Harmonic Testing of Hydraulically Fractured Wells

Hydraulic fracturing is an effective technique for increasing productivity of damaged wells and wells producing in low permeability formation. Various methods have been proposed to estimate reservoir and fracture properties from transient pressure and flow rate data. The basic concept of harmonic testing is the use of a sinusoidal flow rate variation instead of a step change as in conventional well testing. When a pseudo-steady flow regime is achieved after a few periods, both flow rate and wellbore pressure exhibit a sinusoidal behavior. It is then possible to identify the modulus of the response and phase shift between the two signals. These data are used to evaluate the reservoir parameters. In this study, new analytical solutions are presented for analyzing amplitude- and phase-frequency characteristics of fractured wells in homogeneous or double-porosity reservoirs. The influence of wellbore storage effect, fracture storage and conductivity on the pressure modulus and phase shift is investigated. In case of high dimensionless frequencies a set of asymptotic solution is derived. These solutions can be used to solve the inverse problems for obtaining the formation and fracture properties.