Wettability as Related to Capillary Action in Porous l\1edia SOCONY MOBIL OIL CO. JAMES C. MELROSE DALLAS, TEX. ABSTRACT interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This The contact angle is one of the boundary approach has enjoyed a certain degree of success Downloaded from http://onepetro.org/spejournal/article-pdf/5/03/259/2153830/spe-1085-pa.pdf by guest on 26 September 2021 conditions for the differential equation specifying in correlating experimental results. 13 The general­ the configuration of fluid-fluid interfaces. Hence, ization of this model, however, to situations which applying knowledge concerning the wettability of a involve varying wettability, has not been established solid surface to problems of fluid distribution in and, in fact, is likely to be unsuccessful. porous solids, it is important to consider the In this paper another approach to this problem complexity of the geometrical shapes of the indi­ will be discussed. A considerable literature relating vidual, interconnected pores. to this approach exists in the field of soil science, As an approach to this problem, the ideal soil where it is referred to as the ideal soil model. model introduced by soil physicists is discussed Certain features of this model have also been in detail. This model predicts that the pore structure discussed by Purcell14 in relation to variable of typical porous solids will lead to hysteresis wettability. The application of this model, however, effects in capillary pressure, even if a zero value to studying the role of wettability in capillary of the contact angle is maintained. The model is phenomena has not previously been attempted in generalized to situations in which the contact angle detail. In the present paper, additional features of takes on values between zero and 40 degrees. For the model are introduced. These features are the imbibition branch of the capillary - pressure critical in determining the quantitative behavior of function, the model predicts a considerable departure the model. from the usually assumed cos e relationship. In fact, according to the model, it is possible that a GENERAL FEATURES OF displaced wetting phase will not be able to reimbibe, CAPILLARY HYDROSTATICS even when the contact angle does not exhibit BASIC PRINCIPLES hysteresis. When the interstices of a typical porous solid INTRODUCTION are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. The subject of capillarity in porous media has Hence, fluid-fluid interfaces are found within a long been of interest in many branches of engineer­ certain fraction of the pore openings. The funda­ ing and applied science. The earlier investigators mental equation of capillarity specifies the 1 s were those concerned with the physics of soils. - configuration of these fluid-fluid interfaces. This More recently, petroleum engineers and others is known as the Laplace equation, when derived dealing with the problems of petroleum production from mechanics, and as the Gibbs-Kelvin equation from reservoir rock have given much attention to when deri ved thermodynamically .15 6 10 the subject. - Also, important additions to the Given two fluid phases, a and {3, in hydrostatic literature of capillarity have been contributed from equilibrium, the Laplace equation states that the the field of chemical engineering. 11,12 These attest respective fluid pressures in regions close to the to the wide range of industrial applications in interface are related by which capillary phenomena playa role. The present paper is concerned with the role pO _ pf3 = (J"of3(_I_ + _1_) ..... (1) which wettability plays in capillary action in r I r 2 porous media. As is well known, capillary-rise (or Here aa{3 is the surface or interfacial tension and capillary pressure) phenomena have frequently been r1 and r2 are the principal radii of curvature of the Original manuscript received in Society of Petroleum Engi­ surface or interface. The pressure difference, pu_ neers office Nov. 27, 1964. Revised manuscript of SPE 1085 p {3, is the capillary pressure, Pc' As Buff 15 has received June 22, 1965. Paper presented at SPE-AIChE Joint Symposium on Wetting and Capillarity in Fluid Displacement shown, Eq. 1 states the condition for hydrostatic Processes held in Kansas City, May 17-20, 1959. equilibrium within the two-phase confluent region, lReferences given at end of paper. which is referred to as the interface. It thus can SEPTEMBER, 1965 259 be regarded as a two - dimensional principle of related phenomena in porous media have been based hydrostatics. on experiments in which examples of non-zero con­ In the event that the surface of the solid phase tact angle have been largely excluded. y, within which a and (3 are enclosed, has a On the other hand, evidence has accumulated sufficiently symmetrical configuration, the interface which tends to show that in the case of the two a{3 becomes a surface of