On this part, the outcomes obtained from the totally different breakthrough checks beneath oedometric circumstances are offered. First, the (hbox {CO}_2) entry stress of the fabric is assessed beneath totally different ranges of axial efficient stress and totally different (hbox {CO}_2) phases (gaseous and liquid). Then the hydraulic behaviour of the fabric is investigated primarily based on the acquired water permeability at totally different ranges of utilized efficient stress with a purpose to examine its affiliation to the corresponding measured entry stress. The axial efficient stress, (sigma _{textual content {ax}}’), is taken into account primarily based on the Terzaghi’s equation, i.e., (sigma _{textual content {ax}}’ = sigma _{textual content {ax}}) − ( textual content {u}_{textual content {p}}) the place, (sigma _{textual content {ax}}) is the whole axial compressive stress and ( textual content {u}_{textual content {p}}) is the pore-fluid stress. You will need to level out the given definition refers back to the efficient stress utilized on the pattern earlier than (hbox {CO}_2) breakthrough, i.e. whereas the fabric is absolutely saturated with water. After (hbox {CO}_2) breakthrough, (hbox {CO}_2) injection is stopped and the pattern is resaturated with water for the measurement of the corresponding permeability (single section stream).

### Evaluation of the (hbox {CO}_2) entry-pressure

On this marketing campaign, a collection of breakthrough checks has been carried out beneath fixed stress boundary circumstances on the downstream water reservoir. Within the following, the outcomes of 4 breakthrough checks (carried out on pattern OPA-2) are defined intimately and offered in chronological order: loading historical past can have an irreversible affect on the structural (porosity) and due to this fact hydromechanical properties of the fabric. Throughout every subsequent breakthrough take a look at the identical or an elevated stage of axial efficient stress is utilized. Within the following outcomes, (hbox {CO}_2) is injected beneath two ranges of axial efficient stress (10 MPa and 22 MPa) and two ranges of pore water stress are thought-about (2 MPa and eight MPa). The preliminary (hbox {CO}_2) injection stress is the same as the given pore water stress similar to injection of each gaseous ((hbox {u}_{textual content {CO}_2, {textual content {init}}} =) 2 MPa) and liquid (hbox {CO}_2) ((hbox {u}_{textual content {CO}_2, {textual content {init}}} =) 8 MPa).

First, the pattern is saturated beneath low pore water stress ((hbox {u}_{textual content {dw}}) = 200 kPa) and fixed quantity circumstances, i.e. zero axial displacement, with a purpose to assess the swelling stress which is stabilised to three.2 MPa (see Fig. 10a t = 2 days). Afterwards, the whole axial stress and the pore water stress, each upstream and downstream, are elevated by 1 MPa with a purpose to additional improve saturation and upon stabilisation of the axial displacement sooner or later after, a continuing pore stress gradient of 1 MPa between the upstream and downstream sides of the pattern is utilized for the measurement of water permeability, as soon as regular state circumstances are achieved (t = 2 to 4 days). The overall axial stress is then elevated to a goal worth equal to 12 MPa and upon the tip of consolidation, i.e. stabilisation of the axial displacement (t = 5 days), the water permeability is once more evaluated. That is the tip of the pre-exposure section.

As proven in Fig. 10a, (hbox {CO}_2) is launched on the upstream aspect of the pattern at a stress equal to the downstream water stress i.e. 2 MPa. Determine 10b reveals the evolution of the downstream water quantity outflow throughout (hbox {CO}_2) injection (blue plot) along with the corresponding (hbox {CO}_2) overpressure (hbox {u}_{textual content {CO}_2}) – (textual content {u}_{textual content {w,dw}}) (pink plot). Upon overpressure improve from 1 to 2 MPa, a sudden improve of the water outflow on the downstream aspect is obtained indicating the surplus of capillary forces within the pores of the fabric. (hbox {CO}_2) stress is additional elevated (after the dashed strains in Fig. 10) to make sure that breakthrough has occured and as anticipated the downstream outflow is additional elevated.

