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Home All issues Volume 196 (2025) BSGF - Earth Sci. Bull., 196 (2025) 24 Full HTML
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BSGF - Earth Sci. Bull.
Volume 196, 2025
Article Number 24
Number of page(s) 23
DOI https://doi.org/10.1051/bsgf/2025022
Published online 09 December 2025

© S. Allouti et al., Published by EDP Sciences 2025

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

After more than a century of coal exploitation until 2004 and exploration for oil and gas during the 80 s–90 s, renewed interest in evaluating of the gas reserves of the Lorraine Carboniferous basin has emerged in recent years (Gunzburger, 2019). Currently, the Lorraine Basin is undergoing a new investigation, with recent drillings providing both core and well log data. Previous studies described the coal seams distribution (Donsimoni, 1981), the organic geochemistry of coal and kerogen-bearing strata (Fleck, 2001), reconstructed the burial history of the basin, and evaluated gas generation (Izart et al., 2016). However, until recently no attempt was made to quantitatively evaluate the gas generation potential of the basin as part of the assessment of the ultimate gas reserves.

The Total Organic Carbon content (TOC) is a key parameter to assess the gas potential of sedimentary strata (Passey et al., 1990). While major coal strata are well characterized in the Lorraine basin wells, the quantitative estimation of the abundance of kerogen present in surrounding rock facies (clay, siltstone, sandstone, and conglomerate) has never been evaluated in a continuous manner along the formations, as previous studies (Fleck, 2001) relied on sampling approaches that did not capture the full complexity. Yet, the calculation of the total gas generation potential of the Carboniferous deposits requires the appraisal of all organic matter-containing facies.

TOC measurements in the laboratory may be performed by carbon analyzers (Van Krevelen, 1993) or Rock-Eval pyrolysis (Espitalié et al., 1985) applied to core samples and drilling cuts. However, these laboratory measurements are time-consuming and the TOC data is discontinuously determined along the sedimentary profiles. To overcome this drawback, methods involving well-logging methods have been developed to assess TOC contents.

Well-logging techniques have greatly enhanced the exploration of Coalbed Methane (CBM) reservoirs by providing workflows to evaluate coal quality, and reservoir parameters such as fracture density, permeability, and gas content (Morin, 2005; Chatterjee and Paul, 2013; Meng et al., 2013; Sutton, 2014; Ghosh et al., 2016; Su et al., 2018).

The systematic determination of the TOC content of sedimentary logs by such methods has however mostly been developed for marine petroleum source rocks (Nixon, 1973; Meissner, 1987; Meyer and Nederlof, 1984; Mendelzon and Toksoz, 1985; Mann et al., 1986; Mann and Muller, 1988; Passey et al., 1990 ; Bessereau et al., 1991; Schwarzkopf, 1992).

Schmoker (1979, 1981) first published a method to calculate TOC content from density and gamma-Ray logs. Schmoker (1979) proposed a linear relationship between TOC and the formation density log in shales. Generally, shale mineral matrix density presents an average value of 2.7 g/cm3 while matrix density values for organic matter are approximately 1.1 g/cm3. The occurrence of organic carbon vastly influences the formation bulk density and hereafter TOC is calculated from density logs. Meyer and Nederlof (1984) and Mendelzon and Toksoz (1985) used a combination of density, sonic slowness, and electrical resistivity logs to calculate Total Organic Carbon (TOC) for characterizing petroleum systems. They explained that source rocks are characterized by their low density, low sonic slowness, and high electrical resistivity. To improve TOC assessment, Passey et al. (1990) proposed to use a combination of well-logs and developed the ΔlogR technique, which consists of the overlay of porosity (sonic, density, neutron) with resistivity logs. In organic matter-rich sediments, the two geophysical signals exhibit distinct characteristics, and the magnitude of their separation is primarily proportional to TOC, with additional influence from the thermal maturity of the formation (including the presence of oil and gas). Consequently, utilization charts have been developed based on vitrinite reflectance to account for these factors. This method has limitations in terms of accuracy for interwell correlation, as the ΔlogR technique requires the arbitrary selection of a baseline, which varies significantly from well to well due to lithological variations (Yu et al., 2017; Wang, 2022) and thermal maturity of kerogen (Sun et al., 2013). In fact, the thermal maturity of the formations intersected by the wells can influence the porosity, which is susceptible to measurement by density, sonic, and resistivity logs, thereby leading to variations in the log readings between wells.

In shale and coal, the ΔlogR method requires calibration as it tends to underestimate the Total Organic Carbon content in these formations (Sondergeld et al., 2010).To address this, alternative approaches are proposed to determine correction coefficients in organic-rich layers (Sondergeld et al., 2010). Additionally, the inclusion of other well logs, such as natural gamma spectroscopy, is proposed by Li and Zhang (2023).

Bessereau et al. (1991) introduced the CARBOLOG method, which utilizes Sonic slowness and resistivity well logs taking into account the composition of rock, including matrix, water, clay, and organic matter. The method defines the CARBOLOG diagram, where the square root of resistivity is plotted against sonic slowness.

Moreover, statistical methods, such as multivariate analyses, are employed to predict TOC, demonstrating good correlations between density logs and the predicted TOC (Zhang and Xu, 2016; Nyakilla et al., 2022). However, the generalization of these models is not possible for all continental shales and coal due to weak linear correlations with log curves (Hu et al., 2016; Wang et al., 2017). Currently, the most advanced method for calculating Total Organic Carbon (TOC) utilizing well-log data is the application of machine learning algorithms (Huang and Williamson, 1996; Kamali and Mirshady, 2004; Amiri Bakhtiar et al., 2011; Khoshnoodkia et al., 2011; Alizadeh et al., 2012; Cranganu and Dimitrijevic, 2016; Bolandi et al., 2017; Mahmoud et al., 2017, 2019; Nezhad et al., 2018; Wang et al., 2018; Zhu et al., 2018; Elkatatny, 2019; Zhao, 2019; Zhu et al., 2023; Wood, 2023). However, there is currently no standardized algorithm established for the computation of TOC from well logs. This limitation can be primarily attributed to the heterogeneity of lithological formations (Chan et al., 2022). Passey et al. (1990) had already noted that TOC values obtained using their approach were unreliable for organic matter-rich layers with thicknesses less than 1 meter. However, a significant challenge arises from the complexity of sedimentary successions, particularly in continental detrital deposits. This is the case for instance for the fluvial facies which are dominant in the Lorraine Carboniferous Basin and characterized by hundreds of fining upward depositional sequences (conglomerate to sandstone, silt, clay, and coal seams). Therefore, this study aims to calculate Total Organic Carbon (TOC) using well logs across all fluvial-lacustrine sedimentary facies, contributing to the gas reserve calculations.

