High-angle and horizontal wells are routinely drilled to enhance reservoir exposure and increase fluid productivity. The interpretation of nuclear magnetic resonance (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 using methods designed for vertical wells and horizontal layers. Reliable interpretation of the measurements requires an accurate and rapid forward modeling method that integrates NMR physics and tool/instrument specifications, borehole, and 3D formation geometrical properties. The latter is possible with the recent development of a forward modeling algorithm that accurately and efficiently simulates NMR measurements based on 3D spatial sensitivity functions (SSFs). We implement and quantify this forward modeling approximation across dipping formations penetrated by deviated wells in the presence of mud-filtrate invasion. The fast approximation is validated and verified against 3D numerical simulations using challenging synthetic cases of high apparent-dip wells with varying radial front of mud-filtrate invasion. Our work compares the effect of radial length of investigation from the three distinct NMR acquisition shells to better understand borehole NMR measurements acquired in complex 3D geometries. On average, the fast approximation via SSFs reproduces NMR measurements in 3 seconds of central processing unit (CPU) time with maximum root-mean-square errors below 1% and can therefore be used for real-time calculations and interpretations. Modeling results indicate that thinly-bedded formations and their petrophysical properties can be resolved with relatively low measurement resolution in HAHz wells and dipping formations.

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 and layer-thickness 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. 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 effects across spatially complex formations. We have developed a fast and accurate algorithm to simulate borehole NMR measurements using the concept of spatial sensitivity functions (SSFs) that honor NMR physics and incorporate tool, borehole, and formation geometry. Tool sensitivity maps are derived from a 3D multiphysics forward model that couples NMR tool properties, magnetization evolution, and electromagnetic propagation. In addition, a multifluid relaxation model based on Brownstein-Tarr’s equation is introduced to estimate 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. The results indicate that NMR spatial sensitivity is controlled by porosity, electrical conductivity, excitation pulse duration, and tool geometry. We benchmark and verify the SSF-derived forward approximation against 3D multiphysics simulations for a series of synthetic cases with variable bed thickness and petrophysical properties, and in the presence of mud-filtrate invasion in a vertical well. Results indicate that the approximation can be executed in a few seconds in a central processing unit, by a factor of 1000 times faster than rigorous multiphysics calculations, with maximum root-mean-square errors of 1%.

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