Modelling pressure solution: an example of deformation and reactive fluid flow in a geological systemPhD at the University of Liverpool funded by NERC and Enviros QuantiSci Ltd.

Fluid flow, chemical reactions and deformation are coupled processes that occur in virtually all geological systems, e.g.

  • Compaction-driven melt migration in partially molten rocks
  • Coupled metasomatism and deformation e.g. in shear zones
  • Diagenesis and compaction in sediments

In order to understand such systems, it is important to consider the interactions between processes, rather than considering each process in isolation.

Heather Sheldon is currently developing a numerical model of pressure solution in quartz sandstones as an example of a system involving feedbacks between stress, chemistry and fluid flow. The key issues in this work are:

  • To identify the equations that describe fluid flow, deformation and solid-fluid interactions in a quartz sandstone undergoing compaction by pressure solution;
  • To identify and implement a numerical method for solving the coupled system of equations.

Equations describing pressure solution

The strain rate of a rock undergoing pressure solution ultimately depends on the rate at which dissolved material can diffuse out of the grain contacts (Fig.1). This depends on:
  • normal stress acting on the grain contact
  • rate of dissolution (kinetics)
  • effective diffusion coefficient in the contact zone (depends on D and thickness of fluid layer)
  • rate of removal of solute from the pore fluid by: precipitation on free grain surfaces (kinetics) & diffusive/advective transport through the pore spaces

Therefore, a flow law describing pressure solution should include all of these factors, and must be coupled with equations that describe the evolution of pore fluid chemistry due to solid-fluid reactions and macroscale transport.

Figure 1 - The mechanism of pressure solution between 2 quartz grains. Which of these processes is the rate-limiting step?

Developing the numerical model for pressure solution

  • The equaitons describing solid deformation, fluid flow and chemical evolution of the pore fluid are tightly coupled and highly non-linear, making them difficult to solve.
  • Recent developments in the solution of Differential Algebraic Equation (DAE) systems can be applied to this set of equations.
  • A DAE solver developed by the CASE partners in this project, Enviros QuantiSci Ltd., is currently being investigated as a method for solving the pressure solution equations.

Future work

It is hoped that this modelling technique can be adapted to investigate other geological systems, such as melt migration in cumulate crystal piles within magma chambers. Can coupled modelling of reactive fluid flow and deformation explain such phenomena as the formation of chemical layering in cumulate rocks (Fig.2)?

Figure 2 - Textural layering cross-cut by chemical layering in an igneous cumulate (Rhum, UK)
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