Determine 11 reveals the outcomes of the continuing breakthrough take a look at that’s carried out beneath the identical axial efficient stress (i.e. 10 MPa) and liquid (hbox {CO}_2) injection; pore water stress and preliminary (hbox {CO}_2) injection stress equal to eight MPa. Given the chronological order of the presentation of the checks, the primary 2 days of the graph in Fig. 11a reveals the water resaturation of the pattern after the primary gaseous (hbox {CO}_2) injection. Then the whole axial load is elevated to 18.2 MPa adopted by a consolidation section that lasted round 3 days. The pattern’s water permeability is then assessed with the appliance of a stress gradient equal to 1 MPa throughout 2 days when regular state circumstances have been achieved. Lastly, the 2 pore pressures upstream and downstream are set to a stress equal to eight MPa earlier than the start of injection. Determine 11b reveals the evolution of the (hbox {CO}_2) overpressure with time, toghether with the downstream water quantity outflow. A transparent improve of the water outflow is obtained upon (hbox {CO}_2) overpressure improve from 1 to 2 MPa.

After the tip of the second breakthrough take a look at ((sigma _{textual content {ax}} = 18.2) MPa and (hbox {u}_{textual content {dw,w}} = 8) MPa) the pattern is unloaded to a complete axial stress equal to six MPa and resaturated with water beneath low pore stress equal to 1 MPa. After 1 day, the whole axial load and pore water stress (at either side) are elevated to 24 MPa and a pair of MPa respectively as proven in Fig. 12a. Upon completion of consolidation, the water permeability of the pattern beneath 22 MPa axial efficient stress is measured with the appliance of a stress gradient equal to 1 MPa. The 2 sides of the pattern are then set again to a stress equal to 2 MPa and after equilibration, gaseous (hbox {CO}_2) injection from the upstream aspect is initiated beneath the identical pore stress, i.e. 2 MPa. The upstream (hbox {CO}_2) stress is then elevated with 1 MPa steps that final a mean time equal to 1.5–2 days (Fig. 12b). On this take a look at, breakthrough is recognized throughout (hbox {CO}_2) overpressure improve from 2 to three MPa as proven from the downstream water outflow on the downstream aspect in Fig. 12b.

A final breakthrough take a look at is offered on this part beneath the identical axial efficient stress (22 MPa) and liquid (hbox {CO}_2) injection. As proven in Fig. 13a after resaturation the pattern’s whole axial load and pore water stress are elevated to 30 MPa and eight MPa. Liquid (hbox {CO}_2) is then injected from the upstream aspect at an preliminary stress equal to eight MPa. Step-wise injection has been re-initiated at 1 MPa stress steps which have been halted as a result of leak points on the downstream aspect. A second step-wise injection follows and it’s offered when it comes to (hbox {CO}_2) overpressure and downstream water outflow in Fig. 13. A rise of the water outflow is noticed upon improve of the (hbox {CO}_2) overpressure from 3 to 4 MPa, whereas a further (hbox {CO}_2) stress improve has been carried out to make sure breakthrough; certainly, the downstream water outflow will increase much more.

The outcomes of the offered breakthrough checks reveal the next (hbox {CO}_2) entry stress beneath larger axial efficient stress. Below low efficient stress (right here 10 MPa) the affect of the (hbox {CO}_2) section doesn’t instantly mirror on the measured entry stress—clearly beneath the given decision of (hbox {CO}_2) stress improve, i.e. 1 MPa. Below the next and extra practical stage of efficient (22 MPa) the (hbox {CO}_2) entry stress is larger when (hbox {CO}_2) is injected in liquid kind. These outcomes along with these of extra liquid (hbox {CO}_2) injection checks are assembled and mentioned in “Entry-pressure evolution with utilized efficient stress” part.

### Hydraulic response

Earlier than additional evaluation and interpertation of the breakthrough outcomes, the hydraulic response of the fabric when it comes to water permeability is offered and mentioned. It has been demonstrated by numerous experimental outcomes on a number of shale samples that the extent of the utilized efficient stress has an affect on the permeability of shales, particularly at ranges larger than the pre-consolidation stress of the fabric^{20,21,22,23}. Some researchers reported the next stress sensitivity of permeability for samples with excessive clay and low carbonate content material^{24,25}. The lower of permeability is principally attributed to a lower in linked pore quantity community with the rise of the efficient stress, particularly these pores which act as important hyperlinks within the community^{26}.

