Effective medium modeling of diagenesis impact on the petroacoustic properties of carbonate rocks Mathilde Adelinet, Jean-François Barthélémy, Elisabeth Bemer, Youri Hamon
To cite this version:
Mathilde Adelinet, Jean-François Barthélémy, Elisabeth Bemer, Youri Hamon. Effective medium modeling of diagenesis impact on the petroacoustic properties of carbonate rocks. Geophysics, Society of Exploration Geophysicists, 2019, 84 (4), pp.WA43-WA57. 10.1190/geo2018-0559.1. hal-02101736
HAL Id: hal-02101736 https://hal.archives-ouvertes.fr/hal-02101736 Submitted on 17 Sep 2019
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Effective medium modeling of diagenesis impact on the petroacoustic properties of carbonate rocks Mathilde Adelinet, Jean-François Barthélémy, Elisabeth Bemer, Youri Hamon
To cite this version:
Mathilde Adelinet, Jean-François Barthélémy, Elisabeth Bemer, Youri Hamon. Effective medium modeling of diagenesis impact on the petroacoustic properties of carbonate rocks. Geophysics, Society of Exploration Geophysicists, 2019, 84 (4), pp.WA43-WA57. 10.1190/geo2018-0559.1. hal-02101736
HAL Id: hal-02101736 https://hal.archives-ouvertes.fr/hal-02101736 Submitted on 17 Sep 2019
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Page 1 of 49 GEOPHYSICS
Geophysics 1 1 2 3 4 5 6 EFFECTIVE MEDIUM MODELING OF DIAGENESIS IMPACT ON THE 7 8 PETROACOUSTIC PROPERTIES OF CARBONATE ROCKS 9 10 11 Mathilde Adelinet , Jean-François Barthélémy , Elisabeth Bemer, 12 Youri Hamon 13 14 15 ABSTRACT 16 17 18 19 20 21 Carbonate formations are heterogeneous and their velocity - porosity relationships are 22 23 mainly controlled by microstructural parameters. As diagenesis is responsible for important 24 25 changes in the microstructure of carbonate rocks, we propose here to extend the classic effective 26 27 medium approach to mode! the impact of diagenesis on carbonate elastic properties through a 28 29 30 step by step effective medium modeling. Two different carbonate formations are considered. The 31 32 first key step is the characterization of the diagenesis which affected the studied carbonate series. 33 34 An effective medium mode! integrating ail the geological information accessible from thin 35 36 section analysis is then built. The evolution of the micro structural parameters during diagenesis 37 38 39 is thoroughly constrained based on an extensive experimental dataset, including XRD analysis, 40 41 various porosimetry techniques and ultrasonic velocities measurements. Finally, direct 42 43 44 calculations with the mode! provide elastic wave velocities representative of the different 45 46 diagenetic stages. An extrapolation to permeability evolution is also introduced. This approach 47 48 allows the identification of the acoustic signature of specificdiagenetic events, such as 49 50 51 dolomitization, dissolution or cementation, and the assessment of their impact on the flow 52 properties of carbonate formations. 53 54 55 56 57 58 59 60 GEOPHYSICS Page 2 of 49
Geophysics 2 1 2 3 4 5 6 INTRODUCTION 7 8 9 Carbonate formations represent major targets for exploration and development of 10 11 hydrocarbon reservoirs. Giant discoveries in offshoreBrazil or Levant Basin for instance are 12 13 14 driving new research avenues. In a more environmental context, carbonates are considered as 15 16 key indicators of paieoclimates (Eiler et a!., 2011 ). Indeed the various processes leading to their 17 18 accumulation reflect the complex interplay between water chemistry, biotic productivity, 19 20 21 sediment availability and geodynamic context. This is especially true for continental carbonates, 22 23 thus adding hydrologie constrains (Kelts, 1990). Due to their various depositional modes, 24 25 carbonates are characterized by wide ranges of primary fabrics and associated pore types. 26 27 28 Afterwards,these fabricsare affected by different diagenetic processes which can either create or 29 30 occlude porosity (Heydari, 2003; Lambert et al., 2006; Casteleyn et al., 2010, 2011; Makhloufi et 31 32 al., 2013; Neveux et al., 2014; Carpentier et al., 2015; Clark and Vanorio, 2016; Nader et al., 33 34 2016). Besides, carbonate rocks show very specific mechanical compaction processes such as 35 36 37 crystal plasticity and cataclasis (Vajdova et al, 2004; Baud et al., 2009; Nicolas et al., 2016), 38 39 which further complicates the resulting microstructures. 40 41 42 Porosity, fabrics and pore types being the main contrai factors of elastic velocity in 43 44 45 carbonate rocks (Eberli et al., 2003; Baechle et al., 2008; Verwer et al., 2008), it seems natural to 46 47 seek to link elastic properties and diagenesis. However, only a few studies tackle the key issue of 48 49 relating sedimentological and diagenetic features to physical properties measured at the sample 50 51 52 scale and extrapolating the obtained results at the formation scale to derive global evolution laws 53 54 (Brigaud, 201 O; Regnet et al., 2015a, 2015b; Matonti et al., 2015, 2016). Numerous acoustic 55 56 57 58 59 60 Page 3 of 49 GEOPHYSICS
Geophysics 3 1 2 3 experimental data have been acquired on carbonate rocks showing a wide range of variation and 4 5 6 indicating no clear velocity - porosity trends (Adam et al., 2006; Rasolofosaon and Zinszner, 7 8 2003; Rasolofosaon et al., 2008; Bemer et al., 2017). That is why modeling approaches have 9 10 been developed to exp Iain the different elastic behavior observed on carbonates (Dvorkin et al., 11 12 13 1995; Adam et al., 2006; Dou et al., 2011; Ba et al., 2013; Fournier et al., 2018; Regnet et al., 14 15 2018). One of the most famous is the mode! developed by Xu and Payne (2009) which is an 16 17 extension of the mode! of Xu and White ( 1996) proposed for clastic rocks. ln this mode!, the 18 19 authors assume that interparticle pores represent the rnost common pore type in carbonate rocks 20 21. 22 and thereforeprovide a reference porosity - velocity trend. Reference pores are modeled by 23 24 ellipsoids with an aspect ratio equal to 0.15. Mixed pore types are then considered by added 25 26 either stiffnores (ellinsoids with an asoect rntio ofO.Rî or crnc}s (elliosoins with an asnect ratio - " . . . I - -1 - - •. ------. - r - - -· - 27 1 , l - 1 , - ' 28 29 of 0.02) to the reference pores. The aspect ratio of 0.15 representing the reference pores appears 30 31 to be flatter than what is usually observed on thin sections for in�rparticle pores (Lonoy, 2006). 32 33 Using this mode! or other approaches only based on pore aspect ratios (e.g. Fournier et al., 34 35 2018), lower experimental velocity data can only be explained through the presence of cracks 36 37 38 within the studied rocks. Yet, such features are scarcely observed on thin sections for carbonates 39 40 contrary to other rocks, forinstance volcanic ones, where cracks lead to a specific mechanical 41 42 behavior (Adelinet et al., 2010; 2013). Moreover, for some carbonate rocks, velocities remain 43 44 45 low even if the confiningpressure is increased enough to close the majority of cracks and micro 46 47 defects. 48 49 50 We thus propose a different approach to mode! the specificelastic behavior shown by 51 52 53 carbonate rocks where we introduce an interface stiffness around the main solid grains, which 54 55 can be dolomite or calcite in our case. By decoupling the elastic properties of the grain and its 56 57 58 59 60 GEOPHYSICS Page 4 of 49
