Rémi Kazma
email: remi.kazma@inserm.fr

Catherine Bonaïti-Pellié

Jill M Norris

Emmanuelle Génin

On the use of sibling recurrence risks to select environmental factors liable to interact with genetic risk factors

Keywords: diabetes mellitus, type 2, epidemiologic research design, familial aggregation, genetic predisposition to disease, environmental exposure

Gene-environment interactions are likely to be involved in the susceptibility to multifactorial diseases but are difficult to detect. Available methods usually concentrate on some particular genetic and environmental factors. In this paper, we propose a new method to determine whether or not a given exposure is susceptible to interact with unknown genetic factors. Rather than focusing on a specific genetic factor, the degree of familial aggregation is used as a surrogate for genetic factors. A test comparing the recurrence risks in sibs according to the exposure of indexes is proposed and its power is studied for varying values of model parameters. The Exposed versus Unexposed Recurrence Analysis (EURECA) is valuable for common diseases with moderate familial aggregation, only when the role of exposure has been clearly outlined.

Interestingly, accounting for a sibling correlation for the exposure increases the power of EURECA. An application on a sample ascertained through one index affected with type 2 diabetes is presented where gene-environment interactions involving obesity and physical inactivity are investigated. Association of obesity with type 2 diabetes is clearly evidenced and a potential interaction involving this factor is suggested in Hispanics (p=0.045), whereas a clear gene-environment interaction is evidenced involving physical inactivity only in Non-Hispanic Whites (p=0.028). The proposed method might be of particular interest prior to genetic studies to help determine the environmental risk factors that will need to be accounted for to increase the power to detect genetic risk factors and to select the most appropriate samples to genotype.

Introduction

If gene-environment (GxE) interactions are expected to play an important role in multifactorial disease susceptibility [START_REF] Lander | Genetic dissection of complex traits[END_REF] genetic and environmental factors are most often evaluated independently rather than jointly. Joint analysis and GxE interaction testing is usually performed in a second step once the observed effects of each factor has been evidenced [START_REF] Andrieu | Epidemiologic and genetic approaches in the study of gene-environment interaction: an overview of available methods[END_REF][START_REF] Ottman | Gene-environment interaction: definitions and study designs[END_REF][START_REF] Yang | Evolving methods in genetic epidemiology. III. Geneenvironment interaction in epidemiologic research[END_REF] . Using such a strategy, we are likely to miss important genetic or environmental factors which effects could only be detected when accounting for the other factor [START_REF] Kraft | Exploiting geneenvironment interaction to detect genetic associations[END_REF][START_REF] Selinger-Leneman | Does accounting for geneenvironment (GxE) interaction increase the power to detect the effect of a gene in a multifactorial disease?[END_REF] . This was clearly evidenced in the study by Selinger-Leneman et al. [START_REF] Selinger-Leneman | Does accounting for geneenvironment (GxE) interaction increase the power to detect the effect of a gene in a multifactorial disease?[END_REF] where it was shown that the power to detect a genetic risk factor interacting with an environmental risk factor might be considerably reduced when the environmental exposure of individuals is not accounted for. However, this was very dependent on the environmental risk factor prevalence, on its effect on the disease and on its interaction with the genetic factor. In some situations, accounting for the environmental exposure was even detrimental in terms of power. This first study called for the need to develop methods to select environmental factors that might be involved in GxE interaction and should therefore be accounted for in genetic studies.

The problem of selecting environmental exposures to account for in genetic studies becomes even more crucial when performing genome-wide association studies with hundreds of thousands of markers. Indeed, in this context, for each exposure to study, there is such a huge number of tests to perform that one wants to make sure that only relevant exposures are accounted for. The development of methods to select these relevant environmental factors will probably be the first step in order to test for GxE interactions at the genome-wide levels.

In their previous work, Selinger-Leneman et al. [START_REF] Selinger-Leneman | Does accounting for geneenvironment (GxE) interaction increase the power to detect the effect of a gene in a multifactorial disease?[END_REF] have shown that selecting environmental factors based solely on their observed effects is not an efficient strategy and it might be useful to find a statistical tool to determine if they are likely to interact with genetic risk factors. This, however, should be done prior to the genetic analysis and thus involves the use of methods that do not require genotyping data. One such method was proposed by Purcell [START_REF] Purcell | Variance components models for gene-environment interaction in twin analysis[END_REF] for twin data and relies on variance component modeling.

Apart from the fact that it requires twin data, the method also requires exposure status of both sibs which is not always easy to obtain. Our proposed method also uses familial aggregation of the disease as a surrogate for the genetic factors but exposure in indexes only. Indeed, as suggested by Stücker et al. [START_REF] Stücker | Epidemiology of lung cancer: interaction between genetic susceptibility and environmental risk factors[END_REF] , familial aggregation of disease would be different for exposed and unexposed indexes if the environmental factor studied is involved in GxE interaction. A rational for this property is that, in presence of GxE interaction, exposed indexes have not the same distribution of genotypes as unexposed indexes. Their sibs will consequently have a different probability of having the disease from those of unexposed indexes.

In this paper, we used this idea of difference in sibling recurrence risks based on index's exposure to propose a test aimed at selecting environmental factors that are prone to interact with the genetic component of a multifactorial disease and propose a simple statistical test. We study the statistical properties of this test under different models and apply it on a type 2 diabetes (T2D) sample.

Materials and Methods

To evidence a difference in the recurrence risk for siblings of exposed and unexposed individuals, we need data on a sample of sib pairs ascertained through an affected index (sib 1). The variable of interest is the affection status of the other sib (sib 2) and the explicative variable is the exposure status of sib 1. The data can be presented in a contingency table such as table 1.

Odds Ratio of Recurrence and Exposed versus Unexposed Recurrence Analysis

Let K S be the sibling recurrence risk defined as the probability of sib 2 being affected given sib 1 is affected [START_REF] Risch | Linkage strategies for genetically complex traits. I. Multilocus models[END_REF] and K SE and K SĒ these risks when sib 1 is exposed and unexposed respectively to a given environmental factor E. To measure the difference between these two stratified risks, an Odds Ratio of Recurrence (ORR) can be calculated by analogy with an Odds Ratio (OR):

    SE E S E S SE K K K K ORR      1 1 (1)
Deriving the above recurrence risks as a function of observed numbers in the contingency table (table 1), the ORR can be expressed as:

bc ad ORR 
In contrast to the OR of an environmental factor where exposure and disease statuses are measured in the same individual, in the ORR, exposure is measured in the affected index and the disease status is measured in the sib.

In the presence of a GxE interaction involving environmental factor E, we expect the ORR to be different from 1. To test for "ORR = 1", we propose to perform a 1 degree of freedom (df) chi-square test on the contingency table crossing sib 1's exposure with sib 2's affection status (table 1) or the asymptotically similar Wald test based on the logistic regression parameter estimate and its variance. This test will be referred to as the Exposed versus Unexposed Recurrence Analysis (EURECA) test.

Properties of the ORR and of the EURECA test under different models

In order to study the behavior of the ORR and the statistical properties of EURECA, we considered a model of interaction involving a single gene (G) and a single environmental factor (E) even though the method practically only uses environmental information. We computed the expected numbers in each cell of the contingency table and derived the different recurrence risks (table 1) under the different models of geneenvironment interaction defined by the parameters presented in table 2. A disease D with population prevalence f D is considered. It is assumed that D is causally associated only with an environmental factor E and a genetic factor G.

The E factor is dichotomous with population frequency f E and a main effect size on D measured by the exposure relative risk, RR E . To model the possibility for a familial clustering of E, as in Khoury et al. [START_REF] Khoury | Can familial aggregation of disease be explained by familial aggregation of environmental risk factors?[END_REF] , we define the conditional probability of sib 2 being exposed given the exposure status of sib 1 as:

P(sib 2 E+ | Y 1 ) = (1 -C E ) × f E + C E × Y 1 (2)
where Y 1 is a dummy variable that takes the value 1 when sib 1 is exposed and 0 otherwise, and C E is the environmental correlation between the sibs. Thus, when C E = 0, sib 2's exposure status is independent from sib 1's exposure status and its probability is always equal to the prevalence of E in the general population, f E . When C E = 1, correlation between sibs for exposure is complete and sib 2's exposure probability is equal to 1 when sib 1 is exposed and 0 when sib 1 is unexposed.

The G factor corresponds to a predisposing genetic factor localized on an autosomal biallelic genetic locus. The allele that confers predisposition to disease is noted A and has a population frequency of q, whereas the other allele a has a population frequency of 1-q. Frequencies of the different possible genotypes (AA, Aa and aa) are supposed to follow Hardy-Weinberg proportions in the population (i.e., q 2 , 2q(1-q), (1q) 2 , respectively). The main effect of the G factor is measured by the genotypic relative risk (RR G ) which corresponds to the ratio of the disease risk in carriers of the predisposing genotype(s) to the risk in non-carriers of the predisposing genotype(s) among unexposed individuals. In all situations, we compared dominant and recessive genetic models for a given frequency f G of predisposing genotype(s), with f G = q 2 under a recessive model and f G = q 2 +2q(1-q) under a dominant model.

Let B designate the baseline risk i.e. the probability of disease for a non-carrier and unexposed individual. The interaction between E and G is measured by an interaction coefficient I, which corresponds to a departure from a multiplicative model when both E and G are present. In the absence of interaction, the risk of an individual exposed and carrier of the predisposing genotype is the product of B, RR E and RR G . In the presence of interaction, this risk is multiplied by the interaction coefficient I (table 2). The conditional risks of disease given genotype and exposure status and the numbers of the contingency table cells were derived using the ITO matrix method of Li and Sacks 11 modified in order to account for the environmental factor. Computations were done with the Maple 10 software 12 and explanations are given in the Supplementary materials.

