Prediction of Petrophysical Properties Using Machine Learning and Hierarchical Multi-Task Linear Models
Abstract
Petrophysical characterization of reservoir rocks is a fundamental step in the evaluation of oil reservoirs, and is usually executed through laboratory experiments that incur in large costs and schedules. In this work, statistical techniques and machine learning models were evaluated fo the estimation of absolute permeability, oil-water capillary pressure and water-oil relative permeability curves, using mercury injection porosimetry, absolute permeability and porosity data. Through the exploration of several feature engineering and modeling strategies, machine learning and statistical models were assessed and compared to classical linear methods. Multi-task and hierarchical linear models were also evaluated for the estimation of special core analysis parameters from mecrcury injection porosimetry and routine core analysis data. On the evaluated dataset, hiearchical linear models were shown to have better precision, consistency and lower posterior uncertainty metrics when compared to simple linear regression models.
Chapter 1 Introduction
Since the beginning of the 20th century, oil and the combustion engine have transformed many aspects of modern society in fundamental ways. As a cheap and reliable energy source, oil provided the means for revolutions in transportation, manufacturing, commerce and human behavior, in general. It remains a cornerstone of our society in 2020.
As knowledge of the warming effects of carbon in earth’s atmosphere is further developed, conscious and economically sustainable exploitation of remaining oil reserves becomes paramount (Mackay 2009). The high volatility of oil prices induced by supply and demand shocks in recent years further complicates the assessment of oil and gas projects.
Reservoir engineering is a branch of petroleum engineering that studies fluid flow through porous hydrocarbon bearing rocks (Dake 2015). Assessment of oil and gas exploitation projects is commonly performed using numerical simulation models that incorporate geological, fluid and petrophysical information to predict oil and gas production curves. Reservoir uncertainties are particularly important at the beginning of a project, when few wells have been drilled, fluid and rock samples are scarce, and no production data is available.
Figure 1.1: Reservoir Engineering Simulation Models
Petrophysical characterization entails the evaluation of physical and chemical properties of porous media, and its interaction with reservoir fluids. It is commonly performed through laboratory experiments, known in the petroleum industry as routine and special core analysis (Peters 2012). Routine petrophysical experiments characterize rock porosity and absolute permeability, are considered inexpensive and can be performed in little time, usually taking no more than a couple of days per sample. Special core analysis, characterize properties related to the balance of viscous and capillary forces acting at reservoir conditions and, in many situations, can be expensive and demand long experiments, which can take up to several months to be executed (Tiab and Donaldson 2004).
In this work, statistical methods were evaluated for the estimation of petrophysical properties using as input Mercury Injection Capillary Pressure (MICP) and routine core analysis data. This work is organized as follows: on chapter , petrophysical measurement methods and properties are briefly described; on chapter , black-box machine learning models for the prediction of absolute permeability from MICP data are evaluated and compared to classical linear models; on chapter , linear models for the prediction of special core analysis properties, using multi-task and hierarchical models, are studied; limitations and desirable features of the evaluated methods are further discussed on chapter .
References
Dake, L. P. 2015. Fundamentals fo Reservoir Engineering. https://doi.org/10.1016/B978-0-08-098206-9.00004-X.
Mackay, David J. C. 2009. Sustainable Energy–without the Hot Air.
Peters, E. J. 2012. Advanced Petrophysics. Austin: Live Oak Book Company.
Tiab, Djebbar, and E. C. Donaldson. 2004. Petrophysics: theory and practice of measuring reservoir rock and fluid transport properties. Boston: Golf Professional Pub.