Estimation of Mercury Injection Capillary Pressure (MICP) from the Nuclear Magnetic Resonance (NMR) exponential decay with the Machine Learning (ML) Neural Network (NN) approach

Abstract

Information about the capillary pressure has a wide range of applications in the petroleum industry, such as an estimation of irreducible water saturation, calculation of formation absolute permeability, determination of hydrocarbon-water contact and the thickness of the transition zone, evaluation of the seal capacity, and an estimation of relative permeability. All the listed parameters in the combination with petrophysical features, pressures, and fluid properties allow us to evaluate the economic viability of the well or the field overall. For this reason, capillary pressure curves are of great importance for petroleum engineers working on any stage of the field development: starting from exploration and finishing with production stages. Nowadays, capillary pressure experiments are provided either in the lab on the plugs of the rocks, either in the well on the certain stop points with the formation tester tools on the wire or tubes. Core extraction and formation testing are both laborious, expensive, and complicated processes since the newly-drilled well remain in the risky uncased condition during these operations, and for this reason, usually the listed works are provided in the exploration wells only. Afterward, the properties obtained from the exploration wells are assumed to be the same for the extraction or any other kinds of wells. Therefore, these days petroleum engineers have limited access to the capillary pressure curves: the modern tests are provided on the limited points of formation in the limited number of wells. An extension of capillary pressure measurements in the continuous mode for every well will dramatically expand the abilities of modern formation evaluation and significantly improve the field operation management by reducing the degree of uncertainty in the decision-making processes. This work is the first step toward continuous capillary pressure evaluation. Here we describe the procedure of finding the correlation between the results of the lab Nuclear Magnetic Resonance (NMR) experiment and lab Mercury Injection Capillary Pressure (MICP) measurements. Both experiments were provided on the 9 core plugs of the sandstone. Afterward, a Machine Learning (ML) algorithm was applied to generate additional samples of the porous media with different petrophysical properties representing the variations of the real cores of available sandstones. Overall, 405 additional digital rock models were generated. Thereafter, the digital simulations of MICP and NMR experiments were provided on the generated database of digital rocks. All the simulations were corrected for limited resolution of the CT scan. Based on the created database of experiments, we implemented a ML algorithm that found a correlation between the NMR echo data and MICP capillary pressure curves. Obtained correlation allows to calculate capillary pressure curve from the NMR echo data. Since NMR logging may be implemented in every well in the continuous mode, an extension of the created technique provides an opportunity for continuous estimation of capillary pressure for the whole logging interval. This extension is planned as future work.