Jamal Fannir
email: jamal.fannir@univ-lorraine.fr

Irina Panfilov

Didier Sebastien Leclerc

Fannir Jamal

Panfilova Irina

Leclerc Sébastien

Stemmelen Didier

Studying of two

Keywords: MRI / porous media / oil-water displacement / viscous fingering / residual oil,  Interfacial tension N, m -1 θ

Oil viscosity cP

 

Wetting-phase viscosity cP 1 Introduction

Two-phase flow in porous media is very important and widely applicable in the petroleum industry (such as estimation of recoverable oil reserve, optimization of the recovery techniques…) but also in the sector of chemical industry (catalytic reactors, separation and extraction) or in the hydrogeology domain (pollution of aquifers by NAPL). This explains the importance of the studies aiming to improve the description of multi-phase flow in porous media. Notably, the simultaneous flow of two immiscible fluids (water-oil) in porous media is not always well described by Darcy's generalized law, which only takes into account water/oil saturation as additional descriptive variable. This has a substantial impact on the description of the two-phase flow stability under the simultaneous effect of the force of gravity, viscosity and superficial tension.

For the study of two-phase flow in porous media, several kinds of imaging methods have been applied including X-ray, computed tomography scanners (CT) [START_REF] Akin | Computed tomography in petroleum engineering research[END_REF][START_REF] Larachi | X-ray micro-tomography and pore network modeling of single-phase fixed-bed reactors[END_REF][START_REF] Pak | Droplet fragmentation: a new pore-scale process[END_REF] synchrotron imputed micro-tomography [START_REF] Bernard | 3D Quantification of Pore Scale Geometrical Changes Using Synchrotron Computed microtomography[END_REF] and magnetic resonance imaging (MRI) techniques [START_REF] Chen | Quantitative NMR imaging of multiphase flow in porous media[END_REF][START_REF] Zhao | Visualization and Measurement of CO2 Flooding in Porous Media Using MRI[END_REF][START_REF] Zhao | Experimental investigation on spontaneous counter-current imbibition in water-wet natural reservoir sandstone core using MRI[END_REF][START_REF] Mitchell | Magnetic resonance imaging in laboratory petrophysical core analysis[END_REF][START_REF] Li | Polymer Flooding Enhanced Oil Recovery Evaluated with Magnetic Resonance Imaging and Relaxation Time Measurements[END_REF]. Among these methods, only MRI is able to visualize the internal structure of a system in three dimensions with a spatial resolution of the species present. Furthermore, MRI also allows in-situ measurements of flow velocity, saturation and diffusion-dispersion of the fluid flow within the porous media. Another opportunity of the MRI is that it can be used to probe both microscopic and macroscopic properties.

The rapid development of new quantitative magnetic resonance imaging technologies led to new opportunities with interesting results for measurements of fluid flow in porous media. Johns and Gladden [START_REF] Johns | Magnetic resonance imaging study of the dissolution kinetics of octanol in porous media[END_REF] have used MRI technique to visualize the dissolution of entrapped ganglia or "blobs" of octanol within the pore space of a randomly packed bed of glass beads, by a mobile aqueous phase. They also acquired three dimensional images and were able to distinguish the solid, hydrocarbon, and aqueous phases. Finally, they also obtained velocity maps of the mobile aqueous phase. Ersland et al. [START_REF] Ersland | Complementary imaging of oil recovery mechanisms in fractured reservoirs[END_REF] used the MRI techniques to study how the oil recovery is affected by fractures. They have obtained high spatial resolution images of the water-oil flow inside a 1 mm fracture. Furthermore, in a recent work in LEMTA laboratory, MRI has been employed for studies of fluid flow within granular porous media [START_REF] Salameh | NMR Imaging of Water Flow in Packed Beds, diffusion-fundamentals[END_REF]. The authors have shown the possibility of visualization of the velocity field in porous media and accurate measurements of interstitial and averaged velocities in packed beds.

The purpose of the present study is the investigation of the immiscible fluid displacement in porous medium. We focus on the wettability properties of the fluids with the solid surfaces as this is an important factor for secondary recovery of hydrocarbons. Furthermore, several types of forces such as capillary, viscous and gravitational are extremely important to describe the two-phase flow. In this project, MRI was used to experimentally examine the water-oil flux through а vertical porous model.

Using MRI technique, we also study the dynamics of the displacement front, its deformation and the phase trapping during the two-phase flow process.

Displacement in porous media is characterized by the formation of different structures of the phase distribution in porous space. For the same saturation, the fluids can form different shapes. So, these various shapes can be described by the displacing phase saturation S and an additional parameter, responsible for the type of the shape. It is insufficient to only have the specific surface of phase distribution in space, as proposed by several authors, because different shapes can have a surface size of the same order. We recommend using two additional parameters of shape: one to characterize the specific interface between the phases, and the other to evaluate the degree of connectivity between the phases.

The saturation of the displacing phase, the connected displaced phase and disconnected traps, and also the menisci distribution in the zone of the front deformation allow us to complete the phenomenological menisci model proposed in Panfilova and Panfilov 2005 [START_REF] Panfilova | Phenomenological meniscus model for two-phase flow through porous media[END_REF].

Experiments

Experimental system

A scheme of the experimental setup is shown in Figure 1. The setup consists of two parts: the first one is a high resolution of 600 MHz MRI spectrometer equipped with a 14 T vertical magnet, shielded gradient coils providing a maximum gradient strength of 450 mT/m and a 40 mm diameter quadrature resonator. With this system we measure and visualize directly the two-phase flow in a vertical model of porous medium (packed beads or sands) under the ambient condition. The MRI technique allows for non-invasive measurements (2D or even 3D mapping) of the concentration of hydrogen nuclei 1 H in the liquid phase inside the porous media.

These hydrogen nuclei can belong to molecules of water or other liquids. The 1 H species associated with water or hydrocarbon provide the phase distribution images, and it is also possible to distinguish the solid and liquid phases.

The second part is the porous medium column. A tube with 34 mm internal diameter and 14 cm in height was filled and compacted with sands or polystyrene beads. The beads are kept inside the tube by two porous filters and two caps. A syringe pump is connected to the system to inject the water upward at constant flow rate. This pump can inject at a very low rate with an accuracy of ± 0.5%.

