Fluid substitution in multimineralic rocks with large mineral stiffness contrast

Brown and Korringa extended Gassmann's fluid substitution relation for bulk modulus to multimineralic rocks with interconnected pores. Their strikingly simple yet general result requires two additional bulk stiffnesses, which despite mathematical elegance, are less intuitive than those required by Gassmann. This creates a practical problem, so much so that even though virtually all rocks are multimineralic, in practice, Brown and Korringa's result is seldom used. We revisited this fluid substitution problem and obtained an exact relation for the bulk modulus, which, much like Brown and Korringa's result, required two additional bulk stiffnesses. Although fundamentally identical to Brown and Korringa, our exact solution algebraically differs from Brown and Korringa's result, and features two different additional bulk stiffnesses. This reformulation of Brown and Korringa's result led to strict constraints and new approximations for fluid substitution. Estimates using these new approximations spanned a range that quantified the uncertainty associated with performing fluid substitution when mineral distribution is unknown. We found that this uncertainty was insignificant if the stiffness contrast between different minerals was sufficiently small. For the examples considered, this was true when the stiffness ratio between soft and stiff minerals approached 0.4. When the mineral stiffness contrast was large, we developed a new recipe for fluid substitution, which significantly improved on using the conventional approach of Gassmann with Voigt-Reuss-Hill or Hashin-Shtrikman averaging for minerals in the rock matrix.