Characterization of proven Late Cretaceous Reservoir rocks in the Gulf of Gabes: Integrated case study

– Microstructural features control the petrophysical properties of rocks. Of these, pore size is particularly sensitive when non-wetting ﬂ uids saturate the reservoir. The pore networks and physical properties (helium, water and mercury saturation porosity, bulk density, nitrogen permeability, P-wave velocity and thermal conductivity) of different rock types from a productive Upper Cretaceous (Coniacian) reservoir in the tunisian offshore are measured on hydrocarbon-washed samples. The facies sampled of Douleb Member are wackestone, packstone and grainstone textures as well as dolostone, dolomitized packstone and anhydrite textures. Based mainly on the results obtained by mercury injection, the porous facies of the Coniacian Douleb Member are characterized by a complex pore system with a large morphological and pore size variability in the rock. Porosity values range from 0.3 to 23.6%, bulk densities vary from 2.05 to 2.92 g.cm (cid:1) 3 . The permeability is variable from 3760 mD to values below 0.01 mD (measurement limit of the device). P-wave propagation velocity values range from 2060 to 6084 m.s (cid:1) 1 and thermal conductivity varies from 1.43 to 3.77 W.m (cid:1) 1 .K (cid:1) 1 . The oil-impregnated facies with the best petrophysical characteristics are mainly the rudist-rich limestones and dolomites of the ﬁ rst unit (U1) of the Douleb Member. The well-sorted grainstones with small rudist debris and peloids have the best reservoir qualities. Porosity is the ﬁ rst order characteristic that controls petrophysical properties. The variability of permeability values around this ﬁ rst-order relationship is attributed to variations in the size of the pore access thresholds and connectivity. The variability in velocities is due to the shape of the voids, while the variability in thermal conductivity measurements is due to the nature of the contacts between the grains.


Introduction
Carbonate formations are largely prospected for petroleum, water or geothermal resources. The porous network characteristics of the reservoirs (pore volume, pore size, pore shape and connectivity) largely contribute to the reservoir properties: permeability, thermal conductivity and elastic properties (Belikov, 1967;Zinszner and Pellerin, 2007;Nabawy, 2015;Haffen et al., 2017). These porous network characteristics, porosity and transfer properties, permeability and thermal conductivity, are due to a large variety of sedimentary, structural or diagenetic processes (Lucia, 1999;Ali et al., 2010;Verwer et al., 2011;Ghafoori et al., 2018). A large data set is already published on petrophysical properties of carbonate reservoirs (Ehnenberg et al., 2006;Al-Tooqi et al., 2014;Nabawy and Kassab, 2014;El Husseiny and Vanorio, 2016;Salah et al., 2016;Njahi et al., 2017), but a low amount of data is available on strictly reservoirs in place except through the analysis of surface analogues which are not saturated with hydrocarbon.
In Central and Southern Tunisia, these series are generally rich in rudists (Zagrarni et al., 2003;Touir et al., 2009;Boughalmi et al., 2019;Boughalmi, 2020;Negra and Jaballah, 2021). They are characterized by variations in thickness and facies (Salmouna-Jomaa et al., 2014;Jaballah, 2017). These variations appear to be controlled by local (tectonic) and global (eustatic) factors. From the petroleum system point of view, the Late Cretaceous carbonate facies in Tunisia, especially those of the Cenomanian-Turonian (Gattar and Bireno Members) and those of the Coniacian (Douleb Member) belonging to the Turonian-Early Campanian Aleg Formation, are known for their good reservoir quality. In fact, they are productive in several sectors of Tunisia, notably in the region of Sfax and the Gulf of Gabes (Burollet, 1956;M'Rabet et al., 1995;Lansari et al., 2010) and more specifically in several oil fields especially those of Guebiba, Gremda, El Ain, Rhemoura and Miskar (M'Rabet et al., 1995;Chaabouni, 1996;Saïdi et al., 1997;Troudi et al., 1999;Zagrarni et al., 2003;Lansari et al., 2010). Studies have shown that the proven reservoirs in the study area are characterized by facies variations (Jaballah, 2017;Salmouna-Jomaa, 2017;Boughalmi, 2020). These variations can directly affect the reservoir potential of these series and their impregnation by hydrocarbons. In addition, several diagenetic factors either may improve or reduce their reservoir quality (Nabawy and Kassab, 2014).
The objective of this paper is to define the petrophysical characteristics and especially reservoir properties of carbonate oil-bearing core samples within a Coniacian rudist reservoir (Douleb Member, Fig. 1). To better understand the relationship between the various petrophysical properties of rocks, a large set of data is acquired, especially to define relationships between transfer properties and microfacies characteristics. Connected porosity and permeability define the reservoir properties and quality. P-waves velocity is a key parameter to inverse seismic data and convert time to depth while thermal conductivity is a key to model diagenetic processes and organic matter maturation.
Finally, it is proposed arguments to explain why oil impregnation does not concern the whole carbonate reservoir and is defined which facies have the best petrophysical characteristics of the productive well.

