Properties of One-Dimensional Diagenetic Models

Abstract

It is not possible to treat both absolute and relative time in the diagenetic equation of Berner, and the equation cannot therefore be particularized to obtain an expression that isolates the diagenetic contribution to a sediment property. This problem can be solved by using a Lagrangian approach in which the depositional contribution to the sediment property becomes a boundary condition. A simplistic steady-state model is used to define the convective velocities of pore fluid and sediment particles in terms of porosity and the rate of accumulation of compacted sediment. The argument is extended to include values of sedimentation rate in nature and diffusion coefficients in sediment pore fluid, and the changing relative importance of convective and diffusive transport during compaction is considered. A continuity equation is developed for the concentration of a component i in multi-component pore fluid. If the equation is used in a reference frame moving at the convective velocity of the sediment particles, it appears to be possible to follow the course of chemical reaction in a compacting system, even though pore fluid and sediment particles are necessarily moving in opposite directions. The formalism of nonequilibrium thermodynamics will be called for in more complex diagenetic models that treat such additional phenomena as heat flow, stress distribution, and the semi-permeable membrane behavior of aggregates of minerals with high surface area and surface charge. The requirement of linearity between thermodynamic forces and fluxes is well obeyed in electrolyte diffusion, but poorly in chemical reactions. The nonequilibrium thermodynamic approach requires detailed knowledge of a considerable variety of parameters of a system, if it is to yield greater understanding than could be obtained from a set of continuity equations.