The Mathematical Institute, University of Oxford, Eprints Archive

Mathematical modelling of compaction and diagenesis in sedimentary basins

Yang, X. S. (1997) Mathematical modelling of compaction and diagenesis in sedimentary basins. PhD thesis, University of Oxford.



We begin by analysing the simplest case of poroelastic compaction which in a 1-D case results in a nonlinear diffusion equation, controlled principally by a dimensionless parameter $\lambda$, which is the ratio of the hydraulic conductivity to the sedimentation rate. We provide analytic and numerical results for both large and small $\lambda$ in Chapter 3 and Chapter 4. We then put a more realistic rheological relation with hysteresis into the model and investigate its effects during loading and unloading in Chapter 5. A discontinuous porosity profile may occur if the unloaded system is reloaded. We pursue the model further by considering diagenesis as a dehydration model in Chapter 6, then we extend it to a more realistic dissolution-precipitation reaction-transport model in Chapter 7 by including most of the known physics and chemistry derived from experimental studies.

We eventually derive a viscous compaction model for pressure solution in sedimentary basins in Chapter 8, and show how the model suggests radically different behaviours in the distinct limits of slow and fast compaction. When $\lambda \ll 1$, compaction is limited to a basal boundary layer. When $\lambda \gg 1$, compaction occurs throughout the basin, and the basic equilibrium solution near the surface is a near parabolic profile of porosity. But it is only valid to a finite depth where the permeability has decreased sufficiently, and a transition occurs, marking a switch from a normally pressured environment to one with
high pore pressures.

Item Type:Thesis (PhD)
Subjects:D - G > Geophysics
O - Z > Partial differential equations
A - C > Approximations and expansions
H - N > Numerical analysis
Research Groups:Mathematical Geoscience Group
Oxford Centre for Industrial and Applied Mathematics
ID Code:28
Deposited By: Eprints Administrator
Deposited On:09 Mar 2004
Last Modified:29 May 2015 18:15

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