Reservoir Static Property Estimation Using Nearest-Neighbor Neural Network

TL;DR

This work tackles estimating the spatial distribution of reservoir static properties, such as porosity and permeability, from sparse observations. It introduces a nearest-neighbor neural network that uses the target location coordinates and the coordinates and values of its $m$ nearest neighbors to learn non-linear spatial dependencies, addressing the limitations of IDW and Kriging. A random layer injects stochasticity to produce multiple realizations, enabling uncertainty quantification in the interpolated fields. The method is demonstrated on a simplified 2D porosity example with $N=100$ known sites and $m=15$ neighbors, achieving a validation error of about 0.5%.

Abstract

This note presents an approach for estimating the spatial distribution of static properties in reservoir modeling using a nearest-neighbor neural network. The method leverages the strengths of neural networks in approximating complex, non-linear functions, particularly for tasks involving spatial interpolation. It incorporates a nearest-neighbor algorithm to capture local spatial relationships between data points and introduces randomization to quantify the uncertainty inherent in the interpolation process. This approach addresses the limitations of traditional geostatistical methods, such as Inverse Distance Weighting (IDW) and Kriging, which often fail to model the complex non-linear dependencies in reservoir data. By integrating spatial proximity and uncertainty quantification, the proposed method can improve the accuracy of static property predictions like porosity and permeability.

Figures (3)

• Figure 1: The workflow for estimating reservoir static property using nearest-neighbor neural netwrok
• Figure 2: The locations with known porosity values
• Figure 3: Estimated porosity distribution