A New Five-step Method for Advanced Evaluation of Shale Gas Formations and a Field Case Study of Marcellus Shale

Shales are fine-grained, laminated, fissile sedimentary rocks composed primarily of clay, quartz, and feldspar. Shale gas formations contain gas-prone kerogen, derived from woody terrestrial plants. Traditionally, shale formations have been considered as seal and/or source rocks of a petroleum system. However, organic-rich shales are recently considered as unconventional reservoir rocks and provide additional source of energy. The advent of horizontal drilling and hydraulic fracturing treatments has made the economical production of Marcellus shale gas formations viable [1–3].

The Marcellus shale was deposited over 2 million years in anoxic deep marine depositional settings during the Middle Devonian. The orogenic events caused tectonic subsidence in the basin which created accommodation space for the Marcellus shale to be deposited during the Middle Devonian [4]. From bottom to top, the lower Marcellus, Cherry Valley, and upper Marcellus members are encompassed by the Marcellus shale which is the oldest unit of the Hamilton Group [5]. The Marcellus shale consists of black, organic-rich, fissile, pyrite-bearing shale intercalated with calcareous shale or dark-gray argillaceous limestone [6]. The Marcellus shale has 6 wt% average total organic carbon (TOC) and 6% average porosity [7]. The Marcellus shale overlies the Onondaga limestone and underlies the Stafford limestone member of the Skateaneles Formation [5,6].

Conventional petrophysical models are developed to evaluate conventional formations, such as sandstones and carbonates, in which non-clay minerals dominate and interconnected (or effective) pores are occupied by hydrocarbons and/or water. Gamma ray logging is typically used to help identify lithology and estimate volume percentage of shale. Density-neutron and sonic-neutron cross plots are used to evaluate porosity. Water saturation is evaluated using a Pickett plot or directly through the Archie equation [8]. Although these methods are successfully applied to conventional formations, evaluation of unconventional formations (i.e., shale gas) requires improved models and workflows.

Table 1 shows the outcomes of previous petrophysical workflows, models, and case studies for shale formations over the last decade. Lithofacies modeling of the Marcellus shale has been performed based on petrophysical, geomechanical, and geochemical data using core analysis and well logging [9]. The organic matter pore network occupying the free gas and adsorbed gas within shale gas formations has been studied using focused ion beam (FIB)/scanning electron microscope (SEM) imaging technology [10]. A petrophysical model for shales that defines organic and inorganic pores has been proposed to solve for kerogen porosity [11]. Hydraulic fracturing in shale gas formations has been studied using various methods, including, but not limited to, numerical modeling [12], petrophysical analysis [13], and experimental techniques [14]. Nevertheless, petrophysical workflows and models to evaluate the shale formations based on wireline logs and core analysis are limited to a few studies [7,15–18].

Petrophysical evaluation of shale gas formations remain a challenge due to the organic matter, clay minerals, and complex pore networks at the nano-scale present in shale gas formations. To date, there is a lack of an integrated petrophysical evaluation of shale gas formations. This paper provides a new method and an improved model that accurately evaluate all components of shale gas formations, including non-clay minerals, clay minerals, organic matter, and effective and isolated pore space occupied by free and adsorbed gas. We then applied this method through a field case study Marcellus shale and provide insights on how to apply to the new method.

Figure 1 shows a well log data acquired from a well that penetrated the lower Marcellus member, upper Marcellus member, and Stafford limestone, from bottom to top, in a Marcellus shale field. The Cherry Valley member is absent in this study. The Marcellus shale interval is within the dry gas window with ∼97% methane (CH₄). The well log data in Fig. 1 and input parameters in Table 2 are to evaluate the petrophysical properties of the Marcellus shale.

Porosity logs used in this study are bulk density and sonic logs. Since the well was drilled with air as the drilling fluid, the intervals penetrated during drilling were free from filtrate. Compressional and shear slowness logs were used as proxies for sonic log data in the Marcellus shale interval as sonic logs cannot be acquired in an air drilled well. The induction logging device measures formation resistivity as air is non-conducive.

