共查询到20条相似文献，搜索用时 25 毫秒
1.
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
2.
Modeling semi-steady state near-well flow performance for horizontal wells in anisotropic reservoirs
This paper presents a novel methodology to model semi-steady state horizontal well flow performance in an anisotropic reservoir taking into account flow in the near-well region for an arbitrary well trajectory. It is based on an analytical productivity model describing coupled axial reservoir flow and radial well inflow. In order to apply this model in an anisotropic reservoir, the permeability field relative to the radial direction perpendicular to the well trajectory and the axial direction along the well trajectory must first be determined. A classical space transformation is used in concert with rotational transforms to obtain a virtual isotropic model. The transformation preserves the volumes and pressures. It is not a novel concept, but different from previous approaches in the sense that it is only applied in the near-well domain to formulate an equally isotropic media. As a result, the use of this virtual isotropic model requires the Dietz shape factor for an ellipse, transformed from the original cylindrical near-well domain. The Dietz shape factors are determined numerically in this research. The semi-steady state well/near-well model is implemented in a numerical simulator incorporating formation anisotropy and wellbore hydraulics. The specific productivity index along the well trajectory is generated using the virtual configuration. Numerical results for different anisotropy ratios and also incorporating frictional losses in the well are presented. Furthermore, the well/near-well model is applied in coupling with streamline reservoir model for a water flooding case. This appears to be the first coupling of a well hydraulics model and a streamline simulator. It presents the application of the well/near-well model in integrated reservoir simulation in an efficient and accurate manner. The results demonstrate that the coupling approach with a streamline reservoir model and the well/near-well is of great potential for advanced well simulation efficiently. 相似文献
3.
In this article we present a series of tests to study how well suited the TPFA coefficient matrix is as a preconditioner for the MPFA discrete system of equations in an iterative solver, using a flux splitting method. These tests have been conducted for single-phase flow for a wide range of anisotropy, heterogeneity, and grid skewness (mainly parallelogram grids). We use the K-orthogonal part of the MPFA transmissibilities for a parallelogram grid to govern the TPFA transmissibilities. The convergence of the flux splitting method is for each test case measured by the spectral radius of the iteration matrix. 相似文献
4.
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
5.
Eirik Keilegavlen Jeremy E. Kozdon Bradley T. Mallison 《Computational Geosciences》2012,16(4):1021-1042
The governing equations for multiphase flow in porous media have a mixed character, with both nearly elliptic and nearly hyperbolic variables. The flux for each phase can be decomposed into two parts: (1) a geometry- and rock-dependent term that resembles a single-phase flux; and (2) a mobility term representing fluid properties and rock–fluid interactions. The first term is commonly discretized by two- or multipoint flux approximations (TPFA and MPFA, respectively). The mobility is usually treated with single-point upstream weighting (SPU), also known as dimensional or donor cell upstream weighting. It is well known that when simulating processes with adverse mobility ratios, SPU suffers from grid orientation effects. An important example of this, which will be considered in this work, is the displacement of a heavy oil by water. For these adverse mobility ratio flows, the governing equations are unstable at the modeling scale, rendering a challenging numerical problem. These challenges must be addressed in order to avoid systematic biasing of simulation results. In this work, we present a framework for multidimensional upstream weighting for multiphase flow with buoyancy on general two-dimensional grids. The methodology is based on a dual grid, and the resulting transport methods are provably monotone. The multidimensional transport methods are coupled with MPFA methods to solve the pressure equation. Both explicit and fully implicit approaches are considered for time integration of the transport equations. The results show considerable reduction of grid orientation effects compared to SPU, and the explicit multidimensional approach allows larger time steps. For the implicit method, the total number of non-linear iterations is also reduced when multidimensional upstream weighting is used. 相似文献
6.
This paper extends the multipoint flux-approximation (MPFA) control-volume method to quadrilateral grids for which the adjacent cells do not necessarily share corners. Examples are grids with faults and locally refined grids. This paper gives a derivation of the method for such grids. The difference between two-point flux-approximation (TPFA) results and MPFA results for faults and local grid refinements is demonstrated for synthetic problems. Further, the results are compared with results from uniform fine-grid simulations. The effect of repeated fault patterns as well as anisotropy is investigated. Large errors may be found for the TPFA method for flow through a series of faults in an anisotropic medium. Finally, a comparison is done for a reservoir field application. 相似文献
7.