Totally different empirical equations have been proposed within the literature for the outline of acquired experimental information, mostly within the type of exponential features^{27,28,29} or energy legal guidelines^{30,31}. Although Ref.^{32} confirmed that the facility legislation permeability fashions might be approximated by exponential equations, on this examine we selected an influence legislation mannequin to explain the relation between efficient stress and measured water permeability, ok (m(^2)), of our shaly samples:

$$start{aligned} textual content {ok} = textual content {ok}_0 Massive (dfrac{sigma _{ax}’}{sigma _{ax,0}’}Massive )^alpha , finish{aligned}$$

(2)

the place (hbox {ok}_0) (m(^2)) is the permeability that corresponds to an efficient stress (sigma _{textual content {ax,0}}’) (MPa) and (alpha ) is a fabric fixed.

The water permeability of the 2 Opalinus samples has been measured beneath totally different ranges of axial efficient stress (oedometric circumstances) making use of a continuing head stream^{33,34}. A water stress distinction equal to 1 MPa is utilized between the upstream and downstream aspect of the pattern and the permeability ok (m(^2)) of the medium is calculated by the hydraulic conductivity Okay (m/s) whereas contemplating the fluid’s dynamic viscosity (eta _f) (Pa(cdot )s), density (rho _f) (kg/m(^3)) and the gravity acceleration g (m/s(^2)):

$$start{aligned} textual content {ok} = textual content {Okay} dfrac{eta _f}{rho _f textual content {g}}. finish{aligned}$$

(3)

Based mostly on the Darcy’s legislation, the hydraulic conductivity might be calculated as follows:

$$start{aligned} textual content {Okay} = textual content {q}_f dfrac{rho _f textual content {g} textual content {L}}{A Delta textual content {P}}, finish{aligned}$$

(4)

the place, (hbox {q}_f) (m(^3)/s) is the volumetric stream, L (m) the peak of the pattern, A (m(^2)) the world of the pattern, (Delta hbox {P}_f) (Pa) the utilized stress distinction.

Determine 14a reveals the values of water permeability which have been measured for every pattern beneath the corresponding utilized axial efficient stress. As anticipated, permeability decreases with the rise of the utilized efficient stress. The outcomes of the 2 samples are suitable for utilized ranges of efficient stress larger than 10 MPa, whereas beneath decrease efficient stress a big variability is noticed. This response might be defined by the pre-existence of micro-cracks that beneath low confinement stay open and dominate the stream. Upon load improve, pre-existing fissures shut and the stream is once more managed by the porosity of the pattern. It’s certainly most probably that dessication fissures have been created in pattern OPA-1 which was examined one month after the opening of the Opalinus Clay core. Because of this the becoming of equation Eq. (2) doesn’t take into account the 2 first factors of OPA-1 (sq. factors). The fitted parameters are (hbox {ok}_0) = 2.15 (instances 10^{-19}) m(^2), (sigma _{textual content {ax,0}}’) = 0.0004 MPa and (alpha ) = 0.38. The Opalinus Clay (and shales typically) is an anisotropic materials the hydromechanical response of which (together with permeability) depend upon the bedding orientation. On this work, the examined samples have bedding parallel to the stream (vertical bedding) and due to this fact anisotropy associated results on tortuosity for instance usually are not thought-about.

The lowering water permeability with growing efficient stress is as a result of porosity lower. The obtainable porosity values with the corresponding water permeability beneath the identical stage of efficient stress are plotted in Fig. 14b. The porosity (phi ) of every pattern is calculated primarily based on the axial displacement evolution and whereas not all of the displacement values can be found, the plot correctly demonstrates the correspondance between the 2 materials properties; larger water permeability for larger ranges of normalised porosity. The calculated (phi ) values are normalised with the preliminary porosity of every pattern (phi _0) beneath no efficient stress. These are equal to 16.03% for pattern 1 and 18.43% for pattern 2.