2 Geological setting

The Lorraine Carboniferous Basin, located in North-East France, is about 200 km long and 80 km wide. It extends into the German Saar-Nahe Basin where strata outcrop (Schäfer, 2011) (Fig. 1). In the French part, the basin is bounded to the north by the Metz-Hunsrück Fault, a major SW-NE trending thrust fault belonging to Variscan orogeny (Henk, 1993; Hemelsdaël et al., 2023), to the south by the gravity anomaly between Sarrebourg and Gironcourt and to the west by La Marne Fault (Donsimoni, 1981; Izart et al., 2016). It is an intermountain basin (Donsimoni, 1981; Hemelsdaël et al., 2023) that developed during the Hercynian orogeny and therefore contains no marine sediments (Schäfer, 1989, 2011). More precisely, the Lorraine Carboniferous basin developed during the compression phase and late collapse phase of the Variscan belt. The main part of the sedimentary filling consists of up to 8 km of Westphalian-Stephanian detrital sediments covered by Permian and Mesozoic deposits of about 500 m thickness on average (Pruvost, 1934; Donsimoni, 1981; Barrabé and Feys, 1965; Izart et al., 2016).

In this study, well logs investigated stratigraphical interval is comprised between the top of Westphalian C to top Westphalian D. Those regional lithostratigraphical and biostratigraphical subdivisions can be correlated to the international chronostratigraphical chart (Gradstein et al., 2020), and assigned to Middle and Late Pennsylvanian stages, thanks to the datings of zircons from the volcanic tuffs of the Saar and Lorraine basins (Izart et al., 2025). These authors dated the Westphalian B/Westphalian C boundary (313.82 Ma), the mid-part of the Westphalian C (313.24 Ma), the Westphalian D top (307.95 Ma) and the Early Stephanian (304.49 Ma), and proposed a correlation with the other regional substages from the Western European coal basins. The Westphalian B corresponds to the Duckmantian regional substage, the Westphalian C to the Bolsovian, the Westphalian D to the Asturian, and the Early Stephanian to the upper part of the Cantabrian and Barruelian. The marine global stages corresponding to these local substages are respectively the Moscovian and the Kasimovian, assigned to the Middle and Late Pennsylvanian.

At the basin scale, the sedimentary deposits are subdivided into two major series which were defined essentially by palynological and paleobotanical data in galleries and boreholes (Pruvost, 1934; Laveine, 1974; Alpern et al., 1969; Termier, 1923; Izart et al., 2025): i) The Westphalian series displaying approximately 4 km of accumulated deposits with about a hundred coal beds. Their thickness varies from a few centimeters to a maximum of 25 meters exceptionally, with an average of four to five meters. ii) The Stephanian series of about 1.1 km of deposits containing four major coal layers.

Coal layers are interstratified within all grain size siliciclastic series with variable thicknesses of conglomerates, sandstones, siltstones, and claystones. Deposits show differential preservation due to the development of recurrent erosional surfaces.

A wide spectrum of different continental environments (Figs. 2 and 3), studied by Izart et al. (2005) for the Westphalian C and Allouti (2024) for the Westphalian D, can be highlighted, with from source to sink restricted to that intermountain context, alluvial fans, braided rivers, meandering rivers, anastomosed rivers with more or less preserved floodplains, and finally delta-lakes where sediment storage become permanent due to provided suitable accommodation. River systems were interconnected to well-developed lowland swamps and lakes organized in variable continuous areas with rich and diversified plant life indued high organic productivity (Pruvost, 1934; Donsimoni, 1981; Fleck et al., 2001; Izart et al., 2005). Higher proportion of floodplain deposits give appropriate conditions to more widespread distribution of coal. Moreover, organic-rich swamps were to show rapid rate of organic growth and accumulation outpaces clastic sedimentation. This kind of sedimentological evolution and stratigraphical organization is typical of depositional environments for Carboniferous coal-bearing strata (McCabe, 1985; Diessel, 1992; Thomas, 2002). The high frequency sequences reported in the Figures 2 and 3 were determined by Allouti (2024) and their durations (close to 20 ka, precession-scale) were calculated by (Izart et al., 2025, their Fig. 5) thanks to the Bayesian method.

thumbnail Fig. 1

Simplified geological map of the Saar-Lorraine Basin showing the location of Folschviller (Fols 1A) and Diebling (Dbl S1) boreholes. The Carboniferous Basin is accessed by both boreholes at depths of 700 and 600 meters, respectively. Permian and Carboniferous outcrop in Germany. Modified after Pruvost (1934), Donsimoni (1981), Schäfer (2011) and Izart et al. (2016).
thumbnail Fig. 2

Sedimentary logs of Folschviller (Fols 1A) well presenting lithological succession, corresponding depositional environments, architectural element log and sedimentary sequences representative of the Lorraine Carboniferous basin. Data based on well-logs and core analysis.
thumbnail Fig. 3

Sedimentary logs of Diebling (Dbl S1) well presenting lithological succession, corresponding depositional environments, architectural element log and sedimentary sequences representative of the Lorraine Carboniferous basin. Data based on well-logs and core analysis.

3 Materials and methods

3.1 Data availability

3.1.1 Studied wells and core samples

The study is focused on two boreholes, Folschviller (Fols 1A) and Diebling (Dbl S1), which were drilled by La Française de l’Energie company and penetrated the top of the Carboniferous units (Figs. 1–3). Fols 1A reached Westphalian D in the (690–1303 m TVD interval), while Dbl S1 drilled through Westphalian D (875–1265 mTVD interval) and Westphalian C (1265–1440 m TVD interval). Detailed lithologies, depositional environments as well as stratigraphic sequences are synthesized in Figures 2 and 3. Thirty-seven samples were collected from these boreholes, including coals and shaly coals, claystones, siltstones, and sandstones.