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
8.
In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system.
A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic
transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase
flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase
flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system. 相似文献
9.
In this paper, we present a computational framework for the simulation of coupled flow and reservoir geomechanics. The physical
model is restricted to Biot’s theory of single-phase flow and linear poroelasticity, but is sufficiently general to be extended
to multiphase flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization
of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that
these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space
discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure
stability and robustness, we perform an implicit time integration of the fluid flow equations. (2) The strategies for the
solution of the coupled system. We compare different solution strategies, including the fully coupled approach, the usual
(conditionally stable) iteratively coupled approach, and a less common unconditionally stable sequential scheme. We show that
the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational
model has been implemented in an object-oriented reservoir simulator, whose modular design allows for further extensions and
enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach. 相似文献
10.
减饱和法是一种通过减小饱和砂土地基中水的饱和度来处置可液化砂土地基的方法。基于单相流-固耦合理论,将减饱和砂中水-气两相流体等效为单相流体,提出一种可以考虑加载过程中孔隙流体体积模量变化的减饱和砂土静态液化的单相流改进算法,用其进行单调荷载作用下三轴不排水压缩试验数值模拟研究,分析了不同饱和度条件下的减饱和砂土的不排水反应并与饱和砂土三轴不排水试验结果进行对比。研究结果表明,单相流改进算法能够很好地反映减饱和法的抗液化特性。此外,对比不同数值分析方法模拟结果,得出以下结论：采用单相流简化算法分析减饱和砂土的不排水反应时,因为不考虑加载过程中的孔隙流体体积模量变化,所以初始的流体体积模量取值会影响减饱和砂土的强度,初始围压为100 kPa、饱和度为96%的减饱和砂土在单调荷载作用下,气体体积模量取值从100 kPa增加至200 kPa时,减饱和砂试样的峰值偏应力会减小约30%,孔隙压力会增加约40%;通过对比同等条件下的单相流改进算法和两相流算法的应力-应变关系曲线以及饱和度和体积应变变化曲线,两者结果相近,误差在5%以内。综上所述,单相流改进算法是一种较为合理而简洁地模拟减饱和砂土静态液化的计算方法。 相似文献
11.
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
12.
Downhole electrical heating can be used to achieve the high temperatures required for in situ upgrading of oil shale or oil
sands. Heater-well models are needed if this process is to be simulated accurately. The traditional Peaceman approach used
for fluid injection and production wells may not be applicable because it does not capture transient effects, which can be
important in downhole heater models. Standard models also neglect the effects of heterogeneity and temperature dependence
in the rock properties. Here, we develop two new models for representing heater wells in reservoir simulators. The first model
is applicable for homogeneous systems with properties that are not temperature dependent. For such cases, we develop a semi-analytical
procedure based on Green’s functions to construct time-dependent heater-well indexes and heater-block thermal transmissibilities.
For the general case, which can include both fine-scale heterogeneity and nonlinearity due to the temperature dependence of
rock properties, we present a numerical procedure for constructing the heater-well model. This technique is essentially a
near-well upscaling method and requires a local fine-scale solution in the near-well region. The boundary conditions are determined
using a local-global treatment. The accuracy of the new heater-well models is demonstrated through comparison to reference
solutions for example problems. The approach is then applied for the coarse-scale modeling of the in situ upgrading of oil
shale, which entails a thermal-compositional simulation with chemical reactions. The model is shown to provide an accurate
and efficient solution for this challenging problem. 相似文献
13.
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
14.
?ystein Pettersen 《Computational Geosciences》2012,16(2):211-230
The layering in reservoir simulation grids is often based on the geology, e.g., structure tops. In this paper we investigate
the alternative of using horizontal layers, where the link to the geology model is by the representation of the petrophysics
alone. The obvious drawback is the failure to honor the structure in the grid geometry. On the other hand, a horizontal grid
will honor the initial fluid contacts perfectly, and horizontal wells can also be accurately represented. Both these issues
are vital in thin oil-zone problems, where horizontal grids may hence be a viable alternative. To investigate this question,
a number of equivalent simulation models were built for a segment of the Troll Field, both geology-based and horizontal, and
various combinations of these. In the paper, it is demonstrated that the horizontal grid was able to capture the essentials
of fluid flow with the same degree of accuracy as the geology-based grid, and near-well flow was considerably more accurate.
