7. Predicting dynamic porosity evolution: an illustrative example

An example of a dynamic porosity development analysis is presented here based on material published in 2015 [3]. The results of an experiment performed over 1090 days where a Liegè (Belgium) chalk sample was exposed to hydrostatic stress (11.1 MPa, approximately 5 MPa above yield) and continuous flow of 0.219 M MgCl2 (33 and 99 cm<sup>3</sup> /day, pore pressure 0.7 MPa and 130�C). Basic sample measurements were performed of dry/saturated mass, pore volume, solid and bulk volume and hence porosity before and after test, hence the mineral density estimated and confirmed using He-pycnometry (Table 1). The bulk core volume was reduced more than 15% and mineral mass is reduced by more than 18% while the density is increased from 2.7 to 2.9 g/cm3 . The stresses are sufficient to induce pore collapse for these chalks, and the 0.219 M MgCl2-brine (with equal ion strength as seawater) induced dissolution of the calcium carbonate and precipitation of denser Mg-bearing carbonates (e.g., magnesite and dolomite).


Table 1. Basic measurements of the core before and after the 1090 days long-term test [3]. Figure 1 displays SEM images of the core material before and after the flow-through test.

During the test, the axial deformation and the ion concentration of the effluent fluids were measured. In Figure 7a, the Mg and Ca ion concentrations are measured through time. These measurements can be used to find the production rate in g/day using Eq. (33), seen in Figure 7b. A trebling of the inlet flow rate leads to more than a doubling in the calcite dissolution. The mass evolution is used to estimate the dynamic change in density using Eq. (36), and is then combined to estimate the solid volume as function of time as seen by the dotted line in Figure 7c plotted together with the bulk volume, estimated from the axial strain. Thus, the pore volume can be estimated (dashed line in Figure 7c). As can be seen, the pore volume is reduced when bulk compaction dominate the overall process until 200 days. A typical observation from primary creep experiments is that the overall creep rate decreases with time. After 200 days, when the compaction rate has reduced, the flow rate was increased thereby increasing the rate at which dissolution/precipitation occurs, see Eq. (33) where the flow-rate dependency is explicitly shown. At this point of time, the overall porosity dynamics change. In the initial compaction-dominated regime, the overall porosity reduced to a value of as low as 33%, and afterwards it starts increasing (solid line in Figure 7d). At approximately 400 days, the flow rate is then reduced again and the rate of change in porosity is changing accordingly.

In the experiment presented here, both pore and solid volume are subject to change. Since only the bulk volume or the solid volume could be determined from axial strain IC data, respectively, the pore volume was determined. As is exemplified in the presented experiment, the porosity evolution dynamics display a complex behavior because of the reduction in pore volume and solid volume. Their rate depends upon stress, the way in which deformation is

Porosity is an important parameter for understanding the diagenetic processes and petrophysical reservoir systems. Its importance to the mechanical stiffness and strength of porous rocks, and to the resource potential, and rate of hydrocarbons produced from reservoirs is evident. The porosity is a dynamic parameter from the strain and chemical reactions from injection of fluids out of equilibrium with the host rock (e.g., seawater brines at elevated temperature in chalks) that induce additional deformation over time. The adsorption of surface-active ions leads to alterations in the forces binding grains together, leading to instan-

To understand quantitatively how porosity changes dynamically through time, there are series of processes that needs to be incorporated. This chapter presents some of the ways in which the bulk strain can be partitioned into elastic/plastic components, time-dependent, and timeindependent components, and solid volume and pore volume processes. For chalks, the dynamic porosity evolution depends on the relative importance of the different processes at play, that again are functions of the stress, strain, temperature, flow rate, and fluid chemistry. The methods presented here do not cover all possibilities for porosity evolution determination depending upon measurements that are available. When the bulk volume strain and chemical composition of the effluent fluids are known, the following porosity evolution model applies

<sup>ϕ</sup><sup>0</sup> � <sup>ε</sup>volð Þ� <sup>t</sup> Msð Þ<sup>t</sup>

<sup>r</sup>sð Þ<sup>t</sup> � Ms, <sup>0</sup> rs,<sup>0</sup> <sup>=</sup>Vb,<sup>0</sup>

<sup>1</sup> � <sup>ε</sup>volð Þ<sup>t</sup> (37)

Porosity Evolution during Chemo-Mechanical Compaction

http://dx.doi.org/10.5772/intechopen.72795

217

accumulated and the rate of dissolution/precipitation.

ϕðÞ¼ t

\*Address all correspondence to: anders.nermoen@iris.no

1 Institute of Energy Resources, University of Stavanger, Stavanger, Norway 2 International Research Institute of Stavanger (IRIS AS), Stavanger, Norway

3 National IOR Centre of Norway, University of Stavanger, Norway

8. Summary

taneous additional deformation.

Author details

Anders Nermoen1,2,3\* and

From 900 days and onwards, the Ca that was initially found within the core had been produced, after the solid volume was interpreted to be constant and the bulk compaction is facilitated by pore volume reduction, and hence the porosity is decreased to 40.1%.

Figure 7. (a) Ion chromatography of the produced ion concentration of mg and Ca throughout the test. Mg is retained in the core while Ca is produced. (b) Calculated production rate of mg (solid) and Ca (dashed) using Eq. (32), (33) and (36), while (c) displays the total, pore, and solid volume evolution. (d) Observed volumetric creep (dashed line) and estimated porosity evolution as the relative importance of bulk compaction and dissolution/precipitation change.

In the experiment presented here, both pore and solid volume are subject to change. Since only the bulk volume or the solid volume could be determined from axial strain IC data, respectively, the pore volume was determined. As is exemplified in the presented experiment, the porosity evolution dynamics display a complex behavior because of the reduction in pore volume and solid volume. Their rate depends upon stress, the way in which deformation is accumulated and the rate of dissolution/precipitation.