Type I error and power of the EURECA test were asymptotically estimated considering a sample of 1000 sib-pairs by use of 1 df non-central chi-square distributions. Alternatively, we calculated the required number of sib-pairs to reach a power of 0.80 with a type I error rate of 0.05.

Application to type 2 diabetes

The Gene ENvironment Interactions (GENI) study [START_REF] Nelson | Association of the peroxisome proliferator-activated receptor gamma gene with type 2 diabetes mellitus varies by physical activity among non-Hispanic whites from Colorado[END_REF] collected phenotypic and environmental data of type 2 diabetic subjects and their families living in the San Luis

Valley and the Denver metropolitan area in Colorado (USA). Among 452 pedigrees (3090 nuclear families) ascertained through one index sib affected with T2D, we extracted 2699 index-sib pairs for which data was available in the index for at least one of the two studied exposures: obesity and physical inactivity. Of those pairs, 1734 were Hispanics (H) and 965 were Non-Hispanic Whites (NHW). Subjects previously diagnosed by a physician as having T2D and treated with oral hypoglycemic agents or insulin were considered affected. For subjects that did not report having T2D or subjects untreated for T2D, diabetic status was determined by an oral glucose tolerance test using American Diabetes Association criteria (1997). For diabetic subjects, self reported body mass index (BMI) at the time of diagnosis was used. BMI was calculated at recruitment time for other subjects. Individuals having a BMI value exceeding 30 kg/m 2 were classified as obese. Physical activity assessment was done once during the study using a previously validated questionnaire self-administered by the subjects [START_REF] Kriska | Development of questionnaire to examine relationship of physical activity and diabetes in Pima Indians[END_REF] . Energy expenditure was assessed as metabolic equivalent task (MET) units. The MET is the ratio of the metabolic rate during exercise to the metabolic rate at rest 15 . The average METs per week (prior to the diagnosis of T2D for affected individuals) was calculated for each study participant. The METs variable was divided into sex-specific tertiles, and a dichotomous variable was created distinguishing individuals in the lower tertile ("low physical activity") from those in the upper two tertiles.

We carried all the analysis separately for the two population strata (H and NHW) because the two exposures distributions were significantly heterogeneous. We first evaluated the observed main effect of each exposure using conditional logistic regression applied on discordant sib pairs for the T2D affection status. The numbers of available subjects were 198 H and 116 NHW for obesity and 458 H and 309 NHW for physical inactivity. Exposure frequency was measured in the control samples (unaffected sibs) and used as an estimate of exposure prevalence in population.

For each exposure, we randomly selected one sib for each index in order to compute contingency table numbers and global and stratified recurrence risks (K S , K SE and K SĒ ). The numbers of available pairs were 267 H and 321 NHW for obesity and 246

H and 268 NHW for physical inactivity. We derived an ORR for each exposure and applied the EURECA test of interaction using a logistic regression model. In order to account for correlated pairs belonging to the same pedigree, we computed the standard error of the logistic regression parameter using a robust sandwich estimator clustered by family as implemented in Stata/SE 10.1 16 . When exposure of the random sib was available, the pairs were also used to calculate a correlation coefficient between sib pairs for each exposure variable using equation 2.

Results

Behavior of the Odds Ratio of Recurrence under different disease models

To evaluate the pertinence of using the ORR as an indicator of the presence of a GxE interaction, we investigated the variations of the ORR under different models first without correlation between siblings for E (C E = 0). As expected, we observe that, in presence of an interaction, the values of the ORR increase with increasing values of the interaction coefficient I, but they also depend on the other model parameters. Impacts of these parameters are shown in figure 1 for the exposure parameters (f E and RR E ) and in figure 2 for the genetic parameters (f G and RR G ). For a given value of I, ORR is greater for high values of f E and RR E (figure 1) and small values of f G . When prevalence of the predisposing genotype(s) increases (f G = 0.2), the changes in ORR seen with varying RR G tend to disappear and even reverse when interaction values are elevated (figure 2).

ORR is higher for a dominant as compared to a recessive model at fixed f G .

Since environmental correlation between sibs might induce a possible confusion with a GxE interaction, we looked into variations of ORR values for different values of C E , when I = 1 and I = 5 (figure 3). We observe that under the null hypothesis (I = 1), the ORR value (referred to as ORR 0 ) is always equal to 1 in situations where there is no correlation of the E factor (C E = 0) or when there is no effect of E (RR E = 1). On the other hand, in the presence of an effect of E (i.e., RR E  1) associated with a correlation between sibs for this factor (i.e., C E  0), the ORR 0 values are inflated. In presence of a sibling correlation for E, the estimates obtained with a GxE interaction (I = 5, in figure 3) should thus be tested against the value of ORR 0 rather than against 1. The null hypothesis of the test becomes "ORR = ORR 0 ". The value of ORR 0 depends on the disease prevalence, on the environmental parameters and to a lesser extent on the genetic parameters. In order to estimate ORR 0 , we thus need to obtain some estimates these different parameters. Disease prevalence is often known from previous studies in similar populations. The environmental parameters (C E , f E , RR E ) can be estimated using the studied sample when data on the environmental exposure of siblings is available (see the type-2 diabetes example here). If this is not the case, results from previous studies on the effect of the environmental could be used. Only the genetic model is not known. We propose to calculate ORR 0 for different genetic model parameters (f G , RR G ) and then to use as ORR 0 the value the closest to the observed ORR. This "worst case scenario" ensures a robust inference on the test (see example in the section Results, Application to type 2 diabetes). In order to compute the expected ORR 0 , the Maple source code of "EURECA" is available from the corresponding author upon request.

More theoretical derivation of the ORR 0 computation is also given in the Supplementary materials.

Properties of the Exposed versus Unexposed Recurrence Analysis test

In figure 4, the power of the EURECA test of "ORR = ORR 0 " is reported for varying levels of interaction and C E under dominant and recessive models. As expected, the power increases with increasing value of I but more interestingly, this increases All the previous results considered a disease prevalence (f D ) of 0.10. Variations in power as a function of interaction and disease prevalence are presented in figure 6. In summary, it shows that the best performances of this test are obtained with common rather than with rare diseases. When the disease is rare, the sibling recurrence risk (K S ) is low and the difference between the exposed and unexposed index strata due to the GxE interaction is harder to detect.

depends

Application to type 2 diabetes

The results of the T2D application are presented in table 4. For each population strata (H and NHW) and each studied exposure, we show first the environmental parameter estimates: OR E (exposure's odds ratio), f E and C E , and then the proposed GxE interaction analysis: ORR and EURECA test. In order to account for C E , we calculated the ORR expected under the null hypothesis (ORR 0 ). The Center for Disease Control and Prevention (CDC) 2001 diabetes data for the state of Colorado provided diabetes prevalence (f D = 4.5 %) [START_REF]National diabetes surveillance system[END_REF] . Based on this estimate and using the environmental parameters calculated previously on the T2D data, we computed expected ORR 0 values for a wide range of genetic parameters (f G = 0.01-0.5, RR G =0.5-10). An interval of variation of ORR 0 was obtained in this way. To ensure robustness of the test, we considered the "worst-case scenario" and compared the observed ORR to the value of ORR 0 that was the closest to the observed ORR.

In 5).

Since the sex distributions of indexes and of sibs were homogenous between the groups of exposed and unexposed indexes, this variable should not interfere with the EURECA test.

Discussion

Contrasting the sibling recurrence risks based on the exposure status of the index is a simple and attractive approach to select environmental factors involved in a GxE interaction. We propose to measure this contrast by computing an Odds Ratio of Recurrence (ORR) and show that the ORR is a good indicator of a GxE interaction. This ORR is not a direct measure of interaction but rather a measure of the difference between recurrence risks in exposed and unexposed indexes. For example, using the low physical activity in NHW result in table 4, the risk of T2D in a NHW individual is multiplied on average by a factor of 2.13 when his affected index sib has a low physical activity compared to an individual whose affected index sib has a high physical activity.

At this level of information, discriminating between an underlying genetic component interacting with the exposure and the familial clustering of this exposure associated to the disease is quite difficult [START_REF] Mahon | Epidemiologic approaches to family resemblance[END_REF] , but our results show that it is possible, provided that the effect and familial correlation of the environmental factor is well documented.

In the context of a dichotomous environmental variable, the interests of using the ORR, instead of the ratio of recurrence risks, resides in applying a logistic regression as done in most epidemiologic studies, but the same approach can be easily extended to multiclass or continuous environmental factors using the classic general linear models.

The use of continuous variables when available would probably increase the power but would also make the assumption of a linear relation. To test for the difference of the ORR with a null hypothesis value (ORR 0 ), we derive a statistical test, the Exposed versus Unexposed Recurrence Analysis (EURECA) test. To use this test, we need to define the value of ORR 0 . We have derived analytically a formula to compute ORR 0 based on exposure parameter and disease prevalence estimates. These estimates are often easily obtained from the data sample and from the literature. To ensure robustness of the test, we suggest accounting for the impact on ORR 0 of possible variations in these estimates by deriving a range of variation of ORR 0 and to consider in the test the ORR 0 value the closest to the observed ORR. Note that the loss of power due to the uncertainty of the genetic parameters should be minimal since the ORR 0 variations would usually be small as in the illustrative example (from 0.01 to 0.03). Interestingly in our example, we found even under this "worst-case scenario", it is possible to show that observed ORR for some exposure significantly differs from ORR 0 . This is in good agreement with the results of Khoury et al. [START_REF] Khoury | Can familial aggregation of disease be explained by familial aggregation of environmental risk factors?[END_REF] showing that the degree of familial aggregation of most common diseases cannot be entirely explained by a familial clustering of environmental risk factors even if we assume an extreme clustering of the environmental factor.