Signal is acquired and processed using the Bruker Paravision software. Further processing is done with the Matlab software.

Sample material

Porous medium

We have used two different types of materials for tubes and beads according to their wettability. The synthetic porous medium consisted of polystyrene beads or sands with average grain size of 0.5 mm and 0.13 mm respectively. The average estimated porosity measured by the gravimetric method was around 38%, and the intrinsic permeability was calculated using Kozeny-Carman equation for non-consolidated medium:

𝐾 = 𝜑 3 36C(1-φ) 2 𝑑 𝑝 2 ( 1
)
where K is the sample intrinsic permeability, C is the Kozeny-Carman constant (in this study C = 5), φ is the sample porosity, and dp is the mean diameter of the grains.

The porous media characteristics for both materials are given in Table 1. The samples of sand always have different grain sizes even though the grain size spectrum is relatively narrow. Indeed, it is important in our study to determine the average grain size and grain size distribution accurately as it will be used in our calculations and discussion. Therefore, the average grain size of the selected sand was evaluated from grain size populations (not directly from the mass fraction).

Table 2 shows the sand particles size distribution as a function of mass. These data were obtained using different available sieves. Based on the above data, the average sand grain size estimated to be 0.13 mm using a log-normal function (Fig. 2). The value of the permeability shown in Table 1 was calculated from the Kozeny-Carman formula (Eq. 1) with the estimated average grain size.

Fluids

In all experiments, PTX2000 fuel was used as oil phase, and a solution of water and MnCl2 as displaced phase. Physical properties of these fluids are given by the products data sheet and confirmed in our lab using standard measurements techniques (Table 3). The interfacial tension  between oil and water was assumed to be 0.05 N/m [START_REF] Zeppieri | Interfacial Tension of Alkane + Water Sustems[END_REF].

Experimental process

As a first step, the sample tube was filled with oil. A vacuum pump is used to remove air in order to obtain fully saturated samples. At initial state, we install a hydrostatic equilibrium of water-oil contact inside of the porous sample which is calculated with the levels of water and oil in tanks (Fig. 1). In doing so the water oil interface is homogeneously distributed near the bottom filter. The injection rate was controlled by the syringe pump. The water solution (distilled water + MnCl2) was injected into the column from below with the objective to prevent the deformation of water-oil interface by the gravity. The volumetric injection flow rate was varied from 0.08 mL/min to 0.16 mL/min and the corresponding superficial velocity was calculated using the geometry and porosity of the model. For each experiment, the MR sequences were performed during more than 10 hours, a period corresponding to the injection of 3 and more pore volumes (PV) of water [START_REF] Fannir | Two-Phase Displacement In Porous Media Studied By MRI Techniques[END_REF].

Imaging protocol

The magnetic resonance imaging technique is an effective, non-invasive method for determining fluid saturation in porous media by detecting 1 H density. The imaging method used a classical multi-slice spin echo sequence. The MRI echo signal can be described as [START_REF] Chen | Quantitative NMR imaging of multiphase flow in porous media[END_REF][START_REF] Yan | Testing oil saturation distribution in migration paths using MRI[END_REF]:

𝐼(𝑓, 𝑇 𝐸 ) = 𝐼 0 (𝑓) (1 -𝑒𝑥𝑝 (- 𝑇 𝑅 𝑇 1
)) exp (-

𝑇 𝐸 𝑇 2 ) (2)
in which I is the observed intensity of the magnetic signal at resonance frequency f, I0 is the intrinsic magnetic intensity, TE is the echo time, TR is the repetition time, T1 is the longitudinal relaxation time and T2 is the transverse relaxation time. The intrinsic magnetic intensity I0 is in principle proportional to the number of protons 1 H. Taking TR > 5T1 and TE < T2/5, the observed magnetic intensity is close to the intrinsic one, i.e. 𝐼(𝑓, 𝑇 𝐸 ) ≈ 𝐼 0 (𝑓) which makes it possible to build an image in 1 H density almost independent of the relaxation times.

In this study, the MRI was mainly used to measure the oil signal intensity in each sample and to monitor the oil saturation change during the experimental test. We made sure that the NMR signal is only sensitive to oil. Indeed, both water and oil contain protons 1 H and produce NMR signals that are acquired in the same time.

For this reason, we added a strong paramagnetic contrast agent (Mn 2+ ) to reduce the relaxation times of the water [START_REF] Yan | Testing oil saturation distribution in migration paths using MRI[END_REF]. By taking an aqueous solution of MnCl2 at 0.01 mol/l, the relaxation decay of the water phase could be greatly reduced: T2 of water fell from 3 s to below 1 ms. In this way the signal of water disappeared so quickly that it was not possible to image it. However, MnCl2 is not soluble in organic compounds, so there is no effect on the relaxation time of oil (~1 s).

Therefore, the signal of oil was the only measured signal. Consequently, instead of using pure water as the injection phase, we used an aqueous solution of MnCl2 with a neglected T2 time. For the imaging sequences, it is necessary to set the echo time TE between the transverse relaxation time T2 of the aqueous solution and the oil (i.e.

T2w << TE <<T2o) and to take a relatively large repetition time (TR ≃T1o).

MR images are acquired using a slice selection procedure. By changing the orientation of the magnetic field gradients in the imaging procedure, it is possible to obtain vertical sections along the axis of the sample or horizontal axial sections.

Subsequently we realized over time one vertical section (acquisition time about 4 min) followed by 8 horizontal sections (acquisition time also about 4 min).

In this study, the mapping was done with the following acquisition parameters:

-Echo time TE: 15 ms for polystyrene beads and 5 ms for sand experiments.

-Time of repetition TR: 1 s.

-Field of View FOV: 50 × 50 mm 2 .

-Imaging matrix: 256 × 256 pixels with a resolution of 0.19 mm for 1 pixel.

-Slice thickness: 1 mm.

The obtained images were satisfactory from the point of view of high spatial resolution, and it is clearly possible to visualize the oil trapping and the dynamic evolution of the two-phase flow (Fig. 3). From the MR intensity images, the oil saturation can be calculated as following:

So

So = Ii / Iref ( 3
)
where So is the saturation of the oil phase, Ii is the dynamic MR signal intensity at time i, I0 is the reference MR signal intensity (initial image at oil saturation of 100%).

