共查询到20条相似文献，搜索用时 31 毫秒
1.
Subsurface flow models can exhibit strong full-tensor anisotropy due to either permeability or grid nonorthogonality effects.
Upscaling procedures, for example, generate full-tensor effects on the coarse scale even for cases in which the underlying
fine-scale permeability is isotropic. A multipoint flux approximation (MPFA) is often needed to accurately simulate flow for
such systems. In this paper, we present and apply a different approach, nonlinear two-point flux approximation (NTPFA), for
modeling systems with full-tensor effects. In NTPFA, transmissibility (which provides interblock connections) is determined
from reference global flux and pressure fields for a specific flow problem. These fields can be generated using either fully
resolved or approximate global simulations. The use of fully resolved simulations leads to an NTPFA method that corresponds
to global upscaling procedures, while the use of approximate simulations gives a method corresponding to recently developed
local–global techniques. For both approaches, NTPFA algorithms applicable to both single-scale full-tensor permeability systems
and two-scale systems are described. A unified framework is introduced, which enables single-scale and two-scale problems
to be viewed in a consistent manner. Extensive numerical results demonstrate that the global and local–global NTPFA techniques
provide accurate flow predictions over wide parameter ranges for both single-scale and two-scale systems, though the global
procedure is more accurate overall. The applicability of NTPFA to the simulation of two-phase flow in upscaled models is also
demonstrated. 相似文献
2.
Trond Mannseth 《Computational Geosciences》2007,11(1):59-72
We consider discretization on quadrilateral grids of an elliptic operator occurring, for example, in the pressure equation
for porous-media flow. In a realistic setting – with non-orthogonal grid, and anisotropic, heterogeneous permeability – special
discretization techniques are required. Mixed finite element (MFE) and multipoint flux approximation (MPFA) are two methods
that can handle such situations. Previously, a framework for analytical comparison of MFE and MPFA in special cases has been
suggested. A comparison of MFE and MPFA-O (one of two main variants of MPFA) for isotropic, homogeneous permeability on a
uniformly distorted grid was also performed. In the current paper, we utilize the suggested framework in a slightly different
manner to analyze and compare MFE, MPFA-O and MPFA-U (the second main variant of MPFA). We reconsider the case previously
analyzed. We also consider the case of generally anisotropic, homogeneous permeability on an orthogonal grid. 相似文献
3.
In this work, lowest-order Raviart–Thomas and Brezzi–Douglas–Marini mixed methods are considered for groundwater flow simulations.
Typically, mixed methods lead to a saddle-point problem, which is expensive to solve. Two approaches are numerically compared
here to allow an explicit velocity elimination: (1) the well-known hybrid formulation leading to a symmetric positive definite
system where the only unknowns are the Lagrange multipliers and (2) a more recent approach, inspired from the multipoint flux
approximation method, reducing low-order mixed methods to cell-centered finite difference schemes. Selected groundwater flow
scenarios are used for the comparison between hybrid and multipoint approaches. The simulations are performed in the bidimensional
case with a general triangular discretization because of its practical interest for hydrogeologists. 相似文献
4.
We present a new nonlinear monotone finite volume method for diffusion equation and its application to two-phase flow model. We consider full anisotropic discontinuous diffusion or permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which provides the conventional seven-point stencil for the discrete diffusion operator on cubic meshes. We show that the quality of the discrete flux in a reservoir simulator has great effect on the front behavior and the water breakthrough time. We compare two two-point flux approximations (TPFA), the proposed nonlinear TPFA and the conventional linear TPFA, and multipoint flux approximation (MPFA). The new nonlinear scheme has a number of important advantages over the traditional linear discretizations. Compared to the linear TPFA, the nonlinear TPFA demonstrates low sensitivity to grid distortions and provides appropriate approximation in case of full anisotropic permeability tensor. For nonorthogonal grids or full anisotropic permeability tensors, the conventional linear TPFA provides no approximation, while the nonlinear flux is still first-order accurate. The computational work for the new method is higher than the one for the conventional TPFA, yet it is rather competitive. Compared to MPFA, the new scheme provides sparser algebraic systems and thus is less computational expensive. Moreover, it is monotone which means that the discrete solution preserves the nonnegativity of the differential solution. 相似文献
5.
James V. Lambers Margot G. Gerritsen Bradley T. Mallison 《Computational Geosciences》2008,12(3):399-416
We propose a new single-phase local upscaling method that uses spatially varying multipoint transmissibility calculations.
