Laurent Andre
email: l.andre@brgm.fr

Mohamed Azaroual
email: m.azaroual@brgm.fr

Christian Bernstone
email: christian.bernstone@vattenfall.com

Andrea Wittek
email: andrea.wittek@vattenfall.de

MODELING THE GEOCHEMICAL IMPACT OF AN INJECTION OF CO 2 AND ASSOCIATED REACTIVE IMPURITIES INTO A SALINE RESERVOIR

Numerical simulations performed with the TOUGHREACT code focus on the chemical reactivity of deep reservoir rock impacted by an injection of CO 2 and associated reactive impurities (mainly SO 2 and O 2 ). A simplified two-dimensional radial geo-model representing the near wellbore domain of a saline reservoir enabled us to capture the global geochemical behaviour of this underground zone. Two ratios CO 2 /SO 2 are investigated. The results of the numerical simulations highlight the high reactivity of the near-well zone in the case where ancillary gases (SO 2 and O 2 ) are injected with CO 2 with dissolution of carbonates and precipitation of sulfate minerals. Major reactions occur in the reservoir formation, whereas clays of the caprock are only slightly affected by the injection of CO 2 and associated reactive impurities.

INTRODUCTION

Numerical simulations using coupled hydrogeological, thermal, and geochemical codes as TOUGHREACT (Xu and Pruess, 2001) serve as adequate tools to explore different evolution scenarios of gas injection in deep geological structures, and to determine the behavior of the near-wellbore region of the targeted reservoir. Previous numerical studies have demonstrated that massive and continuous injection of pure CO 2 involves a disequilibrium of the physical characteristics (temperature, gas saturation, pressure, capillary pressure…) and geochemical characteristics (dissolution of supercritical CO 2 into the brine, pH variations, dissolution/ precipitation reactions of the porous rock minerals) of the host reservoir [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO 2 -liquid interface during supercritical carbon dioxide injection into a carbonated reservoir, the Dogger aquifer (Paris Basin, France)[END_REF][START_REF] André | Numerical Simulations of the Thermal Impact of Supercritical CO 2 Injection on Chemical Reactivity in a Carbonate Saline Reservoir[END_REF].

However, the presence of impurities in the CO 2 gas stream may impair the engineering processes of capture, transport, and injection: some associated reactive gases, i.e., chemical species other than CO 2 in the injected stream-namely SOx, NOx, H 2 S, or O 2 -may require different adaptations for injection and disposal than if the stream were pure CO 2 . Moreover, the presence of associated gases in the CO 2 stream in relatively high proportions can affect the compressibility of the injected gas and reduce the CO 2 storage capacity of the reservoir. This is because of the space taken up by these gases and the unfavorable volume balance of induced geochemical reactions. Additionally, depending on the type of geological storage, the presence of ancillary gases may have some other specific effects, such as trapping performances. In the case of CO 2 storage in deep saline formations, the presence of gas impurities affects the gas solubility in the aqueous phase, as well as the rate and amount of CO 2 stored through mineral dissolution and precipitation. Hence, we need numerical estimations to forecast how the gas composition might impact the geochemical reactivity inside the host reservoir, potentially modifying the porosity and permeability of the medium and influencing the long-term well injectivity. Two numerical simulations are performed to study the impact of CO 2 , SO 2 and O 2 mixtures on the main physicochemical characteristics of a deep saline aquifer.

NUMERICAL APPROACH

Calculation code

The TOUGHREACT simulator (Xu and Pruess, 2001) is used for all simulations in this study. This code, which issued from TOUGH2 V2 (Pruess et al., 1999), couples thermal, hydraulic and chemical (THC) processes and is applicable to one-, two-, or three-dimensional geologic systems with physical and chemical heterogeneity. TOUGHREACT is coupled with ECO2n (Pruess, 2005), a fluid property module developed specifically to deal with geologic sequestration of CO 2 in saline aquifers. It can be used to model isothermal or nonisothermal multiphase flow in water/brine/CO 2 systems.

TOUGHREACT simulates the chemical reactivity of systems based on an extended thermodynamic database. In this study, we use the database released with the program, i.e., a modified version of the EQ3/6 database (Wolery, 1992).

Thermodynamic equilibrium between the gas phase and the aqueous phase is assumed for CO 2 dissolution. An extension of Henry's law, including salting-out effect, is used to estimate the solubility of CO 2 in the aqueous phase at high pressure and high salinity.

For this work, the dissolution and precipitation reactions of minerals proceed under kinetic constraints. The general form of the rate law proposed by Lasaga (1984) is applied for both dissolution and precipitation of minerals:

! " # $ ± = n n n n 1 A k r
Positive values for r n correspond to the dissolution of the mineral n (negative for precipitation), k n represents the rate constant (mol m -2 s -1 ), A n is the specific reactive surface area per kg H2O , ! n represents the saturation index of the mineral n (! n = Q n /K n ), and ! and " are empirical parameters determined from experiments, usually taken as 1.

The dependence of the rate constant k n with temperature is calculated by means of the Arrhenius equation:

! " # $ % & ' ( ) * + , - - = 15 . 298 1 1 exp 25 T R E k k a n
where E a is the activation energy (J mol -1 ), k 25 the rate constant at 25°C, R is the gas constant (J mol -1 K -1 ) and T the temperature in Kelvin.

For some minerals, specifically alumino-silicates and salts, the dissolution and precipitation also depend on H + (acid mechanism) and OH - (alkaline mechanism) concentrations, in addition to the neutral mechanism. In this case, k n is calculated using the following expression:

OH H n H OH a OH n H H a H nu a nu n a T R E k a T R E k T R E k k ! " # $ % & ' ( ) * + , - - + ! " # $ % & ' ( ) * + , - - + ! " # $ % & ' ( ) * + , - - = 15 .
a T R E k a T R E k T R E k k ! " # $ % & ' ( ) * + , - - + ! " # $ % & ' ( ) * + , - - + ! " # $ % & ' ( ) * + , - - =
The kinetic parameters used for the last two equations are from Palandri and Kharaka (2004).

Mineral dissolution and precipitation reactions involve temporal changes in reservoir porosity. Indeed, variations in the mineral volume fraction owing to chemical reactions allow computing the resulting porosity. Permeability variations are calculated from porosity changes using the "tube-in-series" model (Verma and Pruess, 1988), which allows reaching nil permeability even if porosity is not nil.

Geometrical Model

The saline aquifer is schematically represented by a 2D-radial model including the reservoir and caprock units (Figure 1). Reservoir thickness [m]

Reservoir

Impervious cap

This conceptual model is able to evaluate the evolution of the geochemical reactivity induced by gas injection, both in time and in space. The 200 m thick reservoir is centered on a vertical injection well with a radius of 0.2 m. Maximum radial extent is 100 km. The investigated system is represented by 800 gridblocks comprising the model mesh. Along the radius axis, 29 grid cells are considered between 0.2 m and 1 km, 50 grid cells between 1 km and 10 km, and 20 grid cells between 10 and 100 km. In each interval, the width of the radial elements follows a logarithmic scale. Vertical discretization is achieved by dividing the reservoir into 5 layers (from bottom to top, 20, 40, 80, 40, and 20 m), and the caprock into 3 layers (5, 10, and 25 m).

Reservoir Characteristics

The investigated saline aquifer is a sandstone reservoir of about 200 m thickness. The effective pressure and temperature before any injection are 150 bar and 50°C, respectively.

Since the reservoir rock's porosity ranges between 13 and 18%, an average value of 15% is selected for the calculations. The porosity of the caprock is estimated to be 40%.

The caprock level presents a mean permeability of 0.003 mD, whereas the permeability of the saline reservoir is about 300 mD.