In this study, X-ray diffraction (XRD) bulk mineralogy of 14 Marcellus shale samples from two wells [19] were used for the Marcellus shale gas formation. The average bulk mineralogy (wt%) of the 14 Marcellus shale samples is illite (40.7%), quartz (32.2%), K-feldspar (6.9%), pyrite (6.2%), calcite (4.7%), plagioclase (3.8%), dolomite (2.7%), chlorite (2.3%), kaolinite (0.2%), and others (0.3%) [19]. The presence of pyrite increases the density of the Marcellus shale. The average compressional travel time and density of clay and non-clay minerals of the Marcellus shale in this study were calculated using the compressional wave travel time [20,21] and density [22,23] of each mineral present in the Marcellus shale and relative abundances of minerals in the Marcellus shale [19] (Table 2). Additionally, an average value of the compressional travel time of organic matter, 167.5 μs/ft, was used for the Marcellus shale [24]. Density of organic matter in the Marcellus shale was calculated using vitrinite reflectance [25].

Biot poroelastic coefficient was calculated using the average depth for the Marcellus shale in the studied well and the overburden stress gradient in the study area. [26] constructed a correlation of overburden stress and Biot poroelastic coefficient for different shale formations using uniaxial strain measurements. Applying the linear regression equation of Ref. [26], we calculated the Biot poroelastic coefficient as 0.40 for the Marcellus shale. Additionally, the minimum in situ stress of the Stafford limestone was calculated using an average Biot poroelastic coefficient for Mississippian Indiana limestone which is 0.69 as discussed by Hart and Wang [27]. Bulk density values (∼2.70 g/cm³) indicate high levels of calcium carbonate in the Stafford limestone [5] similar to Indiana limestone which consists of 98% calcium carbonate [27] (Table 2).

Overburden stress and reservoir pressure were calculated based on overburden stress and reservoir pressure gradients of the Marcellus shale. A 1.17 psi/ft value of average overburden stress gradient from 15 Marcellus shale wells [28] was used in this study. Moreover, an average reservoir pressure gradient of 0.68 psi/ft of organic lean and organic-rich intervals of the Marcellus shale from three wells [29] was used. Density and compressional travel time through CH₄ were calculated based on reservoir pressure and temperature [30]. The gas deviation and formation volume factors were calculated using temperature and pressure at reservoir conditions and standard conditions for the zone of interest. Adsorbed gas storage in the Marcellus shale was calculated using Langmuir pressure (500 psi) and volume (200 Scf/ton) values that were reported by Yu and Sepehrnoori [31] (Table 2).

Based on geological studies and the laboratory evaluation of the Marcellus shale in the study area, volume of clay and water saturation (S_w) are 0.4 and zero for the Marcellus shale, respectively. The studied interval does not consist of free water (Table 2).

Through our research and practical experiences in evaluating different geological formations, we developed a new method, including an improved workflow (Fig. 2) and a new unconventional petrophysical model (Fig. 3), to evaluate unconventional shale gas formations. Figure 2 shows an improved and integrated workflow to evaluate petrophysical properties of shale gas formations using conventional well logs. Figure 3 shows an improved unconventional petrophysical model that describes all partitions of shale gas formations.

The new method could be applied in five steps: (a) to understand the petrophysical model as discussed in step 1; (b) to evaluate maturity and TOC as discussed in step 2; (c) to evaluate porosity as discussed in step 3; (d) to evaluate geomechanical properties as discussed in step 4; and (e) to evaluate resources in place and application to stimulation as discussed in step 5.