The study of the statistical properties of EURECA has shown that the test is appropriate to test for common diseases rather than rare ones (figure 6). Interestingly, even when the tests are corrected for the exposure correlation in siblings, powers were found to be higher for elevated values than for lower values of C E . We hypothesize that the sibling correlation actually has a confounding effect on one part, but also emphasizes the existing difference in recurrence risks between strata of indexes due to the GxE interaction. We only tested positive correlation coefficients between siblings for exposure since it is probably the most common situation in familial studies.

GxE interactions are difficult to detect and often require very large sample sizes.

In an effort to increase the power to detect GxE interaction, new methods have been developed that are based on particular sampling designs. Among these methods are the log-linear modeling method that uses case-parent trio data and compares genotype distribution of exposed and unexposed cases conditional on parental genotypes [START_REF] Umbach | The use of case-parent triads to study joint effects of genotype and exposure[END_REF] , methods that use counter-matching designs to enrich the sample with rare exposure or genetic factors [START_REF] Andrieu | Counter-matching in studies of gene-environment interaction: efficiency and feasibility[END_REF] or case-control-combined designs with both population and familial controls [START_REF] Goldstein | Unconditional analyses can increase efficiency in assessing gene-environment interaction of the case-combinedcontrol design[END_REF] . A common feature of all these different methods to detect GxE interactions is their need to have a complete knowledge of the exposure statuses and genotypes of the studied subjects. Among the methods that use familial aggregation of the disease as a surrogate for the latent genetic factor, Purcell [START_REF] Purcell | Variance components models for gene-environment interaction in twin analysis[END_REF] proposed to apply variance components models in twin studies to evidence GxE interactions with an environmental factor measured in both twins. What distinguishes the method we propose here is the type of information used in order to assess the GxE interaction. This method relies on the exposure of the index case and information on the familial recurrence of the disease.

There is no need to have a measure of exposure in the sibs and for easily recognizable diseases, their affection status might be obtained from indexes. Large sample sizes can thus be obtained at a minimal cost. It is true however that if sibs could also be examined, familial recurrence will certainly be better estimated. It will also be possible to assess, directly from the data rather than from the literature, potential environmental correlation between sibs.

The use of the sib recurrence information as surrogate for genetic risk factors has the advantage of requiring no a priori hypothesis on the genetic model underlying disease susceptibility. It also permits to test for the involvement in the disease of genetic factors located anywhere on the genome at no cost in terms of multiple testing. This is an important point as the issue of multiple testing in GxE interaction studies considering thousands of genetic markers coupled with tens of exposures remains to be resolved. On the counterpart, this approach only stipulates a specific environmental factor and tests for its interaction with the genetic component implicated in disease risk increase. As compared to other methods that use both genotypic and environmental information, this method could lack power to detect some interaction with a specified genetic factor. But it provides an easy way to screen for environmental factors potentially implicated in GxE interactions when genotypes are not available.

Association between T2D and obesity was significant both in H and NHW, as previously evidenced in many cross-sectional and longitudinal studies [START_REF] Kriska | Physical activity, obesity, and the incidence of type 2 diabetes in a high-risk population[END_REF] . Concerning interaction, EURECA was significant only in H (p = 0.045) with a particular model of interaction where the interaction effect is in opposite direction compared to the main exposure effect. In an earlier study of recurrence risk estimation in T2D families, analogous results were found and elevated recurrence risk ratios were found in siblings of non-obese as compared to obese patients [START_REF] Weijnen | Risk of diabetes in siblings of index cases with Type 2 diabetes: implications for genetic studies[END_REF] . This kind of interaction illustrates the situations where the GxE interaction is a nuisance element that has to be accounted for in order to better detect a main effect [START_REF] Kraft | Exploiting geneenvironment interaction to detect genetic associations[END_REF][START_REF] Selinger-Leneman | Does accounting for geneenvironment (GxE) interaction increase the power to detect the effect of a gene in a multifactorial disease?[END_REF] . Regarding, low physical activity which had no significant observed effect in any of the two populations, the interaction test was significant in NHW (p = 0.028) but not in H. A previous study that applied family-based association tests and generalized estimating equations models showed a GxE interaction between the peroxisome proliferator-activated receptor γ gene and low physical activity in H too [START_REF] Nelson | Association of the peroxisome proliferator-activated receptor gamma gene with type 2 diabetes mellitus varies by physical activity among non-Hispanic whites from Colorado[END_REF] . Ascertainment of indexes through multiplex families as in the case of the GENI study could make it difficult to extrapolate results to the general population of diabetic patients. Indeed, an enrichment in disease susceptibility alleles is expected in these families and thus sibling recurrence risk estimates are likely to be increased as compared to those expected in the general population [START_REF] Weijnen | Risk of diabetes in siblings of index cases with Type 2 diabetes: implications for genetic studies[END_REF] . However, it should not create an erroneous heterogeneity between exposed and unexposed indexes strata unless there is a correlation between sibs for the environmental factor that is not correctly accounted for. In this example, the results are likely to encourage further studies to select non obese subjects in H populations, in order to search for genetic factors implicated in T2D, whereas studying NHW populations, we would be more interested in searching for an interaction with low physical activity. This illustrates how one can use the ORR point estimates, their confidence intervals and corresponding p-values to rank among many environmental factors those that should be selected in priority to test for a GxE interaction in following genetic studies.

In conclusion, this paper demonstrates that valuable amount of familial information can be exploited towards detecting GxE interactions that underpin multifactorial disease susceptibility. This method is proposed as a strategy that can be used prior to genetic studies to help plan these studies. It can help investigators identify environmental factors liable to interact with genetic factors and that will need to be accounted for in the analysis but could also be used in the study design to select subcategories of the population to enhance genetic factor detection.

Table 1

Distribution of the sample of sib pairs in cross table according to exposure of sib 1 and disease status of sib 2.

The sibling recurrence risk over the whole sample (K S ) and sibling recurrence risks stratified on sib 1's exposure (K SE and K SĒ ) can be derived from the observed numbers (a, b, c and d). The Odds Ratio of Recurrence (ORR) is equal to:

    bc ad K K K K ORR SE E S E S SE       1 1 Sib 1 (affected) exposed unexposed Sib 2 affected a b a+b unaffected c d c+d a+c b+d N K SE = a/(a+c) K SĒ = b/(b+d) K S = (a+b)/N

Table 2

Probability of disease given exposure and genotype statuses according to genetic and environmental model parameters.

Genotype

G- RR E : exposure relative risk; RR G : genotypic relative risk; I: multiplicative interaction coefficient for individuals both exposed and carrier of the predisposing genotype.

(1-f G ) G+ (f G ) Exposure E- (1-f E ) B B.RR G E+ (f E ) B.RR E B.RR G .

Table 3

Sample size (number of sib pairs) required to obtain a power of 0.80 with a type I error rate of 0.05 as a function of the interaction coefficient (I) and the environmental correlation between sibs (C E ).

Fixed parameters: disease prevalence: f D = 0.1; frequency of predisposing genotype(s):

f G = 0.1; genotypic relative risk: RR G = 2; frequency of exposure: f E = 0.

Supplementary materials

Computation of contingency table's observed number given model parameters

An individual can have one of three possible genotypes (for a biallelic genetic locus) and one of two exposure statuses (for a dichotomous environmental variable).

Thus any two siblings may have 36 (6 × 6) possible combinations of genotypes and exposure statuses whose joint probabilities can be obtained by modifying the ITO matrix method of Li and Sacks 12 to account for exposure probabilities (table S1). In table S2 are shown probabilities for an individual to be affected or unaffected given his genotype and his exposure status, expressed according to model parameters.

We first calculate joint probabilities of having an exposed (or unexposed) mandatorily affected sib 1 and an affected (or unaffected) sib 2 used to calculate contingency table 1 numbers. The indices "i" and "j" refer to the cells of the U ij matrix presented in table S1:

P a = P(sib 1 D+ E+ and sib 2 D+) =         3 1 6 1 ) ( ) ( i j ij j D P i D P U (3) P b = P(sib 1 D+ E-and sib 2 D+) =         6 4 6 1 ) ( ) ( i j ij j D P i D P U (4) P c = P(sib 1 D+ E+ and sib 2 D-) =         3 1 6 1 ) ( ) ( i j ij j D P i D P U (5) P d = P(sib 1 D+ E-and sib 2 D-) =         6 4 6 1 ) ( ) ( i j ij j D P i D P U (6)
where D+ is the event of being affected with disease D and E+ is the event being exposed to environmental factor E, "i" represents possible genotype-exposure combinations for sib 1 and "j" possible genotype-exposure combinations for sib 2.

Their sum is equal to the a priori probability of disease in sib 1: P total = P(sib 1 D+) = P a + P b + P c + P d (7) Finally, using equations 3 to 7, we determine contingency table 1 observed numbers:

a = N × P a / P total b = N × P b / P total c = N × P c / P total d = N × P d / P total
where N is the total number of sib-pairs.

Computation of ORR 0 :

The ORR 0 formula derive from the ORR considering a model with no interaction (I = 1).

It is a difficult formula to write on a single page since it depends on 6 parameters: the susceptibility genotype(s) frequency (f G ) and relative risk (RR G ), the environmental factor frequency (f E ) and relative risk (RR E ), the environmental correlation between sibs (C E ) and the disease prevalence in population (f D ). But according to the type 2 diabetes application results, the ORR 0 seems to depend predominantly on the environmental parameters (f E , RR E , and C E ) and on the disease prevalence (f D ) and to a lesser extent on the genetic parameters.

