共查询到20条相似文献，搜索用时 437 毫秒
1.
Stochastic fractal (fGn and fBm) porosity and permeability fields are conditioned to given variogram, static (or hard), and multiwell pressure data within a Bayesian estimation framework. Because fGn distributions are normal/second-order stationary, it is shown that the Bayesian estimation methods based on the assumption of normal/second-order stationary distributions can be directly used to generate fGn porosity/permeability fields conditional to pressure data. However, because fBm is not second-order stationary, it is shown that such Bayesian estimation methods can be used with implementation of a pseudocovariance approach to generate fBm porosity/permeability fields conditional to multiwell pressure data. In addition, we provide methods to generate unconditional realizations of fBm/fGn fields honoring all variogram parameters. These unconditional realizations can then be conditioned to hard and pressure data observed at wells by using the randomized maximum likelihood method. Synthetic examples generated from one-, two-, and three-dimensional single-phase flow simulators are used to show the applicability of our methodology for generating realizations of fBm/fGn porosity and permeability fields conditioned to well-test pressure data and evaluating the uncertainty in reservoir performance predictions appropriately using these history-matched realizations. 相似文献
2.
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
3.
Hierarchical object-based stochastic modeling of fluvial reservoirs 总被引：27，自引：0，他引：27
This paper describes a novel approach to modeling braided stream fluvial reservoirs. The approach is based on a hierarchical set of coordinate transformations involving relative straingraphic coordinates, translations, rotations, and straightening functions. The emphasis is placed on geologically sound geometric concepts and realistically-attainable conditioning statistics including areal and vertical facies proportions. Modeling proceeds in a hierarchical fashion, that is (1) a stratigraphic coordinate system is established for each reservoir layer, (2) a number of channel complexes are positioned within each layer, and then (3) channels are positioned within each channel complex. The geometric specification of each sand-filled channel within the background of floodplain shales is a marked point process. Each channel is marked with a starting location, size parameters, and sinuosity parameters. We present the hierarchy of eight coordinate transformations, introduce an analytical expression for the channel cross-section shape, describe the simulation algorithm, and demonstrate how the realizations are made to honor local conditioning data from wells and global conditioning data such as areal and vertical proportions. 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.
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
6.
Dean S. Oliver 《Mathematical Geology》2002,34(2):185-201
Assessment of uncertainty in the performance of fluvial reservoirs often requires the ability to generate realizations of channel sands that are conditional to well observations. For channels with low sinuosity this problem has been effectively solved. When the sinuosity is large, however, the standard stochastic models for fluvial reservoirs are not valid, because the deviation of the channel from a principal direction line is multivalued. In this paper, I show how the method of randomized maximum likelihood can be used to generate conditional realizations of channels with large sinuosity. In one example, a Gaussian random field model is used to generate an unconditional realization of a channel with large sinuosity, and this realization is then conditioned to well observations. Channels generated in the second approach are less realistic, but may be sufficient for modeling reservoir connectivity in a realistic way. In the second example, an unconditional realization of a channel is generated by a complex geologic model with random forcing. It is then adjusted in a meaningful way to honor well observations. The key feature in the solution is the use of channel direction instead of channel deviation as the characteristic random function describing the geometry of the channel. 相似文献
7.
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
8.
Well Conditioning in a Fluvial Reservoir Model 总被引：3，自引：0，他引：3
This paper describes a method for conditioning an object model of a fluvial reservoir on facies observations. The channels are assumed parametrized at sections normal to their main channel direction. Projections of the observations on these sections generates a map suitable for drawing conditioning values. This map contains the information from every facies observation between two adjacent sections, enabling handling of any well path. Coupling between well observations is also discussed. The methodology is implemented and demonstrated in examples with complex wells. 相似文献
9.
