Fast-forward modeling of borehole nuclear magnetic resonance measurements acquired in deviated wells and spatially heterogeneous formations

Abstract

High-angle and horizontal (HAHz) 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 HAHz wells or through dipping formation layers penetrated by a vertical well. Three-dimensional geometric 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 requires an accurate and rapid forward-modeling method that integrates NMR physics and tool/instrument specifications, borehole, and 3D formation geometric 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. We validate and verify the fast approximation against a 3D multiphysics model using challenging synthetic cases, in highly apparent dip wells with the varying radial front of the 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 3D complex geometries. On average, the fast approximation via SSFs reproduces NMR measurements in 3 s of central processing unit 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.