Conventional petrophysical models have been used to evaluate the petrophysical properties of highly porous and permeable reservoirs, such as sandstones and limestones, that mainly contain non-clay minerals, water, and free hydrocarbons. Shale gas formations, formerly known as source rocks, have a complex pore network with the presence of organic matter, clay minerals, and adsorbed gas. In fact, improved petrophysical models have been necessary to evaluate the petrophysical properties of these formations [16]. Therefore, we propose an improved unconventional petrophysical model (modified from Ref. [16]) for shale gas formations to overcome challenges of inaccurate evaluation with existing petrophysical models which do not specifically evaluate organic matter, adsorbed gas, and clay minerals. Our petrophysical model accurately defines solid matrix and effective and total pore space of shale gas formations that are occupied by water, free gas, and adsorbed gas (Fig. 3).

From a petrophysical standpoint, shale gas formations are composed of solid matrix and pore space filled by fluids. Solid materials comprising the matrix include non-clay minerals, clay minerals, and organic matter. The porosity of organic matter is oil wet. The remainder of the pore space is water wet. Adsorbed gas and clay-bound water occupy the ineffective pores. Adsorbed gas is trapped on the pore walls of the organic matter. Effective porosity is composed of dead-end pores and interconnected pores, forming a network. Interconnected pores are occupied by mobile water and free gas. Dead-end pores are occupied by free gas in organic pores and capillary-bound water. The mobile water (or free water) remains mobile in the interconnected pore space. The water phase remains immobile at the water saturation of clay- and capillary-bound waters [7,11].

The volume of clay minerals comprises extremely fine-grained solid clay with its porosity occupied by clay-bound water. Conversely, the volume of non-clay minerals is the volumetric sum of minerals such as quartz, calcite, and plagioclase with the pore space occupied by mobile water and free gas. Similarly, the total of the solid organic matter and its pore space is occupied by adsorbed and free gas. Shale gas formations consist of inorganic and organic partitions. The organic partition consists of organic matter, adsorbed and free gas whereas the inorganic partition consists of clay and non-clay minerals and water [11,16].

The non-clay minerals of the matrix are mainly quartz, feldspar, carbonates, and iron oxides. The primary clay minerals are illite, kaolinite, smectite, chlorite, and glauconite. Organic matter of shales comprises kerogen, bitumen, pyrobitumen, and char [16]. Porosity within clay minerals is ineffective and is typically occupied by clay-bound water. Inorganic non-clay minerals also contain capillary-bound and mobile water. The adsorbed gas is trapped on the pore walls of solid organic matter. Free gas accumulates within the pore space of the organic matter and inorganic partitions of the matrix such as non-clay minerals [7].

The maturity analysis includes analyses of vitrinite reflectance, density of organic matter, and TOC (Fig. 2). In the absence of direct laboratory analysis of TOC, correlations could be applied. Vitrinite reflectance of shale gas formations could be calculated using an empirical equation developed from the laboratory evaluation of the level of organic metamorphism (LOM) [32]. Density of organic matter could be calculated based on vitrinite reflectance of core samples analyzed in the laboratory [25]. Three different TOCs (wt% and vol. frac.) could be calculated with sonic/resistivity and density resistivity overlay methods [33] and density-based modified Schmoker's [34] method. For the Marcellus shale case study, our TOC calculation methodology was verified using the methodology to calculate the TOC of the Stafford limestone. Once applied and validated through case studies, one could develop understanding of how to fine tune the three TOC evaluation techniques and which one is more accurate and applicable in practice.

The TOC could be calculated using Passey et al. [33] and modified Schmoker's [34] methods. The TOC and density of organic matter were then used in the porosity and gas in place calculations since the TOC correlates directly with quantification of porosity and bulk volume of gas [16].

For the zone of interest in the Marcellus shale, the resistivity and porosity curves were baselined in the upper part of the lower Marcellus member where there is no resistivity separation in the sonic/resistivity overlay method. These baseline values are 57.42 ohm m for the resistivity, 93.14 µs/ft for the compressional travel time, and 2.56 g/cm³ for the bulk density. The percentage of negative values in density–resistivity separation (ΔlogR) and TOC values of the zone of interest are 45%, 39%, and 6% for the sonic/resistivity and density/resistivity overlay methods, and the density-based method, respectively. The negative values indicate zero TOC in these intervals. Therefore, the negative values were corrected to be zero. The calculations of the other petrophysical properties were performed based on the TOC data that are free of negative values.

