The Projection-Pursuit Multivariate Transform for Improved Continuous Variable Modeling

Abstract

Summary Reservoir process-performance evaluation requires the simulation of multiple continuous variables such as porosity, water saturation, and permeability. Geostatistical realizations should reproduce the univariate and multivariate statistics that are deemed representative of the reservoir. A conventional work flow that sequentially applies cosimulation and cloud transformations is frequently used for this multivariate simulation. Although it effectively reproduces univariate properties, a common issue with this work flow is its inability to reproduce all the multivariate relationships that exist between variables. To resolve this issue, the projection-pursuit multivariate transform (PPMT) is applied to reservoir modeling. The PPMT work flow requires fewer steps, no manual tuning, and fewer assumptions than the conventional work flow. Background, essential steps, and practical considerations of the conventional and PPMT work flows are outlined before comparing them in a case study. The PPMT is shown to yield multivariate reproduction that is expected to improve reservoir forecasting.