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Selection of a Suitable Rock Mixing Method for Computing Gardner’s Constant Through a Machine Learning (ML) Approach to Estimate the Compressional Velocity: A study from the Jaisalmer sub-basin, India

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Abstract

The frequent variability of petrophysical properties makes hydrocarbon exploration challenging in carbonate reservoirs. Nowadays, quantitative interpretation (QI) is an essential part of hydrocarbon exploration in a complex reservoir, which needs adequate rock physics data at the well level. However, sometimes the relevant data are not available in earlier discovered oil and gas fields. We observed that the old oil and gas fields in the onshore parts of India have a scarcity of density and compressional velocity (Vp) data at the well level. Gardner's empirical expression provides the scope to estimate Vp from acquired density data and vice versa. However, there are two constants in this relationship, and these are different for different saturation cases of the reservoir due to different mineralogical content in the reservoir rock. The current study aims to identify suitable rock mineral mixing methods and their related uncertainty for estimating Gardner's constants. This uncertainty leads to the estimation of the degree of unwanted flexibility for Vp measurement. Improper selection of the rock mineral mixing method generates uncertainties during the fluid substitution model, mainly where available data are limited. A machine learning (ML) approach based on the naïve Bayes algorithm was adopted in this study to select the appropriate rock mineral mixing method from a limited data set. The study was performed in a carbonate reservoir in an onshore sedimentary basin of western India. The ML study shows that the Reuss rock mineral mixing method is suitable for the computation of Gardner's constant in different saturation models for this carbonate reservoir, with less uncertainty.

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Abbreviations

\(\rho_{{\text{b}}}\) :

Bulk density

a, b :

Gardner’s constants

\(V_{{\text{p}}}\) :

P-wave velocity

\(V_{{\text{s}}}\) :

S-wave velocity

\(V_{{{\text{p2}}}}\) :

P-wave velocity after fluid substitution

\(V_{{{\text{s2}}}}\) :

S-wave velocity after fluid substitution

\(\mu\) :

Shear modulus

\(\rho_{{\text{f}}}\) :

Fluid density

\(\rho_{{\text{m}}}\) :

Matrix density

\(\rho_{{{\text{f1}}}}\) :

Initial fluid density

\(\rho_{{{\text{f2}}}}\) :

Density of saturated fluid

\(\emptyset\) :

Porosity

\(k_{{{\text{sat}}}}\) :

Saturated bulk modulus

\(k_{{{\text{frame}}}}\) :

Porous rock frame bulk modulus

\(k_{{{\text{matrix}}}}\) :

Mineral matrix bulk modulus

\(k_{{{\text{fl}}}}\) :

Fluid bulk modulus

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Acknowledgements

We gratefully acknowledge Gujarat State Petroleum Corporation Limited regarding the encouragement of research activity and various technical data support, analysis, and various application support for research activity. Our sincere gratitude to HLS ASIA and Schlumberger India to acquire the well log data in the study area and provide other technical support in the study area. The authors are profoundly thankful to the Exploration Seismic and Simulation Lab., Department of Applied Geophysics, IIT (ISM) Dhanbad for providing support to carry this research work. Our sincere thanks to all those associated team members and service providers who are directly or indirectly involved in the study area's technical work.

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  1. Department of Applied Geophysics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India

    Pydiraju Yalamanchi & Saurabh Datta Gupta

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  1. Pydiraju Yalamanchi
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  2. Saurabh Datta Gupta
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Correspondence to Saurabh Datta Gupta.

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Yalamanchi, P., Datta Gupta, S. Selection of a Suitable Rock Mixing Method for Computing Gardner’s Constant Through a Machine Learning (ML) Approach to Estimate the Compressional Velocity: A study from the Jaisalmer sub-basin, India. Pure Appl. Geophys. 178, 1825–1844 (2021). https://doi.org/10.1007/s00024-021-02733-y

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