Article pubs.acs.org/EF
Ono−Kondo Model for Supercritical Shale Gas Storage: A Case Study of Silurian Longmaxi Shale in Southeast Chongqing, China He Bi,*,† Zhenxue Jiang,‡ Jianzhong Li,† Fengyang Xiong,§ Peng Li,† and Lei Chen‡ †
Research Institute of Petroleum Exploration & Development, PetroChina, Beijing, 100083, China Unconventional Gas Research Institute, China University of Petroleum (Beijing), Fuxue Road No. 18, Changping, Beijing, China § School of Earth Sciences, The Ohio State University, Columbus, Ohio 43210, United States ‡
ABSTRACT: Shale gas storage is a dominant factor to economically evaluate the shale play. A series of Lower Silurian Longmaxi marine shale samples in southeast Chongqing, China, were collected to investigate the reservoir characteristics, and a suit of methane adsorption isotherms were fitted using a supercritical Ono−Kondo model to better understand the adsorption capacity of Longmaxi shale. The saturated adsorption of a monolayer presents a greatly positive relationship with the total organic carbon (TOC) content. A negative relationship with clay was observed due to the predominant influence of organic matter on the methane adsorption. Methane adsorption also increases with increasing pressure and decreases with increasing temperature. On the basis of the relationships, one new estimation algorithm related to TOC content, pressure, and temperature was established to calculate the methane adsorption capacity on the basis of the Ono−Kondo model. Furthermore, with higher TOC content, the adsorption capacity of shales correspondingly increases and the maximum of the adsorption capacity tends to a deeper depth. Considering geological characteristics of Longmaxi shale, one new gas-in-place (GIP) model was proposed to apply, considering the controlling factors, TOC, porosity, gas saturation, pressure, and temperature. The relationships of GIP, adsorbed gas, and free gas with increasing depth shows that (1) free gas increases rapidly and equally; (2) adsorbed gas initially increases rapidly at less than 1000 m, and then decreases with depth increases; and (3) GIP rapidly increases at shallow depths, and then gently increases more than 1000 m.
1. INTRODUCTION
aromatization, leading to weakening the differences between structures of various kerogens as well as adsorbed gas capacities. Clay is also reported to contribute to the specific surface area for gas adsorption because of intercrystal layers and porous structures.9,11,14,15,24−27 Smectite and illite−smectite mixed layer clays with a larger surface area are considered most effective for gas adsorption.9,27 However, clay is water-sensitive. Water molecules are prone to occupy the surface area of clay minerals or block pore throats, inhibiting the contribution of clay to shale gas storage. Thus, the existence of water would dramatically decrease the gas adsorption capacities of clay minerals.13,18,28−30 Clearly, gas adsorption in organic-rich shale is a comprehensive process controlled by multifactors, and elucidating and quantifying the influence of individual factors is challenging, requiring reliable experimental data collected in well-defined conditions. This study proposes to investigate the dominant geological factors controlling gas adsorption capacity, to establish accessible estimation algorithms for gas adsorption and GIP synthetically influenced by multiple geological factors, and to discuss the trends of shale gas content. This study is the first to propose the Ono−Kondo model to estimate the shale gas adsorption capacity and GIP, considering not only the pressure and temperature but also the internal factors (e.g., TOC). This research is significant to better understand the changes of methane adsorption capacity and GIP over
As a prominent unconventional natural gas system, shale gas has recently been paid much attention by the researchers around the world.1−4 Storage of shale gas is dramatically different from conventional gas reservoirs. Gas-in-place (GIP) is one commonly used parameter to investigate the shale gas storage capacity. Natural gas within shales may occur as free gas, adsorbed gas, and dissolved gas.5 For the overmature shale, such as Longmaxi shale in southeast Chongqing, China, the generated liquid hydrocarbon has been entirely cracked to gas and the dissolved gas in the liquid hydrocarbon and organic matter could be negligible compared to absorbed gas and free gas. Different from conventional