Real-Time Rock-Properties Estimation for Geosteering: Statistical Rock-Physics Driven Inversion of Seismic Acoustic Impedance and LWD Ultra Deep Azimuthal Resistivity.
Authors: Ciabarri Fabio , Tarchiani Cristiano , Alberelli Gioele , Chinellato Filippo , Mele Maurizio , Marini Junio Alfonso , Nickel Michel , Borgos Hilde , Vaaland Dahl Geir 
Published: June 2023

Abstract
This work describes a statistical rock-physics driven inversion of seismic acoustic impedance and Ultra Deep Azimuthal Resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation and litho-fluid facies classes around the wellbore. Despite their limited resolution, surface seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effect of pore space and fluid saturation in the joint acoustic and electrical domains.
The key aspect of the proposed inversion is that it 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 dataset. The training-set is generated combining available borehole information with statistical rock-physics modelling approach. In the inversion process, given co-located measurements of seismic acoustic impedance and logging-while-drilling electromagnetic resistivity data, the pointwise probability distribution of rock-properties is derived directly from the training dataset by applying the kernel density estimation algorithm. A non-parametric statistical approach is employed to approximate non-symmetric volumetric distributions of petrophysical properties and to consider the characteristic non-linear 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 response 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 which accounts for rock-physics modelling 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 based on probabilistic function. This allows transforming physically equivalent measures from one resolution to another and consistently estimate the corresponding changes in the probability distributions. The described rock physics-driven inversion can be performed efficiently during drilling, following the acquisition and inversion of UDAR data, as the time-consuming step of estimating a probabilistic model from the training-set, can be separated from inversion itself. This is of particular interest in geosteering, where the training-phase can be performed before drilling, during well planning operations. After training, the resulting probabilistic model can be stored as a look-up table. Hence, the prediction of rock-properties, given the co-located measurements of seismic acoustic impedance and log-while-drilling electromagnetic resistivity, reduces to a fast look-up table search.
The inversion workflow is validated on a clastic oil-bearing reservoir located offshore Norway, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. A complete set of well logs from four nearby exploration wells is used to construct the training dataset. Porosity, water-saturation, and litho-fluid facies are estimated along the geosteered well path given a 2D curtain section of ultra deep azimuthal resistivity and the corresponding acoustic impedance section available from the 3D surface seismic data. Prior to running the inversion, the acoustic impedance data was properly depth-matched with the resistivity section using a non-rigid matching algorithm. The joint inversion results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50m. These results constitute useful information to support geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.