**7. Discussion and Summary**

Chalk fields in the North Sea are over-pressured and during production and pressure depletion, they compact significantly. The compaction can contribute significantly to hydrocarbon recovery, and for the Valhall field, it is estimated to be responsible for about 50% [2] of the total oil recovery. For the Ekofisk field, the water weakening effect is expected to contribute to about 50% of the total compaction [3]. In the case of the Valhall field, it is believed to be much less than the Ekofisk field [35]. From the results discussed here, this can potentially be explained as a consequence of temperature differences, but another important factor is the pore pressure history. The Ekofisk, at discovery, had an initial reservoir temperature of 130 ◦C, whereas Valhall had a temperature of 93 ◦C. Both mineralogical alterations and the effect of surface charge, due to sulphate adsorption, are less significant at lower temperatures.

The field conditions are different, at the field scale the effective stress is changing due to pressure drawdown. As pointed discussed by Andersen, Foged et al. [14], it is possible to extrapolate lab results to field results by performing strain rate controlled tests. The experimental data presented and discussed in this paper have been performed at a constant hydrostatic stress, and not uniaxial constant strain rate. However, by comparing hydrostatic tests with and without chemical effects, we believe that many of our conclusions will still hold.

The e ffect of water activity is the most uncertain e ffect. The experiments discussed in Section 3, demonstrates quite nicely the transition between a phase consisting of pure fresh water, a mixture of water and glycol to pure glycol and dry samples. The experiments are also explained as a change in surface energy on the microscopic level. However, oil-bearing formations usually consist of a hydrocarbon phase that is immiscible with water. Water is believed to be trapped in small (water-wet) pores and oil resides in larger pores; over geologic time, oil adheres to the rock and change the wettability. During water flooding, the original formation water (ionic strength ~2–3 times seawater) and hydrocarbons are displaced by seawater. The change of water activity from formation water to seawater is not large. A change from a 3M brine to seawater is a change in water activity from ~0.95 to ~0.98 (see Equation (4)). However, there is likely more to this story because at low water saturations (~1–2%), the water activity is not easy to calculate because it is a ffected by surface charge, di ffusive layers and ion interactions with the chalk surface. If most of the water in this case is bound to the chalk surface, the water activity should be much lower than 0.95 (independent on the salinity). Thus, in areas of very low water saturation, an increase in water saturation could give a sudden increase in the water activity, and weaken the chalk and induce compaction. There are some experimental data, where chalk cores have been aged with oil and water saturations about ~5% [36], in those cases when they are flooded with seawater, the creep rate does not change significantly compared to cores that are 100% water-filled. Thus, if these results are correct, the initial water saturation must be lower than 5% to see an e ffect of the water activity. From capillary pressure arguments, one would expect to see more compaction in areas high above the free water level, where the water saturation is low. The field data are scarce, but an observation well at the Ekofisk field shows more compaction close to the tight zone, where the water saturation is higher due to smaller pores [3]. This does not support the water activity hypothesis.

We have quantified the chemical e ffects in the hydrostatic creep experiments by using the de Waal model. Comparing the fitting of the de Waal model to core data, where the chemical e ffects are minimal and where they are present, we have shown that the e ffect of magnesium brines can be modelled by a linear term ~Ct. The constant C is about 0.05%/day, as shown in Figure 6.

The simulated calcite to magnesite (or dolomite) alteration in the core experiments is about 0.07 wt% per day. Thus, we find that the alteration corresponds directly to additional creep strain. The streamline simulations in Figure 11 show that close to the well, there is an alteration of 0.5 wt% change after 5 years of flooding; this should then correspond to about 0.5% additional creep (0.5 m of a 100-m reservoir interval). The chemical water weakening e ffects due to calcium to magnesium carbonate alteration are much smaller, but not insignificant, on the field scale compared to the lab. The main reason for the slow chemical alteration on the field scale is the cooling of the reservoir.

Sulphate, according to [27], adsorbs onto the calcite surface and causes additional elastic deformation of factor of two, compared to NaCl, see Figure 3 (seawater corresponds to 0.024 M Na2SO4). If sulphate is introduced into the core after yield, in the creep phase, the core experience a sudden increase in strain rate [29]. This e ffect is transient, but the increase in volumetric strain due to sulphate is ~1.5%. The simulations and the field data show that sulphate breaks through to the producer in a reasonably short period of time. The sulphate front is lagging behind the water (chlorine) front, due to both precipitation of calcium sulphate and adsorption onto positively charged calcium cites, and one should therefore expect to see some delayed water weakening e ffect, i.e., the reservoir compaction should happen after the water front has passed a reservoir section. In the reservoir models, the grid is coarse and thus the simulation models might not be able to distinguish the sulphate front from the water saturation.

### **8. The Future and Final Remarks**

In the future, basin models will simulate the full chemical evolution of the reservoir with all its attendant consequences. The most di fficult thing to model is how the rock - fluid interactions affects compaction at the various scales. We need core experiments to test rock deformation at realistic conditions, but the drawback is that it is di fficult to tease out the exact mechanisms. The mechanisms are needed in order to ge<sup>t</sup> the speed of chemical interactions at a larger scale. Much has been investigated regarding the chemical e ffects, but perhaps the most uncertain and less studied e ffect is how the oil saturation a ffects compaction. There are some results [37] showing that oil-filled cores compact when flooded with water. Later results shows less e ffects when flooding oil-saturated cores with water [28,36,38]. The water activity is worth pursuing, as it will travel at the speed of the waterfront, but most likely it should only be e ffective at very low initial water saturation (high capillary pressure).

There is still uncertainty related to the e ffect of initial mineralogy. Cores with low carbonate have a di fferent strain history, than cores with non-carbonate content (~5 wt%). Impurities in chalk seem to eliminate the delay in alteration-induced creep.

E ffects of water chemistry on compaction on the lab scale is important. We strongly believe that reservoir models as used by the industry today are too crude to distinguish the di fferent field scale compaction mechanisms. By extracting streamlines from reservoir simulators and conducting chemical alteration and adsorption calculations similar to those shown here, we can see the possibility of predicting the distribution of the alteration fronts, as well as how far the sulphate adsorption front has travelled. This might provide an idea of where to expect the most compaction, both horizontally and vertically. This, in turn, can be checked against observation wells, and potentially 4D seismic data.

**Author Contributions:** Writing–original draft, M.W.M. and A.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** Norges Forskningsråd: 230303.

**Acknowledgments:** The authors like to thank the group working with water weakening of chalk at University of Stavanger for fruitful discussions. In addition, we are grateful for the input from the editors and reviewers of the journal, and the inputs from Lawrence Cathles. The authors acknowledge the Research Council of Norway and the industry partners, ConocoPhillips Skandinavia AS, Aker BP ASA, Vår Energi AS, Equinor ASA, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, and Wintershall DEA, of The National IOR Centre of Norway for support.

**Conflicts of Interest:** The authors declare no conflict of interest.
