A computer-implemented method for estimating a relationship between physical properties of a porous material from a sample thereof, comprising: making a three dimensional tomographic image of the sample of the material; segmenting the image into pixels each representing pore space or mineral grain; subdividing the image into sub-volumes; estimating a porosity for each sub-volume from the image thereof; modeling at least one petrophysical parameter from the image of each sub-volume; determining a relationship between the porosity and the modeled petrophysical parameter using the estimated porosity and the modeled petrophysical parameter from a plurality of the sub volumes; and at least one of storing and displaying the relationship and the modeled petrophysical parameter; wherein the relationship is determined by statistical best fit; wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image; and wherein the segmenting comprises: (a) determining an initial gray scale threshold for each of pore space and rock grain; (b) allocating each pixel in the image to pore space or rock grain for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively, in order to define first and second seeds; (c) interrogating pixels adjacent to each seed; (d) allocating the interrogated adjacent pixels previously not allocated to a seed to the pore space seed or the rock grain seed based on the pixels having gray scale levels within a selected tolerance; (e) increasing the gray scale lower limit for rock grains and decreasing the gray scale upper limit for pore space; and (f) repeating (c), (d) and (e) until the lower limit for rock grains and the upper limit for pore space meet.. making a three dimensional tomographic image of the sample of the material; segmenting the image into pixels each representing pore space or mineral grain; subdividing the image into sub-volumes; estimating a porosity for each sub-volume from the image thereof; modeling at least one petrophysical parameter from the image of each sub-volume; determining a relationship between the porosity and the modeled petrophysical parameter using the estimated porosity and the modeled petrophysical parameter from a plurality of the sub volumes; and at least one of storing and displaying the relationship and the modeled petrophysical parameter; wherein the relationship is determined by statistical best fit; wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image; and wherein the segmenting comprises: (a) determining an initial gray scale threshold for each of pore space and rock grain; (b) allocating each pixel in the image to pore space or rock grain for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively, in order to define first and second seeds; (c) interrogating pixels adjacent to each seed; (d) allocating the interrogated adjacent pixels previously not allocated to a seed to the pore space seed or the rock grain seed based on the pixels having gray scale levels within a selected tolerance; (e) increasing the gray scale lower limit for rock grains and decreasing the gray scale upper limit for pore space; and (f) repeating (c), (d) and (e) until the lower limit for rock grains and the upper limit for pore space meet.. (a) determining an initial gray scale threshold for each of pore space and rock grain; (b) allocating each pixel in the image to pore space or rock grain for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively, in order to define first and second seeds; (c) interrogating pixels adjacent to each seed; (d) allocating the interrogated adjacent pixels previously not allocated to a seed to the pore space seed or the rock grain seed based on the pixels having gray scale levels within a selected tolerance; (e) increasing the gray scale lower limit for rock grains and decreasing the gray scale upper limit for pore space; and (f) repeating (c), (d) and (e) until the lower limit for rock grains and the upper limit for pore space meet..