  
Scale Models ◽  
Optimal Maintenance ◽  
Maintenance Decisions

Defects in track geometry have a notable impact on the safety of rail transportation. In order to make the optimal maintenance decisions to ensure the safety and efficiency of railroads, it is necessary to analyze the track geometry defects and develop reliable defect deterioration models. In general, standard deterioration models are typically developed for a segment of track. As a result, these coarse-scale deterioration models may fail to predict whether the isolated defects in a segment will exceed the safety limits after a given time period or not. In this paper, survival analysis is used to model the probability of exceeding the safety limits of the isolated defects. These fine-scale models are then used to calculate the probability of whether each segment of the track will require maintenance after a given time period. The model validation results show that the prediction quality of the coarse-scale segment-based models can be improved by exploiting information from the fine-scale defect-based deterioration models.

A MULTI-SCALE NONEQUILIBRIUM MOLECULAR DYNAMICS ALGORITHM AND ITS APPLICATIONS

2009 ◽  
Vol 01 (03) ◽  
pp. 405-420 ◽  
Author(s):  
NI SHENG ◽  
SHAOFAN LI
Keyword(s):  
Molecular Dynamics ◽  
Local Equilibrium ◽  
Random Force ◽  
Coarse Grained ◽  
Nonequilibrium Molecular Dynamics ◽  
Fine Scale ◽  
Coarse Scale ◽  
Fe Method ◽  
Time Step ◽  
Multi Scale

In this paper, we introduce a multi-scale nonequilibrium molecular dynamics (MS-NEMD) model that is capable of simulating nano-scale thermal–mechanical interactions. Recent simulation results using the MS-NEMD model are presented. The MS-NEMD simulation generalises the nonequilibrium molecular dynamics (NEMD) simulation to the setting of concurrent multi-scale simulation. This multi-scale framework is based on a novel concept of multi-scale canonical ensemble. Under this concept, each coarse scale finite element (FE) node acts as a thermostat, while the atoms associated with each node are assumed to be in a local equilibrium state within one coarse scale time step. The coarse scale mean field is solved by the FE method based on a coarse-grained thermodynamics model; whereas in the fine scale the NEMD simulation is driven by the random force that is regulated by the inhomogeneous continuum filed through a distributed Nośe–Hoover thermostat network. It is shown that the fine scale distribution function is canonical in the sense that it obeys a drifted local Boltzmann distribution.

Analysis of time-lapse seismic and production data for reservoir model classification and assessment

2018 ◽  
Vol 15 (4) ◽  
pp. 1561-1587 ◽  
Author(s):  
Rafael Souza ◽  
David Lumley ◽  
Jeffrey Shragge ◽  
Alessandra Davolio ◽  
Denis José Schiozer
Keyword(s):  
Time Lapse ◽  
Production Data ◽  
Reservoir Model ◽  
Model Classification

IMAGING ADDITIONAL OIL AND GAS RESERVES, INTEGRATING WELL PRODUCTION DATA AND 3D SEISMIC AVO CLASSIFICATION TO IMAGE REMAINING OIL AND GAS RESERVES—A CASE STUDY ON THE NGATORO FIELD, TARANAKI, NEW ZEALAND

2001 ◽  
Vol 41 (1) ◽  
pp. 679
Author(s):  
S. Reymond ◽  
E. Matthews ◽  
B. Sissons
Keyword(s):  
New Zealand ◽  
Oil And Gas ◽  
Seismic Facies ◽  
Bright Spot ◽  
Production Data ◽  
3D Seismic ◽  
Reservoir Model ◽  
Reservoir Properties ◽  
Well Production

This case study illustrates how 3D generalised inversion of seismic facies for reservoir parameters can be successfully applied to image and laterally predict reservoir parameters in laterally discontinuous turbiditic depositional environment where hydrocarbon pools are located in complex combined stratigraphic-structural traps. Such conditions mean that structural mapping is inadequate to define traps and to estimate reserves in place. Conventional seismic amplitude analysis has been used to aid definition but was not sufficient to guarantee presence of economic hydrocarbons in potential reservoir pools. The Ngatoro Field in Taranaki, New Zealand has been producing for nine years. Currently the field is producing 1,000 bopd from seven wells and at three surface locations down from a peak of over 1,500 bopd. The field production stations have been analysed using new techniques in 3D seismic imaging to locate bypassed oils and identify undrained pools. To define the objectives of the study, three questions were asked:Can we image reservoir pools in a complex stratigraphic and structural environment where conventional grid-based interpretation is not applicable due to lack of lateral continuity in reservoir properties?Can we distinguish fluids within each reservoir pools?Can we extrapolate reservoir parameters observed at drilled locations to the entire field using 3D seismic data to build a 3D reservoir model?Using new 3D seismic attributes such as bright spot indicators, attenuation and edge enhancing volumes coupled with 6 AVO (Amplitude Versus Offset) volumes integrated into a single class cube of reservoir properties, made the mapping of reservoir pools possible over the entire data set. In addition, four fluid types, as observed in more than 20 reservoir pools were validated by final inverted results to allow lateral prediction of fluid contents in un-drilled reservoir targets. Well production data and 3D seismic inverted volume were later integrated to build a 3D reservoir model to support updated volumetrics reserves computation and to define additional targets for exploration drilling, additional well planning and to define a water injection plan for pools already in production.

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