共查询到20条相似文献，搜索用时 515 毫秒
1.
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
2.
The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil–water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification. 相似文献
3.
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
4.
Victor Ginting Felipe Pereira Michael Presho Shaochang Wo 《Computational Geosciences》2011,15(4):691-707
In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves
sampling from a representation of a fracture’s permeability that has been suitably adjusted to the dynamic tracer cut measurement
data. We propose to use a type of dual-porosity, dual-permeability model for tracer flow. This model is built into the Markov
chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the
acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability
fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems
which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance
rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model.
With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate.
A number of numerical examples are presented to illustrate the performance of the method. 相似文献
5.
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
6.
Properly accounting for the mechanical anisotropy of shales can be critical for successful drilling of high inclination wells, because shales are known to be weak along bedding planes. To optimize the drilling parameters in such cases, a sufficiently representative, anisotropic rock mechanical model is therefore required. This paper presents such a model developed to better match results from a dedicated, extensive set of uniaxial and triaxial compression tests performed on plugs of Mancos outcrop shale with different orientations relative to the bedding plane. Post failure inspection of the plugs shows that the failure planes are to some extent affected by the orientation of the applied stress relative to the bedding planes, indicating that the bedding planes may represent weak planes which tend to fail before intrinsic failure occurs, whenever the orientation of these planes is suitable. The simple “plane of weakness” model is commonly used to predict strength as function of orientation for such a rock. A comparison of this model to the experimental data shows, however, that the weak planes seem to have an impact on strength even outside the range of orientations where the model predicts such impact. An extension of this model allowing the weak planes to be heterogeneous in terms of patchy weakness was therefore developed. In this model, local shear sliding may occur prior to macroscopic failure, leading to enhanced local stresses and corresponding reduction in strength. The model is found to give better match with strength data at intermediate orientations. The model is also able to partly predict the qualitatively different variation of Young’s modulus with orientation for this data set. 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.
Linah Mohamed Ben Calderhead Maurizio Filippone Mike Christie Mark Girolami 《Computational Geosciences》2012,16(2):423-436
This paper presents the application of a population Markov Chain Monte Carlo (MCMC) technique to generate history-matched
models. The technique has been developed and successfully adopted in challenging domains such as computational biology but
has not yet seen application in reservoir modelling. In population MCMC, multiple Markov chains are run on a set of response
surfaces that form a bridge from the prior to posterior. These response surfaces are formed from the product of the prior
with the likelihood raised to a varying power less than one. The chains exchange positions, with the probability of a swap
being governed by a standard Metropolis accept/reject step, which allows for large steps to be taken with high probability.
We show results of Population MCMC on the IC Fault Model—a simple three-parameter model that is known to have a highly irregular
misfit surface and hence be difficult to match. Our results show that population MCMC is able to generate samples from the
complex, multi-modal posterior probability distribution of the IC Fault model very effectively. By comparison, previous results
from stochastic sampling algorithms often focus on only part of the region of high posterior probability depending on algorithm
settings and starting points. 相似文献
9.
One of the main factors in the effective application of a tunnel boring machine (TBM) is the ability to accurately estimate the machine performance in order to determine the project costs and schedule. Predicting the TBM performance is a nonlinear and multivariable complex problem. The aim of this study is to predict the performance of TBM using the hybrid of support vector regression (SVR) and the differential evolution algorithm (DE), artificial bee colony algorithm (ABC), and gravitational search algorithm (GSA). The DE, ABC and GSA are combined with the SVR for determining the optimal value of its user defined parameters. The optimization implementation by the DE, ABC and GSA significantly improves the generalization ability of the SVR. The uniaxial compressive strength (UCS), average distance between planes of weakness (DPW), the angle between tunnel axis and the planes of weakness (α), and intact rock brittleness (BI) were considered as the input parameters, while the rate of penetration was the output parameter. The prediction models were applied to the available data given in the literature, and their performance was assessed based on statistical criteria. The results clearly show the superiority of DE when integrated with SVR for optimizing values of its parameters. In addition, the suggested model was compared with the methods previously presented for predicting the TBM penetration rate. The comparative results revealed that the hybrid of DE and SVR yields a robust model which outperforms other models in terms of the higher correlation coefficient and lower mean squared error. 相似文献
10.
Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation 总被引：4，自引：0，他引：4
A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification
or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but
are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to
determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data.
The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the
orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar
gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated
field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method,
which is easily transposable in three dimensions. 相似文献
11.
We deal with a multi-parameter identification problem arising in oil industry. In the general case, we give a local solvability condition to guarantee the well-posedness of the problem. We discuss in detail the identification of two parameters for which some numerical results are given. 相似文献
12.
We deal with a multi-parameter identification problem arising in oil industry. In the general case, we give a local solvability condition to guarantee the well-posedness of the problem. We discuss in detail the identification of two parameters for which some numerical results are given. 相似文献
13.