Due to the injection of a gas phase within the deep system, the relative permeability and the capillary pressure characteristics of the medium must be defined to accurately describe the relative flow of gas with respect to the aqueous solution. Since we lacked petrophysical data for the targeted reservoir, we conducted a bibliographic review to define the representative curves and to implement them into the numerical code. Bachu and Bennion (2007) listed data concerning sandstones.

Owing to the characteristics of the investigated reservoir (k mean # 300 mD; " # 15%; P reservoir = 150 bars; T = 50°C), we found an analogy with the Cardium sandstone and chose it as the reference sandstone (Figure 2). The same characteristic curves for relative permeability and capillary pressure are used for the reservoir and the caprock layer.

For the numerical simulations, the minerals present in the caprock and in the reservoir are selected in conjunction with the mineralogical assemblage determined from core analysis. But some adjustments were made, according to the database used by TOUGHREACT.

The caprock is essentially composed of illite and quartz (77 wt%) while the reservoir rock essentially contains quartz and K-feldspar (91 wt%).

Since a plagioclases series (solid solution) is not included in the database, the endmember albite (NaAlSi 3 O 8 ) was chosen as a substitute. Chlorite (chloritoïd series) is not in the database, so the clinochlore-7A (Mg 5 Al 2 Si 3 O 10 (OH) 8 ) was chosen as a chlorite analogue (Gaus et al., 2005). Magnesite (MgCO 3 ) is used instead of siderite (FeCO 3 ), as it is more stable in the initial system at thermodynamic equilibrium. This substitution is acceptable, since magnesite is also a carbonate -4 -that acts as a pH buffer as well as siderite. Rutile and anatase are common detrital minerals. Anatase, which comes from Ti-bearing minerals, is chosen for this study (Table 1). The water composition for in situ conditions (150 bars, 50°C) is evaluated based on some relevant hypothesis and the thermodynamic calculations relevant for highly saline aqueous systems using the SCALE2000 code [START_REF] Azaroual | 3.1) : Logiciel de calculs thermodynamiques et cinétiques ; application aux saumures pétrolières, hydrothermales et industrielles[END_REF]. The pH and bicarbonate concentration of this brine are recalculated for the reservoir pressure and temperature conditions, assuming that the brine is in thermodynamic equilibrium with respect to calcite. This resulted in a bicarbonate concentration of 103 mg L -1 . Under these conditions, the brine remains slightly undersaturated with respect to the evaporitic minerals (halite, sylvite and anhydrite), but is slightly supersaturated with respect to dolomite and pyrrhotite (iron sulfide).

NUMERICAL SIMULATIONS Initial Conditions and Injection Procedure

The assumptions for numerical modeling are as follows:

! Hydrostatic equilibrium: no regional flow is considered, and a hydrostatic pressure is imposed in the outermost column of the mesh. ! Thermal equilibrium: before starting gas injection, reservoir and caprock are at the same temperature, i.e., 50°C. The numerical simulations are performed in isothermal mode. ! Geochemical equilibrium: the aqueous solutions initially present within the reservoir and caprock are in equilibrium with their respective mineral assemblages at the temperature of the system. ! Injection rates of supercritical CO 2 and SO 2 -O 2 dissolved in brine: these are respectively 30 kg s -1 and 15 kg s -1 . The mass ratio of 2 has been arbitrary chosen for these simulations. Gas and brine are injected over the total thickness of the reservoir during an assumed exploitation period of 30 years.

A -5 -and the mass of SO 2 -O 2 brine, the SO 2 and O 2 concentrations within the solution are defined to ensure consistency with the gas composition of an oxy-combustion capture process (given by data from the industry). Such preliminary simulations are performed with the batch option of the PHREEQC code (Parkhurst and Appelo, 1992). The hypothesis that SO 2 is fully dissolved within the SO 2 -O 2 brine is acceptable, since its solubility is very high at such temperatures.

! The activity model used in the batch simulations is the Davies model. The TOUGHREACT code uses an extended Debye-Hückel model, although admittedly those models are not adapted for highly saline solutions such as in the targeted reservoir (Table 2). For this reason, and for more reliable results, the elemental concentrations of each species of the acidified water are divided by a factor of 10, in order to decrease the ionic strength of the solution (Table 3). This artificial dilution does not drastically modify the simulation results (e.g., reaction paths, dissolution/precipitation magnitudes of minerals) even if it significantly changes the initial saturation state of waters with respect to rock minerals. -2 ] (mol/L) 1.7e-02 5.0e-02 7.2e-01

The "SO 2 -O 2 brines" are very acid, with oxidative and sulfate concentrations higher than in the reservoir brines. These brines are expected to be highly reactive with reservoir minerals.

Results

Case 1: Injection of "a low SO 2 -O 2 brine"

The gas and water injection within the reservoir drive changes of physical parameters (gas saturation, pressure, and so forth) and geochemical properties at different scales, with a major impact on the near-wellbore zone.

First, due to the injection of the gas/solution mixture, the gas saturation changes around the injection well. Because the supercritical CO 2 density is lower than that of the formation brine, CO 2 reaches preferentially the top of the aquifer and expands along it (Figure 3). The caprock is less permeable than the reservoir, but considering the selected permeability, the supercritical CO 2 can penetrate it to a certain extent. The pressure around the injector increases to reach 167 bars during the injection period. (Initially, the pressure ranged between 143 and 160 bars between the top and the bottom of the reservoir.)

The pH of the formation water is controlled by water-rock interactions. Initially, the formation water is in equilibrium with the mineral assemblage of the reservoir: the pH is close to 7.9 (Table 3). Co-injection of supercritical CO 2 and SO 2 -O 2 brine then modifies this equilibrium: the evolution of pH follows the evolution of the gas saturation within the reservoir, with the impacted zone extending up to 3000 m from the injector after an injection period of 30 years (Figure 3). Consequently, the formation water around the injector acidifies, becomes undersaturated with respect to all minerals, and dissolves them (preferentially the carbonates).

As long as reactive carbonates are present, the aqueous solution is in equilibrium with them and the pH is buffered. However, with extended injection, some minerals are exhausted: all carbonates are consumed around the injector and the buffering effect stops. pH is not controlled and decreases to very low values. Near the well, the mineral assemblage is drastically modified, and the pH decreases to a minimum value of 1.4, close to the value of the injected fluid (Table 3). Further within the impacted zone of the reservoir, the pH is buffered to a value ranging between 4 and 6, since not all the carbonates are consumed. The pH is unchanged in the nonimpacted zone.

Calcite is the mineral most affected by injection of the acid solution; it dissolves near the injection well (50 m around it), but it is little impacted elsewhere in the reservoir (Figure 3). The other mineral affected by gas and water injection is anhydrite. The behavior of anhydrite differs in time and space: at first, anhydrite precipitates near the injection well, because the injected fluid contains sulfur, oxidized to sulfate by oxygen. Calcite is dissolved by the acidified injected water, releasing Ca 2+ in solution. With SO 4 2-present in the injected water, these ions combine to form anhydrite. However, when all the calcite is consumed, the Ca 2+ source disappears, and anhydrite precipitation stops. Because the injected solution is undersaturated with respect to anhydrite, the secondary precipitated anhydrite and the original anhydrite (initially present within reservoir) dissolve. This is why some zones present a deficit of anhydrite, whereas others present a positive balance of anhydrite compared to its initial amount (Figure 3).

As a consequence of calcite and anhydrite reactivity, porosity increases near the injector (Figure 3). After an injection period of 30 years, at 10 m from the injection well, a porosity of about 19% is estimated (due to calcite and anhydrite dissolution). This value is probably overestimated: in a real injection, a CO 2 /SO 2 gas mixture would be injected, preventing the dissolution of primary and secondary anhydrite. Consequently, if anhydrite did not dissolve, the expected porosity would range between 16.5 and 17% (values deduced from the porosity variations between 10 and 40 m from injector).

