Namit Gaur

PhD Francis Ortega

PhD Arie O Verkerk

PhD Isabella Mengarelli

Trine Krogh-Madsen

PhD David J Christini

PhD Ruben Coronel

PhD Edward J Vigmond

Validation of quantitative measure of repolarization reserve as a novel marker of drug induced proarrhythmia

Keywords: Repolarization Reserve, Arrhythmias, Torsade de Pointes, human induced pluripotent stem cell cardiomyocytes (hiPSC-CM), All-or-None Repolarization, early afterdepolarization, repolarization failure

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

Introduction

Cardiac repolarization abnormalities can be caused by a large number of cardiac specific or nonspecific pharmaceutical compounds, as well as by genetic mutations [START_REF] Schwartz | Long-QT syndrome: from genetics to management[END_REF], pathologies (e.g. heart failure [START_REF] Coronel | Electrophysiological changes in heart failure and their implications for arrhythmogenesis[END_REF]) or dietary interventions [START_REF] Den Ruijter | Dietary fish oil reduces the occurrence of early afterdepolarizations in pig ventricular myocytes[END_REF]. Action potential (AP) prolongation can lead to life-threatening Torsade de Pointes (TdP) ventricular arrhythmia [START_REF] Dessertenne | Ventricular fibrillation and torsades de pointes[END_REF], whereas regional AP prolongation can contribute to the occurrence of unidirectional block and reentrant arrhythmia. Both mechanisms may deteriorate into ventricular fibrillation (VF) which is lethal.

The ability to maintain repolarization despite the inhibition of one or more repolarizing currents has been termed 'repolarization reserve' . This concept of repolarization reserve has been applied to understand the mechanisms that can lead to repolarization failure (RF). According to this concept, impairment of one particular repolarizing current does not necessarily result in RF due to the presence of other repolarizing currents. Drug effects on a specific repolarizing current (such as the rapid delayed rectifier K+ current (I Kr )) can result in arrhythmic AP prolongation abnormalities in hearts, especially when repolarization reserve is already compromised due to pharmacological, pathological, or preexisting congenital conditions (the Long QT Syndromes). However, no metric exists to quantify repolarization reserve.

In this paper, we demonstrate that repolarization is an all-or-none phenomenon which can be used to quantify repolarization reserve. Based on single cell computer simulations of various cell types, we show that repolarization has a clear threshold. We reproduce the phenomenon in several biological cell types, and introduce a novel, simple, fast and unambiguous, quantitative definition of repolarization reserve, called the repolarization reserve current (RRC). Finally, we show the utility of the metric by demonstrating how it identifies torsardegenic risk for several compounds and how it compares to the established but experimentally less easily applicable risk assessment metric qNet.

Methods

Repolarization Reserve Current

We propose a definition of Repolarization Reserve Current (RRC) as the minimum constant current injected into a single cell 4 ms after the upstroke that produced a repolarization abnormality. A repolarization abnormality was defined as one of the two following conditions occurring before the end of the constant current pulse: 1. A failure to complete repolarization (RF), or 2. An early afterdepolarization (EAD). The latter was defined as a polarizing inflection of membrane voltage with subsequent return to the resting membrane potential. RRC is defined in units of pA/pF.

Cell simulations

The Cardiac Arrhythmia Research Package (CARP) was used for all cell simulations [START_REF] Vigmond | Computational tools for modeling electrical activity in cardiac tissue[END_REF] . RRC was measured in several cellular models: rabbit ventricular cell models: Mahajan-Shiferaw (UCLA-RAB) [START_REF] Mahajan | A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates[END_REF], Shannon-Bers (SHB) [START_REF] Shannon | Potentiation of Fractional Sarcoplasmic Reticulum Calcium Release by Total and Free Intra-Sarcoplasmic Reticulum Calcium Concentration[END_REF]; canine ventricular cell model: Fox-Gilmour (FOX) [START_REF] Fox | Ionic mechanism of electrical alternans[END_REF]; human ventricular cell models: Grandi-Bers (GPB) [START_REF] Grandi | A novel computational model of the human ventricular action potential and Ca transient[END_REF], ten Tusscher-Panfilov (TT1) [START_REF] Ten Tusscher | A model for human ventricular tissue[END_REF], O'Hara-Rudy (ORd) [START_REF] O'hara | Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation[END_REF]; human atrial cell models: Courtemanche-Nattel (CM) [START_REF] Courtemanche | Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model[END_REF], Nygren-Wiles (NYG) [START_REF] Nygren | Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization[END_REF]; guinea-pig ventricular cell model: Luo-Rudy (LRD) [START_REF] Luo | A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes[END_REF]; and hiPSC-CMs [START_REF] Paci | Computational Models of Ventricular-and Atrial-Like Human Induced Pluripotent Stem Cell Derived Cardiomyocytes[END_REF]. ORd and atrial and ventricular hiPSC-CM models were used for further analysis of the RRC concept. To prevent spontaneous activity in hiPSC-CMs, I K1 conductance was increased 4-fold in atrial and 1.5-fold in ventricular hiPSC-CM cell models. All cell models were paced to steady-state at a fixed cycle length (CL=1000 ms) before analysis. For bradycardia simulations shown in Fig. 1, a CL=2000 ms was used.

Drug simulations

The effects of 12 CiPA training compounds were simulated using a conductance-block model of drug block. In this model, conductance of the ion channel targeted by drug is reduced as a function of IC 50 value and drug concentration (denoted by [D]).

𝐺 = 𝐺

𝑐𝑜𝑛𝑡𝑟𝑜𝑙 [1 + ( [𝐷] [𝐼𝐶 50 ] ) ℎ ] -1
where, G control is the maximal conductance of the channel. The 12 compounds are: quinidine, bepridil, dofetilide, sotalol (representing high risk TdP drugs), chlorpromazine, cisapride, terfenadine, ondansetron (representing intermediate risk TdP drugs), diltiazem, mexiletine, ranolazine, and verapamil (representing low risk TdP drugs). In simulations, the drug concentrations were varied between 0.5-25 times C max , the maximum effective therapeutic free plasma concentration. The values of IC 50, Hill coefficient h, and C max were taken from Dutta et al [START_REF] Dutta | Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment[END_REF].

Recently, a metric called qNet has been shown to be a suitable metric to predict TdP risk over a range of drugs and concentrations in in silico studies [START_REF] Dutta | Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment[END_REF]. Using the ORd ionic model [START_REF] O'hara | Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation[END_REF], qNet is the sum-total of charge over the action potential as carried by six major ionic currents: late Na + (NaL), L-type Ca 2+ (CaL), transient outward (to), rapid delayed rectifier K + (Kr), slow delayed rectifier K + (Ks), and inward rectifier K + (K1). It is calculated as

𝑞𝑁𝑒𝑡 = ∫ (𝐼 𝑁𝑎𝐿 + 𝐼 𝐶𝑎𝐿 + 𝐼 𝑡𝑜 + 𝐼 𝐾𝑟 + 𝐼 𝐾𝑠 + 𝐼 𝐾1 ) 𝐴𝑃 𝑑𝑡

Experiments

The study was approved by the Medical Ethics Committee of the Amsterdam UMC, location AMC, and the University Medical Center Göttingen (Az 21/1/11). Written informed consent was obtained from the adult healthy individual from whom the hiPSC line was generated.

Guinea-pig ventricular cardiomyocytes and hiPSC-CMs preparations

Guinea-pigs (n=5) were first anesthetized using a lethal intraperitoneal injection of Fatal Plus (Vortech Pharmaceuticals, MI, USA), 1.5 mL/kg. After removal, hearts were retrogradely perfused with Langendorff apparatus and myocytes were isolated from the left ventricle by enzymatic digestion using Liberase TL (Roche, Basel, Switzerland). For electrophysiological measurements, cells were placed on coverslips previously coated with 0.1% poly-L-lysine solution for 15 minutes. Quiescent, rod-shaped cross-striated cells with smooth surface were selected for measurements. Further details are mentioned in [START_REF] Groenendaal | Cell-specific cardiac electrophysiology models[END_REF].

hiPSC-CM Human inducible pluripotent stem cells (hiPSC) [START_REF] Dudek | Cardiolipin deficiency affects respiratory chain function and organization in an induced pluripotent stem cell model of Barth syndrome[END_REF] were differentiated into cardiomyocytes using a small molecule-based protocol in chemically defined medium and serum-free conditions as described previously [START_REF] Lian | Directed cardiomyocyte differentiation from human pluripotent stem cells by modulating Wnt/$-catenin signaling under fully defined conditions[END_REF]. Enrichment of hiPSC-CMs was accomplished by glucose-depleted culture medium containing 4 mmol/L lactate during day 20-26 of differentiation [START_REF] Tohyama | Distinct Metabolic Flow Enables Large-Scale Purification of Mouse and Human Pluripotent Stem Cell-Derived Cardiomyocytes[END_REF]. For electrophysiological experiments, hiPSC-CM cultures were enzymatically dissociated into single cells and plated at a low density on Matrigel-coated coverslips for 10-12 days [START_REF] Meijer Van Putten | Ion channelopathies in human induced pluripotent stem cell derived cardiomyocytes: a dynamic clamp study with virtual IK1[END_REF]. Previous experiments using these protocols and hiPSC-CM line demonstrated that the vast majority of the cells had a ventricular AP morphology [START_REF] Veerman | hiPSC-derived cardiomyocytes from Brugada Syndrome patients without identified mutations do not exhibit clear cellular electrophysiological abnormalities[END_REF]. To increase the amount of hiPSC-CMs with an atrial AP morphology, 1 µmol/L retinoic acid (Sigma) was added from day 4 to 7 of differentiation. For electrophysiological measurements, we selected spontaneously beating hiPSC-CMs (<1 Hz) which allows overdrive stimulation at a fixed stimulus rate of 1 Hz [START_REF] Verkerk | Patch-Clamp Recording from Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes: Improving Action Potential Characteristics through Dynamic Clamp[END_REF].