Geological setting
The studied well is in the Northeast of the Gulf of Gabes approximately 110 km towards the east-southeast from Sfax (Fig. 2). This well is in the eastern part of the Tunisian Sahel in the open sea. It lies on the Pelagian Platform, where during Early Cretaceous to Eocene an incipient rift system developed. This rift system is composed of a series of horsts and tilted blocks (Martinez and Truillet, 1987;Zouari et al., 1999).
The Gulf of Gabes is a subsident domain of the Pelagian Platform and marks the sinking of the Saharan Platform towards the central Mediterranean (Ben Ayed, 1986). In this oriental area, under a thick Neogene series, subsurface data reveal slightly undulating in NE-SW directions (Ben Ayed, 1986;Martinez and Truillet, 1987;Touati and Rodgers, 1998).
The studied carbonate reservoir corresponds to the Coniacian rudist interval comprising the Late Cretaceous (Fig. 3), Paleogene and Neogene series. It is sealed by the clays of the El Haria Formation. The Cenomanian-Turonian Bahloul Formation, covering the east-central part of Tunisia, is considered as a main source rock for the Cretaceous reservoirs, notably the Douleb one.
Concerning the paleogeographic setting of the Late Cretaceous, the Cenomanian-Turonian transition is marked by laminated limestones with marly intercalations of the Bahloul Formation deposited in a relatively deeper environment (Burollet, 1956;Hanini et al., 2004;Caron et al., 2006;Robaszynski et al., 2007;Zagrarni et al., 2008). The Turonian-Early Campanian Aleg Formation is composed of limestones from deep marine environment that show many variations of thickness due to subsidence (Salaj, 1978). The carbonate Bireno and Douleb Members are the lateral equivalents of some marly intervals of the Aleg Formation towards the Central Tunisia (Lansari et al., 2010;Jaballah and Negra, 2016). During the Campanian-Maastrichtian period, the  micritic chalky limestones and the marls of the Abiod Formation were deposited, covering the marls of the Aleg Formation. This unit is mainly composed of limestones settled in open marine sea with variations in sea level (Burollet, 1956;Khessibi, 1978;Melki and Negra, 2004;Negra and Gili, 2004;Bey et al., 2012).
Facies of the Douleb Member are the object of this study (Fig. 2b); they form a large carbonate platform above a low subsidence floor. The shallow marine sedimentation is bioclastic, oolitic, gravelly and locally rudist-rich lithosomes. This platform can be subdivided into an internal platform, a median to external platform and an emerged zone (Zagrarni, 1996;Saïdi et al., 1997).

Materials and methods
The characterization of the reservoir is obtained by qualitative or semi-quantitative petrographical and sedimentological analyses, and by quantitative petrophysical measurements. The adopted methodology is schematized on the chart of Figure 1S (see Supplementary Material).

Sedimentological study
For sedimentological study, first, macroscopic analysis was done to recognize the main sedimentological features of ten cores totaling 112 m in length, secondly, the microscopic analyses of 176 thin sections were conducted, using optical microscopy (highlighting the texture, structure, bioclasts contents, porosity type and the diagenetic process characterizing the studied interval). The microscopic analysis was also done using the Scanning Electron Microscopy (SEM), on 19 samples. Sedimentological analysis led to the classification of 12 different microfacies noted (Mf1 to Mf12) and summarized in Table 1.

