Parallelization of a Commercial Streamline Simulator and Performance on Practical Models

Batycky, Rod P.; Förster, Malte; Thiele, Marco R.; StC<ben, Klaus

doi:10.2118/118684-ms

Cited by 5 publications

(4 citation statements)

References 17 publications

(16 reference statements)

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“…Unless particular difficulties are present in the original Jacobian system, AMG is an established, highly efficient strategy for solving IMPES-like total-pressure equations (Batycky et al 2009;Geiger et al 2009); thus, AMG should be an efficient choice for the quasi-IMPES pressure equation as well. In fact, because the Jacobian's "elliptic parts" are concentrated inÃ pp (Masson et al 2004), this resulting pressure equation can be expected to have comparable properties.…”

Section: Drs Preconditionermentioning

confidence: 99%

“…Because AMG methods are able to efficiently deal with complex geometries, with discontinuous and varying coefficients, and with anisotropies, they are naturally very attractive for porous-media-flow simulation with its varying permeability fields and resulting heterogeneities. Finally, because AMG in its classical form does not require geometric information, it is also easily integrated into existing reservoir simulators Batycky et al 2009). Hence, in recent years, AMG has become the most popular choice for the pressure-preconditioning step in reservoir-simulation applications.…”

Section: Introductionmentioning

confidence: 99%

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Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Gries

Stüben

Brown³

et al. 2014

SPE Journal

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Fully implicit black-oil simulations result in huge, often very-illconditioned, linear systems of equations for different unknowns (e.g., pressure and saturations). It is well-known that the underlying Jacobian matrices contain both hyperbolic and nearly elliptic subsystems (corresponding to saturations and pressure, respectively). Because a reservoir simulation is typically driven by the behavior of the pressure, constrained-pressure-residual (CPR)type two-stage preconditioning methods to solve the coupled linear systems are a natural choice and still belong to the most popular approaches. After a suitable extraction and decoupling, the computationally most costly step in such two-stage methods consists in solving the elliptic subsystems accurately enough. Algebraic multigrid (AMG) provides a technique to solve elliptic linear equations very efficiently. Hence, in recent years, corresponding CPR-AMG approaches have been extensively used in practice.Unfortunately, if applied in a straightforward manner, CPR-AMG does not always work as expected. In this paper, we discuss the reasons for the lack of robustness observed in practice, and present remedies. More precisely, we will propose a preconditioning strategy (based on a suitable combination of left and right preconditioning of the Jacobian matrix) that aims at a compromise between the solvability of the pressure subproblem by AMG and the needs of the outer CPR process. The robustness of this new preconditioning strategy will be demonstrated for several industrial test cases, some of which are very ill-conditioned. Furthermore, we will demonstrate that CPR-AMG can be interpreted in a natural way as a special AMG process applied directly to the coupled Jacobian systems.

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Section: Drs Preconditionermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Gries

Stüben

Brown³

et al. 2014

SPE Journal

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“…For solving IMPES-like total pressure equations AMG already is successfully applied [4][15], so AMG should be an efficient choice for the quasi-IMPES pressure equation, as well. In fact, since the Jacobian's 'elliptic parts' are concentrated in Ã pp [22], this resulting pressure equation can be expected to have comparable properties.…”

