Correction of motion effect in nuclear magnetic resonance (nmr) logging

Abstract

A method for making NMR measurements includes, in one embodiment, using an NMR tool to acquire NMR measurements that are effected by relative motion of the NMR tool and/or the specimen under investigation. The NMR tool may include a plurality of permanent magnets and a plurality of radio frequency (RF) coils. The relative motion is estimated and used to modify an NMR inversion kernel which is in turn used to transform the NMR measurements into motion-corrected NMR measurements. Corresponding systems, devices, and apparatuses are also disclosed herein.

What is claimed is: 
     
         1 . A method for logging a subterranean wellbore, the method comprising:
 (a) using a nuclear magnetic resonance (NMR) logging tool deployed in a subterranean wellbore to acquire NMR logging measurements, the NMR logging tool including a plurality of permanent magnets and a plurality of radio frequency (RF) coils, the NMR logging measurements being effected by relative motion of the NMR logging tool in the wellbore;   (b) estimating said relative motion of the NMR logging tool in (a);   (c) estimating a motion effect from the relative motion estimated in (b);   (d) modifying an NMR inversion kernel with the motion effect estimated in (c) to obtain a modified kernel;   (e) inverting the NMR logging measurements acquired in (a) using the modified kernel obtained in (d) to compute motion corrected NMR logging data.   
     
     
         2 . The method of  claim 1 , wherein the NMR logging tool comprises an NMR logging while drilling tool. 
     
     
         3 . The method of  claim 1 , wherein (b) comprises estimating said relative motion of the NMR logging tool using at least one sensor selected from accelerometers, magnetometers, gyroscopes, calipers, or standoff sensors. 
     
     
         4 . The method of  claim 1 , wherein (b) comprises modeling transient dynamic behavior of the NMR logging tool in the wellbore. 
     
     
         5 . The method of  claim 1 , wherein the motion effect comprises a motion induced signal decay (MID). 
     
     
         6 . The method of  claim 5 , wherein the MID comprises at least one of a displacement-dependent signal attenuation component and a velocity-dependent signal attenuation component. 
     
     
         7 . The method of  claim 5 , wherein the MID comprises an exponential decay. 
     
     
         8 . The method of  claim 5 , wherein the MID comprises a sum of multiple exponentials summed over a number of components in the MID. 
     
     
         9 . The method of  claim 5 , wherein the MID comprises a first exponential decay having a corresponding first time constant and the NMR inversion kernel comprises a second exponential decay having a corresponding second time constant. 
     
     
         10 . The method of  claim 1 , wherein modifying the NMR inversion kernel in (d) comprises multiplying the NMR inversion kernel by a correction factor obtained from the motion effect estimated in (c). 
     
     
         11 . The method of  claim 1 , wherein the inversion kernel comprises a matrix of kernel elements with each row in the matrix corresponding to an echo. 
     
     
         12 . The method of  claim 11 , wherein:
 the motion-corrected NMR logging data computed in (e) comprises a motion corrected T2 distribution; and   the inversion kernel comprises an NE×NT 2  matrix, wherein NE represents a number of echoes and NT 2  represents a number of points in the T2 distribution.   
     
     
         13 . The method of  claim 1 , wherein the motion-corrected NMR logging data computed in (e) comprises at least one of a motion corrected T1 distribution and a motion-corrected T2 distribution. 
     
     
         14 . The method of  claim 1 , wherein the relative motion is a relative lateral motion of the NMR logging tool in the wellbore. 
     
     
         15 . A method for making nuclear magnetic resonance (NMR) measurements, the method comprising:
 (a) using a nuclear magnetic resonance (NMR) tool to acquire NMR measurements of a specimen, the NMR tool including a plurality of permanent magnets and a plurality of radio frequency (RF) coils, the specimen undergoing relative motion with respect to the NMR tool while the NMR measurements are acquired;   (b) estimating said relative motion in (a);   (c) estimating a motion induced signal decay (MID) from the relative motion estimated in (b);   (d) determining a motion effect kernel (MEK) based on the MID estimated in (c); and   (e) inverting the NMR measurements acquired in (a) using the MEK determined in (d) to compute motion corrected NMR data.   
     
     
         16 . The method of  claim 15 , wherein the MID comprises at least one of a displacement-dependent signal attenuation component and a velocity-dependent signal attenuation component. 
     
     
         17 . The method of  claim 15 , wherein the MEK is obtained by multiplying an NMR inversion kernel by the MID. 
     
     
         18 . The method of  claim 17 , wherein the MID comprises a first exponential decay having a corresponding first time constant and the NMR inversion kernel comprises a second exponential decay having a corresponding second exponential decay. 
     
     
         19 . The method of  claim 15 , wherein:
 the motion-corrected NMR logging data computed in (e) comprises a motion corrected T2 distribution; and   the MEK comprises an NE×NT2 matrix, wherein NE represents a number of echoes and NT2 represents a number of points in the T2 distribution.   
     
     
         20 . The method of  claim 15 , wherein the motion-corrected NMR logging data computed in (e) comprises at least one of a motion corrected T1 distribution and a motion-corrected T2 distribution.