共查询到20条相似文献，搜索用时 879 毫秒
1.
Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space 总被引：2，自引：0，他引：2
Thomas Romary 《Computational Geosciences》2009,13(1):103-122
In oil industry and subsurface hydrology, geostatistical models are often used to represent the porosity or the permeability
field. In history matching of a geostatistical reservoir model, we attempt to find multiple realizations that are conditional
to dynamic data and representative of the model uncertainty space. A relevant way to simulate the conditioned realizations
is by generating Monte Carlo Markov chains (MCMC). The huge dimensions (number of parameters) of the model and the computational
cost of each iteration are two important pitfalls for the use of MCMC. In practice, we have to stop the chain far before it
has browsed the whole support of the posterior probability density function. Furthermore, as the relationship between the
production data and the random field is highly nonlinear, the posterior can be strongly multimodal and the chain may stay
stuck in one of the modes. In this work, we propose a methodology to enhance the sampling properties of classical single MCMC
in history matching. We first show how to reduce the dimension of the problem by using a truncated Karhunen–Loève expansion
of the random field of interest and assess the number of components to be kept. Then, we show how we can improve the mixing
properties of MCMC, without increasing the global computational cost, by using parallel interacting Markov Chains. Finally,
we show the encouraging results obtained when applying the method to a synthetic history matching case. 相似文献
2.
Updating Markov chain models using the ensemble Kalman filter 总被引：1，自引：0，他引：1
3.
A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach. 相似文献
4.
5.
M. Panzeri E. L. Della Rossa L. Dovera M. Riva A. Guadagnini 《Computational Geosciences》2016,20(3):637-653
We present a methodology that allows conditioning the spatial distribution of geological and petrophysical properties of reservoir model realizations on available production data. The approach is fully consistent with modern concepts depicting natural reservoirs as composite media where the distribution of both lithological units (or facies) and associated attributes are modeled as stochastic processes of space. We represent the uncertain spatial distribution of the facies through a Markov mesh (MM) model, which allows describing complex and detailed facies geometries in a rigorous Bayesian framework. The latter is then embedded within a history matching workflow based on an iterative form of the ensemble Kalman filter (EnKF). We test the proposed methodology by way of a synthetic study characterized by the presence of two distinct facies. We analyze the accuracy and computational efficiency of our algorithm and its ability with respect to the standard EnKF to properly estimate model parameters and assess future reservoir production. We show the feasibility of integrating MM in a data assimilation scheme. Our methodology is conducive to a set of updated model realizations characterized by a realistic spatial distribution of facies and their log permeabilities. Model realizations updated through our proposed algorithm correctly capture the production dynamics. 相似文献
6.
Representing Spatial Uncertainty Using Distances and Kernels 总被引：8，自引：7，他引：1
Assessing uncertainty of a spatial phenomenon requires the analysis of a large number of parameters which must be processed
by a transfer function. To capture the possibly of a wide range of uncertainty in the transfer function response, a large
set of geostatistical model realizations needs to be processed. Stochastic spatial simulation can rapidly provide multiple,
equally probable realizations. However, since the transfer function is often computationally demanding, only a small number
of models can be evaluated in practice, and are usually selected through a ranking procedure. Traditional ranking techniques
for selection of probabilistic ranges of response (P10, P50 and P90) are highly dependent on the static property used. In
this paper, we propose to parameterize the spatial uncertainty represented by a large set of geostatistical realizations through
a distance function measuring “dissimilarity” between any two geostatistical realizations. The distance function allows a
mapping of the space of uncertainty. The distance can be tailored to the particular problem. The multi-dimensional space of
uncertainty can be modeled using kernel techniques, such as kernel principal component analysis (KPCA) or kernel clustering.
These tools allow for the selection of a subset of representative realizations containing similar properties to the larger
set. Without losing accuracy, decisions and strategies can then be performed applying a transfer function on the subset without
the need to exhaustively evaluate each realization. This method is applied to a synthetic oil reservoir, where spatial uncertainty
of channel facies is modeled through multiple realizations generated using a multi-point geostatistical algorithm and several
training images. 相似文献
7.