For grids of comparable resolution, more reliable results were obtained by a horizontal grid than a geo-grid. A geo-grid with
local grid refinement and a horizontal grid produced almost identical results, but the ratio of computing times was almost
20 in favor of the horizontal grid. In the one-phase regions of the reservoir, relatively coarse cells can be used without
significant loss of accuracy. 相似文献
15.
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
16.
We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs.
The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates
in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of
a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure
of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological
model. As such, the method is a multiscale one that preserves all the important information across all the relevant length
scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing
method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly
reduced computational cost. The speed-up in the computations is up to over three orders of magnitude, depending on the degree
of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including
one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and
without the capillary pressure. 相似文献
17.
Pore-scale models are becoming increasingly useful as predictive tools for modeling flow and transport in porous media. These
models can accurately represent the 3D pore-structure of real media. Currently first-principles modeling methods are being
employed for obtaining qualitative and quantitative behavior. Generally, artificial, simple boundary conditions are imposed
on a model that is used as a stand-alone tool for extracting macroscopic parameters. However, realistic boundary conditions,
reflecting flow and transport in surrounding media, may be necessary for behavior that occurs over larger length scales or
including pore-scale models in a multiscale setting. Here, pore-scale network models are coupled to adjacent media (additional
pore-scale or continuum-scale models) using mortars. Mortars are 2D finite-element spaces employed to couple independent subdomains
by enforcing continuity of pressure and flux at shared boundary interfaces. While mortars have been used in the past to couple
subdomains of different models, physics, and meshes, they are extended here for the first time to pore-scale models. The approach
is demonstrated by modeling single-phase flow in coupled pore-scale models, but the methodology can be utilized to model dynamic
processes and perform multiscale modeling in 3D continuum simulators for flow and transport. 相似文献
18.
The Oberbeck-Boussinesq (OB) approximation is widely employed as a simplifying assumption for density-dependent flow problems. It reduces the governing differential equations to simpler forms, which can be handled analytically or numerically. In this study, a modified OB model is formulated to account for the variation of rock permeability and porosity with temperature during the hot fluid injection process in an oil-saturated porous medium under the assumption of local thermal equilibrium (LTE). The mathematical model is solved numerically using a fully implicit control volume finite difference discretization with the successive over relaxation (SOR) method to handle the non-linearity. Subsequently, the numerical model is validated with the analytical solution of the simplified problem successfully. Through detailed sensitivity analyses, the simulation results reveal the hot fluid injection rate as the most important operational parameter to be optimized for a successful thermal flood. The numerical runs show that that for single-phase core-flood simulation, the effect of temperature on the rock absolute permeability and porosity can be neglected without introducing any significant errors in the estimated recovery and temperature profile. 相似文献
19.
Louis J. Durlofsky 《Mathematical Geology》2000,32(4):421-438
20.
J.D. Jansen 《Computational Geosciences》2002,6(2):195-206
This paper concerns the computation of near-well flow in numerical reservoir simulation with unstructured grids. In particular, it uses spherical trigonometry to derive analytical expressions for the flow towards a well modeled as either a number of point sources or a constant-flux line source. The expression for the point source representation is based on projections of the grid block boundaries on spheres with unit radius around the sources. The expression for the line source is based on projection on a prolate spheroid. The computation of the surface area is done through transformation to prolate spheroidal coordinates and subsequent projection on a sphere at infinity. The point source expression for a single source is exact for grid block boundaries with straight edges; the line source expression is an approximation. Both representations are fully volume conserving, such that the sum of the fluxes through the grid block boundaries surrounding a source adds up exactly to the total source flow rate. Both representations can be used to accurately model complicated wells in the form of segments. The point source representation is simpler to implement and not necessarily less accurate than the line source representation. 相似文献