Bayesian inversion for rapid multiwell interpretation of well logs and core data: Applications to unconventional organic-shale formations

Abstract

Multimineral analysis is widely used to calculate in situ porosity, fluid saturation, and mineralogy of rocks penetrated by a well. It delivers weight/volumetric concentrations of rock solid/fluid constituents by combining multiple borehole geophysical measurements and often is referred to as petrophysical joint inversion. Recently, a probabilistic method was developed for improved petrophysical estimation of rock constituents and their uncertainty from well logs. This method mitigates borehole and instrument-related environmental effects present in the measurements and efficiently propagates the uncertainty from measurement noise and rock-physics models (RPMs) to compositional/petrophysical estimations. The probabilistic estimation method is extended to the challenging conditions of multiple neighboring wells penetrating similar rock formations where borehole/drilling environmental conditions, borehole instruments, and measurement noise may vary from well to well. A calibration step is performed in a few key wells with core data and/or advanced borehole measurements; it enables the same RPMs and prior models to be implemented in nearby wells but with limited measurements. In addition, a precomputed surrogate model constructed with radial basis function interpolation is implemented for accurate and efficient nuclear-property calculations. The multiwell interpretation method is verified using synthetic and field examples of organic-rich shale formations. Results find that the probabilistic method (1) improves rock petrophysical/compositional estimations by mitigating borehole environmental effects and incorporating a priori knowledge, (2) yields regionally consistent compositions among wells, and (3) quantifies the uncertainty of the estimations. As a result, the probabilistic approach is especially suitable for assessing petrophysical/compositional properties in multiwell settings with complex rock constituents and/or limited borehole measurements.