Scale Up in the Near-Well Region

Durlofsky, Louis J.; Milliken, William J.; Bernath, A.

doi:10.2118/51940-ms

Cited by 14 publications

(12 citation statements)

References 14 publications

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“…He introduced a well-driven flow by applying appropriate boundary conditions. Durlofsky et al (2000) proposed an extended local region around the well for the fine scale solution for the near well upscaling as shown in fig. 2.17.…”

Section: Near-well Upscalingmentioning

confidence: 99%

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Upscaling for Thermal Recovery

Abubakar¹,

Muggeridge²,

King³

2014

SPE International Heavy Oil Conference and Exhibition

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Thermal recovery is one of the most widely applied EOR methods worldwide. It is used mainly to improve the recovery of more viscous oils. Heat is used primarily to reduce the viscosity of oil but may also improve recovery by other mechanisms such as oil expansion, steam distillation and reduction in capillary forces. As a result, the prediction of thermal recovery performance requires more complex and computationally demanding numerical simulations than is the case when evaluating a waterflood. The simulator has to evaluate the impact of both heat transfer and compositional behaviour on the fluid flows.In most cases the engineer will have to use coarser grids in the simulation models than would be needed for a waterflood in order to keep simulation times within acceptable limits. However, it has been shown in the modelling of other EOR processes that in fact much finer grids may be needed to capture the frontal dynamics of the displacement than would be the case in waterflooding. As a result, the simulation of steamflooding on the field scale is unlikely to capture the impact of small scale heterogeneity on flow, as well as being severely affected by numerical dispersion. The ideal solution is to use homogenization to capture the effects of sub-grid-block heterogeneity combined with advanced numerical techniques such as dynamic/adaptive gridding or higher order schemes to reduce the impact of numerical diffusion and dispersion. However, such methods are not currently available in the commercial simulators available to most engineers.The alternative is to use upscaling, but as yet there are no upscaling methodologies suitable for thermal oil recovery methods. Upscaling is a way of altering the inputs to numerical flow models so that simulations run on a coarse grid. These will a) predict the impacts on flow of sub-grid heterogeneity (homogenization) and b) will be less affected by numerical dispersion. For waterflooding this is typically achieved by calculating the effective absolute permeability for each coarse grid cell. In many cases, it is also necessary to upscale the well index and the transmissibilities of the well blocks. Upscaling the absolute permeability, the well index and the well block transmissibilities, ensures that the overall pressure drop for single phase flow between wells is correctly predicted in the coarse grid, whilst upscaling the relative permeabilities ensures that the two-phase flow effects (pressure drop, breakthrough time and water cut development) are correctly modelled. Although there is a significant literature on single-phase upscaling and the development of pseudo relative permeabilities for waterflooding applications, these methods do not capture the heat transport or the impact of temperature on the oil mobility. ivIn this research, a combination of pseudoisation procedures (by making reasonable assumptions) with the Buckley-Leverett solution approximated for thermal EOR processes is used to derive analytical pseudo-relative permeabilities for both hot water and steam ...

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Section: Near-well Upscalingmentioning

confidence: 99%

“…Many researchers (e.g. Ding, 1995;Durlofsky et al 2000;Muggeridge et al 2002;Chen and Wu, 2008) have also shown procedures to estimate well index appropriately.…”

Section: Near-well Upscaling In 3-d Modelsmentioning

confidence: 99%

Upscaling for Thermal Recovery

Abubakar¹,

Muggeridge²,

King³

2014

SPE International Heavy Oil Conference and Exhibition

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“…In most cases, the coarse-scale parameters are approximated based on fine-scale parameters and/or some local flow calculations, subjected to generic boundary conditions. Therefore, the performance of these methods often depends on the choice of the local boundary conditions and may not adequately capture the key features of the fine-scale flow behaviour, especially in the near-well region (Durlofsky et al 2000).…”

Section: Approachmentioning

confidence: 99%

“…We argue that, in addition to the computational difficulties, a more fundamental reason for upscaling is that, for a given configuration of wells in a reservoir, there is only a limited degree of freedom in the input/output dynamics of the system [i.e., 13 The assumption of fixed boundary conditions might also lead to a poor capturing of near-well effects on the global flow pattern unless a near-well upscaling technique is added (Ding 1995 andDurlofsky et al 2000).…”