Petrophysical study
Prior to the petrophysical measurements, samples were washed thoroughly to extract the oil and mineral salts existing in their porosity. Xylene or toluene is used to extract oils and methanol is used to remove mineral salts using an electrical Soxhlet extractor. After that, they were dried properly without any effect on the clay minerals in an oven at a temperature of 60°C till they have reached a constant weight.
Measurements of porosity, permeability, P-waves velocity and thermal conductivity are carried out on 26 samples, 2.54 cm (1 inch) in diameter and between 3.4 and 4.1 cm in length. They belong to the Coniacian interval of the well drilled in the Gulf of Gabes. Except for permeability measurements made in the ETAP laboratory (Tunisia), all the measurements are made at the GeoRessources Laboratory (Nancy).

Porosity measurements
The porosity is defined as the ratio of void volume to total volume of a material (Zinszner and Pellerin, 2007). In the rock, porosity could be composed by connected or isolated pores with various shapes (Norton and Knapp, 1977).
Helium, water and mercury are fluids used to saturate the samples and to determine the pore volume. The mercury injection porosimetry gives the distribution of the porous volume versus the threshold. The porosity classification proposed by Al-Marzouqi et al. (2010) is used. Microporosity has pore size lower than 0.5 mm, the pore size of the mesoporosity ranges from 0.5 and 5 mm, while microporosity has pore size higher than 5 mm.

Porosity by water saturation
The triple weight method, or Archimeds method, uses a wetting fluid (water) to saturate the porosity (Dullien, 1979) and follows the procedure of the standard RILEM (Rilem, 1978). Samples were placed in a vacuum chamber for 24 h, beside distilled water was degassed and then used to fill samples' chamber following the progression of the sample capillarity fringe. Once, samples were completely submerged, they stayed at least 24 h until they reached a constant weight. The connected porosity is given by: With ' is the porosity (%), W 1 is the weight of sample saturated under vacuum with water (g), W 2 is the weight of saturated sample under hydrostatic condition (immersed under water; g) and W d is the dry weight of the sample (g). The bulk density (d b ) is calculated as follows: With d b is the bulk density (g.cm À3 ).

Porosity by helium saturation
The "UltraPoreTM300" helium porosimeter uses the "Boyle" law to determine the grain volume from the expansion of a known mass of helium into calibrated sample holder. Helium, being a rare and light gas, has the property of easily penetrating and saturating the pores of the sample.
Boyle's law is expressed as follows: Table 1. Microfacies description of the Coniacian interval of the studied-well.

Mf1
Dolomitized packstone: rich in rudists Mf2 Grainstone: fine-grained, well sorted with small rudists, peloids and some benthic foraminifera Mf3 Packstone-grainstone: small rudist-debris, echinoderms and some peloids Mf4 Packstone: calcispheres, planktonic foraminifera and some debris Mf5 Packstone: miliolids, ostracods, planktonic foraminifera and peloids Mf6 Packstone: large rudist debris, peloids and some intraclasts Mf7 Wackestone: fragmented rudists Mf8 Packstone: oolites, micritized bioclasts, echinoderms, gastropods and benthic foraminifera Mf9 Dolostone Mf10 Anhydrite facies Mf11 Packstone: peloids, some benthic foraminifera and echinoderm-debris Mf12 Sandy wackestone: calcispheres, rare planktonic foraminifera and some intraclasts With P 1 is the initial pressure (atm), V 1 is the initial volume (cm 3 ), T 1 is the initial absolute temperature (°C), P 2 is the expanded pressure (atm), V 2 is the expanded volume (cm 3 ) and T 2 is the expanded absolute temperature (°C). The equation used to calculate grain volume is derived from the basic Boyle's law equation as follows: With V holder is the holder's volume (cm 3 ) and V grain is the volume of solid phase (cm 3 ). Knowing the mass of the sample under dry condition, the grain density (d sp ), g.cm À3 , is calculated as follows (Zinszner and Pellerin, 2007): The porosity is calculated using the solid phase density obtained from helium pycnometer test and the bulk density obtained from triple weight measurements with the following equations (Zinszner and Pellerin, 2007):

