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1.
Statistical assignment of upscaled flow functions for an ensemble of geological models 总被引：1，自引：0，他引：1
Upscaled flow functions are often needed to account for the effects of fine-scale permeability heterogeneity in coarse-scale
simulation models. We present procedures in which the required coarse-scale flow functions are statistically assigned to an
ensemble of upscaled geological models. This can be viewed as an extension and further development of a recently developed
ensemble level upscaling (EnLU) approach. The method aims to efficiently generate coarse-scale flow models capable of reproducing
the ensemble statistics (e.g., cumulative distribution function) of fine-scale flow predictions for multiple reservoir models.
The most expensive part of standard coarsening procedures is typically the generation of upscaled two-phase flow functions
(e.g., relative permeabilities). EnLU provides a means for efficiently generating these upscaled functions using stochastic
simulation. This involves the use of coarse-block attributes that are both fast to compute and correlate closely with the
upscaled two-phase functions. In this paper, improved attributes for use in EnLU, namely the coefficient of variation of the
fine-scale single-phase velocity field (computed during computation of upscaled absolute permeability) and the integral range
of the fine-scale permeability variogram, are identified. Geostatistical simulation methods, which account for spatial correlations
of the statistically generated upscaled functions, are also applied. The overall methodology thus enables the efficient generation
of coarse-scale flow models. The procedure is tested on 3D well-driven flow problems with different permeability distributions
and variable fluid mobility ratios. EnLU is shown to capture the ensemble statistics of fine-scale flow results (water and
oil flow rates as a function of time) with similar accuracy to full flow-based upscaling methods but with computational speedups
of more than an order of magnitude. 相似文献
2.
We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities
or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an
initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global
(LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce
flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued
until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of
LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore,
the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a
new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG
over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration
of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative
to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another
attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is,
the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic
boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic
refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured
grids. 相似文献
3.
Modern geostatistical techniques allow the generation of high-resolution heterogeneous models of hydraulic conductivity containing millions to billions of cells. Selective upscaling is a numerical approach for the change of scale of fine-scale hydraulic conductivity models into coarser scale models that are suitable for numerical simulations of groundwater flow and mass transport. Selective upscaling uses an elastic gridding technique to selectively determine the geometry of the coarse grid by an iterative procedure. The geometry of the coarse grid is built so that the variances of flow velocities within the coarse blocks are minimum. Selective upscaling is able to handle complex geological formations and flow patterns, and provides full hydraulic conductivity tensor for each block. Selective upscaling is applied to a cross-bedded formation in which the fine-scale hydraulic conductivities are full tensors with principal directions not parallel to the statistical anisotropy of their spatial distribution. Mass transport results from three coarse-scale models constructed by different upscaling techniques are compared to the fine-scale results for different flow conditions. Selective upscaling provides coarse grids in which mass transport simulation is in good agreement with the fine-scale simulations, and consistently superior to simulations on traditional regular (equal-sized) grids or elastic grids built without accounting for flow velocities. 相似文献
4.
Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be “upscaled” to one “equivalent homogeneous” coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented. 相似文献
5.
The multiscale finite-volume (MSFV) method has been developed to solve multiphase flow problems on large and highly heterogeneous
domains efficiently. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure
problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure
and obtain an approximate fine-scale pressure distribution. However, if flow takes place in presence of gravity (or capillarity),
the basis functions are not good interpolators. To treat this case correctly, a correction function is added to the basis
function interpolated pressure. This function, which is similar to a supplementary basis function independent of the coarse-scale
pressure, allows for a very accurate fine-scale approximation. In the coarse-scale pressure equation, it appears as an additional
source term and can be regarded as a local correction to the coarse-scale operator: It modifies the fluxes across the coarse-cell
interfaces defined by the basis functions. Given the closure assumption that localizes the pressure problem in a dual cell,
the derivation of the local problem that defines the correction function is exact, and no additional hypothesis is needed.
Therefore, as in the original MSFV method, the only closure approximation is the localization assumption. The numerical experiments
performed for density-driven flow problems (counter-current flow and lock exchange) demonstrate excellent agreement between
the MSFV solutions and the corresponding fine-scale reference solutions. 相似文献
6.