The method is demonstrated on two-dimensional Cartesian and adaptive Cartesian grids. For each cell face in the coarse upscaled
grid, we create a local fine grid region surrounding the face on which we solve two generic local flow problems. The multipoint
stencils used to calculate the fluxes across coarse grid cell faces involve the six neighboring pressure values. They are
required to honor the two generic flow problems. The remaining degrees of freedom are used to maximize compactness and to
ensure that the flux approximation is as close as possible to being two-point. The resulting multipoint flux approximations
are spatially varying (a subset of the six neighbors is adaptively chosen) and reduce to two-point expressions in cases without
full-tensor anisotropy. Numerical tests show that the method significantly improves upscaling accuracy as compared to commonly
used local methods and also compares favorably with a local–global upscaling method. 相似文献
6.
Ivar Aavatsmark 《Computational Geosciences》2007,11(3):199-206
Control-volume formulations for elliptic equations often use two-point flux stencils, even for skew grids. Any two-point flux
stencil may be interpreted as a multipoint flux stencil. This yields a definition of the permeability (or conductivity) tensor.
Formulas for calculating the permeability tensor, based on the user-specified quantities in the two-point flux stencil, are
given. Numerical test examples demonstrate the validity of the derivation.
相似文献
7.
Kernel Principal Component Analysis for Efficient,Differentiable Parameterization of Multipoint Geostatistics 总被引：6，自引：5，他引：1
This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale
non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex
geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied
to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion,
also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields
defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition
of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves
only the two-point statistics of a random field, which is insufficient for reproducing complex structures.
In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely
used in machine learning applications, it does not appear to have found any application for geological model parameterization.
With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance
matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels,
which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics
of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds
using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than
the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations
that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel
PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can
be used with gradient-based history matching to provide models that match production history while maintaining multipoint
geostatistics consistent with the underlying training image. 相似文献
8.
Małgorzata P. Kaleta Remus G. Hanea Arnold W. Heemink Jan-Dirk Jansen 《Computational Geosciences》2011,15(1):135-153
Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production
data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous
programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where
the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently,
the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order
forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the
linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function
is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate
of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method
was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching
procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational
efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where
the gradients are obtained with simple finite differences. 相似文献
9.
In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been
shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme
has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme
may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity
segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is
approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the
local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments. 相似文献
10.
We have used different techniques for permeability prediction using porosity core data from one well at the Maracaibo Lake,
Venezuela. One of these techniques is statistical and uses neuro-fuzzy concepts. Another has been developed by Pape et al.
(Geophysics 64(5):1447–1460, 1999), based on fractal theory and the Kozeny–Carman equations. We have also calculated permeability values using the empirical
model obtained in 1949 by Tixier and a simple linear regression between the logarithms of permeability and porosity. We have
used 100% of the permeability–porosity data to obtain the predictor equations in each case. The best fit, in terms of the
root mean-square error, was obtained with the statistical approach. The results obtained from the fractal model, the Tixier
equation or the linear approach do not improve the neuro-fuzzy results. We have also randomly taken 25% of the porosity data
to obtain the predictor equations. The increase of the input data density for the neuro-fuzzy approach improves the results,
as is expected for a statistical analysis. On the contrary, for the physical model based on the fractal theory, the decrease
in the data density could allow reaching the ideal theoretical Kozeny–Carman model, on which are based the fractal equations,
and hence, the permeability prediction using these expressions is improved. 相似文献
11.
Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting. 相似文献
12.
13.
Modeling the effects of completion techniques and formation heterogeneity on CO2 sequestration in shallow and deep saline aquifers 总被引：1，自引：1，他引：0
This work studied the effect of completion techniques and reservoir heterogeneity on CO2 storage and injectivity in saline aquifers using a compositional reservoir simulator, CMG-GEM. Two reservoir models were
built based on the published data to represent a deep saline aquifer and a shallow aquifer. The effect of various completion
conditions on CO2 storage was then discussed, including partial perforation of the reservoir net pay (partial completion), well geometry, orientation,
location, and length. The heterogeneity effect was addressed by considering three parameters: mean permeability, the vertical
to horizontal permeability ratio, and permeability variation. Sensitivity analysis was carried out using iSIGHT software (design
of experiments) to determine the dominant factors affecting CO2 storage capacity and injectivity. Simulation results show that the most favorable option is the perforation of all layers
with horizontal wells 250–300 m long set in the upper layers. Mean permeability has the most effect on CO2 storage capacity and injectivity; k
v/k
h affects CO2 injectivity storage capacity more than permeability variation, V
k. More CO2 can be stored in the heterogeneous reservoirs with low mean permeability; however, high injectivity can be achieved in the
uniform reservoirs with high mean permeability. 相似文献
14.
An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of
auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these
non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends
on the parameter τ, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities
directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general
arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper,
we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in
the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method
avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction
of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation
codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image
and in honouring the auxiliary data. 相似文献
15.