In any case, these values need to be considered as indicative (qualitative) and not effectively quantitative, because of some limiting working hypotheses (dilution of the initial brine, limitations of kinetic parameters, etc.).

All other minerals react but in fewer proportions than calcite and anhydrite (2 to 5 orders of magnitude lower), and their impact on porosity is negligible. Because of the assumptions made regarding caprock permeability, supercritical CO 2 is able to slightly penetrate within it. But the CO 2 amounts are too low and the impact on chemical reactivity and porosity variations are too limited to be seen in the graphical representations of the numerical simulations. Moreover, additional data are needed to better define the hydraulic properties of the caprock and improve the quality of these simulations.

Case 2: Injection of a "high SO 2 -O 2 brine"

The same simulation as in the case 1 was performed. At the temperature of the reservoir (i.e. 50°C), the "high-SO 2 brine" is slightly oversaturated with respect to anhydrite. Consequently, after an injection period of 12 years, the anhydrite precipitation fully clogs the porosity around the injection well, indicating the end of the injection if no measures were taken to keep the injectivity stable.

To analyze anhydrite precipitation conditions, we conducted another simulation with a new injected solution. In this last case, the original reservoir brine, still 10-times diluted, was not initially equilibrated with the mineralogical assemblage of the reservoir before adding SO 2 and O 2 . In this case, the injected solution was undersaturated with respect to anhydrite. The resulting impact of the co-injection of supercritical CO 2 and acidified brine is a decrease in pH around the injection well and a co-dissolution of both carbonates and anhydrite (since the solution is under-saturated with respect to anhydrite) (Figure 4). Since the acidity is higher than for the "low SO 2 -O 2 brine" (Table 3), the impacted zone is also more extended than in the first case (about 50 m in case 1 compared to 200 m in case 2).

The other minerals of the assemblage were also impacted by this strong acidification. They were relatively less impacted than carbonates or anhydrite, but the dissolution of some of them (K-feldspar) and precipitation of others (quartz, kaolinite) must be carefully tracked.

In this last case, the higher acidity of the injected fluid is neutralized to a lesser extent by reactions with minerals: less important variations in porosity are observed in the near-well domain, whereas the impacted zone is extended by the dissolution and precipitation reactions.

CONCLUSIONS

The objectives of this paper were to present the results from numerical simulations of the coinjection of acid gases within a deep saline aquifer. Since the TOUGHREACT code cannot represent the co-injection of these components in a gaseous (nonwetting phase) mixture, some limiting hypotheses were done: CO 2 injection was simulated as in a supercritical form, whereas SO 2 and O 2 injections were simulated as in dissolved species within an aqueous solution.

After an injection period of 30 years, simulation results indicate: ! The injected supercritical CO 2 dissolves in solution, increasing its ability to dissolve carbonates. Since calcite is one of the components of the mineralogical assemblage, it dissolves around the injection well and therewith increases porosity. But because of the negligible calcite in the mineralogical assemblage, the impact on pore volume is quite limited. ! SO 2 reacts rapidly around the injection well, forming sulfates because of the traces of oxygen in the injected gas. Through the recombining of Ca 2+ (coming from calcite) and SO 4 2-(issued from SO 2 and O 2 ), anhydrite precipitates. The SO 2 concentration (low or high) determines the extent of the anhydrite deposition occurring in a radius around the injection well. ! The higher the SO 2 concentration in the injected stream, the larger the radius of anhydrite deposition around the well. However, the SO 2 concentration seems to have no influence on the geochemical mechanisms in terms of (for instance) reaction paths. ! Calcite and anhydrite are the most reactive minerals. All the other initial minerals are also affected by the injection of acid solution, but in less proportion and with a minor impact on porosity and permeability. ! When calcite and anhydrite present opposite behaviors, numerical simulations forecast that calcite dissolution will have a more important impact on porosity than anhydrite precipitation. Consequently, increasing porosity is expected around the injection well, supposing an increase in well injectivity and a potential long-term injection period.

However, we must consider these results as qualitative, highlighting only the global trends of the investigated system. Indeed, the real impact (quantitative estimation) is still very difficult to predict. For example, how the dissolution/precipitation of a particular mineral will affect rock porosity will depend on the characteristics of the rock (e.g., micro/macroporosity, connected porosity). Thus, our results must be interpreted cautiously.

Figure 1 .

 1 Figure 1. Scheme of the geometrical 2-D radial model (vertical cross-section).

Figure 2 .

 2 Figure 2. Relative permeability (upper figure) and capillary pressure (lower figure) curves for Cardmium sandstone (symbols are from Bennion and Bachu, 2005). Fitted curves are implemented in TOUGHREACT code.

Figure 3 .

 3 Figure 3. State of the reservoir and caprock after an injection period of 30 years. From top to bottom: gas saturation (Sg), pH with x-axis up to 4000 m, volumic fraction of calcite, volumic fraction of anhydrite and porosity with x-axis up to 400 m.

Figure 4 .

 4 Figure 4. State of the reservoir and caprock after an injection period of 30 years. From top to bottom: pH with x-axis up to 4000 m, volumic fraction of anhydrite, volumic fraction of calcite and porosity with x-axis up to 400 m.

Table 1 .

 1 Selected mineralogical composition of the caprock and the reservoir rocks.

		Minerals	Wt%
		Illite	60
		Quartz	17
		Albite	6
	Caprock	Clinochlore-7A	5
		K-Feldspar	4
		Hematite	4
		Magnesite	3
		Anatase	1
		Quartz	81
		K-Feldspar	10
	Reservoir	Albite	5
		Calcite	3.6
		Anhydrite	0.4

Chemical composition of water

Detailed physico-chemical characteristics of the formation water are provided in Table

2

. The chemical analyses are performed in the laboratory at ambient conditions (1 bar, 25°C).

Table 2 .

 2 Chemical composition of the aquifer water.

	Element	Concentration (mg L -1 )
	Na (as Na + ) K (as K + ) Ca (as Ca 2+ ) Mg (as Mg 2+ ) N (as NH 4 + ) Fe (as Fe 2+ ) Cl (as Cl -) Br (as Br -) I (as I -) S (as SO 4 2-)	90283 624 13652 2206 11 127 171449 1162 7.4 566.2
	Total Dissolved Salt	280 000

Table 3 .

 3 Chemical characteristics of the fluids used for numerical calculations.

		Reservoir	Low SO 2 -	High SO 2 -
		brine	O 2 brine	O 2 brine
	pH	7.9	1.5	0.2
	pe	-3.9	17.7	19.0
	TDS (g/kg H2O )	38.6	~38.6	~38.6
	[SO 4

ACKNOWLEDGMENT

This work is part of the OXYGAS (phase II) project funded by VATTENFALL. The authors acknowledge the VATTENFALL Directorate and BRGM Research Directorate for allowing publication of these results at the Symposium.

 Environ. Geol., 54, 1707-1722, 2007. Bennion B., and Sci., 301, 16-33, 2001.


Mohamed Azaroual
email: m.azaroual@brgm.fr

Laurent André

Yannick Peysson
email: yannick.peysson@ifpen.fr

Jacques Pironon
email: jacques.pironon@univ-lorraine.fr

Daniel Broseta
email: daniel.broseta@univ-pau.fr

Fabian Dedecker
email: f.dedecker@itasca.fr

Patrick Egermann
email: patrick.egermann@storengy.com

Jean Desroches
email: jdesroches1@slb.com

Joëlle Hy-Billiot
email: joelle.hy-billiot@total.com.