Results

The MRI raw data acquired are processed with Matlab software to obtain the visualization of the displacement of the oil by the injected aqueous solution (water + manganese chloride). These images have a resolution of 256 × 256 pixels for a field of view (FOV) of 5 x 5 cm 2 . The centre of the FOV for vertical sections is located at 6.7 cm above the lower filter (bottom of the sample). For each model, data are recorded on vertical and horizontal sections with an interval of 15 minutes between each series of images. The recorded data are then processed with Matlab to retrieve the images on which statistical analyzes can be done. To compare the tests at different rates, we introduce the porous volume parameter (PV). It corresponds to the pore volume calculated from the height of the sample imaged by MRI. We note that the displacement of the oil by water does not correspond to a pistonlike flow, but generates fingers leading to a trapping of the oil during the two-phase flow. At the end of the displacement process, the total residual oil saturation, averaged through the sample volume, is equal to 38%. Indeed, the residual oil saturation obtained at the end of the process is an average saturation throughout the model, while it is observed that the saturation is not uniformly distributed. It is therefore necessary to observe in detail what happens at each position along of the model.

Experiment with a packed polystyrene beads model

The analysis of the last image (Fig. 5) where the oil saturation was stabilized, shows an increasing distribution of the residual oil saturation as a function of the vertical position. However, it is easy to observe that the residual oil saturation is much greater in the higher sections of the model than in the lower ones. These differences are caused by the development of fingerings along the model. We also note that the continuous field of low oil saturation, observed in Figure 5 For this test, two types of residual oil were observed. The first type corresponds to the large oil droplets grouped into small discontinuous formations elongated in the direction of flow; the second type of residual oil corresponds to the oil films which cover the oil-wet polystyrene beads.

The visualization (Fig. 5) and statistical analysis (Fig. 6) of this experimental test show that from a total residual oil saturation, around one-third of the residual oil is trapped due to the development of digitations and the capillary pressure. The last approximately two-third of residual oil was trapped in the form of thin films due to hydrophobic behaviour of the bead surface. In Figure 6, the lower and intermediate oil saturations correspond to the film-form of trapped oil and the high saturation of oil represents the oil droplets.

Ref stage Final stage

Experiment with packed sand column

The experiments on polystyrene and borosilicate beads have shown the internal structure of the porous model and the saturation distribution of phases in space and time. It was even possible to see the beads of 0.6 mm diameter with the spatial resolution of MRI tool of 0.19 mm for 1 pixel. Unfortunately, this size of grains of porous medium does not allow for the capillary forces to be important because of the large diameter of the pores. To study the simultaneous effect of the viscous, capillary and gravity forces, we have to reduce the grain size and also use some particle-size distribution. For this purpose, we used silica sand, and the experiments were done at different injection rates (0.08, 0.12 and 0.16 mL/min). The concentration of the manganese chloride was increased two times (0.02 mole/L) due to the small adsorption effect of the sand on the solution.

Reference images of the sand model were acquired before starting the experiments in order to check its compatibility with our imaging protocols. As the impact of the system on the signal and especially on the relaxation times was not too important, the sand model was deemed acceptable. The sand was compacted using a vibrating table, and an estimation of the porosity and the permeability was done.

The oil extraction by water flooding in the packed sand model was performed with the same injection rates than in the polystyrene bead model, i.e. 0.08, 0.12 and 0.16 mL/min. The experiments were repeated several times for each rate to check reproducibility.

A series of twelve consecutive images with an interval of 15 minutes is shown in The vertical and horizontal cross-sections from Figure 7 show that the loss of connectivity of the oil phase between the water fingers leads to the formation of the trapped oil. For this experiment the final residual oil saturation after injection of 3 pore volumes of water equals to 11 %.

To better understand the mechanism of the pulsating movements observed on the condition of slow water pumping, a series of pictures is given in Figure 8. (Fig. 9a), the displacement front is quite stable comparing with higher injection rate (Fig. 9b), while the displacement front was faster when increasing the injection rate twice (Fig. 9c).

Table 4 summarizing the average residual oil saturation for each case, remaining oil saturation is much lower than polystyrene beads model due to the wettability effect (water-wet). Each experiment was repeated to confirm the obtained results.

The oil saturation results ranged from around 10 % to 14 % at three different injection rates. The residual oil saturation for the various injection flow rate is quite in the same magnitude with a regular slight increase for the cases of slow displacement. Most experiments with low injection rate show the stabilization of oil saturation up to Sor after 1.5 -2 of PV injected, and for the rapid displacement one PV injected was enough to replace the mobile oil.

Discussion

In order to investigate the interaction of viscosity, gravity and capillary forces on oil displacement mechanism and residual oil saturation, the experimental results of sand model are analysed using proper dimensionless numbers.

Dimensionless groups

In fluid dynamics theory, the following main dimensional groups are usually suggested to compute the relative magnitudes of the prevailing forces in water flooding processes:

(I) Capillary number (Ca) which is defined as the ratio of the viscous forces to the capillary forces at pore scale and it is expressed as [START_REF] Løvoll | Competition of gravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study[END_REF]:

𝐶𝑎 = 𝑑 2 𝑣 𝑤 𝐾 𝑐𝑜𝑠 𝜃 (4)
where μ𝑤 is the wetting-phase viscosity, 𝝂 is Darcy velocity of the injected phase through porous medium (water injection rate divided by the cross-sectional area of the porous medium), K is the intrinsic permeability, σ is the interfacial tension between wetting and non-wetting phases, θ is the contact angle and d is the average pore size. and (II) the Bond number (Bo) which is defined as the ratio of buoyancy forces to capillary forces:

𝐵𝑜 = 𝑔𝑑 2  𝑐𝑜𝑠 𝜃 ( 5
)
where Δρ is the difference of density between the two fluids and 𝑔 is the gravity acceleration.

The pore size d can be calculated as the hydraulic diameter deduced from the average grain diameter dp and the porosity :

𝑑 = 2𝜑 3(1-𝜑) 𝑑 𝑝 (6)
In the following, the residual oil saturation from each sand experiment are analysed using the above-mentioned groups, taking into account different injection rates.