Peter C. Lichtner 《Geochimica et cosmochimica acta》1985,49(3):779-800
A time-space continuum model for transport of hydrothermal fluids in porous media is presented which provides for simultaneous, reversible and irreversible chemical reactions involving liquids, gases and minerals. Homogeneous and heterogeneous reactions are incorporated in the model in a similar fashion through source/sink terms added to the continuity equation. The model provides for moving reaction fronts through surfaces of discontinuity across which occur jump discontinuities in the various field variables satisfying generalized Rankine-Hugoniot relations. Reversible reactions including aqueous complexing, oxidation-reduction reactions, mineral precipitation and dissolution reactions and adsorption are explicitly accounted for by imposing chemical equilibrium constraints in the form of mass action equations on the transport equations. This is facilitated by partitioning the reacting species into primary and secondary species corresponding to a particular representation of the stoichiometric reaction matrix referred to as the canonical representation. The transport equations for the primary species combined with homogeneous and heterogeneous equilibria result in a system of coupled, nonlinear algebraic/partial differential equations which completely describe the evolution of the system in time. Spatially separated phase assemblages are accommodated in the model by altering the set of independent variables across surfaces of discontinuity. Constitutive relations for the fluid flux corresponding to primary species are obtained describing transport of both neutral and charged species by advection, dispersion and diffusion. Numerical implementation of the transport equations is considered and both explicit and implicit finite difference algorithms are discussed. Analytical expressions for the change in porosity and permeability with time are obtained for an assemblage of minerals reacting reversibly with a hydrothermal fluid under quasi-steady state conditions. Fluid flow is described by Darcy's law employing a phenomenological expression relating permeability and porosity. Finally an expression for the local retardation factor of solute species is derived for the case of advective transport in a single spatial dimension which accounts for the effects of homogeneous and heterogeneous equilibria including adsorption on the rate of advance of a reaction front. The condition for the formation of shock waves is given. 相似文献
14.
In this paper one type of joint element –six –node isoparametric joint element for 2-D problem is introduced .The corresponding formulae used for finite element analysis has been derived and given here .
Using the program written by us several examples of calculations and comparisons have been done .The results show that such a joint element model can eb used successfully to simulate the joints ,intercalations and structural planes in rock masses and can give a more accurate results than that of the joint element ordinary used .Especially it has the obvious advantages when using it for representing the nonflat joints and wave –like form weak intercalations.
A sixteen –node isoparametric joint element model for 3-Dproblem and the corresponding formulate are also given in the paper . 相似文献
15.
等参数节理单元及其应用 总被引：2，自引：0，他引：2
岩体中必然存有各种结构面,这些结构面使岩体的性状变得十分复杂.通常岩体中的节理、软弱夹层等是岩体相对薄弱的部分,因此对于岩体工程,例如水工建筑物的抗滑稳定、矿山边坡和路堑边坡以及地下洞室的稳定性,它们往往起着控制作用.这些年来,人们对岩体软弱结构面的研究愈来愈重视,国内、外开展了大量的现场和实验室试验以及模拟分析工作,积累了宝贵资料. 相似文献
16.
Paraelasticity (PE) is a hysteretic, fully reversible model with rate-independent damping and with variable secant stiffness.
PE has been proposed in the companion paper (Niemunis et al. in Acta Geotech, 2011) for the 3D case. Here, paraelasticity
is extended for demanding application in geomechanics by implementation of a reversible dilatancy–contractancy. Moreover,
an implicit FE implementation for Abaqus and calculation of a boundary value problem are presented. 相似文献
17.
弹塑性固体中间断位移的刚性进化 总被引：2，自引：0，他引：2
基于位移间断条件和间断位移刚性进化的单自由度动力系统,建立了一个弹塑性固体中间断位移的刚性进化分析模型,用于探讨岩土材料位移间断破坏的力学机制。首先,应用材料的强度理论,得到了弹塑性固体的位移间断条件。当位移间断出现后,完整固体分裂为两个部分,其中可滑移体部分可视作一个刚体,位移间断的进化依赖于间断面（界面）的刚度、界面与率和状态相关的摩擦律、动力输入等组成的一个单自由度系统。最后,给出了一个简单的摩擦型固体例子阐明模型的具体应用,重点说明了静、动转化过程和凝聚力丧失的进化输入。 相似文献
18.
We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well. 相似文献
19.
Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties
such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task.
Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to
overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable
before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference
have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering.
In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of
them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most
common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal
densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational
cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of
the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally,
a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared
with the ones computed by the maximum likelihood estimation approach. 相似文献
20.
Yalchin Efendiev Akhil Datta-Gupta Xianlin Ma Bani Mallick 《Mathematical Geosciences》2008,40(2):213-232
In this paper, the Markov Chain Monte Carlo (MCMC) approach is used for sampling of the permeability field conditioned on
the dynamic data. The novelty of the approach consists of using an approximation of the dynamic data based on streamline computations.
The simulations using the streamline approach allows us to obtain analytical approximations in the small neighborhood of the
previously computed dynamic data. Using this approximation, we employ a two-stage MCMC approach. In the first stage, the approximation
of the dynamic data is used to modify the instrumental proposal distribution. The obtained chain correctly samples from the
posterior distribution; the modified Markov chain converges to a steady state corresponding to the posterior distribution.
Moreover, this approximation increases the acceptance rate, and reduces the computational time required for MCMC sampling.
Numerical results are presented. 相似文献