Borehole petrophysical imaging of induction and acoustic data

Summary form only given. Two of the most important answer products of the traditional petrophysical processing are porosity and hydrocarbon saturation, which are usually presented as logging curves representing volumetric averages of the corresponding petrophysical properties only. In general, those petrophysical properties are distributed inhomogeneously around the wellbore. For cases, such as the existence of mud-filtrate invasion, those logging curves could be far off from the true values, thus leading to erroneous formation evaluation. As a result, for accurate formation evaluation, it is preferable to obtain the distributions of those petrophysical properties around the wellbore. Moreover, in general, multi-physics measurements are required to obtain both porosity and fluid saturations. Advancements in modern well logging technology have made this possible. For example, the tri-axial induction tool and sonic tool are capable of making three-dimensional induction and sonic measurements at multiple depths of investigation at multi-frequencies. In other words, these tools can make measurements in a wide spatial and spectral coverage. In addition, these tools can also see past the altered zone by mud-filtrate invasion and provides measurements for the unaltered zone. The availability of these measurements makes it possible to derive porosity and fluid saturation images around the borehole, which could result in enhanced porosity and hydrocarbon saturation estimates, thus leading to improved reservoir characterization. In this paper, an inversion method is developed for directly obtaining porosity and fluid saturation distributions by simultaneously inverting borehole induction and sonic measurements via petrophysical relationships. The inversion is accomplished by fitting both induction and sonic measurements in an automated manner using the state of the art regularization technique and modern parallel computation techniques. We present several examples covering situations like mud-filtrate invasion, fault, fractures, as well as water flooding, which show the proposed joint inversion reduces the non-uniqueness of determining porosity and fluid saturation distributions, which cannot be achieved with inversions using sonic data or induction data only. We show that the induction measurements and acoustic measurements can benefit each other so that improved porosity and fluid saturations distributions can be obtained. Induction measurements can extend the spatial reach of the acoustic measurements while the acoustic measurements can better condition the induction measurements in such a way that the saturation images can be obtained with enhanced resolution.