gas that mostly consists of free gas, adsorbed gas of shale gas accounts for 20−85% of the original GIP.5−7 Adsorbed gas storage capacity is synthetically controlled by geochemical characteristics, mineralogical composition, pore structure, existing water, and pressure and temperature regimes.8−10 Organic matter has been well documented that dominantly contributes to the methane adsorption capacity, which shows a positive correlation with adsorbed gas according to previous studies.12−19 High maturity promotes the positive influence of organic matter to gas adsorption capacity, due to the increasing organic nanopores and specific surface area providing more adsoption sites for methane molecule.15,17,20−23 Gas adsorption capacities of type III kerogens were investigated to be greater than those of type II and type I kerogens, as aromatic-rich organic matter has a stronger affinity for methane molecules.13,17 Increasing maturity of organic matter promotes © XXXX American Chemical Society
Received: December 22, 2016 Revised: January 22, 2017 Published: February 2, 2017 A
DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
ground and then used to determine the average bulk composition. Xray diffraction measurements of randomly oriented powder samples were conducted to determine matrix mineral compositions. 2.3. Methane Isothermal Adsorption Model. 2.3.1. Absolute Adsorption Based on Ono−Kondo Model. Most previous research calculating the adsorbed gas content was based on the Langmuir adsorption isotherm model. Langmuir theory assumes that (1) the methane is a monolayer adsorbate; (2) the surface of the solid adsorbent is homogeneous with constant adsorption heat; (3) the molecules of the adsorbates do not undergo horizontal reactions; and (4) the dynamic adsorption is equalized. In actual geologic conditions, adsorption of shale gas is multilayer adsorption with forces operating between the molecules, and thus the Langmuir assumptions do not apply well in terms of characterization of adsorption behavior. Several multilayer adsorption theories have been proposed, such as the Brunauer−Emmett−Teller (BET) theory, the Dubinin−Radushkevich (DR) theory, and the Dubinin−Astakhove (DA) theory. The theories were widely used to estimate the adsorption content of some gases (e.g., nitrogen) on microporous solids; however, the saturation vapor parameters, such as the saturation vapor pressure, and only adsorption in microporous solids used in the equations of these theories would not be suitable for methane adsorption behavior in actual geologic conditions. In addition, the methane occurring in the shale is considered as a behavior of dynamic equilibrium between adsorbed gas and free gas. The Ono−Kondo lattice theory33−38 is advantageous for estimating multilayer adsorption in a supercritical state and in slot-type nanopores and considers the interconversion between adsorbed gas and free gas. Therefore, the Ono−Kondo model is proposed to better estimate the methane content adsorbed onto nanoscale shale in this study. The Ono−Kondo theory has a simple but theoretical basis, gives correct limiting behavior, can be used under supercritical conditions, describes experimental data over an extended range of pressure and temperature, predicts adsorption behavior over an extended range of conditions, and calculates the data more accurately.37 The theory predicts behavior similar to the DR model but for a wider range of conditions and appears to correlate data more accurately.37 Ono−Kondo lattice theory and the model are the first used in the shale gas adsorption and GIP through this research. On the basis of the Ono−Kondo lattice theory, a molecule in the porous solid has two occurrence states, adsorbed state and free state. The nanoscale pores of the shale can be simplified as silt pores divided into N adsorbed layers for methane adsorption. The composition of the silt pore space can be regarded as adsorption layers and vacancies. The methane molecules occupying on the layers are considered as adsorbed gas, while the methane molecules occurring in the vacancies are considered as free gas. As long as the adsorbed gas moves to a vacancy, the movement can be considered as interconversion between the adsorbed gas and free gas. If this exchange occurs at equilibrium, the enthalpy change (ΔH) and entropy change (ΔS) can be expressed as
geological periods and the assessments of the exploration and development of shale gas.