Considering no effect of the genetic factor (RR G = 1), the ORR 0 can be expressed as:

                        1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0                       D E D E E E E D D E D E E E E E E E E E E f C f RR f RR C f f C f RR f C f RR C f RR RR C ORR
But in order to obtain the expected range of values of ORR 0 as presented in table 4, computations were done for different values for the genetic model: f G from 0.01 to 0.5 and RR G ranging from 0.5 to 10.

Table S1

Sib-sib joint probabilities matrix U ij for genotypic and exposure distributions modified from the ITO matrix method of Li and Sacks 12 .

Sib 1 Total E1+ E1- AA i = 1 Aa i = 2 aa i = 3 AA i = 4 Aa i = 5 aa i = 6 Sib 2 E2+ AA j = 1   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f  2 2 E f q Aa j = 2   2 2 1 2 1 q q      1 / 2 1 E E E f f       q q q q    1 1 1     1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f       q q q q    1 1 1     1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 1 2 E f q q aa j = 3   2 2 1 4 1 q q      1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 2 2 1 4 1 q q       1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 2 2 1 4 1 q q       1 / 2 1 E E E f f     2 2 1 E f q E2- AA j = 4   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f  2 2 E f q Aa j = 5   2 2 1 2 1 q q      1 / 2 1 E E E f f       q q q q    1 1 1     1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f   2 2 1 2 1 q q      1 / 2 1 E E E f f       q q q q    1 1 1     1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 1 2 E f q q aa j = 6   2 2 1 4 1 q q      1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 2 2 1 4 1 q q       1 / 2 1 E E E f f   2 2 1 4 1 q q      1 / 2 1 E E E f f     q q q   2 1 2 1 2     1 / 2 1 E E E f f     2 2 2 1 4 1 q q       1 / 2 1 E E E f f     2 2 1 E f q Total (ω i )  1 2 E f q     1 1 2 E f q q     1 2 1 E f q  1 2 E f q     1 1 2 E f q q     1 2 1 E f q 1
A: allele that confers susceptibility to disease; E1X: exposure status of sib 1 (X = + if exposed and X =if unexposed); E2Y: exposure status of sib 2 (Y = + if exposed and Y =if unexposed); q: frequency of allele A in population; f E1X : frequency of exposed status X in sib 1 (equal to the same frequencies as in population); f E2Y/E1X : frequency of exposed status Y in sib 2 given exposure status X of sib 1 (equal to same frequencies as in population if exposure correlation coefficient for sib-pairs is null, C E = 0).

  RR E .I E+: exposed; E-: unexposed; f E : proportion of exposed individuals in population; G+: carrier of the predisposing genotype(s); G-: non-carrier of the predisposing genotype(s); f G : proportion of carriers of the predisposing genotype(s) in population; B: baseline risk;

Figure 1

 1 Figure 1Odds Ratio of Recurrence (ORR) as a function of the gene-environment

Figure 2

 2 Figure 2Odds recurrence ratio (ORR) as a function of the gene-environment

Figure 3

 3 Figure 3Odds Ratio of Recurrence (ORR) as a function of the sibling correlation

Figure 4

 4 Figure 4Power of the EURECA test as a function of the interaction coefficient I

Figure 5

 5 Figure 5Required sample size (number of sib pairs) to obtain a power of 0.80

Figure 6

 6 Figure 6Power of the EURECA test as a function of the interaction coefficient I

  on C E and is larger for high C E values than for low C E values. Alternatively, But considering situations with elevated interaction coefficients (I > 3) and with high correlation for exposure in sibs (C E > 0), sample sizes are more reasonable.Considering the same frequencies with a sibling correlation of 0.25 and varying values of RR E and RR G , the required sample sizes are shown in figure5. As expected, these sizes are smaller when G and E have strong effects, but they seem to be more sensitive to G than to E.

	table 3 reports the number of sib pairs that are needed to reach a power of 0.80 with a
	type I error rate of 0.05 for increasing values of I and C E under a plausible disease
	model (frequent factors, f G = 0.1 and f E = 0.2; with moderate effects, RR G = 2 and RR

E = 2). In situations with no C E and small I, sample sizes are very high and thus unlikely to be recruited.

  H, obesity has an ORR equal to 0.67 (95 % CI: 0.40,1.11). Remarkably in this stratum, obesity has a strong significant observed effect of 2.48 (95 % CI: 1.18, 5.22), which, associated with a C E of 0.22 and a f E of 0.29, gives an expected ORR 0 varying between 1.25 and 1.27. In this example, we used 1.25 (closest value to the observed ORR of 0.67) to perform the EURECA test and obtained a p-value of 0.045. In NHW, obesity has also a significant observed effect with an OR of 3.87 (95 % CI: 1.54, 9.65) but the interaction test is not significant.

Considering physical inactivity, the interaction test is significant in the NHW sample only (p = 0.028) and the ORR is 2.13 (95 % CI: 1.08,

4.19)

. This exposure has no significant observed effect and does not aggregate in sib-pairs, which is a situation where the proposed test usually lacks power to detect the GxE interaction (as shown in table

3 and figure

Table 4

 4 Results of the application on type 2 diabetes data.

	2; exposure

H: Hispanics; NHW: Non-Hispanic Whites; OR E : Odds Ratio estimate of the environmental factor; f E : Estimated frequency of the environmental factor; C E : Estimated sibling correlation for the environmental factor; ORR 0 : Interval of variation of the expected Odds Ratio of Recurrence under the null hypothesis; * Closest bounding value used to perform the test; ORR: Odds Ratio of Recurrence; CI: confidence interval; EURECA: Exposed versus Unexposed Recurrence Analysis.

Acknowledgments

The authors wish to thank Marie-Claude Babron for her comments on the manuscript. RK's doctoral work is funded by a grant from the Presidency of the University Paris-Sud.

Table S2

Probabilities for an individual to be affected (P (D+ | k)) or unaffected (P (D-| k)) for the six possible combinations of genotype and exposure statuses.


Quentin Guilloteau

Sophie Cerf
email: sophie.cerf@inria.fr

Eric Rutten

Raphaël Bleuse

Bogdan Robu
email: bogdan.robu@grenoble-inp.fr

Under Control: A Control Theory Introduction for Computer Scientists Session @ VELVET 2023

Goal of this tutorial

The Feedback Loop

The idea

Use the knowledge about the current state of the system to respond Autonomic Computing (IBM 2003) The (famous) PID Controller (discretized) First, a Model ... (i.e., how does the system behave (Open-Loop))

y(k + 1) = k ∑ i=0 a i y(k -i) + k ∑ j=0 b j u(k -j)
... then a PID Controller (i.e., the Closed-Loop behavior) The controller gains define this behavior!

u k = K p × Error k + K i × ∑ k Error k + K d × (Error k -Error k-1 )

Sensors & Actuators

Figure

  Figure: MAPE-K Loop

2

  Figure: Closed Loop Behavior

Sophie CERF | UGA , INRIA , G-INP | 13/12/2023


Issam Takla
email: issam.takla@polytech-lille.fr

Yun Jia
email: yun.jia@polytech-lille.fr

Thomas Rougelot

Nicolas Burlion

Influence of pre-carbonation on hydro-mechanical properties of cement paste subjected to leaching

Keywords: CO2 storage, Carbonation, Leaching, Cement paste, time-dependent strain, Permeability, mechanical properties

Depleted oil reservoirs have been one of the most practical options for CO2 sequestration. To ensure the overall sealing performance of oilwell for CO2 injection, it is necessary to understand the long-term hydro-mechanical behaviour of cement paste used as oilwell casing. In the presence of high CO2 concentration and water, cement paste is firstly carbonated and then may be degraded by carbonic acid in CO2 storage. The present work aims to experimentally investigate the pre-carbonation effects on the leaching of oilwell cement paste, with special attention to hydro-mechanical properties. By using a series of uniaxial compression tests and triaxial compression tests with permeability measurements, permeability and mechanical properties of sound and pre-carbonated materials, before and after leaching treatment, are measured and analysed. Moreover, the time-dependent behaviour of pre-carbonated material subjected to leaching is studied via a coupled creep test. The obtained results exhibit that after leaching treatment, comparing with the initially sound samples, the pre-carbonated samples exhibit higher mechanical properties, lower permeability, and smaller creep deformation. Therefore, one can conclude that the degradation of mechanical and hydraulic properties induced by leaching is reduced by the pre-carbonation of cement paste and the carbonation has a positive effect against leaching. To verify and understand the macroscopic experimental observations, some micro-indentation tests are performed at a mesoscopic scale and a mineralogy and chemistry analysis are also conducted via SEM-EDS and Raman spectroscopy tests. Experimental investigation, micromechanical analysis and microstructure will advance the understanding of long-term durability of CO2 geological storage.

Introduction

In order to reduce carbon dioxide CO2 concentration in the atmosphere, depleted oil and gas reservoirs have been one of the most practical options for CO2 sequestration due to its numerous advantages, such as high geological stability, absence of leakage paths and availability of infrastructures. In gas and oil exploitations, cement paste is widely used as oilwell casting to isolate the production zones and provide mechanical support. In the oilwell for CO2 injection, the carbonic acid, which is formed with the dissolution of CO2 in water, firstly reacts with the portlandite of cement paste. This carbonation process results in the formation of calcite and improves the mechanical and transport properties of cementitious materials [START_REF] Wang | Accelerated mineral carbonation curing of cement paste for CO2 sequestration and enhanced properties of blended calcium silicate[END_REF]. Once the depletion of portlandite is achieved, the carbonic acid induces the leaching of calcite [START_REF] Sugama | Advanced Cements for Geothermal Wells[END_REF]. This leaching process may create mechanical damage and alter transport properties of cement paste, potentially perturbing the storage integrity [2,3,4,5,6,7,8,].

