Mixing laws and fluid substitution for interpretation of magnetic resonance measurements
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Nuclear magnetic resonance (NMR) relaxation time measurements are affected by pore structure and saturating fluids. Interpretation of NMR distributions as pore-size distributions and estimation of permeability from NMR logs using methods such as the Schlumberger Doll Research (SDR) model assume a homogeneous surface relaxivity and remain reliable only for measurements obtained from homogeneous single-fluid saturated rocks. However, heterogeneous rock formations commonly consist of laminations, vugs, and a mixed solid composition, which result in non-uniform values of surface relaxivity. Furthermore, most rock formations penetrated by wells contain multiple fluids and are commonly affected by mud-filtrate invasion. Therefore, presence of spatial heterogeneity and multiple fluids in rock formations render the petrophysical interpretation and analysis of longitudinal relaxation time T1 and transverse relaxation time T2 measurements challenging. Thus, it is necessary to correct for spatial heterogeneity by decomposing the NMR response of the heterogeneous formation into that of its homogeneous components. Presence of multiple fluids is corrected by replacing the hydrocarbon NMR response in the original logs with the corresponding water response in order to obtain NMR distributions of the 100% water saturated formation. Subsequently, the petrophysical quantities of interest such as permeability and pore-size distribution are determined. NMR mixing laws define the physics of how NMR data from different homogeneous components combine. It was observed that a linear mixing law best describes a laminated formation and a non-linear mixing law best describes a dispersed formation. In this work, NMR mixing laws are derived and applied to give a better interpretation of NMR logs obtained from highly heterogeneous formations by extracting the NMR distributions of each homogeneous component. A physics-based NMR fluid substitution method is also developed, which takes into account capillary-pressure effects and pore-size distributions and does not require knowledge of permeability and surface relaxivity. The method consists of two steps. First, the hydrocarbon NMR response is removed from the initially water-hydrocarbon saturated NMR data. Next, the NMR distribution of the resulting hydrocarbon-depleted system is transformed to that of a completely water-saturated system. Several laboratory measurements and field cases are used to successfully verify the mixing laws and the fluid substitution method.