Multi-scale modeling of three-phase–three-component processes in heterogeneous porous media

Niessner, Jennifer; Helmig, Rainer

doi:10.1016/j.advwatres.2007.05.008

Cited by 47 publications

(26 citation statements)

References 41 publications

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“…They presented steady-state upscaling procedures for relative permeability and capillary pressure for three limiting cases (capillary limit, viscous limit, and vertical equilibrium). Three-phase flow problems have also been addressed within multiscale modeling frameworks; see, e.g., [30] and [22]. The work presented in this paper is quite different in that we develop dynamic three-phase upscaling procedures relevant for the nearwell region.…”

Section: Introductionmentioning

confidence: 98%

Near-well upscaling for three-phase flows

Nakashima

Durlofsky

2011

Comput Geosci

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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 wellblock 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.

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Section: Introductionmentioning

confidence: 98%

Near-well upscaling for three-phase flows

Nakashima

Durlofsky

2011

Comput Geosci

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“…In this technical note, we extend a multi-scale multi-physics algorithm recently developed by Niessner and Helmig [15,16] by the possibility of using not only an upscaled saturation equation, but also an upscaled pressure equation. The algorithm of Niessner and Helmig [15,16] focussed on coupling three-phase-three-component (or two-phase-two-component) processes occurring in a smaller subregion and on a fine scale (which was already a volume-averaged scale) to two-phase flow on a coarse scale taking place in the whole considered domain.…”

Section: Motivationmentioning

confidence: 99%

“…Highly complex processes may take place in one part of the system necessitating a fine spatial and temporal resolution, while in other parts of the system, physically simpler processes take place allowing an examination on coarser scales. Considering the porous medium, its heterogeneous structure shows a high dependence on the spatial scale [16]. Fig.…”

Section: Motivationmentioning

confidence: 99%

Multi-physics modeling of flow and transport in porous media using a downscaling approach

Niessner

Helmig

2009

Advances in Water Resources

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“…In standard upscaling (e.g., [4]) or multiscale modeling (e.g., [19,22,27]) procedures, subgrid effects are captured through detailed deterministic preprocessing and/or reconstruction computations for each block in each realization. EnLU, by contrast, performs a portion of the upscaling computations (specifically the calculation of upscaled absolute permeability) deterministically, while the bulk of the time-consuming (two-phase upscaling) computations are replaced by very fast stochastic techniques.…”

Section: Introductionmentioning

confidence: 99%

Statistical assignment of upscaled flow functions for an ensemble of geological models

2010

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Upscaled flow functions are often needed to account for the effects of fine-scale permeability heterogeneity in coarse-scale simulation models. We present procedures in which the required coarse-scale flow functions are statistically assigned to an ensemble of upscaled geological models. This can be viewed as an extension and further development of a recently developed ensemble level upscaling (EnLU) approach. The method aims to efficiently generate coarse-scale flow models capable of reproducing the ensemble statistics (e.g., cumulative distribution function) of finescale flow predictions for multiple reservoir models. The most expensive part of standard coarsening procedures is typically the generation of upscaled two-phase flow functions (e.g., relative permeabilities). EnLU provides a means for efficiently generating these upscaled functions using stochastic simulation. This involves the use of coarse-block attributes that are both fast to compute and correlate closely with the upscaled two-phase functions. In this paper, improved attributes for use in EnLU, namely the coefficient of variation of the fine-scale single-phase velocity field (computed during computation of upscaled absolute permeability) and the integral range of the fine-scale permeability variogram, are identified. Geostatistical simulation methods, which account for spatial correlations of Y. Chen (B) Chevron Energy Technology Company, the statistically generated upscaled functions, are also applied. The overall methodology thus enables the efficient generation of coarse-scale flow models. The procedure is tested on 3D well-driven flow problems with different permeability distributions and variable fluid mobility ratios. EnLU is shown to capture the ensemble statistics of fine-scale flow results (water and oil flow rates as a function of time) with similar accuracy to full flow-based upscaling methods but with computational speedups of more than an order of magnitude.

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Multi-scale modeling of three-phase–three-component processes in heterogeneous porous media

Cited by 47 publications

References 41 publications

Near-well upscaling for three-phase flows

Near-well upscaling for three-phase flows

Multi-physics modeling of flow and transport in porous media using a downscaling approach

Statistical assignment of upscaled flow functions for an ensemble of geological models

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