Laurent Andre
email: l.andre@brgm.fr

Behaviour of the CO2 injection well and the near wellbore during carbon dioxide injection in saline aquifers

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The understanding of these phenomena based on laboratory experiments and numerical modelling allowed a better interpretation of the coupled processes and the development of advanced concepts of CO 2 storage in saline aquifers. The project demonstrates firstly that injection of large quantity of CO 2 in deep saline aquifers will lead to a strong water desaturation of the near wellbore because of drying mechanisms. In this context, drying mechanisms can precipitate the salt present in the aquifer and then lead to injectivity alteration due to permeability decrease.

Numerical modelling coupling hydraulic and thermal processes were shown to be able to simulate the observed evolution of liquid and gas saturations and to estimate the salt depositions.

The numerical simulations approaches were validated with respect to laboratory experiments in controlled conditions allowing the determination of the most important parameters for injectivity design (porosity, relative permeability and capillary pressure curves…). The experimental observations, established at the centimetre scale, were up-scaled in order to extrapolate the results at the near wellbore scale and then, to forecast the impact of CO 2 injection on petrophysical properties of the host rock.

INTRODUCTION

The "Near Wellbore" project was focused on the study of main physical, physicochemical and thermo-kinetic phenomena occurring in the well and the near wellbore domain. The understanding of these phenomena based on scientific and technical knowledge will reduce the uncertainties on the injectivity and the predictive results of numerical simulations on the sustainability and security of CO 2 storage. This knowledge will also help to identify ranges of CO 2 storage capacity in saline aquifers. Indeed, it is now established that the amount and the quality of the injected CO 2 play a key role on the preservation of the injectivity of the reservoir and on the number and type of required injection wells. On the other hand, depth, location, temperature and pressure conditions, and petrophysical characteristics of the targeted reservoir, as well as the quality of the caprock are parameters that must be characterized because of their influence on the required number of wells, on the evolution of the injectivity and on the technical management of the conditions of pressure at the wellhead and at the bottom of the well. Also, the multiphase area developing around the near well is a very sensitive and reactive zone were numerous coupled processes have been identified, including hysteretic behaviors, and may play a key role during the CO 2 injection phase as technical stop and restart stages will happen. In summary, the integration of the empirical macroscopic parameter defined as the Injectivity index, II, (Figure 1) is the key condition of success of a CGS (Carbon Geological Storage) operation. This parameter expresses the behavior of the reservoir under imposed P-T-Q-t conditions, i.e. injection pressure (P), temperature (T), flow (Q) and their time evolution (t). As illustrated in Figure 1, II primarily depends on the evolution of the relationship between water saturation (S w ) of the porosity and relative permeability (K r ). This relationship depends, in turn, on the properties of the injected fluids and on the characteristics of the target reservoir rock (bio-and geochemical reactivity, initial petrographic and hydrodynamic properties …).

MULTIPHASE REACTIVE TRANSPORT AND NEAR WELLBORE BEHAVIOR

Based on recent numerical and experimental simulations, the near-well injection zone is identified to be particularly impacted by supercritical CO 2 injection and the most sensitive area [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO 2liquid interface during supercritical carbon dioxide injection into a carbonated reservoir, the Dogger aquifer (Paris Basin, France)[END_REF]2010), where chemical (e.g., mineral dissolution/precipitation) and physical (e.g., temperature, pressure and gas saturation) phenomena have a major impact on the porosity and permeability and thus, at the end, on the well injectivity. et al., 2007;Gaus et al. 2008).

Figure 2 represents the simulation result of twophase reactive transport (CO 2 -initially porous carbonate rock saturated with water) using TOUGHREACT (Xu et al., 2004) showing the individualization and the succession of five (5) major zones of specific physical and physicochemical properties around the injection well. These zones have the following characteristics:

-Zone 1 (initial unperturbed state): the porous medium contains only the initial aqueous solution. The pores are saturated with water (initial state) under conditions of thermodynamic equilibrium between minerals of the rock matrix and pore water.

-Zone 2 (monophasic acidified zone): pH decreases due to CO 2 dissolution (forming carbonic acid H 2 CO 3 ) in the aqueous phase. The porous medium is still saturated with water. This is a more acidic front before the arrival of supercritical CO 2 phase. This solution at lower pH is aggressive for most of the porous matrix minerals, including carbonates and to a lesser degree aluminosilicates.

-Zone 3 (multiphase zone): the porosity of the porous medium contains two phases, namely the aqueous phase and the supercritical CO 2 . The pH and the composition of the aqueous phase vary with water saturation with a drying trend of the rock and creating conditions for capillarity.

-Zone 4 (dried zone): pH and ionic strength increase sharply due to the drying-out of the medium. This produces a strong tendency of the system triggering reactive mass exchange processes between major phases (residual water -supercritical CO 2 -minerals). The pore solutions become highly saline, with values of the ionic strength of about 7 to 7.5 (equivalent mol / kg H 2 O) although the initial aqueous solution was only at 0.1 (Zone 1).

-Zone 5 (extreme conditions of capillarity and dehydration reactions): the aqueous phase is totally removed and the porous medium contains only supercritical CO 2 and a small quantity of metastable and capillary water in the fine pores and microcracks.

The various physical phenomena and physicochemical predominantly of each zone were analyzed separately in the framework of the "Near Wellbore" project by implementing new measurement techniques and some new theoretical approaches. The integration of results from different disciplines allows understanding multiphase reactive transport inducing heat and mass transfers between phases. temperature curve along the well calculated with PipeSIM looks suspicious (Figure 3): a brutal change of the slope occurs when the pressure exceeds a value ranging between 72 bars and 76 bars for the cases investigated (depending on the volumetric flow rate and the equation of state (EOS) considered for CO2).

The CO

The simulations carried out with PROSPER use the Peng-Robinson EOS (Peng-Robinson, 1976) to model the behavior of CO2. The simulator described here (NEW SIMULATOR) uses the Span-Wagner EOS (Span-Wagner, 1996). PipeSIM calculations are run using alternatively these two equations of state.

In the previous simulations, the convective heat transfer coefficient between tubing and the fluid inside it was considered constant (11 W.m -2 .K -1 ) all along the well. This is not the case in reality, as the heat transfer coefficient is usually dependent on numerous parameters evolving with depth and time (e.g. the fluid velocity, density, viscosity). The heat exchange between the fluid and the pipe is often expressed by mean of a correlation, relating the Reynolds, Prandtl and Nusselt numbers of the flow. In the current version of this new simulator, the correlation implemented is that of Gnielinski (62) -see [START_REF] Incropera | Fundamentals of heat & mass transfer[END_REF].

The temperature vs. pressure curves associated to each case are presented in Figure 3. The numbers in the caption are the flow rate values (in ton/day), while the two-letters acronyms "SW" and "PR" denote respectively "Span-Wagner" and "Peng-Robinson" (the equations of state of CO2 used for the current case).

The present simulator is denoted "NEWSIM" in the caption ("PipeSIM" and "PROSPER" are self-explanatory). Figure 3 shows that the results obtained with the new simulator are much closer to those obtained with PROSPER than those obtained with PipeSIM. The associated curves do not exhibit the strange change in slope mentioned earlier, which tends to demonstrate a lack of coherence in the PipeSIM results. The new simulator predicts a temperature 10 to 13% lower than PROSPER, and a pressure slightly 4 to 5% higher. To summarize, these discrepancies can be explained by one or a combination of the following reasons:  The use of the Span-Wagner (1996) EOS instead of the Peng-Robinson (1976) EOS. This trend is similar to that observed in the PipeSIM results when one switches from one EOS to the other: the bottom-hole temperature sustains a 4% to 5% relative decrease, while the bottom-hole pressure increases 4 to 5%.  The use of a variable CO 2 /tubing heat transfer coefficient (described by the Gnielinski's correlation; see [START_REF] Incropera | Fundamentals of heat & mass transfer[END_REF]) instead of a constant one.