Effective porosity of shale gas formations could be interpreted using sonic and density logs. These tools give bulk density and compressional travel time of the penetrated geological formation. Therefore, for the Marcellus shale, the porosity was estimated indirectly using measured bulk density and compressional travel time data and those of minerals present in the Marcellus shale—namely, bulk mineralogy, volume of clay, and TOC (wt% and vol. frac.) from the density/resistivity and sonic/resistivity overlay methods, and the density-based method (Fig. 2). The effective porosity was estimated based on the petrophysical model that takes the clay minerals, non-clay minerals, organic matter, and fluid partitions of the shale gas formations into account using compressional travel times, bulk density, and TOC (vol%) values of the partitions (Fig. 3).

Initial gas in place is composed of adsorbed gas, free gas, and dissolved gas. The gas dissolved into liquid hydrocarbons and formation water is negligible in the dry gas region. Adsorbed gas is determined through adsorption isotherm analyses. The adsorbed gas volume can be dominant over that of free gas if the shale formation has pores residing mostly inside the organic matter. In fact, the initial gas in place of the shale would be underestimated if the gas adsorbed on the organic pores is not considered. The gas in place of shale gas formations was calculated depending on adsorbed and free gas, trapped in the organic solid and inorganic pores, respectively, as in Eq. (21). Once the porosity, water saturation, thickness, cross-sectional area, and volume factor of the formation are known, free gas can be calculated using Eq. (23). The adsorbed gas storage in the shale was quantified by the Langmuir isotherm [40]—derived from crushed rock samples as in Eq. (24). Furthermore, adsorbed gas can be calculated using the cross-sectional area of the reservoir, thickness, bulk density, and adsorbed gas storage using Eq. (25). The technically recoverable portion of the initial gas in place was calculated based on a recovery factor as in Eq. (22) [7,10,41]. Stimulation candidates were determined based on the maturity analyses, porosity evaluation, and geomechanical properties of shale gas formations (Fig. 2).

A field case study of the Marcellus shale was conducted following our five-step methodology, beginning with the petrophysical model. The results of the subsequent steps are summarized in four sections: (a) maturity analysis, (b) porosity evaluation, (c) geomechanical properties, and (d) initial gas in place and technically recoverable resources. The average calculated TOC (wt%), porosity, geomechanical properties, as well as the gas in place values for the upper Marcellus member, lower Marcellus member, and Marcellus shale using the resistivity/density and resistivity/sonic overlay methods, and the density-based method are shown in Tables 3–5. The composite well log for this Marcellus shale well showing the Stafford limestone, the upper Marcellus member, and the lower Marcellus member includes the raw log, computed TOC, porosity, geomechanical properties, and technically recoverable resources logs (Fig. 4). In Fig. 4, shaded areas outlined with rectangles represent the stimulation candidates (Int₁, Int₂, and Int₃) for the Marcellus shale based on the TOC, porosity, geomechanical properties, and technically recoverable resources results.

The vitrinite reflectance was calculated as 1% for an LOM of 10.5 for the Marcellus shale as suggested by Passey et al. [33]. The average TOC (wt%) for the Marcellus shale was calculated as 0.3% and 0.6% by sonic/resistivity and density/resistivity overlays in Eq. (5), respectively. The density-based method, on the other hand, shows a 2.8% average TOC for the Marcellus shale using Eq. (6). Additionally, the TOC of the Stafford limestone is 0%, 0.04%, and 0% for the sonic/resistivity and density/resistivity overlay methods, and the density-based method, respectively. This is confirmed with the scarcity of ΔlogR separations in the Stafford limestone (Fig. 1). Therefore, this shows that our TOC calculation methods are tested and verified.