Biological Experimental Methods

Electrophysiology

APs were measured at 37°C using the perforated patch-clamp technique with an A-M Systems (Sequim, WA, USA) model 2400 patch-clamp amplifier and an Axopatch 200B amplifier (Molecular Devices, Sunnyvale, CA, USA) for guinea-pig and hiPSC-CMs, respectively. Data acquisition and amplifier control was accomplished using RTXI (rtxi.org; guinea-pig) or custom software (hiPSC-CMs). Extracellular Both atrial and ventricular hiPSC-CMs are frequently depolarized, often exhibit a decreased (less negative) maximum diastolic potential [START_REF] Verkerk | Patch-Clamp Recording from Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes: Improving Action Potential Characteristics through Dynamic Clamp[END_REF]. We used dynamic clamp (for review, see [START_REF] Ortega | Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing[END_REF]) to inject an in silico 4 A/F I K1 with a K ir 2.1-like current-voltage relationship [START_REF] Meijer Van Putten | Ion channelopathies in human induced pluripotent stem cell derived cardiomyocytes: a dynamic clamp study with virtual IK1[END_REF] [START_REF] Verkerk | Patch-Clamp Recording from Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes: Improving Action Potential Characteristics through Dynamic Clamp[END_REF] to obtain close-to-physiological resting membrane maximum diastolic potentials and to prevent spontaneous activity during the RRC stability test.

Repolarization reserve current measurement and stability test

Data acquisition and experimental protocols were performed using a customized module for the Real-Time eXperimental Interface (RTXI) [START_REF] Patel | Hard real-time closed-loop electrophysiology with the Real-Time eXperiment Interface (RTXI)[END_REF]. RRC magnitude was measured through a threshold protocol, where a post-stimulus current was injected every third stimulation during 1 Hz pacing. With stepwise increments of 10 and 2 pA for guinea-pig and hiPSC-CMs respectively, the current was increased until a large (> 40%) change in APD was detected when compared to previous post-stimulus injection. The value of the current increment was lower in hiPSC-CMs because C m is approximately 5-6 times smaller in hiPSC-CMs (see below). After RRC measurement, a randomized protocol to test stability of RRC was performed during a 100-beat protocol at 1 Hz pacing. During every third beat of this protocol, there was a 50% chance of application of a post-stimulus current, which would either be sub (10% below RRC) or supra (10% above RRC) RRC. The threshold level of ± 10% was chosen as the minimum percentage change of RRC where clearly different AP morphology would be experimentally observed, i.e., normal versus abnormal repolarization.

Data analysis

MATLAB scripts were used to calculate AP metrics. R scripts were used to construct data plots. Due to less negative resting membrane potential during post-stimulus current injections, APD was calculated as a return to 50% repolarization (APD 50 ). An APD 50 value of CL during current injection was defined as RF.

Statistics

Data are presented as mean ± S.E.M. Two groups were compared with unpaired t-test or repeated measures ANOVA followed by pairwise comparison using the Student-Newman-Keuls test. P<0.05 was considered statistically significant.

Results

Simulation studies

Species differences of Repolarization Reserve Current. Simulations

The protocol for the determination of RRC is shown in Fig 1A . In this example using ORd with a CL of 2000 ms, an inward current greater than 0.7 pA/pF causes an EAD. This current was defined as the repolarization reserve current (RRC) for that particular cell and CL. The normal AP at CL=2000 ms is indicated in green.

To test the generality of the concept of determination of RRC, we applied the technique of measurement of RRC to several ionic cell models. In all these models of different species and heart regions, there was a threshold of injected current that led to repolarization abnormalities. The composite results of these numerical experiments are presented in Fig 1B.

Ionic mechanisms of repolarization abnormalities

The ionic mechanisms underlying the development of repolarization abnormalities during a human [START_REF] O'hara | Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation[END_REF]. However, in that case, the initial charge carrier for EAD was I CaL as it recovers from inactivation. Here the initial charge carrier is I inj .

Moreover, here the membrane potential reversed polarity at -55.5 mV, a voltage at which I CaL is fully recovered from inactivation.

RRC calculations

Biological studies

Typical superimposed APs with increasing amount of injected current and eventual repolarization failure are shown in a ventricular (Figure 3A) and an atrial hiPSC-CMs (Figure 3B). A boxplot of RRC of all cells is shown in Figure 3C. The repolarization reserve is significantly higher in atrial-like hiPSC-CMs. On average, RRC is 1.34±0.11 pA/pF in atrial (n=8) and 0.84±0.09 pA/pF in ventricular (n=8) cells. Next, we analyzed the AP repolarization rate (dV/dt) as a function of membrane voltage in ventricular and atrial hiPSC-CMs (Figure 3D). Atrial-like hiPSC-CMs have a significantly higher repolarization rate at -30 mV, more positive potentials, and repolarization rate correlates with RRC (p=0.0002).

We next studied whether the RRC depends on cell size and APD. Figure 4A shows the RRC in pA versus the capacitance of ventricular (left panel) and atrial (right panel) hiPSC-CMs. In both cell types there is a clear correlation (p=0.00004; ventricular, p=0.00006; atrial). Figure 4B shows the RRC (in pA/pF) versus the capacitance and no correlation (p=0.02465; ventricular, p=0.62479; atrial) is observed, indicating that RRC (in pA/pF) is unrelated to cell size. Figure 4C shows that there is no clear relation (p=0.04064;ventricular, p=0.84536; atrial) between the APD 50 vs RRC. In guinea-pig cells, no correlation was found between the RRC (in nA) versus the capacitance (p=0.48872), and the APD 50 vs RRC (p=0.91129) (Figure 4D).

Risk level stratification of CiPA training compounds

We compared the RRC and the q Net metric over a range of drug doses ranging from 0.5 to 25 times C max , the maximum plasma clinical drug exposure, in a simulation study. ORd model and human iPSC-CMs models (atrial and ventricular [START_REF] Paci | Computational Models of Ventricular-and Atrial-Like Human Induced Pluripotent Stem Cell Derived Cardiomyocytes[END_REF]) were used. Figure 5 shows RRC and q Net as a function of C max for drugs in high (indicated by red), intermediate (indicated by blue) and low (indicated by green) risk categories. The RRC and q Net metrics have very similar capabilities in classifying the 12 drugs tested into low, intermediate and high risk levels, although several misclassifications occurred. For example, chlorpromazine and mexiletine display a different order of repolarization reserve metric in the human ventricular cell model. Importantly, while q Net is limited to computational studies, RRC can be used to test drugs experimentally. In the computational study, RRC and q Net are highly correlated (Figure 6) in each of the models of human ventricular cell (R=0.99), iPSC human atrial cell (R=0.98) and iPSC human ventricular cell (R=0.94). Three drugs in each of the low (Diltiazem), intermediate (Chlorpromazin) and high (Bepridil) TdP risk categories is shown.

Effect of Drugs on RRC

In a final set of experiments, we tested the effects of I CaL and I Kr blockade on the RRC in ventricular like hiPSC-CMs. Pre-incubation with 100 nmol/L nifedipine, to block ~50% I CaL [START_REF] Eroglu | Differential effects on out-of-hospital cardiac arrest of dihydropyridines: real-world data from population-based cohorts across two European countries[END_REF] resulted in a significantly higher RCC, while pre-incubation with 100 nmol/L E-4031, almost complete block of I Kr [START_REF] Gibson | Human stem cellderived cardiomyocytes detect drug-mediated changes in action potentials and ion currents[END_REF], resulted in a significantly lower RRC (Figure 7). In this case, shortening of APD was associated with a higher RRC, while longer APDs were associated with a lower RRC.

Discussion

This study shows that RRC is a stable, fast, simple and reproducible metric that can be obtained from a single cell and that has significant heterogeneity between cells. It is a straightforwardly obtained metric to quantify repolarization reserve, and it can identify drug effects in simulation studies that may lead to TdP (Figure 5). We show that RRC is not necessarily correlated to APD prior to current injection within a cell population. The RRC was also measured in biological models (hiPSC-CM) of ventricular and atrial cells showing a high degree of similarity with the simulations.

We have demonstrated, for the first time, that prolonged repolarization leads to an all-or-none phenomenon for depolarizing current injection. We exploited this property to develop a new measure for quantifying repolarization reserve. To quantify this reserve, we added the critical constant inward current from the beginning of the AP leading to repolarization abnormalities. We then verified the procedure in real myocytes using guinea-pig ventricular myocytes and atrial and ventricular hiPSC-CMs.