The aim of upscaling is to determine equivalent homogeneous parameters at a coarse-scale from a spatially oscillating fine-scale parameter distribution. To be able to use a limited number of relatively large grid-blocks in numerical oil reservoir simulators or groundwater models, upscaling of the permeability is frequently applied. The spatial fine-scale permeability distribution is generally obtained from geological and geostatistical models. After upscaling, the coarse-scale permeabilities are incorporated in the relatively large grid-blocks of the numerical model. If the porous rock may be approximated as a periodic medium, upscaling can be performed by the method of homogenization. In this paper the homogenization is performed numerically, which gives rise to an approximation error. The complementarity between two different numerical methods – the conformal-nodal finite element method and the mixed-hybrid finite element method – has been used to quantify this error. These two methods yield respectively upper and lower bounds for the eigenvalues of the coarse-scale permeability tensor. Results of 3D numerical experiments are shown, both for the far field and around wells. 相似文献
7.
Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior
is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal
with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model).
Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit
algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation).
The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous
elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities.
The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/
sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary
pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local
problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute
the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz
iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of
nonlinear compressible multiphase flow in strongly heterogeneous formations. 相似文献
8.
Homogenization has proved its effectiveness as a method of upscaling for linear problems, as they occur in single-phase porous media flow for arbitrary heterogeneous rocks. Here we extend the classical homogenization approach to nonlinear problems by considering incompressible, immiscible two-phase porous media flow. The extensions have been based on the principle of preservation of form, stating that the mathematical form of the fine-scale equations should be preserved as much as possible on the coarse scale. This principle leads to the required extensions, while making the physics underlying homogenization transparent. The method is process-independent in a way that coarse-scale results obtained for a particular reservoir can be used in any simulation, irrespective of the scenario that is simulated. Homogenization is based on steady-state flow equations with periodic boundary conditions for the capillary pressure. The resulting equations are solved numerically by two complementary finite element methods. This makes it possible to assess a posteriori error bounds. 相似文献
9.
Emil M. Constantinescu Adrian Sandu Gregory R. Carmichael 《Computational Geosciences》2008,12(2):133-151
We discuss an adaptive resolution system for modeling regional air pollution based on the chemical transport model STEM. The
grid adaptivity is implemented using the generic adaptive mesh refinement tool Paramesh, which enables the grid management
operations while harnessing the power of parallel computers. The computational algorithm is based on a decomposition of the
domain, with the solution in different subdomains being computed with different spatial resolutions. Various refinement criteria
that adaptively control the fine grid placement are analyzed to maximize the solution accuracy while maintaining an acceptable
computational cost. Numerical experiments in a large-scale parallel setting (~0.5 billion variables) confirm that adaptive
resolution, based on a well-chosen refinement criterion, leads to the decrease in spatial error with an acceptable increase
in computational time. Fully dynamic grid adaptivity for air quality models is relatively new. We extend previous work on
chemical and transport modeling by using dynamically adaptive grid resolution. Advantages and shortcomings of the present
approach are also discussed. 相似文献
10.
Alexandre Boucher 《Mathematical Geosciences》2009,41(3):265-290
Super-resolution or sub-pixel mapping is the process of providing fine scale land cover maps from coarse-scale satellite sensor
information. Such a procedure calls for a prior model depicting the spatial structures of the land cover types. When available,
an analog of the underlying scene (a training image) may be used for such a model. The single normal equation simulation algorithm
(SNESIM) allows extracting the relevant pattern information from the training image and uses that information to downscale
the coarse fraction data into a simulated fine scale land cover scene. Two non-exclusive approaches are considered to use
training images for super-resolution mapping. The first one downscales the coarse fractions into fine-scale pre-posterior
probabilities which is then merged with a probability lifted from the training image. The second approach pre-classifies the
fine scale patterns of the training image into a few partition classes based on their coarse fractions. All patterns within
a partition class are recorded by a search tree; there is one tree per partition class. At each fine scale pixel along the
simulation path, the coarse fraction data is retrieved first and used to select the appropriate search tree. That search tree
contains the patterns relevant to that coarse fraction data. To ensure exact reproduction of the coarse fractions, a servo-system
keeps track of the number of simulated classes inside each coarse fraction. Being an under-determined stochastic inverse problem,
one can generate several super resolution maps and explore the space of uncertainty for the fine scale land cover. The proposed
SNESIM sub-pixel resolution mapping algorithms allow to: (i) exactly reproduce the coarse fraction, (ii) inject the structural
model carried by the training image, and (iii) condition to any available fine scale ground observations. Two case studies
are provided to illustrate the proposed methodology using Landsat TM data from southeast China. 相似文献
11.
