scholarly journals Estimation of a Permeability Field within the Two-Phase Porous Media Flow Using Nonlinear Multigrid Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Tao Liu ◽  
Jie Song
Keyword(s):  
Porous Media ◽  
Multigrid Method ◽  
Computational Cost ◽  
Estimation Method ◽  
Porous Media Flow ◽  
Computational Accuracy ◽  
Two Phase ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Method ◽  
Permeability Field

Estimation of spatially varying permeability within the two-phase porous media flow plays an important role in reservoir simulation. Usually, one needs to estimate a large number of permeability values from a limited number of observations, so the computational cost is very high even for a single field-model. This paper applies a nonlinear multigrid method to estimate the permeability field within the two-phase porous media flow. Numerical examples are provided to illustrate the feasibility and effectiveness of the proposed estimation method. In comparison with other existing methods, the most outstanding advantage of this method is the computational efficiency, computational accuracy, and antinoise ability. The proposed method has a potential applicability to a variety of parameter estimation problems.

Multiscale estimation with spline wavelets, with application to two-phase porous-media flow

2000 ◽  
Vol 16 (2) ◽  
pp. 315-332 ◽  
Author(s):  
Geir Nævdal ◽  
Trond Mannseth ◽  
Kari Brusdal ◽  
Jan-Erik Nordtvedt
Keyword(s):  
Porous Media ◽  
Porous Media Flow ◽  
Two Phase ◽  
Spline Wavelets

Singular Perturbation Solution for a Two-Phase Stefan Problem in Outward Solidification

2019 ◽  
Author(s):  
Minghan Xu ◽  
Saad Akhtar ◽  
Mahmoud A. Alzoubi ◽  
Agus P. Sasmito
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Analytical Solution ◽  
Singular Perturbation ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Computational Cost ◽  
Perturbation Solution ◽  
Two Phase ◽  
Moving Boundary Condition

Abstract Mathematical modeling of phase change process in porous media can help ensure the efficient design and operation of thermal energy storage and pipe freezing. Numerical methods generally require high computational power to be applicable in practice. Therefore, it is of great interest to develop accurate and reliable analytical frameworks. This study proposes a singular perturbation solution for a two-phase Stefan problem that describes outward solidification in a finite annular space. The problem solves cylindrical heat conduction equations for both solid and liquid phases, with consideration of a moving boundary condition. Perturbation method takes the advantages of small Stefan number as the perturbation parameter, which intrinsically occurs in porous media. Furthermore, a boundary-fixing technique is used to remove nonlinearity in the moving boundary condition. Two different time scales are separately expanded and evaluated to facilitate the construction of a composite asymptotic solution. The analytical solution is verified against a general numerical model using enthalpy method and local volume-averaged thermal properties. The results indicate that the temperature profile of both phases can be well modeled by singular perturbation theory. The analytical solution is found to have similar conclusions to the numerical analysis with much lesser computational cost.

scholarly journals Complexity Reduction of Multiphase Flows in Heterogeneous Porous Media

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 144-151 ◽  
Author(s):  
Mehdi Ghommem ◽  
Eduardo Gildin ◽  
Mohammadreza Ghasemi
Keyword(s):  
Porous Media ◽  
Model Reduction ◽  
Flow Behavior ◽  
Computational Cost ◽  
Heterogeneous Porous Media ◽  
Production Optimization ◽  
Dynamic Mode ◽  
Two Phase ◽  
Fine Grid ◽  
Mode Decomposition

Summary In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in heterogeneous porous media. We propose intrusive and nonintrusive model-reduction approaches that enable a significant reduction in the size of the subsurface flow problem while capturing the behavior of the fully resolved solutions. In one approach, we use the dynamic mode decomposition. This approach does not require any modification of the reservoir simulation code but rather post-processes a set of global snapshots to identify the dynamically relevant structures associated with the flow behavior. In the second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper-orthogonal-decomposition modes. Furthermore, we use the discrete empirical interpolation method to approximate the mobility-related term in the global-system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE-10 benchmark permeability field, and present a numerical example in two-phase flow. One can efficiently use the proposed model-reduction methods in the context of uncertainty quantification and production optimization.