Weidmann has shown that applying outward currents during the plateau to induce premature repolarization was an all-or-none phenomenon [START_REF] Weidmann | Effect of current flow on the membrane potential of cardiac muscle[END_REF]. We have applied inward current (of opposite polarity) during the plateau to prevent repolarization. APD prolongation was associated with increased current amplitude up to the point at which either RF or an EAD occurred (Figure 1E). Thus, any arbitrary APD cannot be obtained by adjusting the magnitude of the injected current in steps as small as 0.01 pA/pF. Therefore, for all practical purposes, there exists a point of discontinuity where the current either causes an EAD or RF, and APD increases abruptly, consistent with an all-or-none repolarization.

We then demonstrated that RRC is reproducible and stable. Most cells responded consistently to the application of sub-and supra-RRC currents (Figure 2C). In a small number of cells, however there was a single error event that did not correspond to the expected stimulus response. These single events may be attributed to beat-to-beat variations in the cell or transient environmental factors. If there were more than one error, the errors were always consistent for each cell. This suggests a slower change in the cell state, rather than a beat-to-beat variation, was responsible. These changes could be due to many possible mechanisms, such as the opening of I KATP channels in response to increased ADP or a change in Ca 2+ kinetics leading to reduced inward Ca 2+ currents.

Prediction of drug-induced Torsade de Pointes

In multicellular models, electrotonic loading may cause portions of the tissue to act as current sinks, therefore decreasing the total amount of current available for repolarization. If current received by a sink is greater than the RRC, RF/EAD may occur that can lead to the formation of TdP. This has been demonstrated in simulations where reduced repolarization reserve by 50% I Kr block led to the formation of microreentry circuits between intramural endocardial-epicardial layers [START_REF] Dutta | Early afterdepolarizations promote transmural reentry in ischemic human ventricles with reduced repolarization reserve[END_REF]. Therefore, a tissue substrate with higher repolarization reserve may prevent electrotonically-triggered EADs. The RRC metric is a measure for the arrhythmogenic propensity of the underlying tissue substrate.

The prediction of drug-induced TdP is an unresolved issue in drug development. The current TdP surrogate markers, i.e., I Kr block and QT prolongation are nonspecific and prevent the development of efficacious, nontorsadegenic drugs [START_REF] Turner | Drug-induced Proarrhythmia and Torsade de Pointes: A Primer for Students and Practitioners of Medicine and Pharmacy[END_REF]. Therefore, the comprehensive in-vitro proarrhyhmia assay (CiPA) was proposed as a paradigm to assess drug TdP risk. The paradigm combines drug effects on multiple ion channels in vitro with in-silico modeling of drug effects on the human ventricular myocyte model, ORd [START_REF] Sager | Rechanneling the cardiac proarrhythmia safety paradigm: A meeting report from the Cardiac Safety Research Consortium[END_REF].

Recently, it was shown that a simulated net charge based metric (q Net ) enables good classification of 12 CiPA training compounds into their known risk categories over a range of drug concentrations [START_REF] Dutta | Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment[END_REF]. This metric relies on summing the charge provided by six major currents over a cycle length. Given that a cell that returns to its resting level undergoes a net voltage change of zero, the total amount of charge that is introduced into the cell over the cycle length must be zero. Therefore, q Net can also be viewed as the negative of the amount of charge not carried by the six major currents, and its applicability is less clear. Moreover, q Net is expected to be model-dependent and a function of cell type. This was evident in our simulations which showed near zero values of q Net in ORd but an order of magnitude higher in human hiPSC-CM models. This difference could be due to the presence of significant amount of hyperpolarization-activated funny current (I f ) in hiPSC-CMs but not in human ventricular cells.

On the other hand, RRC was of same order of magnitude across different cell types (Figure 1B, Figure 5).

Experimentally, it would be extremely difficult to measure q Net as it would require applying six highly specific channel blockers. Furthermore, the RRC takes whole-cell dynamics into account rather than only a selected group of ion currents. Although this is more straightforward and takes the net current into account our approach has the disadvantage that potential novel critical repolarizing currents are overlooked and the risk of TdP is underestimated. However, this is also the case by applying the q Net technique. Our simulations indicate that RRC metric is at least as good as q Net in classifying the risk levels of known drugs that carry risk for TdP. Importantly, while q Net is limited to computational studies, RRC can be used to test drugs experimentally and is simple to measure.

Recently, Varshneya et al [START_REF] Varshneya | Slow Delayed Rectifier Current Protects Ventricular Myocytes From Arrhythmic Dynamics Across Multiple Species: A Computational Study[END_REF] examined how I Ks and I Kr changed the arrhythmia dynamics across several species. They considered several different ionic models and used I CaL perturbations, which they acknowledged to be problematic since the baseline differed between models. RRC could have been used, and has the advantage that it does not need to be normalized between models. Also, changes in RRC reflect changes in developing arrhythmias.

Tissue Level Arrhythmogenesis

In multicellular models, electrotonic loading may cause portions of the tissue to act as current sinks, therefore decreasing the total amount of current available for repolarization in the source region. For example, if a region has a lower plateau potential than that of an adjacent region, it will act as an intracellular current sink. If current received by the sink is greater than its RRC, RF/EAD may occur that can lead to the formation of TdP. This has been demonstrated in simulations where reduced repolarization reserve by 50% I Kr block led to the formation of microreentry circuits between intramural endocardial-epicardial layers [START_REF] Varshneya | Slow Delayed Rectifier Current Protects Ventricular Myocytes From Arrhythmic Dynamics Across Multiple Species: A Computational Study[END_REF]. Therefore, a tissue substrate with higher repolarization reserve may prevent electrotonically-triggered EADs. The RRC metric is a measure for the arrhythmogenic propensity of the underlying tissue substrate.

Future studies may help characterize the relationship between RRC and propensity for conduction block.

With some basic tissue measurements and RRC, it may be possible to formulate a more precise metric for ease of inducing reentrant arrhythmia.

Advantages

RRC can give a quantitative measure of the importance of a channel for repolarization for cells which are not fully characterized, as well as give as indication of how susceptible a tissue is to repolarization-induced arrhythmia. Because RRC is a simple functional metric, it can be measured in cardiac cells with a straightforward protocol without the need to apply channel blockers. Because it does not rely on any particular channel currents, it can be calculated for any species or for any genetic mutation. The latter is important given that mutant channels may behave quite differently and their contribution to repolarization may not be straightforward to determine. RRC is determined by a global, functional behavior, and can be followed by specific characterization of individual channels contributing to reduced repolarization reserve. By using hiPSC atrial and ventricular cardiomyocytes, we showed that the screening method works for personalized therapies using cells derived from the patient.

Relation with APD

It has been suggested that a reduced repolarization reserve is equivalent to prolonged repolarization [START_REF] Roden | Taking the "idio" out of "idiosyncratic": predicting torsades de pointes[END_REF]. We show that RRC is not always correlated to APD prior to current injection. Second, it implies that indeed between patients with the same QT interval, different arrhythmia risks may exist, and that patients with highly different QT intervals may not be at different risks of arrhythmias [START_REF] Milberg | Divergent Proarrhythmic Potential of Macrolide Antibiotics Despite Similar QT Prolongation: Fast Phase 3 Repolarization Prevents Early Afterdepolarizations and Torsade de Pointes[END_REF]. From a mechanistic point of view this observation implies that two sections of the heart can be prone to EADs and arrhythmogenesis while their APD is not the same, or that two cardiac regions have the same APD but a different risk of EADs.

Conclusion

Repolarization is an all-or-none phenomenon. RRC constitutes a straightforward and easy to implement method to quantify repolarization reserve. The method can be used in high throughput applications.

Figure captions

Highlights

 Repolarization is an all-or-none phenomenon  The threshold current preventing repolarization (RRC) defines its reserve  RRC was measured in many types of simulated and biological cells  RRC can be used to screen drugs for arrhythmogenicity  RRC has no requirement of prior knowledge of underlying ionic currents

  solution containing (in mmol/L): 137 NaCl, 5.4 KCl, 2 CaCl 2 , 1 MgSO 4 , 10 HEPES, and 10 glucose, with pH 7.35 (NaOH). Patch pipettes (borosilicate glass; 2-3 MΏ) were filled with solution containing (in mmol/L): 136 KCl, 10 NaCl, 10 CaCl 2 , 5.5 glucose, 0.5 MgCl 2 , 11 KOH, 10 HEPES, 0.52 Amphotericin B, with pH 7.1 (HCl) and osmolality 295 mmol/kg. Total membrane capacitance (C m ) was measured by integrating the area under the capacitance current transients during the average of 500 voltage pulses (10 mV/20 ms) at -80 mV for guinea-pig or by dividing the time constant of the decay of the capacitive transient in response to 5 mV hyperpolarizing voltage clamp steps from -40 mV by the series resistance for hiPSC-CMs. Adequate access for current clamp experiments was defined by a resistance below 50 MΏ. RRC was measured in 29 guinea-pig cardiomyocytes and 16 hiPSC-CMs. Accuracy of C m is reliant on low access resistance, thus guinea-pig cells with an access resistance above 20 MΏ (6/29) were not included in metrics dependent on C m . Prior to any experimental protocol, cardiomyocytes were paced for a minimum of 200 beats at 1 Hz stimulation with 3 ms, 1.2X threshold current pulses through the patch pipette to minimize transient behavior.

