共查询到20条相似文献，搜索用时 250 毫秒
1.
包气带水分入渗过程受多种因素的影响。定量研究层状非均质岩性结构和入渗速率对其影响,有助于解决根据不同条件选择单相流模型或水气二相流模型模拟包气带水分入渗过程的问题。结合填埋场等场地地层条件及污废水入渗特征,分别建立了“上细下粗”和“上粗下细”包气带层状非均质岩性结构水分入渗单相流和水气二相流模型,探讨不同层状非均质岩性结构条件下模型的适用性。在“上粗下细”岩性结构模型基础上,进一步探究入渗速率对水气两相运移结果的影响。基于论文模型研究表明:（1）在包气带岩性结构为“上细下粗”的条件下,气相的影响基本可以忽略,可直接采用单相流模型对包气带水分运移进行模拟;在“上粗下细”岩性结构和本次模型设定的底部压力保持不变及污废水泄漏前场地未接受降水入渗补给等条件下,当包气带上下层介质渗透率比值大于16倍时,气相会对水相运移产生明显影响,且下层介质渗透率越小、上下层介质渗透率比值越大,单相流与两相流的运移结果差别越大,需要采用水气二相流模型模拟包气带水分运移。（2）在包气带“上粗下细”岩性结构条件下,入渗速率越大,气相对水流入渗的阻滞作用越明显,此时包气带水分运移模拟应采用水气二相流模型。 相似文献
2.
3.
Method for Stochastic Inverse Modeling of Fault Geometry and Connectivity Using Flow Data 总被引：1，自引：1，他引：0
This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect the numerical simulation
of physical processes. Our goal is to use dynamic data and process-based simulation to update structural uncertainty in a
Bayesian inverse approach. We propose a stochastic fault model where the number and features of faults are made variable.
In particular, this model samples uncertainties about connectivity between the faults. The stochastic three dimensional fault
model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and
fault zone layout, by minimizing the mismatch between observed and simulated data. 相似文献
4.
5.
In this paper, we introduce a novel stochastic model for the permeability tensor associated with stationary random porous media. In the light of recent works on mesoscale modeling of permeability, we first discuss the physical interpretation of the permeability tensor randomness. Subsequently, we propose a nonparametric prior probabilistic model for non‐Gaussian permeability tensor random fields, making use of the information theory and a maximum entropy procedure, and provide a physical interpretation of the model parameters. Finally, we demonstrate the capability of the considered class of random fields to generate higher levels of statistical fluctuations for selected stochastic principal permeabilities. This unique flexibility offered by the parameterization of the model opens up many new possibilities for both forward simulations (e.g. for uncertainty propagation in predictive simulations) and stochastic inverse problem solving. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
7.
In subsurface flow modeling, compositional simulation is often required to model complex recovery processes, such as gas/CO 2 injection. However, compositional simulation on fine-scale geological models is still computationally expensive and even prohibitive. Most existing upscaling techniques focus on black-oil models. In this paper, we present a general framework to upscale two-phase multicomponent flow in compositional simulation. Unlike previous studies, our approach explicitly considers the upscaling of flow and thermodynamics. In the flow part, we introduce a new set of upscaled flow functions that account for the effects of compressibility. This is often ignored in the upscaling of black-oil models. In the upscaling of thermodynamics, we show that the oil and gas phases within a coarse block are not at chemical equilibrium. This non-equilibrium behavior is modeled by upscaled thermodynamic functions, which measure the difference between component fugacities among the oil and gas phases. We apply the approach to various gas injection problems with different compositional features, permeability heterogeneity, and coarsening ratios. It is shown that the proposed method accurately reproduces the averaged fine-scale solutions, such as component overall compositions, gas saturation, and density solutions in the compositional flow. 相似文献
8.
9.
Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow 总被引：1，自引：0，他引：1
Todd Arbogast 《Computational Geosciences》2002,6(3-4):453-481
We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique. 相似文献
10.
Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in
heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches
in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented
and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails
solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse
scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred
to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale
well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional
models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over
a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement
to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of
parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine
scale solutions in near-well scale-up calculations. 相似文献
11.
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast. 相似文献
12.
13.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
14.
Numerical approximation based on different forms of the governing partial differential equation can lead to significantly
different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently
modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations
for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure–saturation
and modified pressure–saturation are examined. Each of these three highly nonlinear formulations is approximated using finite
difference method and is linearized using both Picard and Newton–Raphson linearization approaches. Model simulations for several
test cases demonstrate that pressure based form provides better results compared to the pressure–saturation approach in terms
of CPU_time and the number of iterations. The modification of pressure–saturation approach improves accuracy of the results.
Also it is shown that the Newton–Raphson linearization approach performed better in comparison to the Picard iteration linearization
approach with the exception for in the pressure–saturation form. 相似文献
15.
Konstantin Brenner Mayya Groza Laurent Jeannin Roland Masson Jeanne Pellerin 《Computational Geosciences》2017,21(5-6):1075-1094
Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom. 相似文献
16.
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
17.
The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous media. 相似文献
18.
Flow of fluids and transport of solutes in porous media are subjects of wide interest in several fields of applications: reservoir
engineering, subsurface hydrology, chemical engineering, etc. In this paper we will study two-phase flow in a model consisting
of two different types of sediments. Here, the absolute permeability, the relative permeabilities and the capillary pressure
are discontinuous functions in space. This leads to interior boundary value problems at the interface between the sediments.
The saturation Sw will be discontinuous or experience large gradients at the interface. A new solution procedure for such problems will be
presented. The method combines the modified method of characteristics with a weak formulation where the basis functions are
discontinuous at the interior boundary. The modified method of characteristics will provide a good first approximation for
the jump in the discontinuous basis functions, which leads to a fast converging iterative solution scheme for the complete
problem.
The method has been implemented in a two-dimensional simulator, and results from numerical experiments will be presented.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
19.
When fluid flows in porous media under subsurface conditions, significant deformation can occur. Such deformation is dependent on structural and phase characteristics. In this paper, we investigate the effect of multiphase flow on the deformation of porous media at the pore scale by implementing a strongly coupled partitioned solver discretized with finite volume (FV) technique. Specifically, the role of capillary forces on grain deformation in porous media is investigated. The fluid and solid subdomains are meshed using unstructured independent grids. The model is applied for solving multiphase coupled equations and is capable of capturing pore scale physics during primary drainage by solving the Navier-Stokes equation and advecting fluid indicator function using volume of fluid (VOF) while the fluid is interacting with a nonlinear elastic solid matrix. The convergence of the coupled solver is accelerated by Aitken underrelaxation. We also reproduce geomechanical stress conditions, at the pore scale, by applying uniaxial stress on the solid while simultaneously solving the multiphase fluid-solid interaction problem to investigate the effect of external stress on fluid occupancy, velocity-field distribution, and relative permeability. We observe that the solid matrix exhibits elasto-capillary behavior during the drainage sequence. Relative permeability endpoints are shifted on the basis of the external stress exerted. 相似文献