588 russell-dickey. POROSITY AND PERMEABILITY [Ch. 32 



under pressure. The volume of mercury forced into the porous medium 

 under these conditions is close to the pore volume. The porosity is 

 then computed as shown above. Some investigators have attempted 

 to estimate porosity microscopically by obtaining a statistical average 

 of the void space on a thin section. As will be shown later, porosity is 

 related to grain size, interstitial surface area, and permeability. In 

 fact, for clean unconsolidated sands, a fair estimate of porosity can be 

 made if the permeability is known and if the interstitial surface area 

 is measured by the gas-adsorption method (Brunauer, 1943; Carman, 

 1941) . It is impossible in such a short discussion to treat all the meth- 

 ods used for determining porosity. However, it is felt that the ex- 

 amples given above will introduce the reader to the complexity of the 

 subject and point out to him some of the advantages and disadvantages 

 of the more common techniques. 



Permeability 



Fancher, Lewis, and Barnes (1933) made an extensive investigation 

 of the permeability of various consolidated and unconsolidated mate- 

 rials. Wyckoff, Botset, Muskat, and Reed (1934) showed that the 

 effect of the viscosity of the fluid should be separated from formulas 

 expressing fluid flow, and that a constant could be used to express the 

 transmissibility of the porous medium. Although, as Slichter deduced, 

 the permeability constant should depend on the square of the pore 

 diameters, the complexity of the pore system in natural porous media 

 is such that none of these investigators was able to derive a valid re- 

 lation between the geometrical constants of the medium and its perme- 

 ability. 



Darcy's law was introduced above together with a constant of pro- 

 portionality k, which was characteristic of the matrix through which 

 oil, gas, and water flow. It is now possible to identify this k with per- 

 meability, recognized by the American Petroleum Institute: "A meas- 

 ure of the fluid-transmitting capacity of a porous medium. The unit of 

 permeability is the darcy. A material has the permeability of one 

 darcy when one atmosphere pressure differential across one centimeter 

 length causes a viscous flow of one cubic centimeter per second of a 

 fluid of one centipoise viscosity through a cross section of one square 

 centimeter" (A.P.I., 1941). In conformity with A.P.I. Code 27 (1942), 

 numerous permeameters of different design exist for measuring perme- 

 ability. Fundamentally, a permeameter consists of a suitable core 

 holder, a pump for forcing fluid through the core, a manometer to 

 measure the pressure drop across the core, and a flow meter for measur- 

 ing the rate of flow of fluid through the core. 