The capillary number is an important parameter to determine the stability of water displacement process. For low capillary number, less than 10E-5, flow is dominated by capillary forces [START_REF] Blunt | Multiphase flow in permeable media[END_REF]. Somewhat surprisingly, the result at low flow rate has showed (Table 4) a slight increase of the residual oil. Table 5 shows the relationship between the capillary number (Ca) and residual oil saturation (Sor) at different water injection rates. At low flow rate the capillary number decreases which can explain the increase of residual oil trapped in the porous medium because of capillary fingers growth. The experiments on sands with dominated capillary forces, Qinj = 0.08 mL/min, have demonstrated a little lower "washing effect" for the displacement of oil. It confirms the contribution of the viscous forces on the displacement process at higher capillary numbers.

As for the Bond number, it becomes important when the buoyancy forces are noticeable. This condition requires a vertical direction of flow and a variation in fluid density between wetting and non-wetting phases, which is the case in our experiments.

The results show that in sand model experiments, the Bond number is equal to Bo = 1.26E-04. It is the same for all cases of sand models because there are no changes in fluid properties nor grain size. The gravitational forces are therefore relatively small compared to those of capillarity in our experiments.

Both Ca and Bo numbers confirm the important effect of the capillary phenomena.

Therefore, the oil displacement largely depends on the capillary forces in the porous medium.

Displacement mechanism and wettability effect

The three displacement forces of gravity, viscosity and capillarity can act as stabilizing or destabilizing forces of the displacement front depending on the case study. In our case, the properties of the different fluids used remain constant, especially with regards to the viscosity and the density. The viscosity contrast between the two fluids (2.9 cP for oil and 1 cP for water) is not very high, which makes it possible to suppose that initially the viscous effects are not dominant.

Furthermore, the direction of the main flow is opposite to the gravity. Thus, the gravity forces would tend to oppose the development of the fingerings along the model and to stabilize the displacement of the moving front. However, the MRI images of the experiments show that the flow is not in the form of a piston and generates fingerings of different scales.

If the capillarity effects are negligible (which is not the case here at all), it has long been known [START_REF] Marle | Cours de production, Les écoulements polyphasiques en milieu poreux[END_REF], the displacement front is unstable when the injection velocity is greater than a critical value whose estimation is:

𝑣 𝑐 = 𝐾 𝑔 (𝜌 𝑤 -𝜌 0 ) 𝜑( 𝑜 - 𝑤 ) (7)
For experiments with sand, this critical velocity is about 0.040 mm.s -1 calculated from the data in Tables 1 and2. As for the injection rates, they lead to interstitial velocities between 0.0038 and 0.0075 mm.s -1 below the critical value. However, the intrinsic permeability estimated here from the Kozeny-Carman formula (Eq. 1)

has an uncertainty. Given the fairly large grain size distribution, it is likely that the intrinsic permeability is much lower than K = 1.5E-11 m 2 estimated in Table 1. It is therefore likely that the displacement of the oil by the water in our experiments might result in viscous digitations.

In order to settling the question, one can refer to the phase diagram proposed by connecting the viscosity ratio to the capillary number. The values log (2/1) = 0.47 and log (Ca) ~ -5 confirm that the experiments are located at the crossing between stable displacement and capillary fingering.

Moreover, even if the porous medium was prepared in homogenous way, the local heterogeneities on micro-scale cause the appearance of fingers and non-symmetry in horizontal sections (fig. 7). Nevertheless, the destabilizing effect of viscous difference cannot be compensated by gravity or capillarity forces. Finally, the forces that remain to be larger impact of the water flooding process and developing fingers are mainly the capillary forces, but to a lesser degree the viscosities difference between the two fluids.

The oil-wet and water-wet porous media have been tested. In the oil-wet pores (polystyrene beads), oil is the wetting phase, so that the polystyrene beads will prefer contact with the oil rather than water. In such a configuration, the capillary force acts as a resistance force that prevent oil movement and preserve it in contact with beads surface. The calculation gives -4.7 < log (Ca) < -4.4 with log (2/1) unchanged, which proves that the situation is not fundamentally modified for the phase diagram compared to that of sand.

Conversely in water-wet pores (packed sand), oil is the non-wetting phase, and the capillary force no longer acts as a resistance force, but as the positive contribution for the momentum balance. Consequently, in our experimental results we can observe that the remaining oil in the oil-wet medium is approximately three times greater than the water-wet medium, Sor is 38 % for polystyrene beads and 11% for sand at the same experimental conditions. Nevertheless, the oil displacement process in sand model is also impacted by the sample permeability and the capillary forces as the pore size is smaller than in polystyrene model, d is 2.36E-04 m comparing with 4.03E-05 m for sand model (Eq. 6).

Conclusions

High We emphasize that MRI technique is well adapted to distinguish the distribution of fluids in comparison with other imaging modalities because it only "see" the 1 H in liquid phase.

The importance of water channelling or fingering phenomena was obviously found.

Obviously the size of the beads/grains and the value of porosity play an important role in the deformation of the moving front. The relationship between the residual oil saturation and dimensionless numbers were also investigated. The water-oil displacement process and the amount of trapped oil mainly controlled by the wettability of matrix and capillary force. In this study, the flooding process gives the following dimensionless number: 6.4E-6 < Ca < 3.8E-5 and 1.2E-4 < Bo < 2.5E-3, which confirms the important effect of the capillarity.

The flooding images (Fig. 8) have shown that the advance of the displacement front happens in the form of occasional jumps and is controlled by the viscous and capillary forces but also by the heterogeneity of the medium. The analysis of the results based on the phase diagrams proposed by Lenormand [START_REF] Lenormand | Liquids in porous media[END_REF] confirms that the experiments are located at the intersection of the stable viscous displacement and capillary fingering regimes, which explains that relatively small amplitude fingers are observed.