  AP in the ORd model, are investigated next. During the unperturbed AP (AP in Fig 1A, green), the major repolarizing currents are I to during phase 1, I Kr in phase 2 and I K1 in phase 3 (Fig 1C). The largest depolarizing currents are I CaL and I NaL . Other currents are also shown (Na + -K + pump current (I NaK ), Na + -Ca 2+ exchanger current (I NaCa ) and I Ks ). During the repolarization reserve protocol, the human AP is significantly prolonged (Fig 1A; red). With an injected current of 0.7 pA/pF, at t=882 ms, the inward injected current (I inj ) is larger than the net ionic current (sum total of all depolarizing and repolarizing currents; I Net ; indicated by dashed line) excluding I inj (Fig 1D). The I net (=0.698 pA/pF) at this time is primarily due to outward I Kr and I K1 with minor contributions from outward I NaK and inward I NaCa . The AP reverses direction at -55.5 mV (Fig 1A), with I inj providing inward current for depolarization. Upon depolarization to -40 mV, I CaL begins to reactivate and provides the upstroke of the EAD. Thus, the initial charge carrier for the EAD was I inj and I CaL reactivation occurred secondary to it. In this case, the repolarization abnormality (in the form of EAD) occurred because the I inj current exceeded I Net determined by I Kr and I K1 (with minor contribution from I NaK ) at -55.5 mV. Note that the magnitude of I inj (-0.7 pA/pF) is large and dominates all the major plateau phase currents. APD is a threshold function of injected current (Fig 1E). Thus, once the injected current exceeds the RRC (0.7 A/F), APD increases significantly from 942 ms (at I inj =0.69 pA/pF) to 2018 (at I inj =0.71 pA/pF) ms. Reactivation of I CaL was also shown to cause EADs when blocking I Kr

Fig

  Fig 2A shows the protocol for measurement of RRC. The injected current is first increased until repolarization abnormalities (either RF or EAD) occur to determine RRC. Then, a stability test is performed,

Figure 1 .

 1 Figure 1. Quantification of repolarization reserve (RR). (A) Protocol to define RR. Constant current is

Figure 2 .

 2 Figure 2. RR iin guinea-pig ventricular myocytes. (A) Typical example of RRC measurement in a biological guinea-pig cardiomyocyte with APs (top) and injected currents (bottom). Every third beat, the cell is injected

Figure 3 .

 3 Figure 3. RR in human-induced pluripotent stem cell cardiomyocytes (hiPSC-CMs). Typical APs in a ventricular (A) and an atrial hiPSC-CM (B) with injected constant current of increasing magnitude until RF

Figure 4 .

 4 Figure 4. Heterogeneity of RRC in guinea-pig ventricular myocytes and human iPSC cells. (A) RRC (in pA) and membrane capacitance (C m ) show positive correlations in ventricular (p=0.00004) and atrial iPSC cells (p=0.00006). (B) When RRC is expressed in pA/pF, there is no correlation (p=0.02465) with C m . (C) APD 50 has a weak correlation (p=0.04064) with RRC in ventricular and no correlation (p=0.84536) in atrial iPSC cells with RRC. (D) RRC (pA) vs membrane capacitance in guinea pig shows no correlation

Figure 5 .

 5 Figure 5. RRC and q Net for the 12 CiPA training compounds for a range of doses (0.5-25x C max ) at 2000 ms cycle length (CL) in human ventricular (A), human iPSC atrial (B) and human iPSC ventricular (C) cell

Figure 6 .

 6 Figure 6. RRC and q Net is highly correlated in (A) human ventricular cell model (R=0.99) (B) human iPSC atrial cell model (R=0.98) and (C ) human iPSC ventricular cell model (R=0.94). One drug from each of the

Figure 7 .

 7 Figure 7. Effect of drugs on action potential duration (APD) and repolarization reserve current (RRC) in

Figure 4

 4 Figure 4

Figure 6

 6 Figure 6

Figure 7

 7 Figure 7

This study received financial support from the French Government as part of the "Investments of the Future" program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04 This project has received funding from the Fondation Leducq (Research Grant number 16 CVD 02)


Nicolas C M Marty
email: n.marty@brgm.fr

Virginie Hamm

Christelle Castillo

Dominique Thiéry

Christophe Kervévan

Modelling water-rock interactions due to long-term cooled-brine reinjection in the Dogger carbonate aquifer (Paris basin) based on in-situ geothermal well data

Keywords: geothermal doublet, porosity, Dogger aquifer, water-rock interaction, geochemical modelling, sonar

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

Introduction

Located at a depth of 1500-2000 m, the carbonate Dogger reservoir is the main geothermal aquifer exploited in the Paris region of France. This geothermal resource heats approximately 210,000 dwellings in the Ile-de-France region [START_REF] Hamm | Assessment of complex well architecture performance for geothermal exploitation of the Paris basin: A modeling and economic analysis[END_REF] (100-350 m 3 h -1 ) and typically varies between 40 and 60 °C with a minimum temperature of 35 °C. All geothermal operations from the 1970s to 1990s operated according to this principle [START_REF] Lopez | 40 years of Dogger aquifer management in Ile-de-France[END_REF]; however, more recent geothermal operations conducted in the Dogger aquifer employ a heat pump (e.g. Arcueil-Gentilly, Bagneux, Neuilly-sur-Marne, etc.) to optimise the available geothermal resource, resulting in a lower return temperature. This implies that reinjection of cooled brines at the Dogger aquifer occurs at lower temperatures (approximately 25 °C) than previously [START_REF] Cordier | Modélisation numérique d'un doublet géothermique exploitant le Dogger dans le secteur de Bagneux dans le cadre de l'étude de faisabilité d'un doublet géothermal mise en oeuvre par le SIPPEREC[END_REF].

To date, the majority of studies on the thermal effect on Dogger formation geochemistry have focused on the hydro-geochemical impact of the reinjection of hot fluids into the aquifer from the perspective of heat storage [START_REF] Castillo | Physico-chimie et réactivité des fluides du Dogger du Bassin Parisien soumis aux conditions de stockage de chaleur[END_REF][START_REF] Gille | Suivi et modélisation du comportement hydro-géochimique du Dogger, soumis à la réinjection de fluides « chaud » et « froid[END_REF]. Only a few studies have quantified the hydrogeochemical impact of cooled-fluid reinjection in a carbonate aquifer [START_REF] Borozdina | Thermochemical modelling of cooled brine injection into low enthalpy sedimentary reservoirs[END_REF][START_REF] Nick | Mixed CO2-Water Injection Into Geothermal Reservoirs: A Numerical Study[END_REF][START_REF] Wong | Reactive Transport Modelling of Injection Fluid-Reservoir Rock Interaction[END_REF]. Geothermal energy production in the carbonate Dogger formation began in the early 1970s in the Paris basin [START_REF] Lopez | 40 years of Dogger aquifer management in Ile-de-France[END_REF]. The typical lifetime of a geothermal doublet is approximately 30 years (duration of the initial operating permits); therefore, as older wells are shut down, new wells are commissioned. Thus, bottom-hole analysis of former injection wells could allow us to observe and quantify the effects of potential water-rock interactions induced by cooled-brine reinjection, especially in a carbonate aquifer such as the Dogger. Unfortunately, most of these wells were plugged when the abandonment procedure was completed and are thus inaccessible. However, as part of the CO2-DISSOLVED project and through collaboration with the local geothermal operator (Chelles Chaleur, subsidiary of the Coriance group), the unique opportunity was granted to access the open-hole part of a former injection well in Chelles (Paris basin, France). This injector was utilised for 24 years from 1986 to 2010 but remains accessible as a backup injection well for the current geothermal doublet. An in-situ experimental campaign was conducted in March 2016 to analyse the reservoir geometry at the well outlet using an innovative sonar tool provided and operated by Flodim (Cavity Survey and Well Logging Services Company, https://www.flodim.fr/).