Bayesian lithology/fluid inversion—comparison of two algorithms 总被引：1，自引：0，他引：1
Algorithms for inversion of seismic prestack AVO data into lithology-fluid classes in a vertical profile are evaluated. The
inversion is defined in a Bayesian setting where the prior model for the lithology-fluid classes is a Markov chain, and the
likelihood model relates seismic data and elastic material properties to these classes. The likelihood model is approximated
such that the posterior model can be calculated recursively using the extremely efficient forward–backward algorithm. The
impact of the approximation in the likelihood model is evaluated empirically by comparing results from the approximate approach
with results generated from the exact posterior model. The exact posterior is assessed by sampling using a sophisticated Markov
chain Monte Carlo simulation algorithm. The simulation algorithm is iterative, and it requires considerable computer resources.
Seven realistic evaluation models are defined, from which synthetic seismic data are generated. Using identical seismic data,
the approximate marginal posterior is calculated and the exact marginal posterior is assessed. It is concluded that the approximate
likelihood model preserves 50% to 90% of the information content in the exact likelihood model. 相似文献
8.
Two methods for generating representative realizations from Gaussian and lognormal random field models are studied in this paper, with term representative implying realizations efficiently spanning the range of possible attribute values corresponding to the multivariate (log)normal probability distribution. The first method, already established in the geostatistical literature, is multivariate Latin hypercube sampling, a form of stratified random sampling aiming at marginal stratification of simulated values for each variable involved under the constraint of reproducing a known covariance matrix. The second method, scarcely known in the geostatistical literature, is stratified likelihood sampling, in which representative realizations are generated by exploring in a systematic way the structure of the multivariate distribution function itself. The two sampling methods are employed for generating unconditional realizations of saturated hydraulic conductivity in a hydrogeological context via a synthetic case study involving physically-based simulation of flow and transport in a heterogeneous porous medium; their performance is evaluated for different sample sizes (number of realizations) in terms of the reproduction of ensemble statistics of hydraulic conductivity and solute concentration computed from a very large ensemble set generated via simple random sampling. The results show that both Latin hypercube and stratified likelihood sampling are more efficient than simple random sampling, in that overall they can reproduce to a similar extent statistics of the conductivity and concentration fields, yet with smaller sampling variability than the simple random sampling. 相似文献
9.
Markov chain Monte Carlo methods for conditioning a permeability field to pressure data 总被引：3，自引：0，他引：3
Generating one realization of a random permeability field that is consistent with observed pressure data and a known variogram
model is not a difficult problem. If, however, one wants to investigate the uncertainty of reservior behavior, one must generate
a large number of realizations and ensure that the distribution of realizations properly reflects the uncertainty in reservoir
properties. The most widely used method for conditioning permeability fields to production data has been the method of simulated
annealing, in which practitioners attempt to minimize the difference between the ’ ’true and simulated production data, and
“true” and simulated variograms. Unfortunately, the meaning of the resulting realization is not clear and the method can be
extremely slow. In this paper, we present an alternative approach to generating realizations that are conditional to pressure
data, focusing on the distribution of realizations and on the efficiency of the method. Under certain conditions that can
be verified easily, the Markov chain Monte Carlo method is known to produce states whose frequencies of appearance correspond
to a given probability distribution, so we use this method to generate the realizations. To make the method more efficient,
we perturb the states in such a way that the variogram is satisfied automatically and the pressure data are approximately
matched at every step. These perturbations make use of sensitivity coefficients calculated from the reservoir simulator. 相似文献
10.
