Surface Relaxation and Pore Size Distribution

Surface Relaxation and Pore Size Distribution 3.6.6.1 Fast Diffusion Limit 

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3)  

Temperature and measured surface relaxivity have shown only a weak dependence [21, 27] in some cases, whereas the opposite temperature dependence between silicate and carbonate surfaces has been shown in others [28]. 

Natural rocks seldom have a single pore size but rather a distribution of pore sizes. If all pores are in the fast-diffusion limit, have the same surface relaxivity and have no diffirsional coupling, then the pores will relax in parallel with a distribution of relaxation times that corresponds to the distribution of the pore sizes. The magnetization will decay as a sum of the exponentials as described by Eq. (3.6.4). 

The Tj 2 denotes Ti or T2, and if it is the latter, negligible diffusion effects are assumed. The surface relaxivity is estimated as the value that best overlays the two curves. The ratio of Ti/T2, at a H frequency of 2 MHz for 48 rocks had a median value of 1.6 with a standard deviation of 0.7 [29]. 

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