Streamline computations for porous media flow including gravity

Bratvedt, Frode; Gimse, Tore; Tegnander, Cathrine

doi:10.1007/bf00141262

Cited by 158 publications

(108 citation statements)

References 9 publications

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“…To take into account the gravity segregation effects, we introduce an additional operator splitting for the transport equations as described at the end of Section 3. This operator splitting method was first introduced within streamline simulation [3,4,2], but can also offer certain benefits for finite-volume methods, e.g., as discussed in [9]. The segregation residual equations for water and polymer are given by…”

Section: Discretization and Splitting Of The Equationsmentioning

confidence: 99%

The single-cell transport problem for two-phase flow with polymer

et al. 2015

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Polymer injection is a widespread strategy in enhanced oil recovery. Polymer increases the water viscosity and creates a more favorable mobility ratio between the water and the oil phase. Pressure-transport splitting of the equations combined with reordering strategies can be used to significantly increase the computational speed of two-phase flow simulations with polymer ([10]). Such scheme relies on a robust single-cell solver, which computes the saturation and polymer concentration of a cell, given the total flux and the saturation and polymer concentration of the neighboring cells. In this paper, we consider a standard but relatively comprehensive polymer model and show that, in the case of a two-point flux approximation, the single-cell problem always admits a solution and that the solution is unique. The uniqueness part of the proof is essentially based on monotonicity arguments while the existence part is based on bracketing. In particular, it shows that also the pressure equation must be chosen with care. For the segregation part, we observe that, even if the polymer belongs to the water phase, water-phase upwinding of the polymer concentration leads to ill-posedness and we present an alternative which guarantees well-posedness.

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Section: Discretization and Splitting Of The Equationsmentioning

confidence: 99%

The single-cell transport problem for two-phase flow with polymer

et al. 2015

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“…This approach is described, amongst others, by Gmelig-Meyling (1990,1991) and Bratvedt et al (1996). In Jessen et al (2004), we developed an adaptation of gravity operator splitting for compositional problems.…”

Section: Operator Splitting For Gravitymentioning

confidence: 99%

“…Most of these shortcomings of streamline methods are well-known, and solution strategies have been proposed. For example, operator splitting techniques have been developed to account for gravity as in Bratvedt et al (1996), and for capillary flow as in Berenblyum et al (2003) and high streamline densities can in cases alleviate mapping errors. In compositional simulation, however, numerical solutions are much more sensitive to errors because of the strong nonlinear couplings introduced by the phase behavior.…”

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confidence: 99%

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Gerritsen¹

2008

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Executive SummaryGas-injection processes are widely and increasingly used for enhanced oil recovery (EOR). In the United States, for example, EOR production by gas injection accounts for approximately 45% of total EOR production and has tripled since 1986. The understanding of the multiphase, multicomponent flow taking place in any displacement process is essential for successful design of gas-injection projects. Due to complex reservoir geometry, reservoir fluid properties and phase behavior, the design of accurate and efficient numerical simulations for the multiphase, multicomponent flow governing these processes is nontrivial. In this work, we developed, implemented and tested a streamline based solver for gas injection processes that is computationally very attractive: as compared to traditional Eulerian solvers in use by industry it computes solutions with a computational speed orders of magnitude higher and a comparable accuracy provided that cross-flow effects do not dominate. We contributed to the development of compositional streamline solvers in three significant ways: improvement of the overall framework allowing improved streamline coverage and partial streamline tracing, amongst others; parallelization of the streamline code, which significantly improves wall clock time; and development of new compositional solvers that can be implemented along streamlines as well as in existing Eulerian codes used by industry.We designed several novel ideas in the streamline framework. First, we developed an adaptive streamline coverage algorithm. Adding streamlines locally can reduce computational costs by concentrating computational efforts where needed, and reduce mapping errors. Adapting streamline coverage effectively controls mass balance errors that mostly result from the mapping from streamlines to pressure grid. We also introduced the concept of partial streamlines: streamlines that do not necessarily start and/or end at wells. This allows more efficient coverage and avoids the redundant work generally done in the near-well regions. We improved the accuracy of the streamline simulator with a higher order mapping from pressure grid to streamlines that significantly reduces smoothing errors, and a Kriging algorithm is used to map from the streamlines to the background grid. The higher accuracy of the Kriging mapping means that it is not essential for grid blocks to be crossed by one or more streamlines. The higher accuracy comes at the price of increased computational costs, but allows coarser coverage and so does not generally increase the overall costs of the computations. To reduce errors associated with fixing the pressure field between pressure updates, we developed a higher order global time-stepping method that allows the use of larger global time steps. Third-order ENO schemes are suggested to propagate components along streamlines. Both in the two-phase and three-phase experiments these ENO schemes outperform other (higher order) upwind schemes. Application of the third order ENO scheme leads to ii...

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“…That will move streamlines and generate transverse flux. However we can take into account for gravity segregations 4 and capillary effects 9 using an operator splitting method recently, the transverse flux because of incompressible flow has not been solved well. In conventional simulators the pressure and saturation will be solved on the grid block coordinate.…”

Section: Transverse Fluxmentioning

confidence: 99%

“…1 Technically, the oil industry literature on streamtubes dates back to the 1930's, but the three-dimensional streamline approaches are much more recent. [2][3][4][5][6][7][8] Many of the features that we take for granted in finite difference simulation are still missing from streamline approaches.…”

Section: Introductionmentioning

confidence: 99%

Timestep Selection During Streamline Simulation via Transverse Flux Correction

Osako

Datta‐Gupta

King

2003

SPE Reservoir Simulation Symposium

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This research presents a novel approach for timestep selection during streamline simulation that is based on three elements. First, we reformulate the equations to be solved by a streamline simulator to include all of the three-dimensional flux terms -both aligned with and transverse to the flow directions. These transverse flux terms are totally neglected within the existing streamline simulation formulations. Second, we propose a simple grid-based corrector algorithm to update the saturation to account for the transverse flux. Third, we provide a discrete CFL (Courant-Friedrich-Levy) formulation for the corrector step that leads to a mechanism to ensure numerical stability via the choice of a stable timestep for pressure updates. This discrete CFL formulation now iv provides us with the same tools for timestep control as are available within conventional reservoir simulators.We demonstrate the validity and utility of our approach using a series of numerical experiments in homogeneous and heterogeneous ¼ five-spot patterns at various mobility ratios. For these numerical experiments, we pay particular attention to favorable mobility ratio displacements, as they are known to be challenging to

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Streamline computations for porous media flow including gravity

Cited by 158 publications

References 9 publications

The single-cell transport problem for two-phase flow with polymer

The single-cell transport problem for two-phase flow with polymer

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Timestep Selection During Streamline Simulation via Transverse Flux Correction

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