Radial profiling of near-borehole formation velocities by a stepwise inversion of acoustic well logging data

The radial heterogeneity of near-wellbore formation is frequently encountered in petroleum exploration and production. It usually manifests as the variations of formation wave velocities in radial position. Mapping radial variations of formation velocities is of great significance in identifying invaded zones and determining rock properties, which are valuable for engineering measures, such as fracturing, wellbore stability evaluation and optimal well completion. A stepwise inversion scheme is developed to image the radial profiles of formation Pand S-wave velocities. Instead of determining the formation velocity variation and its corresponding radial position simultaneously as traditional methods do, the inversion procedure is divided into two steps: the velocity array is determined by semblance processing of contiguous receiver pairs of acoustic array data, and then the thickness of the layer (radial position) is obtained based on ray theory. The inversion results from Step 1 could be used to guide the operation and decide whether Step 2 is necessary. In addition, calculation on the arrival time of waves is not required in this inversion method, thus mitigating the inaccuracy in processing field data with noises. Firstly, the wave field characteristics of heterogeneous formation models have been analysed, indicating that both amplitude and arrival time differences are caused by heterogeneity. The waveforms are then processed using the stepwise inversion method to estimate the radial profiles of formation wave velocities, where the factors influencing the inversion procedure are also studied. It is shown that, longer TR spacing is required for a specific investigation depth with the decreasing of velocity ratio; the resolution of the velocity inversion profile degrades with the increasing number of receiver pairs. The modelling-based inversion results and the application to field data indicate that, in addition to profiling formation P-wave velocity, our proposed methodology also has encouraging application in mapping formation S-wave velocity. The efficiency and accuracy of the stepwise inversion method enables real-time implementation with fast calculation speed, thus providing useful information of monopole acoustic well logging for engineering.