The average TOC (vol%) that was calculated based on the organic matter density using Eq. (7) is 0.6 using the sonic/resistivity overlay method log, 1% using the density/resistivity overlay method, and 5.4% using the density-based method. The density of the organic matter used in these calculations was derived from the kerogen density and vitrinite reflectance relationship in Eq. (2) which was established based on the core analysis of the Marcellus shale [25]. Kerogen was taken as a reference to calculate $ρTOC$ in the Marcellus shale since both TOC and kerogen relate to the organic matter of the Marcellus shale. Using the calculated R_o of 1%, we estimated a $ρTOC$ of 1.32 g/cm³ for the zone of interest.

The resistivity/density and resistivity/sonic overlay methods show very low TOC (wt%) values that are lower than 1% although the Marcellus shale exhibits intervals with high resistivity separations. A 10.5 calibration limit of LOM and a correction multiplier were proposed to address potential underestimation of the TOC in overmature shale gas formations [16,17]. Although we took a value of 10.5 for LOM, very low TOC values were calculated using the resistivity/density and resistivity/sonic overlay methods. Despite its intricacy, the TOC was underestimated when the resistivity/density and resistivity/sonic overlay methods are applied in this study. However, the density-based method for TOC estimation demonstrated a simpler yet effective approach, resulting in an average TOC value of 2.8% for the Marcellus shale. This is consistent with high resistivity, low bulk density, and high acoustic travel time responses and hence high resistivity separations of organic-rich intervals in the studied Marcellus shale interval. A notable advantage of the density-based method lies in its derivation from well log data specifically obtained from Devonian shales, including the Marcellus shale. In fact, the density-based method is a more reliable approach for estimating TOC in the Marcellus shale compared to the resistivity/density and the resistivity/sonic overlay methods.

The average TOC (wt%) values are higher in the lower Marcellus member (3.0%) than the upper Marcellus member (2.4%) based on the density-based method (Table 3 and Fig. 4). The sonic/resistivity, density/resistivity, and density-based methods suggest that TOC (wt%) values approach 2.2%, 3.8%, and 7.1% at the bottom of the lower Marcellus member. The TOC results in the bottom of the lower Marcellus member conform to previous work suggesting TOC values that range from 2% to 10% [42] and that are 6% on average [7] in the Marcellus shale.

In summary, the density-based method is a more reliable approach to interpret TOC in the Marcellus shale compared to the resistivity/density and the resistivity/sonic overlay methods.

The two porosity models (Eqs. (13) and (15)) were applied and our evaluations are summarized in Table 3. A positive correlation exists between the TOC and porosity values of the upper and lower Marcellus members when the three TOC calculation techniques are applied (Table 3). Organic matter typically exhibits higher porosity than the shale matrix. Higher amounts of TOC in shales can lead to an increase in total porosity due to the low-density (and resulting low-velocity nature) of the organic matter. The majority of organic pores are effective. In fact, an increase in organic matter contributes to the effective porosity. Specifically, for the density-based method, the lower Marcellus shale exhibits an average TOC of ∼3.0% and an average porosity of 8.8%, while the upper Marcellus shale shows an average TOC of 2.4% and an average porosity of 7.8%. This suggests that, in the Marcellus shale, the effective porosity contributes more significantly to the pore network than isolated pores.

The average sonic porosity of 7.4% is lower than the average density porosities of 8.5% and 11.0% from the density-based method and the resistivity/density overlay method, respectively. First, the difference between sonic and density derived porosities can be attributed to the fact that porosity is indirectly estimated from sonic travel time and bulk density measured through the formation using sonic and density logs. Second, sonic logging cannot fully detect all the porosity in the Marcellus shale due to the presence of extensive fractures which are discontinuities. Third, relatively low compressional slowness (avg. 91 μs/ft) was measured by sonic log for organic matter and gas bearing Marcellus shale. This measurement is close to the lower boundary of a range (60–200 μs/ft) proposed for compressional slowness of shales in Ref. [22]. In fact, relatively low compressional slowness yields relatively low sonic derived porosity as suggested by Eq. (15). Complex relations of porosity with travel time and geomechanical properties of the rock can play role on the difference unlike relatively simple relation between porosity, bulk density, and matrix density.