A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow
Clint Dawson 《Computational Geosciences》2008,12(4):451-472
We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations
and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of
flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods
is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity
and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for
a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified
LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical
and numerical aspects of surface–subsurface flow modeling are presented.
This work was supported by National Science Foundation grant DMS-0411413. 相似文献
16.
Computer models are commonly used by regulators and managers to make predictions regarding groundwater flow and contaminant
concentrations at various locations and times. However, the uncertainty associated with those predictions is often overlooked,
despite the fact that an assessment of such uncertainty is critical in the formulation of policy decisions. One method of
quantifying the uncertainty of model predictions, based on the collective uncertainties of the model parameter input values,
is to use an approximation of the three-point Gauss–Hermite quadrature formula. The Gauss–Hermite approximation is a convenient
substitute for simple Monte Carlo sampling, because it requires fewer model runs and provides an immediate sensitivity analysis
of parameter main effects and two-way interactions. For example, a model with four parameters, each with its own associated
uncertainty, needs to be run only 33 times to complete the Gauss–Hermite analysis. For an application to a contaminant-transport
model, the Gauss–Hermite approximation compares well to the full method, with considerable savings in computing effort. By
comparison, Latin hypercube sampling can be more flexible, but it is more complex to use in some circumstances and cannot
as easily generate the detailed sensitivity analysis that the Gauss–Hermite approach offers.
Received, October 1997 Revised, August 1998 Accepted, August 1998 相似文献
17.
复杂砂岩储层基于相控建模的渗透率计算方法 总被引：1，自引：0，他引：1
渗透率是油气储层评价的主要参数之一,复杂砂岩的储层岩性复杂,非均质性强,应用常规方法建立渗透率模型精度低,不能满足开发后期的需要。鉴于岩性对渗透率的影响作用,采用相控建模方法来计算渗透率,以能够反映岩性特征的测井参数作为划相参数。应用K~均值聚类法,进行测井相分析,依据岩性建立不同的渗透率模型,其相关性明显高于常规方法建立的渗透率解释模型,经计算得到的渗透率更接近于岩心分析数据。通过实际资料处理结果表明,经相控建模计算的渗透率方法,有效提高了渗透率计算精确度。 相似文献
18.
We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. 相似文献
19.
Basin Modeling in the Kuqa Depression of the Tarim Basin (Western China): A Fully Temperature-dependent Model of Overpressure History 总被引：1，自引：0，他引：1
Guangren Shi 《Mathematical Geosciences》2008,40(1):47-62
The fully temperature-dependent model of the effective pressure of the solid matrix and its related overpressure has been
derived from the pressure balance equation, mass conservation, and Darcy’s law, and is directly useful in basin modeling.
Application of the model in the Kuqa Depression of the Tarim Basin in western China proves that this overpressure model is
highly accurate. The case of the present-day values of the calculated overpressure histories of Wells Kela2 and Yinan2 approach
the field-measured data with mean absolute relative residuals of 3% and 5%, respectively. This indicates that the overpressure
simulation is a practical alternative to using rock mechanics experiments for effective pressure measurement. Since calculation
of the overpressure history uses the geohistory model and geothermal history model simulation outcomes, the relevant data
used and the output of the two models of the Kela2 well are given as examples.
The case studies show that the pore fluid density and viscosity used in the calculation of overpressures should be temperature-dependent,
otherwise the calculation results would deviate far from the field-measured pressure data. They also show that the most sensitive
parameter governing overpressure is permeability, and permeability can be calculated by using either the Kozeny–Carman formula
or the porosity–power function. The Kozeny–Carman formula is better if accurate data for the specific surface area of the
solid matrix (S
a
) exists, otherwise, the porosity–power function is used. Furthermore, it is vital for calculating an accurate overpressure
history that one can calibrate S
a
in the Kozeny–Carman formula, or index m in the porosity–power function by using field-measured pressure data as a constraint.
In these specific case studies, the outcome found by using the Kozeny–Carman formula approaches the outcome found by using
the porosity–power function with m=4, and both approach the field-measured pressure data. 相似文献
20.
Benjamin Faigle Rainer Helmig Ivar Aavatsmark Bernd Flemisch 《Computational Geosciences》2014,18(5):625-636
A sequential solution procedure is used to simulate compositional two-phase flow in porous media. We employ a multiphysics concept that adapts the numerical complexity locally according to the underlying processes to increase efficiency. The framework is supplemented by a local refinement of the simulation grid. To calculate the fluxes on such grids, we employ a combination of the standard two-point flux approximation and a multipoint flux approximation where the grid is refined. This is then used to simulate a large-scale example related to underground CO2 storage. 相似文献