2. SAMPLING AND METHODS 2.1. Samples and Preparation. The southeast Chongqing area is located in the southeastern portion of Sichuan Basin, China, which belongs to the Yangzi quasi-platform depression tectonic units of the Yangtze Platform (Figure 1). Southeast Chongqing mainly includes
Figure 1. Regional overview of southeast Chongqing, China, and the location of sample wells. the Qianjiang, Pengshui, Youyang, and Xiushan areas. The western portion is part of the eastern margin of the Sichuan Basin and develops gentle folds exposing Jurassic-Triassic strata. The eastern portion is characterized by fractures and intensively deformed folds with outcrops of Triassic-Silurian strata. The principle anticlines and faults are Caledonian structural layers of the Yanshan fold, mainly formed during the Yanshanian Period of the Mesozoic Era. The lower Silurian Longmaxi shale was deposited in a restricted marine basin environment, developing abundant organic matter. The lower Silurian strata experienced deep burial during the early Mesozoic, following intense uplifting from the late Mesozoic into the Cenozoic. The preservation conditions and accumulation of Longmaxi shale gas was greatly changed. At present, Longmaxi shale in the area is characterized by wide lateral distribution, great thickness, and shallow burial depth. Due to the intense uplift, erosion, and faulting, free gas might have been mostly lost, leading to undersaturation.19 The lack of bulk material from well drilling and logging during the initial stage of exploration has increased the difficulty of resource assessment of the shale. Therefore, research on the gas adsorption behavior and GIP is significant for exploration and exploitation of Longmaxi organic-rich shale. A total of 65 core samples of the Longmaxi shale were collected from an exploratory well (CQ-1) in Pengshui Block at an interval of 642−761 m. Each core sample was ground into powder of 80−100 mesh sizes (sieve pore diameter of 180−150 μm), yielding 100 g. These powdered subsamples were used for conducting measurements of total organic carbon (TOC), thermal maturity, and X-ray diffraction to determine the geological characteristics of the Longmaxi shale. Data of methane adsorption isotherms were collected from Tian et al.31 The methane adsorption measurements were performed at 35.4, 50.6, and 65.4 °C with the pressures up to 15.0 MPa for eight dry Longmaxi shale samples.31 These eight samples were collected from the same well as CQ-1 in this study. 2.2. TOC, Thermal Maturity, and X-ray Diffraction Analysis. TOCs of the samples were measured using a CS230HC carbon and sulfur analyzer. Prior to the measurement, samples were treated with hydrochloric acid to remove carbonates. Because the Longmaxi shale lacks vitrinite, instead, pyrobitumen reflectance was measured using a Zeiss microscope and an MPV−I microphotometer. X-ray diffraction analysis was conducted with a ZJ207 Bruker D8 advance X-ray diffractometer to identify mineral composition and provide information on unit cell dimensions.32 The analyzed material was finely
(1)
ΔH − T ·ΔS = 0 where T is the absolute temperature. The entropy change ΔS can be expressed as
ΔS = k·ln W1 − k·ln W2
(2)
where W1 is the thermodynamic probability that the methane molecule occupies on the certain side in the layer i and the infinitely distant site is vacant, W2 the thermodynamic probability that the methane molecule occupies in the infinitely distant site and the certain site in the layer i is vacant, and k is the Boltzmann’s constant equaling 1.38 × 10−23 J/K. If the total thermodynamic probability of the entire system is W0, the equations under the mean-field approximation are expressed as
B
W1/W0 = xi(1 − xf )
(3)
W2/W0 = (1 − xi)xf
(4) DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 2. Organic matter abundance, thermal maturity, and mineral constitutes of shale samples. Here, xi is the probability of adsorbed gas occupying on the certain side in the layer i and xf is the probability of free gas occurring in the vacancies.
xi = ρi /ρad , xf = ρf /ρad
ln{[x1(1 − xf )]/[(1 − x1)xf ]} + ε(x 2 + 4x1 − 6xf )/(k · T ) + εs /(k·T ) = 0
On the basis of the study of the surface excess adsorption, the total methane adsorption capacity nabs, which is the sum of the methane adsorption capacity of every layer, could be expressed as
(5)
where ρi is the molar density of the absorbed methane in layer i, ρf is the molar density of the free methane, and ρad is the molar density of the maximum methane adsorption. When eqs 3 and 4 are substituted into eq 2, the equation is changed as ΔS = k·ln{[xi(1 − xf )]/[(1 − xi)xf ]}
nabs = n0 ∑ (xi − xf )
nabs = n0
(6)
ρf ρad
(11)
( kε·T )⎤⎦ ε + ρad exp( k·T ) s
s
(12)
where n0 is the saturated adsorption capacity of the monolayer. 2.3.2. Excess Adsorption and Absolute Adsorption. The results of isothermal adsorption experiments has been documented as the excess methane adsortpion.9,17,18,28,31 Therefore, the measured isothermal adsorption results cannot be used directly. Generally, the excess adsorption results are required to correct into absolute methane adsorption to reflect the real adsorption of shale gas.9,10,18,28,31 Hence, the relationship between excess adsorption and absolute adsorption should be studied first. On the basis of the Gibbs adsorption model,40−44 the correlation between excess adsorption (nexcess) and absolute adsorption (nabs) can be expressed as eqs 13 and 14.
