Topological Data Analysis to Solve Big Data Problem in Reservoir Engineering: Application to Inverted 4D Seismic Data

Abstract

Abstract Data analysis is one of the most important topics in any industry. In petroleum engineering, the large, complex, and multi-dimensional reservoir data sets (big data) presents a challenge for engineers to study the masses of unstructured information and make decisions. A new approach to analyze complex data is called Topological Data Analysis (TDA) which aims to extract meaningful information from such data. TDA relies on the concept that complex data has shapes where shape has meanings. It analyzes the shape of complex data, identifying clusters and their statistical significance. The objective of this paper is to introduce TDA to reservoir engineering using an example of inverted 4D seismic data for studying reservoir connectivity and compartmentalization. In this paper, we introduce the principles of TDA and discuss its potential in reservoir engineering, which could allow identification of reservoir engineering data behavior, recognition of new opportunities, detection of anomalies and events, and minimizing uncertainties. The TDA procedures are introduced using inverted 4D seismic data set to study reservoir connectivity and compartmentalization. The process to generate and process the data set is explained. Similarity distance function and lenses are defined and used to create TDA graphs for feature identification and analysis. It is shown that TDA is able to predict the compartmentaliztion of the reservoir models with various process configurations. Variance normalized Euclidean and topological neighborhood function are used successfully to compartmentalize the reservoir model. Using normalized input dataset, correlation and principle component analysis also create similar compartments. The success of TDA in discovering meaningful patterns is attributed to the similarity distance function representing the objective of study, one or more lenses exposing the data, and the right combination of input data, similarity distance function and lenses. A promising big data analysis method, TDA, is introduced to reservoir engineering application with principles, procedures and examples. It has been shown that TDA can automatically discover critical intelligence within the 4D seismic data set for studying reservoir connectivity and compartmentalization, which are essential to the accuracy of forecasts and development plans, the validity of reservoir simulation, and the success of performance diagnostics and optimization.