Control-Relevant Upscaling

Ghahani, S.A. Vakili

doi:10.2118/113647-ms

Cited by 4 publications

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been shown that it is also possible to make use of spatial correlations in the states (pressures, saturations) to reduce the order of reservoir models using system-theoretical techniques, but application of these possibilities in optimization, data assimilation or upscaling has hardly yet been pursued. For some early attempts, see Heijn et al (2004), Van Doren et al (2006, Markovinović and Jansen (2006), Gildin et al (2006), Vakili-Ghahani et al (2008 and Cardoso et al (2008).…”

Section: Reparameterization and Model Reductionmentioning

confidence: 99%

Closed-Loop Reservoir Management

Jansen

Brouwer

Douma

2009

SPE Reservoir Simulation Symposium

Self Cite

213

View full text Add to dashboard Cite

Closed-loop reservoir management is a combination of model-based optimization and data assimilation (computer-assisted history matching), also referred to as 'real-time reservoir management', 'smart reservoir management' or 'closed-loop optimization'. The aim is to maximize reservoir performance, in terms of recovery or financial measures, over the life of the reservoir by changing reservoir management from a periodic to a near-continuous process. The key sources of inspiration for our work are measurement and control theory as used in the process industry and data assimilation techniques as used in meteorology and oceanography. We present results of a numerical example to illustrate the scope for closed-loop water flooding using real-time production data under uncertain reservoir conditions. The example concerns a 12-well water flood in a channelized reservoir. Optimization was performed using a reservoir simulator with functionality for adjoint-based life cycle optimization under rate and pressure constraints. Data assimilation was performed using the ensemble Kalman filter. Applying an optimization frequency of respectively once per 4 years, once per 2 years, once per year and once per 30 days resulted in an increase of net present value (NPV) with 6.68, 8.29, 8.30 and 8.71% compared to a conventional reactive control strategy. Moreover, the results for the 30-day cycle were very close (0.15% lower NPV) to those obtained by open-loop optimization using the 'true' reservoir model. We illustrate that for closed-loop reservoir management with a fixed well configuration, the use of considerably different reservoir models may lead to near-identical results in terms of NPV. This implies that in such cases the essential information may be represented with a much less complex model than suggested by the large number of grid blocks in typical reservoir models. We also illustrate that the optimal rates and pressures as obtained by open-or closedloop optimization are often too irregular to be practically applicable. Fortunately, just as is the case for the data assimilation problem, the flooding optimization problem usually contains many more control variables than necessary, allowing for optimization of long-term reservoir performance while maintaining freedom to perform short-term production optimization.

show abstract

Section: Reparameterization and Model Reductionmentioning

confidence: 99%

Closed-Loop Reservoir Management

Jansen

Brouwer

Douma

2009

SPE Reservoir Simulation Symposium

Self Cite

213

View full text Add to dashboard Cite

show abstract

Control-Relevant Upscaling

Vakili-Ghahani

2009

SPE Journal

View full text Add to dashboard Cite

Summary 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 behaviors of the fine- and coarse-scale models. This distance is measured with the aid of the Hankel or energy norms, in which we use Hankel singular values as a measure of the combined controllability and observability and Markov parameters as a measure of the response of the system, respectively. The method is particularly attractive to scale up simulation models in flooding-optimization or history-matching studies for a given configuration of wells. An advantage of our upscaling method is that it 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, either of the full or of the upscaled model. It also does not depend on a particular control strategy but instead uses the dynamical system equations directly. Its dependency on well locations, however, implies that it should be (partially) repeated when those locations 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.

show abstract

Control-Relevant Selective Grid Coarsening

Vakili

2009

SPE Annual Technical Conference and Exhibition

View full text Add to dashboard Cite

From a system-theoretical point of view there are only a limited number of degrees of freedom in the input-output dynamics of a reservoir system. This means that, for a given configuration of wells, a large number of combinations of the state variables (pressure and saturation values) are not actually controllable and observable from the wells, and accordingly, they are not affecting the input-output behavior of the system. In an earlier publication we therefore proposed a control-relevant upscaling (CRU) methodology that uniformly coarsens the reservoir model based on the relevant level of information and control. Here we present a selective (i.e. non-uniform) grid coarsening method to allow treatment of very large models with high degree of heterogeneity in their parameter fields. In this control-relevant selective coarsening (CRSC) method, the criterion for selective grid size adaptation is based on the controllability and observability properties of the reservoir system; hence we selectively coarsen only the weakly controllable and observable parts of the model. The CRSC method is particularly attractive for use in flooding optimization or history matching studies for a given configuration of wells. We applied our algorithm to two numerical examples and found that the CRSC algorithm can accurately reproduce results from the corresponding fine-scale simulations, while speeding up the simulation. Introduction Conventional upscaling At present the computational limits for reservoir flow simulation restrict the model order to typically 104 to 106. Here, the model order is defined as the number of time-dependent variables (i.e. state variables such as grid block pressures, saturations or component accumulations) which is typically equal to the number of active grid blocks times the number of components (i.e. hydrocarbon components and water) in the simulation. The number of time-independent model parameters is usually of the same order of magnitude because they are also proportional to the number of grid blocks (e.g. grid block permeabilities and porosities). However, geological subsurface models often represent the subsurface heterogeneity with 106 to 109 parameters ('voxels') and some form of upscaling is therefore required to transfer the relevant features of a geological model to a flow simulation model. The uncertainty of the geological parameters is increasingly taken into account by simulating an ensemble of model realizations, which significantly increases the computational demands, especially when it is also required to perform repeated simulations for flooding optimization or history matching. In particular, we consider the application of reservoir simulation for 'closed-loop reservoir management', which involves the use of simulation models during the producing life of a reservoir for near-continuous flooding optimization based on frequently updated, 'evergreen', reservoir models (see e.g. Jansen et al. 2009). Even although the rapid increase of cluster computing facilitates such operational use of reservoir simulation, reducing the number of grid blocks, and thus the model order, through upscaling remains a computational and practical necessity. There are different upscaling techniques varying from simple averaging methods on uniform Cartesian cells to sophisticated flow-based techniques on adaptive and unstructured grids. Extensive reviews of the different methods were written by e.g. Wen et al. (1996), Renard and Marsily (1997) and Durlofsky (2005).

show abstract

Control-Relevant Upscaling

Cited by 4 publications

References 45 publications

Closed-Loop Reservoir Management

Closed-Loop Reservoir Management

Control-Relevant Upscaling

Control-Relevant Selective Grid Coarsening

Contact Info

Product

Resources

About