Geophysics 4 1 2 3 interface, vve add an additional compliance at the macroscale intended to represent the 4 s 6 mechanical response of grain contacts (Rasolofosaonand Zinszner, 2003 ). This is in agreement 7 8 with observed sedimentological features (Brigaud et al., 201 O; Regnet et al., 2015a). We then use 9 10 the effectivemedium modeling as a tool to provide elastic velocities at different diagenesis 11 12 stages. This study is based on experimental results derived from a specific characterization 13 14 15 workflow designed to provide a comprehensive dataset including both input and constraining 16 17 data for effective medium modeling (Berner et al., 2018). 18 19 20 21 METHODS 22 23 Experimental approach 24 25 26 The folloY\1ed experünental ,vorkflovv· includes a nc,n-destïuctivetesting sequence 27 28 29 performedon the main sample and a series of microstructure �nalyses performed on subsamples. 30 31 The successive non-destructive characterization steps are: petroacoustic testing, porosity 32 33 measurement, NMR analysis on the brine-saturated sample and brine permeability measurement. 34 35 36 The main sample is then eut into several subsamples to obtain a vertical thin section, powder for 37 38 XRD analysis and small parts for mercury injection and possibly microscanner imaging. This last 39 40 analysis being costly, it is not performedon the whole sample set. 41 42 43 44 The key steps of the workflow are the petroacoustic testing performedon the main 45 46 samples and the petrographic characterization performed on the vertical thin sections. The other 47 48 measurements are more standard and their contribution arises from their consistent combination. 49 50 51 52 Petrographic characterization 53 54 55 56 57 58 59 60 Page 5 of 49 GEOPHYSICS
Geophysics 5 1 2 3 One thin section per sample (eut along the axis of the oriented samples) has been 4 5 6 analyzed forfaciologic and diagenetic purposes (texture, fabric, grain types, pore types, 7 8 mineralogy, cementation or dissolution features ...). Ail thin sections are impregnated with blue 9 10 epoxy to identify the pore space) and stained with alizarin red-S to differentiate carbonate 11 12 13 minerais: (calcite is stained, while dolomite remains unstained; Dickson, 1966) and potassium 14 15 ferricyanid for distribution of ferrous iron. 16 17 18 Pre-microscopie observations are carried out under reflected and transmitted iight with a 19 20 21 binocular microscope (Nikon SMZ 800) to have a large scale view of the samples and 22 23 characterize their general texture ançl porosity distribution. Petrographic observations are then 24 25 performed with a Nikon Eclipse LVl00 POL microscope. 26 27 28 29 The thin section analysis provides qualitative structural information on the organization 30 31 of the different microstructural components (matrix, cernent, pores). The sedimentary texture are 32 33 described using the classification of Dunham (1962), whereas the dolomite fabrics are described 34 35 36 using the classification of Sibley and Gregg (1987). The porosity is described followingthe 37 38 classificationof Choquette and Pray (1970) and Lonoy (2006). 39 40 41 Image analysis on scanned thin sections has moreover been performedto provide a 42 43 44 surfacic estimation of the porosity and the minerai content by extracting the different colors 45 46 through threshold methods. The image analysis is performedwith JMicroVision, which is a 47 48 freeware software designed to describe, measure, quantify and classify components of ail kinds 49 50 51 of images and especially developed to analyze high definition images of rock thin sections 52 53 (http://www.jmicrovision.com/index.htm). 54 55 56 57 58 59 60 GEOPHYSICS Page 6 of 49
Geophysics 6 1 2 3 Petroacoustic testing 4 5 6 7 The petroacoustic ceil has been designed to perform velocity measurements under an 8 9 isotropie confining pressure (up to 70 MPa). The sample is set in an impermeable Viton® jacket 10 11 to prevent any communication between the pore fluidand the confining fluid. The tests can thus 12 13 14 be performed at various differentiai pressLJïes (i.e. difference between the confining pressure and 15 16 the pore pressure), and with various saturating fluids. All the tests have been carried out at a 17 18 differentialpressure representative of in situ conditions. 19 20 21 22 The upper and lower heads of the cell include a double P and S transducer (half-moon 23 24 ceramic, central frequency of 500 kHz). The first specificity of our approach is to analyze the 25 26 27 28 29 (Rasolofosaon and Zinszner, 2003). This method consists in applying a Fourier transformto the 30 31 recorded signal and to compare it, in the frequencydomain, with a reference signal recorded in a 32 33 homogeneous medium of perfectlyknown velocity (in this case an aluminum sample). Carbonate 34 35 36 heterogeneity induces scattering effects usually referred to as "path dispersion" (Cadoret et al., 37 38 1995). Contrary to the first break picking which leads to overestimated acoustic velocities, the 39 40 computation of the phase velocity allows a minimization of the heterogeneity effect 41 42 (Rasolofosaonet al., 2008). The error on phase velocity measurements can be considered as Jess 43 44 45 than 2%, with a corresponding error on Vp /Vs ratio Jess than 4% (Bemer et al., 2018). 46 47 48 The second specificityis to followthe fluid substitution method developed by 49 50 51 Rasolofosaonand Zinszner (2003). This approach consists in subsequently measuring the 52 53 acoustic velocities for various saturating liquids of different bulk modulus, the current saturating 54 55 fluid being replaced with a miscible one to ensure successive fully saturated states. The 56 57 58 59 60 Page 7 of 49 GEOPHYSICS
Geophysics 7 1 2 3 substitution sequence is the following: brine (25 g/l NaCI), ethylene glycol, methanol, ethanol, 4 5 6 heptane, ethanol, brine (25 g/1 NaCl). The key contribution of fluid substitution tests is to al!ow a 7 8 direct checking of the validity of Biot-Gassmann's equation without referring to less-controlled 9 10 dry measurements and without any assumption on the solid rnatrix bulk modulus (Berner et al., 11 12 13 . 2018). The obtained results moreover permit the direct identification of any weakening or 14 15 dispersion effects. 16 17 18 Comhined microstructure characterization 19 20 21 22 The construction of a relevant microstructure mode] requires consistent informationon 23 24 the minerai content and the porous phase, especiallythe proportion of rnicroporosity and 25 26 1microporosity. The location of the microporosity has a!so to be specified. The experimental 27 28 29 workflow systernatically includes X-Ray Diffraction (XRD) analysis to identify the minerai 30 31 phases and deterrninetheir volume fractions, and two differenttechnics of pore-size 32 33 characterization: Nuclear Magnetic Resonance (NMR) and Mercury Injection Capillary Pressure 34 35 36 (MICP). These rnethods are detailed in our cornpanionpaper (Berner et al., 2018). We focus here 37 38 on the key issues underlying their interpretation. 39 40 41 NMR and MICP explore different physical parameters and sample sizes: the NMR T2 42 43 44 relaxation time is related to the pore volume over surface ratio and the T2 distribution is obtained 45 46 forthe whole sarnple, white MICP gives information on the pore throat size distribution fora 47 48 srnallpart of the sample. The NMR analysis can be perturbed by pore coupling effects induced 49 50 51 by the rnixingof molecules from nearby compartrnents through diffusion process. When no pore 52 53 coupling is observed, a comparative study between NMR and MICP data obtained on carefully 54 55 selected carbonate samples of various origins has shown that a eut-offof200 ms in the NMR T2 56 57 58 59 60 GEOPHYSICS Page 8 of 49