Figure 1 :

 1 Figure 1: Experimental setup: (1) 600 MHz NMR system; (2) Computer for data

Figure 2 :

 2 Figure 2: Sand Grain frequency vs grain size matching with Log-normal function.

Figure 3 :

 3 Figure 3: MRI vertical slice of a stack of polystyrene beads contained in a PVC

Figure 4

 4 Figure4shows the consecutive series of images in vertical and horizontal

Figure 4 :

 4 Figure 4: Consecutive MRI images of the water-oil displacement in the model of

Figure 5 :

 5 Figure 5: Residual oil saturation image in a vertical section (a) for the displacement

Figure 6 :

 6 Figure 6: Histogram of residual oil distribution corresponding to its population in

Figure 7

 7 Figure 7 from the first water appearance in FOV (i.e. 1h50 after the start of water

Figure 7 :

 7 Figure 7: Consecutive MRI images of the water-oil displacement in the model of

Figure 8 :Figure 9 :

 89 Figure 8: Oil-water displacement in the sand model, Qinj = 0.12 mL/min: (a, b, c,

Figure 10 shows

 10 Figure 10 shows the histogram of the residual oil saturation of the sand model. The

Figure 10 :

 10 Figure 10: Histogram of residual oil distribution corresponding to its population in

Figure 11 :

 11 Figure 11: Averaged oil saturation vs injected PV for the model of packed sand.

  -resolution MRI technique was used to investigate two-phase fluids flow of oil and water in porous media. In this study, experiments were conducted on a vertical porous medium formed from packed polystyrene beads or sand (two materials with different wetting properties). Positive impact on imaging procedure was observed by adding MnCl2 to the injected water phase. It has shortened the T2 of water relaxation time to 0.7 ms instead of 2.35 s without any effect on the T2 of the oil phase. Given the relatively slow displacement of the phases involved (more than 10 hours for an experiment), the MRI technique has allowed us to have a near 3D and highly accurate description of fluid movements.

Table 1 :

 1 The porous media characteristics for polystyrene beads and packed sand.

	Porous medium	Model tube material	Porosity (%)	MnCl2 (mole/l)	Permeability (m 2 )	Model net length (cm)	Model internal diameter (cm)
	Polystyrene beads	Plastic	38	0.01	2.9E-10	10	3.4
	Packed Sand	Glass	39	0.02	1.5E-11	10	3.4

Table 2 :

 2 Sand particles size distribution versus mass and grain population

	Size of sieve (mm)	Average size of population (mm)	Mass (g)	Number of grains (supposed to be spherical)	Frequency %
	0.025	0.040	0.11	188867	3.614
	0.05	0.075	2.82	605232	11.581
	0.1	0.130	82.63	3405372	65.159
	0.16	0.205	92.75	974786	18.652
	0.25	0.325	19.62	51749	0.990
	0.4	0.450	0.16	206	0.004

Table 3 :

 3 Fluids properties at standard condition (20 o C).

	Oil density	Oil viscosity	Water density	Water	
	(kg/m 3 )	(cP)	(kg/m 3 )	viscosity	(N/m)
				(cP)
	800	2.96	1000	1	0.05

Table 4 :

 4 Residual oil saturation at different injection rates for the packed sand model.

	Qinj (mL/min)	0.08	0.12	0.16
	Sor (series 1)	13.8 %	11.3 %	11.8 %
	Sor (series 1)	13.9 %	9.7 %	12.3 %

Table 5 :

 5 Capillary number vs residual oil saturation at different injection rates for sand models.

	Qinj (mL/min)	0.08	0.12	0.16
	Sor (series 1)	13.8 %	11.3 %	11.8 %
	Ca	6.41E-06	9.61E-06	1.28E-05

Acknowledgments

This work is supported by LEMTA (Laboratoire d'Energétique et de Mécanique Théorique et Appliquée, UMR 7563) and partially financed by TOTAL.


Thibaud Chazal

MD Myrto Costopoulos

Ph armD Elisabeth Maillart

MD Carole Fleury

PharmD Dimitri Psimaras

MD Paul Legendre

MD Marc Pineton De Chambrun

MD Julien Haroche

PhD Catherine Lubetzki

PhD Zahir Amoura

MD, MSc Magali Legarff-Tavernier

PharmD Fleur Cohen Aubart

Dr Fleur Cohen-Aubart

The cerebrospinal fluid CD4/CD8 ratio and interleukin-6 and -10 levels in neurosarcoidosis: a multicenter, pragmatic, comparative study

Keywords: sarcoidosis, central nervous system, cerebrospinal fluid, interleukin, cytokine, tocilizumab

  L'archive ouverte pluridisciplinaire

Methods:

We conducted a retrospective study of CSF biomarkers in patients with neurosarcoidosis who underwent CSF analysis between 2012 and 2017 as well as various control populations.

Results:

We analyzed 43 patients with neurosarcoidosis, 14 with multiple sclerosis (MS), and 48 with other inflammatory disorders. The IL-6 levels were higher in sarcoidosis patients than in MS patients (median 8 versus 3 pg/mL, p=0.006). The CD4/CD8 ratio was higher in sarcoidosis patients than in MS patients and in patients with other inflammatory disorders (median 3.18 versus 2.36 and 2.10, respectively, p=0.008). The IL-6 level was higher in patients with active neurosarcoidosis than in nonactive neurosarcoidosis patients (median 13 versus 3 pg/mL, p=0.0005). In patients with neurosarcoidosis, a CSF IL-6 concentration >50 pg/ml was associated with a higher risk of relapse or progression-free survival (Hazard Ratio 3.60; 95% Confidence Interval 1.78- 23.14). A refractory neurosarcoidosis patient was treated with an anti-IL-6 monoclonal antibody that produced a complete neurological response.

Conclusions:

The CSF CD4/CD8 ratio and IL-6 concentration are increased in neurosarcoidosis compared to MS and other inflammatory disorders. A CSF IL-6 concentration > 50 pg/mL is associated with relapse or progression of neurosarcoidosis. IL-10 levels may be elevated in neurosarcoidosis. Comparison between active (ePost>0) and non-active (ePost=0) patients.

Neurosarcoidosis n=43

Multiple

* statistically significant

Sarcoidosis is a multisystem disease characterized by the formation of noncaseating granulomas in various organs [1]. Central nervous system (CNS) involvement is clinically present in 5% of cases, and represents a major cause of disability [START_REF] Cohen Aubart | Neurosarcoidosis: Diagnosis and therapeutic issues[END_REF].

