scholarly journals Dynamic Coarsening and Local Reordered Nonlinear Solvers for Simulating Transport in Porous Media

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 2021-2040 ◽  
Author(s):  
Øystein S. Klemetsdal ◽  
Knut-Andreas Lie
Keyword(s):  
Field Model ◽  
Flow Equation ◽  
Transport Equations ◽  
Test Cases ◽  
Triangular Form ◽  
Solution Approach ◽  
Nonlinear Solver ◽  
Nonlinear Solvers ◽  
Sequential Solution ◽  
Original Grid

Summary We present a robust and flexible sequential solution approach in which the flow equation is solved on the original grid, whereas the transport equations are solved with a new dynamic coarsening method that adapts the grid resolution locally to reduce the number of cells as much as possible. The resulting grid is formed by combining precomputed coarse partitions of an underlying fine model. Our approach is flexible and makes very few assumptions on cell geometries and the topology of the grid. To further accelerate the transport step, we combine dynamic coarsening with a local nonlinear solver that permutes the discrete transport equations into an optimal block-triangular form so that these can be solved very efficiently using a nonlinear back-substitution method. Efficiency and utility of the overall approach are assessed through a number of conceptual test cases, including the Olympus field model.

Fast Simulation of Polymer Injection in Heavy-Oil Reservoirs on the Basis of Topological Sorting and Sequential Splitting

SPE Journal ◽  
2014 ◽  
Vol 19 (06) ◽  
pp. 991-1004 ◽  
Author(s):  
Knut-Andreas Lie ◽  
Halvor Møll Nilsen ◽  
Atgeirr Flø Rasmussen ◽  
Xavier Raynaud
Keyword(s):  
Single Point ◽  
Transport Equations ◽  
Phase System ◽  
Nonlinear Transport ◽  
Two Phase ◽  
Triangular Form ◽  
Polymer Injection ◽  
Nonlinear Solver ◽  
Upwind Methods ◽  
Topological Sorting

Summary We present a set of algorithms for sequential solution of flow and transport that can be used for efficient simulation of polymer injection modeled as a compressible two-phase system. Our formulation gives a set of nonlinear transport equations that can be discretized with standard implicit upwind methods to conserve mass and volume independent of the timestep. In the absence of gravity and capillary forces, the resulting nonlinear system of discrete transport equations can be permuted to lower triangular form with a simple topological-sorting method from graph theory. This gives an optimal nonlinear solver that computes the solution cell by cell with local iteration control. The single-cell systems can be reduced to a nested set of nonlinear scalar equations that can be bracketed and solved with standard gradient or root-bracketing methods. The resulting method gives orders-of-magnitude reduction in run times and increases the feasible timestep sizes. In fact, one can prove that the solver is unconditionally stable and will produce a solution for arbitrarily large timesteps. For cases with gravity, the same method can be applied as part of a nonlinear Gauss-Seidel method. Altogether, our results demonstrate that sequential splitting combined with single-point upwind discretizations can become a viable alternative to streamline methods for speeding up simulation of advection-dominated systems.

An Adaptive Sequential Fully Implicit Domain-Decomposition Solver

SPE Journal ◽  
2021 ◽  
pp. 1-13
Author(s):  
Ø. S. Klemetsdal ◽  
A. Moncorgé ◽  
H. M. Nilsen ◽  
O. Møyner ◽  
K-. A. Lie
Keyword(s):  
Domain Decomposition ◽  
Reservoir Simulation ◽  
Rock Properties ◽  
Solution Strategy ◽  
Flow And Transport ◽  
Solution Strategies ◽  
Fully Implicit ◽  
Fluid Behavior ◽  
Nonlinear Solver ◽  
Nonlinear Solvers

Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Non-realisability problem with the conventional method of moments in wet-steam flows

2017 ◽  
Vol 232 (5) ◽  
pp. 473-489
Author(s):  
Ali Afzalifar ◽  
Teemu Turunen-Saaresti ◽  
Aki Grönman
Keyword(s):  
Size Distribution ◽  
Conventional Method ◽  
Method Of Moments ◽  
Transport Equations ◽  
Test Cases ◽  
Wet Steam ◽  
Spatial Gradients ◽  
Droplet Sizes ◽  
The Moment ◽  
Moment Set

The method of moments offers an efficient way to preserve the essence of particle size distribution, which is required in many engineering problems such as modelling wet-steam flows. However, in the context of the finite volume method, high-order transport algorithms are not guaranteed to preserve the moment space, resulting in so-called ‘non-realisable’ moment sets. Non-realisability poses a serious obstacle to the quadrature-based moment methods, since no size distribution can be identified for a non-realisable moment set and the moment-transport equations cannot be closed. On the other hand, in the case of conventional method of moments, closures to the moment-transport equations are directly calculated from the moments themselves; as such, non-realisability may not be a problem. This article describes an investigation of the effects of the non-realisability problem on the flow conditions and moment distributions obtained by the conventional method of moments through several one-dimensional test cases involving systems that exhibited similar characteristics to low-pressure wet-steam flows. The predictions of pressures and mean droplet sizes were not considerably disturbed due to non-realisability in any of the test cases. However, in one case that was characterised by strong temporal and spatial gradients, non-realisability did undermine the accuracy of the predictions of measures for the underlying size distributions, including the standard deviation and skewness.

