Upscaling permeability

Liu, HH J Rutqvist, Q Zhou and G.S. Bodvarsson, Upscaling of nonrutl stress-permeability... 

UPSCALING OF NORMAL STRESS-PERMEABILITY RELATIONSHIPS FOR FRACTURE NETWORKS OBEYING FRACTIONAL LEVY MOTION... 

A key parameter for modeling T-H-M-C processes is the relationship between in situ stress and permeability. Since this relationship is generally measured at small scales, upscaling is needed for large-scale models. Few studies on upscaling of this relationship have appeared in the literature. In this study, we develop closed-form upscaled normal stress-permeability relationships... 

An important step for upscaling the stress-permeability relationship is to relate local permeability (at a 1.56 m scale) to parameters b, bmax. and fracture frequency f. We assume that at the 1.56 m scale, local permeabilities can be considered to result from horizontal and vertical fractures. Different assumptions regarding relations among local permeability and the relevant parameters (f, b and b ,x) will give rise to different upscaling relationships. In this paper, we present two useful relationships. 

Figured. Outline of stochastic stress and fluid flow analysis for upscaling the srrmll-scale (e.g.. 1.56 m x 1.56 m) stress-permeability relation to a gridblock scale for a large-scale model.

In other words, the permeability ratio is not scale-dependent in this case, and a numerical upscaling procedure is not needed. For a given initial stress and a stress change, the permeability ratio is determined solely by the parameter Rb- A large Rb corresponds to a large portion of residual aperture (b,) in the total aperture b, and therefore gives rise to a relatively weak response to mechanical process. 

Abstract A new upscaling method has been developed using 3D numerical tools (RESOBLOK 3DEC). This method has been successfully compared with standard analytical approaches in the case of a simple fracture network. This method has been applied to determine the equivalent permeability, stiffness and Biot tensor of a real fracture rock-mass at different scales. The effects of the fracture network properties and of the state of stress on the result have been investigated. 

A new upscaling method has been proposed by INERIS to determine the equivalent hydro mechanical properties of a fractured rock-mass. This method is based on the 3D numerical simulations of the behaviour of a "sample" of fractured rock-mass submitted to different hydromechanical boundary conditions. The simulations are defined in order to determine the equivalent permeability, stiffness and Biot tensor of a fractured rock-mass. 

Similar upscaling techniques, motivated by the need to reduce grid block number, are important in practice. But the equivalent permeabilities within any reservoir will change if the reservoir is produced by different arrangements or patterns of wells, because the parallel and serial nature of the flow has changed. Upscaled quantities are not properties of the formation but are also related to the production method. However, several simulators compute fixed upscaled properties and use them in contrasting production scenarios. 

Because the T-unit sediments are relatively unconsolidated, the variations in clay content have the most control over porosity and permeability. Permeability is the critical rock property that controls the flow behavior of the heavy oil in Tambaredjo field and is therefore a critical part of the 3D geostatistical modeling. A 3D geostatistical model was built with 42 wells, which has a cell size of 25 x25 m and was designed to be used without upscaling during the dynamic modeling. Because this project has no seismic data and very limited core information, the porosity, permeability, and water saturation were based on the reservoir properly curves calculated from the multiwell petrophysical analysis. 

There are clearly opportunities for further research in this area, particularly in relating the homogenisation methods to the upscaling and multiscale methods. The results of [23] that show the need for dual permeability models as effective media for 2-phase flow are particularly interesting. Dual permeability behaviour has been observed in the field, [35], in apparently unfractured reservoirs. 

The ideas involved in dual-porosity and dual-permeability models could be more widely applicable to upscaling than is generally realised. By using models that are designed to characterise behaviour involving two time scales, the need for fine scale models can be reduced. 

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