The results of this study will aid our understanding of water-rock interactions at the well outlet, which is a major concern of the CO2-DISSOLVED project (http://co2dissolved.brgm.fr/). CO2-DISSOLVED is an innovative carbon capture and storage (CCS) concept involving the capture, injection, and storage of dissolved CO2 (rather than supercritical) in a deep saline aquifer coupled with geothermal heat recovery [START_REF] Kervévan | CO2-DISSOLVED: a Novel Concept Coupling Geological Storage of Dissolved CO2 and Geothermal Heat Recovery -Part 1: Assessment of the Integration of an Innovative Low-cost, Water-based CO2 Capture Technology[END_REF][START_REF] Kervévan | CO2-Dissolved: A novel approach to combining CCS and geothermal heat recovery[END_REF][START_REF] Kervévan | Main results of the CO2-DISSOLVED project: First step toward a future industrial pilot combining geological storage of dissolved CO2 and geothermal heat recovery[END_REF]. Once out of the injection well, the acidified brine is expected to be chemically reactive with the reservoir porous matrix, particularly in the presence of carbonate minerals [START_REF] Castillo | Reactive Transport Modelling of Dissolved CO2 Injection in a Geothermal Doublet. Application to the CO2-DISSOLVED concept[END_REF][START_REF] Gray | Chemical mechanisms of dissolution of calcite by HCl in porous media: Simulations and experiment[END_REF][START_REF] Snippe | Experimental and numerical investigation of wormholing during CO2 storage and water alternating gas injection[END_REF]. In order to quantify these effects, both experimental and numerical modelling studies have been conducted in parallel as part of the CO2-DISSOLVED project. The most notable results were obtained with the carbonate samples, showing the rapid development of a network of wormholes around the injection pipe outlet [START_REF] Randi | CO2-DISSOLVED: a Novel Concept Coupling Geological Storage of Dissolved CO2 and Geothermal Heat Recovery -Part 3: Design of the MIRAGES-2 Experimental Device Dedicated to the Study of the Geochemical Water-Rock Interactions Triggered by CO2 Laden Brine Injection[END_REF]. A numerical simulation of this experiment performed with the MARTHE-PHREEQC code [START_REF] Thiéry | Modélisation 3D du Transport Réactif avec le code de calcul MARTHE v7.5 couplé aux modules géochimiques de PHREEQC[END_REF] reproduced the massive dissolution of calcite near the injection pipe and the formation of wormholes due to the heterogeneous hydraulic conductivity reasonably accurately [START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF]. As demonstrated in numerous studies, the formation of wormholes depends on several parameters such as the ratios of reaction rate, convection rate and diffusion rate (i.e. Peclet and Damköhler numbers) [START_REF] Snippe | Experimental and numerical investigation of wormholing during CO2 storage and water alternating gas injection[END_REF][START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF][START_REF] Izgec | Numerical and experimental investigation of acid wormholing during acidization of vuggy carbonate rocks[END_REF] and material heterogeneities (i.e. permeability and chemical composition) [START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF][START_REF] Smith | CO2-induced dissolution of low permeability carbonates. Part I: Characterization and experiments[END_REF]. Regarding the Chelles doublet, no dissolved CO2 has been added in the injected cooled brine. Contrariwise, the artesian production mode of the doublet led to CO2 degassing at surface. Near neutral pH of the reinjected brine resulted in a solution close to equilibrium with respect to calcite and therefore, the Damköhler number was low, thus promoting uniform dissolution [START_REF] Snippe | Experimental and numerical investigation of wormholing during CO2 storage and water alternating gas injection[END_REF][START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF].

The aim of this study is to provide reference data for the predicted effects of reactive processes at the well outlet when reinjecting a cooled brine (i.e. a 'standard' cooled geothermal brine). Moreover, it is critical to be able to compare the modelling results to actual bottom-hole measured data in order to evaluate the validity of model predictions. In contrast to other geothermal reservoirs [e.g. [START_REF] Massiot | Fracture width and spacing distributions from borehole televiewer logs and cores in the Rotokawa Geothermal Field[END_REF][START_REF] Massiot | Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation[END_REF], such reservoir data are extremely scarce for the Dogger carbonate aquifer and have not previously been made available to the scientific community; therefore, this study provides insights into water-rock interactions in this specific environment. The second objective of this study is to give insights to better interpret predictions of the CO2-DISSOLVED system related to adding dissolved CO2 to the reinjected brine. This is because this CCS method has not yet been tested at full scale, so no equivalent in-situ data can be obtained; therefore, modelling remains the only approach to estimate the potential impacts of dissolved CO2 reinjection on the exploited reservoir. In a such context, the hole stability [START_REF] De Lary | Quantitative risk assessment in the early stages of a CO2 geological storage project: implementation of a practical approach in an uncertain context[END_REF] and permeability increase leading to a risk of thermal breakthrough in the nearby production wells [START_REF] Castillo | Reactive Transport Modelling of Dissolved CO2 Injection in a Geothermal Doublet. Application to the CO2-DISSOLVED concept[END_REF][START_REF] Castillo | Geochemical and reactive transport modeling of the injection of cooled Triassic brines into the Dogger aquifer (Paris basin, France)[END_REF] are intensively investigated.

Materials and methods

Chelles geothermal doublet

The Chelles geothermal district heating doublet was exploited continuously since its commissioning in 1986 until its closure in 2010 in artesian production mode with a maximal flow rate of 250 m 3 h -1 (Figure 1). This system operated at high flow rates and a wellhead pressure lower than the bubble point, leading to the partial release of gases initially dissolved in the Dogger pore water and their partial trapping high in the geothermal pipe [START_REF] Ungemach | Mise en service opérationnelle d'une ligne de dégazage : brûlage du biogaz géothermal sur le doublet de Chelles[END_REF]. The geothermal reservoir has a gas production capacity of approximately 0.125 m 3 per m 3 of Dogger fluid. The gas phase is mainly composed of CH4 and other alkanes (55%), N2 (35%), and CO2 (10%) [START_REF] Ungemach | Mise en service opérationnelle d'une ligne de dégazage : brûlage du biogaz géothermal sur le doublet de Chelles[END_REF][START_REF] Marty | Low enthalpy geothermal fluids from the Paris sedimentary basin-1. Characteristics and origin of gases[END_REF][START_REF] Criaud | Twelfth Workshop on Geothermal Reservoir Engineering[END_REF]. From 2000-2010, a special degassing device was employed for gas extraction and burning [START_REF] Ungemach | Mise en service opérationnelle d'une ligne de dégazage : brûlage du biogaz géothermal sur le doublet de Chelles[END_REF]. Unfortunately, gas extraction was not monitored over time; therefore, the partial pressure of CO2 in equilibrium with the reinjected fluids remains uncertain. In contrast, flow and temperature data of the Chelles doublet GCHE1/GCHE2 are available from the Dogger database (https://dogger-idf.brgm.fr); however, data regarding the injection well are very sporadic between 1986 and 2010 (see injection_history file in Electronic Annex). Indeed, only typical injections have been recorded during winters of the first 5 years (one recording per year) and data are not continuous between years 5 to 24 years (about one recording per month). Therefore, average flow rates and injection temperatures of the injection well (GCHE1) during summer (133 m 3 h -1 and 52 °C) and winter (148 m 3 h -1 and 48 °C) were considered in this study. Such a discretisation in two steps is supported by recorded data from similar doublets in the Paris basin [START_REF] Lopez | 40 years of Dogger aquifer management in Ile-de-France[END_REF]. Conversely, a constant temperature of 66 °C was monitored at the production well (GCHE2).

The section of the GCHE1 well has been drilled in 1985 with a diameter of 8½'' (Figure S1).

However, the exact geometry of the injection chamber has not been determined after the

Examination of the injection well post-geothermal production

The injection well (GCHE1) integrity was examined in March 2016 by combining ABI technique (Acoustic Borehole Imaging) and a sonar tool developed by Flodim. The technical principle of the sonar probe involves sound propagation (at lower frequency than for ABI) and recording the reflection of the acoustic signal against the cavity wall. The cavity wall is clearly imaged if the density contrast between the fluid and the ground is strong and the wall is regular. The measurement range is several centimetres to hundreds of metres. Currently, sonar does not allow continuous acquisition. The probe performs 360° rotations with a fixed measurement step (5° in this study) at a fixed depth. Once the rotation is complete, the probe moves to another depth to resume measurements.

Numerical tools

MARTHE-PHREEQC reactive transport modelling software is an extension of MARTHE software [http://marthe.brgm.fr/, 17], which has been upgraded by coupling with the PHREEQC chemical module [START_REF] Parkhurst | Description of input and examples for PHREEQC version 3 -A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF]. The coupling algorithm is purely sequential; at each time step, MARTHE computes the hydraulic head field and hence the velocity in the entire domain. It then transports all considered dissolved chemical elements and also transports heat to determine the temperature field on which geochemical reactions depend. Then, the geochemistry is computed using the PHREEQC module. The THERMODDEM thermodynamic database [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF] (http://thermoddem.brgm.fr/) was used in this study. The B-dot model, an extension of the Debye-Hückel activity model, is valid up to salinities of about 1 mol L -1 [START_REF] Hörbrand | Validation of hydrogeochemical databases for problems in deep geothermal energy[END_REF][START_REF] Trémosa | Long-term assessment of geochemical reactivity of CO2 storage in highly saline aquifers: Application to Ketzin, In Salah and Snøhvit storage sites[END_REF].

Experimental results

The cavity extension was measured by the sonar tool at depths of approximately every 0. Surfaces and thus volumes of irregular polygons have been directly calculated by the tool software knowing the coordinates of the vertices and the thickness of the investigated area (Figure 3a). Despite the observed slight shift of data with depth, the productive layers identified in 1985 (Table 1) were in reasonable agreement with the maximum altered volumes of rock. These volumes were converted to equivalent radii, assuming a cylindrical geometry for the cavity (Figure 3b) following:

(Eq. 1)
where req is the equivalent radius (m), V the volume given by the sonar tool (m 3 ) and h the thickness of the area investigated (m).