The density derived porosity (8.5%) in this study is higher than the 6% average porosity of Ref. [7] and 7% average porosity of Ref. [43]. Depending on actual or assumed bulk mineralogy of the Marcellus shale in the studied wells, different bulk density and matrix density values were used resulting in different porosity values in each study.

In summary, porosity of the Marcellus shale (8.5%) that was obtained using density-based model is more reliable than that from resistivity/density and resistivity/sonic overlay.

Geomechanical properties of the Marcellus shale were evaluated using the models presented in step 4 of our methodology. Tectonic stress is zero in the region. Average Poisson's ratio, shear modulus, Young's modulus, bulk modulus, and minimum in situ stress of the Marcellus shale are 0.21, 1.5 million psi, 3.7 million psi, 2.2 million psi, and 2773 psi, respectively. Table 4 summarizes our results for upper and lower Marcellus shale and Stafford limestone.

Our study shows that the Young's modulus and minimum in situ stress of the upper Marcellus member are 3.6 million psi and 2854 psi, respectively, while the Young's modulus and minimum in situ stress of the Stafford limestone are 4.6 million psi and 3747 psi, respectively. This indicates that there are distinct contrasts in minimum in situ stress and geomechanical properties, especially the Young's modulus along the upper Marcellus-Stafford limestone boundary and the lower portion of the upper Marcellus member (Fig. 4 and Table 4). This implies that the boundaries with higher in situ stresses will act as a barrier to prevent growth of fractures. Therefore, fracture propagation would be hindered along the upper Marcellus-Stafford limestone boundary and the lower portion of the upper Marcellus member with the larger minimum in situ stress and modulus contrasts [39].

The accuracy of measurements, such as compressional and shear slowness, and bulk density and assumptions such as overburden stress gradient and Biot poroelastic coefficient and pore pressure can introduce uncertainty in the calculations of geomechanical properties and minimum in situ stress. Mineral composition, porosity, and fluid properties of the Marcellus shale affect the compressional and shear slowness measurements.

In summary, geomechanical properties of the Marcellus shale can be evaluated using travel time of compressional and shear waves. The Marcellus shale was compared with overlying Stafford limestone in terms of geomechanical properties to select stimulation candidates.

Table 5 shows the gas in place calculated using the density/resistivity overlay, sonic/resistivity overlay, and the density-based methods for the upper Marcellus member, lower Marcellus member, and Marcellus shale, respectively. Average adsorbed gas storage via Langmuir isotherms for density and sonic log is 176.1 Scf/ton for the zone of interest using Eq. (24). Gas in place from the density-based method is more reliable since the resistivity/density and resistivity/sonic overlay methods yield underestimated TOC values. Marcellus shale contains 48 Bcf of adsorbed gas and 74 Bcf of free gas in a drilling unit of one square mile. Free gas in the Marcellus shale ranges from 57% to 66% (approximately 2/3). This implies that Marcellus shale is composed of interconnected and organic matter porosity that are occupied by free gas.

