Generating Mechanical Stratigraphy in Layered Rock Masses Using Numerical Averaging of Cohesive-frictional Strength

A fundamental question in geomechanical modeling relates to the most accurate and efficient workflow for transforming observed complexity in the earth to a simplified numerical model, with minimal loss of information. This workflow, oftentimes referred to as "upscaling", is a technique for converting a detailed geologic model to a coarser-grid simulation such that the development of stress and deformation in the two systems are comparable. Standard logging tools provide estimates of petrophysical rock properties at a resolution of decimeters, and numerous predictive algorithms have been described that subsequently enable the generation of elastoplastic mechanical properties from such wireline-based petrophysical observations. However, these log-generated mechanical properties can be highly variable over the length scale of a single element in a geomechanical model. The log data must therefore be "upscaled" to mechanical units that are of a tractable size for numerical simulation, and the mechanical properties assigned to these units need to represent the bulk deformation behavior of the heterogeneous material contained within them. To address this question, we examine different techniques for numerically "averaging" observed heterogeneity into a representative value, while restricting ourselves to a "layer cake" geometry. We also identify important length scales in the problem that influence how deformation is distributed amongst, or localized within, mechanical units. Using this insight we are able to develop methods to intelligently generate units of mechanical stratigraphy, dependent on the model application, that are based on a distribution of mechanical properties with depth. To help validate the numerical methods used to "average" mechanical properties into an upscaled value, we apply the technique to strength data generated from laboratory testing of layered composite samples. Stress and plastic strain development in large-scale geomechanical models that have been mechanically upscaled are compared with equivalent models containing full geologic complexity, and show good agreement.