The near wellbore dynamics

As shown in Figure 2, the desiccation of the porous medium appears as a major phenomenon with various consequences as salts precipitation [START_REF] Peysson | Permeability alteration die to salt precipitation driven by drying in the context of CO 2 injection[END_REF], modification of the local geomechanical constraints due to the salts precipitation, modification of internal forces and the impact of injected fluids on the interfacial tensions including capillary/osmotic phenomena. Desiccation of porous media submitted to gas injections is a well-known process at the laboratory [START_REF] Mahadevan | Flow-through drying of porous media[END_REF][START_REF] Mahadevan | Water removal from porous media by gas injection: experiments and simulation[END_REF] and the field [START_REF] Kleinitz | Halite scale formation in gas producing wells[END_REF] scales. This process is taken into account only recently in the modelling of CO 2 storage in deep saline aquifers [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO 2liquid interface during supercritical carbon dioxide injection into a carbonated reservoir, the Dogger aquifer (Paris Basin, France)[END_REF][START_REF] Zeidouni | Analytical solution to evaluate salt precipitation during CO2 injection in saline aquifers[END_REF].

First, the massive and continuous injection of CO 2 in a saturated porous medium involves water displacement and evaporation: mobile water is removed by the injected dehydrated supercritical CO 2 allowing tow phase flow system (brine -CO 2 ). At the end, immobile residual water entrapped in pores or distributed on grain surface as a thin film, is in contact with the flowing dry CO 2 (i.e. with very low water vapor pressure). Consequently, a continuous and extensive evaporation process leads both to the apparition of a drying front moving into the medium, and the precipitation of salts and possibly secondary minerals in residual brines.

This study investigates the consequences on permeability degradation of the porous medium potentially induced by desiccation through the petrophysical properties of different subsystems.

Experimental evaluations of drying of brine are investigated at the laboratory scale on centimetre plugs of different materials. These experiments are then interpreted using a numerical modelling approach coupling hydraulic and thermal processes able to simulate the evolution of liquid and gas saturations in space and in time. A very fine discretization of the plugs allows capturing the continuous evolution of water and gas profiles in the porous medium and estimating the liquid saturation and the permeability evolution during drying process.

The experiments of gas injection were performed on two materials:

-with a low permeability sandstone ("Grès de Môlière" =14.0 % and K 0 =8 µD) in order to increase the capillary effects to be able to study them and quantify their effect. Indeed, those effects play a key role in drying processes, -with a high permeability sandstone ("Grès des Vosges" =21.8 % and K 0 =60 mD) in order to study rocks with properties close to the ones found in targeted reservoirs of CO 2 storage.

Sandstones samples of 6 cm long initially saturated with brine (salinity of 160 g L -1 ) are placed in storage conditions (80°C-120°C -50 bars) and in a cell transparent to X-ray. Dry gas (nitrogen) is injected in the fully saturated core plugs (Figure 4). Four long pressure stages are imposed to desaturate progressively the rock plug. The local water saturation in the sample is measured with X-ray attenuation techniques. Pressure difference and outlet gas flow rate are monitored during the experiment. The system evolves until complete drying. The experiments were performed at 90 and 120 °C with "Grès de Môlière" samples and at 90°C for "Grès des Vosges" core.

Numerical simulation of multiphase flow and drying-out (lab scale)

The TOUGH2 simulator [START_REF] Pruess | TOUGH2 User"s Guide, Version 2.0[END_REF]) with the EOS7C module [START_REF] Oldenburg | EOS7C Version 1.0: TOUGH2 Module for Carbon Dioxide or Nitrogen in Natural Gas (Methane) Reservoirs[END_REF] was used for all the simulations carried out for this study (core experiments and field scale). This code couples thermal and hydraulic processes and is applicable to one-, two-, or three-dimensional geologic systems with physical heterogeneity. The EOS7C is a fluid property module developed specifically to deal with mixtures of non-condensable gases (like CO 2 or N 2 ) and methane. It can be used to model isothermal or non-isothermal multiphase flow in water/brine/CH 4 /(CO 2 or N 2 ) systems.

Modelling approach consists to simulate the injection of nitrogen in a plug fully saturated with water. A two-phase Darcy flow is solved using relative permeability and capillary pressure curves. Thermodynamic equilibrium between concomitant phases (brine -N 2 ) is calculated at each time step to evaluate the water vapour fraction in the gas and the dissolved gas in the brine.

A 1D column model of 6 cm long is used as a conceptual framework for determining the evolution of the water content induced by the injection of N 2 , in both time and space. The column is represented by 10 grid blocks composing the model mesh. The thickness of each grid cell is constant (0.6 cm). The rock constituting the matrix is supposed inert with respect to N 2 , i.e. without chemical reactivity.

The variations of relative permeability and capillary pressure according to water saturation are given in Figure 5. Relative permeability for aqueous (k rl ) and gaseous (k rg ) phases and capillary pressure (P cap ) models are described according to the Van Genuchten formulation. Due to the low permeability of the medium, we observe a very high sensitivity of the model to relative permeability and capillary pressure characteristics, in particular to the entry pressure. As shown by Figure 5, the Van Genuchten model does not fit properly the measured data when liquid saturation is close to 1. This very weak shift has an impact on the breakthrough time.

For "Grès de Môlière" rock, high pressure mercury injection and standard centrifugation have been done to measure the capillary pressure curve. The model parameters are deduced: S lr = 0.22, S gr = 0.05, P 0 = 645161 Pa and m = 0.95. When these parameters are correctly defined, the code can reproduce, with a good agreement, the first 3 stages of the experiment including the mean water saturation and the outlet gas flow rate (Figure 5).

These three first stages correspond to the desaturation of the porous medium according to a classical piston effect. The desaturation state is proportional to the pressure gradient applied to the core whereas the evaporation process is negligible: at the end of stage 3, the water content is close to the residual liquid saturation. During the first 3 stages, the calculated average water saturation in the core fit quite well the measured data. Some discrepancies are observed close to the inlet and the outlet of the column which are mainly due to the selected boundary conditions imposed to the numerical model.

In the last stage (stage 4) desiccation of the medium is the dominant mechanisms. Even if the global tendency is roughly reproduced, this stage presented some difficulties to reproduce correctly measured data.

Indeed, the only way to fit both gas flow rate and desiccation time consists to increase the gas permeability when liquid saturation is lower than the residual liquid saturation. By increasing the relative gas permeability, the outlet gas flow rate is growing; the evaporation process goes faster and the time needed to totally desiccate the core decreases. These numerical simulations of laboratory experiments at 90°C allow checking the relevance of the model but also the determination of the most sensitive and ad hoc parameters of the integrated approaches (optimized relative permeability and capillary pressure curves). Finally, the good coherence between measured and calculated data is very encouraging. We also demonstrated that the petrophysical parameters established at 90°C are applicable at 120°C without any adjustment for the same rock [START_REF] André | Numerical Simulations of the Thermal Impact of Supercritical CO 2 Injection on Chemical Reactivity in a Carbonate Saline Reservoir[END_REF].

Extrapolation at field scale (2D-radial approach)

When extrapolated to the near wellbore field and because of the gravity forces and the supercritical CO 2 density (lower than the one of the brine), the reservoir desaturates faster at the top. The porous medium is dried on about 12 m at the reservoir top, whereas at the bottom, only the first meter is totally desiccated (Figure 7). Inside the drying zone, solid salt (i.e., halite) precipitates. If salt is present in all the desaturated zone, the spatial repartition of salt deposits varies according to the resultant prevalent transport forces (advection, diffusion, capillarity, evaporation, etc.) inside the reservoir: the amounts are higher at the bottom of the reservoir and more limited at the top for simulation conditions and specific chararacteristics of the reservoir. The pattern of solid saturation (= solid volume/pore volume) indicates that 40% of the porosity is occupied by salt at the bottom, whereas only 10% at the top is filled. The porosity and consequently the permeability are more impacted at the bottom of the reservoir (Figure 7). The permeability decrease is represented by the empirical function k_red (= k/k0). This function clearly shows that high permeability reductions are expected close to the well (skin effect in the first cell party with the well) and at the lower part of the reservoir (in the first meter inside the reservoir). At the end, we investigated specifically the influence of shutdown periods during the injection phase. Numerical simulations were performed considering the case of CO 2 injection into an aquifer open with a nominal flow of 1Mm 3 /y and several short shutdown periods. Pc-Kr models were built to be fully representative of rock types with permeabilities of 10 and 100 mD for an integrated approach to ensure consistency between original K, Kr and Pc. The results show little effect related to re-imbibition layers well. The temporary shutdown of the wells does not seem to pose a major problem on the injectivity with a homogeneous model including hysteresis effects.