Technically recoverable resources for the Marcellus shale were estimated using a recovery factor of 10%. Sonic/resistivity overlay, density/resistivity overlay, and density-based methods result in 11.29 Bcf, 14.38 Bcf, and 12.20 Bcf of technically recoverable resources for 640 acres area, respectively. The sonic/resistivity overlay method provides a lower initial gas in place than the density/resistivity overlay method since sonic derived porosity is less than the density derived porosities. Difference in gas in place results can be attributed to the fact that we indirectly estimated the petrophysical properties using sonic, bulk density, and resistivity data. Moreover, our assumptions and input parameters can influence variations in porosity and hence gas in place results. As previously discussed, sonic logging cannot fully detect the extensive fracture network of the Marcellus shale. Additionally, relatively low compressional slowness measured by sonic logs, which is 91 μs/ft on average for organic matter and gas bearing Marcellus shale, can result in the difference between sonic and density derived porosities and gas in place results.

The Marcellus shale is heterogenous in terms of lithology, TOC, porosity, and geomechanical properties. Therefore, an efficient and effective fracturing treatment is required to increase recovery factor. Two stimulation candidate zones (Int₁ and Int₂) were identified which have relatively higher separations in porosity and resistivity log overlays, average TOC (3.2%), average porosity (8.8%), and potential technically recoverable resources (2.47 Bcf) in the upper and middle parts of the upper Marcellus member (Fig. 4). Moreover, the larger contrasts in minimum in situ stress and Young's modulus contrasts along the upper Marcellus-Stafford limestone boundary and lower part of the upper Marcellus member imply that the upper Marcellus member is an ideal candidate for stimulation treatments (Table 4). Additionally, a third stimulation candidate (Int₃) with relatively high separations in porosity and resistivity log overlays, TOC (2.0–7.1%), average porosity (9.0%), and potential technically recoverable resources (3.50 Bcf) was proposed in the lower part of the lower Marcellus member. The lower contact of the lower Marcellus member is not seen in the zone of interest (Fig. 4). However, a potential boundary between the lower Marcellus member and Onondaga limestone, as discussed by Lash and Engelder [5] with contrasts in minimum in situ stress and elastic modulus, can act as a barrier against fracture propagation.

In summary, Marcellus shale has a gas in place of 122 Bcf per square miles. The lower Marcellus member has two times resources in place than that of the upper Marcellus member. Free gas is approximately two times of the adsorbed gas. Resources estimate using the density-based method is the most accurate in the study area.

An in depth and comprehensive formation evaluation of shale gas formations was carried out to help optimize stimulation treatments and to increase economic recovery. Conclusions include:

• On the basis of our research and practical experiences in evaluating different geological formations, we developed a new formation evaluation method, including an improved workflow (Fig. 2) and a new unconventional petrophysical model (Fig. 3), to evaluate unconventional shale gas formations in five steps. We shared our experiences and lessons learned in evaluation of multi-scale multi-physics shale gas formations through a field case study.

• Out of the three methods available for TOC evaluation, density-based method is a preferred method in the evaluation of Marcellus shale compared to the resistivity/density and resistivity/sonic overlay methods. TOC of the upper Marcellus member (2.4%) is lower than that of the lower Marcellus member (3.0%). Additionally, the highest TOC (7.1%) was observed at the base of the lower Marcellus member. Average TOC is 2.8 wt% for the Marcellus in our study area.

• The modified density porosity model is more reliable than that from resistivity/density and resistivity/sonic overlay. Average porosity is 8.5% for the Marcellus in our study area. The lower Marcellus shale shows an average TOC of 3.0% and an average porosity of 8.8%, whereas the upper Marcellus shale has an average TOC of 2.4% and an average porosity of 7.8% based on our density-based method.

• Young's modulus and minimum in situ stress of the upper Marcellus member are 3.6 million psi and 2854 psi, respectively, while the Young's modulus and minimum in situ stress of the Stafford limestone are 4.6 million psi and 3747 psi, respectively. The large contrasts in minimum in situ stress and Young's modulus at the upper Marcellus-Stafford limestone boundary and lower part of the upper Marcellus member could serve as barriers for fracture height growth.

• The Marcellus shale has a gas in place of 122 Bcf per square miles. The lower Marcellus member has two times resources in place than that of the upper Marcellus member. Free gas is approximately two times of the adsorbed gas.