Modelling strategy

Dogger formation parameters

The mineralogical composition of the Dogger formation (Table 2) was established from the volume percentages given in [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO2-liquid interface during CO2 injection into a carbonate reservoir, the Dogger aquifer (Paris Basin, France)[END_REF] and [START_REF] Gille | Suivi et modélisation du comportement hydro-géochimique du Dogger, soumis à la réinjection de fluides « chaud » et « froid[END_REF]. The Dogger assemblage consists essentially of calcite and dolomite. Siderite, illite, albite, and K-feldspars are present as accessory minerals. The chemical composition of the Dogger brine was calculated for a temperature of 66 °C according to the value recorded at the production well. The simulation assumed a thermodynamic equilibrium between the Dogger pore water [START_REF] Castillo | Reactive Transport Modelling of Dissolved CO2 Injection in a Geothermal Doublet. Application to the CO2-DISSOLVED concept[END_REF][START_REF] Criaud | Caractérisation et modélisation du réservoir géothermique du Dogger, Bassin Parisien, France[END_REF] and the mineralogical assemblage reported in Table 2. Note that the formation of albite and K-feldspars is unlikely at 66 °C and only dissolution reactions occurred during equilibration. In addition, a CO2 partial pressure of 100 mbar (log pCO2 = -1.0 atm) was assumed for the Dogger formation. Such a partial pressure is in the lower range of values reported for this aquifer [START_REF] Coudrain-Ribstein | Temperature-carbon dioxide partial pressure trends in confined aquifers[END_REF]. Constraints assumed for the fluid composition calculation are reported in Table 3. The fluid is in equilibrium with carbonates (calcite, dolomite, and siderite), illite, and quartz (Table 4). It is also close to equilibrium with sulphate bearing minerals such as barite (BaSO4) and celestine (SrSO4).

Table 2. Mineralogical assemblage of the Dogger formation (data extracted from André, Audigane, Azaroual and Menjoz [START_REF] André | Numerical modeling of fluid-rock chemical interactions at the supercritical CO2-liquid interface during CO2 injection into a carbonate reservoir, the Dogger aquifer (Paris Basin, France)[END_REF] and Gille [START_REF] Gille | Suivi et modélisation du comportement hydro-géochimique du Dogger, soumis à la réinjection de fluides « chaud » et « froid[END_REF]).

Mineral

Chemistry of injected fluids

The numerical simulations considered fluid reinjection at different temperatures according to different periods (heat extraction being more important in cold periods). In the heat exchanger, calculations did not consider the mineralogical assemblage of the Dogger because no mineral phase was theoretically present. However, potential secondary phases such as calcite, and barite were implemented. If oversaturated, their precipitation should occur primarily in the heat exchanger and in the downstream pipe portion (i.e. in the coldest zone).

As a first approximation, CO2 degassing was not considered and the fluid chemistry at 48 °C and 52 °C was calculated from simple cooling of the Dogger pore water ("No degassing" case, Table 5). As expected, the temperature decrease destabilises the carbonate minerals, which are then undersaturated (Table 6). However, between 1986 and 2010, the Chelles geothermal doublet operated in artesian mode, resulting in degassing at the wellhead that favoured carbonate precipitation instead. A second model ("Partial degassing" case, Table 5) was then established assuming partial degassing of CO2 until a calcite saturation index of -0.01 (i.e.

almost in equilibrium with this carbonate). This value was adjusted to reasonably match with the observed calcite dissolution using a single-layer geometry. Finally, a third solution chemistry was calculated considering the CO2 atmospheric partial pressure (i.e. log PCO2 = -3.45

(atm)) related to calcite precipitation ("Total degassing" case, Table 5). Regardless of the fluid chemistry (i.e. CO2 degassing), the cooling of brines leads to barite and quartz precipitation (Table 6). Nonetheless, silica precipitation is known to be a slow process at considered temperatures [e.g. 37] and Si concentrations reported in Table 5 are probably under estimated.

Note that numerous studies have reported quartz, barite, and calcite scaling in geothermal wells [e.g. [START_REF] Bozau | Hydrogeochemical modelling of corrosion effects and barite scaling in deep geothermal wells of the North German Basin using PHREEQC and PHAST[END_REF][START_REF] Tarcan | Hydrogeochemical factors effecting the scaling problem in Balçova geothermal field, İzmir, Turkey[END_REF][START_REF] Akin | Modeling of Calcite Scaling and Estimation of Gas Breakout Depth in a Geothermal Well by Using PHREEQC[END_REF]; however, this study was not focused on such surface and subsurface processes.

Geometries and key modelling assumptions

Two distinct but simplified geometries were considered: homogeneous and heterogeneous (Figure 4). A single-layer homogeneous model was first applied to simulate the geothermal reservoir. The mesh was radial type with X, Y, and Z coordinates coinciding with the radius, angle, and layer of the model, respectively. A homogeneous porosity of 15% was assumed in the geological formation [i.e. average porosity, 2]. The model assumed upper and lower impervious walls following the approximate analytical solution of Vinsome and Westerveld [START_REF] Vinsome | A simple method for predicting cap and base rock heat losses in thermal reservoir simulators[END_REF] (thermal conduction perpendicular to the aquifer) implemented in MARTHE. This analytical solution avoiding the vertical discretization of the clay layers so considerably reduced the number of meshes in the model, thereby decreased the computation time. Note that a single-layer geometry leads to an over estimation of the cooling down of the reservoir [START_REF] Le Brun | Hydraulic and thermal impact modelling at the scale of the geothermal heating doublet in the Paris Basin[END_REF], however, such an assumption is widely used when the knowledge of the geothermal reservoir is low (e.g. in the case of predictive modelling). Moreover, even if several productive layers have been identified (Table 1), the open hole extension shown on Figure 3b appears to be relatively homogeneous and thus a single layer geometry could be a correct assumption for assessing mineralogical transformations. A second, heterogeneous model was proposed using the Chelles injection well data (e.g. the productive layers identified by flowmeter, Table 1). The Dogger reservoir was discretised into five layers with specific properties. The mesh was also radial type and assumed upper and lower impervious walls using an analytic solution for the heat diffusion. Injected flows were distributed according to the contribution of the productive layers (Table 1). In contrast, according to flowmeter data, unproductive layers were considered as impervious layers only contributing to heat diffusion. The general parameters used for the simulations were defined using data from previous literature and are summarised in Table 7. A radial extension of 1000 m was assumed whatever the geometry considered. Table 7. General parameters used for the simulations.

Simulation parameters Values

Initial temperature (°C) 66

Volumetric heat capacity of the mineral (J m -3 °C-1 ) 2 10 6

Heat capacity of the water (J kg -1 °C-1 ) 4185

Thermal conductivities of the mineral (W m -1 °C-1 ) 2.5

Thermal conductivities of the water (W m -1 °C-1 ) 0.6

Molecular diffusion (m 2 s -1 ) 1. 5 10 -10 Mesh refinement (m) 0.025-20

Time step (month) 1

Division of the time step 33000

Numerical results and discussion

The numerical results for the single-layer model are predominantly focused on the mineralogical evolution whereas those for the multi-layer model mainly deal with porosity modifications and temperature profiles. According to the work of Castillo and co-workers [START_REF] Castillo | Reactive Transport Modelling of Dissolved CO2 Injection in a Geothermal Doublet. Application to the CO2-DISSOLVED concept[END_REF],

gibbsite, quartz, goethite, barite, anhydrite, hydromagnesite, and celestine were selected here as potential secondary minerals. Note that the hydromagnesite phase was considered instead of magnesite (another Mg-carbonate) because the latter forms at temperatures above 60-80 °C [START_REF] Gautier | Hydromagnesite solubility product and growth kinetics in aqueous solution from 25 to 75 °C[END_REF]. Similarly, precipitation of anhydrite rather than gypsum was assumed because the predicted temperatures were over 40 °C [START_REF] Hill | The Transition Temperature of Gypsum to Anhydrite[END_REF].

Single-layer geometry

Calcite alteration was observed in the near field of the injection well (from 0 to <1.5 m, Figure 5). The numerical results were affected by the modelling assumptions; calcite alteration decreased from "No degassing" to "Partial degassing" to "Total degassing" cases.

Regardless of the injected fluids (Table 5), the model indicated dolomite dissolution up to about 15 m from the injection well occurring concomitantly to a calcite precipitation (from >1.5 to 15 m, Figure 5). Dolomite/ankerite conversion (approximately equivalent to dolomite/calcite conversion) has been observed in several experiments [START_REF] Debure | Study of Iron-Bearing Dolomite Dissolution at Various Temperatures: Evidence for the Formation of Secondary Nanocrystalline Iron-Rich Phases on the Dolomite Surface[END_REF][START_REF] Gysi | CO2-water-basalt interaction. Low temperature experiments and implications for CO2 sequestration into basalts[END_REF]; thus, even if such reaction is probably overestimated (i.e. minerals processed at local equilibrium), a similar process is expected in the Dogger formation. Note that the amount of precipitated calcite was also promoted by the Ca concentrations in the injected fluids (Table 5) and the amount of mineral is lower for the "Total degassing" case. Regarding other mineralogical transformations, the amounts of microcline and albite remained constant. Considering the low amounts of accessory minerals (illite and siderite) as well as precipitated secondary minerals (gibbsite, quartz, goethite, and barite), their impacts on porosity evolution were very limited; these numerical results are reported in the Supplementary Data. The formation of anhydrite, hydromagnesite, and celestine was not observed in any simulation case. As calcite and dolomite constitute 80% of the initial mineralogical assemblage of the Dogger formation (Table 2), modelling assumptions affected the resulting porosity (Figure 6a) while temperature profiles remained identical whatever the injected fluid chemistry (Figure 6b). The total degassing of the cooled injected fluid was unlikely as its effect on porosity was very limited (i.e. no significant variation around the injection well). Additionally, the low Ca concentration of the injected fluid (Table 5) limited the calcite precipitation promoted by the dolomite/calcite conversion and a slight porosity increase was predicted despite the molar volumes of minerals (i.e. 36.9 cm 3 mol -1 for CaCO3 and 64.4 cm 3 mol -1 for CaMg(CO3)2).