The MultiScale Finite Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and thus, the resulting approximate fine-scale solution. Detection of non-physical transmissibility coefficients that lead to non-monotone solutions is achieved using local information only and is performed algebraically. For these ‘critical’ primal coarse-grid interfaces, a monotone local flux approximation, specifically, a Two-Point Flux Approximation (TPFA), is employed. Alternatively, a local linear boundary condition can be used for the dual basis functions to reduce the degree of non-monotonicity. The local nature of the two strategies allows for ensuring monotonicity in local sub-regions, where the non-physical transmissibility occurs. For practical applications, an adaptive approach based on normalized positive off-diagonal coarse-scale transmissibility coefficients is developed. Based on the histogram of these normalized coefficients, one can remove the large peaks by applying the proposed modifications only for a small fraction of the primal coarse grids. Though the m-MSFV approach can guarantee monotonicity of the solutions to any desired level, numerical results illustrate that employing the m-MSFV modifications only for a small fraction of the domain can significantly reduce the non-monotonicity of the conservative MSFV solutions. 相似文献
12.
Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be upscaled to one equivalent homogeneous coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented. 相似文献
13.
A multi-resolution workflow to generate high-resolution models constrained to dynamic data 总被引：2，自引：0，他引：2
Céline Scheidt Jef Caers Yuguang Chen Louis J. Durlofsky 《Computational Geosciences》2011,15(3):545-563
Distance-based stochastic techniques have recently emerged in the context of ensemble modeling, in particular for history
matching, model selection and uncertainty quantification. Starting with an initial ensemble of realizations, a distance between
any two models is defined. This distance is defined such that the objective of the study is incorporated into the geological
modeling process, thereby potentially enhancing the efficacy of the overall workflow. If the intent is to create new models
that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for each
model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present
a multi-resolution framework for ensemble modeling. A distance-based procedure is employed, with emphasis on the rapid construction
of multiple models that have improved dynamic data conditioning. Our intent is to construct new high-resolution models constrained
to dynamic data, while performing most of the flow simulations only on upscaled models. An error modeling procedure is introduced
into the distance calculations to account for potential errors in the upscaling. Based on a few fine-scale flow simulations,
the upscaling error is estimated for each model using a clustering technique. We demonstrate the efficiency of the method
on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show
that the error modeling procedure can accurately capture the error in upscaling, and can thus reproduce the fine-scale flow
behavior from coarse-scale simulations with sufficient accuracy (in terms of uncertainty predictions). As a consequence, an
ensemble of high-resolution models, which are constrained to dynamic data, can be obtained, but with a minimum of flow simulations
at the fine scale. 相似文献
14.
Large-scale flow models constructed using standard coarsening procedures may not accurately resolve detailed near-well effects.
Such effects are often important to capture, however, as the interaction of the well with the formation can have a dominant
impact on process performance. In this work, a near-well upscaling procedure, which provides three-phase well-block properties,
is developed and tested. The overall approach represents an extension of a recently developed oil–gas upscaling procedure
and entails the use of local well computations (over a region referred to as the local well model (LWM)) along with a gradient-based
optimization procedure to minimize the mismatch between fine and coarse-scale well rates, for oil, gas, and water, over the
LWM. The gradients required for the minimization are computed efficiently through solution of adjoint equations. The LWM boundary
conditions are determined using an iterative local-global procedure. With this approach, pressures and saturations computed
during a global coarse-scale simulation are interpolated onto LWM boundaries and then used as boundary conditions for the
fine-scale LWM computations. In addition to extending the overall approach to the three-phase case, this work also introduces
new treatments that provide improved accuracy in cases with significant flux from the gas cap into the well block. The near-well
multiphase upscaling method is applied to heterogeneous reservoir models, with production from vertical and horizontal wells.
Simulation results illustrate that the method is able to accurately capture key near-well effects and to provide predictions
for component production rates that are in close agreement with reference fine-scale results. The level of accuracy of the
procedure is shown to be significantly higher than that of a standard approach which uses only upscaled single-phase flow
parameters. 相似文献
15.