• In the Marcellus shale case study, three stimulation intervals were suggested by applying the methodology.

The new method and acquired knowledge help understand and evaluate shale gas reservoirs in the Marcellus shale in particular and in general globally, which can be applied to optimize stimulation treatments and increase economic recovery. Areas for further research include: (1) obtaining additional XRD data for the case study, (2) evaluating natural fractures through borehole image logs, and (3) incorporating core data to calibrate the TOC and porosity results.

The authors gratefully acknowledge the financial support of Turkish Petroleum Corporation, National Petroleum Exploration and Production Company of Turkey. The assistance of Paul Dudenas, manager of East Resources, in obtaining well log is appreciated.

• Turkish Petroleum Corporation.

• National Petroleum Exploration and Production Company of Turkey.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

h =

thickness, ft

p =

reservoir pressure, psi

v =

Poisson's ratio

A =

cross-sectional area, ft²

E =

Young's modulus, psi

G =

shear modulus, psi

K =

bulk modulus, psi

R =

true formation resistivity, ohm m

B_g =

formation volume factor, ft³/Scf

G_a =

adsorbed gas in place, Bcf

G_c =

adsorbed gas storage, Scf/ton

G_f =

free gas in place, Bcf

G_r =

technically recoverable resources, Bcf

G_t =

initial gas in place, Bcf

P_l =

Langmuir pressure, psi

R_B =

resistivity on Δt_B when curves are baselined in clay rich rocks, ohm m

R_o =

vitrinite reflectance, %

S_w =

water saturation

V_Cl =

volume of clay minerals

V_l =

Langmuir volume, Scf/ton

V_P,Cl =

volume of pore space in clay minerals

$VP,TOCA$ =

volume of pore space in the organic matter whose pore space is occupied by adsorbed gas

V_TOC =

volume of organic matter

$VTOCA$ =

volume of organic matter that is occupied by adsorbed gas

LOM =

level of organic metamorphism

RF =

recovery factor

TOC =

total organic carbon, wt%

TOC_S,D =

total organic carbon from resistivity and sonic and density porosity log overlays, wt%

V_A, V_B, _…,V_J =

volumes of fractions of solids and pore space in a shale gas reservoir

α =

Biot poroelastic coefficient

ΔlogR =

curve separation measured in logarithmic resistivity cycles

ΔlogR_D =

curve separation between resistivity and density logs measured in logarithmic resistivity cycles

ΔlogR_S =

curve separation between resistivity and sonic logs measured in logarithmic resistivity cycles

ΔlogR_S,D =

curve separation between resistivity and porosity logs measured in logarithmic resistivity cycles

Δt =

sonic log reading, µs/ft

Δt_B =

compressional transit time in inorganic baseline interval, µs/ft

Δt_c =

compressional slowness, µs/ft

Δt_Cl =

sonic log reading in clay minerals, µs/ft

Δt_F =

sonic log reading in fluids, µs/ft

Δt_Ncl =

sonic log reading in non-clay minerals, µs/ft

Δt_s =

shear slowness, µs/ft

Δt_TOC =

sonic log reading in organic matter, µs/ft

ρ_b =

bulk density, g/cm³

ρ_in =

density of inorganic intervals, g/cm³

ρ_B =

density value of baseline, g/cm³

ρ_Cl =

density of clay minerals, g/cm³

ρ_TOC =

density of organic matter, g/cm³

ρ_Ncl =

density of non-clay minerals, g/cm³

ρ_F =

fluid density, g/cm³

σ_min =

minimum in situ stress, psi

σ_ob =

overburden stress, psi

σ_tect =

tectonic stress, psi

ϕ_Cl =

clay porosity

ϕ_Den =

density porosity

ϕ_Eff =

effective porosity

ϕ_Son =

sonic porosity

$ϕTOCA$ =

organic matter porosity that is occupied by adsorbed gas

ϕ_Tot =

total porosity