Moreover, the geological storage is located at serval kilometres beneath the Earth's surface. Under the geothermal gradient, high downhole temperature may induce a further evolution of the hydromechanical properties of cement paste [START_REF] Wang | Increasing efficiency of carbon dioxide sequestration through high temperature carbonation of cement-based materials[END_REF]. As a result, a long-term integrity and durability of CO2 storage requires a good understanding of the hydro-mechanical behaviour of cement paste subjected to high temperature and two mentioned successive chemical processes: carbonation and then leaching.

In the literature, number of experimental tests have been performed to study separately the carbonation or leaching processes of cement-based materials. On one hand, previous studies [10,11,12 ,13,14,15,16] exhibit that carbonation induces a decrease in porosity and permeability as well as an increase in mechanical strength. However, very few authors have studied the carbonation process under a high temperature close to the real temperature level of CO2 storage, just to mention a three. Takla et al. [START_REF] Takla | Effects of the Storage of CO2 on Multiaxial Mechanical and Hydraulic Behaviors of Oil-Well Cement[END_REF] have studied the effect of carbonation on the mechanical and hydraulic behaviour of an oilwell cement paste under high temperature T=90°C. They found that with respect to the initially sound material, carbonated samples exhibited a remarkable permeability decrease about one order of magnitude as well as 100% ~150% increase of mechanical strength. Recently, Borje et al. [START_REF] Bjørge | Carbonation of silica cement at high-temperature well conditions[END_REF] have studied the microstructural changes induced by the carbonation of Portland cement by using different experimental techniques. Wang et al. [Erreur ! Source du renvoi introuvable.] have also studied the carbonation performance and carbon dioxide uptake rate of cement paste in the temperature range (20 °C-300 °C). The obtained results demonstrated that carbonation reaction increased obviously with increasing temperature.

On the other hand, a large number of experimental studies have been performed to study the leaching of cementitious materials [START_REF] Adenot | Durabilité du béton : Caractérisation et modélisation des processus physiques et chimiques de dégradation du ciment[END_REF]20,[START_REF] Carde | Modelling the loss of strength and porosity increase due to the leaching of cement pastes[END_REF][START_REF] Chen | Decalcification shrinkage of cement paste[END_REF][START_REF] Jia | A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching[END_REF][START_REF] Kamali | Material and environmental parameter effects on the leaching of cement pastes: experiments and modelling[END_REF][START_REF] Lin | Effect of calcium leaching on the properties of cement-based composites[END_REF][START_REF] Yurtdas | Couplage comportement mécanique et perméabilité -cas d'une pâte de ciment pétrolier dégradée chimiquement à 90 °C[END_REF]. Leaching of cement paste dissolves the solid phases (for instance, portlandite, calcium silicate hydrates, and ettringite etc.) and induces a porosity/permeability increase as well as a reduction of mechanical properties. Moreover, the leached material exhibits a more ductile behaviour than the sound one [START_REF] Jia | A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching[END_REF][START_REF] Yurtdas | Couplage comportement mécanique et perméabilité -cas d'une pâte de ciment pétrolier dégradée chimiquement à 90 °C[END_REF]. The leaching kinetics depend strongly on temperature [20]. According to Kamali [Erreur ! Source du renvoi introuvable.], for a cement paste of CEM I type with a water/cement ratio of 0.4, the leaching process was accelerated by a factor of 2.3 when the temperature increased from 25°C to 85°C. However, only one of carbonation and leaching processes has been studied in these research work. To the best of the authors' knowledge, the leaching of pre-carbonated cement-based material under high temperature has not yet been investigated.

The present work focuses on the impact of pre-carbonation on the leaching of a cement-based material under high temperature, with special attention to hydro-mechanical properties. In view of this objective, the tested cementitious material is prepared under two carbonation conditions: one group is kept in aluminium sheets to avoid the CO2 contact (CO2-free environment), called "sound samples"; the other ones are exposed to an accelerated carbonation, called "carbonated samples". After that, some sound and pre-carbonated samples are subjected to leaching. Consequently, four types of cement paste are obtained in the experimental program. Their permeability, failure strength and creep deformation are firstly studied via a series of uniaxial compression test, triaxial compression tests with permeability measurements and coupled creep tests. After that, micro-indentation tests are performed to identify the mechanical properties of studied materials at a mesoscopic scale. Additionally, the chemical and mineral analysis is conducted using SEM-EDS and Raman spectroscopy technology on different types of specimens to verify the theoretical chemical processes and understand the experimental observations.

Materials and samples preparation

The present study is performed in the framework of the feasibility study of depleted oil reservoirs for CO2 sequestration, coordinated by Total Company. The emphasis focuses on the influence of precarbonation on hydro-mechanical properties of an oilwell cement paste subjected to leaching and high temperature.

As aforementioned, in the oilwell for CO2 injection, the hydro-mechanical properties of cement paste will be firstly improved by carbonation and then degraded by further leaching. To reproduce the mentioned chemical reactions in a reasonable period of time, laboratory samples have been prepared in in an accelerated way: carbonation is performed in a climate chamber with a high gaseous CO2 concentration while leaching is realized by using the ammonium nitrate solution. The choice of ammonium nitrate rather than carbonic acid for the leaching is to accelerate the leaching kinetics with almost the same products [START_REF] Carde | Use of ammonium nitrate solution to simulate and accelerate the leaching of cement paste due to deionized water[END_REF]. Moreover, the adopted temperature of 90°C can also accelerate the leaching kinetics of cement paste. The studied material and sample preparation are presented in this section.

Materials

Actually, the studied cement paste is being used as cement casing of oilwells, whose composition has been provided by French company Total. It is made with a water/cement ratio of 0.4 and a G class cement commonly used in oil-well industry. The G class cement is defined by American Petroleum Institute (API), in accordance with standard 10A API [28]. Thanks to its special chemical composition, this cement is largely used in the construction of oil wells. Because of the complexity of engineering application and extreme conditions of temperature and pressure that is subjected to, the class G cement is characterized by the constancy of important requirements, such as high durability, fluid loss control and high sulphate resistance, etc…With respect to the composition provided by Total (Table 1), all the laboratory samples were prepared in the Laboratory of Mechanics, Multi-physics, Multi-scale (LaMcube).

Components

Quantity (kg/m Before the sample preparation, 18 preliminary tests using the cement paste samples (20×20×160 mm 3 ) have been performed at the temperature of T=90°C to estimate the curing period. As the laboratory samples are conserved in water, the water consumption related to the hydration can be replaced by the entrance of external water. Once the relative mass variation of samples is inferior to 2% during a week, the mass stability is achieved, and a quasi-complete hydration is obtained. As the microstructure of cement paste is almost stabilized, it is possible to suppose that with respect to the post-treatment procedures (i.e. carbonation and leaching processes), the effect of further hydration can be neglected. Therefore, one month of curing period was adopted in the present study while T= 90°C was used to reproduce the real temperature level in CO2 reservoir.

After mixing all the components at atmospheric temperature, the cement paste was cast in cylindrical stainless-steel moulds (Ø 36, H= 100 mm). The moulds were kept in distilled water (saturated with lime) at 90°C for 3 days. After a rapid demoulding, samples were kept in distilled water at 90°C for one month. Consequently, cylindrical cores used for the laboratory tests were cut from the central parts of cured samples (Ø 36, H= 100 mm). Dimension of cores was 22mm in length and 20 mm in diameter.

These samples were prepared under two carbonation conditions: one group was protected by aluminium sheets to avoid the CO2 contact (CO2-free environment), called "sound samples"; the other ones were exposed to an accelerated carbonation, called "carbonated sound samples". After that, some of previous samples (i.e. sound and carbonated sound samples) were subjected to leaching to obtain "leached sound samples" and "leached carbonated samples", respectively. In total, four types of cement paste were investigated in the present work: sound (case1), carbonated sound (case 2), leached sound (case 3) and leached carbonated (case 4) samples. According to the carbonation and leaching processes adopted in the samples' preparation, they will be given in the next sections. A schematic summary of the specimen categories and different laboratory tests are given in Fig. 1.

Specimen carbonation

Inspired by previous research works [START_REF] Thiery | Investigation of the carbonation front shape on cementitious materials: Effects of the chemical kinetics[END_REF][START_REF] Wierig | Longtime studies on the carbonation of concrete under normal outdoor exposure[END_REF][START_REF] Roy | Durability of concrete accelerated carbonation and weathering studies[END_REF], the carbonation of sound samples was realized in a climatic chamber Binder®, under a temperature of 90°C and related humidity of 65%. The adoption of this relative humidity is to accelerate the carbonation process. As a result, carbonated cement paste, similar to the in-situ oilwell one, can be obtained within an acceptable period of time (about 28 days). In the climatic chamber, CO2 was injected at a rate of 100 cm 3 /min. At the end of one day, the injected CO2 volume was then equal to the chamber volume (0.15 m 3 ) [START_REF] Sisomphon | Carbonation rates of concretes containing high volume of pozzolanic materials[END_REF]. To compensate the partial consumption of CO2 during carbonation and the potential CO2 leaks in the climatic chamber, the continuous injection was adopted during the carbonation. Its objective is to obtain the highest CO2 concentration in the climatic chamber and then maximize the kinetics of carbonation without modifying the carbonation products [START_REF] Yuan | Comparison of concrete carbonation process under natural condition and high CO2 concentration environments[END_REF]. [START_REF] Mason | Chemical and Mechanical Properties of Wellbore Cement Altered by CO2-Rich Brine Using a Multianalytical Approach[END_REF] During the carbonation, at predefined intervals, one of the samples was taken out the climate chamber and split along its longitudinal axis. Phenolphthalein solution was then sprayed onto its surface area to determine the carbonation depth. Four different samplings are given in Fig. 2 (7, 14, 21 and 28 days). One observes that the pink colour disappears progressively with time, indicating that the carbonation front gradually penetrates towards the centre of sample. This observation is due to the fact that phenolphthalein changes into pink in the non-carbonated zone (i.e., sound zone) while it remains transparent in the carbonated zone where pH is smaller than 9. For a given moment, four measurements of carbonation thickness were taken on each edge of sample and the mean value was used as the carbonation depth (Fig. 2). After 28 days exposure, no pink colour was observed in the sample, indicating that pH of the whole sample was smaller than 9. Assuming that pH<9 represents a complete/quasi-complete carbonation, carbonated sound samples (case 2) were obtained at the end of 28 days.