Building of models in the Earth Sciences often requires the solution of an inverse problem: some unknown model parameters need to be calibrated with actual measurements. In most cases, the set of measurements cannot completely and uniquely determine the model parameters; hence multiple models can describe the same data set. Bayesian inverse theory provides a framework for solving this problem. Bayesian methods rely on the fact that the conditional probability of the model parameters given the data (the posterior) is proportional to the likelihood of observing the data and a prior belief expressed as a prior distribution of the model parameters. In case the prior distribution is not Gaussian and the relation between data and parameters (forward model) is strongly non-linear, one has to resort to iterative samplers, often Markov chain Monte Carlo methods, for generating samples that fit the data likelihood and reflect the prior model statistics. While theoretically sound, such methods can be slow to converge, and are often impractical when the forward model is CPU demanding. In this paper, we propose a new sampling method that allows to sample from a variety of priors and condition model parameters to a variety of data types. The method does not rely on the traditional Bayesian decomposition of posterior into likelihood and prior, instead it uses so-called pre-posterior distributions, i.e. the probability of the model parameters given some subset of the data. The use of pre-posterior allows to decompose the data into so-called, “easy data” (or linear data) and “difficult data” (or nonlinear data). The method relies on fast non-iterative sequential simulation to generate model realizations. The difficult data is matched by perturbing an initial realization using a perturbation mechanism termed “probability perturbation.” The probability perturbation method moves the initial guess closer to matching the difficult data, while maintaining the prior model statistics and the conditioning to the linear data. Several examples are used to illustrate the properties of this method. 相似文献
11.
Q区块目的层为砂泥岩薄互层,常规方法预测的储层精度不能满足油田时下的需求。通过调研,认为薄互层具有各向异性,“两宽一高”地震数据的出现,为各向异性解释提供了数据基础。通过理论分析,采用分方位马尔科夫链地质统计反演预测储层展布规律。该方法将马尔科夫链转移概率与贝叶斯遗传概率相结合,利用地震波组特征进行约束,同时,方位信息的加入为储层预测精度的提高提供了选项。突破了以往只在碳酸盐岩及基岩各向异性反演的认知限制,使碎屑岩薄储层中的各向异性得以体现。通过理论与实践结合,证实了优势方位的储层预测精度优于其他方位。 相似文献
12.
Uncertainty in future reservoir performance is usually evaluated from the simulated performance of a small number of reservoir realizations. Unfortunately, most of the practical methods for generating realizations conditional to production data are only approximately correct. It is not known whether or not the recently developed method of Gradual Deformation is an approximate method or if it actually generates realizations that are distributed correctly. In this paper, we evaluate the ability of the Gradual Deformation method to correctly assess the uncertainty in reservoir predictions by comparing the distribution of conditional realizations for a small test problem with the standard distribution from a Markov Chain Monte Carlo (MCMC) method, which is known to be correct, and with distributions from several approximate methods. Although the Gradual Deformation algorithm samples inefficiently for this test problem and is clearly not an exact method, it gives similar uncertainty estimates to those obtained by MCMC method based on a relatively small number of realizations. 相似文献
13.
An integrated approach to shallow aquifer characterization: combining geophysics and geostatistics 总被引：1，自引：0，他引：1
We present a method of aquifer characterization that is able to utilize multiple sources of conditioning data to build a more
realistic model of heterogeneity. This modeling approach (InMod) uses geophysical data to delineate bounding surfaces within
sedimentary deposits. The depositional volumes between bounding surfaces are identified automatically from the geophysical
data by a region growing algorithm. Simple geometric rules are used to constrain the growth of the regions in 3-D. The nodes
within the depositional volume are assigned to categorical lithologies using geostatistical realizations and a dynamic lookup
routine that can be conditioned to field data. The realizations created with this method preserve geologically expected features
and produces sharp juxtapositions of high and low hydraulic conductivity lithologies along bounding surfaces. The realizations
created with InMod also have higher variance than models created only with geostatistics and honor the volumetric distribution
of sediments measured from field data. 相似文献
14.
In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation. 相似文献
15.
16.
Reservoir characterization needs the integration of various data through history matching, especially dynamic information
such as production or 4D seismic data. Although reservoir heterogeneities are commonly generated using geostatistical models,
random realizations cannot generally match observed dynamic data. To constrain model realizations to reproduce measured dynamic
data, an optimization procedure may be applied in an attempt to minimize an objective function, which quantifies the mismatch
between real and simulated data. Such assisted history matching methods require a parameterization of the geostatistical model
to allow the updating of an initial model realization. However, there are only a few parameterization methods available to
update geostatistical models in a way consistent with the underlying geostatistical properties. This paper presents a local
domain parameterization technique that updates geostatistical realizations using assisted history matching. This technique
allows us to locally change model realizations through the variation of geometrical domains whose geometry and size can be
easily controlled and parameterized. This approach provides a new way to parameterize geostatistical realizations in order
to improve history matching efficiency. 相似文献
17.
Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions 总被引：1，自引：0，他引：1
Rúben Nunes Amílcar Soares Leonardo Azevedo Pedro Pereira 《Mathematical Geosciences》2017,49(5):583-601
Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation. 相似文献
18.
Estimation of Geological Attributes from a Well Log: An Application of Hidden Markov Chains 总被引：1，自引：0，他引：1
Geophysical well logs used in petroleum exploration consist of measurements of physical properties (such as radioactivity, density, and acoustic velocity) that are digitally recorded at a fixed interval (typically half a foot) along the length of the exploratory well. The measurements are informative of the unobserved rock type alternations along the well, which is critical for the assessment of petroleum reservoirs. The well log data that are analyzed here are from a North Sea petroleum reservoir where two distinct strata have been identified from large scale seismic data. We apply a hidden Markov chain model to infer properties of the rock type alternations, separately for each stratum. The hidden Markov chain uses Dirichlet prior distributions for the Markov transition probabilities between rock types. The well log measurements, conditional on the unobserved rock types, are modeled using Gaussian distributions. Our analysis provides likelihood estimates of the parameters of the Dirichlet prior and the parameters of the measurement model. For fixed values of the parameter estimates we calculate the posterior distributions for the rock type transition probabilities, given the well log measurement data. We then propagate the model parameter uncertainty into the posterior distributions using resampling from the maximum likelihood model. The resulting distributions can be used to characterize the two reservoir strata and possible differences between them. We believe that our approach to modeling and analysis is novel and well suited to the problem. Our approach has elements in common with empirical Bayes methods in that unspecified parameters are estimated using marginal likelihoods. Additionally, we propagate the parameter uncertainty into the final posterior distributions. 相似文献
19.
Investigation of the sampling performance of ensemble-based methods with a simple reservoir model 总被引：1，自引：0，他引：1
The application of the ensemble Kalman filter (EnKF) for history matching petroleum reservoir models has been the subject of intense investigation during the past 10 years. Unfortunately, EnKF often fails to provide reasonable data matches for highly nonlinear problems. This fact motivated the development of several iterative ensemble-based methods in the last few years. However, there exists no study comparing the performance of these methods in the literature, especially in terms of their ability to quantify uncertainty correctly. In this paper, we compare the performance of nine ensemble-based methods in terms of the quality of the data matches, quantification of uncertainty, and computational cost. For this purpose, we use a small but highly nonlinear reservoir model so that we can generate the reference posterior distribution of reservoir properties using a very long chain generated by a Markov chain Monte Carlo sampling algorithm. We also consider one adjoint-based implementation of the randomized maximum likelihood method in the comparisons. 相似文献
20.
In the analysis of petroleum reservoirs, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the reservoir. Generally, scientists approach this problem by computing a sensitivity matrix and then perform a singular value decomposition in order to determine the number of degrees of freedom i.e. the number of independent parameters necessary to specify the configuration of the system. Here we propose a complementary approach: it uses the concept of refinement indicators to select those degrees which have the greatest sensitivity to an objective function quantifying the mismatch between measured and simulated data. We apply this approach to the problem of data integration for petrophysical reservoir charaterization where geoscientists are currently working with multimillion cell geological models. Data integration may be performed by gradually deforming (by a linear combination) a set of these multimillion grid geostatistical realizations during the optimization process. The inversion parameters are then reduced to the number of coefficients of this linear combination. However, there is an infinity of geostatistical realizations to choose from which may not be efficient regarding operational constraints. Following our new approach, we are able through a single objective function evaluation to compute refinement indicators that indicate which realizations might improve the iterative geological model in a significant way. This computation is extremely fast as it implies a single gradient computation through the adjoint state approach and dot products. Using only the most sensitive realizations from a given set, we are able to resolve quicker the optimization problem case. We applied this methodology to the integration of interference test data into 3D geostatistical models. 相似文献