CONCLUSIONS

For the flows in the wells, the numerical simulation results show trends highlighting the problem of "Injectivity gap" allowing a failure to achieve a controllable pressure range at the bottom of the injection well because of phase change in the injection well. The involvement of industrials (ie, Schlumberger, GDF Suez and Total) in the project brings validated injection scenarios thanks to the implementation of numerical tools.

Most of the efforts to study the mechanisms at the interfaces of geochemical phases (CO 2 scbrines) were focused on CO 2 solubility in capillary water. Detailed speciation of carbonic acid is well established for the range of relative humidity and drying conditions studied in the project. A comprehensive approach for estimating the interfacial tension of the brine-CO 2 sc system, based on the theory of electrolytic systems was developed [START_REF] Leroy | Predicting the surface tension of aqueous 1:1 electrolyte solutions at high salinity[END_REF].

Drying processes are investigated through laboratory experiments and numerical simulations to evaluate the dynamic of the water saturation decrease in sandstones and the consequences of induced salt depositions on the injectivity. We demonstrate that in low permeability porous media, the relative permeability of gas phase significantly increases when water saturation is lower than the irreducible water saturation. When this parameter is adjusted, the numerical code is able to reproduce the drying time and the outlet gas flow rate measured at laboratory scale on cores, using a two-phase Darcy flow and thermodynamic equilibrium between phases. At field scale, the rocks characteristics defined at laboratory scale are used to predict the behaviour of the near-well zone according to the injection gas flow rate. We demonstrated that the precipitation process and the amount of salt deposits are related to different parameters: -the salinity of the initial brine: the more concentrated the brine is, the more massive the salt deposit is; -the irreducible water content: water entrapped in pores is evaporated by gas injection. The higher this content is, the more important the amount of precipitated salt is; -the gas injection flow rate and the capillary forces within the system. Finally, all these parameters have to be known (and defined) in order to improve the management of the long-term injection of CO 2 in the saline aquifers. According to the carried out reservoir simulations, several important results can be noted: i) for high permeabilities (> 100 mD), the mechanism of re-wetting of the aquifer is larger but no impact is observed in terms of injectivity because of high permeability; ii) for low-permeability media (<100 mD), the mechanism of re-imbibition is less marked and well find its ability to moderate injection after restart iii) the heterogeneities do not appear to play a major role in these findings and; iv) the key parameter is the curve of relative permeability to water. It is therefore recommended to measure this parameter accurately during the design phase.

Figure 1 .

 1 Figure 1. Coupled key processes to integrate in numerical tools to study the injection scenarios based on the control of relative permeabilities and interfacial mechanisms of mass and heat transfers between phases.

Figure 2 .

 2 Figure 2. Typical fictive radii of the processes occurring in the near well region after a continuous injection of CO 2 during 30 years with a flow rate of 1 Mm 3 /y (Andréet al., 2007; Gaus et al. 2008).

Figure 3 .

 3 Figure 3. Pressure vs. Temperature curves obtained with the three simulators, considering four flow rates and two different equations of states.

Figure 4 .

 4 Figure 4. Experimental procedure to investigate the drying out of the core under a continuous flux of nitrogen.

Figure 5 .

 5 Figure 5. Relative permeability and capillary pressure curve according to water saturation (S l ).

Figure 6 .

 6 Figure 6. -Results of drying-out experiments with gaseous N 2 at laboratory scale (Peysson et al. 2010) compared with results of numerical modeling performed with TOUGH2 code (André et al. 2010).

Figure 7 .

 7 Figure 7. Permeability reduction, k_red (=k/k0) inside a 100 m radius around the injector well after ten years of CO 2 injection.

Figure 8 .

 8 Figure 8. Vertical section illustrating the saturation tank of gas around the injection well for a mid-horizontal permeability 100mD (RT1) in the deep layers and 10mD (RT2) in the upper layers. This saturation state is the last day of the injection history, after six years of injections interrupted by two years of rest.

  temperature and volumetric flow rate) are set at the wellhead. The injection temperature is set at 5•C, while the injection pressure is set at 100 bars. Several volumetric flow rates are considered: 500 t/day, 1000 t/day, 2000 t/day and 2750 t/day. The far field temperature in the formation varies linearly from 5•C at wellhead (0 m) to 21•C at 1000m. The geological formation was made of limestone and sandstone, but as the thermal parameters input were not available, we chose the same parameters for both layers, assuming it would not change much the results.

2 injection well behavior: a "Pseudo" steady-state calculation example This test case was jointly run by Total and Schlumberger. It consists of a single-cased offshore well, located in a shallow water zone (300m depth). The well is vertical, and its total depth is 1000m. The boundary conditions (pressure, This example was tested by Schlumberger with PipeSIM, and by Total, with PROSPER, each software based on different theoretical approaches and practice assumptions. PipeSIM is only able to perform steady-state calculations, in contrast to PROSPER, which allows obtaining results for 10 days, 100 days and 1000 days after the start of injection. Considered times are, however, fairly large, and probably sufficiently close to steady-state to allow a meaningful comparison between the results of the two simulators. The codes provided fairly different results. Note that the pressure vs.

ACKNOWLEDGMENT

This work is carried out within the framework of the "Proche Puits" project, co-funded by the French National Agency for Research (ANR). The authors are grateful to all project partners (TOTAL, GDF Suez, Schlumberger, Itasca, CNRS, University of Lorraine, and University of Pau) to allow the publication of this work.

The project "Proche Puits" ("Near Wellbore") co-funded by the French National Agency for Research (ANR) started in December 2007 and ended in May 2011. The project consortium gathered three companies (TOTAL, Schlumberger, and GDF-Suez), two applied research institutes (BRGM and IFP Energies nouvelles), two academic research laboratories (CNRS and Université de Lorraine) and a SME (ITASCA).


Laurent André

Mohamed Azaroual

Yannick Peysson

Brigitte Bazin

Impact of porous medium desiccation during anhydrous CO2 injection in deep saline aquifers: up scaling from experimental

Keywords: supercritical CO2, drying-out effects, coupled modelling, relative permeability

Introduction

Geological sequestration of CO 2 into deep saline aquifers offers a promising solution for reducing net emissions of greenhouse gases into the atmosphere. Nevertheless, this emerging technology based on massive CO 2 injection in saline reservoirs can cause a major disequilibrium of the physical and geochemical characteristics of the host aquifer. Based on recent experiments and numerical simulations, the near-well injection zone is identified to be particularly impacted by supercritical CO 2 injection and the most sensitive area [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO2liquid interface during supercritical carbon dioxide injection into a carbonated reservoir, the Dogger aquifer (Paris Basin, France)[END_REF][START_REF] André | Numerical Simulations of the Thermal Impact of Supercritical CO2 Injection on Chemical Reactivity in a Carbonate Saline Reservoir[END_REF], where chemical (e.g., mineral dissolution/precipitation) and physical (e.g., temperature, pressure and gravity) phenomena have a major impact on the porosity and permeability and thus, at the end, on the well injectivity.