3.1.2 Organic petrography and Rock-Eval analysis

The rock and coal samples were crushed, sieved (<180 µm mesh), and analyzed by Rock-Eval pyrolysis at the Institut des Sciences de la Terre d’Orléans (ISTO) (France) (analytical procedure described in Le Meur et al. (2021). The major parameters considered were TOC (wt%) and Tmax (°C). Organic petrography and vitrinite reflectance measurements were assessed by EGS-exploration (Switzerland).

3.1.3 Well logs data

The well logs are presented in Log Ascii Standard (LAS) format for both the boreholes Fols 1A and Dbl S1. Data were imported into Techlog© Schlumberger software and then exported to Microsoft Excel© to evaluate TOC using ΔlogR and Schmoker methods. Gamma-Ray, Sonic, and Density Logs are used to determine shale volume, total porosity, and lithological interpretation. TOC computation involves Sonic, Density, and Resistivity Logs. The caliper is also available for both wells to control potential washout/breakout detected by borehole diameter widening in some coal layers.

3.2 Methods of calculating total organic carbon using well-logs

3.2.1 Well log responses for characterizing coal deposits

Various methods for identifying and characterizing coal layers and organic-rich strata in subsurface rock units, including gamma-ray, density, resistivity, sonic slowness, and caliper measurements are described in the literature (Seidle, 2011; Keskinsezer, 2019; Thomas, 2002).

The gamma-ray method involves measuring the intensity of naturally occurring gamma rays. Coal layers typically exhibit low gamma ray values, whereas clayey formations present high values. Also, gamma ray values are lower in lithologies such as sandstones and conglomerates (Hollub and Schafer, 1992; Karacan, 2009; Seidle, 2011; Keskinsezer, 2019). Therefore, this tool cannot be used alone to identify organic-rich sediments.

In regards to the use of density logs, coal and organic-rich strata typically exhibit lower density values compared to other lithologies (Mavor et al., 1994; Zhou and Esterle, 2008; Keskinsezer, 2019).

In terms of resistivity, coal layers exhibit higher values, but only when the water content is low (Keskinsezer, 2019). The resistivity of coal is dependent on its rank, with lignite and anthracite displaying very low resistivity and subbituminous and bituminous coal displaying a range from low to high resistivity values (Mavor et al., 1994; Thomas, 2002). In addition, resistivity may be influenced by factors such as water saturation and salinity as well as quantity of clay or conductive minerals like pyrite (Sondergeld et al., 2010) and must therefore be combined with other tools to determine the organic matter content of strata.

Sonic logs are valuable tools for identifying coal layers (Rider and Kennedey, 2011; Seidle, 2011). The sonic wave transit time in coal range generally between those of sandstone and shale. However, anthracite coal, with a transit time of approximately 90 µs/ft, exhibits a response closely resembling that of shale, making accurate discrimination more challenging. While sonic logs are useful in assessing coal quality, their application to coal gas reservoir engineering is limited by certain constraints such as breakout and washout. Nonetheless, sonic logs combined with the previously mentioned tools may serve as indicators of organic matter content (Passey et al., 1990; Meyer and Nederlof, 1984).

The caliper log is used for measuring the diameter of the borehole and serves as an effective quality control for other wireline logs, including density, gamma-ray, and sonic logs. By applying this tool, errors in the identification of coal layers caused by unusually low formation density and gamma ray responses across severe washouts can be prevented. It should be noted that while washout is often considered an indicator of permeability, as well as an indicator of coal mechanical friability (Thomas, 2002).

3.2.2 Schmoker method

Schmoker (1979) developed a method for estimating TOC contents of Appalachian Devonian marine shale using a density log RHOb. Schmoker and Hester (1983) suggested that TOC has a positive linear correlation with the reciprocal of bulk density:

TOC=ARHOb−B.(1)

Schmoker (1979, 1981) considered the rock is composed of mineral matrix, interstitial pores, pyrite, and organic matter. In this case, the formation bulk density is a function of fractional densities and volumes of these four components. The volume of pyrite was assumed to increase linearly with the organic matter content because the decomposition of organic matter generates reducing conditions that promote pyrite formation in anoxic environments. For this reason, pyrite was treated as a separate component from the matrix. The values of A and B in equation (1) are calculated by incorporating density values for pyrite, organic matter, and matrix at 5.0, 1.01, and 2.69 g/cm3, respectively.

TOC=154.497RHOb−57.261.(2)

3.2.3 Δ log R method

Passey et al. (1990) proposed Δ log R method for estimating TOC content from well-log data. Currently, the Δ log R is a widely used method for marine clay series. The Δ log R technique requires the superposition of resistivity with porosities logs (sonic slowness ΔT, density RHOb or neutron porosity Фn; in Eqs. (3)–(5)) and the availability of organic matter maturity data (e.g., vitrinite reflectance). The integration of sonic slowness and resistivity logs facilitates the identification of a baseline cutoff. A distinct separation between the two curves indicates the presence of source rock zones, while the overlap of the curves signifies non-source rock intervals. (Fig. 4).

ΔlogR=log10(RRBaseline)+0.02*(Δt−Δt Baseline),(3)

ΔlogR=log10(RRBaseline)+4*(ϕt−ϕtBaseline),(4)

ΔlogR=log10(RRBaseline)−2,5*(RHOb−RHObBaseline).(5)

In this study, equation (3) is used to calculate Δ log R. The amount of organic carbon is directly proportional to Δ log R, consequently, TOC can be calculated using equation (6).

TOC=ΔlogR*10(2.297−0.1688*LOM).(6)

If the Level of Maturity (LOM) is known, the ΔlogR separation of different lithologies using well logs data can be used to estimate the TOC. LOM is a scale of organic matter thermal evolution applicable to fine-grained sedimentary rocks proposed by Hood et al. (1975). LOM values were estimated from vitrinite reflectance (%Ro) values using equation (7).

