This work describes a statistical rock-physics-driven inversion of seismic acoustic impedance (AI) and ultradeep azimuthal resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation, and facies classes around the wellbore. Despite their limited resolution, seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effects of pore space and fluid saturation in the joint acoustic and electrical domains.

The proposed inversion does not explicitly use a forward model, rather the correlation between the petrophysical properties and the resulting geophysical responses is inferred probabilistically from a training data set. The training set is generated by combining available borehole information with a statistical rock-physics modeling approach. In the inversion process, given colocated measurements of seismic AI and logging-while-drilling (LWD) electromagnetic resistivity data, the pointwise probability distribution of rock properties is derived directly from the training data set by applying the kernel density estimation (KDE) algorithm. A nonparametric statistical approach is used to approximate nonsymmetric volumetric distributions of petrophysical properties and to consider the characteristic nonlinear relationship linking water saturation with resistivity. Given an a priori facies classification template for the samples in the training set, it is possible to model the multimodal, facies-dependent behavior of the petrophysical properties, together with their distinctive correlation patterns. A facies-dependent parameterization allows the effect of lithology on acoustic and resistivity responses to be implicitly considered, even though the target properties of inversion are only porosity and saturation.

To provide a realistic uncertainty quantification of the estimated rock properties, a plain Bayesian framework is described to account for rock-physics modeling error and to propagate seismic and resistivity data uncertainties to the inversion results. In this respect, the uncertainty related to the scale difference among the well-log data and seismic is addressed by adopting a scale reconciliation strategy. The main feature of the described inversion lies in its fast implementation based on a look-up table that allows rock properties, with their associated uncertainty, to be estimated in real time following the acquisition and inversion of UDAR data. This gives a robust, straightforward, and fast approach that can be effortlessly integrated into existing workflows to support geosteering operations.

The inversion is validated on a clastic oil-bearing reservoir, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. The results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50 m. These constitute useful information to drive geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.

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