A Correlation-Based Transition Model Using Local Variables—Part II: Test Cases and Industrial Applications

2004 ◽  
Vol 128 (3) ◽  
pp. 423-434 ◽  
Author(s):  
R. B. Langtry ◽  
F. R. Menter ◽  
S. R. Likki ◽  
Y. B. Suzen ◽  
P. G. Huang ◽  
...  
Keyword(s):  
Guide Vane ◽  
Current Model ◽  
Mathematical Formulation ◽  
Low Pressure ◽  
Transport Equations ◽  
Parallel Execution ◽  
Test Cases ◽  
Transition Model ◽  
Compressor Cascade ◽  
Low Pressure Turbine

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) methods using unstructured grids and massive parallel execution. The model is based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models), but form a framework for the implementation of correlation-based models into general-purpose CFD methods. Part I of this paper (Menter, F. R., Langtry, R. B., Likki, S. R., Suzen, Y. B., Huang, P. G., and Völker, S., 2006, ASME J. Turbomach., 128(3), pp. 413–422) gives a detailed description of the mathematical formulation of the model and some of the basic test cases used for model validation. Part II (this part) details a significant number of test cases that have been used to validate the transition model for turbomachinery and aerodynamic applications, including the drag crisis of a cylinder, separation-induced transition on a circular leading edge, and natural transition on a wind turbine airfoil. Turbomachinery test cases include a highly loaded compressor cascade, a low-pressure turbine blade, a transonic turbine guide vane, a 3D annular compressor cascade, and unsteady transition due to wake impingement. In addition, predictions are shown for an actual industrial application, namely, a GE low-pressure turbine vane. In all cases, good agreement with the experiments could be achieved and the authors believe that the current model is a significant step forward in engineering transition modeling.

A Correlation-Based Transition Model Using Local Variables: Part I — Model Formulation

2004 ◽  
Author(s):  
F. R. Menter ◽  
R. B. Langtry ◽  
S. R. Likki ◽  
Y. B. Suzen ◽  
P. G. Huang ◽  
...  
Keyword(s):  
Mathematical Formulation ◽  
Turbulence Models ◽  
Transition Process ◽  
General Purpose ◽  
Transport Equations ◽  
Parallel Execution ◽  
Test Cases ◽  
Transition Model ◽  
Significant Step ◽  
Transition Modeling

A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern CFD approaches such as unstructured grids and massive parallel execution. The model is based on two transport equations, one for intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike e.g. turbulence models), but form a framework for the implementation of correlation-based models into general-purpose CFD methods. Part I (this part) of this paper gives a detailed description of the mathematical formulation of the model and some of the basic test cases used for model validation, including a 2-D turbine blade. Part II of the paper details a significant number of test cases that have been used to validate the transition model for turbomachinery and aerodynamic applications. The authors believe that the current formulation is a significant step forward in engineering transition modeling, as it allows the combination of correlation-based transition models with general purpose CFD codes.

Simulating one of the CIB W14 round robin test cases using the SMARTFIRE fire field model

2001 ◽  
Vol 36 (7) ◽  
pp. 661-677 ◽  
Author(s):  
Z. Wang ◽  
F. Jia ◽  
E.R. Galea ◽  
M.K. Patel ◽  
J. Ewer
Keyword(s):  
Field Model ◽  
Round Robin ◽  
Test Cases ◽  
Round Robin Test

scholarly journals A New and Efficient Nonlinear Solver for Load Flow Problems

2020 ◽  
Vol 10 (3) ◽  
pp. 5851-5856
Author(s):  
A. H. Khoso ◽  
M. M. Shaikh ◽  
A. A. Hashmani
Keyword(s):  
Power Systems ◽  
Electric Power Systems ◽  
Load Flow ◽  
Significant Issue ◽  
Order Accuracy ◽  
Flow Problems ◽  
Nonlinear Solver ◽  
Nonlinear Solvers ◽  
Simulation Results ◽  
Number Of Iterations

Load Flow (LF) analysis is a fundamental and significant issue in electric power systems. Because of the nonlinearity of the power mismatch equations, the accuracy of the nonlinear solvers is important. In this study, a novel and efficient nonlinear solver is proposed with active applications to LF problems. The formulation of the Proposed Method (PM) and its workflow and mathematical modeling for its application in LF problems have been discussed. The performance of the PM has been validated on the IEEE 14-bus and 30-bus test systems against several existing methods. The simulation results show that the PM exhibits higher order accuracy, faster convergence characteristics, smaller number of iterations, and lesser computation times in comparison with the other benchmark methods.

scholarly journals Image Reconstruction of Two-Dimensional Highly Scattering Inhomogeneous Medium Using MAP-Based Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hong Qi ◽  
Yaobin Qiao ◽  
Shuangcheng Sun ◽  
Yuchen Yao ◽  
Liming Ruan
Keyword(s):  
Image Reconstruction ◽  
Inhomogeneous Medium ◽  
Measurement Errors ◽  
Field Model ◽  
Test Cases ◽  
Two Dimensional ◽  
Map Estimation ◽  
A Posteriori ◽  
Markov Random ◽  
Initial Distributions

A maximum a posteriori (MAP) estimation based on Bayesian framework is applied to image reconstruction of two-dimensional highly scattering inhomogeneous medium. The finite difference method (FDM) and conjugate gradient (CG) algorithm serve as the forward and inverse solving models, respectively. The generalized Gaussian Markov random field model (GGMRF) is treated as the regularization, and finally the influence of the measurement errors and initial distributions is investigated. Through the test cases, the MAP estimate algorithm is demonstrated to greatly improve the reconstruction results of the optical coefficients.

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