Rapid modeling of borehole measurements of nuclear magnetic resonance via spatial sensitivity functions

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2022-05-06

Authors

Albusairi, Mohammad

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Abstract

Borehole measurements of Nuclear Magnetic Resonance (NMR) are routinely used to estimate in situ rock and fluid properties. Conventional NMR interpretation methods often neglect bed-boundary, mud-filtrate invasion, layer-thickness, and layer-dip effects in the calculation of fluid volumetric concentrations and NMR relaxation-diffusion correlations. Such effects introduce notable spatial averaging of intrinsic rock and fluid properties across thinly-bedded formations or in the vicinity of boundaries between layers exhibiting large property contrasts. Furthermore, the interpretation of NMR measurements entails major technical challenges in horizontal layers penetrated by high-angle and horizontal wells (HAHz) or across dipping layers penetrated by a vertical well. Three-dimensional (3D) geometrical effects, coupled with spatially and petrophysically heterogeneous rocks, may bias petrophysical estimates obtained from borehole NMR measurements when using interpretation procedures designed for vertical wells and horizontal layers. Forward modeling and inversion methods can mitigate the aforementioned effects and improve the accuracy of true layer properties in the presence of mud-filtrate invasion and borehole environmental and 3D geometrical effects across spatially complex formations. This dissertation introduces a fast and accurate algorithm to simulate borehole NMR measurements using the concept of spatial sensitivity functions (SSFs) that honor NMR physics and explicitly incorporate tool, borehole, and geometrical properties. To that end, a 3D multiphysics forward model is developed that couples NMR tool properties, magnetization time evolution, and electromagnetic propagation to derive the 3D spatial sensitivity maps associated with a specific borehole instrument. Additionally, a multifluid relaxation model based on Brownstein-Tarr’s equation is introduced to estimate layer-by-layer NMR porosity decays and relaxation-diffusion correlations from pore-size-dependent rock and fluid properties. The latter model is convolved with the SSFs to reproduce borehole NMR measurements acquired with advanced pulsing sequences (e.g., diffusion-editing and saturation recovery sequences). Results indicate that the spatial sensitivity of NMR measurements is controlled by porosity, electrical conductivity, excitation pulse duration, and tool geometry. The SSF-derived forward approximation is benchmarked and verified against 3D multiphysics simulations for a series of synthetic cases with variable bed thickness and petrophysical properties, as well as in the presence of mud-filtrate invasion. It is shown that the approximation can be executed in a few seconds of central processing unit (CPU), by a factor of 1000 times faster than rigorous multiphysics calculations, with maximum root-mean- square errors (RMSE) of 1%. On average, the fast approximation via SSFs reproduces borehole NMR measurements in 0.08 seconds of CPU time per logging measurement and can therefore be used for real-time calculations and interpretations. Next, the NMR forward modeling approximation is implemented to simulate measurements acquired across dipping formations penetrated by deviated wells in the presence of mud-filtrate invasion. Borehole NMR measurements are simulated by transforming a dipping layered model penetrated by an arbitrary well trajectory into an apparent layered model probed by a vertical well. This work compares the effect of radial length of investigation (DOI) from the three distinct NMR acquisition shells at 3.81 cm (1 in), 6.35 cm (2.5 in) and 10.16 cm (4 in), to integrate borehole NMR measurements acquired in 3D complex geometries. It is found that thinly-bedded formations and their petrophysical properties can be resolved with limited measurement resolution in HAHz wells and highly dipping formations. In thinly-bedded layers (e.g., thinner than 0.15 m) probed by a vertical well, spatial averaging effects bias the NMR porosity logs acquired with high vertical resolution (e.g., sampling rate equals to 2.54 cm). Conversely, formation geometrical and petrophysical properties can be accurately estimated across high apparent-dip formations. It is found that the shallower NMR acquisition shell (3.81 cm) is the least affected by bed-boundary averaging with increasing apparent dip. Moreover, the increase in apparent dip shifts the location of apparent bed boundaries. The latter phenomenon is more pronounced at deeper radial DOI. Interpretation procedures must mitigate such geometrical effects to accurately detect true bed boundaries and estimate layer-by-layer petrophysical properties

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