ABSTRACT:

Pressure solution creep is an important contributor to permeability and porosity change in the upper crust. Engineering projects such as enhanced geothermal systems and petroleum extraction are impacted in the short- and long-term by changes in porous and fracture permeability, and are expectedly influenced by similar creep processes. Of currently available models for pressure solution, few are extendable for variable conditions of stress and temperature, and none have successfully constrained final (equilibrium) compaction magnitudes. With past models and experiments primarily focused on granular media, behavior in fractures remains largely untested at pore or reservoir scale. In this work, a micromechanical model is developed for pressure solution creep that maintains complete dependence on aqueous concentrations and is transferable for arbitrary conditions of stress and temperature. Equilibrium compaction is constrained with a form of “critical stress”; dependent on conditions of pore structure and applied effective stress. Compared to laboratory experiments on granular quartz, predictions are accurate across a range of conditions (400-500°C, 20-150 MPa, and mean particle diameter of 3-120µm). The model is applied to rough fractures to illustrate important feedbacks between elastic deformation and chemical-mechanical creep. Probing analyses of environments typical of enhanced geothermal systems indicate potential importance for pressure solution, particularly following events that disrupt reservoir equilibrium.

1. INTRODUCTION

Intergranular pressure solution is an important chemo-mechanical creep process in crustal rocks. In rock fractures and porous aggregates, mechanical load is concentrated at a finite number of contact points, and if these locations are hydrated, by a thin water film [1-4] and/or by a dynamic island-channel network [5-7], then the activity of stressed minerals in contact with the fluid is elevated. Under these conditions enhanced dissolution and supersaturation within the contact is thermodynamically favored [8, 9]. A chemical potential gradient may then evolve for the diffusive migration of aqueous species across the grain boundary for eventual precipitation to hydrostatically stressed pore walls. Combined, these serial processes lead to porosity and permeability reduction by compaction of the solid and infilling of voids, providing a potentially important contribution to diagenesis and fault healing [10-12] and the evolution of engineered, fractured reservoirs [cf. 13]. After [14], a simple finite element equation system is proposed to examine the three serial processes of pressure solution. It is shown that complete control can be maintained on interfacial and pore fluid aqueous concentrations without the iterative solution of a linear equation system. The solution is applicable to open and closed systems and to granular aggregates or fractures. It is shown that important feedbacks exist between elastic deformation and chemo-mechanical creep. The potential is explored for pressure solution reactivation following shear dilation on previously equilibrated fractures.

2. IMPLICIT PRESSURE SOLUTION MODEL

This section presents the fundamental thermodynamic, kinetic, and diffusive relationships for the composite model. Fick's law for diffusion is solved for boundaries of constant flux within stressed mineral contacts, although alternate boundary conditions produce only slightly different results. All geometric parameters are derived in terms of a representative elementary volume (REV) for physical clarity.

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