LOM=0.0989×Ro5−2.1587×Ro4+12.392×Ro3−29.032×Ro2+32.53×Ro−3.0338.(7)

Thermal maturity values for the Westphalian D formation in the Lorraine Carboniferous Basin, Fols 1A and Dbl S1 wells are available in Table 1. The equation for LOM was determined from digitalization of the % Ro correlation table established by Hood et al. (1975).

thumbnail Fig. 4

Sonic/Resistivity Overlay is showing ΔlogR separation in the coal rich intervals for Fols 1A and Dbls1 wells. The relative scaling and resistivity curves correspond to a 50 μs/ft increment, representing one decade of resistivity.
thumbnail Fig. 5

Calibration of TOC by Schmoker (1979, 1981): (a) Linear relationship among Rock Eval TOC (wt%) and 1/density (cc/g) in Fols 1A and Dbl S1 wells as calibrated by the method published by Schmoker (1979, 1981); (b) Comparison of Rock Eval TOC with TOC calculated using the equation published by Schmoker for Fols 1A and proposed modified equation for calibration of Dbl S1 wells.
Table 1

Vitrinite reflectance (%Ro) and level of organic maturity determined after Hood et al. (1975) for samples from Fols 1A and DBLS 1 wells.

4 Results

4.1 TOC calculation using Schmoker

The widely used TOC calculation method proposed by Schmoker (1979, 1981) is represented by equation (2) with constants A and B of 154.497 and 57.261 respectively. These values are not always suitable for any well and may thus be adjusted for our reference wells Fols 1A and Dbl S1. These constants are typically gauged from the linear regression of TOC Rock-Eval and density log (Schmoker and Hester, 1983; Yu et al., 2017).

In the case of the Fols 1A borehole the crossplots of the TOC Rock-Eval versus 1/density and TOC Schmoker versus TOC Rock-Eval (Figs. 5a and 5b) reveal a linear relationship that closely matches with equation (2) with acceptable correlation coefficients. In this case, correction of A and B may not be applied.

In the case of the borehole Dbl S1, the same graphs show significant deviations (Fig. 5) revealing that the A and B parameters of the original Schmoker method induce an underestimation of TOC values. Consequently, constants A and B are changed to 256.02 and 100.4 respectively for the Dbl S1 borehole (Fig. 5a; Eq. (8)).

TOC=256.02RHOb−100.4.(8)

Figure 5b shows the relationship obtained between Rock-Eval TOC and TOC calculated using the adapted Schmoker equation. The TOC values are calculated using the Schmoker relationship, and are used as a reference for the other developed relationship.

4.2 TOC calculation using Δ log R

Continuous sonic and resistivity logs are available for the Fols 1A and Dbl S1 boreholes. Prior to overlaying the curves, appropriate scaling is necessary to ensure that each resistivity cycle corresponds to 50 µs/ft. Following scaling, the curves require baseline definition. Baseline resistivity and sonic values are established at 150 ohm.m and 65 μs/ft for the Fols 1A well and 100 ohm.m and 80 μs/ft for the Dbl S1 well (Tab. 2 and Fig. 4). Equation (3) is then used to calculate the ΔlogR separation in this study (Fig. 4), which enables the estimation of TOC using equation (6).

For Fols 1A and Dbl S1 wells, TOC values were calculated by applying the ΔlogR method and equal to 8 wt% for coal layers. These values are approximately ten-fold lower than the TOC values obtained from Rock-Eval analysis, which range from 20 to 75 wt% in Fols 1A and 10 to 85 wt% in Dbl S1, with maximum values of 75 and 85 wt%, respectively. For shaly lithologies, mean TOC values are 0.5 wt% in both wells, which is lower than the values obtained from Rock-Eval analysis in Fols 1A (7 wt% TOC on average) and Dbl S1 (3 wt% on average) (Track 2 in Figs. 6 and 7 respectively).

Table 2

Delta log R baseline values used for TOC calculations.

thumbnail Fig. 6

Assessment of Total Organic Carbon (TOC) in Fols 1A well using different calculation methods based on well log data.
thumbnail Fig. 7

Assessment of total organic carbon (TOC in wt%) in Dbl S1 well using different calculation methods based on well log data.

4.3 TOC calculation using modified Δ log R method

4.3.1 TOC Schmoker vs. TOC Δ log R evaluation

The Schmoker and calibrated Schmoker methods as defined above allow to calculate TOC values in good agreement with Rock Eval data measured on the various lithologies (coal, shaly coals, coaly shales, sandstones, conglomerates) present in our wells (Figs. 6 and 7). The Schmoker method may then be considered as the most appropriate for our study. In contrast, the ΔlogR method tends to underestimate TOC values for coaly and shaly lithologies. Cross-plot analyses using TOC Schmoker/ TOC ΔlogR versus geophysical parameters (Sonic slowness, bulk density, and resistivity) are tested. Only the cross-plot using sonic slowness showed a consistent trend (Fig. 8a) in which values greater than 80 μs/ft and 100 μs/ft for Fols 1A and Dbl S1 respectively represented a logarithmic trend with a convergence limit of 10. The consideration of bulk density (color scale (Fig. 8a)) shows that these points correspond to low-density values related to coal and coaly facies. Changes in density values from 1.7 to 2.3 g/cm3 correspond to increasing shale volume on carbonaceous lithologies. All data points showing sonic slowness values lower than 70 μs/ft and high density (more than 2.3 g/cm3) are related to non-source rock formations (sandstones and conglomerates) and displayed no correlation with sonic slowness.

The cut-off values of 80 μs/ft and 100 μs/ft were applied to select shale, shaly coal, and coal from Figure 8a. For coaly lithologies, the minimum sonic slowness value is 80 μs/ft for Fols 1A and 100 μs/ft for Dbl S1, while the maximum value is 140 μs/ft for Fols 1A and 160 μs/ft for Dbl S1. The analysis of the data reveals a logarithmic increase in the ratio in relation to sonic slowness, ranging from 0.1 to 10 as shown in Figure 8b. Equations (9) and (10) represent this relationship for Fols 1A and Dbl S1 wells, respectively.

(TOCSchmoker)/(TOCΔlogR)=19.15*ln(ΔT)−83.48,(9)

(TOCSchmoker)/(TOCΔlogR)=23.298*ln(ΔT)−101.(10)

Therefore, to mitigate the discrepancy between TOC values calculated by ΔlogR and measured by Rock-Eval, equations (11) and (12) are applied as sonic slowness filters to wells Fols 1A and Dbl S1 respectively. Proportional corrections are thus applied to shaly and coaly lithologies while values for non-source rock formations are left unaltered.