Section: Motivationmentioning

confidence: 99%

Control-Relevant Upscaling

Ghahani

2008

All Days

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The conventional reason for upscaling in reservoir simulation is the computational limit of the simulator. However, we argue that, from a system-theoretical point of view, a more fundamental reason is that there is only a limited amount of information (output) that can be observed from production data, while there is also a limited amount of control (input) that can be exercised by adjusting the well parameters; in other words, the input-output behavior is usually of much lower dynamical order than the number of grid blocks in the model. Therefore, we propose an upscaling approach to find a coarse model that optimally describes the input-output behavior of a reservoir system. In this control-relevant method, the coarse-scale model parameters are calculated as the solution of an optimization problem that minimizes the distance between the input-output behavior of the fine- and coarse-scale models. This distance is measured with the aid of the Hankel- or energy norms, where Hankel singular values are used as a measure of the combined controllability and observability of the system. The method is particularly attractive to scale up simulation models in flooding optimization and/or history matching studies for a given configuration of wells. An advantage of our upscaling method is that it intrinsically relies most heavily on those parameter values that directly influence the input-output behavior. It is a global method, in the sense that it relies on the system properties of the entire reservoir. It does not, however, require any forward simulation, neither of the full nor of the upscaled model. it also does not depends on a particular control strategy, but instead uses the dynamical system equations directly. A drawback, however, is its dependency on well positions, which implies that it should be (partially) repeated when those positions are changed. We tested the method on several examples and for nearly all cases obtained coarse scale models with a superior input-output behavior compared to common upscaling algorithms. Introduction Simulation of flow in porous media is an important tool to predict and optimize reservoir performance. As a precursor to the simulation, reservoir data are collected from different sources with various temporal and spatial scales, which are usually integrated into detailed geological models with a large number of cells (107 to 108). The large size of geo-models makes it often impossible to undertake reasonable multiphase flow simulations, sensitivity analysis, uncertainty assessment of a large number of realizations, computer-assisted history matching or life-cycle optimization. In order to perform these processes within a practical time frame and/or a reasonable cost, an upscaling procedure is required to transfer the flow and transport processes from the detailed fine-scale model to a lower-order, coarser representation. The approximated coarse-scale model (typically up to 106 cells) should reduce the complexity, while retaining the main properties of the reservoir system. Upscaling background Various upscaling techniques have been developed in both hydrology and petroleum engineering. These methods vary from simple averaging methods on Cartesian cells to sophisticated flow-based techniques on unstructured grids. Extensive reviews on upscaling were written by e.g. Wen et al. (1996), Renard and Marsily (1997) and Durlofsky (2005). Upscaling methods are classified based on the type of the parameters that are scaled up. In single-phase upscaling, we only consider the pressure (flow) equation and calculate equivalent permeability and porosity values, whereas in two-phase upscaling both pressure and transport equations are considered. Therefore, in addition to the single-phase parameters, equivalent relative permeability and capillary pressure curves are calculated. In principle, upscaling includes both parameters and equations. However, in most single-phase upscaling procedures, coarse-scale equations are chosen to have the same mathematical form as the fine-scale equations.

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“…It was known that for the well-driven flow in the porous media, the standard upscaling methods did not work in the vicinity of the wells [5,13]. In the recent paper [3], Chen and Yue developed a multiscale coarse grid algorithm for solving steady flow problem involving well singularities in heterogeneous porous medium based on the over-sampling multiscale finite element method (MsFEM) [10].…”

Section: Introductionmentioning

confidence: 99%

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

Jiang¹,

Yue²

2007

ESAIM: M2AN

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Abstract. Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul. 1 (2003) 260-303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.Mathematics Subject Classification. 65N30, 65N15.

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Scale Up in the Near-Well Region

Abstract: This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February 1999.

Cited by 14 publications

References 14 publications

Upscaling for Thermal Recovery

Upscaling for Thermal Recovery

Control-Relevant Upscaling

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

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