Finally, only partial CO2 degassing of the injected fluid could explain the field observations.

According to the work of Deng and co-workers [START_REF] Deng | Alteration and Erosion of Rock Matrix Bordering a Carbonate-Rich Shale Fracture[END_REF], dissolution of 35% is a reasonable threshold for a fast-reacting mineral (i.e. calcite), above which erosion of the altered layer occurs. Following the removal of the altered layer, the open-hole aperture increases.

Assuming an initial porosity of 15% in the current model, a porosity increase of more than 50% would lead to disaggregation of the remaining matrix. The remaining minerals (e.g. albite and microcline) are expected to fall to the bottom of the injection well or be further transported. The "Partial degassing" model led to a porosity increase of up to 50% at 0.25 m (Figure 6a). An open-hole aperture of 0.25 m was then estimated, which is in reasonable agreement with the experimental data. Note that more recent doublets use two pumps to keep fluids under pressure and avoid the bubble point [START_REF] Lenoir | Geothermal exploitation of the Dogger in the Paris basin maintenance, renewal and reliability of the geothermal loop[END_REF]. Therefore, the porosity profile obtained without degassing corresponds to the open-hole expected under such conditions.

Multi-layer geometry

Mineralogical transformations calculated using the multi-layer model were similar to those already described with the single-layer model; the open-hole formation resulted in carbonate dissolution. Therefore, only the porosity profiles after 24 years of geothermal production are reported in Figure 7 whereas open-hole extensions are given in Table 7. As already observed with the previous model, the absence of fluid degassing led to an overestimation of open-hole formation (up to 6.2 m for layer 4). In contrast, the porosity change that was modelled assuming that total degassing was negligible. The best fit to the experimental data was obtained considering partial degassing of injected fluids. Assuming a threshold of 35% for carbonate alteration [START_REF] Deng | Alteration and Erosion of Rock Matrix Bordering a Carbonate-Rich Shale Fracture[END_REF] and specific initial porosities for each layer (Table 1), the numerical results indicated an open-hole radius ranging from 0.37 m (layer 1) to 1.18 m (layer 4). Nonetheless, the reactivity of unproductive layers may buffer the alteration of productive layers, which is therefore likely to be overestimated if those unproductive layers are assumed to be impermeable. Such a reactivity is supported by experimental results

effectively showing an alteration of layers identified as unproductive from flowmeter measurements (Figure 3). This explains why the use of a single-layer geometry allowed a better approximation of the alteration front progression in the Dogger aquifer. The geothermal doublet induces the formation of a "cold bubble" in the reservoir around the injector [START_REF] Hamm | Assessment of complex well architecture performance for geothermal exploitation of the Paris basin: A modeling and economic analysis[END_REF][START_REF] Castillo | Geochemical Parameters as Precursors to Predict the Decline of Temperature in the Dogger aquifer[END_REF]. The migration of the "cold bubble" was similar regardless of fluid chemistry assumptions and therefore, only one temperature profile is reported on Figure 8. After 24 years of geothermal production, the cold injection front progressed up to 700 m, which corresponds to half the distance between the injection and the production wells. The numerical results indicated that a decrease in temperature at the production well was unlikely and was in accordance with recorded data (i.e. no thermal breakthrough). Nonetheless, numerous studies have shown a dissymmetry of the temperature profile resulting from the shape of the velocity profile induced by fluid extraction at the production well [e.g. 13]; the production well has been neglected here as the modelling of the exact progression of the "cold bubble" was not an objective of this study. The consideration of two injection periods (48 °C in winter and 52 °C in summer) led to an inhomogeneous temperature profile in the near field of the injection well. Consistent with the temperature dependence of the mineral solubility [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF], both the temperature decrease and the mass transport led to a calcite alteration that was attenuated when enabling CO2 degassing.

Model limitations

The modelling results of open-hole extension remain uncertain because several processes can affect its progression. The effects of porosity changes on the resulting permeability were neglected in this study. Following the Kozeny-Carman relationship, a porosity increase would lead to a permeability increase favouring mass transport and rock alteration. In contrast, the particles released by cement alteration could be mobilised and transported further, where particle re-deposition could cause clogging in the productive layer and a reduction of permeability [START_REF] Deng | Alteration and Erosion of Rock Matrix Bordering a Carbonate-Rich Shale Fracture[END_REF][START_REF] Sbai | Numerical modeling of formation damage by two-phase particulate transport processes during CO2 injection in deep heterogeneous porous media[END_REF]. Unfortunately, the balance between higher porosity leading to higher permeability and porosity clogging by particles leading to a decrease of mass transport properties is difficult to determine. Therefore, our models assumed constant permeability and imposed average flow rates monitored at GCHE1. Moreover, the reinjection of cooled brine in the GCHE1 borehole could have a thermomechanical impact on the integrity of the reservoir rock that cannot be considered by MARTHE-PHREEQC. The current sonar technique is limited to the identification of open-hole walls and cannot detect porosity increases inside the rock matrix and/or the possible formation of wormholes in carbonated rock [START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF][START_REF] Ott | Wormhole formation and compact dissolution in single-and two-phase CO2brine injections[END_REF]. However, despite these uncertainties, the model and field results were in reasonable agreement, even if a simplified geometry was considered. Nevertheless, the noniterative sequential coupling algorithm of the MARTHE-PHREEQC code implies using a relatively small time step fulfilling the Neumann criterion, thus leading to a high number of iterations and then a high computation time (i.e. several days). The time step used for this study (80 s, Table 7) is the best compromise between calculation efficiency and numerical dispersion possibly observed when the Neumann criterion is not strictly respected, which is the case for the smallest cells at the immediate vicinity of the well. However, keeping in mind that for all these cells, water-rock interactions rapidly became negligible as calcite was entirely dissolved, time step could be relaxed without negative consequence on calculation accuracy. Using parameters as close as possible to actual well operation data as well as simplified geometries that are widely used in predictive modelling, this study attempted to quantify the water-rock interaction processes in the near-well area of the exploited reservoir. Because of the partial monitoring of production data and more specifically a lack of data on the chemistry of the injected fluids (e.g. rate of CO2 degassing) as well as drawbacks of current reactive transport software (e.g. transport of eroded particles is not accounted for), the accuracy of the numerical results had some limitations. Nonetheless, the simulation results confirmed significant carbonate alterations in the near-well part of the reservoir on the same orders of magnitude as the average measured open-hole aperture (0.21 m). This gave us more confidence in our modelling approach and suggested that the observed geometry alteration could mainly have a geochemical origin. Best-fit results were obtained for partial CO2 degassing in the reinjected brine, which is also consistent as the geothermal doublet was operated in artesian mode.

Conclusions

Although previous studies on the CO2-DISSOLVED concept involving cooled CO2-rich brine reinjection in a geothermal well (i.e. CO2 concentration less than 1 mol L -1 under field conditions, so that CO2 remains entirely dissolved in brine) used a similar modelling approach, they lacked reference field data for evaluating the predictive capability of the models. Therefore, the results of this study, based on unique bottom-hole data showing the geochemical impact of brine reinjection in a "standard" geothermal doublet, constitute a valuable baseline for future calibration of reactive transport models. These reactive transport models could then be more confidently used to perform the pre-dimensioning calculations of dissolved CO2 injection in a doublet, which forms the first operational test-phase of the CO2-DISSOLVED system.

  //www.gouvernement.fr/en/energy-transition). Energy exploitation involves the reinjection of cooled brine into the carbonated reservoir after calorie extraction by heat exchangers [e.g. 1, 2, 3]. The local reinjected fluid temperature depends on the production temperature (55-85 °C), the energy requirements at the surface, and the operating flowrate

  values may reflect the presence of fractures in the Dogger aquifer. This also raises the question about the representativeness of the sample studied by the authors.

Figure 1 .

 1 Figure 1. Location and schematic representation of the Chelles geothermal doublet.

5 m.

 5 Investigations were focused on the exploited part of the geothermal reservoir (from -1650 to -1710 m FOD), where the well is characterised by the absence of open-hole casing.Maximum and minimum extensions are reported in Figure2. The shape and volume of the cavity were irregular in both horizontal and vertical orientations. Nonetheless, regardless of the amount of dissolved rock, preferential alteration leading to cavity formation was clearly identified in the SW direction. This observation fully agrees with the tilt of the GCHE1 well (Figure1); i.e., the direction of injected flow strongly influences the shape of the formed cavity. Note that ABI data (GCHE1_ABI file in Electronic Annex) of the well section located below the productive layers do not indicate any enlargement/damage of the bore hole due to drilling operations, thus supporting an initial open hole diameter of 0.1 m.

