Porosity

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Fundamentals: www.gateinpetroleum.com Porosity Porosity is one of the most important rock properties in describing porous media.

1 Fundamentals: Porosity Porosity is one of the most important rock properties in describing porous media. It is defined as the ratio of pore volume to bulk volume of a rock sample. The porosity of a rock is the fraction of the volume of space between the solid particles of the rock to the total rock volume. The space includes all pores, cracks, vugs, inter- and intracrystalline spaces. The porosity is conventionally given the symbol f, and is expressed either as a fraction varying between 0 and 1, or a percentage varying between 0% and 100%. Vp Vb Even though it is a dimensionless quantity, expressed either in decimal or percentage, it is best to remember that it represents a volume ratio of pore space to the bulk space. Figure below illustrates a simple example of porosity for a granular media. Figure - Cross-sectional view of a porous media (white areas are pore space, pattern areas are grains)

2 It is within these pore spaces that the oil, gas and/or water reside. Therefore a primary application of porosity is to quantify the storage capacity of the rock, and subsequently define the volume of hydrocarbons available to be produced. From a drilling perspective, the rate of penetration and the volume of drilling fluid lost to a formation by invasion are related to porosity. Consider the following example of the effect of porosity on fluid loss. Several types of porosity have been defined based on the degree of connectivity or the time of pore development. Total porosity is the ratio of the total pore space of the media to the total bulk volume. Effective porosity is the ratio of interconnected pore space to the bulk volume of the rock. Figure 2.3 is an example of total vs. effective porosity in a vuggy rock. Notice the pathway for fluid to migrate in connected pores and the isolated nature of others. Production of hydrocarbons is dependent upon the fluid to flow in the porous media. Grain Packing: Textural parameter of importance is the packing or arrangement of grains. As shown in Figure below, for uniform grains the porosity will be different for cubic vs. rhombohedral structures, with the cubic packing the maximum for uncompacted sand grains. Question 1: Determine the porosity for the cubic packing arrangement in Figure above. Solution: Define the unit cell with sides equal to twice the radius of the sand grain, 2r. The bulk volume of the cell becomes, Vb = (2r) 3 = 8r 3

Figure - Example of cubic and rhombohedral packing The volume of an individual sand grain is, Vg = 4/3 π r 3. Within the unit cell there are 8 1/8 sand grain spheres, or one grain volume.

3 Figure - Example of cubic and rhombohedral packing The volume of an individual sand grain is, Vg = 4/3 π r 3. Within the unit cell there are 8 1/8 sand grain spheres, or one grain volume. Porosity can now be determined from basic equation. Vb Vg Vb = 8r3 ( 4 3 ) πr3 8r 3 = 1 ( π ) = Notice the radius of the sand grains cancel and therefore porosity is a function of packing. The theoretical porosities for various grain packing arrangements can be calculated. The theoretical maximum porosity for a cubic packed rock made of spherical grains of a uniform size is , and is independent of grain size. The maximum porosity of other packing arrangements is shown in Table below. The calculations of these ideal porosities is relatively simple.

Figure Porosities of different ordered packing arrangements Question 2: Routine core analysis use core with cross section area of 3 cm 2 and length of the core is 5 cm.

4 Figure Porosities of different ordered packing arrangements Question 2: Routine core analysis use core with cross section area of 3 cm 2 and length of the core is 5 cm. Dry core weighing 50 grams saturated for 24 hours in saline water of density 1.02 gm/cc. Weight of saturated core is measured 56 grams. Calculate the porosity of the system? A % B % C % D % Solution: pore volume bulk volume When core is saturated with water, volume of absorbed water is equal to pore volume of core sample. weight of absorbed water = wet weight dry weight

5 = 56 grams 50 grams Volume of absorbed water = pore volume = weight of water density Pore Volume = (56 50) = = 39. 2% Reference 1. Petrophysics MSc Course Notes by Dr. Paul Glover 2. Horgan, G. W.; B. C. Ball (1994). "Simulating diffusion in a Boolean model of soil pores". European Journal of Soil Science. 3. Glasbey, C. A.; G. W. Horgan; J. F. Darbyshire (September 1991). "Image analysis and threedimensional modelling of pores in soil aggregates". Journal of Soil Science 4. SPE Handbook

Chapter 2. Reservoir Rock and Fluid Properties

Chapter 2. Reservoir Rock and Fluid Properties Chapter 2 Reservoir Rock and Fluid Properties Table of Contents Pages 1. Introduction... 3 2. Rock and Minerals... 3 3. Porosity... 4 3.1. Porosity Classification... 6 3.2. Range of porosity values for