Probabilistic petrophysical and compositional interpretation of well logs and core data via Bayesian inversion

A critical component of Formation Evaluation is the estimation of in situ petrophysical properties and solid/fluid composition of rocks from multiple well logs and core laboratory measurements. Commercial software solutions abound; they typically use linear/quasi-linear multi-mineral analysis to calculate the concentrations of rock solid/fluid constituents from multiple well logs. However, these methods are often susceptible to abnormal borehole and geometrical conditions such as layer-boundary effects and instrument/borehole-related biases. Moreover, conventional multi-mineral analysis rarely includes uncertainty quantification, much less assessing the impact of measurement noise, abnormal borehole conditions, and inaccurate rock-physics models (RPM) on the calculated rock fluid/solid concentrations. The objective of this dissertation is to develop a general probabilistic interpretation method for estimating in situ petrophysical/compositional properties of rocks from well logs and core data. It consists of two sequential Bayesian inversion steps: First, borehole measurements (e.g., density, resistivity, and gamma ray) are “deconvolved” into a layer-by-layer earth model with associated uncertainty via separate well-log inversion. Second, inverted earth-model physical properties are used to estimate volumetric concentrations of fluid and solid rock constituents via petrophysical joint inversion. In each step, Bayesian inversion implements Markov chain Monte Carlo (MCMC) and outputs an ensemble of earth models. Final interpretation results incorporate field-specific a priori knowledge and uncertainty due to measurement noise, instrument/borehole-related biases, and RPM errors. Additionally, a gradient-based MCMC method is introduced for separate well-log inversion to improve the computational efficiency of the probabilistic estimation method. The gradient-based MCMC implements a Gauss-Newton algorithm with Hessian-based sampling to draw samples efficiently from the posterior probability distribution. Compared to the standard random-walk MCMC method, gradient-based MCMC inversion decreases the computational time by more than 90%. A pre-computed surrogate model is also introduced for the rapid calculation of nuclear properties based on radial basis function (RBF) interpolation, which entails ~0.1% of the computational time compared to performing full nuclear-property calculations with less than 0.1% relative error. Finally, the probabilistic inversion method is applied to the interpretation of well logs acquired in multiple neighboring wells. After the mitigation of borehole environmental effects, the inverted earth model is instrument/borehole-independent, allowing a common baseline to effectively compare rock properties across the various wells and detect common rock classes. This procedure also enables the implementation of RPMs and prior compositional models calibrated per rock class to match core laboratory and/or advanced borehole measurements available in a few key wells. The calibrated RPMs and priors are readily implemented in nearby wells penetrating the same rock formations but with a limited number of well logs. The developed multi-well interpretation method is verified using synthetic examples with challenging geological conditions, including thin laminations, significant property contrasts, deep mud-filtrate invasion, complex rock constituents, and various logging instrumental designs (e.g., laterolog vs. induction resistivity). Successful field applications are also documented for the petrophysical interpretation of thinly-laminated shaly sandstones and unconventional organic-shale formations. Results confirm that the probabilistic interpretation method yields more accurate petrophysical estimations compared to the conventional multi-mineral analysis method. Estimated petrophysical and compositional properties and their uncertainty are in good agreement with both core laboratory measurements and interpreted elemental capture spectroscopy logs