Petrophysical Parameter Calculation Based on NMR Echo Data in Tight Sandstone

Bound water saturation ( $S_{\mathrm {wb}}$ ) and permeability are the important petrophysical parameters. However, the traditional methods for the calculation of $S_{\mathrm {wb}}$ and permeability based on the nuclear magnetic resonance (NMR) transverse relaxation time ( $T_{2}$ ) distributions are not applicable for tight sandstone because the NMR data have a low signal-to-noise ratio and the calculation models have certain disadvantages. In this paper, we present a new method for the calculation of $S_{\mathrm {wb}}$ and permeability using integral transforms (ITs) of the NMR echo data in tight sandstone. First, the tapered cutoff function was established using the Laplace transform function of the exponential hyperbolic sine function based on the film model; $S_{\mathrm {wb}}$ was directly calculated from the echo data using the exponential hyperbolic sine transform without an inversion of the $T_{2}$ distribution. The position and slope of the median point, both of which control the shape of the tapered cutoff function, were determined by core experiments. Subsequently, the tapered cutoff function representing the proportion coefficients of the free fluids in the pore space was added to the arithmetic mean of the $T_{2}$ ( $T_{\mathrm {2am}}$ ) as a weight to construct the weighted $T_{\mathrm {2am}}$ ( $T_{\mathrm {2wam}}$ ). $T_{\mathrm {2wam}}$ was highly suitable for reflecting the seepage ability of the pores and was directly calculated from the NMR echo data using an IT without an inversion. A new permeability calculation model was developed based on $T_{\mathrm {2wam}}$ . The numerical simulation and core experimental results verified the effectiveness of the new method.