(7)
where ε is the energy of the adsorbate−adsorbate interactions. Then, in the case of thermodynamic equilibrium occurring between adsorbed gas and free gas, the eq 1 could be transformed as35,39
ln{[xi(1 − xf )]/[(1 − xi)xf ]} + ε(z1xi + 1 + z1xi − 1 + z 2xi − z 0xf ) /(k·T ) = 0
2ρf ⎡⎣1 − exp ρad − ρf
If the change in enthalpy is approximately calculated under the mean-field approximation with the neighboring absorbate sides occupied, the enthalpy change can be expressed as ΔH = − ε(z1xi + 1 + z1xi − 1 + z 2xi − z 0xf )
(10)
(8)
For a cubic configuration of the lattice, the coordination numbers z0 and z2 are 6 and 4, respectively, and by definition, z1 = (z0 − z2)/2. Then, the equation of methane could be transformed as
⎛ ρf ⎞ ⎟⎟ nexcess = nabs·⎜⎜1 − ρad ⎠ ⎝
(13)
nexcess = nabs − ρf ·Vads·CSTP
(14)
or
ln{[xi(1 − xf )]/[(1 − xi)xf ]} + ε(xi + 1 + xi − 1 + 4xi − 6xf ) /(k·T ) = 0
(9)
Here, the methane density ρf is the free methane phase density based on the pressure and temperature and can be calculated using the gas state equation.18,31,45 Values of ρf are available on the U.S. National Institute of Standards and Technology website. Vads is the volume of
Considering the condition of monolayer methane adsorption, the energy of the methane−pore interaction (εs) should be added. Equation 9 could be transformed as C
DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels adsorbed gas and CSTP is a unit conversion coefficient from quality to volume under the conditions of standard temperature and pressure. The absolute adsorption isotherm of methane can be described by the Ono−Kondo adsorption mode [eq 12]. When eq 12 is substituted into eq 13, the excess adsorption model is obtained, expressed as follows:
2ρf ⎡⎣1 − exp
nexcess = n0
ρf ρad ρad − ρf
( kε·T )⎤⎦ ⎛⎜ ρf ⎞⎟ ·⎜1 − ⎟ ε ρad ⎠ + ρad exp( k·T ) ⎝
indicating an overmature characteristic. Mineralogical compositions of the samples are also shown in Figure 2. The quartz contents range from 25.9% to 69.7%, averaging 38.7%. Other brittle minerals include feldspar and carbonate minerals (calcite and dolomite), which mainly present as cements in fractures. The clay contents are in the range of 9.6−46.2%, with an average of 31.7%, and dominated by illite, illite−smectite mixed layer, and chlorite. 3.2. Methane Adsorption Isotherms and Fitting. The excess adsorption isotherms of methane were collected from Tian et al.32 to determine the unknown parameters of the Ono−Kondo model. Then, the Ono−Kondo absolute adsorption isotherms were obtained.1 Substituting the known parameters, nexcess, ρf, and T into eq 15, the unknown parameters, no, εs/k, and ρad were fitted and could be obtained using regression analysis (Table 1). The
s
s
(15)
The unknown parameters in eq 15 are no, εs/k, and ρad. These parameters can be determined by fitting eq 15 to the measured excess adsorption isotherms using a least-squares minimization procedure.18,31 Once these unknown parameters are determined, the absolute methane adsorption based on eq 12 can be obtained to better understand the actual adsorption of shale gas. 2.4. Geological GIP Model. GIP is the sum of adsorbed and free gas contents as the dissolved gas is negligible compared to adsorbed and free gas. The content of adsorbed gas could be estimated using the absolute methane adsorption estimation algorithm, and free gas could be estimated based on the data of porosity and gas saturation under the given pressures and temperatures. The pore volume occupied by free gas should be the total pore volume removing the volume occupied by adsorbed gas, if the adsorbed gas content is calculated by the absolute adsorption model31,46 [eq 16]. Otherwise, the pore volume occupied by adsorbed gas would be accounted twice for both free gas and adsorbed gas, leading to the overestimation of GIP.31 Thus, the expression of GIP could be written as eq 17.
