共查询到20条相似文献，搜索用时 31 毫秒
1.
A Fixed-Path Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables 总被引：4，自引：0，他引：4
Weidong Li 《Mathematical Geology》2007,39(2):159-176
The Markov chain random field (MCRF) theory provided the theoretical foundation for a nonlinear Markov chain geostatistics.
In a MCRF, the single Markov chain is also called a “spatial Markov chain” (SMC). This paper introduces an efficient fixed-path SMC algorithm for conditional simulation of discrete spatial variables
(i.e., multinomial classes) on point samples with incorporation of interclass dependencies. The algorithm considers four nearest
known neighbors in orthogonal directions. Transiograms are estimated from samples and are model-fitted to provide parameter
input to the simulation algorithm. Results from a simulation example show that this efficient method can effectively capture
the spatial patterns of the target variable and fairly generate all classes. Because of the incorporation of interclass dependencies
in the simulation algorithm, simulated realizations are relatively imitative of each other in patterns. Large-scale patterns
are well produced in realizations. Spatial uncertainty is visualized as occurrence probability maps, and transition zones
between classes are demonstrated by maximum occurrence probability maps. Transiogram analysis shows that the algorithm can
reproduce the spatial structure of multinomial classes described by transiograms with some ergodic fluctuations. A special
characteristic of the method is that when simulation is conditioned on a number of sample points, simulated transiograms have
the tendency to follow the experimental ones, which implies that conditioning sample data play a crucial role in determining
spatial patterns of multinomial classes. The efficient algorithm may provide a powerful tool for large-scale structure simulation
and spatial uncertainty analysis of discrete spatial variables. 相似文献
2.
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
3.
A stochastic channel embedded in a background facies is conditioned to data observed at wells. The background facies is a fixed rectangular box. The model parameters consist of geometric parameters that describe the shape, size, and location of the channel, and permeability and porosity in the channel and nonchannel facies. We extend methodology previously developed to condition a stochastic channel to well-test pressure data, and well observations of the channel thickness and the depth of the top of the channel. The main objective of this work is to characterize the reduction in uncertainty in channel model parameters and predicted reservoir performance that can be achieved by conditioning to well-test pressure data at one or more wells. Multiple conditional realizations of the geometric parameters and rock properties are generated to evaluate the uncertainty in model parameters. The ensemble of predictions of reservoir performance generated from the suite of realizations provides a Monte Carlo estimate of the uncertainty in future performance predictions. In addition, we provide some insight on how prior variances, data measurement errors, and sensitivity coefficients interact to determine the reduction in model parameters obtained by conditioning to pressure data and examine the value of active and observation well data in resolving model parameters. 相似文献
4.
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
5.
6.
A standard procedure for conditioning a stochastic channel to well-test pressure data requires the minimization of an objective function. The Levenberg–Marquardt algorithm is a natural choice for minimization, but may suffer from slow convergence or converge to a local minimum which gives an unacceptable match of observed pressure data if a poor initial guess is used. In this work, we present a procedure to generate a good initial guess when the Levenberg–Marquardt algorithm is used to condition a stochastic channel to pressure data and well observations of channel facies, channel thickness, and channel top depth. This technique yields improved computational efficiency when the Levenberg–Marquardt method is used as the optimization procedure for generating realizations of the model by the randomized maximum likelihood method. 相似文献
7.
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
8.
Geologic uncertainties and limited well data often render recovery forecasting a difficult undertaking in typical appraisal
and early development settings. Recent advances in geologic modeling algorithms permit automation of the model generation
process via macros and geostatistical tools. This allows rapid construction of multiple alternative geologic realizations.
Despite the advances in geologic modeling, computation of the reservoir dynamic response via full-physics reservoir simulation
remains a computationally expensive task. Therefore, only a few of the many probable realizations are simulated in practice.
