A novel method to calculate relative permeability of fluids based on fractal theory and core NMR experiment

Xinmin Ge^{1, 2}, Yiren Fan^{1, 2}, Donghui Xing^{1, 2}, Yongjun Xu^{1, 2}

¹School of Geosciences in China University of Petroleum. Qingdao 266580, Shandong Province, China

²CNPC Key Well Logging Laboratory in China University of Petroleum. Qingdao 266580, Shandong Province, China

An analytical relative permeability model based on fractal theory and NMR principle is described. The relationship between NMR transversal relaxation time (NMR T2) and resistivity index is deduced by fractal theory and capillary bundle model. The reciprocity theory of percolation field and electricity field is used to get the relationship between resistivity index and relative permeability. The ‘Brooks-Corey/Burdine’ equation was adopted to construct the relationship between relative permeability and NMR transversal relaxation time. By introducing the NMR parameters, the relative permeability model is improved since that it quantified the influence of pore structure. The results show that for water (wetting phase in water-gas system), the predicted permeability is exactly consistent with the experiment data, whereas for gas (the non-wetting phase in water-gas system), the fitted results is to some degree deviated from the experiment data and need more extensive research.