Variable Dimension Fractal-Based Conversion Method between the Nuclear Magnetic Resonance T₂ Spectrum and Capillary Pressure Curve

Abstract

Pore structure is the primary control factor of pore fluid distribution and flow capacity. It is an important content in reservoir evaluation. The capillary pressure curve is a major method to obtaining pore structure characteristics. The NMR T2 spectrum reflects pore size distribution. Both of them have a connection. Investigating methods of converting the NMR T2 spectrum into a capillary pressure curve is the key step to use nuclear magnetic resonance (NMR) logging data to quantitatively characterize the pore structure. The pore throat size distribution obtained by the NMR T2 spectrum and capillary pressure curve has fractal features. However, studies about the relationship between the capillary pressure curve and NMR T2 spectrum by the fractal characteristic have not been reported. This paper studies the relationship between the capillary pressure curve and NMR T2 spectrum by the fractal characteristic and proposes a method of converting the NMR T2 spectrum to the capillary pressure curve. To fully consider the influence of the pore structure, the dimension coefficient is set to be a variable that is related to the pore structure. The proposed model is verified by 20 rock samples in Nanpu sag, China by comparing the new method of calculate capillary pressure curves and experimental capillary pressure curves. Results show that the new method improves the accuracy of the conversion method between the NMR T2 spectrum and capillary pressure curve in the complex pore structure reservoirs. This research provides a new way to enrich pore structure characteristic parameters for high-precision reservoir evaluation and has certain guidance and reference significance for the research work of petrophysics, reservoir evaluation, and NMR logging data application.

Research on the Shale Porosity–TOC Maturity Relationship Based on an Improved Pore Space Characterization Method

“…Influential factors of quantitative pore structure characterization from NMR T2 distribution include the content and maturity of organic matter, pore surface wettability, and measurement parameters. [15,16] Small angle scattering (SAS)…”

An Improved Rock Resistivity Model Based on Multi-Fractal Characterization Method for Sandstone Micro-Pore Structure Using Capillary Pressure

“…where, 𝑟(𝜇𝑚) is the diameter of a pore and 𝐷 𝑟 is between 0 < 𝐷 𝑟 < 3. 𝑟 min (𝜇𝑚) and 𝑟 max (𝜇𝑚) are the minimum and maximum fractal pore sizes, respectively. According to fractal geometry of porous media and Laplace equation, the relationship between capillary pressure 𝑃 𝑐 and saturation 𝑆 𝑣 is expressed as [21] 𝑆 𝑣 = ( 𝑃 𝑐𝑚𝑖𝑛 𝑃 𝑐 )…”

“…Since fractal geometry theory was proposed by Mandelbrot [15] in the 1970s, it has been widely used in petroleum geology [16][17][18]. Lots of studies show that sandstone pore structure exhibits fractal characteristics, and the fractal theory can be extended to apply in pore structure characterization method from capillary pressure curve and nuclear magnetic resonance T2 spectrum for porous media of sedimentary rock [19][20][21]. For instance, Gao et al conducted a fractal analysis of dimensionless capillary pressure function [22].…”