Porosity by mercury injection
The use of mercury (non-wetting phase) as a saturating liquid provides access to a more complete data set with the distribution of invaded pore volumes vs. their threshold sizes, the percolation threshold, and the trapped and the free porosities (Washburn, 1921;Wardlaw and Taylor, 1976;Wardlaw and Cassan, 1978;Kloubek, 1981;Wardlaw and McKellar, 1981;Li and Wardlaw, 1986).
Mercury is a non-wetting liquid and a pressure must be applied to enter the voids of the sample. Injection pressure depends on the radius of the capillaries; it is defined by Young-Laplace's law: With P (Pa) is the pressure, d (mm) is the length distance of two opposite walls of a pore expressed by an effective radius, s is the surface tension of mercury (485 dynes.cm À1 ) and u is the contact angle (130°). Micrometrics Autopore IV series 9200 porosimeter allows pressures range from 0.004 to 220 MPa, i.e. the pore access sizes range between 307 mm and 0.005 mm.
Testing process is decomposed in three main sequences. The first is a drainage sequence, composed of two phases, a low pressure injection phase from 0.004 to 0.2 MPa, and a high pressure injection phase from 0.1 to 220 MPa. The second is an imbibition sequence from 220 to 0.1 MPa. The third is a drainage sequence again, from 0.1 to 220 MPa. The duration of the test is four hours.
Several porosity volumes and threshold values are determined. The connected porosity is saturated during the first drainage sequence, it is the mercury's volume injected at 220 MPa. It is divided into low and high pressures porosity parts, measured between 0.004 and 0.1 MPa and 0.1 and 220 MPa, respectively. The trapped and the free porosities, TrP and FP, respectively, are obtained using the two last sequences. Due to the measurement conditions, these two porosity parameters must be interpreted using only the high-pressure porosity part, CP, obtained during the first drainage sequence. These values are characteristic of the porosity volume connected through thresholds between 7 and 0.004 mm. Trapping is mainly controlled by the ratio between the pore size and pore throat. If this ration is higher than 6, mercury is trapped in ink-bottle shape pores (Wardlaw and Yu, 1988).
From the cumulative injection curve, three threshold values are determined using the first drainage curve. First, the percolation threshold defined as the inflexion point of the curve, it is built graphically from the curve. Two other diameters values are defined at the beginning and the end of the injection sequences, d1 and d2, and these elements define the spreading of threshold values (ST). "d1" is defined as the last point of the low deep section at the beginning of the injection curve and "d2" is the first point of the plateau in the final part of the injection curve. The last element, defined to describe the porosity distribution, is the incremental intrusion curve decomposed in several porosity families.

Permeability
Permeability (K) refers to the ability of a material to transfer fluids, and therefore it is closely related to the intrinsic properties of the porous network, mainly the size, the shape, and the connectivity (Scheidegger, 1974;Homand and Duffaut, 2000).
The gas permeameter "UltraPermTM 400" uses Darcy's law to calculate the permeability from the gas flow rate and the measured upstream and downstream pressures.
Measurements are performed using Nitrogen under low confining pressure (2 MPa). As permeability measurements did not exhibit slip-flow phenomena between gas molecules and solid walls, Klinkenberg effect was not considered (Klinkenberg, 1941).
Darcy's Law: With Q is the volumetric flow rate (m 3 .s À1 ), K is the permeability coefficient (mD), A is the area of the sample section perpendicular to the flow (cm 3 ), DP is the pressure difference between the top and the bottom of the sample (atm), L is the length of the sample (cm) and m is the viscosity of fluid (cP).

P-wave velocity
The measurement of the velocity of compressed or primary longitudinal P-waves representing the vibration of the particles parallel to the direction of propagation of the wave (Zinszner and Pellerin, 2007;Boulanouar et al., 2013). The propagation velocity depends on the mineralogical content, the grain shape and contact, the porosity, and the pore space geometry, particularly the cracks distribution (Homand and Duffaut, 2000). This measure makes it possible to evaluate elastic physical properties of rocks, like Young's modulus or Poisson's ratio (Bourbié et al., 1986;Wang and Nur, 1992).
The measuring equipment is composed by two piezoelectric transducers of frequency 54 Hz and a Pundit Lab pulse generator. After determining the path's length (L) and the propagation time of the ultrasonic waves (t), the propagation velocity of P-waves is given by the formula:

Thermal conductivity
Thermal Conductivity Scanning (TCS) technique is based on the variation of temperature at a sample surface following a known and controlled heat input (Popov et al., 1983(Popov et al., , 1985(Popov et al., , 1999. The experimental device is composed by a movable block composed of two temperature sensors sensitive to electromagnetic radiation and a source of heat located between both captors so that it is possible to measure the temperature of the sample before and after heating. To obtain an absolute value of the thermal conductivity of the analysed material, two known thermal conductivity standards (lstd) are placed on each side of the sample. The thermal conductivity of the material will be determined from lstd and the ratio of temperature differences: Quartz standards are used for dry samples.

