Joint inversion for facies and petrophysical properties based on a bi‐level optimization model

Abstract

AbstractIn many subsurface studies, facies and petrophysical properties are two important reservoir parameters that are closely correlated. They are routinely used in well interpretation, hydrocarbon reserve calculation and production profile prediction. These two parameters have commonly been determined in two separate tasks because of their mathematical differences (facies are discrete, and petrophysical properties are continuous). However, this is incorrect because facies and petrophysical properties are often strongly correlated. Therefore, we propose a new joint inversion method of facies and petrophysical properties based on a bi‐level optimization model. In the bi‐level optimization model, the upper‐level problem is the petrophysical property inversion while the lower‐level problem can identify the facies and add a facies‐related constraint for the upper‐level optimization. We also develop a new genetic algorithm for the discrete‐continuous inversion problem based on the bi‐level optimization model because the inversion problem usually has multiple local solutions. In addition, rock physics and statistics are combined in the inversion process. A rock physics model is used to establish the basic relationships between the petrophysical and elastic parameters, and the statistical approach is used to describe the intrinsic connection among the multiple reservoir parameters based on well log data. The numerical experiments indicate that the traditional separate prediction method and the new joint inversion method can quickly obtain more accurate results. In the application examples of real data, the inversion results can be matched to the well log data within the limits of the input data resolution, which further verifies the reliability and application potential of this new method.