Section: Dynamic Rowsum (Drs) Preconditionermentioning

confidence: 99%

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Gries

Stüben

Brown³

et al. 2013

All Days

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Fully implicit petroleum reservoir simulations result in huge, often very ill-conditioned linear systems of equations to solve for different unknowns, for example, pressure and saturations. It is well known that the full system matrix contains both hyperbolic as well as nearly elliptic sub-systems. Since the solution of the coupled system is mainly determined by the solution of their elliptic (typically pressure) components, (CPR-type) two-stage preconditioning methods still belong to the most popular approaches to tackle such coupled systems. After a suitable extraction and decoupling, the numerically most costly step in such two-stage methods consists in solving these elliptic sub-systems. It is known that algebraic multigrid (AMG) provides a technique to solve elliptic linear equations very efficiently. The main advantage of AMG-based solvers -their numerical scalability -makes them particularly efficient for solving huge linear systems.Depending on the application, the system's properties range from simple to highly indefinite. Unfortunately decoupling pressure and saturation related parts may introduce further difficulties. Consequently, in complex industrial simulations, the application of AMG to elliptic sub-systems might not be straightforward. In fact, an important goal in defining an efficient two-stage preconditioning strategy consists in extracting elliptic sub-systems that are suitable for an efficient AMG solution and, at the same time, ensure a fast overall convergence of the two-stage approach.The importance of this will be demonstrated for several industrial cases. In particular, some of these cases are very hard to solve by AMG if applied in a standard way.Preliminary results for a CPR-type coupling of SAMG to CMG's PARASOL, a variable degree variable ordering ILU preconditioner using FGMRES, are compared to using PARASOL by itself. Alternative preconditioning operators will be presented giving elliptic sub-systems which are not only more suitable for applying AMG efficiently but also help accelerate the CPR-type process. Comparisons with one-level iterative methods will show the acceleration by AMG is highly superior. Finally, a strategy is presented that combines all linear solver parts in one single AMG-iteration. In this sense CPR can be seen as a special case of AMG for systems. This, in turn, yields a -formally -very simple but simultaneously very flexible solution approach.

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“…Streamline simulation is an attractive alternative to overcome the drawbacks in conventional finite difference simulations, since it offers substantial computational efficiency while minimizing numerical diffusion and gridorientation effects [4]. A total of 300 seismic inversion realizations are flow simulated using parallel simulation algorithms [5] over 8 CPUs. Instead of moving fluids from cell to cell, streamline simulation breaks up the reservoir into 1D systems, or tubes.…”

Section: Flow Simulation Parameterization and Streamline Simulationsmentioning

confidence: 99%

Ranking of Stochastic Seismic Inversion Realizations Using Streamline Simulations

Virk

Muneeb²

2011

All Days

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Because stochastic seismic inversion generates a large number of elastic impedance realizations, only a few of these realizations must be selected for more rigorous geological interpretation and reservoir modelling. Static sand body volume (SBV) and SBV geometrically connected to the wells are generally used as the ranking measures. However, this approach does not take into account the dynamic flow field and the impact of reservoir heterogeneity and petrophysical properties on the fluid flow. Hence, this approach under or overestimates the P10, P50 & P90 ranking most of the time and invalidates the field development studies in turn. The main goal of this study is to prove the concept of using dynamic measures to rank the seismic inversion realizations and develop a ranking work flow. Streamline simulations, because of its generic option of reduced flow physics provides a faster way to run hundred of millions cell realizations, enabling a quick ranking based on dynamic measures. Typical seismic inversion models consists of several million cells (6 million in this case), and flow simulation over models of this size is computationally extensive. To reach reasonable runtimes, the size of the model is reduced; either by extracting a sector model (2 million cells sector in this case), or by decimating/up-scaling the full field model (1.7 million cells in this case). Tracer simulations over both of the reduced size models are compared with the full field tracer simulation model. The upscaled model is shown to be a closer approximation to the full field model. Finally, the tracer upscaled model is compared with a physically more realistic waterflood upscaled simulation model and is shown as a valid approximation. The sensitivity of various dynamic parameters to connectivity variations is analyzed to determine which parameter is the best suited ranking measure. Due to significant variability in spatial sand bodies distribution and connectivity between the sand bodies across the realizations, cumulative oil recovery (COR) has proved to be a much better ranking measure in comparison to the recovery factor (RF) . The static and dynamic ranking measures are compared. The difference between SBV or connected sand body volume (CSBV) and COR rankings highlights the importance of ranking based on dynamic measures. Additionally, the factors which can generally influence the ranking based on dynamic measure (COR) are determined and it is concluded that the changes in ranking will be dependent on the CSBV and petrophysical properties of the connected sand bodies across the realizations. Finally, ranking based on the best ranking measure as well on a combination of COR, STOIIP and RF is done and individual realizations (P10, P50 and P90) are selected in order to cover the range of uncertainty in spatial distribution and volumes of sand bodies. This uncertainty range can be translated into economic uncertainty for the determined optimum number of wells and distances. The approach defined in this paper to rank and select the P10, P50 & ...

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Parallelization of a Commercial Streamline Simulator and Performance on Practical Models

Cited by 5 publications

References 17 publications

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

Ranking of Stochastic Seismic Inversion Realizations Using Streamline Simulations

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