An application of an Embedded Model Estimator to a synthetic non-stationary reservoir model with multiple secondary variables

TL;DR

This paper introduces Ember, a novel non-stationary spatial modeling method combining Geostatistics and Random Forests, applied to a 3D reservoir model with multiple secondary variables, enabling location-specific stochastic simulations.

Contribution

It extends Random Forests for non-stationary spatial modeling by integrating simpler interpolation algorithms and producing location-dependent stochastic simulations.

Findings

Successfully applied to a synthetic reservoir model

Produces a model envelope for conditional distributions

Enables variable influence and variability in simulations

Abstract

A method (Ember) for non-stationary spatial modelling with multiple secondary variables by combining Geostatistics with Random Forests is applied to a three-dimensional Reservoir Model. It extends the Random Forest method to an interpolation algorithm retaining similar consistency properties to both Geostatistical algorithms and Random Forests. It allows embedding of simpler interpolation algorithms into the process, combining them through the Random Forest training process. The algorithm estimates a conditional distribution at each target location. The family of such distributions is called the model envelope. An algorithm to produce stochastic simulations from the envelope is demonstrated. This algorithm allows the influence of the secondary variables as well as the variability of the result to vary by location in the simulation.