TOC=ΔlogR*10(2.297−0.1688*LOM)*(19.15*ln(ΔT)−83.48),(11)

TOC=ΔlogR*10(2.297−0.1688*LOM)*(23.298*ln(ΔT)−103.48.(12)

Figure 6 (track 8) and 6 (track 6) show the consistency between assessed and measured TOC values once the corrections are applied. The box plot (Fig. 9) for the Fols 1A borehole shows that upon application of the logarithmic factor to the ΔlogR method, 50 % of coal sample points analyzed exhibit TOC ranging from 30 wt% to 60 wt%. Also, 50 % of shaly lithology sample points analyzed exhibit an average TOC amount ranging from 3 wt% to 6 wt%. Similarly, after correction of the ΔlogR method via the logarithmic factor, the box plot for the Dbl S1 borehole (Fig. 9) indicates that 50 % of coal sample points analyzed exhibit a TOC amount ranging from 20 wt% to 70 wt%, with 50 % of shaly lithology sample points analyzed exhibiting an average TOC amount ranging from 3 wt% to 6 wt%.

thumbnail Fig. 8

Calculated TOC ratio using Schmoker and Delta log R methods in Fols 1A and Dbl S1 wells: (a) as a function of Sonic Slowness and bulk density: in color code for all lithologies, (b) as a function of Sonic Slowness only for coaly lithologies.
thumbnail Fig. 9

Assessment of total organic carbon (TOC in wt%) in Fols 1A and Dbl S1 wells using different calculation methods based on well log data as box plot analysis.

4.3.2 “Δ. log R separation” and TOC calibration

In the method proposed by Passey et al. (1990), the relationship between TOC values and the separation ΔlogR is given by equation (6), which requires the consideration of LOM (Level of Organic Maturity, a factor proportional to vitrinite reflectance) (Hood et al., 1975). The results for our sample sets (LOM=10.12–10.65; %Ro = 0.84 to 0.96 and TOC as determined by Rock-Eval) are consistent with ΔlogR method for facies with TOC lower than 10 wt%. However, for TOC greater than 10 wt%, the data points fall outside the range, indicating that equation (6) may not be appropriate for coaly facies (Fig. 10). These findings have important implications for the interpretation of well-log data, as they suggest that the linear LOM trends proposed by Passey et al. (1990) may not apply for coaly facies. Therefore, alternative equations may be proposed for TOC determination in coal-rich deposits. Two approaches are used to calibrate TOC values over a large range: i) Rock-Eval TOC (using the depth average where the sample was taken) and ii) TOC calculated using the method by Schmoker (1979, 1981) as validated previously vs Δ log R.

In Figure 11 (borehole Fols 1A), two correlation equations may be derived from Rock-Eval TOC vs Δ log R, a polynomial Eq. (13) (red solid line) and an exponential (Eq. (14)) (red dashed line). When considering TOC calculated after Schmoker (1979, 1981) and Δ log R, a polynomial (Eq. (15)) (blue solid line) and an exponential Eq. (16) (blue dashed line) are derived.

TOC=22.117*ΔlogR2+6.997*ΔlogR,(13)

TOC=e2.6136*ΔlogR,(14)

TOC=16.262*ΔlogR2+6.5631*ΔlogR,(15)

TOC=e2.4374*ΔlogR.(16)

In Figure 12 (borehole Dbl S1), a correlation between Rock-Eval TOC and ΔlogR results in a polynomial (Eq. (17)) (red solid line). Correlation between Schmoker TOC and ΔlogR leads to a polynomial Eq. (18) (blue solid line).

TOC=−8.5903*ΔlogR2+64.702*ΔlogR−12.655,(17)

TOC=−3.2901*ΔlogR2+45.123*ΔlogR−2.4875.(18)

thumbnail Fig. 10

Examining the Relationship between TOC (wt%) values and Delta log R using the diagram of Passey et al. (1990) for Fols1A and Dbl S1 wells.
thumbnail Fig. 11

Correlation equations between Rock-Eval measurements (red dots) and calculated using Schmoker (1979, 1981) (black dots) TOC (wt%) versus delta log R (Passey et al., 1990) for Fols 1A well using different calibration equations.
thumbnail Fig. 12

Correlation equations between Rock-Eval measurements (red dots) and calculated using Schmoker (1979, 1981) (black dots) TOC (wt%) versus Delta log R (Passey et al., 1990) for DBL S1 well using different calibration equations.

4.4 TOC calculation using multivariate regression

As the density log is not always available for all the wells of our basin, it is interesting to further explore the relationship between calculated TOC using Schmoker (1979, 1981) and various borehole logs. Therefore, we conducted multivariate regression analyses using gamma ray (GR), sonic (Δt), and resistivity (R) logs in regard to TOC as determined by the Schmoker method validated by TOC Rock-Eval. Based on a total of 8785 measurements for Fols 1A and 6381 measurements for Dbl S1, the multivariable regression analysis led to the following equations:

Fols1A:TOC=0.73*Δt−0.065*GR+0.02*R−46.29,(19)

DblS1:TOC=0.82*Δt−0.066*GR+0.02*R−64.15.(20)

With determination coefficient R2 of 0.82 and 0.73 respectively. This indicates a strong relationship between TOC and the geophysical variables (gamma ray, sonic, and resistivity logs) for both boreholes (Fig. 6 Track 7 and Fig. 7 Track 5).

5 Discussion

The analysis of logs signals in Fols 1A and Dbl S1 boreholes revealed discrepancies in the equations used to calculate TOC primarily due to sonic slowness value deviations of 20 μs/ft between the two boreholes. Fols 1A exhibits less dispersion around correlation curves and a higher correlation coefficient compared to Dbl S1. The divergence stems from contrasting sediment composition. The siltites, sandstones, and conglomerates from the Fols 1A borehole are litharenites rich in pseudo-detrital matrix with abundant micritic siderite cementation, while those from Dbl S1 are of better sorting (mineralogical and grain sized based sorting) with low pseudo-detrital matrix contribution and far lessauthigenic siderite. The predominant types of cement are later diagenetic phases such as dickite and illite. Furthermore, the burial history of the two boreholes varies. Fols 1A experienced greater burial and compaction due to its structural position on the flank of a syncline) compared to Dbl S1, which is positioned on the hinge zone of an anticline.

