One-dimensional radial flow equation, of which permeabilityrnand porosity are in inversely proportional to the radius, isrnequivalent to the equation of linear flow. In other words, if werntake the radial variations of permeability and porosity intornconsideration, we can represent the linear flow by onedimensionalrnradial flow equation. To expand this idea and tornapply it for various types of inner and outer boundary shapes,rnwe defined the S-function by “The functions of reservoirrnproperties in radail direction which should be used for a radialrncomposite model in order to represent the pressure transientrnbehavior at the well location for given inner- and/or outer-rnboundary shapes“. The pressure behavior of the radial multicompositernmodel includes lots of pressure type curves. Forrnexample, one can reproduce the pressure transient behavior ofrnchannel type, sealing fault and hydraulic fractured well, etc byrnthe radial multi-composite model with assigning thernpermeability and porosity distribution along radial directionrnadequately.rnWe found that the approximate S-function can be easilyrnestimated from steady state streamlines. The compositernmodels with the S-functions reproduce “sealing fault”,rn“channel type”, “horizontal sink” and “the reservoir which hasrndifferent transmissibility regions”. We compared the resultsrnwith the conventional analytical solutions by commercialrnsoftware, and obtained excellent agreement.rnNot only its high novelty and expandability, but itsrncalculation speed and visibility, this methodology (S-function)rnwill be a powerful tool for pressure transient analyses.
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