K.-A. Lie O. Møyner J. R. Natvig A. Kozlova K. Bratvedt S. Watanabe Z. Li 《Computational Geosciences》2017,21(5-6):981-998
For the past 10 years or so, a number of so-called multiscale methods have been developed as an alternative approach to upscaling and to accelerate reservoir simulation. The key idea of all these methods is to construct a set of prolongation operators that map between unknowns associated with cells in a fine grid holding the petrophysical properties of the geological reservoir model and unknowns on a coarser grid used for dynamic simulation. The prolongation operators are computed numerically by solving localized flow problems, much in the same way as for flow-based upscaling methods, and can be used to construct a reduced coarse-scale system of flow equations that describe the macro-scale displacement driven by global forces. Unlike effective parameters, the multiscale basis functions have subscale resolution, which ensures that fine-scale heterogeneity is correctly accounted for in a systematic manner. Among all multiscale formulations discussed in the literature, the multiscale restriction-smoothed basis (MsRSB) method has proved to be particularly promising. This method has been implemented in a commercially available simulator and has three main advantages. First, the input grid and its coarse partition can have general polyhedral geometry and unstructured topology. Secondly, MsRSB is accurate and robust when used as an approximate solver and converges relatively fast when used as an iterative fine-scale solver. Finally, the method is formulated on top of a cell-centered, conservative, finite-volume method and is applicable to any flow model for which one can isolate a pressure equation. We discuss numerical challenges posed by contemporary geomodels and report a number of validation cases showing that the MsRSB method is an efficient, robust, and versatile method for simulating complex models of real reservoirs. 相似文献
16.
扩展有限元法模拟裂纹时独立于网格,因此该方法是目前求解裂纹问题最有效的数值方法。为了在计算代价不大的情况,实现大型结构分析中考虑小裂纹或提高裂纹附近精度,在裂纹附近一般采用小尺度单元,其他区域采用大尺度单元。提出了分析三维裂纹问题的多尺度扩展有限元法,在需要的地方采用小尺度单元。基于点插值构造了六面体任意节点单元。所有尺度单元都采用8节点六面体单元,这样六面体任意节点单元可方便有效地连接不同尺度单元。采用互作用积分法计算三维应力强度因子。边裂纹和中心圆裂纹算例分析结果表明,该方法是正确和有效的。 相似文献
17.
18.
Particle-tracking simulation offers a fast and robust alternative to conventional numerical discretization techniques for modeling solute transport in subsurface formations. A common challenge is that the modeling scale is typically much larger than the volume scale over which measurements of rock properties are made, and the scale-up of measurements have to be made accounting for the pattern of spatial heterogeneity exhibited at different scales. In this paper, a statistical scale-up procedure developed in our previous work is adopted to estimate coarse-scale (effective) transition time functions for transport modeling, while two significant improvements are proposed: considering the effects of non-stationarity (trend), as well as unresolved (residual) heterogeneity below the fine-scale model. Rock property is modeled as a multivariate random function, which is decomposed into the sum of a trend (which is defined at the same resolution of the transport modeling scale) and a residual (representing all heterogeneities below the transport modeling scale). To construct realizations of a given rock property at the transport modeling scale, multiple realizations of the residual components are sampled. Next, a flow-based technique is adopted to compute the effective transport parameters: firstly, it is assumed that additional unresolved heterogeneities occurring below the fine scale can be described by a probabilistic transit time distribution; secondly, multiple realizations of the rock property, with the same physical size as the transport modeling scale, are generated; thirdly, each realization is subjected to particle-tracking simulation; finally, probability distributions of effective transition time function are estimated by matching the corresponding effluent history for each realization with an equivalent medium consisting of averaged homogeneous rock properties and aggregating results from all realizations. The proposed method is flexible that it does not invoke any explicit assumption regarding the multivariate distribution of the heterogeneity. 相似文献
19.
地球空间数据集成多尺度问题基础研究 总被引：21，自引：0，他引：21
多尺度数据集成是地球空间数据集成中最难处理的问题。将多尺度数据的集成分解为空间和时间多尺度数据集成,在分析应用项目对数据尺度需求的基础上,就两种多尺度数据集成的传统和数据意义上的集成方法进行了详细的探讨。 相似文献