The application of the Schmoker method on this case study well-log data leads to TOC values that are consistent with those obtained from Rock-Eval measurements on rock samples. The Schmoker equation for TOC calculations considers the contribution of organic matter, pyrite, interstitial porosity, and rock matrix as variables. Schmoker (1979, 1981) demonstrated a proportional relationship between the abundance of organic matter and pyrite and integrated this into equation (1). Yet, his study was based on claystone deposited in the marine environment. It is well known that in the anoxic sulfate-rich marine waters, organic matter is a substrate for the growth of sulfate-reducing bacteria communities which generate reduced sulfur. In the presence of detrital minerals, reduced iron is combined with sulfur to produce iron sulfide, hence the relationship observed by Schmoker (1979, 1981). In this case study, sediments were deposited in a fluvial-lacustrine system without connection to the marine environment (Donsimoni, 1981; Izart et al., 2005; Fleck et al., 2001) and therefore poor in sulfate. As a consequence, the coal layer present is lean in pyrite.

As considered by Schmoker (1979, 1981), porosity may be considered as constant for a given facies (marine claystone in his study cases) and thus may not influence TOC calculation. In the present case study, regarding the diversity of facies from coal to conglomerate, the influence of porosity changes may be questioned. Conglomerate aside, the studied facies present porosities up to 5% for coaly facies and values lower than 10% for sandstones, siltstones, and claystones. Calculations applied to our most porous facies (tight sandstones) led to lean to no TOC contents, consistent with Rock-Eval measurements. This might indicate that bulk density may not be highly influenced solely by porosity. In this case, porosity changes between our facies may be considered negligible. It may also be noted that all rock facies contain the same type of mineralogy (only grain size classes change) (Hering, 1976; Fleck, 2001), with densities ranging from 2.57 g/cm3 for sandstones to 2.7 g/cm3 for claystone. Well-log density of our coal varies between 1.1 g/cm3 and 1.8 g/cm3. The density contrast between organic matter and sandstones as well as siltstones may thus be considered as similar. In regards to the above-mentioned considerations, the changes in the bulk density well-log signal may then be essentially a function of kerogen content. This might explain why the Schmoker method may be efficient in the calculation of the TOC in the present case study.

The presence of pyrite significantly impacts well-log responses, particularly in terms of density and electrical resistivity, thereby influencing interpretations and calculations based on these parameters, such as the determination of Total Organic Carbon (TOC) using methods like the Schmoker or ΔlogR techniques. Studies by Clavier et al. (1976), Kennedy (2004), and Jiang et al. (2018) have extensively documented these effects.

Pyrite is distinct from other components of organic-rich rocks due to its very low resistivity and high density. In claystone layers deposited in marine environments, the presence of pyrite can affect log signals and, consequently, TOC calculations. To address this, new methods have been developed to correct for pyrite influence in clay-rich samples. Jiang et al. (2018) incorporated pyrite volume considerations into their updated equation based on density to improve accuracy.

In this study, 20 sandstone samples, 14 claystone and siltstone samples, 17 shaly coal samples, and 36 coal samples were analyzed using X-ray diffraction (XRD) and petrographic methods. The pyrite content in these samples is very low, averaging 0.50% in clays and siltstones, 0.8% in carbonaceous clays, approximately 1% in clayey coals, and nearly 0% in coals (Fig. 13). This low pyrite content reflects the fluvial-lacustrine depositional environment, which is isolated from marine settings and therefore lacks sulfate, resulting in kerogen that is low in pyrite. This suggests that the Schmoker method is well adapted and needs some adjustment of the coefficients A and B to provide accurate values for TOC Rock-Eval measurements (Section 4.1).

However, Section 4.2 demonstrates that the ΔlogR method results in a tenfold underestimation of TOC compared to Rock-Eval measurements on our samples. Kennedy (2004) noted that pyrite effects on electric resistivity tools are significant, as at concentrations above a few per cent, pyrite can reduce formation electric resistivity. Sondergeld et al. (2010) explain that pyrite in organic-rich intervals can substantially affect TOC evaluation due to its conductive nature, which reduces rock resistivity and decreases Δ log R. Sondergeld et al. (2010) applied a correction factor of 4 to their TOC calculations for marine shales.

Within LCB samples analyzed here, the maximum pyrite content reaches 1 % (Fig. 13), which might partially affect the underestimation of TOC but does not fully explain the tenfold discrepancy observed. This suggests that other factors, such as water saturation, may also perturb resistivity signals, as discussed below.

Passey et al. (1990) suggest that the presence of coal intervals induces a significant resistivity deflection compared to adjacent intervals such as sandstones, siltstones, and shales. Indeed, Telford et al. (1990) measured high resistivity values ranging from 0.6 × 105 to 1 × 105 Ohm.m on dry bituminous coal samples. This may account for ΔlogR values in accordance with high TOC of coaly intervals. However, the resistivity increase observed in the well-logs here is not as strong as expected.

Figure 14 recalls the data presented in Figure 10 with the addition of TOC vs. ΔlogR data obtained for sub-bituminous and bituminous coal from the literature. The dark shaded area is relative to dry coal samples for which ΔlogR values are calculated using equation (3) with sonic slowness of 150 μs/ft (maximum observed in our well-log data for coal layers), resistivity values for dry coal (McCabe and Tholey, 1945; Telford et al., 1990), (Tab. 3) versus TOC data chosen from literature for pure coals of various rank (Mastalerz et al., 2011) (Tab. 3). These values once positioned in Figure 14 suggest the true relationship that ΔlogR and TOC should have for dry coal layers. The blue shaded area is relative to wet coal samples for which ΔlogR values are similarly calculated, but using resistivity for wet coal from literature (Tab. 3). These values illustrate the ΔlogR and TOC for wet coal seams. It is noteworthy that these results do align with the TOC vs. ΔlogR relationship of our wells and sample sets. This implies that the water saturation of our coal-rich layers significantly influences the calculations. Indeed, the presence of moisture decreases resistivity (McCabe and Tholey, 1945; Keskinsezer, 2019) and hence the TOC vs. ΔlogR relationship presents a greater slope than for dry coal. This slope approaches that observed for TOC values obtained by Rock-Eval measurements, completed by TOC values calculated using the method by Schmoker (1979, 1981). This suggests that the ΔlogR values calculated from our well log data is strongly underestimated because it is influenced by the presence of formation water in coal beds. Indeed, in Fols 1A and Dbl S1 wells, resistivity values for coal beds are only 300 to 400 Ohm.m while a dense fracture network is observed (Privalov et al., 2022).