Petrophysical properties
The results of measurements of density, porosity, permeability, P-waves velocity, and thermal conductivity are presented in Table 1S (see Supplementary Material).

Connected porosity values
The obtained values with the three methods (water, helium, and mercury saturations) are homogeneous and almost consistent with high regression coefficients (R 2 = 0.99) showing the certainty of the porosity values with different measurement methods despite of different size of samples used in the different methods (Fig. 8a). Three rock-types of samples are distinguishable based mainly on water and helium porosimetry data (Fig. 8b). The first one (Rt1) consists of samples that have porosity lower than 3%. In the second group (Rt2), porosity ranges from 14 to 19%; for the third one (Rt3), porosity values range from 21 to 24%.
If water porosity and helium porosity values show a good correlation (Fig. 8b); however, porosity values obtained by Hginjection tests are quite dispersed compared to helium porosity values (Fig. 8c). In fact, this probably illustrates the sample size effect. Indeed, samples used for Hg-injection test are much   smaller than those used in the other two techniques (water and helium saturation) which may have induced some uncertainty and therefore resulted into dispersion of the data (Bertrand et al., 2021).
Because of the homogeneity of the results obtained by water and helium saturation, to discuss the correlation with the other petrophysical parameters (density, permeability, P-waves velocity and thermal conductivity), only the porosity measured by helium saturation will be taken into consideration to draw relationship with other properties.

Pore throat distribution
The Hg-porosimetry gives valuable data about the pore volume distribution according to the access thresholds or pore diameters distribution, the percolation threshold (Katz and Thompson, 1986) are ranging from 3 to 15 mm (Tab. 2; Fig. 9). However, this relative homogeneity of this parameter covers an important variation of the injection curve shapes illustrated by the spreading between d1 and d2 values. According to the classification of Ali et al. (2010), the main part of the porosity is defined as mesopores and macropores (Tab. 3). Three types of samples show a small fraction of micropores, Mf6, Mf1 and Mf2 (Tab. 3; Figs. 9A', 9C' and 9D'). The spreading of the pore throats becomes tighter when the grain sorting is better.
A large distribution (ST: 199.8 mm) is observed for the facies Mf6 (Fig. 9A), its texture is packstone-grainstone with peloids and rudists. It is very poorly sorted facies with debris of variable sizes. On the other hand, Mf1, Mf2 and Mf7 facies are well-sorted rudist-rich facies with a ST ranging between 5 and 19.7 mm.
The pore throat distribution could be divided in several pore families according to its wideness and its segmentation. Three classes for the poorly sorted material (Mf6, Fig. 9A'), dolomitized material (Mf9, Fig. 9B'), two classes for the more sorted material (Mf1 and Mf2, Figs. 9C' and 9D') and one class for the well sorted one (Mf 7, Fig. 9E').
The trapped porosity (TrP; Fig. 9), calculated for threshold lower than 6 mm (see Sect. 3.2.1.3), remains relatively high (50% and more). These values demonstrate a strong porosity shape heterogeneity, ink-bottle shapes, for the meso-and micropore network due to the heterogeneity of the sediment granulometry.
Thus, dispersion of the pore throat size increases from the wackestone to the packstone passing through the group of dolomitized samples. The percolation threshold ranges over less than one order of magnitude from 3 to 15 mm whereas the wideness of the pore size distribution ranges over more four orders of magnitude from 0.1 mm to more than 200 mm for the packstone. The threshold spreading is clearly dependent on the spreading of the clasts' size.