Neurosarcoidosis is a challenging condition [START_REF] Hoitsma | Neurosarcoidosis: a clinical dilemma[END_REF]. First, CNS localization of sarcoidosis may be the first manifestation of the disease and should be differentiated from a broad range of inflammatory, infectious and neoplastic conditions, such as multiple sclerosis, infectious meningitis, neoplasia (solid tumors and lymphoma), histiocytic disorders and other autoimmune conditions. Next, the diagnosis of sarcoidosis relies on the documentation of noncaseating granulomas, but the accessibility of the CNS for a biopsy is low [START_REF] Zajicek | Central nervous system sarcoidosis-diagnosis and management[END_REF]. Finally, the course of neurosarcoidosis involves frequent relapses despite treatment with glucocorticosteroids and immunosuppressive drugs [START_REF] Bitoun | Treatment of neurosarcoidosis: A comparative study of methotrexate and mycophenolate mofetil[END_REF].

We lack biomarkers for diagnosis and prognosis in neurosarcoidosis. Cerebrospinal fluid (CSF) analysis usually reveals lymphocytic meningitis, sometimes with low glycorrhachia levels and specific oligoclonal bands [START_REF] Wengert | Neurosarcoidosis: correlation of cerebrospinal fluid findings with diffuse leptomeningeal gadolinium enhancement on MRI and clinical disease activity[END_REF]. However, all these biological findings have been reported in other inflammatory, infectious or neoplastic conditions.

Typical sarcoidosis granulomas comprise histiocytic cells (epithelioid and multinucleated giant cells) and T CD4 lymphocytes. Therefore, patients with sarcoidosis harbor a blood T CD4 lymphopenia together with an enrichment of T CD4 lymphocytes in the organs. The CD4/CD8 ratio serves as a biomarker in the bronchoalveolar lavage (BAL); a value of this ratio greater than 3.5 has been demonstrated as a reliable marker for the diagnosis of sarcoidosis rather than other interstitial lung diseases [START_REF] Welker | Predictive value of BAL cell differentials in the diagnosis of interstitial lung diseases[END_REF]. The value of the CSF CD4/CD8 ratio has been evaluated in a small study of 7 patients; 2 of them had an elevation of the T CD4 lymphocyte subpopulation [START_REF] Stern | Neurosarcoidosis: cerebrospinal fluid lymphocyte subpopulations[END_REF]. However, this study was too small to allow conclusions to be drawn.

CSF interleukin (IL)-6 and IL-10 levels have been used in various neurological conditions. In particular, the concentrations of these cytokines have been evaluated in cerebral lymphoma, multiple sclerosis, and Behcet disease (BD) with neurological involvement [START_REF] Wang | The diagnostic and prognostic value of interleukin-10 in cerebrospinal fluid for central nervous system lymphoma: a meta-analysis[END_REF][START_REF] Nguyen-Them | The CSF IL-10 concentration is an effective diagnostic marker in immunocompetent primary CNS lymphoma and a potential prognostic biomarker in treatment-responsive patients[END_REF][START_REF] Ikeguchi | CSF and clinical data are useful in differentiating CNS inflammatory demyelinating disease from CNS lymphoma[END_REF][START_REF] Saruhan-Direskeneli | Cytokines and chemokines in neuro-Behcet's disease compared to multiple sclerosis and other neurological diseases[END_REF][START_REF] Akman-Demir | Interleukin-6 in neuro-Behcet's disease: association with disease subsets and long-term outcome[END_REF]. The CSF IL-6 is elevated in a broad spectrum of neurological diseases, including infectious diseases and neuro-BD. An elevated CSF IL-10 concentration seems to be a reliable marker of lymphoma, but the comparative groups in previous studies did not include patients with neurosarcoidosis [START_REF] Wang | The diagnostic and prognostic value of interleukin-10 in cerebrospinal fluid for central nervous system lymphoma: a meta-analysis[END_REF][START_REF] Sasagawa | Diagnostic value of interleukin-10 in cerebrospinal fluid for diffuse large B-cell lymphoma of the central nervous system[END_REF][START_REF] Sasayama | Cerebrospinal fluid interleukin-10 is a potentially useful biomarker in immunocompetent primary central nervous system lymphoma (PCNSL)[END_REF]. Thus, we aimed to study the lymphocyte subpopulations counts and IL-6 and IL-10 levels in the CSF of patients with neurosarcoidosis, and compared the results with those of patients with other inflammatory disorders of the CNS.

Methods

The lymphocyte population counts and IL-6 and 10 levels were analyzed from backup CSF samples obtained from patients with an inflammatory CNS disorder between 2012 and 2017 in one internal medicine department and 2 neurology departments at the Pitié-Salpêtrière Hospital (Paris, France). The study was approved by the ethics committee Comité de Protection des Personnes Ile de France VI, and was conducted in accordance with the Declaration of Helsinki.

Continuous variables are reported as the mean (standard deviation -SD) or median (interquartile range -IQR) and were compared using a Mann-Whitney test, Kruskal-Wallis test or Wilcoxon matched-pairs signed-rank test. Categorical variables are reported as the count (percentage) and compared using Fisher's exact test. Survival curves were built using the Kaplan-Meier method considering the time from the first IL-6 concentration measurement to relapse, progression or last follow-up. All of the tests were two-sided, and a p-value < 0.05 was considered statistically significant. All statistical analyses were performed using GraphPad V6.0 (GraphPad, La Jolla, CA, USA).

The dataset used and analyzed during the current study is available from the corresponding author on reasonable request.

Results

Clinical characteristics

Out (range 17-58). Eleven patients had remitting-relapsing subtype, and 3 had primary progressive disease. Two patients had only brain localizations, whereas 12 had brain and spine localizations. Eight patients had no treatment at the time of lumbar puncture, one was receiving corticosteroids, 2 were receiving azathioprine, 2 glatiramere acetate, and one was receiving interferon-beta. In the "others" group, there were 26 men and 22

women, and the median age at the time of the first measurement was 48 (range: 18-86).

CSF lymphocyte population counts

The results of the CSF lymphocytes population counts analysis are shown in Table 1.