In Figure 14, the light gray shaded area represents TOC values calculated for dry (dark shaded area) and wet coal (blue shaded area) using equation (6) with a LOM of 10.6. In all cases, TOC is strongly underestimated for TOC>10% (as observed for Fig. 6, track 1, 14, and 15). This suggests that the calibration equation proposed by Passey et al. (1990) for marine shale to determine TOC from resistivity data may not be valid for coal layers. As suggested earlier, our calibration equations (Figs. 11 and 12) may be used for other wells to overcome this problem. However, a more thorough approach would be to measure laboratory resistivity and sonic slowness of dry and water-saturated samples for major coaly lithologies and establish the relationship to Rock-Eval TOC to propose a new ΔlogR vs. TOC equation.

The observation that moisture decreases resistivity has been demonstrated by McCabe and Tholey (1945) and Keskinsezer (2019). In Table 4, resistivity data for dry coal samples were compiled from references such as McCabe and Tholey (1945) and Telford et al. (1990), covering various coal ranks. Additional data were sourced from laboratory measurements (McCabe and Tholey, 1945), where samples were saturated with water for 24 h. These measurements reveal that resistivity decreases significantly upon water saturation, mirroring the conditions in water-saturated coal seams. In this study, the analysis was extended by calculating the ΔlogR separation under both dry and wet conditions. The results show that the separation decreases when samples are wet, comparable to what occurs in situ within water-saturated coal seams. Consequently, TOC values calculated under wet conditions using the original ΔlogR method were significantly underestimated compared to expected values reported by Mastalerz et al. (2011) for similar coal ranks. Figure 14 illustrates the relationship between expected TOC values and ΔlogR measurements for wet samples. The data points align more closely with results obtained from the corrected equations proposed in this study. This finding highlights the importance of conducting sonic and resistivity measurements under varying moisture conditions. To improve TOC estimates, laboratory testing is recommended to measure ΔlogR separation and TOC (via Rock-Eval) for coal samples of different ranks under wet conditions. Developing new, tailored equations that relate ΔlogR separation (between sonic and resistivity logs) to TOC would enhance accuracy, particularly for values exceeding 10 wt%, and provide a more reliable model derived from laboratory data.

Kenomore et al. (2017) explained that in shale reservoirs, when the formation’s porosity is less than 3–4%, resistivity increases significantly due to the absence of electrically conductive fluids. Consequently, the ΔlogR separation can be very high and should not be used under such conditions. In this case study, the matrix porosity appears to be less than 4%, which places the coal layers within this category where resistivity is expected to increase. However, in coalbed methane (CBM) reservoirs, the effective porosity is predominantly defined by the fracture porosity within the cleat system. This cleat porosity can significantly counteract the impact of low matrix porosity, as the fractures are often filled with water, which dramatically reduces resistivity. This phenomenon underscores a key aspect of the unconventional nature of these CBM reservoirs-Source Rock,

Tables 4 and 5 present the determination coefficient and the Root Mean Squared Error (RMSE) calculated for each of the proposed TOC calculation equations using well log data of Fols 1A and Dbl S1 wells. Figures 6 and 7 present in yellow the difference between TOC calculated using the different equations proposed and values obtained by using the equation based on Schmoker (1979, 1981). RMSE allows to rank of the proposed equations to calculate TOC as follows: i) modified ΔlogR (Eqs. (11) and (12)) ii) multivariate analysis (Eqs. (19) and (20)) iii) TOC ΔlogR equation calibrated with Rock-Eval and calculated TOC using the method by Schmoker (1979, 1981). Eqs. (13) and (18).

thumbnail Fig. 13

Percentage of pyrite in different lithologies of Fols 1A and Dbl S1 wells. Data obtained from XRD and petrographic analyses.
thumbnail Fig. 14

Measured Rock Eval and calculated Schmoker TOC (wt%) values plotted against Delta log R for the Fols 1A well.
Table 3

Table of resistivity data as a function of coal rank and TOC values for different coal types: Resistivity data as a function of coal rank and TOC values for different coal types. The resistivity values for bituminous coal (Max and Min) (Telford et al., 1990), while the resistivity values for sub-bituminous coal B and medium- and high-volatile bituminous coal (C, B and A) were derived from the reference data study of McCabe and Tholey. (1945). TOC values for each coal type were based on the Passey equation and Rock Eval TOC values as reported by Mastalerz et al. (2011).

Table 4

Equations used in the calculation of TOC for the Fols 1A well. R2: determination coefficient for each method. RMSE: Root Mean Squared Error for each method compared to TOC values obtained using the method by Schmoker (1979, 1981).

Table 5

Equations used in the calculation of TOC for the Dbl S1. R2: determination coefficient for each method. RMSE, Root Mean Squared Error for each method compared to TOC values obtained using the method by Schmoker (1979, 1981).

6 Conclusion

In the literature, TOC determination using well-logs is most commonly applied to quite homogenous marine shale deposits. Our objective was to adapt such techniques to the very heterogeneous fluviatile deposits in two reference wells of the Carboniferous Lorraine basin. We therefore focused on Schmoker’s method (1978, 1979), ΔlogR (Passey et al., 1990) and multivariate regression analysis in accordance to the well-log data available. Continuous TOC determination profiles were obtained despite the complexity of facies changes. The average TOC content in the shales of Fols 1A Well ranges from 3.5 wt % to 4.5 wt %, while for coal layers, it ranges from 40 wt % to 50 wt %. In Dbl S1 Well, the average TOC content in shales varies from 4.8 wt % to 6.2 wt %, while in coal layers, it ranges from 30 wt % to 45 wt %. Accordingly, quality assessment based on TOC (Kenomore et al., 2017), source rocks range from very good for shaly lithologies to excellent for coal layers.

