Diagenesis mathematics

Dewers, T. and Ortoleva, P.J. 1990. Interaction of reaction, mass transport, and rock deformation during diagenesis mathematical modelling of integranular pressure solution, stylolites, and differential compaction/cementation. In l.D. Meshri and P.J. Ortoleva (Editors), Prediction of Reservoir Quality through Chemical Modelling, Memoir, 49. Am. Assoc. Pet. Geol. Tulsa, OK. 

Once the radionuclides reach the sediments they are subject to several processes, prime among them being sedimentation, mixing, radioactive decay and production, and chemical diagenesis. This makes the distribution profiles of radionuclides observed in the sediment column a residuum of these multiple processes, rather than a reflection of their delivery pattern to the ocean floor. Therefore, the application of these nuclides as chrono-metric tracers of sedimentary processes requires a knowledge of the processes affecting their distribution and their relationship with time. Mathematical models describing some of these processes and their effects on the radionuclide profiles have been reviewed recently [8,9,10] and hence are not discussed in detail here. However, for the sake of completeness they are presented briefly below. 

For steady-state conditions this equation is set equal to 0, because at a given depth x, concentration does not change with time. Steady-state models are generally more amenable to mathematical solution than are non-steady-state models. Unfortunately, diagenesis in many shoal-water carbonate sediments is significantly influenced or even dominated by non-steady-state processes. 

Lasagna, A.C., and Holland, H.D. (1976) Mathematical aspects of non-steady state diagenesis. Geochim. Cosmochim. Acta 40, 257-266. 

In recent years various workers f1-7J have successfully developed models based on the mathematics of diffusion (8) to describe vertical profiles of selected chemical parameters in marine sediments dominated by sulfate reduction. Several papers 9, 10) have also proposed models for nitrogen diagenesis in the upper aerobic zone of such sediments. Most of these models, however, deal with only one or two relatively well behaved parameters, such as SO5" or CO2, which do not interact strongly with other components of the sediment besides organic matter. A truly comprehensive model for such sediment should deal simultaneously with all of the major chemical parameters of the system and ideally should be formulated as an initial value prob-... 

The formulation of this model is based on the mathematics of diagenesis developed by Berner Using the chain rule of partial differentiation (.12, p. 335) Berner showed that for any property of a sediment, P, that is a continuous differentiable function of depth, X, and time, t. 

Van Cappellen P. and Berner R. A. (1988) A mathematical model for the early diagenesis of phosphorus and fluorine in marine sediments apatite precipitation. Am. J. Sci. 288, 289-333. 

Clayton, C.J. (1994) Microbial and organic processes. In Quantitative Diagenesis Recent Developments and Applications to Reservoir Geology (Eds Parkers, A. Sellwood, B.W.). NATO ASl Series C Mathematical and Physical Sciences, 453, 125-160. Kluwer Academic, Dordrecht. 

The limitations in terms of predicting compaction and fluid pressure seem at the present stage not to be the mathematical modelling but the poor constraints of the 3D distribution of sediment properties in the basin. The most difficult problem is to predict the distribution of sediment properties based on facies analyses, provenance, diagenesis and structural geology. We are faced with the problem that realistic basin modelling requires a fairly detailed input with respect to the distribution of different lithologies and their physical properties in a basin. 

Boudreau BP (2000) The mathematics of early diagenesis from worms to waves. Reviews of Geophysics 38 389-416. 

Peaceman DW, Rachford HH (1955) The numerical solution of parabolic and elliptic differential equations. Journal of Society of Industrial and Applied Mathematics 3(i) 28-4i Perrier B, Quiblier J (1974) Thickness changes in sedimentary layers during compaction history methods for quantitative evaluation. AAPG Bulletin 58(3) 507-520 Perry EA Jr, Hower J (1970) Burial diagenesis in Gulf Coast pelitic sediments. Clays and Clay Minerals 16 15-30... 

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