Stochastic simulation of categorical variables using a classification algorithm and simulated annealing 总被引：4，自引：0，他引：4
P. Goovaerts 《Mathematical Geology》1996,28(7):909-921
An important step of reservoir characterization is the stochastic modeling of the geometry of lithofacies which control large-scale heterogeneities of petrophysical properties. Although multiple realizations are necessary to appreciate the uncertainty in the spatial distribution of facies, a common short cut consists of retaining the first realization drawn. This paper presents an alternative to this potentially hazardous selection: (1) a categorical map is generated by allocating a single facies to each grid node according to the local probabilities of occurrence of the facies, and (2) the map then is post-processed using a steepest descent-type algorithm so as to improve reproduction of spatial continuity and transition probabilities between facies. The procedure is illustrated using a synthetic dataset. A waterflood simulation shows that retaining a single realization would yield, in average, larger errors in production forecasts (water cuts and recovered oil) than the single postprocessed facies map. 相似文献
10.
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
11.
Anne Randi Syversveen Ragnar Hauge Jan Inge Tollefsrud Ulf Lægreid Alister MacDonald 《Mathematical Geosciences》2011,43(7):763-781
We present an approach for modeling facies bodies in which a highly constrained stochastic object model is used to integrate
detailed seismic interpretation of the reservoir’s sedimentological architecture directly in a three-dimensional reservoir
model. The approach fills the gap between the use of seismic data in a true deterministic sense, in which the facies body
top and base are resolved and mapped directly, and stochastic methods in which the relationship between seismic attributes
and facies is defined by conditional probabilities. The lateral geometry of the facies bodies is controlled by seismic interpretations
on horizon slices or by direct body extraction, whereas facies body thickness and cross-sectional shape are defined by a mixture
of seismic data, well data, and user defined object shapes. The stochastic terms in the model are used to incorporate local
geometric variability, which is used to increase the geological realism of the facies bodies and allow for correct, flexible
well conditioning. The result is a set of three-dimensional facies bodies that are constrained to the seismic interpretations
and well data. Each body is defined as a parametric object that includes information such as location of the body axis, depositional
direction, axis-to-margin normals, and external body geometry. The parametric information is useful for defining geologically
realistic intrabody petrophysical trends and for controlling connectivity between stacked facies bodies. 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.
History matching and uncertainty quantification of facies models with multiple geological interpretations 总被引：2，自引：0，他引：2
Hyucksoo Park Céline Scheidt Darryl Fenwick Alexandre Boucher Jef Caers 《Computational Geosciences》2013,17(4):609-621
Uncertainty quantification is currently one of the leading challenges in the geosciences, in particular in reservoir modeling. A wealth of subsurface data as well as expert knowledge are available to quantify uncertainty and state predictions on reservoir performance or reserves. The geosciences component within this larger modeling framework is partially an interpretive science. Geologists and geophysicists interpret data to postulate on the nature of the depositional environment, for example on the type of fracture system, the nature of faulting, and the type of rock physics model. Often, several alternative scenarios or interpretations are offered, including some associated belief quantified with probabilities. In the context of facies modeling, this could result in various interpretations of facies architecture, associations, geometries, and the way they are distributed in space. A quantitative approach to specify this uncertainty is to provide a set of alternative 3D training images from which several geostatistical models can be generated. In this paper, we consider quantifying uncertainty on facies models in the early development stage of a reservoir when there is still considerable uncertainty on the nature of the spatial distribution of the facies. At this stage, production data are available to further constrain uncertainty. We develop a workflow that consists of two steps: (1) determining which training images are no longer consistent with production data and should be rejected and (2) to history match with a given fixed training image. We illustrate our ideas and methodology on a test case derived from a real field case of predicting flow in a newly planned well in a turbidite reservoir off the African West coast. 相似文献
14.
河流相油气储层的井震结合相控随机建模约束方法 总被引：14，自引：4，他引：10
河流相油气储层的研究传统上多是只依据井点资料,先在井上进行沉积相的划分,而后进行剖面相的分析,最后再结合平面沉积参数等值线图编制平面相图,这样往往会造成"见砂画河,吾跟勘探走"的局面,这种平面相图在井间可能存在着较大的误差。然而,平面相图的正确与否直接影响着储层建模中相控的结果。为此作者提出了一种井震结合进行沉积相图编制的新方法,即"以河找砂,指导勘探行"的思路,并在此基础上进行分层次地相控约束随机建模。同时提出相控建模的三个基本的约束条件,即首先要保证随机建模模型的"相序"符合地质规律;其次要保证建模实现的微相分布统计概率与单井沉积微相数据离散化至三维网格后的统计概率相一致;第三要确保三维数据中每种微相的变差函数特征与定量地质知识库一致。因而,从沉积形成与演化的成因角度来指导沉积储层随机建模过程,应用多参数协同、分层次约束的方法,以河道的平面展布和垂向演化来控制建模的结果,使其更逼近地下地质的真实。 相似文献
15.
