Abstract: The growth of a hydraulic fracture increases the period of free oscillations in the well connected to the fracture. Simultaneously, the decay rate of free oscillations decreases. The properties of forced oscillations in a well also change during fracture growth. All of these effects result from the changing impedance of the hydraulic fracture that intersects the well. Hydraulic fracture impedance can be defined in terms of the hydraulic resistance and the hydraulic capacitance of a fracture. Fracture impedance can be determined directly by measuring the ratio of down hole pressure and flow oscillation or indirectly from well head impedance measurements using impedance transfere functions. Well head pressure measurements can also be used to evaluate fracture impedance by comparing them to pressure oscillations computed with hydraulic models that include fractures with different impedances.

Abstract: An improved tilt meter mechanism characterized by a pyramidal pendulum support for a tilt sensor, and means for leveling the support to zero the sensor. A pair of motor driven gibs movable along vertical rails are provided, and a biasing mechanism urges angled faces of the support firmly against the gibs. To zero the tilt sensor, the motors associated with the gibs are individually actuated to move the gibs in directions substantially normal to the X-Y measurement plane of the sensor to bring the X-Y measurement plane into alignment with a gravitationally normal reference plane.