F ´ ISICA DEL PETR ´ OLEO REVISTA MEXICANA DE F ´ ISICA 49 SUPLEMENTO 3, 10–13 NOVIEMBRE 2003 A description of rock-fluid interactions based on self charge-regulated interfaces H.J. Franco Vivas Reservoir Modeling and Simulation Department, Exploration and Production, PDVSA Intevep, P.O. Box 76343 Caracas 1070-A, Venezuela Recibido el 13 de diciembre de 2001; aceptado el 11 de septiembre de 2002 A model for self charge–regulated interfacial systems for studying rock–fluid electrokinetic phenomena is introduced. Multivalent anions and cations on aqueous solution in contact with an electrically charged ion–penetrable coating or membrane, may be considered. This coating holds certain functional groups, of acidic or basic nature, that relinquish or accept an arbitrary number of hidronium ions, as well as, undergoes ion interchange with the electrolytic solution. Amphoteric and zwitterionic surfaces are considered on a detailed chemical multiequilibria basis while non–ideal ionic behavior is introduced using activity coefficients under the Debye-H¨ uckel approximation. The DLVO theory of colloid stability may be used for the resulting disjoining pressure. Its electrostatic part was deduced while empirical equations may add the remaining structural and Van der Waals parts. Important physical magnitudes in the description of porous media, are among the model features. Keywords: Electrokinetic phenomena; rock–fluid interaction; charge regulation. Se presenta un modelo de sistema interfacial auto regulado para el estudio de fen´ omenos electrocin´ eticos de interacci´ on roca–fluido. Es posible considerar aniones y cationes multivalentes en soluci´ on acuosa, en contacto con una membrana ion–permeable, el´ ectricamente cargada que cubre una superficie inerte. Esta membrana retiene ciertos grupos funcionales de naturaleza ´ acida o b´ asica que ceden o aceptan un n´ umero arbitrario de iones hidronio, as´ ı mismo, experimenta intercambio i´ onico con la soluci´ on electrol´ ıtica. Se consideran superficies anf´ oteras y zwitteri´ onicas en una descripci´ on detallada de multiequilibrios qu´ ımicos, cuando la no–idealidad i´ onica se introduce usando coeficientes de actividad bajo la aproximaci´ on Debye-H¨ uckel. La teor´ ıa DLVO de estabilidad coloidal puede ser empleada para la presi´ on desuni´ on resultante. Se deduce su parte electrost´ atica mientras que las restantes partes, estructural y de Van der Waals, se a˜ naden mediante ecuaciones emp´ ıricas. Entre las caracter´ ısticas del modelo se encuentran magnitudes f´ ısicas importantes para la descripci´ on de medios porosos. Descriptores: Fen´ omenos electrocin´ eticos; interacci ´ on roca–fluido; regulaci´ on de carga. PACS: 68.43.-h; 68.08.Bc; 68.08.-p; 82.33.-z; 82.45.-h; 82.65.+r 1. Introduction A model for interface–diffuse–reservoir three region inter- facial system, in which the classical constant electric charge and/or constant electrical potential approximations have been removed, is introduced. A detailed description of the inter- facial surface chemistry is featured for the interface region while the Poisson–Boltzmann equation is used for finding an expression for the electrostatic part of the disjoining pressure at the diffuse region. 2. The interface region: its chemistry The chemistry at the interfacial region, including its surface, is relevant for processes that involve the ion exchange reac- tions that are expected according to surface nature or charac- teristics [1, 2]. For a generic amphoteric interfacial surface let us con- sider the three chemical reactions that follow. Firstly, we take the dissociating chemical processes of acidic functional groups AH (n−1)(1−) Z a −(n−1) bonded to the surface: AH (n−1)(1−) Z a −(n−1) ⇋AH n− Za−n +H + (1) K A,n ; n=0, 1,...,Z a . Secondly, the dissociating chemical processes of interfacial ionic pairs in the presence of anions D Z d − in the electrolytic solution: (AH Z a +1 ) Z d D ⇋ Z d (AH + Z a +1 )+ D Z d − (2) K D,Z d ; Z d =1, 2,...,N vd ; n =0. Finally, the dissociating processes of interfacial ionic pairs in the presence of cations E Z e + in solution: A Z e E Z a ⇋ Z e (A Z a − )+ Z a E Z e + (3) K E,Z e ; Z e =1, 2,... ,N ve ; n = Z a . For the case of a generic zwitterionic surface we also con- sider the presence of a neutral basic group B. As before, the dissociating chemical processes of acidic functional groups AH (n−1)(1−) Z a −(n−1) is considered except that AH + Z a +1 is now not included, i.e., n starts running from the value of 1: AH (n−1)(1−) Z a −(n−1) ⇋AH n− Za−n +H + (4) K A,n ; n=1, 2,...,Z a . Hydronium ion released by base B at the given aqueous solution pH, ionic strength and temperature: BH [Z b −(n−1)](1+) Z b −(n−1) ⇋BH (Z b −n)(1+) Z b −n +H + (5) K B,n ; n=1, 2,...,Z b .