THE INTERACTION OF TUBE WAVES WITH BOREHOLE FRACTURES, PART II - ANALYTICAL MODELS

We develop a series of analytical models that can be used to interpret Stoneley-wave reflections from fractures intersecting a borehole, thu s facilitating the determination of effective fracture apertures from logs. The first model considers the combined effects of borehole enlar gements (e.g., washouts) and fractures on the reflection coefficient o f Stoneley waves. The result is expressed in terms of the washout volu me, which can be obtained from a caliper log, as well as the fracture width. The predictions of this model are in excellent agreement with f inite-difference calculations. Next we develop an analytical elastic m odel that generalizes the rigid formation model. It also agrees with f inite-difference calculations. Finally, we establish the equivalence b etween a closely spaced multiple fracture and a permeable medium. In a ll the examples, the generalization of the result for the single fract ure in a rigid formation can be accomplished with standard logging mea surements.