Geophysics 8 1 2 3 distribution could be used to separate the microporosity fromthe macroporosity, in accordance 4 5 6 with a pore throat diameter eut-offof 2 µm for Ml CP distributions (Vincent et al., 201 1 ). 7 8 9 Microscanner imaging has been perforrnecl to provide additional information on the 10 11 repaiiition of micropores within the samples. Subsamples of 8-mœ diameter are imaged fortwo 12 13 14 saturation states: dry and saturated by a 40 g/1 Kl-brine. Image subtraction can then be carried 15 16 out to identify the macropores and the microporous areas and derive the macroporosity and 17 18 microporosity volume fractions. The threshoid between macroporosity and rnicroporosity is then 19 20 21 associated to the image resolution which is equal to 8 µm for the imaged 8-mm subsamples. The 22 23 information provided by microscanner imaging is the more physically consistent for effective 24 25 medium modeling. It is however not available for ail the samples and obtained on a smaller 26 27 volume than the NMR data. 28 29 30 31 The informationderived from the NMR, MICP and microscanner analyses are finally 32 33 integrated to derive consistent fractions of microporosity and macroporosity for effective 34 35 36 medium modeling. 37 38 39 Effective medium modeling 40 41 Theory 42 43 44 45 For sedirnentary rocks such as sandstones, it is usually easy to derive a relationship 46 47 between elastic properties and microstructure description. However, due to their complex 48 49 50 microstructures, carbonate rocks do not appear to follow any simple or direct specific 51 relationship. The challenging issue is then to derive consistent elastic properties for carbonate 52 53 54 rocks frommicrostructure information. The effective medium theory offers a neat way to achieve 55 56 57 58 59 60 Page 9 of 49 GEOPHYSICS
Geophysics 9 1 2 3 this objective. Indeed, it relies on physical models that describe within a Representative 4 5 Elementary Volume (REY) the macroscopic properties of a medium based on microstrüctural 6 7 8 characteristics. Such a theory can be used through a direct way, i.e. the elastic properties of the 9 10 rock are calculated from an exhaustive description of the microstructure, or through an inverse 11 12 13 approach, i.e. some microstructure features are derived from macroscopic properties such as 14 15 velocities. The effective medium modeling used in this study is a homogenization approach 16 17 relying on Eshelby's inclusion theory (Eshelby, 1957). The conceptual frameworkof the t_heory 18 19 consists in considering an ellipsoidal inclusion embedded within an infinitemedium and the 20 21 disruption of the strain field in the medium due to this inclusion. As different inclusions are 22 23 24 present within a rock, for instance grains, pores or cracks, we have to use a homogenization 25 26 27 28 found in the literature. As carbonate rocks have complex microstructures and relatively high 29 30 31 porosities, we choose to use the self-consistent approach. In this scheme, an inclusion is 32 33 embedded within a medium which has the elastic properties of the effectivemedium. There are 34 35 36 no limits in porosity and it is well-adapted for unorganized mediums such as carbonate rocks. 37 38 Table 3 reports the elastic moduli allocated to the pure minerai phases present in the studied 39 40 samples. 41 42 43 As elastic velocities measured on carbonate samples are often lower than what would be 44 45 46 expected from simple modeling (Eberli et al., 2003; Regnet et al., 2018), several authors have 47 48 introduce some cracks into the theoretical microstructure in order to better reproduce the 49 50 51 measured values (Xu and Payne, 2009; Zhao et al., 2013; Fournier et al., 2018). However, cracks 52 53 are rarely observed in geological thin sections. That is why we choose another approach to mode! 54 55 the specific behavior of carbonates. We introduce a compliant interfacearound the main 56 57 58 59 60 GEOPHYSICS Page 10 of49
Geophysics 10 1 2 3 carbonate grains intended to represent the mechanical response of grain contacts (Rasolofosaon 4 s 6 and Zinszner, 2003). ln this approach, the grains have the mechanical properties of the 7 8 considered mineralogical phase (calcite or dolomite in our case) but the grain interface may have 9 10 different properties allowing a softer macroscopic behavior, anà finally lower velocities than the 11 12 13 ones modeled without this compiiant interface. 14 15 16 From a theoretical point of view, carbonate grains are modeled as rigid inclusions with a 17 18 smooth interface (Barthélémy, 2005). These inclusions differ from cohesive inclusions through 19 20 21 some mechanical discrepancies. First, the tangential component of the displacement fields at the 22 23 interface may be discontinuous but not the normal one, which prevents debonding or 24 25 interpenetration of grains. Second, at the interface between the homogenized medium and the 26 27 inclusion, the stress vector cr· n is purely normal: 2829 30 31 [fl · n = 0 (1) 32 33 cr· CT n 2 34 n = nn ( ) 35 36 37 where n is the unit vector normal to the interface and CTnn is the normal component of the stress 38 39 vector on the interface. 40 41 42 43 Contrary to pores, the strain field is nul! within the solid inclusions. However, if the 44 45 inclusion is surrounded by a smooth interface,the displacement discontinuities contribute to the 46 47 average of the strain field. The only constraint on the stress field is to ensure the continuity of the 48 49 50 stress vector at the interfacebetween the homogenized medium and the inclusion. Finally, we 51 52 obtain a linear relationship between the stress vector at the interface and the displacement 53 54 discontinuity: 55 56 57 58 59 60 Page 11 of49 GEOPHYSICS
Geophysics 11 1 2 3
Geophysics 1 12 2 3 As diagenetic events in carbonates are associated with aqueous fluid flows, the saturating fluid 4 5 6 used in the effective medium modeling is brine whose elastic parameters are given in Table 5. 7 8 Accordingiy, the ultrasonic velocities considered here correspond to the brine-saturated 9 10 measurements. The range of porosity covered by the samples from each family is sufficiently 11 12 13 large to ensure a reasonable calibration of the interface parameters. At the end of this first step, 14 15 the derived microstructural mode! is representative of samples having experienced ail the 16 17 diagenetic events. 18 19 20 21 The accurate diagenetic study performedon the thin sections is then used to individualize 22 23 the different diagenetic events and translate them into a step-by-step evolution of the effective 24 25 medium mode!. Finally, elastic properties are computed through the entire theoretical diagenetic 26 27 path. To do so, we consider that the interfacestiffness parameters determined through inverse 28 29 30 analysis are representative of one specific minerai abject (calcite or dolomite grains) and do not 31 32 evolve during diagenesis, which is a very strong hypothesis. 33 34 35 36 The main unknown remains the time of the diagenetic events. We thus use an arbitrary 37 38 temporal scale to represent the different diagenetic steps. We assume that ail the samples are 39 40 representative of the finalstage of diagenesis and have thus experienced all the previous 41 42 diagenetic steps identified in the paragenesis. They may however have been more or less 43 44 45 impacted by the last diagenetic process. We thus use their different macroporosity and 46 47 microporosity values to calibrate the evolution of the final diagenetic step. The evolutions during 48 49 50 the previous diagenetic steps are then definedbased on the constraints imposed by the final 51 diagenetic step and additional assumptions on the initial stage based on our general knowledge 5352 54 on carbonate systems. 55 56 57 58 59 60 Page 13 of49 GEOPHYSICS
Geophysics 13 l 2 3 PETROGRAPHIC CHARACTERIZATION: DEFINITION OF PARAGENESIS 4 5 6 7 Family 1 8 9 10 The five investigated sampi es roughly exhibit the same kind of texture, which may be 11 12 13 described as a thrombolytic one (Riding, 1991) . The latter is composed of large scale coaiescent 14 15 "mesoclots" (up to 4 mm long and 2 mm wide) forming a bushy, dendritic frame, loosely packed. 16 17 These mesoclots have a sweeping feather-like extinction and a calcitic mineralogy. Samples Fl- 18 19 20 12, Fl-15, Fl-17 and FI -21 are very similar and show the development of a dolomite cernent 21 22 (Figure 2A). This cernent is however poorly represented in sample F 1-13 (Figure 2B). Important 23 24 cement-reduced growth framework porosity (as definedin Choquette and Pray, 1970) is 25 26 observed and image analysis estimations range from 8% (sarnple Fl-15) to 18% (sarnple Fl -17). 27 28 29 These observations could point to a direct covariance between dolomite cementation and 30 31 porosity. The minerai contents and porosity estimated trough image analysis are reported in 32 33 Table 1. 34 35 36 37 Severa! diagenetic phases can be identified and are presented in Figure 3 according to 38 39 their relative timing established through crosscutting relationships observed during petrographic 40 41 analyses and described below. Note that the proposed paragenesis should be considered with 42 43 44 caution as it is only based on the observation of a few samples. 45 46 47 Millimetric silica orbicules with an irregular morphology are firstobserved in some 48 49 mesoclots and even sometimes around mesoclots. They are composed of amorphous quartz 50 51 52 (Silica 1), formed of anhedral crystals with wavy borders. The size of the quartz crystals is 53 54 variable and range from 200 to 500 µm. 55 56 57 58 59 60 GEOPHYS\CS Page 14of49
