82 The Leading Edge January 2009 SPECIAL SECTION: R o c k P h y s i c s Rock physics What is the cementation exponent? A new interpretation I n 2003, 182 billion barrels of oil reserves worth about US $4.5 trillion were discovered worldwide (Johnson et al., 2004). Moreover, between 1950 and 2002 the total volume of reserves discovered has run to more than 1500 billion barrels for oil and 7.5 trillion cubic feet for gas (Bentley, 2002). More than half of these resources have already been produced and have driven the global economy for the last 50 years. While these hydrocarbon discoveries were aided by exper- tise in geology, geophysics, and engineering (as well as plain good luck!), all of the assessments of the volume of hydrocar- bon reserves were made using data from petrophysical mea- surements together with a set of relationships that originated with Archie in 1942. erefore, it would be difficult to over- estimate the impact of either the petrophysical techniques or Archie’s relationships on the worldwide economy. Archie’s laws link the electrical resistivity of a rock to its porosity, to the resistivity of the water that saturates its pores, and to the fractional saturation of the pore space with the water. ey are used to calculate the hydrocarbon saturation of the reservoir rock from which the reserves are then calcu- lated. Archie’s laws contain two exponents, m and n, which Archie called the cementation exponent and the saturation exponent, respectively. e conductivity of the hydrocarbon- saturated rock is highly sensitive to changes in either expo- nent. Fortunately, the saturation exponent does not vary much (n=2±½). However, the cementation exponent com- monly takes values from just over 1 to around 5. Water and oil saturations calculated with Archie’s equations are highly sensitive to this level of variability in the cementation expo- nent, but, thankfully, there are a number of ways in which the cementation exponent can be calculated with precision (e.g., Tiab and Donaldson, 1994). Despite the importance of the cementation exponent, few petrophysicists, commercial or academic, are able to de- scribe its real physical meaning. Some authors (e.g., Ellis and Singer) even relegate the cementation exponent to the status of a “fitting parameter” in an empirical relationship. While this position was probably valid 20 years ago, Archie’s laws and their parameters have a healthier theoretical foundation today. e purpose of this paper is to investigate the elusive physical meaning of the cementation exponent. Traditional interpretations Archie began by naming the ratio of the resistivity of the rock ρ 0 to that of the pore water ρ w the resisitivity formation factor (1) e term formation factor was used because it was ap- proximately constant for any given formation. e forma- tion factor varies from unity, F = 1, which represents the case where ρ 0 = ρ w (i.e., when φ → 1), and increases as the porosity decreases, with F → ∞ as φ → 0. e formation factor can be PAUL GLOVER , Université Laval less than unity, but only when the rock matrix is less resistive than the pore water, and this is extremely rare. e first series of experiments carried out by Archie led him to the conclusion that the formation factor depends upon porosity in the form of an inverse power law (2) with an exponent m. He called the exponent the cementation exponent (factor or index) because he believed it to be related to the degree of cementation of the rock fabric. is consti- tutes the first attempt to understand the meaning of the ce- mentation exponent, however qualitative it may be. It is clear from the form of the equation that higher values of m make the formation factor more sensitive to changes in the rock`s porosity and are associated with higher values of tortuosity (lower connectivity) (Ellis and Singer, 2007). e range of values for the cementation exponent is rela- tively small. A value of m = 1 is not observed for real rocks, and represents a porous medium composed of a bundle of capillary tubes which cross the sample in a straight line. Rocks with a low porosity but a well developed fracture net- work sometimes have cementation exponents that approach unity because the network has flow paths that are fairly di- rect. Here we get the first taste that the cementation exponent has something to do with the connectedness of the pore and fracture network (where, for the time being, connectedness is considered to be a qualitative term for the general availability of pathways for transport). A cementation exponent equal to 1.5 represents the ana- lytical solution for the case where the rock is composed of perfect spheres (Sen et al., 1981; Mendelson and Cohen, 1982). In fact, m=1 and m=1.5 were until recently the only two cases where an analytically derived value of the cemen- tation exponent was known. A series of papers from 2004 onwards has shown that Archie’s law can be derived by ap- plying continuum percolation theory to fractal porous me- dia (e.g., Ewing and Hunt, 2006). Most porous arenaceous sediments have cementation exponents between 1.5 and 2.5 (Glover et al., 1997). Values higher than 2.5, and as high as 5, are generally found in carbonates where the pore space is less well connected (Tiab and Donaldson, 1994). In general, the value of the cementation exponent increases as the degree of connectedness of the pore network diminishes, which rather supports it being called the cementation exponent. Incidentally, values of the cementation exponent less than unity are possible, and arise particularly in the modified Ar- chie’s law for two conducting phases (Glover et al., 2000). In this model there is an exponent representing each phase, and if the exponent related to the conducting pore fluid is greater than unity, the other exponent, which represents the con- ducting rock matrix, takes a value less than unity. It is as if, in a 3D porous medium, there is only so much connectedness possible. If a certain high degree of connectedness is taken by SPECIAL SECTION: R o c k p h y s i c s