Specimen leaching

In the present work, the same leaching processes were applied on two categories of laboratory samples at different carbonation states: initially sound samples (case 1) and carbonated sound samples (case 2).

To determine the leaching front in these two materials, two indicators have been used in the present work: Phenolphthalein solution for initially sound material and darker grey colour for pre-carbonated material. The samples were placed in a cooking vessel of 5 litres and leached in an ammonium nitrate solution at 90°C. The initial concentration of the ammonium nitrate solution was 6 mol/l, which wasn't renewed during leaching. For a cooking vessel, a maximum of 20 samples could be contained to guarantee a sufficient concentration of leaching solution. The leaching process of laboratory samples is given as follows. Firstly, the salt of ammonium nitrate is mixed in distilled water in the cooking vessels and then kept 24 hours under ambient temperature. The prepared ammonium nitrate solution is then put in the oven at 90°C for 24 hours in order to attains the same temperature as the laboratory samples.

Afterwards, the samples (conserved initially at 90°C) are put in the cooking vessels installed in the oven at 90°C, for leaching process.

For each group, after a certain rection time, one of sample was split and examined to identify the leaching depth. The leaching of initial sound samples is firstly presented. The freshly split surface was sprayed with the phenolphthalein solution. After a few seconds, two distinct zones could be observed: a pink colour was observed in the sound zone and a grey colour was presented in the degraded zone. This observation can be explained by the fact the phenolphthalein remains transparent in leached zone, in which pH is less than 9. The evolutions of leaching front in leached sound sample are given in Fig. 3a at four degradation times (i.e, 1, 2, 4 and 5 days). It is observed the leaching area increases progressively with time (Fig. 3a). When no pink colour is observed in the whole sample (Fig. 3a), a complete or almost complete leaching is achieved and the leached carbonated samples (case 3) are obtained at the end of 5 days.

For pre-carbonated samples, as their pH is smaller than 9, phenolphthalein cannot be used as a good indicator of leaching. However, one observes that the pre-carbonated cement paste progressively becomes darker with the advancement of leaching front. Therefore, once the light grey zone disappears in the whole sample (Fig. 3b), it's considered that the pre-carbonated sample is complete/quasicomplete leached. As a result, the leached carbonated samples (case 4) are obtained after 10 days of leaching treatment. By comparing the leaching kinetics in cases 3 and 4, one observes that the leaching of pre-carbonated material needs much more time than that of the sound one, even up to two times: the sound samples are almost completely leached at the end of 5 days while the leaching of carbonated samples is relatedly slow and lasts up to 10 days. Consequently, the pre-carbonated cement paste (case 2) is more resistant to leaching than the initially sound one.

Experimental setup for laboratory tests

In order to study the effects of carbonation on the permeability and mechanical characterises of oilwell cement paste subjected to leaching and high temperature, four categories of samples obtained in the previous section were used to perform four types of laboratory tests: uniaxial compression tests, triaxial compression tests accompanied with permeability measurements, micro-indentation tests and coupled creep test. Additionally, by using SEM-EDS and Raman spectroscopy technology, the mineralogy and All the tests (except micro-indentation tests) were carried out by using an auto-compensated and auto-equilibrium triaxial cell system (Fig. 4). It is composed of a conventional triaxial cell and two fluid reservoirs which control the water pressure, respectively, on the lower and upper sides of sample. The axial displacement is measured by two LVDT in the cell while the lateral strain is measured with a strain ring. The confining pressure, deviatoric stress and fluid injection pressures (upstream and downstream) are, respectively, measured by four pressure sensors. The cell is installed in an oven, where a temperature of 90°C is kept.

Triaxial compression tests with permeability measurement

As indicated by Total, mean stress in an oilwell may be up to 20MPa. Therefore, confining pressure in the range of 0 MPa to 20 MPa is adopted to investigate the hydro-mechanical behaviour of cement paste under different levels of mechanical loading. In this section, four categories of cement paste (i.e. sound, Before the realisation of triaxial compression tests with permeability measurements, one group of preliminary permeability tests have been conducted on four initially sound samples (case 1) under Pc=3MPa. A mean value of permeability of 1.1×10 -18 m² was obtained with a standard deviation of 0.2×10 -18 m² (minimal value: 9.6×10 -19 m², maximal value: 1.4×10 -18 m²). One can observe that the dispersion of experimental results is extremely limited. Moreover, the permeability measurements take a long period of time, even up to 14 days. Therefore, only one permeability measurement has been performed for a given confining pressure. The experiment set up of triaxial compression tests accompanied with permeability measurement under the confining pressure Pc=3MPa is presented as follows:

I.

The sample was firstly put in a sheath of Viton® synthetic rubber and placed in the cell. The strain ring and LVDT were installed. The cell was heated up to 90°C during 24h in order to get a homogenous temperature in the cell.

II.

The sample was firstly subjected to an initial hydrostatic stress phase with a given confining pressure Pc=3MPa. Meanwhile, the fluid pressure of upstream reservoir was rapidly set to 2.5

MPa while the atmospheric pressure was kept in downstream area. The permeability was then measured after getting a stable flow.

III.

The valve of fluid exit was turned off to get a homogenate interstitial pressure (2.5MPa). A deviatoric stress was then applied and increased until the failure of studied sample to determine the triaxial compressive strength.

The permeability measurement was also performed under other confining pressures (0, 10 and 20MPa).

By applicating the Darcy's law, the permeability of studied material can be obtained by using the volumetric flow [START_REF] Takla | Effects of the Storage of CO2 on Multiaxial Mechanical and Hydraulic Behaviors of Oil-Well Cement[END_REF].

Coupled triaxial creep tests

The creep test aims to study the evolution of time-dependent deformation of pre-carbonated cement paste during the leaching and T= 90°C. To reduce the duration of laboratory test and get a first sight on the long-term deformation behaviour of studied material, an accelerated way is adopted in the present study: the ammonium nitrate (accelerated leaching) is used for leaching while a high deviatoric stress of 35 MPa is applied on the sample. This deviatoric stress is equal to 50% the failure strength of a carbonated sample at Pc= 3 MPa and very close to the failure strength of a leached carbonated sample at the same confining pressure.

In the triaxial creep test, one pre-carbonated sample (case 2) was installed in the same cell used for triaxial test (Fig. 4). The evolutions of axial deformation were recorded by two LVDT until the sample failure (about 2500 hours). At the beginning of the laboratory test, the sample was subjected to a hydrostatic stress of 3 MPa. After that, the deviatoric stress increased to 35MPa. While the mechanical loading was kept constant, the NH4NO3 solution (6 mol/l) was injected in the upstream reservoir with a fluid pressure of 2.5 MPa while an atmospheric pressure was found at the downstream side of studied sample. Moreover, in order to illustrate the influence of pre-carbonation on the time-dependent mechanical characteristics of cement paste subjected to leaching, this test will be compared with another creep test performed on sound sample [START_REF] Yurtdas | Etude experimentale du couplage entre le comprtement Thermo -Hydro -Mécanique et la dégradation chimique d'une pâte de ciment pétrolier[END_REF].

Micro-indentation tests

Micro-indentation is an appropriate and non-destructive method to identify the mechanical properties of geomaterial. In order to identify the material property at mesoscopic scale and verify the experimental results obtained on macroscopic scale (i.e. in uniaxial and triaxial compression tests), a series of microindentation tests were performed on these four types of cement paste.

A Micrope® indentation system was used in the present work. It is composed of a loading frame and a data acquisition system. The piston motor allows to ensure an exceedingly small load speed (about 1µm/min). The applied force is measured by a force sensor while the displacement is measured by two LVDT. Based on the preliminary tests, the round punch of 1 mm diameter is adopted with respect to the size of cement paste components.

The tested samples (Ø 20, H= 22 mm) were prepared under ambient temperature. The middle of the sample was cut transversely by a wire saw machine, parallel to its end-surfaces. To get a good parallelism between two extremities, a polishing machine, composed of a rotating disc with sandpaper (P800), was used. The obtained cross-section was mounted in a special mould and placed on the rotating disc. Two extremities of sample were then rectified while the parallelism was checked by using a vernier calliper. Finally, test points were chosen on two main axes of examined sample (Fig. 5).

The micro-indentation tests are presented in detail as follows. For a given cement paste, a series of preliminary tests were firstly realized to identify the yield strength of studied material. After that, an elastic test was then performed with the application of a mechanical load, which was smaller than the yield strength. Finally, the value of Young's modulus was calculated by using the slope of unloading line [START_REF] Ibrahim | Caractérisation des propriétés mécaniques des géomatériaux par technique de microindentation[END_REF]. However, due to the heterogeneity of cementitious materials, a large degree of scatter may be observed in the measurements [START_REF] Mason | Chemical and Mechanical Properties of Wellbore Cement Altered by CO2-Rich Brine Using a Multianalytical Approach[END_REF]. In view of this, for a given distance with respect to the sample centre, four measurement points are chosen to insure the reliability of experimental results (Fig. 5).

