Problems Homework NO. 1 2.1 Compute the porosity of a formation composed of uniform spherical grains of radius r arranged in the most "open" cubic packing. (The unit cube with side of length 2r spans eight grains; see Fig. 1.) 2.1.1 Most sandstone formations have porosities well below 30%. Can you suggest several reasons why this is the case? 2.2 What is the porosity (or liquid volume fraction) of an 11 lb/gal mud, assuming that it consists of water and clay particles of density 2.65 g/cm³? The density of water is 8.3 lb/gal (1.00 g/cm³). Fig. 1 Cubic or open packing of uniform-sized spherical particles. 2.3 In the formation of a mudcake, an annulus of lower porosity mud is formed by expelling some of the water in the mud into the formation. A typical mudcake density is 2.0 g/cm³. What is its porosity, assuming that it was formed from the 11 lb/gal mud from the previous example? Extra problem for bonus* 2.4* The volume of water expelled from the mud, during the creation of the mudcake, will displace the formation fluid, creating the so-called invasion zone. The thickness of this zone, in which the formation fluid has been displaced by mud filtrate, will depend on the formation porosity. Show that the radius of invasion n' is given by: 17 + Irbh (2.1) where dV is the volume of mud filtrate/unit length displaced into the formation, is the porosity, and is the borehole radius.