Geophysics 14 1 2 3 A cement phase consisted in a dog tooth, non ferroan calcite cernent (Figure 2C, white 4 5 6 arrnw) is then observed. lt occurs as a first generation of voids filling (lining the mesoclots) and 7 8 clearly predates the dolomite cernent (Figure 2C, black arrow). Crystal sizes range from 30 to 9 10 60 µm. 11 12 13 14 A few stylolites are observed in sample F 1-21, but with no clear cross-cutting 15 16 relationships between these structures and the other diagenetic phases. The dolomite cernent may 17 18 however have postdated the stylolitization, as the crystals are not affected by stylolites. 19 20 21 Additional observations would be needed to precise this relative timing and the origin of the 22 23 stylolitization. 24 25 26 Do!oœitization occurs in varying proportions for al! the studied samples as a dclcmite 27 28 cernent in the porosity. lt exhibits a planar-e texture (Sibley and Gregg, 1987; mainly euhedral 29 30 31 crystals) with crystal sizes ranging from 100 to 250 �lm (Figure 2C and Figure 2D, black arrow). 32 33 These crystals show a concentric zoning with a cloudy (sometimes brown) core and a limpid, 34 35 36 clear rim (10 to 50 µm). 37 38 39 This last rim shows a very irregular periphery and has thus clearly been corroded, 40 41 possibly painting to a late alteration (dissolution) of the crystals. This dissolution phase has also 42 43 44 affectedthe mesoclots and may have created a vuggy micro-porosity (selective dissolution; 45 46 Figure 2E and Figure 2F, black arrow). 47 48 49 A phase of quartz cernent(Silica 2) is observed in ail the samples and particularly in 50 51 samples F1-12 and F1-21. This cernentis composed of anhedral to subeuhedral limpid crystals 52 53 54 ranging from 50 to 400 µm and showing a drusy to granular development (Figure 20, black 55 56 57 58 59 60 Page 15 of 49 GEOPHYSICS
Geophysics 1 15 2 3 arrow). It is developed in the porosity and clearly engulfs the dolomite cernent, therefore post 4 5 6 dating it. 7 8 9 ln sample F 1-12, scarce gypsum cernent is observed. It forms cloudy inclusion-rich 10 11 crystals, displaying a tabular anhedral habitus (Figure 2H, black arrow). lt develops in the 12 13 14 growth framework porosity, and engulfs dolomite crystals, thus postdating them (Figure 2H, 15 16 white arrow). The relative timing with the Silica 2 cernent cannot be determined as no 17 18 crosscutting relationships are observed. 19 20 21 22 Family 2 23 24 25 The six investigated samples are dolomitized bioclastic wackestone to packstone (Figure 26 27 28 4 ). When preserved, bioclasts correspond to debris of echinoderms, lamellibranch and rare 29 30 benthic foraminifera. The matrix is pervasively but selectively dolomitized, as well as some 31 32 bioclasts or intraclasts. Porosity estimations (2D image anaiysis) range from O to 5%, and the 33 34 pore space is mainly made of moldic macropores (associated to bioclast dissolution) and 35 36 37 intercrystalline micropores (within the dolomitized matrix). The minerai contents and porosity 38 39 estimated trough image analysis are reported in Table 1. 40 41 42 Severa! diagenetic phases can be identified and are presented in Figure 5 according to 43 44 45 their relative timing established through crosscutting relationships observed during petrographic 46 47 analyses and described below. As forFamily 1, the proposed paragenesis should be considered 48 49 with caution as it is only based on the observation of a few samples. 50 51 52 53 A syntaxial cernent mainly distributed as overgrowths (50 µm to up to 1 mm) around 54 55 crinoid fragments (Figure 4A and Figure 4B, white arrow) is observed in ail the sampies. It is 56 57 58 59 60 GEOPHYSICS Page 16 of 49
Geophysics 1 16 2 3 composed of inclusion-rich crystals of slightly ferroan calcite, frequentlyshowing cleavage 4 5 twins. 6 7 8 9 A fabric-preserving replacement (inversion) of aragonitic allochems (mainly 10 11 lamellibranchs) by a non-ferroan inclusion-rich calcite is observed. The neomorphic calcites are 12 13 14 identified by the presence of solid organic and/or inorganic inclusions that concentrated along 15 16 the original sheli growth lines and are still visible in the replaced allochem (Figure 4A and 17 18 Figure 4C, black arrow). The replacement fabric is characterized by a mosaic of coarse (50 to 19 20 100 µm) polygonal inclusion-rich non-ferroanlow-magnesian calcite (LMC) crystals, which 21 22 23 either crosscuts the original fabric or develops followingthe host shell microstructures. 24 25 26 27 28 high-magnesian calcite, which was not previously inverted in low-magnesian calcite (Figure 29 30 31 4D). 32 33 34 Dolomitization occurs in ail the studied samples either through replacement or 35 36 cementation. The degree of dolomitization depends on the considered sample (Table 1). 37 38 39 Dolomite replacement is characterized by a unimodal dolomicrosparite, with crystals ranging 40 41 from 10 to 50 µm (Figure 4E) and showing a cloudy core and a more limpid overgrowth. More 42 43 rarely, dolomite cernentis observed in moldic porosity. It exhibits a planar-e texture (mainly 44 45 46 euhedral crystals) with crystal sizes ranging from 100 to 200 µm (Figure 4F). Observation of 47 48 dolomite having affected syntaxial cernent (Figure 48) or developed in moldic porosity suggests 49 50 that the dolomitization process postdated these two phases. . 51 52 53 54 55 56 57 58 59 60 Page 17 of 49 GEOPHYSICS
Geophysics 1 17 2 3 For sample F2-2, an additional calcite cement phase ;s observed in moldic or shelter 4 5 6 porosity (Figure 4G, black arrow). It corresponds to a drusy pore-filling cement, composed of 7 8 equant subhedral non-ferroan calcite crystals (100 to 300 µm). 9 10 11 Finally, gypsurn cernent is scarcely observed in samples F2-4 and F2-7. lt forrns cloudy 12 13 14 inclusion-rich crystals, displaying a tabular to bladed anhedral habitus (Figure 4H, black arrow). 15 16 It develops in moldic porosity, partially or totally filling some molds. 17 18 19 20 EXPERIMENTAL CHARACTERIZATION: MICROSTRUCTURE INFORMATION AND 21 22 PETROACOUSTIC PROPERT!ES 23 24 25 The minerai phases identifiedthrough the interpretation of XRD signais are calcite, 26 27 28 dolomite and silicate (grouping quartz and a smalt fraction of feldspars). Table 2 gives for each 29 30 studied sample the minerai content deduced from XRD analysis. The results are consistent with 31 32 the thin section analysis (Table 1 ). F1 samples show significantcontents of both calcite and 33 34 dolomite and the largest silicate content of the two sample sets. Except for sample F2-2, F2 35 36 37 samples are predominantly dolomite samples, with small amounts of silicate. However, as no 38 39 quartz phase has been observed on thin sections, we do not considered a silicate phase in the 40 41 mode! describing Farnily2. 42 43 44 45 The total porosity of the samples is deduced fromthe brine volume provided by the NMR 46 47 analysis of the brine-saturated samples and their bulk volume (Table 3). Additional porosity 48 49 measures are obtained from the difference between the brine-saturated and dry weights of the 50 51 52 samples. The comparison of the two measures shows that residual brine remains within the 53 54 sample after drying at 60°C (Berner et al., 2018). Effectivemedium modeling considers ail the 55 56 57 58 59 60 GEOPHYSICS Page 18 of49
