Sen P N, Schwartz L M, Mitra P P
Schlumberger-Doll Research, Ridgefield, CT 06877-4108.
Magn Reson Imaging. 1994;12(2):227-30. doi: 10.1016/0730-725x(94)91523-7.
The NMR pulsed field gradient spin-echo (PFGSE) amplitude M(k,t) is a direct measure of the diffusion propagator of the molecules of a fluid diffusing in the pores of a porous medium. For small values of k = gamma g delta, where g is the gradient strength, delta is the duration of the gradient pulse, and gamma the gyromagnetic ratio, the PFGSE amplitude gives the diffusion coefficient D(t). The exact short-time diffusion coefficient, D(t)/D0 = 1-(4 square root of D0tS)/(9 Vp square root of pi)-D0tHS/(12Vp) + rho tS/6Vp, provides an important method for determining the surface to pore-volume ratio S/Vp. Here the mean surface curvature H = <1/R1 + 1/R2>. Combining early D(t) with the magnetization decay one obtains the surface relaxivity rho. The long-time effective diffusion constant derived from PFGSE gives information on the tortuosity of the connected space. The diffusion coefficient measured by PFGSE equals that derived from electrical conductivity only when rho = 0. Exact solutions with partially absorbing boundary conditions for a periodic structure are used to illustrate the influence of rho on the diffusion coefficient. M(k,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model-independent way of obtaining the structure factor.
核磁共振脉冲场梯度自旋回波（PFGSE）幅度M(k,t)是对在多孔介质孔隙中扩散的流体分子扩散传播子的直接测量。对于k = γgδ的小值，其中g是梯度强度，δ是梯度脉冲的持续时间，γ是旋磁比，PFGSE幅度给出扩散系数D(t)。精确的短时扩散系数，D(t)/D0 = 1 - (4√(D0tS))/(9Vp√π) - D0tHS/(12Vp) + ρtS/6Vp，提供了一种确定表面积与孔隙体积比S/Vp的重要方法。这里平均表面曲率H = <1/R1 + 1/R2>。将早期的D(t)与磁化衰减相结合可得到表面弛豫率ρ。从PFGSE导出的长时间有效扩散常数给出了关于连通空间曲折度的信息。仅当ρ = 0时，通过PFGSE测量的扩散系数才等于从电导率导出的扩散系数。使用具有部分吸收边界条件的周期性结构的精确解来说明ρ对扩散系数的影响。M(k,t)可以很好地由连通孔隙空间的结构因子与适当的高斯传播子的卷积来表示。这个假设提供了一种获得结构因子的与模型无关的方法。