Permeability
The three rock-types considered previously using helium porosity and facies criteria have specific nitrogen permeability properties (Fig. 10). This large distribution is not only linked to the porosity variation but depends on the percolation threshold value and on the wideness of the threshold distribution, probably significant of connectivity variations (Nooruddin et al., 2014;Mielke et al., 2017). In this way, the permeability decreases with the percolation threshold value and with the wideness of the pore throats distribution illustrates by the Mf6, Mf9, Mf1 and Mf7 facies (Fig. 9). -The Rt3 composed of Mf2 samples (Figs. 6C and 6D), with the highest porosity (between 21 and 24%) but an intermediate permeability (between 21 and 360 mD) is controlled by an intermediate threshold wideness (Fig. 9).
These porosity-permeability relations are in accordance with the rock fabric-petrophysical classes proposed for the non-vuggy carbonate by Lucia (1999Lucia ( , 2004. They illustrate the grain size and textural dependences of these properties ( Fig. 1-2.20 in Zinszner and Pellerin, 2007). Measured values are in the same range than values obtained by Soete et al. (2015) or Watanabe et al. (2019) but higher than measured values on Lebanon samples by Salah et al. (2020). The correlation coefficient is quite good considering the facies variability.

Bulk density
The data set ranges over 2.65 and 2.45 g.cm À3 for volumetric mass density. The main correlation line with porosity, well drawn for the calcite materials, demonstrates the absence or the very low amount of unconnected porosity for  Boughalmi et al.: BSGF 2023, 194, 8  samples below the correlation line, especially for the low porosity samples (Fig. 11). The samples above the correlation line are clearly mixed samples with a low fraction of dolomite or anhydrite.

P-waves velocity
The P-waves velocity range from 2060 to 6094 m.s À1 . It presents a quasi-linear distribution regarding to the porosity (Fig. 12). These values are consistent with the results obtained by  Salah et al. (2020). For each Rt, dispersion around the mean line is the conjugate effect of grain size, the type of contact between grains, void shape and microfractures.
The Rt1 group, those with speed ranging from 5063 to 6094 m.s À1 and porosity, lower than 4% is formed by microfacies Mf4, Mf5, Mf8, Mf12, and the increase of the P-wave velocity dues to a decrease of the matrix content (Figs. 7B-7E, respectively). In this group of low porosity, anhydrite samples (Mf10, Fig. 7A) present a large set of planar structures that could explain the important variability of the P-waves.
The Rt2 group, with porosity from 14 to 19%, and P-wave velocity from 2364 to 4762 m.s À1 is formed by Mf1, Mf3, Mf11, Mf7, Mf9 and Mf6 microfacies and ordered with increasing P-wave velocity. This order illustrated the effect of the contact shape from punctual and discontinuous planar from Mf6 (Figs. 13A and 14A) and, planar and continuous for the others. Mf1 and Mf9 facies are dolomitic, with grains constituting a rigid network useful for P-wave propagation (Figs. 6B, 13B and 14B), these facies representative of the main behavior. The dolomite content does not induce significant variation of the P-wave velocity as already proposed by Verwer et al. (2011).
The Rt3 group is composed of Mf2 samples. Porosity values vary from 21 to 24% and velocities from 2060 to 2797 m.s À1 . Samples of this group presents a large degree of cementation and associated change of the porosity shape (Figs. 6C, 13C and 13D). Fournier et al. (2014) calculated P-wave velocity/porosity relationship involving pore shape, pore shape of their samples ranges from 0.1 and 0.2. These values are acquired under 40 MPa confining pressure. Concerning the Tunisian samples taken for this study, porosity ranges from 12 and 13%, while the P-wave velocity ranges from 4200 and 2000 m.s À1 , measured under atmospheric conditions, similar data are obtained by Salah et al. (2020). Using the Figure 8a of Fournier et al. (2014), the inclusion aspect ratio of the porosity ranges from 0.1 and 0.05 corresponding to a flatter pore shape. Pore shape difference could be linked to difference in experimental conditions, and in particular the confining pressure difference. Indeed, P-wave velocity increases for measurements performed under low confining pressure range and this increase is attributed to closing of micro-cracks (Gardner et al., 1974;Vernik, 1994), but microcracks are not observed in thinsections, only stylolithes are present in numbers and could explain the variability if they are opened, but interpretation of these petrophysical values remains subject to discussion.