The Schmoker method lead to best results but can only be used when density logs are available. In the case only resistivity and sonic data are accessible, a proposed modified ΔlogR equations was utilized as the original ΔlogR method tends to significantly underestimate values for coaly lithologies. Alternatively, if gamma ray, sonic, and resistivity data are present, the use of the derived equations from the multivariate regression analysis is recommended. This combination of available well-log data in this basin, along with additional Rock-Eval and petrophysical data from core samples, can serve as the basis for future studies employing machine learning applications that reduce error and increase the precision of TOC predictions in the Lorraine Basin and could be further tested on other coal-rich basins.

Acknowledgments

The authors would like to thank Prof. Khalid Essa for scientific discussions, Dr. Alizerrouki ahmed for helping in improve the manuscript, Schlumberger (SLB) for providing the Techlog© academic license. We are grateful to the editor and the reviewers for their time and suggestions for improving the manuscript. This research was funded through REssources GAzières de LORaine (REGALOR) − Research program cofounded Etat (Pacte Lorraine), Région (Région Grand Est), and Europe (Fond Européen de DEveloppement Régional − FEDER); 2018-2023.

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Cite this article as: Allouti S, Michels R, Mouketo MM, Malartre F, Izart A, Géraud Y, Privalov V, Nassif F, Pironon J, de Donato P. 2025. Total organic carbon evaluation using geophysical well-logs in Lorraine Coal Basin (NE France), BSGF - Earth Sciences Bulletin 196: 24. https://doi.org/10.1051/bsgf/2025022

All Tables

Table 1

Vitrinite reflectance (%Ro) and level of organic maturity determined after Hood et al. (1975) for samples from Fols 1A and DBLS 1 wells.

In the text
Table 2

Delta log R baseline values used for TOC calculations.

In the text
Table 3

Table of resistivity data as a function of coal rank and TOC values for different coal types: Resistivity data as a function of coal rank and TOC values for different coal types. The resistivity values for bituminous coal (Max and Min) (Telford et al., 1990), while the resistivity values for sub-bituminous coal B and medium- and high-volatile bituminous coal (C, B and A) were derived from the reference data study of McCabe and Tholey. (1945). TOC values for each coal type were based on the Passey equation and Rock Eval TOC values as reported by Mastalerz et al. (2011).

In the text
Table 4

Equations used in the calculation of TOC for the Fols 1A well. R2: determination coefficient for each method. RMSE: Root Mean Squared Error for each method compared to TOC values obtained using the method by Schmoker (1979, 1981).

In the text
Table 5

Equations used in the calculation of TOC for the Dbl S1. R2: determination coefficient for each method. RMSE, Root Mean Squared Error for each method compared to TOC values obtained using the method by Schmoker (1979, 1981).

In the text

All Figures

thumbnail Fig. 1

Simplified geological map of the Saar-Lorraine Basin showing the location of Folschviller (Fols 1A) and Diebling (Dbl S1) boreholes. The Carboniferous Basin is accessed by both boreholes at depths of 700 and 600 meters, respectively. Permian and Carboniferous outcrop in Germany. Modified after Pruvost (1934), Donsimoni (1981), Schäfer (2011) and Izart et al. (2016).
In the text
thumbnail Fig. 2

Sedimentary logs of Folschviller (Fols 1A) well presenting lithological succession, corresponding depositional environments, architectural element log and sedimentary sequences representative of the Lorraine Carboniferous basin. Data based on well-logs and core analysis.
In the text
thumbnail Fig. 3

Sedimentary logs of Diebling (Dbl S1) well presenting lithological succession, corresponding depositional environments, architectural element log and sedimentary sequences representative of the Lorraine Carboniferous basin. Data based on well-logs and core analysis.
In the text
thumbnail Fig. 4

Sonic/Resistivity Overlay is showing ΔlogR separation in the coal rich intervals for Fols 1A and Dbls1 wells. The relative scaling and resistivity curves correspond to a 50 μs/ft increment, representing one decade of resistivity.
In the text
thumbnail Fig. 5

Calibration of TOC by Schmoker (1979, 1981): (a) Linear relationship among Rock Eval TOC (wt%) and 1/density (cc/g) in Fols 1A and Dbl S1 wells as calibrated by the method published by Schmoker (1979, 1981); (b) Comparison of Rock Eval TOC with TOC calculated using the equation published by Schmoker for Fols 1A and proposed modified equation for calibration of Dbl S1 wells.
In the text
thumbnail Fig. 6

Assessment of Total Organic Carbon (TOC) in Fols 1A well using different calculation methods based on well log data.
In the text
thumbnail Fig. 7

Assessment of total organic carbon (TOC in wt%) in Dbl S1 well using different calculation methods based on well log data.
In the text
thumbnail Fig. 8

Calculated TOC ratio using Schmoker and Delta log R methods in Fols 1A and Dbl S1 wells: (a) as a function of Sonic Slowness and bulk density: in color code for all lithologies, (b) as a function of Sonic Slowness only for coaly lithologies.
In the text
thumbnail Fig. 9

Assessment of total organic carbon (TOC in wt%) in Fols 1A and Dbl S1 wells using different calculation methods based on well log data as box plot analysis.
In the text
thumbnail Fig. 10

Examining the Relationship between TOC (wt%) values and Delta log R using the diagram of Passey et al. (1990) for Fols1A and Dbl S1 wells.
In the text
thumbnail Fig. 11

Correlation equations between Rock-Eval measurements (red dots) and calculated using Schmoker (1979, 1981) (black dots) TOC (wt%) versus delta log R (Passey et al., 1990) for Fols 1A well using different calibration equations.
In the text
thumbnail Fig. 12

Correlation equations between Rock-Eval measurements (red dots) and calculated using Schmoker (1979, 1981) (black dots) TOC (wt%) versus Delta log R (Passey et al., 1990) for DBL S1 well using different calibration equations.
In the text
thumbnail Fig. 13

Percentage of pyrite in different lithologies of Fols 1A and Dbl S1 wells. Data obtained from XRD and petrographic analyses.
In the text
thumbnail Fig. 14

Measured Rock Eval and calculated Schmoker TOC (wt%) values plotted against Delta log R for the Fols 1A well.
In the text

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