revolution. The radii of liquid phases encountered in oil reservoirs, i.e., curvature can then be written in well- known petroleum and formation water, the contact angle differential forms, and Eq. 1 becomes a differential measured through the water phase is often far from equation. However, this is also true in principle zero. 17 ,18 It seems highly probable that this even if the boundary surface lacks the required this situation can arise simply from the adsorption symmetry. The solution to Eq. 1 will always of polar constituents, which are present in describe the configuration of the interface, which petroleum in considerable quan tities, on the high­ is the central problem of capillarity. energy surface of the reservoir rock. As Zisman The boundary conditions for Eq. 1 are of two and co-workers have shown, when such adsorption types, both of which must be known if solutions to occurs on a high -energy surface, it becomes Eq. 1 are to be found. The first type, as suggested comparable to typical low - energy surfaces in above, specifies the spatial configuration of the hydrophobicity. 19,20 Furthermore, the adsorption solid surface, while the second is expressed in processes involved can clearly be expected to give Downloaded from http://onepetro.org/spejournal/article-pdf/5/03/259/2153830/spe-1085-pa.pdf by guest on 26 September 2021 terms of the contact angle ea{3y, which the interface rise to considerable hysteresis in the water-oil a{3 subtends at the surface of the solid phase. contact angle. Experimental evidence for such Whereas aa{3 is a property of the two-phase surface hysteresis has in fact been presented by Benner, of contact, ea{3y is a thermodynamic property which Dodd, and Bartell. 21 It should be mentioned, depends on the three interfacial tensions, aa{3, a ay however, that to date very little experimental work and a{3y, in the immediate neighborhood of the has been carried out under conditions other than of the three-phase line of contact. room temperature and atmospheric pressure. This dependence is given by the classical Young equation, which actually corresponds to a one­ HYDROSTATIC HYSTERESIS dimensional principle of hydrostatics. 15 Since, The contact-angle hysteresis just referred to is however, no means exist for observing the quantities separate and distinct from the hysteresis in aaYand a{3y independently, Young's equation cannot capillary rise which is occasioned by the intercon­ be used to compute values of the contact angle. nected "ink - bottle" type of pore morphology The wettability of a solid surface, with respect to characteristic of porous media. More specifically, any two given fluid phases, can therefore be the latter effect is due to the fact that, within each specified only by values of the contact angle e individual pore space, a definite range of stable obtained from direct measurements. An interpreta­ fluid - fluid interface configurations exists. The tion, in terms of Young's equation, of contact-angle configurations having the greatest and least data taken from the literature has been presented possible values of the mean interface curvature elsewhere .16 correspond to the maximum and minimum values of The approach, by means of which wettability the capillary pressure sustained by the interface effects in porous media are to be studied in this and, hence, to the capillary rise. paper, can now be briefly stated. First, the intrinsic The conditions which establish the limits of wettability of the fluid-fluid-solid system (a{3y) is stability for interface configurations in porous defined by a specified value of the contact angle, media will be discussed in more detail below, in ea{3y. Second, the relationship of e to the capillary connection with the analysis of the ideal soil pressure is determined entirely within the context model. Because the relationship between interface of solutions to Eq. 1, taking the boundary conditions curvature and capillary pressure, Eq. 1, actually to be specified by (1) the contact angle and (2) the gives the condition for hydrostatic equilibrium in geometrical configurations of the surfaces of the the two-fluid phase system, the resulting hysteresis solid phase. The latter will in turn be specified by in capillary rise will be referred to as hydrostatic a detailed examination of the ideal soil model. For hysteresis. such a model, this approach appears to be the only The importance of this type of hysteresis has conceivable one which can claim tube well-founded, been particularly emphasized by soil physi­ in the sense that any such approach must rely cists, 1,2,4,5 who have unfortunately dealt entirely exclusively on the known physical principles which with cases of zero contact angle. Hydrostatic govern static capillary phenomena. hysteresis has been, however, in many instances completely ignored by those interested in contact­ CONTACT ANGLES AND ADSORPTION angle hysteresis.