Fig. 5 Test points on the cross-section of sample

Results and discussions

The obtained experimental results are analysed and discussed in this section. A series of chemical equations are firstly presented to analyse the expected leaching effects on the evolution of composition of sound and pre-carbonated materials. Moreover, SEM-EDS and Raman spectroscopy results provide the additional information on the composition of the studied cement paste, in accordance with chemical equations. Finally, the effects of pre-carbonation on the permeability and mechanical (instantaneous or delayed) properties of cement paste subjected to leaching are discussed.

In the literature, the leaching of cementitious material has been largely discussed as well as the carbonation of cementitious material. However, the leaching of carbonated cementitious material under high temperature has been little investigated. In the laboratory tests, the use of concentrated ammonium nitrate solutions is an accelerated method to reproduce the degradation of cement-based materials by carbonic acid. The dissolution of ammonium nitrate can be written as:

NH4NO3 → HNO3 + NH3 (1)
The calcium carbonate reacts with nitric acid and forms calcium nitrate:

CaCO3 + 2HNO3 → Ca(NO3)2 + CO2 + H2O (2)
Therefore, the general equation for the leaching of carbonated cement paste can be written as follows:

CaCO3 + 2 NH4NO3 → Ca(NO3)2 + 2NH3 ↑+ CO2 ↑ + H2O (3)
The calcium nitrate Ca(NO3)2 is a soluble hygroscopic salt in the monohydrated state Ca(NO3)2.H2O , which is transformed into anhydrous form Ca(NO3)2 under high temperature.

On the other hand, the leaching of sound cement paste in ammonium nitrate induces a drop of pH and a decomposition of portlandite as well as a creation of the salt of calcium nitrate:

Ca(OH)2+ 2NH4NO3 → Ca(NO3)2 + 2NH3 ↑+2H2O (4)
By comparing the equations ( 3) and ( 4), the leaching of sound cement paste (Eq. 4) concerns principally the leaching of portlandite while in the carbonated sample, it is the calcium carbonate that is dissolved.

As the solubility of portlandite is of three orders of magnitude bigger than that of calcite, the leaching of portlandite is easier than that of calcium carbonate. This phenomenon can be used to explain the different in the leaching kinetics of sound and pre-carbonate cement pastes (Fig. 3). Additionally, one observes that the same chemical products are obtained in the samples with and without precarbonations. To confirm the previous results, SEM, EDS and Raman spectroscopy tests are also realized to analyse the evolutions of microstructure, chemistry and mineralogy.

Microstructure, chemistry and mineralogy analysis

The SEM images have been performed on two leached samples: a leached sound sample (case 3) after 5 days of leaching and a leached carbonated sample (case 4) after 10 days of leaching (Fig. 1). According to the position of leaching front (Fig. 3), similar leaching levels are attained in these two samples. By using a metal lathe (turning machine), two samples were cut to obtain a fresh plane surface. After that, the obtained specimens were firstly examined by environmental SEM (Fig. 6). One observes that the leached carbonated sample is more porous than the leached sound one. A preliminary conclusion will then be drawn: the pre-carbonation exhibits a protective effect against leaching at the micro-structure level.

After that, Energy-dispersive X-ray spectroscopy (EDS) is performed to investigate the relative constitution of two leached materials (cases3 and 4). For each sample, 3 or 4 measures have been performed at different locations by using different measurement sizes. The atomic percentages of different components are given in table 4. The standard deviation is also calculated to exhibit the variability of measurements. Even though EDS may be not sufficiently accurate to provide a quantitative proportion of light elements, the difference between two types of samples can still be observed by comparing the obtained carbon element. For instance, a quasi-negligible quantity of carbon (smaller than 1%) is observed in the leached sound sample (case 3) while the leached carbonated sample (case 4) presents about 6% of carbon. As calcium carbonate is the unique component in the cement paste containing the carbon element, one can conclude that there are still some calcium carbonates in the leached carbonated sample (case 4). Moreover, by comparing the nitrogen (N) quantity in two samples, it is noted that the quantity of calcium nitrate salt Ca(NO3)2 in the leached carbonated sample (Case 4) is slightly lower than that in leached sound material (Case 3). This phenomenon may be related to the low precision of SEM-EDS in the quantification of light elements (such as, N) and a more quantitative technique (for instance: Rama spectroscopy) will be required for the further confirmation. In conclusion, these observations tend to exhibit that calcium carbonate has not been totally consumed in the leached carbonated sample (case 4) and will be further verified by using Raman spectroscopy.

(a) (b) Fig. As the Raman spectroscopy is well known to be capable of identifying the evolution of mineral composition in cement paste, it is used here to study the effect of pre-carbonation on the leaching of cement paste. In this section, three types of samples (cases 2, 3 and 4) are studied by Raman spectroscopy analysis (Fig. 7). The carbonated sound sample (case 2) will be firstly studied and compared with two leached cases (cases 3 and 4). In the carbonated sample (case 2), the calcium carbonate is clearly observed with three peak values of 280.79, 710.99 and 1085.64 cm -1 while no calcium nitrate peak is observed due to the absence of leaching. On the other hand, the calcium nitrate peaks are clearly observed in two leached samples without or with pre-carbonation (cases 3 and 4).

Moreover, after leaching, the calcium nitrate peak in the initially sound sample (about 1050.79 cm -1 ) is slightly greater than that of pre-carbonated sample (about 1049.70 cm -1 ). These observations allow us to confirm the chemical discrepancies between two types of leached samples (Cases 3 and 4): more calcium nitrate salt is created in the leached sound sample (case 3). The mineralogy and chemistry analysis can help us understand the influence of pre-carbonation on the permeability and mechanical characteristics of cement paste subjected to leaching, which will be presented in the next section.

Permeability and compression strength

To understand the influence of pre-carbonation on the leaching process of the studied cement paste, permeability and compression strength of four types of cement paste will be studied in this section.

The permeability values are given in Table 3. In each case, the influence of confining pressure on the permeability evolution of cement paste is also analysed. In general, one observes that the permeability of studied material decreases when the applied confining pressure increases. For instance, in pre-carbonated samples, a permeability decrease of one order of magnitude is observed when the confining pressure increases from 3 to 20MPa. This observation is in accordance with previous works [START_REF] Pei | The effects of high temperature heating on the gas permeability and porosity of a cementitious material[END_REF]. Although only one sample is tested in the present study, the results of permeability could still be considered as a complementary indicator for the evolution of microstructure.

Case

Table. 3 Permeability for different types of cement paste

The leaching effects on the permeability of non-carbonated samples (cases 1 and 3) are then studied. The permeability of leached sound sample (case 3) is approximately one order of magnitude higher than that of sound sample (Case 1). For instance, under the confining pressure Pc=3MPa, the permeability of the leached sound sample (case 3) is equal to K=3.0×10 -17 m 2 while a permeability value of K=1.1×10 -18 m 2 is obtained in the sound sample (case 1). On the other hand, the leaching effects on two carbonated samples (cases 2 and 4) show that the permeability of leached carbonated sample (case 4) is approximately two orders of magnitude smaller than that of leached sound sample (Case 2). For instance, under the confining pressure Pc=3MPa, the permeability of the leached carbonated sample (case 4) is equal to K=3.0×10 -18 m 2 while a permeability value of K=4.9×10 -20 m 2 is obtained in the carbonated sound sample (case 2).

The influence of carbonation on the permeability of leached cement paste is also studied by comparing the permeability values of two leached samples (cases 3 and 4). The permeability value of the leached sound sample (case 3) is about 10 times greater than that of the leached carbonated sample (case 4). For instance, under Pc=3MPa, K=1.1×10 -17 m 2 in case 3 while K=1.1×10 -18 m 2 in the case 4.

After the leaching treatment, the permeability of pre-carbonation cement paste is always smaller than that of initially sound one: at least one order of magnitude under low confining pressure (Pc=3 and 10MPa) and a factor of 4 under Pc=20MPa. Therefore, one observes that the permeability decrease induced by the leaching is reduced by the pre-carbonation of cement paste.

Finally, the permeability values obtained on sound (case 1) and leached carbonated (case 4) samples are compared. One observes that the permeability values obtained in two cases are very close to each other and depend on the confining pressure. Under Pc=3Mpa, permeability of sound material (case 1) is twice that of the leached carbonated one (case 4) while almost the same values are obtained in these two cases under Pc=10MPa. Under Pc=20MPa, the permeability of case 1 is even smaller than that of case 4. One can observed that the effects of carbonation, which induces a decrease of permeability, are not totally cancelled by the leaching process. Again, this observation confirms the protective effect of the pre-carbonation against leaching of cement paste, in terms of permeability.

Compression strength

The obtained compression strength on four categories of samples is compared in Fig. 8. By comparing the results obtained in the samples with (cases 1 and 2) and without (cases 3 and 4) leaching, one observes that the leaching processes induce a decrease of material strength. For instance, by comparing the cases 1 and 3, a decrease of about 77% is observed in the leached sound samples (case 3)

with respect to the sound samples (case 1). Moreover, according to the carbonated samples (cases 2 and 4), a decreasing order of 55% is obtained in leached carbonated samples (case 4) versus the carbonated sound samples (case 2). One can observe that the decrease of mechanical strength created by the leaching is also weakened by the pre-carbonation of cement paste. The same remark is drawn by comparing the results of leaching sound (case 3) and leaching carbonated (case 4) samples: the failure strength of leached sound sample is about 79% of that of leached carbonated sample. Again, it is observed that the leaching effects of cement paste is offset by the carbonation.

