Curvilinear depletion trends in d¹³C and d¹⁸O values are commonly observed in both contact- and regionally-metamorphosed marbles that have experienced infiltration-driven metamorphism. Interpretations of these trends with conventional box models of fluid-rock interaction conclude that variations in the curvature of these ¹³C-¹⁸O trends are a continuous function of the X(CO₂) value of the pore fluid. A major problem with this interpretation is that in many cases, the values of X(CO₂) required by the curvature of the ¹³C-¹⁸O depletion trend are significantly higher than the maximum values defined by the mineral assemblages present in these marbles (Bowman, 1998). Transport theory provides a possible resolution of these inconsistencies.

Transport theory demonstrates that under conditions of equilibrium exchange and advection-only fluid infiltration, only L-shaped trends of ¹³C-¹⁸O depletion will develop, regardless of the X(CO₂) value of the infiltrating fluid, except for the special case where X(CO₂)=0.5 (Baumgartner and Rumble, 1988). At X(CO₂)=0.5, there will be no separation of the C and O isotope exchange fronts, and a linear trend of ¹³C-¹⁸O depletion results. However, if the C and O exchange fronts are broadened or dispersed--either by hydrodynamic dispersion or from the influence of isotope exchange kinetics--curvilinear trends of ¹³C-¹⁸O depletion will result. The curvature of such trends then is a measure of the degree of hydrodynamic dispersion or influence of exchange kinetics experienced by the marbles during infiltration-driven metamorphism. During the high temperature infiltration of carbonate rocks during metamorphism, it may be more likely that broadening of the C and O exchange fronts will be the result of hydrodynamic rather than kinetic dispersion. Applications of transport theory demonstrate that the observed curvilinear trends of ¹³C-¹⁸O depletion in marbles likely contain information on the degree of hydrodynamic dispersion of the fluid flow system, rather than define close limits on the pore fluid composition, during infiltration-driven metamorphism.