  The average calculated radius was 0.21 m. Considering an initial well radius of 0.1 m, approximately 6 m 3 of the Dogger formation was dissolved during the operating period of the injection well (1986-2010). The average radius was compared with numerical results in order to evaluate the effect of various modelling assumptions (i.e. the geometry considered and the chemistry of the injection solution).

Figure 2 .

 2 Figure 2. a) Maximum extension of the cavity observed at -1701.3 m FOD and b) minimum extension of the cavity observed at -1705.2 m FOD. Experimental data were measured by the sonar tool every ~0.5 m.

Figure 3 .

 3 Figure 3. a) Volumes measured by the sonar tool every 0.5 m and b) calculated equivalent radii assuming a cylindrical cavity.

Figure 4 .

 4 Figure 4. Schematic representations of the two model geometries: a) single-layer geometry and b) multi-layer geometry using flowmeter data from 1985.

Figure 5 .

 5 Figure 5. Calcite (CaCO3) and dolomite (CaMg(CO3)2) profiles calculated with the single-layer model after 24 years of cooled brine injection. No degassing, partial degassing, and total degassing correspond to the different modelling cases based on injected fluid chemistry (see section 4.2).

  experimental results indicated an average radius of 0.21 m for the open hole. The modelling case omitting gas extraction ("No degassing" model) showed total dissolution of carbonate minerals up to 1 m around the injection well; the formation of an open hole around the injection well was clearly an overestimate. In contrast, the numerical modelling indicated that

Figure 6 .

 6 Figure 6. a) Porosity profile calculated with the single-layer model after 24 years of cooled brine injection. No degassing, partial degassing, and total degassing correspond to the different modelling cases based on injected fluid chemistry (see section 4.2). b) Temperature profile calculated with the single-layer model after 24 years of cooled brine; results are identical for all the injected fluid chemistries considered.

Figure 7 .

 7 Figure 7. Porosity profile calculated with the multi-layer model after 24 years of cooled brine injection. No degassing, partial degassing and total degassing correspond to modelling assumptions made on fluid chemistries (see section 4.2).

Figure 8 .

 8 Figure 8. Temperature profile calculated with the multi-layer model after 24 years of cooled brine injection. Note that results were identical whatever modelling assumptions made on fluid chemistries (see section 4.2).

Field

  investigations of the Chelles former injection well after 24 years of continuous geothermal operation offered a novel opportunity to evaluate reservoir mineralogical transformations at the well outlet induced by cooled-brine reinjection during a typical geothermal exploitation period. Sonar data acquired on the open-hole part of this well showed significant and uneven distortion of the initial cylindrical geometry. The investigation technique, used for the first time in the Paris basin, is a promising tool for borehole examinations, especially when a camera is not practical due to groundwater turbidity as in the Dogger aquifer.

Table 1 .

 1 Measured permeabilities are greater than the one of the Oolithic limestone studied by Randi et al.[START_REF] Randi | Experimental and numerical simulation of the injection of a CO2 saturated solution in a carbonate reservoir: Application to the CO2-DISSOLVED concept combining CO2 geological storage and geothermal heat recovery[END_REF] (i.e. 88 mD). Such

	drilling operation (i.e. no caliper measurement). Nonetheless, the numerous drilling
	operations carried out in the Dogger aquifer do not indicate any enlargement/damage of the
	borehole. In particular, the GCHE4 well that has been drilled in 2013 at the immediate vicinity
	of GCHE1, using similar operational conditions in terms of tool (rotary drilling), geometry
	(8½'' diameter), and geological formation targeted (Dogger aquifer). Caliper data are
	available for GCHE4 and they confirm an effective diameter of the open hole consistent with
	the nominal drilling diameter. As a consequence, we assumed an initial radius of 0.1 m for
	the open hole of the GCHE1 injection well. Regarding the structure of the geothermal
	reservoir, the GCHE1 well is characterised by five productive layers of the Dogger aquifer [2,
	28]: two layers of Comblachian units from -1668 m to -1683 m FOD (French Ordnance
	Datum), which contribute up to 14.7% of the total flow, and three layers of Oolithic units from

Table 1 .

 1

	Facies	Layer	Altitude (m FOD*)	Flow contribution (%)	Porosity (%)	Permeability (D)
	Comblachian	1 2	-1667.8 / -1669.8 -1682.4 / -1683.3	7.3 7.4	12.5 15.8	1.03 2.09
		3	-1692.1 / -1698.4	29.4	17.4	1.28
	Oolithic	4	-1702.3 / -1703.7	51.0	15.7	9.60
		5	-1707.1 / -1708.6	4.9	14.9	0.92
	*French Ordnance Datum

Production levels identified by flowmetry analyses conducted in 1985.

Table 3 .

 3 Chemistry of the Dogger pore water at 66 °C.

		Mineral name in		Volume
		THERMODDEM		fraction
	Calcite	Calcite		0.7
	Dolomite-des Dolomite(disordered)	0.1
	Siderite	Siderite		0.05
	Illite	Illite(IMt2)		0.05
	Albite	Albite(low)		0.05
	K-Feldspaths Microcline		0.05
	Element	Concentration (mol L -1 )		Constraint
	Al	1.67 10 -07		Gibbsite
	Ba	1.09 10 -06		Barite
	C(4)	5.24 10 -03		PCO2
	Ca	1.12 10 -02		Calcite
	Cl	3.14 10 -01
	Fe	8.39 10 -05		Siderite
	K	9.38 10 -03		Illite(IMt2)
	Mg	1.63 10 -02	Dolomite-des
	Na	2.70 10 -01
	S(6)	9.01 10 -03
	Si	5.06 10 -04		Quartz
	Sr	5.23 10 -04
	pH	6.48
	pe	-3.51
	log PCO2 (atm)	-1.0

Table 4 .

 4 Saturation indices of the Dogger pore water at 66 °C (SI = log IAP/K, where IAP is the ionic activity product and K the thermodynamic constant).

	Phases	Saturation indices (SI)
	Calcite	0
	Dolomite(disordered)	0
	Siderite	0
	Gibbsite	0
	Illite(IMt2)	0
	Albite(low)	0.48
	Microcline	1.09
	Quartz(alpha)	0
	Celestite	-0.19
	Barite	0

Table 5 .

 5 Injected brine compositions as a function of temperature and CO2 partial pressure.

	Concentrations (mol L -1 )

Table 6 .

 6

				Saturation indices (SI)
	Phases	No degassing 48 °C 52 °C	Partial degassing 48 °C 52 °C	Total degassing 48 °C 52 °C
	Calcite	-0.20	-0.16	-0.01	-0.01	0	0
	Dolomite (disordered)	-0.59	-0.46	-0.21	-0.16	-0.12	-0.08
	Siderite	-0.21	-0.17	-0.03	-0.03	-1.69	-1.79
	Illite (IMt2)	-0.77	-0.59	-0.38	-0.30	-0.07	-0.23
	Albite (low)	0.11	0.19	0.30	0.34	0.81	0.74
	Microcline	0.96	0.99	1.16	1.14	1.66	1.54
	Quartz (alpha)	0	0	0	0	0	0
	Celestite	-0.24	-0.23	-0.24	-0.23	-0.23	-0.21
	Barite	0	0	0	0	0	0
	Goethite	-0.59	-0.48	-0.25	-0.22	0	0

Saturation indices of injected brines as a function of temperature and CO2 degassing (SI =

log IAP/K, where IAP is the ionic activity product and K the thermodynamic constant).

Table 7 .

 7 Open-hole extension modelled for the multi-layer geometry. No degassing, partial degassing and total degassing correspond to modelling assumptions made on fluid chemistries (see section4.2)

	Productive	Observed radius (m)		Modelled radius (m)
	layer	min-max	average	No degassing Partial degassing Total degassing
	1	0.23-0.25	0.24 ±0.01	2.03	0.37	0.1 *
	2	0.21-0.28	0.24 ±0.02	2.96	0.56	0.1 *
	3	0.21-0.29	0.25 ±0.02	2.23	0.45	0.1 *
	4	0.14-0.25	0.19 ±0.05	6.16	1.18	0.1 *
	5	0.11-0.14	0.13 ±0.01	1.89	0.38	0.1 *
		* no extension, 0.1 m being the initial radius of the borehole

Acknowledgments

The authors thank the anonymous reviewers for their comments and suggestions. This work was supported by the ANR (French National Research Agency), within the framework of the "CO2-DISSOLVED" project (ANR-12-SEED-0009), and Geodenergies (http://www.geodenergies.com/), as part of the "PILOTE CO2-DISSOLVED" project. The authors would also like to thank Chelles Chaleur and Coriance for making the well available to our team during the three-day experimentation period. FLODIM are also greatly acknowledged for applying their proprietary sonar investigation tool to the novel context of a former geothermal injection well. The authors thank O. Audouin from CFG service for his technical support on the well characterisation.