Thermal conductivity
Thermal conductivity values range from 1.4 to 3.8 W.m À1 .K À1 (Fig. 15). This result is consistent with data found in the bibliography (Hartmann et al., 2005;Pasquale et al., 2015;Mielke et al., 2017). The facies Mf10, presents the highest value due to the high thermal conductivity of the Anhydrite (around 5 W.m À1 .K À1 , Clauser and Huenges, 1995;Pasquale et al., 2015) with regard to calcite one (3.5 ± 0.5 W.m À1 .K À1 ; Clauser and Huenges, 1995) and the low porosity of the material. Similar analysis is made for facies Mf9 with high dolomite content, indeed, the thermal conductivity of dolomite is 4.8 ± 0.54 W.m À1 .K À1 (Clauser and Huenges, 1995;Pasquale et al., 2015), while the relative lowest value of the facies Mf5, dolomite also, is attribute to the more dispersed dolomite grains than in MF9.
Except these previous facies, Figure 15 deciphers a sharp control of the porosity on this property for the other calcite facies. It seems that the thermal conductivity is less sensitive to the shape of the porous network and to the grain contact than Pwave velocities.

Petrophysical properties and rock-types characteristics
The twelve microfacies are gathered in three groups of facies, they have their own petrophysical and sedimentological characteristics.

The first rock-type (Rt1)
Samples of the first group Rt1 show the lowest porosity and permeability values and the highest P-wave velocity and thermal conductivity values. These properties depend on their low porosity and high density, themselves controlled by sedimentological and diagenetic processes (Salah et al., 2016;Njahi et al., 2017;Corbett et al., 2017). They regroup the lowest porous microfacies including Mf4, Mf5, Mf8, Mf10 and Mf12.  According to their density and mineral composition, two sets of samples are recognized. Those with a calcite composition, correspond to the fine micritic units rich in quartz (Fig. 14C), sulfures (Fig. 14D), phosphates and glauconite, and those with an anhydrite composition and a higher solid phase density.
Several facies (Mf4, Mf5, Mf8 and Mf12) are also affected by a silicification of the matrix with hexagonal-shaped automorphic quartz crystals (Fig. 14C), by precipitation of pyrite (Fig. 14D) and phosphates (Fig. 7B) decreasing the porosity of these facies. They explained mainly the highest thermal conductivity values. The pore threshold of finegrained facies initially low at sediment deposition is reduced by diagenetic processes. So, the low permeability is likely related to their low porosity (from 0.3 to 2.9%), their low threshold values and small induced percolation threshold (Nooruddin et al., 2014).
In the Rt1, P-wave velocity values, result from the low porosity however, measured values are lower than the pure mineral one (Tab. 2S; see Supplementary Material). The gap between these values, signs up the clay content and the shape of the contact between grains (Fournier et al., 2014).
The anhydrite facies are related to high values for P-wave and thermal conductivity properties due to textural effects and the high properties of the constituting minerals.

The second rock-type (Rt2)
The Rt2   different values. This group is formed by the oil-impregnated bioclastic facies presenting a medium to good reservoir quality (i.e. porosity and permeability values).
Variations of the bioclast size and matrix content clearly control the wideness of the threshold distribution directly linked to the high permeability values and to the low P-wave velocity and thermal conductivity values. The permeability increases with the percolation thresholds values and with the widening of the throat wideness ( Fig. 16) (Ehnenberg et al., 2006;Rashid et al., 2015;El Husseiny and Vanorio, 2016). Dolomitic facies have specific comportment; the permeability is low while the percolation threshold and the wideness of the throats are high like those of high permeability samples highlighting a role of the pore shapes specific for these facies.
A relationship between these parameters is classically described (Katz and Thompson, 1986) even if other parameters (tortuosity, fractal tubular bundle) may act an important function (Buiting and Clerke, 2013;Rashid et al., 2015). The combined effect of both parameters is illustrated by le Mf11 samples suite, where the permeability increases with increase of the percolation threshold (average pore: AP) and throat wideness. The enlargement of the pore threshold distribution is linked to the increase of grain size dispersion and especially for the Mf6 facies, with a crack network development.
Limestones with large debris of rudists and peloids (Mf6) are characterized by low to medium velocity (between 2364 and 3939 m.s À1 ) and medium to high porosity (between 15 and 19%). Variations of velocities and porosity are the results of badly-sorted grain sizes. The presence of dolomite and anhydrite in the samples leads to an increase in properties (thermal conductivity, and P-wave velocity) due to both the properties of the minerals and the nature of the contact between the grains.