Among these perturbations, the desiccation of the porous medium appears as a major phenomenon with various implications as salts precipitation [START_REF] Peysson | Permeability alteration die to salt precipitation driven by drying in the context of CO2 injection[END_REF], modification of the local geomechanical constraints due to the salts precipitation, modification of internal forces and impact of injected fluids on the interfacial tensions including capillary/osmotic phenomena. Desiccation of porous media submitted to gas injections is a well-known process at the laboratory [START_REF] Mahadevan | Flow-through drying of porous media[END_REF][START_REF] Mahadevan | Water removal from porous media by gas injection: experiments and simulation[END_REF] and the field [START_REF] Kleinitz | Halite scale formation in gas producing wells[END_REF] scales. This process is taken into account only recently in the modelling of CO 2 storage in deep saline aquifers [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO2liquid interface during supercritical carbon dioxide injection into a carbonated reservoir, the Dogger aquifer (Paris Basin, France)[END_REF][START_REF] Zeidouni | Analytical solution to evaluate salt precipitation during CO2 injection in saline aquifers[END_REF].

First, the massive and continuous injection of CO 2 in a saturated porous medium involves water displacement and evaporation: mobile water is removed by the injected supercritical CO 2 according to a two-phase system (brine -CO 2 ). At the end of this phase, immobile residual water, entrapped in pores or distributed on grain surface as a thin film, is in contact with the flowing dry CO 2 (i.e. with very low water vapour pressure). Consequently, a continuous and extensive evaporation process leads both to the apparition of a drying front moving into the medium, and the precipitation of salts and possibly secondary minerals in residual brines.

This study investigates the consequences on well injectivity of the porous medium desiccation through the petrophysical properties of different subsystems. This work is based on both experimental and numerical modelling approaches. Experimental evaluations of drying of brine are investigated at the laboratory scale on centimetre plugs of different materials. These experiments are then interpreted using a numerical modelling approach coupling hydraulic and thermal processes able to simulate the evolution of liquid and gas saturations in space and in time. A very fine discretization of the plugs allows capturing the continuous evolution of water and gas profiles in the porous medium and estimating the liquid saturation and the permeability evolution during drying process.

The parameters established at the centimetre scale are tentatively up scaled in order to extrapolate the results at the near wellbore scale and then, to forecast the impact of CO 2 injection on petrophysical properties of the host rock.

Experimental approach

The experiments of gas injection were performed on two materials: -a low permeability sandstone ("Grès de Môlière" =14.0 % and K 0 =8 µD) in order to have a better experimental control of the pressure, to limit the gas flow rate and to increase the capillary effects that play a key role in drying processes, -a "high" permeability sandstone ("Grès des Vosges" =21.8 % and K 0 =60 mD) in order to study rocks with properties close to the ones found in targeted reservoirs of CO 2 storage.

Sandstone samples of 6 cm long initially saturated with brine (salinity of 160 g L -1 ) are placed in storage conditions (80°C-120°C -50 bars) and in a cell transparent to X-ray. Dry gas (nitrogen) is injected in the fully saturated core plugs (Figure 1). Four long pressure stages are imposed to desaturate progressively the rock plug. The local water saturation in the sample is measured with X-ray attenuation techniques. Pressure difference and outlet gas flow rate are monitored during the experiment. The system evolves until complete drying. The experiments were performed at 90 and 120 °C with "Grès de Môlière" samples and at 90°C for "Grès des Vosges" core.

Modelling approach

The TOUGH2 simulator [START_REF] Pruess | TOUGH2 User's Guide[END_REF] with the EOS7C module [START_REF] Oldenburg | EOS7C Version 1.0: TOUGH2 Module for Carbon Dioxide or Nitrogen in Natural Gas (Methane) Reservoirs[END_REF] was used for all the numerical simulations carried out for this study (core experiments and field scale). This code couples thermal and hydraulic processes and is applicable to one-, two-, or three-dimensional geologic systems with physical heterogeneity. The EOS7C is a fluid Constant Injection Pressure (N 2 )

Constant outlet pressure property module developed specifically to deal with mixtures of non-condensable gases (like CO 2 or N 2 ) and methane. It can be used to model isothermal or non-isothermal multiphase flow in water/brine/CH 4 /(CO 2 or N 2 ) systems.

Modelling of core experiments with low permeability

Modelling approach consists to simulate the injection of nitrogen in a plug fully saturated with water. A twophase Darcy flow is solved using relative permeability and capillary pressure curves. Thermodynamic equilibrium between concomitant phases (brine -N 2 ) is calculated at each time step to evaluate the water vapour fraction in the gas and the dissolved gas in the brine.

A 1D column model of 6 cm long is used as a conceptual framework for determining the evolution of the water content induced by the injection of N 2 , in both time and space. The column is represented by 10 grid blocks composing the model mesh. The thickness of each grid cell is constant (0.6 cm). The rock constituting the matrix is supposed inert with respect to N 2 , i.e. without chemical reactivity.

The variations of relative permeability and capillary pressure according to water saturation are given in Figure 2. Relative permeability for aqueous (k rl ) and gaseous (k rg ) phases and capillary pressure (P cap ) models are described according to the Van Genuchten formulation.

For the liquid phase:

  lr lr l * 2 m m / 1 * * rl S 1 S S S with S 1 1 S k                  
where S l is the liquid phase saturation, S lr the residual liquid phase saturation and m a non-dimensional characteristic parameter of the law.

For the gas phase:

    gr lr lr l 2 2 rg S S 1 S S S ŵith S 1 . S 1 k       
where S gr is the residual gas phase saturation.

Capillary pressure is calculated by the following expression:

  m 1 m / 1 * 0 cap 1 S . P P           
where P o is the pressure coefficient in Pascal (Pa).

For "Grès de Môlière" rock, high pressure mercury injection and standard centrifugation have been done to measure the capillary pressure curve.

The model parameters are deduced: S lr = 0.22, S gr = 0.05, P 0 = 645161 Pa and m = 0.95.

Modelling of field experiments

A 1D radial model is proposed as a conceptual framework for determining the transient evolution of the water content induced by the injection of CO 2 . The 1-m-thick reservoir is centred on a vertical injection well (Figure 3). The maximum radial extent is 100 km. Along the radius axis, the discretization is very fine close to the well (5 grid cells of 1 mm, then 5 grid cells of 2 mm, 77 grid cells of 5 mm and 960 grid cells of 10 mm up to 10 m from the injection well). 100 grid cells are assumed between 10 m and 100 m, 100 grid cells between 100 m and 10 km and 20 grid cells up to 100 km. In each interval (between 10 m and 100 km), the width of the radial elements follows a logarithmic scale. The objective of such refinement near the injection well is to capture more precisely both the details and the migration of the desiccation front in the near-well region. No regional flow is considered and a hydrostatic status is initially assumed for the pressure within the reservoir and maintained constant at the lateral boundary. The initial temperature and pressure of the targeted reservoir are 80 °C and 240 bar, respectively.

The capillary pressure is determined experimentally with high pressure injection measurements. A standard Corey model is used for relative permeability curves of both liquid and gaseous phases whereas a Van Genuchten model is used to fit the experimental capillary pressure curve. For "Grès des Vosges" rock, S lr = 0.19, P 0 = 333 000 Pa and m = 0.675 (Figure 4).

Results

Modelling of core experiments

Three parameters have been followed during the experiments with "Grès de Môlière" rocks at 90°C: -Mean water saturation in the core and outlet gas flow rate (Figure 5); -The distribution of water content in the column (given by X-ray measurements) (Figure 6).

Due to the low permeability of the medium, we observe a very high sensitivity of the model to relative permeability and capillary pressure characteristics, in particular to the entry pressure. As shown by Figure 2, the Van Genuchten model does not fit properly the measured data when liquid saturation is close to 1. This very weak shift has an impact on the breakthrough time.