nf =
φ·Sg ρshale
·
P·Tsc − ρf ·Vads·CSTP Psc·Z·T
GIP = nf + nabs =
φ·Sg ρshale
·
P·Tsc + nexcess Psc·Z·T
Table 1. Fitted Parameters of the Excess Adsorption Modela
a
(16)
sample
no (m3/t)
εs/k
ρad (mol/L)
#4-04 #4-08 #4-33 #4-47 #4-54 #4-61 #4-64 #4-65
0.94 1.25 1.08 1.35 1.42 1.62 1.67 1.65
−1273.18 −1303.07 −1389.74 −1486.46 −2242.74 −1714.08 −1386.83 −1647.56
47.46 52.11 65.69 75.70 567.38 113.36 56.13 99.99
1 mmol/g rock = 22.4 m3/t rock.
fitted ρad values are very large, exceeding methane’s liquid density at its boiling point (424 mg/cm3 = 26.5 mol/L), which was also obtained in previous studies.18,31 Therefore, the saturated adsorption phase density under the critical condition was used instead of the fitted ρad values. The van der Waals equation51 [eq 18] was used to calculate saturated methane adsorption phase density under the critical condition (Pc = 4.58 MPa and Tc = 190.56 K).
(17)
where nf is the content of free gas, φ is the porosity, Sg is the gas saturation, ρshale is the density of a shale sample, P is the actual pressure of the layer, T is the actual temperature of the layer, Psc is the pressure at the standard condition (0.1 MPa), Tsc is the temperature at the standard condition (273 K), and Z is the compressibility factor.
3. RESULTS 3.1. Organic and Mineral Constitutes. The TOC contents of the Longmaxi shale are in the range of 0.47−8.49 wt % (Figure 2), with an average value of 2.28 wt %. The shale generally presents with higher TOC contents on the bottom and lower TOC contents at the top. Thin section analysis reveals that the organic fragment mainly consists of maceral assemblages, presenting as pelletoid, diffused, and flocculated organic matter, and pyrobitumen formed by the retained oil cracking15,47−50 (Figure 3). The calculated equivalent vitrinite reflectances range from 2.67% to 2.81% Ro (Figure 2),
ρad =
8 × 106·Pc = 23.13 mol /L R ·Tc
(18)
When we substituted the known parameters, nexcess, ρf, ρad, and T, into eq 15, and fitted the unknown parameters, no and εs/k, could be derived again using regression analysis (Table 2). When the fitted parameters are substituted into eq 12, the absolute adsorption isotherms of methane could be obtained to help understand shale gas adsorption behavior (Figure 4). Figure 4 indicates that the absolute adsorption capacities are generally higher than the excess adsorption capacities as the Table 2. Fitted Parameters of the Excess Adsorption Modela
Figure 3. Microphotographs of the Longmaxi shale, presenting pyrobitumen and macerals. The pyrobitumen is yellow-gray, occurring as banded. The brightest areas are the pyrite framboids.
a
D
sample
no (m3/t)
εs/k
#4-04 #4-08 #4-33 #4-47 #4-54 #4-61 #4-64 #4-65
1.39 1.90 1.74 2.24 2.42 2.66 2.61 2.74
−844.672 −834.659 −817.682 −835.656 −913.868 −914.376 −861.46 −891.712
1 mmol/g rock = 22.4 m3/t rock. DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
Figure 4. Comparisons between absolute adsorption capacities and excess adsorption capacities of the cited samples.