Experimental design techniques typically focus on a few discrete geologic realizations as they are inherently more suitable
for continuous engineering parameters and can only crudely approximate the impact of geology. A flow-based pattern recognition
algorithm (FPRA) has been developed for quantifying the forecast uncertainty as an alternative. The proposed algorithm relies
on the rapid characterization of the geologic uncertainty space represented by an ensemble of sufficiently diverse static
model realizations. FPRA characterizes the geologic uncertainty space by calculating connectivity distances, which quantify
how different each individual realization is from all others in terms of recovery response. Fast streamline simulations are
employed in evaluating these distances. By applying pattern recognition techniques to connectivity distances, a few representative
realizations are identified within the model ensemble for full-physics simulation. In turn, the recovery factor probability
distribution is derived from these intelligently selected simulation runs. Here, FPRA is tested on an example case where the
objective is to accurately compute the recovery factor statistics as a function of geologic uncertainty in a channelized turbidite
reservoir. Recovery factor cumulative distribution functions computed by FPRA compare well to the one computed via exhaustive
full-physics simulations. 相似文献
9.
Weidong Li 《Mathematical Geology》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating
categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces
a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation
(or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional
probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general
solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’
theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional
simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models
are nonlinear. 相似文献
10.
A Blocking Markov Chain Monte Carlo Method for Inverse Stochastic Hydrogeological Modeling 总被引：3，自引：2，他引：1
An adequate representation of the detailed spatial variation of subsurface parameters for underground flow and mass transport
simulation entails heterogeneous models. Uncertainty characterization generally calls for a Monte Carlo analysis of many equally
likely realizations that honor both direct information (e.g., conductivity data) and information about the state of the system
(e.g., piezometric head or concentration data). Thus, the problems faced is how to generate multiple realizations conditioned
to parameter data, and inverse-conditioned to dependent state data. We propose using Markov chain Monte Carlo approach (MCMC)
with block updating and combined with upscaling to achieve this purpose. Our proposal presents an alternative block updating
scheme that permits the application of MCMC to inverse stochastic simulation of heterogeneous fields and incorporates upscaling
in a multi-grid approach to speed up the generation of the realizations. The main advantage of MCMC, compared to other methods
capable of generating inverse-conditioned realizations (such as the self-calibrating or the pilot point methods), is that
it does not require the solution of a complex optimization inverse problem, although it requires the solution of the direct
problem many times. 相似文献
11.
Thomas Romary 《Computational Geosciences》2010,14(2):343-355
In history matching of lithofacies reservoir model, we attempt to find multiple realizations of lithofacies configuration
that are conditional to dynamic data and representative of the model uncertainty space. This problem can be formalized in
the Bayesian framework. Given a truncated Gaussian model as a prior and the dynamic data with its associated measurement error,
we want to sample from the conditional distribution of the facies given the data. A relevant way to generate conditioned realizations
is to use Markov chains Monte Carlo (MCMC). However, the dimensions of the model and the computational cost of each iteration
are two important pitfalls for the use of MCMC. Furthermore, classical MCMC algorithms mix slowly, that is, they will not
explore the whole support of the posterior in the time of the simulation. In this paper, we extend the methodology already
described in a previous work to the problem of history matching of a Gaussian-related lithofacies reservoir model. We first
show how to drastically reduce the dimension of the problem by using a truncated Karhunen-Loève expansion of the Gaussian
random field underlying the lithofacies model. Moreover, we propose an innovative criterion of the choice of the number of
components based on the connexity function. Then, we show how we improve the mixing properties of classical single MCMC, without
increasing the global computational cost, by the use of parallel interacting Markov chains. Applying the dimension reduction
and this innovative sampling method drastically lowers the number of iterations needed to sample efficiently from the posterior.
We show the encouraging results obtained when applying the methodology to a synthetic history-matching case. 相似文献
12.
改进模拟退火法在估计河流水质参数中的应用 总被引：3，自引：0，他引：3
将模拟退火法应用于求解分析河流水团示踪试验数据，确定河流水质参数的函数优化问题。针对标准SA算法收敛速度缓慢的弱点，采取了增加附加约束条件、设置内阈值提前降温和增加记忆功能等综合措施对算法进行了改进。算例表明，综合改进措施能够明显地提高算法收敛速度，并可以得到满意的参数计算结果。计算结果也表明，内循环次数不会对外循环次数产生明显的影响。由于算法对目标函数没有附加要求，而且算法的收敛性与待估参数的初值无关，因此，改进SA算法在分析河流水质试验数据、确定水质参数方面．将会具有非常广的应用范围。 相似文献
13.