The CD4/CD8 ratio significantly differed between the 3 groups. Moreover, the CD4/CD8

CSF IL concentrations

The CSF IL concentrations are shown in Table 1. The CSF IL-6 concentration differed between the 3 groups. The IL-6 level was higher in the neurosarcoidosis and other inflammatory disorder groups than in the MS group. Sixteen patients had an IL-6 level > 20 pg/mL: 13 patients with neurosarcoidosis and 3 patients with R-group histiocytosis.

The IL-6 concentration was higher in neurosarcoidosis patients with active disease compared with those with non-active disease ( There were no differences in IL-6 (8.00 for treated and 6.00 for non-treated, p=0.60) and IL-10 (2.00 versus 2.00, p=0.21) levels between treated and non-treated patients at the time of the analysis, among patients with neurosarcoidosis.

Outcomes of neurosarcoidosis

We studied the outcomes of the 43 patients with neurosarcoidosis. The median duration of their disease since the diagnosis of neurosarcoidosis was 15 months (range: 0-141).

Discussion

In this study, we report the results of CSF biomarkers in neurosarcoidosis, MS and other inflammatory CNS disorders. We showed that the CD4/CD8 ratio and IL-6 levels were significantly higher in sarcoidosis than MS. We also showed that the IL-6 concentration was significantly higher in neurosarcoidosis patients with active disease compared to those with non-active disease. A high CSF IL-6 concentration (>50 pg/mL) was associated with a shorter time to relapse or progression of neurosarcoidosis. Moreover, a patient with refractory neurosarcoidosis improved after treatment with tocilizumab, which is an anti-IL-6 monoclonal antibody.

CSF CD4/CD8 ratio as a diagnostic marker in neurosarcoidosis

Neurosarcoidosis is challenging to diagnosis and can mimic a broad range of inflammatory diseases. Various CSF biomarkers, e.g., CSF angiotensin conversion enzyme (ACE), have been studied for diagnostic and prognostic purposes but yield low reliability [START_REF] Bridel | Cerebrospinal fluid angiotensin-converting enzyme for diagnosis of neurosarcoidosis[END_REF]. In our study, a CD4/CD8 ratio >5 was highly suggestive of neurosarcoidosis (9 out of 11 patients) and was never observed in MS patients.

Moreover, a CSF CD4/CD8 ratio>5 was suggestive of active neurosarcoidosis (8 patients out of 9). The CD4/CD8 ratio has been previously evaluated in the lung for pulmonary manifestations of sarcoidosis [START_REF] Shen | Diagnostic Performance of Bronchoalveolar Lavage Fluid CD4/CD8 Ratio for Sarcoidosis: A Meta-analysis[END_REF], in the aqueous humor of sarcoid uveitis patients [START_REF] Dave | Increased Aqueous Humor CD4+/CD8+ Lymphocyte Ratio in Sarcoid Uveitis[END_REF][START_REF] Kojima | The CD4/CD8 ratio in vitreous fluid is of high diagnostic value in sarcoidosis[END_REF], and in the CSF in a small study of neurosarcoidosis and yielded variable reliability [START_REF] Hyldgaard | Value of s-ACE, BAL lymphocytosis, and CD4+/CD8+ and CD103+CD4+/CD4+ T-cell ratios in diagnosis of sarcoidosis[END_REF]. In our larger study, we demonstrated that CSF CD4/CD8 ratio could be useful for diagnostic and prognostic purposes in neurosarcoidosis patients.

CSF IL-6 level as a prognostic marker in neurosarcoidosis

The CSF IL-6 concentration was elevated in neurosarcoidosis and other inflammatory disorders. In neurosarcoidosis patients, the CSF IL-6 concentration significantly decreased with treatment. Moreover, a CSF IL-6 concentration > 50 pg/mL was associated with a higher risk of relapse and progression. IL-6 expression has been found to be upregulated in granulomas [START_REF] Christophi | Gene expression profiles in granuloma tissue reveal novel diagnostic markers in sarcoidosis[END_REF]. Moreover, IL-6 is essential for the differentiation of Th17 cells, an IL-17-producing helper CD4+ T cell subset that is involved in sarcoidosis pathogenesis [START_REF] Broos | Increased T-helper 17.1 cells in sarcoidosis mediastinal lymph nodes[END_REF]. The CSF IL-6 concentration may be elevated in other inflammatory disorders. In neurosarcoidosis, an elevated CSF IL-6 level seems to be associated with a higher risk of relapse and worse progression-free survival.

Targeting IL-6 in neurosarcoidosis

Neurosarcoidosis is a challenging condition. Glucocorticoids are the cornerstone of treatment for neurosarcoidosis, but they have cumulative toxicity. Immunosuppressive drugs have been used with variable efficacy [START_REF] Bitoun | Treatment of neurosarcoidosis: A comparative study of methotrexate and mycophenolate mofetil[END_REF]. Infliximab, a chimeric monoclonal antibody directed against tumor necrosis factor-α, has emerged as a therapeutic option [START_REF] Gelfand | Infliximab for the treatment of CNS sarcoidosis: A multi-institutional series[END_REF][START_REF] Cohen Aubart | Long-term outcomes of refractory neurosarcoidosis treated with infliximab[END_REF]. However, infliximab may have serious adverse effects, and patients have high relapse rates (36-50%) after treatment interruptions. Thus, there is a need for new therapeutic options in neurosarcoidosis. Here, we found that tocilizumab, an anti-IL-6

receptor monoclonal antibody, which was used without increasing the daily steroid dose, was efficacious for treating one neurosarcoidosis patient for whom infliximab was contraindicated. Tocilizumab has been used to treat uveitis, an inflammatory condition that shares pathogenic mechanisms with sarcoidosis [START_REF] Calvo-Rio | Anti-Interleukin-6 Receptor Tocilizumab for Severe Juvenile Idiopathic Arthritis-Associated Uveitis Refractory to Anti-Tumor Necrosis Factor Therapy: A Multicenter Study of Twenty-Five Patients[END_REF]. Tocilizumab should probably be investigated in patients with sarcoidosis who are refractory to conventional therapy.