Geophysics 18 2 3 saturated volume including even the less accessible pores and the consistent porosity values are 4 5 6 thus the NMR ones. 7 8 9 As described in our companion paper (Berner et al., 2018), the microporosity and 10 11 macroporosity fractions reported in Table 3 have been determined fromthe combined 12 13 14 information derived from NMR and MlCP analyses and microscanner imaging. The values 15 16 selected foreffective medium modeling correspond to the volume fractions deduced from the 17 18 NMR T2 distributions by applying a 200 ms threshold. A more reliable set of values deduced 19 20 21 fromm icroscanner imaging is also provided for sample F 1-13 which exhibits pore coupling 22 23 (Fleury and Soualem, 2009). 24 25 26 Figure 6./1.... plots the P-\vave and S-\vave- veloc-ities measured vn the bïine-satuïatêd 27 28 29 samples as a functionof porosity. The corresponding values are reported in Table 4. The 30 31 measurements on FI and F2 samples have been performed at differential pressures equal to 32 33 respectively 25 MPa and 20 MPa and have not been impacted by weakening or dispersion 34 35 36 phenomena (Berneret al., 2018). For a given porosity, F2 samples show higher P-wave and S 37 38 wave velocities than FI samples. At the first order it is related with higher contents of dolomite 39 40 in F2 samples. Dolomite having higher bulk and shear moduli than calcite (Table 2), velocities 41 42 are usually higher in dolomitic rocks than in calcite ones. Figure 6B represents the ultrasonic 43 44 45 measurements in a rock physics template: Vp /V5 ratio versus P-wave impedance lp = pVp. 46 47 Except for sample Fl-17, FI samples show higher Vp /V5 ratio than F2 samples. Both families 48 49 are clearly separated in the diagram implying that primary and secondary structures in these 50 51 52 carbonates have an incidence on their geophysical response. 53 54 55 56 57 58 59 60 Page 19of49 GEOPHYSICS
Geophysics 1 19 2 3 The comparison of the measured velocities to the model developed by Xu and Payne 4 5 6 (2009), especially in the more discriminating Vp /V5 versus lp template provided forcalcite and 7 8 dolomite solid matrix by Zhao et al. (2013), suggests that flattened pores (with aspect ratios iess 9 10 than O .15) would have to be taken into account in the mode! to reproduce the measured 11 12 13 velocities. Such forms of inclusion not being observed on the thin sections, we choose to add a 14 15 compliant interface to carbonate grains rather than use flattened porosity inclusions. 16 17 18 EFFECTIVE MODELING RESULTS 19 20 21 22 Family 1 23 24 25 As described in the petrographic analysis, FI samples exhibit large scale calcitic 26 27 28 mesoclots and a calcite cernentforming the global rock frame, a dolomite cernent developed 29 30 between the calcite mesoclots, a framework porosity and micropores located both within the 31 32 dolomite cernent and the calcite rnesoclots (Figure 2). The various characterizations performed 33 34 on FI samples have not provided quantitative data on the distribution of the micropores between 35 36 37 their two host phases. As the dissolution step identified in the paragenesis rnainlyconcerned the 38 39 dolomite cernent, we allocate the totality of the rnicroporosity to this phase. This assumption can 40 41 naturally be discussed, but additional data from high resolution SEM would be required to go 42 43 44 further. 45 46 47 The microstructure mode) proposed for Farnily1 is described in Figure 7 A. lt is based on 48 49 a double scale approach. At the last diagenetic stage, the rnacroscopicscale consists in spherical 50 51. 52 grains of calcite with a cornpliantinterface, quasi-equant rnacropores, spherical grains of quartz 53 54 and microporous grains of dolomite. The microscopie scale corresponds to the microporous 55 56 57 58 59 60 GEOPHYSICS Page 20 of 49
Geophysics 20 2 3 grains which are composed of a dolomite matrix and quasi-equant micropores. The volume 4 5 6 fractions of these different phases having been determined for each sample (Table 2 and Table 7 8 3), this final mode! is first used to assess the normal and tangential stiffness of the interface 9 10 through inverse analysis of the measured brine-saturated velocities (Table 4). 11 12 13 14 Concerning the diagenetic evolution, we only take into account the events observed on all 15 16 the investigated samples during the petrographic analysis (Figure 8A). The initial state 17 18 corresponds to the end of the first diagenetic event identified in the petrographic analysis (Figure 19 20 21 3), i.e. the formation of the first phase of silica (Si. 1) and the development of the calcite cernent. 22 23 At the beginning of our diagenesis modeling, the rock is then composed of calcite grains with a 24 25 compliant interface (representing the rock frame composed of calcite mesoclots and syntaxial 26 27 28 cernent),macropores and amorphous quartz. This first stage corresponds to the early induration 29 30 by cementation. We assume a total initial porosity of 40% which is a classical value for 31 32 carbonate muds (Eberli et al., 2003). A small volume fraction of 1 % is taken forthe Si. 1 phase. 33 34 35 36 Three main diagenetic events are then considered (Figure 8A). Firstly, dolomite cernent 37 38 precipitates into the macroporosity of the initial calcite framework (Stage 1: dolomitization). 39 40 Then, newly dolomite grains are dissolved and become microporous (Stage 2: dissolution). 41 42 During this stage, dolomite grains becoine the second effective medium mode! embedded within 43 44 45 the first one composed of calcite grains, macropores and amorphous quartz. Finally, quartz 46 47 cernent precipitates into the residual macroporosity (Stage 3: cementation). 48 49 50 51 The corresponding evolutions of the total porosity, the macroporosity and the 52 53 microporosity are represented in Figure 9. During stage 1, the total porosity decreases due to a 54 55 reduction of the macroporosity associated to the increase in dolomite content (dolomite 56 57 58 59 60 Page 21 of 49 GEOPHYSICS
Geophysics 21 2 3 precipitation). During stage 2, the total porosity increases due to the creation of microporosity 4 5 6 within the dolomite grains, while the macroporosity remains constant. Finally, during stage 3, the 7 8 total porosity decreases due to the precipitation of quartz into the residual macroporosity (the 9 10 microporosity remains constant). The total porosity level at the end of stage l corresponds to the 11 12 13 macroporosity level maintained during stage 2 beforethe beginning of quartz cementation in 14 15 stage 3. Sam pie Fl-21 is characterized by the highest values of total porosity and macroporosity 16 17 together with a low quartz content. It has then been considered as representative of the end of 18 19 stage 2 and its porosity values have been used to constrain the constant macroporosity level of 20 21 22 stage 2 and the constant microporosity level of stage 3, respectively set to 15% and 6.5%. The 23 24 four other samples are then reported on the porosity evolution curves according to their total 25 26 poïosity and thcir fractions of macïûpoïosity and micïopûïûsity (Figuïe 9) and thus attributed a 27 28 29 position on the arbitrary time scale. The two positions proposed for sample Fl-13 correspond to 30 31 the macroporosity and microporosity fractions derived from NMR (filled markers) and 32 33 microscanner imaging (white markers). 34 35 36 37 Ali the mode] parameters are then known and we can use direct effective medium 38 39 modeling to compute the evolution of elastic wave velocities during the diagenesis. The red 40 41 curves in Figure I OA report the results obtained for Family I in a velocity- porosity diagram. 42 43 44 The comparison with the measured velocities illustrates the quality of the calibration. Figure 1 OB 45 46 presents the temporal evolution of the elastic velocities during diagenesis. Ultrasonic 47 48 measurements have been reported on the velocity curves using the time calibration described 49 50 above. The first diagenetic stage is associated with a sharp increase of elastic velocities, 51 52 53 corresponding to the filling of macropores with dolomite crystals. Then the dissolution of 54 55 dolomite grains leads to a slight decrease of velocities. Finally the quartz cementation increases 56 57 58 59 60 GEOPHYSICS Page 22 of 49