scholarly journals On a new Wigner-Ville distribution associated with linear canonical transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong-Cai Xin ◽  
Bing-Zhao Li
Keyword(s):  
Modulation Frequency ◽  
Computational Cost ◽  
Estimation Method ◽  
Superior Performance ◽  
Linear Canonical Transform ◽  
Two Phase ◽  
Cross Term ◽  
Time Frequency ◽  
Definition Of ◽  
Non Stationary Signal

AbstractLinear canonical transform as a general integration transform has been considered into Wigner-Ville distribution (WVD) to show more powerful ability for non-stationary signal processing. In this paper, a new WVD associated with linear canonical transform (WVDL) and integration form of WVDL (IWVDL) are presented. First, the definition of WVDL is derived based on new autocorrelation function and some properties are investigated in details. It removes the coupling between time and time delay and lays the foundation for signal analysis and processing. Then, based on the characteristics of WVDL over time-frequency plane, a new parameter estimation method, IWVDL, is proposed for linear modulation frequency (LFM) signal. Two phase parameters of LFM signal are estimated simultaneously and the cross term can be suppressed well by integration operator. Finally, compared with classical WVD, the simulation experiments are carried out to verify its better estimation and suppression of cross term ability. Error analysis and computational cost are discussed to show superior performance compared with other WVD in linear canonical transform domain. The further application in radar imaging field will be studied in the future work.

Efficient Uncertainty Quantification for Biotransport in Tumors With Uncertain Material Properties

2018 ◽  
Author(s):  
Alen Alexanderian ◽  
William Reese ◽  
Ralph C. Smith ◽  
Meilin Yu
Keyword(s):  
Porous Media ◽  
Random Field ◽  
Material Properties ◽  
Pressure Field ◽  
Input Parameter ◽  
Gaussian Random Field ◽  
Porous Media Flow ◽  
Expansion Technique ◽  
Low Dimensional ◽  
Permeability Field

We consider modeling of single phase fluid flow in heterogeneous porous media governed by elliptic partial differential equations (PDEs) with random field coefficients. Our target application is biotransport in tumors with uncertain heterogeneous material properties. We numerically explore dimension reduction of the input parameter and model output. In the present work, the permeability field is modeled as a log-Gaussian random field, and its covariance function is specified. Uncertainties in permeability are then propagated into the pressure field through the elliptic PDE governing porous media flow. The covariance matrix of pressure is constructed via Monte Carlo sampling. The truncated Karhunen–Loève (KL) expansion technique is used to decompose the log-permeability field, as well as the random pressure field resulting from random permeability. We find that although very high-dimensional representation is needed to recover the permeability field when the correlation length is small, the pressure field is not sensitive to high-oder KL terms of input parameter, and itself can be modeled using a low-dimensional model. Thus a low-rank representation of the pressure field in a low-dimensional parameter space is constructed using the truncated KL expansion technique.

Kinematical measurement of hydraulic tortuosity of fluid flow in porous media

2015 ◽  
Vol 26 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Y. Jin ◽  
J. B. Dong ◽  
X. Li ◽  
Y. Wu
Keyword(s):  
Porous Media ◽  
Flow Direction ◽  
Estimation Method ◽  
Mean Value ◽  
Calculation Model ◽  
Flow In Porous Media ◽  
Porous Media Flow ◽  
Average Value ◽  
The Mean ◽  
The Impact

It is hard to experimentally or analytically derive the hydraulic tortuosity (τ) of porous media flow because of their complex microstructures. In this work, we propose a kinematical measurement method for τ by introducing the concept of local tortuosity, which is defined as the ratio of fluid particle velocity to its component along the macro flow. And then, the calculation model of τ is analytically deduced in terms of that τ is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and τ is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-flow direction. The new estimation method is verified by flow through different types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by different methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic definition of hydraulic tortuosity is also proven.

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