New pore size distribution calculation model based on chord length and digital image

In this study, we propose a model to calculate pore size distribution based on the chord length and digital image. First, the chord length cumulative frequency function of the unit circle is deduced. Next, a dimensionless chord length cumulative frequency function of the arbitrary size circle is derived. The chord length data are generated by cutting a combination of the specific step size of the pore size in varying proportions. Conversely, the value of the chord length is also obtained from the segmented CT image data by direct calculation. Using the dimensionless chord length cumulative frequency function, we formulate the balance equation, which indicates that the chord length distribution generated by cutting a combination of the specific step size of the pore size in varying proportions is the same as the chord length distribution that is obtained from direct calculation in the segmented CT image data. By solving the balance equation, the pore size distribution is obtained. Our model calculation results are compared with the max ball model calculation results. Furthermore, the pore size distribution of the shale sample is calculated based on our model. The results indicate that pore radii mostly less than 50 nm and small pores are dominant in shale.