Geophysics 22 2 3 once again the velocities. Experimental data fit wel! with the mode! curves. As sample Fl-21, 4 s 6 sample Fl-17 seems to be representative of the beginning of stage 3, while samples F 1-12 and 7 8 Fl-15 appear as more representative of the end of stage 3. These observations are in accordance 9 10 with their relative quartz contents. Sampie F1-13 shows a very low quartz content, which would 11 12 13 be contradictory with its positioning at the end of stage 3 as would have been implied by the 14 15 macroporosity and microporosity fractionsderived fromNMR data impacted by pore coupling. 16 17 The use of the values derived from microscanner imaging (white markers) results in a shifting 18 19 towards early times more consistent with the low quartz content of sample F 1-13. These results 20 21 22 show that reliable assessment of the macroporosity and macroporosity fractions is of paramount 23 24 importance. 25 26 27 28 Family 2 29 30 31 As described in the petrographic analysis, F2 samples are dolomitized bioclastic 32 33 wackestone to packstone: The matrix is selectively dolomitized. Porosity is split into moldic 34 35 36 macropores and intercrystalline micropores within the dolomitized matrix. The microstructure 37 38 mode! proposed for Family 2 is once again a double scale effective medium mode! (Figure 7B). 39 40 At the last diagenetic stage, the macroscopic scale consists in a calcite matrix, representing bath 41 42 non-dolomitized grains of neomorphic calcite (resulting from the HMC/aragonite inversion 43 44 45 diagenetic phase) and syntaxial cernent, quasi equant macropores (aspect ratio equal to 0.8) and 46 47 microporous grains of dolomite with a compliant interface. The microscopie scale corresponds to 48 49 the dolomite microporous grains composed of a dolomite matrix and quasi equant micropores 50 51 52 (aspect ratio equal to 0.8). As for Family 1, this final model is used to assess the normal and 53 54 55 56 57 58 59 60 Page 23 of 49 GEOPHYSICS
Geophysics 1 23 2 3 tangential stiffness of the interface through inverse analysis of the measured brine-saturated 4 5 6 velocities. 7 8 9 In tenns of diagenesis, the petrographic analysis has identified different main diagenetic 10 11 phases (Figure 5). Besicles,NMR measurements clearly show that the replacing dolomite is 12 13 14 microporous; v,e have thus added another possible diagenetic step corresponding to the 15 16 dissolution of dolomite (which could have occurred at the same time than the replacement of 17 18 calcite by dolomite). Our diagenesis modeling begins with a tight carbonate rock whose porosity 19 20 21 has been occluded by the development of syntaxial cement and which has thus already 22 23 experienced some diagenetic processes after sedimentation. Three diagenetic phases which 24 25 create porosity into the rock are then considered (Figure 8B). Firstly, macroporosity is created )6 27 into the calcite matrix (Stage 1: dissolution). Then part of the initial calcite grains are replaced by 28 29 30 dolomite grains with no change in porosity (Stage 2: replacement). Finally dolomite grains are 31 32 partially dissolved resulting in the creation of microporosity (Stage 3: dissolution). The total 33 34 35 porosity at the end of stage 1 corresponds to the constant macroporosity assumed for stage 3. 36 37 Sample F2-2 is the lowest porosity sample and its porosity level is close to the mean 38 39 macroporosity of the whole sample set which has been used to define the constant macroporosity 40 41 level of 7% for stage 3. This sample has then been considered as representative of the beginning 42 43 44 of stage 3. The fiveother samples have then been reported on the porosity evolution curves 45 46 according to their total porosity. 47 48 49 The blue curves in Figure 9B summarizes the evolution of the total porosity, the 50 51 microporosity and the macroporosity for F2 mode!. Once again we observe a good agreem�nt 5352 54 when we compare the elastic waves velocities computed through direct effective medium 55 56 57 58 59 60 GEOPHYSICS Page 24 of 49
Geophysics 24 1 2 3 modeling to the experimental data (blue data in Figure I 0A). Finally, Figure 1 OC presents the 4 5 6 �volution of the elastic velocities during d iagenesis together with the measured velocities 7 8 reported according to the above-described time calibration. Due to the different initial states 9 10 considered for the diagenesis modeling, the modeled range of velocity evolution is smaller for 11 12 Family 2 than for Family 1. Indeed, the initiai state considered for Famiiy 1 corresponds to the 13 14 15 initial carbonate mud with a high porosity level whereas the initial state considered for Family 2 16 17 corresponds to a more advanced state in the sediment history associated to a low-porosity rock. 18 19 The creation of macroporosity during stage I is naturally associated with a velocity decrease. 20 21 22 The replacement of calcite by dolomite during stage 2 leads to an increase in P- and S-wave 23 24 velocities, as previously intuited from the cornparison of the experimental ultrasonic data 25 26 obtairi.ed on Fl and F2 samp!es. Firrn!!y the transformation of the dolomite phase into 27 28 29 microporous grains during stage 3 leads to a relatively sharp velocity decrease. As expected frorn 30 31 their differentporosity levels, sample F2-4 appears to be representative of an intermediate 32 33 diagenetic state between sample F2-2 (beginning of stage 3) and samples F2-3, F2-5, F2-6 and 34 35 36 F2-7 (end of Stage 3). 37 38 39 40 41 DISCUSSION 42 43 44 45 The temporal calibration phase of the effective medium mode! is the most difficult to 46 47 achieve due to the different diagenesis phases recorded on a same thin section for which only 48 49 relative timings are available. Due to the Jack of data on the absolute date of each diagenetic 50 51 52 event, the time evolution is obviously arbitrary at the moment. To tackle this issue advanced 53 54 petrographic analysis could be added to the experimental characterization workflow, such as the 55 56 57 58 59 60 Page 25 of 49 GEOPHYSICS
Geophysics 1 25 2 3 characterization of carbonate U-Pb isotopes via laser ablation, to obtain absolute timing foreach 4 5 6 diagenesis phase (Vahrenkamp et al., 2014; Mangenot et al., 2018). As this is not the primary 7 8 objective of this paper, we choose to display the modeling results in a rock physics template that 9 10 does not involve time. Figure 11 plots the evolution of the elastic properties together with the 11 12 13 experimental results in the standard Vp /Vs ratio versus P-wave impedance template. 14 15 16 The modeling results provided for F 1 carbonate formationdo not show distinct area for 17 18 each diagenetic stage. The end of stage 1 and stages 2 and 3 are associated to V /V ratios within 19 p s 20 21 the measurement error. Moreover, in this representation, the experimental data somewhat deviate 22 23 fromthe modeling data. On the contrary, the different stages characterizing the diagenesis of F2 24 25 càrbonate formation clearly followa specific path within the lp - Vp/Vs space. The six F2 26 27 28 samples are located at the end of the diagenetic path, according to the time calibration based on 29 30 porosity and velocity data. Samples F2-2 and F2-4 appear to be representative of an earlier stage 31 32 of diagenesis, such as previously described. Note that sample F2-2 is the most cemented sample 33 34 35 which could explain the higher observed discrepancy. 36 37 38 One key question remains open: can the experimental velocities measured on the studied 39 40 samples be considered as having been only differently affected during the last diagenetic stage or 41 42 are they the integration of ail the successive diagenetic processes experienced more or Jess 43 ' 44 45 intensely by the samples? The second option is naturally more likely and could explain some 46 47 differences observed for Fl samples. To implement the proposed approach in a more consistent 48 49 way, we will have to consider additional informationfrom basin modeling to assess the residence 50 51 52 time of each sample within the different diagenetic stages. 53 54 55 56 57 58 59 60 GEOPHYSICS Page 26 of 49
