Tracking Pore to Pore Exchange Using Relaxation Exchange Spectroscopy

We observe the movement of water over time between pores of differing sizes in Castlegate sandstone. To achieve this, we perform an NMR transverse relaxation exchange experiment for several mixing times. The resulting data are converted to 2D $T_2$ distributions using a 2D inverse Laplace transform (ILT). We show for the first time that quantitative analysis of ILT distributions enables one to extract characteristic times for different pores sizes. This information is potentially useful for permeability determination as well as better understanding of exchange between specific pore subpopulations.

Figure 1

Two-dimensional pulse sequence for the fast measurement of transverse relaxation exchange. The time interval $\tau$ is kept fixed and the numbers ($n$, $m$) of 180° rf pulses in the first and second $T_2$ encoding periods are independently varied. The measurement is performed as a function of the mixing time ${\tau }_m$.

Figure 2

1D projection (along $T_1$) of the $T_1-T_2$ 2D correlation spectrum. The right inset shows an x-ray CT image of the Castlegate sandstone core, field of view width, 2 mm. The left inset gives the pore size distribution derived from x-ray CT.

Figure 3

2D $T_2$ exchange distribution for a 160 ms mixing time.

Figure 4

Off-diagonal intensities, $N_{\alpha \beta }(t)$, as a function of mixing time.

Figure 5

Intensities, $N_{\alpha \alpha }(t)$, of diagonal peaks $A$, $B$, and $C$. Note that peak $D$ exhibited an intensity constant at around 32%. The semilogarithmic inset shows the biexponential character of $N_{BB}(t)$.