Based on the SEM and Raman spectroscopy analysis, the observed difference between leached sound sample (Case 3) and leached carbonated sample (Case 4) can be explained by the fact that calcium carbonate in the carbonated sample has not been totally consumed by leaching (Table 2).

Therefore, a bigger mechanical strength and a smaller permeability are observed in the leached carbonated sample (case 4) with respect to the leached sound sample (case 3).

Creep deformation

As the long-term durability of oilwell also requires a good understanding of the effects of precarbonation on the time-dependent behaviour of cement paste during leaching, a coupled creep test is performed on the carbonated sound sample (case 2) with the injection of ammonium nitrate solution (6 mol/l). The evolution of axial deformation is shown in Fig. 9. The zero time corresponds to the beginning of chemical fluid injection. In the test, due to the injection of chemical fluid, the measured axial deformation increases progressively with the degradation of cement paste. After 1500 hours, a rapid increase of axial deformation is observed as an important part of sample is degraded. Afterwards, the deformation continues to increase until the sample failure, which is characterized by a rapid increase of deformation.

These observations are related to the fact that leaching creates an increase of porosity and a decrease of compressibility of studied material. Once the incompressibility becomes small enough, a sample compaction occurs and then a sudden change of axial deformation takes place. The sample failure is observed at 2500 hours.

In order to illustrate the effect of pre-carbonation on the creep behaviour of cement paste during leaching, the above test should be compared with the same test performed on initially sound material. As this test has been conducted in our laboratory, the triaxial creep test performed by Yurtdas et al. [START_REF] Yurtdas | Etude experimentale du couplage entre le comprtement Thermo -Hydro -Mécanique et la dégradation chimique d'une pâte de ciment pétrolier[END_REF] is used for the comparison. In the present work, we have used the same material and experimental conditions (leaching processes and mechanical loading) as them [START_REF] Yurtdas | Etude experimentale du couplage entre le comprtement Thermo -Hydro -Mécanique et la dégradation chimique d'une pâte de ciment pétrolier[END_REF]. Meanwhile, the applied deviatoric stress is equal to 50% failure strength of studied materials before leaching. Therefore, they have adopted a deviatoric stress of 16 MPa (50% of the failure strength of sound material at Pc= 3 MPa and T=90°C) while in the present work, the deviatoric stress of 35MPa (50% of the failure strength of pre-carbonated material at Pc= 3 MPa and T=90°C) is used.

Fig. 10 Evolutions of axial deformation in coupled creep tests for the pre-carbonated and sound samples [34] during leaching

The evolutions of axial deformations in pre-carbonated and sound samples are analysed (Fig. 10).

One can observe that the leaching of carbonated cement paste is 55 times slower than that of sound material: the total leaching of a pre-carbonated sample takes 2470 hours while it takes only 45 hours for a sound sample. Moreover, in the sound sample, more important deformation is observed at the end of leaching test: the sound sample is broken with an axial deformation of 24% while a maximum axial deformation of 1.5% is obtained in the pre-carbonated sample. Again, the carbonation exhibits a positive effect against leaching, regarding the time-dependent behaviour of cement paste: with respect to the sound sample, a smaller leaching rate and a small axial deformation are observed in the precarbonated sample.

Young's Modulus

In the present work, a series of micro-indentation tests have been performed to identify the hardness evolution of studied cement paste. According to a given distance from surface (i.e. 2, 6 and 10mm), four measurements are performed for each type of cement paste. One observes that the obtained values are very close to each other with a variation coefficient smaller than 9%. The low variability of measurements confirms the reliability of experimental program as well as a good sample preparation.

The mean values are presented in Fig. 11.

By comparing the obtained results of cases 1 and 2 (Fig. 11), it is observed that the carbonation induces an increase of Young's modulus. On the other hand, the leaching induces a stiffness decrease of order 63% by comparing the samples of Cases 1 and 3. These observations are coherent with the previous research [38,[START_REF] Li | Chemical Reactions of Portland Cement with Aqueous CO2 and Their Impacts on Cement's Mechanical Properties under Geologic CO2 Sequestration Conditions[END_REF]. Finally, the comparison of two leached samples (Cases 3 and 4) exhibits that after leaching, the stiffness of initially sound material is about 80% lower than that of pre-carbonated sample. Once again, it is observed that the carbonation exhibits a good protection of studied material against leaching. Moreover, the results obtained in micro-indentation tests confirm, at the mesoscopic scale, the experimental results of permeability and mechanical strength obtained at the macroscopic level.

As this study focuses on the related values of Young's modulus obtained on different types of samples, the values of Young's modulus obtained by micro-indentation tests will not be compared with those obtained by other methods in the literature.

Fig. 11 Values of Young's modulus obtained on four types of cement paste

Conclusions

In the present work, a series of experiment tests have been performed to characterize the effects of precarbonation on the hydro-mechanical properties of a G class cement paste subjected to leaching and high temperature T=90°C. Based on the experimental observations, the following conclusions can be obtained:

• SEM images show that after leaching, the initially sound material is more porous than the precarbonated one. EDS and Raman spectroscopy analysis exhibit that after leaching, the initially sound and pre-carbonated materials have the same chemical components. Moreover, their chemical proportion are very similar except the carbon (C), since calcium carbonate in the precarbonated sample has not been totally consumed by leaching.

• For the leaching kinetics, the leaching of pre-carbonated material is at least one order of magnitude slower than that of sound material. This observation can be explained by the fact that the solubility of portlandite presented in sound material is about three orders of magnitude bigger than that of calcite in pre-carbonated one. As a result, comparing with the initially sound material, a smaller axial deformation is created during the leaching of pre-carbonated material in the coupled creep test. • According to the permeability, after leaching treatment, the pre-carbonated cement paste is about one order of magnitude lower than that of initially sound material. This observation is due to the fact that the permeability evolution depends strongly on the initial carbonation state of sample, which controls the porous network (quantity, diameter and connectivity of pores).

• For the mechanical strength and Young's modulus, the Young's modulus of leached sound sample is equal to 79% of that of leached carbonated one while the failure strength of leached sound sample is about 80% of that obtained on the leached carbonated sample. The compression strength of leached carbonated sample is almost equal to that of initially sound one. The Young's modulus obtained at the macroscopic level is confirmed by the experimental results of micro-indentation tests, performed at the mesoscopic level.

In conclusion, a pre-carbonation plays a positive role against the leaching of cementitious material in view of the long-term durability of oilwell. In the near future, analysis of microtopography will be performed on different types of cement paste to analyser the dependence of permeability on the microstructure of studied materials. Experimental investigation, micromechanical analysis and microstructure will advance the understanding of long-term durability of CO2 geological storage.

Fig 1 .

 1 Fig 1. Schematic summary of the experimental program

Fig. 2

 2 Fig.2 Evolution of carbonation front in the carbonated sound samples (case 2)

Fig. 3

 3 Fig.3 Evolution of leaching front in two leched samples: (a) leached sound samples (case 3); (b) leached carbonated samples (case 4)

  ) 10 days (10 mm) chemistry was also conducted on three categories of samples (cases 2,3 and 4). Different types of laboratory tests performed on different categories of samples are summarised in Fig 1.

Fig. 4

 4 Fig. 4 Schema of triaxial cell system

  sound and leached carbonated samples) are studied under four different confining pressures Pc (0, 3, 10 and 20 MPa).

Fig. 7

 7 Fig. 7 Raman test performed on carbonated sound, leached sound and leached carbonated samples

Fig. 8

 8 Fig. 8 Evolution of compression strength in function of applied confining pressures

Fig. 9

 9 Fig. 9 Evolution of axial deformation over time (Pc= 3 MPa, T=90°C) for a pre-carbonated sample

Table . 1

 . Composition of the studied cement paste

		3 )
	Cement G class	1308.3
	Water	578.5
	D175 (antifoaming) 5.2
	D80 (dispersant)	8.1
	Water/Cement ratio 0.4

Chemical and mineral analysis

			Specimen preparation
	Laboratory tests			Specimen type
	1. Uniaxial compression test
	2. Triaxial compression test with permeability measurement 3. Micro-indentation test	Case 1: Sound	Case 2: Carbonated sound	Case 3: Leached sound	Case 4: Leached carbonated
	4. Coupled creep test
	SEM/Raman Spectroscopy

Table . 2

 . Atomic percentage of different components in two leached samples

		Chemical element	C	N	O	Mg Al	Si	S	Ca	Fe
	Leached Sound sample	Mean value (%)	0.75 11.91 65.02 0.70 1.03 4.74 1.21 13.85 0.79
	(case 3)	Standard deviation	0.55 1.13 2.06 0.17	1.02 1.05 1.66 1.25 0.82
	Leached carbonated sample	Mean value (%)	5.76 10.02 63.31 0.68 0.64 3.94 0.85 14.20 0.61
	(case 4)	Standard deviation	0.31 0.49 0.26 0.06 0.06 0.15 0.09 0.22 0.03

6. SEM images of two leached samples: (a) leached sound sample; (b) leached carbonated sample

Acknowledgments

The authors gratefully acknowledge Total for entrusting this study to the Coupled Thermo-Hydro-Mechanical-Chemical (THMC) team of the Laboratory of Mechanics, Multi-physics, Multi-scale (LaMcube), Lille -France, and for the permission to publish these results.

Compliance with Ethical Standards:

Funding: This study is funded by Total.

Conflict of Interest: The authors declare that they have no conflict of interest.