Estimating the surface relaxivity as a function of pore size from NMR T2 distributions and micro-tomographic images

In the present work, we formulate and solve an inverse problem to recover the surface relaxivity as a function of pore size. The input data for our technique are the T2 distribution measurement and the micro-tomographic image of the rock sample under investigation. We simulate the NMR relaxation signal for a given surface relaxivity function using the random walk method and rank different surface relaxivity functions according to the correlation of the resulting simulated T2 distributions with the measured T2 distribution. The optimization is performed using genetic algorithms and determines the surface relaxivity function whose corresponding simulated T2 distribution best matches the measured T2 distribution. In the proposed methodology, pore size is associated with a number of collisions in the random walk simulations. We illustrate the application of the proposed method by performing inversions from synthetic and laboratory input data and compare the obtained results with those obtained using the uniform relaxivity assumption.