Chapter 3 – Permeability 3.1 Permeability is a measure of the ability of a porous media to transmit fluids. It is a critical property in defining the flow capacity of a rock sample. The unit of measurement is the darcy, named after the French scientist who discovered the phenomenon. This chapter will begin with the factors which affect permeability and then lead to the experimental law defining permeability for porous media. The last three sections of this chapter investigate the relationship between porosity and permeability, the distribution of these rock properties and finally lab methods of measuring permeability. 3.2 Factors affecting permeability Numerous factors affect the magnitude and/or direction of permeability. 1. Textural properties a. Pore size/ grain size b. Grain size distribution c. Shape of grains d. Packing of grains 2. Gas slippage 3. Amount, distribution, and type of clays 4. Type and amount of secondary porosity 5. Overburden pressure 6. Reactive fluids 7. High velocity flow effects Let us begin by investigating the role of textural properties on the permeability. Experimental evidence has shown that k  cd2, where c is a characteristic of the rock properties and d is the grain diameter. The dimensions of permeability are L2, which is directly related to the cross-sectional area of the pore throats. Therefore as grain size increases, so will the pore throat size and a subsequent increase in permeability occurs. In Figure 3.1, an artificial mixing of sands illustrates the significant effect of grain size on permeability. As can be seen, an approximate 25:1 increase in permeability occurs from coarse to very fine grains.Chapter 3 – Permeability 3.2 Figure 3.1 Effect of grain size and sorting on permeability Also shown in Figure 3.1 is the effect of sorting on the permeability. It is not as dramatic as grain size, however, the illustration does show an increase in sorting (better or well sorted) will improve the permeability. This is why in gravel pack operations the selection of the gravel is important, both from a size and sorting viewpoint. The effect of shape and packing on permeability can be seen in Figure 3.2. Figure 3.2 Textural parameters and permeability [Link, 1982]Chapter 3 – Permeability 3.3 Notice in these examples, the more angular the grains or the flatter the grain shape, a more pronounced anisotropy develops. 3.2.1 Klinkenberg's Effect, Gas Slippage The true absolute permeability of porous rock is an intrinsic property of the rock, reflecting its internal structure. The permeability of a rock is a constant value, unchanged by different types of fluids that have different viscosities or other physical properties. This rule is followed by all liquids at laminar flow rates that are nonreactive with the rock. However, when gases are used as the flowing fluid at low pressures, calculated permeability may be greater than true permeability of the rock. In liquid laminar flow, the layer of molecules adjacent to and contacting the solid walls of the pores, or tubes, is stationary. The velocity profile of the liquid is maximum at the center of the passageway and zero at the walls. However, when using gas in the same flow system, the gas velocity profile is not zero at the walls, but has a finite velocity in the direction of flow. Gas molecules are in constant motion, colliding with one another after traveling an average distance equal to the "mean free path." At lower pressures, the mean free path is greater, and the distance between molecular collisions is increased. Internal resistance to flow is provided by gas molecular collisions with the walls. At any location on a wall, there will be some periods when no gas molecule is in contact with the wall, yet the congregation of gas molecules is continuing its movement through the pore due to molecular diffusion (slip) and not pressure differential. During these periods of no wall contact, flow is being achieved without the normally expected friction loss at the wall. The result is that the gas molecules get through the porous medium more easily than expected (i.e., the calculated permeability of the rock or capillary tube would be artificially high). As might be expected, gas flow at higher pressures reduces the mean free path between molecular collisions, and the calculated permeability more closely approximates the true absolute permeability of the rock. Klinkenberg (1941) conducted experiments on this phenomenon and conclude that (1) gas permeability is a function of the gas composition, (2) gas permeability is a function of mean pressure, and (3) the equivalent liquid permeability is independent of the above two factors. He presented a useful relationship,Chapter 3 – Permeability 3.4 pb1Lkgk (3.1) where: kg = apparent permeability calculated from gas flow tests; kL = true absolute permeability of the rock; p = mean flowing pressure of the gas in the flow system, measured in atmospheres; b = Klinkenberg's factor, a constant for a particular gas in a particular porous medium. Notice the term (1 + b/P) is always greater than or equal to 1.0, therefore the apparent permeability to gas is always greater than or equal to the true absolute permeability of the rock. This is shown in Figure 3.3, where kL is the minimum value extrapolated to the y-axis. Figure 3.3 Permeability of a core sample to air at various pressures Also note, that as pressure is increased, the term in the parentheses approaches 1.0, and the apparent gas permeability approaches the true absolute value. In practice when laboratory tests use gas as the flowing fluid, the following steps are performed: 1) A gas flow rate is established, and permeability is calculated from observed flow parameters;Chapter 3 – Permeability 3.5 2) Another flow test is conducted at a different rate (different P), and permeability is recalculated; 3) Calculated permeabilities are plotted versus the reciprocal of P (pressure is always measured in terms of atmospheric pressure in units of atmospheres) and extrapolate to p, i.e., y-intercept, which gives the equivalent liquid permeability. The klinkenberg correction to reduce gas permeability varies with the magnitude of the absolute permeability. Actually, the constant b declines with