But, when this parameter is correctly defined, the code can reproduce, with a good agreement, the first 3 stages of the experiment including the mean water saturation and the outlet gas flow rate (Figure 5). These three first stages correspond to the desaturation of the porous medium according to a classical piston effect. The desaturation state is proportional to the pressure gradient applied to the core whereas the evaporation process is negligible: at the end of stage 3, the water content is close to the residual liquid phase saturation (Figure 6). During the first 3 stages, the calculated average water saturation in the core fit also the measured data (Figure 6). Some discrepancies are observed close to the inlet and the outlet of the column which are mainly due to the selected boundary conditions imposed to the numerical model. The last stage (stage 4) corresponds to the real desiccation of the medium. Even if the global tendency is reproduced, this stage presented some difficulties to fit measured and calculated data. With the relative permeability curves shown in Figure 2, the calculated desiccation time was too long and the gas flow rate was underestimated. Indeed, the only way to fit both gas flow rate and desiccation time (during stage 4) consists to increase the gas permeability when liquid saturation is lower than the residual liquid phase saturation. By increasing the relative gas permeability, the outlet gas flow rate is growing; the evaporation process goes faster and the time needed to totally desiccate the core decreases. Consequently, for 0 < S l < 0.22, k rg is not threshold to 1: it follows a linear model with k rg = 20 when S l = 0 and k rg = 1 when S l = S lr = 0.22.

These numerical simulations of laboratory experiments at 90°C allow checking the relevance of the model but also the determination of the most sensitive and ad hoc parameters of the integrated approaches (optimized relative permeability and capillary pressure curves). Then, from this set of parameters, we try to model the evaporation process on "Grès de Môlière" sample at 120°C. All the parameters established at 90°C are re-used for this test and obtained results are presented in Figure 7. The good coherence between measured and calculated data is very encouraging. We demonstrated that the petrophysical parameters established at 90°C are applicable to 120°C without any adjustment for the same rock.

Modelling at field scale

The same methodology as the one presented before was applied to "Grès des Vosges" sample. At laboratory scale, experiments of N 2 injection were performed to study the desiccation processes. Then a first modelling approach allowed defining the main parameters needed for field calculations (as capillary pressure and relative permeability curves). It is interesting to note here that no modification of gas relative permeability was necessary for this material. Because of the higher intrinsic permeability, the gas permeability does not have to be increased in order to satisfy the gas flow rate and the desiccation time. The k rg -curve presented in Figure 4 is thus applied for field calculations.

The set of defined parameters is then applied to capture the behaviour of the near-well zone. Three scenarios were analysed:

-1-A progressive increase of pressure to reach, at the end, a pressure gradient of 12 bar (in 3 stages); -2-A constant pressure gradient of 12 bar between the injection well and the reservoir pressure.

-3-A constant pressure gradient of 24 bar between the injection well and the reservoir pressure.

In the scenario 1, the desaturation of the porous medium is progressive, in relation to the pressure stages imposed to the system. We observe nevertheless that the change of pressure is immediately followed by an abrupt decrease of water content before raising a plateau. Whatever the position with respect to the wellbore, the mechanisms of dessication are exactly the same and the values of the desaturation plateau are similar (Figure 8a). The last plateau of residual water amount (before total drying-out) is close to the value of the residual liquid phase saturation. Then, this water is evaporated by the gas flow.

In the scenario 2, the desaturation process is very fast (Figure 8b). But, the global mechanism is the same: water is removed from the porous medium, up to reach the residual liquid saturation. In a second step, the irreducible water is evaporated; this process is stopped by the total drying-out of the porous medium (Figure 8b). The scenario 3 presents the same results as the second one. Always the same amount of water is evaporated (Figure 8c). From these three scenarios, it is expected that the same amount of evaporated water will provide the same amount of precipitated salt. However, the numerical results indicate that the amount of salt precipitated in the scenario 3 is 5-times lower than in the two other scenarios (Table 1).

Table 1 Amount of precipitated salt in the cell located at 5 cm from the injection well. Amount of precipitated salt (g) Scenario 1

5.9 Scenario 2 6.4 Scenario 3 0.9

This difference is probably due to capillary effects. When the injection flow rate is sufficiently high (scenario 3), the capillary effects are reduced by the convection flow rate. No capillary water flow can go against the major gas flow and only residual water is evaporated. In the two other scenarios (1 and 2), a capillary water flow operates against the main gas flow feeding the evaporated cells with "new" fresh brine. Consequently, the amount of evaporated water is higher than the residual water providing more important amounts of precipitated salts.

This point is particularly interesting: the amount of salt deposits due to water evaporation does not depend only on the initial salinity of pore brine. It is also dependent on the injection flow rate and the capillary characteristics of the rock. A good estimation of rock characteristics and in particular of capillary properties is needed to thus define the adequate injection flow rate minimizing the precipitation risks.

Conclusions

Drying processes are investigated through laboratory experiments and numerical simulations to evaluate the dynamic of the water saturation decrease in sandstone and the consequences of induced salt depositions on the injectivity.

We demonstrate that in porous media of low permeability, the relative permeability of gas phase significantly increases when water saturation is lower than the residual liquid phase saturation. But, when this parameter is adjusted, the numerical code is able to reproduce the drying time and the outlet gas flow rate measured at laboratory scale on cores, using a two-phase Darcy flow and thermodynamic equilibrium between phases. The determined parameters are not temperature-dependent, for explored conditions, and they can be used at various temperatures. For rocks with higher permeability, this modification of relative permeability curves is not necessary. The code can represent the evolutions of water content in cores with a good accuracy.

At field scale, the rocks characteristics defined at laboratory scale are used to predict the behaviour of the nearwell zone according to the injection gas flow rate. We demonstrated that the precipitation process and the amount of salt deposits are related to different parameters:

-the salinity of the initial brine: the more concentrated the brine is, the more massive the salt deposit is; -the residual water content: water entrapped in pores is evaporated by gas injection. The higher this content is, the more important the amount of precipitated salt is; -the gas injection flow rate and the capillary forces within the system: the numerical calculations show that the capillary properties of the rock prevent a sudden evaporation of the irreducible water by continuously feeding the injection zone with "new" brine coming from reservoir zones distant from the injection well. But, a gas injection rate sufficiently high can reduce the capillary forces and then limit the precipitation of salts close to the injection well. All these parameters have to be known (and defined) in order to improve the management of the long-term injection of CO 2 in the saline aquifers.

Figure 1

 1 Figure 1 Experimental procedure to investigate the drying out of the core under a continuous flux of nitrogen.

Figure 2

 2 Figure 2 Relative permeability and capillary pressure curves according to liquid saturation (Sl).

Figure 3

 3 Figure 3 Geometrical 1D radial model for supercritical CO2 injection.

Figure 4

 4 Figure 4 Relative permeability and capillary pressure curves according to liquid saturation (Sl).

Figure 5

 5 Figure 5 Variations of the mean water content in the core and outlet gas flux (experiment at 90°C): points are measured data whereas lines are calculated values.

Figure 6

 6 Figure 6 Variation of water content in the core (experiment at 90°C): points are measured data (X-ray measurements) whereas lines are calculated values.

Figure 7

 7 Figure 7 Variations of the mean water content in the core and outlet gas flux (experiment at 120°C): points are measured data whereas lines are calculated values.

Figure 8

 8 Figure 8 Variation of water content around the well: (a) CO2 injection by stages; (b) massive CO2 injection rate with an abrupt DP = 12 bar; (c) massive CO2 injection rate with an abrupt DP = 24 bar.

Acknowledgements

This work was carried out within the framework of the "Proche Puits" project, co-funded by the French National Agency for Research (ANR).