The Scaleup of Two-Phase Flow in Porous Media Using Phase Permeability Tensors
- G.E. Pickup (Heriot-Watt U.) | K.S. Sorbie (Heriot-Watt U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 1996
- Document Type
- Journal Paper
- 369 - 382
- 1996. Society of Petroleum Engineers
- 4.3.4 Scale, 5.5.3 Scaling Methods, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.5 Reservoir Simulation, 7.2.2 Risk Management Systems, 1.8.5 Phase Trapping, 5.1.5 Geologic Modeling, 5.3.1 Flow in Porous Media, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc)
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First presented at the SPEAnnual Technical Conference & Exhibitionheld in New Orleans, 25-28 September, 1994, as "Development andApplication of a New Two-Phase Scaleup Method Based on TensorPermeabilities".
The effects of different levels of geological heterogeneity on a fluiddisplacement process may be captured at a larger scale using scaleuptechniques. In the context of reservoir simulation, these are algorithms whichshould reproduce the results of fine grid calculations on a coarser grid. Thesetechniques are referred to as pseudo-isation, the main objective being toproduce pseudo-functions which can be used on the coarse grid. When carried outsuccessfully, the pseudo-functions (e.g. pseudo relative permeabilities)incorporate the interaction between the fluid mechanics and the heterogeneityas well as correcting for numerical dispersion. These pseudo-functions alsodepend on the viscous/capillary and viscous/gravity ratios and are valid forthe boundary conditions relevant to the particular flows.
For single phase flow, the scaleup problem involves the derivation ofeffective permeability which, in general, is a tensor quantity. Multi-phaseflow is more complex since scaled-up dynamic transport quantities must becalculated which depend on phase saturation, flow rate etc. In this paper, wepresent a method which extends the idea of tensor (absolute) permeability totensor effective phase permeabilities. They are extensions of conventionalfunctions which also include the off-diagonal phase crossflow terms which maybe important in certain systems. Two- phase tensor methods are presented whichare valid (a) in the capillary equilibrium limit and (b) for arbitrary valuesof viscous/capillary and viscous/gravity ratios. Numerical examples of theapplication of these methods are presented for ripple-bedded systems where thetwo-phase crossflow effects are significant, and where oil trapping within thelamina structure
may occur under certain conditions. The results show that it is important touse phase tensors in upscaling where gravity effects are significant, in orderto generate the correct vertical flows.
The modelling of two-phase flow through porous media is important forforecasting hydrocarbon recovery in oil and gas reservoirs. This process iscomplicated by the fact that rocks may be very heterogeneous over a wide rangeof length scales. If the effects of these heterogeneities are to be taken intoaccount in full-scale simulations, a method is required for averaging flowproperties from small-scale models, for incorporation in larger-scale ones. Thecalculation of effective flow properties (sometimes known as pseudoproperties)has been studied, from different view points, by a number of authors. Generallyspeaking, scaleup can only be carried out successfully when there is aseparation of length-scales. In fact, many sedimentary rocks do exhibitheterogeneities at distinct length scales, e.g. laminae (em), beds (m),formations (10m). Corbett et al have shown that it is feasible to scaleuptwo-phase flow using such geologically based length scales.
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