Geophysics 26 2 3 Finally, to explore further avenues, we test the possibility of predicting the evolution of 4 5 6 permeability during diagenesis based on our effective medium modeling approach. Numerous 7 8 much more adapted approaches exist in the literature to mode! permeability in rocks (e.g. Dou et 9 10 al., 2011; Ba et al., 2013). But our objective is to predict permeability using microstructural 11 12 13 models weli constrained by geological and mechanical data. The idea is only to replace pure 14 15 phase mechanical parameters by flowparameters (permeability) (Table 5). Effective medium 16 17 modeling is then applied to calculate a homogenized penneability tensor at the macroscale 18 19 (Barthélémy, 2009). Figure 12 presents the results of this extrapolation to permeability 20 21 22 prediction. No calibration with experimental data has been performed here. T�e only objective is 23 24 to illustrate the impact of the different diagenetic stages on the permeability response. 25 26 27 28 CONCLUSION 29 30 31 lt is generally difficult to properly mode! acoustic properties of carbonate rocks due to the 32 33 numerous contrai factors. We base our modeling approach on an extensive experimental dataset 34 35 36 that we use to constrain the conceptual effectivemedium mode! and assess the microscopie 37 38 properties. Contrary to standard approach, we do not introduce compliant pores in our mode) to 39 40 reproduce the measured velocity, which is consistent with the observations on thin sections. We 41 42 reproduce the grain contact behavior by adding a compliant interface to carbonate grains. The 43 44 45 normal and tangential stiffness of this interface are determined through inverse analysis of the 46 47 measured elastic velocity. We then perform direct calculations to define velocity- porosity 48 49 trends during diagenesis. 50 51 52 53 Our approach has to be improved by adding other experimental constraints, such as real 54 55 timing of diagenetic stages. However, it appears as a simple but realistic approach to fil! the gap 56 57 58 59 60 Page 27 of 49 GEOPHYSICS
Geophysics 27 1 2 3 between the petrophysical evolution of carbonates during diagenesis and their elastic properties. 4 5 6 Ali parts of a carbonate formation have not been affected by the same diagenetic events. This 7 8 approach cou Id then be used to test the impact of different diagenesis scenarios on the e!astic 9 10 response of carbonate rocks. Results of such modeling could provide improved input data to 11 12 13 perform synthetic seismic fromstratigraphie models p9pulated with velocity data. 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 GEOPHYSICS Page 28 of 49
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Geophysics 34 1 2 3 Regnet, J. B., Robion, P., David, C., Fortin, J., Brigaud, B. and Yven, B., 2015a, Acoustic 4 5 6 and reservoir properties ofmicroporous carbonate rocks: lmplication of micrite particle size and 7 8 morphology: Journal of Geophysical Research: Solid Earth, 120(2), 790-811. 9 10 11 Regnet, J. B., David, C., Fortin, J., Robion, P., Makhloufi, Y. and Collin, P. Y., 2015b, 12 13 14 Tnfluenceof microporosity distribution on the mechanical behavior of oolithic carbonate rocks: 15 16 Geomechanics for Energy and the Environment, 3, 11-23. 17 18 19 Regnet, J.B., Fortin, J., Nicolas, A., Pellerin, M. and Guéguen, Y., 2018, Elastic 20 21 22 properties of continental carbonate analogs: fromcontrolling factors to an applicable model for 23 24 acoustic velocity predictions. Geophysics, accepted. 25 26 27 28 Riding, R., 1991, Classification ofmicrobial carbonates, in R. Riding, ed., Calcareous 29 30 algae and stromatolites, Springer, 21-51. 31 32 33 Sibley, D. F. and Gregg, J., 1987, Classification of Dolomite Rock Texture: Journal of 34 35 36 sedimentary petrology, 57, 967-975. 37 38 39 Vahrenkamp, V., Barata, J., Van Laer, P.J., Swart1 P. and Murray, S., 2014, Micro 40 41 Rhombic Calcite of a Giant Barremian (Thamama B) Reservoir Onshore Abu Dhabi-Clumped 42 43 44 !sotope Analyses fix Temperature, Water Composition and Timing of Burial Diagenesis: SPE- 45. 46 172033-MS. 47 48 49 Vajdova, V., Baud, P. and Wong, T. F., 2004, Compaction, dilatancy, and failure in 50 51 52 porous carbonate rocks: Journal of Geophysical Research: Solid Earth, 109(B5). 53 54 55 56 57 58 59 60 Page 35 of49 GEOPHY5IC5
Geophysics 35 1 2 3 Verwer, K., Braaksma, H. and Kenter, J. A., 2008, Acoustic properties of carbonates: 4 5 6 E:ffects of rock texture and implications for fluid substitution: Geophysics, 73(2), BS l-B65. 7 8 9 Vincent B., Fleury M., Santerre Y. and Brigaud B., 2011, NMR relaxation of neritic 10 11 carbonates: an integrated petrophysical and petrographical approach. Journal of Applied 12 13 14 Geophysics, 74, 38-58. 15 16 17 Xu, S. and Payne, M. A., 2009, Modeling elastic properties in carbonate rocks: The 18 19 Leading Edge, 28(1), 66-74. 20 21 22 23 Xu, S.Y. and White, R.E., l996, A physical mode! for shear-wave velocity prediction: 24 25 Geophysical Prospecting, 44, 687-717. 26 27 28 29 Zhao, L., Nasser, M. and Han, O., 2013, Quantitative geophysical pore-type 30 31 characterization and its geological implication in carbonate reservoirs: Geophysical Prospecting, 32 33 61, 827-841. 34 35 36 37 LIST OF TABLES 38 39 Table 1. Quantitative estimation of the different components observed in the scanned thin 40 sections. Proportions within bracket are normalized with respect to the solid content (i.e. 41 by removing the porosity from the calculations) ...... 36 42 43 Table 2. Sample minerai contents deduced from XRD analysis (expressed in volume 44 fraction over the solid part) ...... 36 45 Table 3. Total porosity and fractions of microporosity and macroporosity deduced from 46 NMR measurements. Values in bracket provided for sample Fl-13 correspond to the 47 microporosity and macroporosity fractions derived from microscanner imaging...... 37 48 Table 4. Ultrasonic velocities measured on brine-saturated samples ...... 37 49 50 Table S. Pure phase moduli used in the effective medium approach (Mavko et al., 1998) and 51 arbitrary permeability attributed to these phases ...... 38 52 53 54 Tables 55 56 57 58 59 60 GEOPHYSICS Page 36 of 49
Geophysics 36 1 2 3 Table 1. Quantitative estimation of the àifferent components observed in the scanned thin 4 5 sections. Proportions within bracket are normalized with respect to the soiid content (i.e. by 6 removing the porosity from the calculations). 7 8 Resolved Sample Calcite Dolomite Quartz 9 porosity 10 11 Fl-12 64% (75% norm.) 21 % (24% norm.) <1 % (1 % norm.) 14% 12 Fl-13 81 % (94% norm.) 4% (5% norm.) Geophysics 1 2 3 Table 3. Total porosity and fractions of microporosity and macroporosity deduced from NMR 4 5 measurements. Values in bracket provided forsample Fl-13 correspond to the microporosity and 6 macroporosity fractions clerived from microscanner imaging. 7 NMR NMR 8 NMR 9 Sample microporosity macroporosity porosity 10 fraction fraction 11 12 12 14.1% 39% 61% 13 14 13 15.3% 53% (27% µCT) 47% (73% µCT) 15 15 15.1% 32% 69% 16 17 17 18.9% 35% 65% 18 19 21 21.7% 27% 73% 20 2 6.7% 77% 23% 21 22 3 20.3% 54% 47% 23 24 4 15.3% 53% 47% 25 19.5% 78% 22% 26 5 27 6 22.8% 58% 42% 28 29 7 21.4% 56% 44% 30 31 32 33 34 35 Table 4. Ultrasonic velocities measured on brine-saturated samples. 