The third rock-type (Rt3)
The Rt3 regroups Mf2 facies samples, with the highest porosity and the lowest bulk density. They are the grainstones with small rudists and peloids, corresponding to the most porous oil-soaked facies.
This rock-type is formed by single facies with well-sorted small rudist-debris and peloids (Mf2). The porosity is qualified as high to very high. It is a very well classed facies: well-sorted small grains showing matrix porosity (Figs. 13D and 13F), intra/ intergranular (Fig. 13C) and intercrystal porosity (Fig. 13F).
Microscopic study has shown that Rt3 facies, as Rt2, are mainly affected by dissolution (Fig. 14A) and matrix dolomitization (Fig. 13F) that create a significant secondary porosity (intercrystal or moldic). Although these samples have the highest porosity, their permeability is intermediate from 10 mD to 1 D. These transfer properties are correlated to the intermediate threshold sizes. The lowest values of Pwave velocity (2324 m.s À1 on average) and thermal conductivity (lower than 1.8 W.m À1 .K À1 ), are obtained in the most porous facies (Mf2) corresponding to grainstones containing small sized and well sorted peloids and rudists (Wyllie et al., 1958).

Vertical evolution of petrophysical parameters
Petrophysical parameters (porosity, permeability, P-wave velocity, and thermal conductivity) measured on 26 samples all along the core, are shown in Figure 17. The representative samples of each microfacies defined in the study, have the same petrophysical properties, all along the studied interval, regardless of the depth, which means that there is no effect of the burial on these properties: -Fine micritic facies (Mf4, Mf5, Mf8 and Mf12) and anhydrites facies (Mf10) show low porosity, very low permeability, very high P-wave velocity, and high thermal conductivity.
-Facies with small and well-sorted rudist debris and peloids (Mf2) always show very high porosity, high permeability, low P-wave velocity, and low thermal conductivity.
-Facies with small rudist debris, echinoderms and peloids (Mf3) have average values of porosity, permeability, Pwave velocity, and thermal conductivity. -The facies with large debris of rudists and peloids (Mf6) generally show good porosity, high to excellent permeability notably in fractured units, an average P-wave, and thermal conductivity values. -Finally, the dolomite facies (Mf9) show high values of porosity, permeability, and thermal conductivity. However, the velocity of the P-wave is variable, it is fair when the facies are filled with small crystals of anhydrite and becomes higher when the facies contains only dolomite (Lucia, 2004;Ehnenberg et al., 2006).
These different laboratory analyses carried out on the rocks allow us to have an idea about the behaviour of the petrophysical properties of underground rocks and to propose hypotheses concerning the favourable location of the organic matter in the sub-surface. So, it is recommended to pay a particular attention to layers characterized by low P-wave velocity, low density and low thermal conductivity. These declines are usually associated to good porosity values (Tab. 4).

Conclusion
This study concerns a reservoir level well known in Cretaceous formations and focuses on an interval of about 112 m. Samples from the existing reservoir were collected  by drilling and characterized after washing the hydrocarbons. The measured properties (permeability, thermal conductivity, and P-wave velocity) are compared with the characteristics of the materials (petrography, granulometry, porosity, size of access to voids).
From a petroleum perspective and based on petrophysical analyses, it appears that only facies found in rock-types Rt2 and Rt3 belonging to the first unit (U1) are oil-impregnated (according to the macroscopic study). They have a petroleum interest and can be considered as a reservoir layer. These facies consist of dolomites (Mf9), wackestones-packstones and grainstones rich in rudists (Mf1, Mf2, Mf3, Mf6 and Mf7). In this unit, the rock-type Rt2 regroups fine grainstones containing small and well sorted rudist-debris and peloids (Mf2) and shows the best petrophysical characteristics (porosity and permeability).
The obtained results show a strong influence of the granulometric dispersion, due to sedimentological origin and to diagenetic dolomitization, of the pore volume and of the width of the distribution of the access thresholds. These two characteristics and the percolation threshold exert an important control on permeability. The two other measured properties are mainly controlled by their mineralogical and porosity contents. Their lower measured values than the calculated one illustrated a strong control of the contact properties as well for transfer of thermal fluxes or elastic stresses. Determination of these characteristics, partly depending on the pore shapes that influence the permeability too, could be the next step of analysis to understanding the links between material characteristics and their transfer properties. Figure 1S. Integrated sedimentological and petrophysical analysis workflow for Douleb carbonate reservoir study. Table 1S. Petrophysical properties of the studied sequence. Table 2S. P-wave velocity and thermal conductivity of minerals (Clauser and Huenges, 1995).