16.
Modeling of Fluvial Reservoirs with Object Models 总被引：16，自引：0，他引：16
An object model for fluvial reservoirs that has been developed from 1985 to present is described. It uses a formal mathematical object model (marked point process) describing the distributions of four facies: channel, crevasse, barrier, and background. Realisations from the model are generated using the Metropolis-Hastings simulation algorithm with simulated annealing conditioning on the volume ratios and well observations. The main challenge has been to find a suitable parameterization of the geology of fluvial reservoirs, and to find and implement the generating function of the channels in the simulation algorithm. The model and simulation algorithm can be conditioned on arbitrary well paths including horizontal wells and paths with partly missing observations, well test data, well contacts, seismic data, and general geological knowledge. 相似文献
17.
为了适当地完成储层表征的过程,一个有效的方法就是把现场所有可以利用的信息融合成一个一致性的模型。在实际生产中实现这种融合并非简单的任务,所以有必要运用如地震反演等特殊方法。应用地震反演可以使测井数据和地震数据的有效结合成为可能,并且可以得到一个模型,该模型在预测过程中可通过流体数字模拟来验证。地震反演可以通过多种方法进行,主要分为两大类:一类是确定性方法(其代表是回归反演和约束稀疏脉冲反演),另一类是随机方法(其代表是地质统计学反演)。在本次研究中,通过随机反演结果和确定性反演结果的对比展示了随机反演是如何改进储层表征过程的。事实上,随机反演,可以运用较高的采样率(和储层模型的网格大小相接近),来产生一个更可靠的模型。随机反演的另一个好处就是随机方法可产生一些基本的统计测量值来改进解释精度,并且在储层表征过程中能生成大量的实现,从而使储层模型的不确定性研究成为可能。 相似文献
18.
19.
Lianlin Li Behnam Jafarpour M. Reza Mohammad-Khaninezhad 《Computational Geosciences》2013,17(1):167-188
Development of subsurface energy and environmental resources can be improved by tuning important decision variables such as well locations and operating rates to optimize a desired performance metric. Optimal well locations in a discretized reservoir model are typically identified by solving an integer programming problem while identification of optimal well settings (controls) is formulated as a continuous optimization problem. In general, however, the decision variables in field development optimization can include many design parameters such as the number, type, location, short-term and long-term operational settings (controls), and drilling schedule of the wells. In addition to the large number of decision variables, field optimization problems are further complicated by the existing technical and physical constraints as well as the uncertainty in describing heterogeneous properties of geologic formations. In this paper, we consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA). In addition, by taking advantage of the robustness of SPSA against errors in calculating the cost function, we develop an efficient field development optimization under geologic uncertainty, where an ensemble of models are used to describe important flow and transport reservoir properties (e.g., permeability and porosity). We use several numerical experiments, including a channel layer of the SPE10 model and the three-dimensional PUNQ-S3 reservoir, to illustrate the performance improvement that can be achieved by solving a combined well placement and control optimization using the SPSA algorithm under known and uncertain reservoir model assumptions. 相似文献
20.
致密煤层气藏三维全隐式数值模拟 总被引：2，自引：0，他引：2
我国煤层普遍存在低渗、低储层压力和低含气饱和度等不利条件,许多研究表明,低渗透多孔介质中的气体运移存在启动压力梯度。为了让数值模拟模型能更加准确地描述致密煤储层中流体的运移特性,基于前人的研究成果,建立了考虑启动压力梯度的致密煤层气藏三维、非平衡吸附、拟稳态条件下气、水两相耦合流动数值模拟模型,并给出了模型的全隐式有限差分格式和数值求解方法。最后利用沁水盆地某生产井的试井资料进行了模拟计算,模拟结果表明,在其他条件相同的情况下,启动压力梯度的存在使得煤层的降压效果变差,且延迟了产气高峰的到来。对比该井的开采资料,模拟结果是合理的,模型能正确反映致密煤层气藏中流体的运移特征。 相似文献