Estimation of hydraulic fracture geometry from pumping pressure

Abstract

A pump is coupled through a discharge line to a wellbore, which in turn intersects a fracture, the wellbore and fracture being filled with fluid to form a fluid system. Sensors are located in position at the top and, under certain circumstances, at the bottom of the wellbore. The dimensions of the fracture are calculated from data generated by the sensors by analyzing the incident and reflected waves within the fluid system the acoustic waves being generated by pressure pulses from a pump and travel from the pump through the fluid into the fracture. In preferred embodiments of this invention, transfer functions are developed by analysis of the data, so that the data recorded by sensors at the top of the wellbore accurately represent pressure fluctuations at the bottom of the wellbore. Transfer functions relating pressure fluctuations at the top of the wellbore to pressure fluctuations at the bottom of the wellbore, i.e., at the mouth of the fracture, exhibit resonant phenomena in the fracture from which fracture length can be determined. A Fourier transform is generated of transfer fucntions relating the impulse at the top of the annulus to the impulse response at the fracture entrance and through the fracture, to provide a time domain analysis of the waves in the fracture. This way, travel times of waves in the fracture can be determined, and this data used to estimate the length and height of the fracture, given that the wave speed in the fracture is known.