Based on the algorithm for gradual deformation of Gaussian stochastic models, we propose, in this paper, an extension of this method to gradually deforming realizations generated by sequential, not necessarily Gaussian, simulation. As in the Gaussian case, gradual deformation of a sequential simulation preserves spatial variability of the stochastic model and yields in general a regular objective function that can be minimized by an efficient optimization algorithm (e.g., a gradient-based algorithm). Furthermore, we discuss the local gradual deformation and the gradual deformation with respect to the structural parameters (mean, variance, and variogram range, etc.) of realizations generated by sequential simulation. Local gradual deformation may significantly improve calibration speed in the case where observations are scattered in different zones of a field. Gradual deformation with respect to structural parameters is necessary when these parameters cannot be inferred a priori and need to be determined using an inverse procedure. A synthetic example inspired from a real oil field is presented to illustrate different aspects of this approach. Results from this case study demonstrate the efficiency of the gradual deformation approach for constraining facies models generated by sequential indicator simulation. They also show the potential applicability of the proposed approach to complex real cases. 相似文献
14.
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
15.
16.
碳酸盐岩缝洞型储层历经多期构造运动以及强烈的风化、剥蚀和淋滤作用,储集空间类型多样,形态极不规则且随机分布,导致储层三维空间描述困难,现有的碎屑岩储层建模方法难以直接借鉴。文中提出碳酸盐岩缝洞型储层应该按照大型洞穴、溶蚀孔洞、大尺度裂缝、小尺度裂缝的"多类多尺度建模"的基本思路。以钻井和地震识别成果作为大型洞穴确定性数据,以地震波阻抗的大型洞穴发育概率体作为井间约束数据,在垂向岩溶分带和平面古地貌分区的岩溶相控下,采用具有趋势的序贯指示模拟方法,建立大型洞穴离散分布模型;以大型洞穴分布作为"相控"约束条件,以井孔解释的溶蚀孔洞作为硬数据,采用序贯指示模拟算法,建立溶蚀孔洞随机分布模型;根据蚂蚁体地震属性自动拾取的断裂信息,人机交互补充和修正地震解释断层数据,建立确定性的大尺度裂缝离散分布模型;基于大尺度裂缝离散分布模型建立井间裂缝发育概率体,根据井孔裂缝密度、裂缝产状,结合退火模拟和基于目标的示性点过程模拟方法,建立小尺度裂缝离散分布模型。以塔河油田四区奥陶系缝洞型油藏为例,建立研究区缝洞型储集体空间展布模型,再现缝洞型储层的结构形态。 相似文献
17.
Markov chains and embedded Markov chains in geology 总被引：2，自引：0，他引：2
Geological data are structured as first-order, discrete-state discrete-time Markov chains in two main ways. In one, observations are spaced equally in time or space to yield transition probability matrices with nonzero elements in the main diagonal; in the other, only state transitions are recorded, to yield matrices with diagonal elements exactly equal to zero. The mathematical differences in these two approaches are reviewed here, using stratigraphic data as an example. Simulations from chains with diagonal elements greater than zero always yield geometric distributions of lithologic unit thickness, and their use is recommended only if the input data have the same distribution. For thickness distributions lognormally or otherwise distributed, the embedded chain is preferable. The mathematical portions of this paper are well known, but are not readily available in publications normally used by geologists. One purpose of this paper is to provide an explicit treatment of the mathematical foundations on which applications of Markov processes in geology depend. 相似文献
18.
Weidong Li 《Mathematical Geosciences》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear. 相似文献
19.
To study sedimentary phenomena, we introduce random-genetic models in which genetic hypotheses and structural random elements occur for the main part. Starting from geologic hypotheses we choose principal factors which may be random functions or random variables. These factors are: depth, nature of the facies, sedimentation rate, and subsidence. Equations of evolution link the factors. Depth is a Markov process, but generally the resultant sequence does not make a Markov chain or Markov process. Three examples of such models are given with the results of simulations. 相似文献
20.
Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models 总被引：11，自引：0，他引：11
Lin Y. Hu 《Mathematical Geology》2000,32(1):87-108
This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models. 相似文献