Application of Gaussian and Exponential Inversion for 2D Relaxation Maps in Source Rock Oil and Gas Reservoirs

Nuclear magnetic resonance is a standard tool used for the characterization of oil- and gas-bearing geological formations, where the distribution of exponential transverse relaxation times (T2E) corresponding to 1H of fluids provides information on porosity, pore size distribution, and even wettability. In source rock reservoirs with organic-rich shales, signals from solid-like components such as kerogen and bitumen contribute with a distribution of Gaussian decays (T2G). These signals are combined with longitudinal relaxation measurements, and T1–T2 relaxation maps are routinely used to characterize hydrocarbon reservoirs. Distinguishing exponential and Gaussian contributions is not straightforward, and several methods involving both novel pulse sequences and data processing have been developed in recent years. We report a numerical method to invert two-dimensional (2D) data acquired in the time domain to render a 2D representation of the relaxation times of synthetic data resembling those of source rock samples. A crossover between exponential and Gaussian signals is proposed, and a test on the deviations of known parameters is analyzed in a wide range of conditions. The proposed method is robust in the determination of short-lived signals corresponding to solid-like components.