Lossy transmission line model of hydrofractured well dynamics

The real-time detection of hydrofracture growth is crucial to the successful operation of water, CO₂ or steam injection wells in low-permeability reservoirs and to the prevention of subsidence and well failure. In this paper, we describe propagation of very low frequency (1-10 to 100 Hz) Stoneley waves in a fluid-filled wellbore and their interactions with the fundamental wave mode in a vertical hydrofracture. We demonstrate that Stoneley-wave loss energy to the fracture and the energy transfer from the wellbore to the fracture opening is most efficient in soft rocks. We conclude that placing the wave source and receivers beneath the injection packer provides the most efficient means of hydrofracture monitoring. We then present the lossy transmission line model of wellbore and fracture for the detection and characterization of fracture state and volume. We show that this model captures the wellbore and fracture geometry, the physical properties of injected fluid and the wellbore-fracture system dynamics. The model is then compared with experimentally measured well responses. The simulated responses are in good agreement with published experimental data from several water injection wells with depths ranging from 1000 ft to 9000 ft. Hence, we conclude that the transmission line model of water injectors adequately captures wellbore and fracture dynamics. Using an extensive data set for the South Belridge Diatomite waterfloods, we demonstrate that even for very shallow wells the fracture size and state can be adequately recognized at wellhead. Finally, we simulate the effects of hydrofracture extension on the transient response to a pulse signal generated at wellhead. We show that hydrofracture extensions can indeed be detected by monitoring the wellhead pressure at sufficiently low frequencies. (C) 2000 Elsevier Science B.V. All rights reserved.