Limitations

Our study has several limitations. The clinical characteristics of the patients were assessed retrospectively. However, this allowed definite diagnoses, since in the setting of neuroinflammatory disorders, the diagnoses might be modified after several months of evolution. The number of samples did not allow multivariate analyses. Finally, we did not obtain CSF samples from patients without neurological diseases.

In conclusion, in this multicenter comparative study, we showed that the CSF lymphocyte population counts and IL-6/IL-10 concentrations were useful diagnostic and prognostic markers. Moreover, IL-6 was found to be an interesting target for the treatment of neurosarcoidosis.

  At the time of the first CSF lymphocyte population counts and/or IL determination, 28 patients were receiving treatment for neurosarcoidosis (corticosteroids for 27 and/or immunosuppressive drugs for 19, including 8 patients treated with infliximab, an antitumor necrosis factor (TNF)-α monoclonal antibody). The IL-6 concentration was measured repeatedly in 28 patients (all treated with steroids, 5 with a first line immunosuppressive drugs, and 23 with a combination of infliximab and low-dose methotrexate in addition to steroids) and decreased under treatment (median at baseline 10, at last determination 6 pg/mL, p=0.015). The patients with an IL-6 concentration at baseline > 50 pg/mL had a worse progression or relapse-free survival than those with IL-6 ≤ 50 pg/mL (Figure2, p=0.0054, hazard ratio 3.60; 95% confidence interval 1.78-23.14). The time course of IL-6 is shown in Figure S1. The median follow-up was 12 months (range 3-84 months).Additionally, a 43-year-old woman who had a past history of multiple sclerosis received a diagnosis of multiorgan sarcoidosis with CNS involvement. She was treated with tocilizumab, an anti-IL-6 receptor monoclonal antibody, because of the progression of the neurological localization of sarcoidosis despite treatment with steroids and cyclophosphamide. Additionally, the anti-TNF-α monoclonal antibody, which can be used in refractory neurosarcoidosis, was contraindicated because of her history of multiple sclerosis. The oral prednisone daily dose was not increased, and the patient received the first infusion of tocilizumab in December 2016. After 3 administrations, her brain MRI showed a disappearance of all gadolinium-enhanced lesions (Figure3). The treatment was maintained until July 2018 without side effects. Her prednisone dosage was tapered to 5 milligrams/day.

Figure 1 .

 1 Figure 1. Receiver Operating Characteristics (ROC) curves of cerebro-spinal fluid

Figure 2 .

 2 Figure 2. Relapse/progression-free survival in neurosarcoidosis patients depending on

Figure 3 .

 3 Figure 3. Magnetic resonance imaging (T1-weighted imaging with gadolinium) before

Figure S1 .

 S1 Figure S1. Time course of IL-6 levels in neurosarcoidosis patients (pg/mL)

Table 1 . Cerebrospinal fluid lymphocyte population counts and interleukin (IL) concentrations

 1

	sclerosis n=14	p**	Others n=48	p***

Table 2 . Cerebrospinal fluid CD4/CD8 ratio and interleukin-6 level in neurosarcoidosis patients.

 2

  of 192 patients who had at least one determination of CSF lymphocyte population In the MS group, there were 7 men and 7 women, and the median age at the time of the first CSF analysis was 36

counts or IL concentrations, 83 were excluded because they had no definite diagnosis of CNS involvement. Thus, we analyzed the results of 47 patients with neurosarcoidosis, 14 with MS and 48 with various CNS inflammatory disorders (including 10 L-group histiocytosis

[START_REF] Emile | Revised classification of histiocytoses and neoplasms of the macrophage-dendritic cell lineages[END_REF]

, 8 neurolupus, 7 R-group histiocytosis

[START_REF] Emile | Revised classification of histiocytoses and neoplasms of the macrophage-dendritic cell lineages[END_REF]

, 6 pSS, 4 neuro-BD, and 4 tuberculosis with CNS localization patients). In the neurosarcoidosis group, 3 patients were further excluded because CNS localization was not confirmed and 1 additional patient was excluded because she had both MS and neurosarcoidosis; therefore, 43 patients (19 women and 24 men, mean age at the time of the first concentration measurement 41 years -range: 19-58) were ultimately analyzed in this group. Among these patients, at the time of the first CSF lymphocyte population counts/IL concentration measurement, 26 patients had an ePOST score >0 and were considered "active neurosarcoidosis", whereas 17 were "non-active".

  ratio was higher in neurosarcoidosis patients than in MS patients. Eleven patients had a CD4/CD8 ratio >5: 9 patients with neurosarcoidosis (8 with active and 1 with non-active disease), 1 patient with pSS and 1 patient with neuro-BD. No patient with MS had a CD4/CD8 ratio >5 (the highest ratio in this group was 3.90). The receiver operating

characteristic (ROC) curves for CD4/CD8 ratio are shown in the Figure

1

. With a CD4/CD8 cut-off of 3.9, the sensitivity was 28.57% and the specificity 100.0 %, when comparing sarcoidosis versus MS. With a CD4/CD8 cut-off of 3.9 the sensitivity was 28.57% and the specificity 87.18% when comparing sarcoidosis with MS and others. CSF CD19 percentages were low in all groups, except in 4 patients with R-group histiocytosis. CSF CD19 percentages did not differ between the groups. We observed the presence of CD19 lymphocytes in the CSF of 6/12 (50%) MS, 19/29 (66%) neurosarcoidosis, and 15/29 (52%) other patients.

Table 2 )

 2 . The ROC curves are shown in the Figure 1. With an IL-6 cut-off of 19.5 pg/mL the sensitivity was 28.95 and the specificity 100.0 %, comparing neurosarcoidosis to MS. With an IL-6 cut-off of 25 pg/mL

	the sensitivity was 26.32 and the specificity 91.23% comparing neurosarcoidosis versus
	MS and others. All MS patients had IL-6 levels ≤ 20 pg/mL. In the group with no
	sarcoidosis and no-MS diagnosis, called "others", IL-6 and IL-10 levels did not differ
	between active and non-active patients. The CSF IL-10 concentration was generally low
	but sometimes elevated in neurosarcoidosis and other inflammatory disorders, although
	never in MS. There were no differences between IL-10 concentrations between groups.

This work was not supported by any funding.