36 37 Density Sample 3 V (km/s) Vs (km/s) 38 (g/cm ) p 39 40 12 2.428 5.024 2.656 41 42 13 2.413 4.902 2.536 43 15 2.378 4.760 2.526 44 45 17 2.363 4.622 2.580 46 47 21 2.308 4.353 2.225 48 2 2.645 5.529 2.990 49 50 3 2.46 4.824 2.669 51 52 4 2.556 5.284 2.925 53 5 2.464 4.803 2.639 54 55 6 2.434 4.607 2.57] 56 57 58 59 60 GEOPHYSICS Page 38 of 49 Geophysics 38 1 2 3 4 7 2.453 4.721 2.655 5 6 7 8 9 10 Tabie 5. Pure phase moduli used in the effective mediu1Y1 approach (Mavko et al., 1998) and 11 arbitrary permeability attributed to these phases. 12 13 Bulk modulas Shear modulus Permeability Minerai phase 14 (GPa) (GPa) (mD) 15 4 16 Calcite 77 32 1 . 10· 17 2 18 Dolomite 95 45 1 .10· 19 Quartz 38 44 1 . 10·4 20 6 21 1 .10 (permeability Liquid water 2.3 0 22 of pores) 23 24 Grain interface Derived from inversion of experimental data 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 39 of 49 GEOPHYSICS Geophysics 39 2 3 LIST OF FiGURES 4 5 6 Figure 1. General methodology proposed to model the evolution of carbonate elastic 7 properties during diagenesis ...... 39 8 Figure 2. Petrographic overview of Fl samples (transmitted light plane-polarized 9 photomicrographs) ...... 41 10 Figure 3. Tentative paragenesis for Family 1 ...... 41 11 12 Figure 4. Petrographic overview of F2 samples (transmitted light plane-polarized 13 photomicrographs) ...... 43 14 Figure 5. Tentative paragenesis for Family 2 ...... 43 15 Figure 6. Ultrasonic velocity measurements performed on brine-saturated Fl and F2 16 samples from family. A: P- and S-wave velocities versus porosity. B: VPVS ratio versus P- 17 wave in1pedance...... 43 18 19 Figure 7. Conceptual effectivemedium models evolving with diagenesis ...... 44 20 Figure 8. Petrographic analysis: selected staining thin sections of F1 and F2 samples 21 illustrating the different key diagenetic events ...... 45 22 Figure 9. Total, macro and microporosity evolution during diagenesis modeling. Data are 23 displayed in red for F1 carbonates and in blue for F2 carbonates...... 46 24 Figure 10. Modeling of elastic wave velocities during diagenesis. A: Comparison between 25 26 mode! and experimental data in a P-wave velocity versus total porosity diagram. Band C: 27 Evolution of P-wave (bright colors) and S-wave velocities (light colors) during diagenesis. 28 Experimental data are marked as circles for F1 and triangles for F2...... 47 29 Figure 11. Representation of modeling results in V PVS versus Jp rock physics template. The 30 main diagenetic stages are represented with arrows. Experimental data are marked as 31 circles for Fl samples and triangles for F2 samples ...... 48 32 33 Figure 12. Extrapolation to permeability modeling using the same effective medium model 34 evolution...... 49 35 36 37 Figures 38 39 40 41 42 Laboratory 43 Diagenetic study 44 Jrom thinsections 45 46 47 Mo<:lellng 48 Thir;rect.:o::s E·,:ohi-'ïg effective Cçfc!,,!c;t{or, of 49 Poro �:uJ�t:·� · m�:i1'J.mcccc1·d:'��;: eüis:ic•,··e!oc,;r:.ie! 50 XRD toit,'l::ge.n�tic p.�G,Sf'$ dr,ri'ngc·!c;;.,,er,,E:l� 51 lJ}CJ'tJSO:�icl··'P ., YS 52 53 54 55 Figure l. General methodology proposed to mode] the evolution of carbonate elastic properties 56 during diagenesis. 57 58 59 60 GEOPHYSICS Page 40 of 49 Geophysics 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 41 of 49 GEOPHYSICS Geophysics 41 2 3 Figure 2. Petrographic overview of Fl sampi es (transmitted iight plane-polarized 4 s photomicrographs ). 6 7 8 9 10 DIAGENETIC EVENT EARLY ,.,.� LATE 11 12 Sedimentation 13 14 Silica 1 (arnorphous quartz) 1S Dog-tooth cernent 16 17 Bed-parallel slylolitization ??? 18 Dolomite cernent 19 20 Dissolution (corrosion of the dolomite) 21 Silica 2 (Granular quartz cernent) - 22 23 Gypsum - 24 1111 ffltll11 2S - 26 Fig-ureV 1- . Tent:-itive ln:-ir;:igenesis ô - for- - - -F:-imilv------.,1 1. 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 GEOPHYSICS Page 42 of 49 Geophysics 42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 43 of 49 GEOPHYSICS Geophysics 43 2 3 Figure 4. Petrographic overview of F2 samples (transmitted light plane-polarized 4 5 photom icrographs ). 6 7 8 9 10 DIAGENETIC EVENT EARLY LATE 11 12 Sedimentation 13 14 Syntaxial cernent 15 HMC/aragonite allochems inversion 16 17 Dissolution 18 19 Dolomite replacement / cernent 20 Equant subhedral, non-ferroan calcite crystals 21 22 Gypsum 23 - 24 25 Figure 5. Tentative paragenesis for Family 2. 76 27 28 29 30 31 6000 2.05 32 @ ® 33 2.00 Î sooo t 34 .è;' 35 'ü 1.95 36 .!:! 4000 +l +# - 37 C: \f 1.90 + 38 Vl 39 > 1.85 -o 3000 ,,r T 40 'i' ,T._ T,1:J: !, T * ,1' 41 .L '.1 -r" "t� -:r- •.r + "· 1.80 42 Fl-VP L a, 2000 •• 43 C: 0 : Fl-VS 44 1.75 -�  F2-VP 45 F2-VS 2 t+ r. � � 46 0.05 QlO Q15 Q20 0.25 0.30 8000 10000 12000 14000 16000 47 Porosity IP (g/cm3.m/s) 48 49 Figure 6. Ultrasonic velocity measurements performedon brine-saturated Fl and F2 samples 50 from family. A: P- and S-wave velocities versus porosity. B: V /V ratio versus P-wave 51 p 5 52 impedance. 53 54 55 56 57 58 59 60 GEOPHYSICS Page 44 of 49 Geophysics 44 2 3 rr,,crop('1·1_ A. Family 1 4 5 6 dolonut, 7 8 • • 9 • • 10 • • q • • • • •• 11 • • • 12 ·�•-:)orphous Process 1 Process 2 Process 3 ('\,.!'ll 15:.]) 13 dolomitization dissolution quartz cementation 14 15 16 B. Family 2 17 ili Geophysics 45 2 3 A. Samples Fl 4 5 6 .t..1 A.3 7 8 ► ► 9 10 11 12 13 DIAGENF.T!C EVl:NTS Early ► Late 14 15 16 1 1 17 18 1 1 19 20 21 22 23 24 25 26 ► ► 27 28 29 30 31 DIAGENETIC EVENTS Early ► Late 32 33 Syn�ùxial �ern�nt / r�plzicernen! - 34 Dissoiuüon 35 36 37 38 39 Figure 8. Petrographic analysis: selected staining thin sections of FI and F2 samples illustrating 40 the different key diagenetic events. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 GEOPHYSICS Page 46 of 49 Geophysics 46 1 2 3 STAGE 1 STAGE 2 STAGE 3 4 5 G.4 6 Fl-21 7 Fl-17 F1·12 Fl·l3 8 Fl-15 9 10 - -a- • :�tt-:ro 11 -·•·· l"l.v,c ... 0.3"' --- T:Wtl --- lL 12 > ------;;• iGO------V, 13 e ,O 0 14 � · 0.2 o.. 15 - ...,_ �•1 lUC 16 - ·• • ;-.�'-'rrn ... 17 ---- l:J:11 18 19 20 21 22 Arbitrary timc 23 24 25 Figure 9. Total, macro and microporosity evolution during diagenesis modeling. Data are 26 displayed in red for F 1 carbonates and in blue for F2 carbonates. 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 47 of 49 GEOPHYSICS Geophysics 47 1 2 3 e,-----:::--:------,-----�------;:::::======:;i 4 F1-VP 5 F1-VS 6 5 F2-VP 7 F2-VS "' 8 E �4 9 >, -;:; 10 0 11 ,; 12 _!,! 3 - -,;;"' ., ; ·1 l 13 w /, 14 .. 15 2 16 17 ® 18 d.0�0:-----0-0-0 . ----0-.1-0----0�_ 1 _0 ____0�_2_0 ____0�2_5 ____0__ 3 _0____ 0_3_5 ____ 0�40 19 To:ai ;>0ros1ty 20 21 6.....-----�-----�----� ô.....-----�-----�----� 22 23 5 24 25 26 E �4 /' c:';,,t 27 Fl-21 ë3 28 29 ,!,! 3 30 ·' 31 32 2 2 33 34 35 1 L.-___ _.. __._ __ ....._ _ ..______; 1 © 0 10 20 30 40 50 60 0 10 20 30 40 50 60 36 Arbitrary time Arbitrary time 37 38 Figure 1 O. Modeling of elastic wave velocities during diagenesis. A: Comparison between mode( 39 and experimental data in a P-wave velocity versus total porosity diagram. B and C: Evolution of 40 P-wave (bright colors) and S-wave velocities (light colors) during diagenesis. Experimental data 41 42 are marked as circles for Fl and triangles for F2. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 GEOPHY51C5 Page 48 of 49 Geophysics 48 1 2 3 2.00 ------�----�----� 4 Fl 5 F2 6 7 8 1.95 9 10 11 12 13 1 Q 90 14 15 16 'UA J 17 18 1.85 19 , : ,....,, 20 ••..,..t. 21 22 1.80 \ 23 \ 24 fJ. 25 26 27 1.75 ------28 8 10 12 14 16 29 IP (�1/cm3.km/s) 30 31 Figure 11. Representation of modeling results in Vp /V5 versus ]p rock physics template. The 32 main diagenetic stages are represented with arrows. Experimental data are marked as circles for 33 34 Fl samples and triangles for F2 samples. 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page49 of 49 GEOPHYSICS Geophysics 49 2 3 4 STAGE 1 STAGE 2 STAGE 3 î0 ° .,...-----,------r----r------, 5 6 FT1l 7 � 8 1 o• 9 10 11 12 13 14 15 16 17 18 19 1 20 10 21 22 23 24 10� ---�---�---�---�---�---� 10 20 30 40 50 60 25 Arbitrary time 26 27 Figure 12. Extrapolation to permeability modeling using the same effective medium mode( 28 29 evolution. 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60