1. Introduction

Understanding how chemically reactive and mechanically deformable rock-fluid systems consisting of solids and voids evolve is very important to several fields in the Earth sciences. Examples include the lithification of sedimentary strata [1] and long-term creep behavior of crustal rocks [2]. In addition, a range of industrial processes are affected by chemo-mechanical interactions, including, e.g., pharmaceutical and food processing industries, and geotechnical engineering concerning roadwork construction, mass transportation, and slope stability.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

precipitation lead to changes to grain texture and morphology, and the mineral surface's affinity to oil and water. These are factors, together with porosity, that dictate not only the flow property of the porous rock but also the mechanical parameters that control the stiffness, strength, and the rate at which compaction by grain reorganization and pore collapse occurs. The general processes that are described here is applied to understand how the porosity of chalks develops (Figure 1a, b display unaltered and altered chalks) dynamically in a controlled triaxial cell experiments (Figure 2a), with control of temperature, pore pressure, side stress,

This chapter deals with some of the constitutive relations that are used to describe the evolution of porous bodies. We incorporate a discussion of how rock-fluid chemistry may impact the grain volume, and review the ways in which total volume reduction may be facilitated in compressive systems. The discussion summarized in the development of a porosity evolution equation in which all effects are included. The usage of the porosity evolution equation is

The basic equations that are used to quantify the porosity evolution through time are presented. The analysis is based on the work presented in Nermoen, et al. [3]. The overall bulk

The pore volume, and hence the porosity, itself is not a conserved quantity. In that case, the bulk volume (size of the object of study) and the solid volume evolution have to be used. Since

> <sup>¼</sup> <sup>1</sup> � Vs Vb

When both the bulk volume and the pore volume change dynamically from known measurements before the experiment starts (Vb,<sup>0</sup> and Vp, <sup>0</sup> are known), then the time-evolution of the

Vb ¼ Vs þ Vp (1)

Porosity Evolution during Chemo-Mechanical Compaction

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ΔVb ¼ ΔVs þ ΔVp (2)

ΔVp ¼ ΔVb þ ΔVs (3)

(4)

volume of a bi-phase material equals the sum of the solid volume and pore volume

the volumes are additive by nature, the changes in pore volume can be calculated

At any given time through dynamic porosity evolution, the porosity is given by

porosity is given by

<sup>ϕ</sup> <sup>¼</sup> Vp Vb

Any changes in solid volume and pore volume lead to changes in the bulk

and overburden stress of cylindrical samples (Figure 2b).

exemplified with references to already published experimental results.

2. Constitutive equations for porosity evolution

Figure 1. (a) SEM image of an unaltered chalk (Liegè, Belgium [3]). Calcite grains partially organized in coccolith rings and foraminifers. (b) Reworked Liegè chalk from the same core as (a) after 1090 days of continuous mechanical compaction and flow of reactive 0.219 M MgCl2 brine at 130C (Table 1).

The pore volume fraction, the pore size distribution, and the mineral surfaces are key parameters to ensure safe disposal of radioactive waste and captured CO2, and to understand how ores' deposit evolves with time. In petroleum sciences, chemo-mechanical processes are important to accurately predict the porosity since it is inside the pores where hydrocarbons are stored, and it is through the pores, the hydrocarbons are being produced by miscible and immiscible fluid migration across reactive mineral surfaces that again are subject to change. Both pore volume and production rate are crucial to determine the recoverable hydrocarbon potential.

Reactive pore fluids in nonequilibrium with their host rocks lead to dissolution and precipitation transforming the mineral assembly into another, see for example, [3–5]. Dissolution and

Figure 2. (a) Triaxial cell setup controlling axial and radial stress, the pore pressure, flow rate, and temperature. (b) Additive partitioning of the total bulk strain into a pore and solid volume component. Here, uniaxial strain is assumed (constant diameter) such that lengths relate to volumes.

precipitation lead to changes to grain texture and morphology, and the mineral surface's affinity to oil and water. These are factors, together with porosity, that dictate not only the flow property of the porous rock but also the mechanical parameters that control the stiffness, strength, and the rate at which compaction by grain reorganization and pore collapse occurs. The general processes that are described here is applied to understand how the porosity of chalks develops (Figure 1a, b display unaltered and altered chalks) dynamically in a controlled triaxial cell experiments (Figure 2a), with control of temperature, pore pressure, side stress, and overburden stress of cylindrical samples (Figure 2b).

This chapter deals with some of the constitutive relations that are used to describe the evolution of porous bodies. We incorporate a discussion of how rock-fluid chemistry may impact the grain volume, and review the ways in which total volume reduction may be facilitated in compressive systems. The discussion summarized in the development of a porosity evolution equation in which all effects are included. The usage of the porosity evolution equation is exemplified with references to already published experimental results.
