Two new composite, or dual-volume, wellbore models are presented. Both models describe a two-compartment wellbore coupled through a pseudosteady-state flow equation. The models differ in how the wellbore is coupled to the reservoir.
The first model describes the pressure response in a well with a "leaky packer". This model may exhibit two unit-slope lines during wellbore storage, one at earliest times corresponding to the volume of the tubing, and a second one corresponding to the volume of the tubing plus the tubing-casing annulus.
Gringarten noted that apparent wellbore storage coefficients for naturally fractured reservoirs are often one or two orders of magnitude higher than calculated from wellbore geometry, and attributed this effect to storage in natural fractures intersecting the wellbore.1 The second, "near-wellbore fracture storage," model accounts for storage in the fracture system intersecting the wellbore, completion damage, and storage in the wellbore proper.
Both models give pressure responses that are very similar to those exhibited by the model proposed by Fair to describe phase segregation and thermal effects.2, 3 This may explain the success of the Fair model in modeling many situations in which neither phase segregation nor thermal effects are likely to occur.
The "near-wellbore fracture storage" model also gives a pressure response that is almost identical to that exhibited by a pseudosteady-state dual porosity reservoir with wellbore storage. Gringarten observed that a majority of tests in fractured reservoirs appear to exhibit pseudosteady-state rather than transient dual porosity behavior.1 The proposed "near-wellbore fracture storage" model may account for the behavior interpreted as pseudosteady state dual porosity in many of these cases.
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