Basic-Porosity-Concept PDF

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Basic porosity concepts for petroleum engineering. ...

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ww www.g w.g w.gatein atein ateinp petr etrole ole oleum um um.com .com Porosity Fundamentals: 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)

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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 = 8r3 © All rights reserved by Gate In Petroleum. No part of this document may be reproduced or utilized in any form without the written permission. Visit us at .www.gateinpetroleum.com

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Figure - Example of cubic and rhombohedral packing

The volume of an individual sand grain is, Vg = 4/3 π r3. Within the unit cell there are 8 – 1/8 sand grain spheres, or one grain volume. Porosity can now be determined from basic equation. 𝟒 𝟑 𝟑 𝐕𝐛 − 𝐕𝐠 𝟖𝐫 − ( 𝟑) 𝛑𝐫 𝛑 ) = 𝟎. 𝟒𝟕𝟔𝟒 = ∅= = 𝟏 − ( 𝟔 𝐕𝐛 𝟖𝐫 𝟑

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 0.4764, 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. © All rights reserved by Gate In Petroleum. No part of this document may be reproduced or utilized in any form without the written permission. Visit us at .www.gateinpetroleum.com

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Figure – Porosities of different ordered packing arrangements

Question 2: Routine core analysis use core with cross section area of 3 cm2 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. 38.2 % B. 39.2 % C. 59.2 % D. 41.2 % 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 © All rights reserved by Gate In Petroleum. No part of this document may be reproduced or utilized in any form without the written permission. Visit us at .www.gateinpetroleum.com

ww www.g w.g w.gatein atein ateinp petr etrole ole oleum um um.com .com = 𝟓𝟔 𝒈𝒓𝒂𝒎𝒔 − 𝟓𝟎 𝒈𝒓𝒂𝒎𝒔 𝐕𝐨𝐥𝐮𝐦𝐞 𝐨𝐟 𝐚𝐛𝐬𝐨𝐫𝐛𝐞𝐝 𝐰𝐚𝐭𝐞𝐫 = 𝐩𝐨𝐫𝐞 𝐯𝐨𝐥𝐮𝐦𝐞 = 𝐰𝐞𝐢𝐠𝐡𝐭 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫 ∗ 𝐝𝐞𝐧𝐬𝐢𝐭𝐲 𝐏𝐨𝐫𝐞 𝐕𝐨𝐥𝐮𝐦𝐞 =

∅=

(𝟓𝟔 − 𝟓𝟎) = 𝟓. 𝟖𝟖 𝟏. 𝟎𝟐

𝟓. 𝟖𝟖 ∗ 𝟏𝟎𝟎 = 𝟑𝟗. 𝟐% 𝟏𝟓

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

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