### Entry-pressure evolution with utilized efficient stress

On this part, the extent of efficient stress will likely be evaluated in relation with the corresponding stage of utilized efficient stress. As proven above, the hydraulic response of the studied materials when it comes to measured water permeability has been associated to the utilized ranges of axial efficient stress by the use of evolving porosity. Nevertheless, the hyperlink between porosity and entry stress (PE) is much less straight ahead for the reason that definition of the latter is a perform of a pore/throat of diameter *d*:

$$start{aligned} textual content {PE} = textual content {p}_{textual content {c}} = dfrac{4 gamma textual content {cos}theta }{d}. finish{aligned}$$

(5)

From this basic definition it may be deduced that breakthrough will happen on the pore/throat with the upper diameter. In shales, at low ranges of efficient stress, it’s probably that pre-existing micro-fissures nonetheless stay open and therefore breakthrough will likely be pushed by them (largest *d*). As efficient stress will increase, these micro-fissures will have a tendency to shut and due to this fact each throat dimension and porosity will lower. Reference^{23} reported each lowering porosity and dominant pore dimension in shallow Opalinus Clay with depth. This related tendency between the 2 parameters (pore dimension and porosity) and depth (overburden stress) stays empirical, however it serves as an additional motivation on this examine for the analysis of the affect of efficient stress on the corresponding entry stress worth by the use of pore construction modifications.

The outcomes of the measured (hbox {CO}_2) entry stress of the examined Opalinus Clay with the corresponding axial efficient stress are summarised in Desk 2 and plotted in Fig. 15a. The efficient stress is calculated contemplating the utilized whole axial stress and the downstream pore water stress which corresponds to the preliminary utilized (hbox {CO}_2) injection stress. The outcomes from the gaseous (hbox {CO}_2) injection are separated from the liquid (hbox {CO}_2) outcomes, since floor stress ((gamma )) and wetting properties (contact angle, (theta )) of the (hbox {CO}_2)/water interface change with stress (and due to this fact section)^{35,36}. The obtained values of (hbox {CO}_2) entry stress are constant for liquid (hbox {CO}_2) injection (indicative values of (gamma ) = 30 mN/m and (theta =40^{circ }) from Ref.^{36}), nonetheless, for gaseous (hbox {CO}_2) injection (decrease (hbox {CO}_2) stress) the equal values of floor angle and make contact with angle lead to larger entry stress. This discrepancy between experimental outcomes and principle requires additional investigation for the higher understanding of the sealing response of the given materials and its implication to actual storage. As an example, the consideration of extra hydromechanical mechanisms associated to phenomena resembling partial desaturation and suction improve from gaseous (hbox {CO}_2) injection, could also be obligatory for a extra acceptable interpretation of those outcomes.

For each (hbox {CO}_2) phases the measured entry stress will increase with the rise of the axial efficient stress. This outcome reveals the significance of the correct definition of the hydromechanical boundary state of the caprock materials for the analysis of its entry stress. Although the obtained common pattern reveals a decrease entry stress upon gaseous (hbox {CO}_2) injection in comparison with the corresponding liquid, for low efficient stress (10 MPa), an analogous entry stress has been measured for each (hbox {CO}_2) phases—inside the 1 MPa vary of the growing injection step. This outcome reveals the excessive affect of open porosity (open fissures) to the sealing capability of the fabric that dominates the response. Because the efficient stress will increase, pre-existing cracks shut and porosity decreases, thus the section distinction displays in a extra vital means on the response. The outcomes are fitted utilizing an exponential match primarily based on empirical legal guidelines of porosity evolution with efficient stress^{37,38}.

The obtainable values of the calculated normalised porosity (phi /phi _0) of the 2 samples are additionally plotted with the corresponding measured entry values (Fig. 15b); these are just for liquid (hbox {CO}_2) injection. Impressively sufficient, a close to linear pattern is obtained, highlighting the significance of open porosity on the sealing capability of the fabric; larger (hbox {CO}_2) entry stress for decrease ranges of normalised porosity. That is in step with the definition of the capillary entry stress, however, extra experimental outcomes are required for extra concrete conclusions.