significant factor controlling the methane adsorption on the shale surface. A similar phenomenon has been reported by previous studies.1,7,15,17,18,31,52 The organic fraction developed abundant nanometer-scale pores, which contribute a large amount of surface area. The surface area in the shale samples has been documented to be the most important place for the methane adsorption.7,21,53 Because of its significant contribution to the surface area, organic matter becomes critical to methane adsorption. In addition, the type and maturity of the organic matter also influence the methane adsorption. Zhang et al.17 and Hao et al.19 reveal that the methane adsorption capacities of type III kerogens were greater than those of type II and type I kerogens, indicating that aromatic-rich organic matter would have a stronger affinity for methane. Increasing maturity of organic matter promotes aromatization, leading to weakening of the difference in methane adsorption between different kerogen types. Nanopores in organic matter were much more abundant with high maturity, forming due to the
multilayers of methane molecules occupying the space near the pore wall are thought to be absorbed entirely due to the adsorption ability of the specific surface area of shales. If the total shale gas content is constant and measured adsorption isotherms are directly used to estimate the methane adsorption, adsorbed gas content would be underestimated and free gas content would be overestimated. Therefore, correcting the measure of adsorption isotherms is significant for shale gas assessment.
4. DISCUSSION 4.1. Effect of TOC and Mineral Composition on Methane Adsorption. The correlation of absolute adsorption capacity of methane with TOC and mineral constitutes is shown in Figure 5. As revealed in Figure 5A, saturated adsorption of the monolayer, n0, has a positive relationship with TOC, yielding a correlation coefficient (R) as high as 0.94. This implies that the abundance of organic matter may be a E
DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
Figure 5. Correlations of saturated adsorption of monolayer with TOC (A) and clay content (B), and correlation (C) between normalized saturated adsorption and clay.
Figure 6. Correlations of absolute methane adsorption capacity with temperature.
formation and discharge of petroleum during the thermal conversion of organic matter.63 Mineral constitutes, particularly clay minerals, have also been reported as a dominant factor controlling the methane adsorption.9,13,27 Previous studies found that, because of intercrystal layers and porous structures, clay could provide abundant surface area or adsorption sites for methane adsorption.27,54,55 However, Figure 5B shows an obviously negative correlation between clay and n0. This phenomenon appears to suggest that development of clay inhibits the methane adsorption on the Longmaxi shale surface. However, if the saturated adsorptions are normalized to per-gram TOC, an obviously positive correlation with clay can be obtained (Figure 5C). This phenomenon reveals the more significant influence of organic matter on the adsorption of methane.1,53 4.2. Effect of Pressure and Temperature on Methane Adsorption. As illustrated in Figure 4, methane adsorption capacity increases with increasing pressure. Initially, methane adsorption increases rapidly at pressures less than 4 MPa, and then rises gently with increasing pressure until reaching a maximum value at approximately 9.5−10.5 MPa. Then, the adsorption gradually reaches equilibrium. Until the pressure
Figure 7. Absolute methane adsorption of the Longmaxi shale as a function of depth and TOC content determined by eq 21 with the geothermal gradient of 22 °C/km and the pressure gradient of 9.8 MPa/km.
becomes greatly high, methane adsorption capacity appears to decrease and methane desorption emerges.1 Due to the exothermic process of adsorption, adsorption capacity reduces rapidly with increasing temperature, showing a negative power relation.2 Figure 6 shows the distribution and trend of the maximum absolute adsorption capacities at different temperatures, and an obvious negative correlation could be observed between absolute methane adsorption capacity and temperature with a correlation coefficient as high as 0.997−0.999. The trend is similar to the Lower Ganchaigou shale samples reported by Li et al.2 However, methane adsorption capacity of the Longmaxi shale is F
DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
nabs = (A 0 + A1·TOC)·
2ρf ⎡⎣1 − exp ρf ρad ρad − ρf
( kε·T )⎤⎦ ε + ρad exp( k·T ) s
s
(20)
where nabs is the absolute methane adsorption capacity, ρf is the molar density of the free methane determined by pressure and temperature, ρad is the molar density of maximum methane adsorption, εs is the energy of the methane−micropore interaction, T is the absolute temperature, TOC is the abundance of organic matter, and A0 and A1 are constants. Substituting corrected absolute methane adsorption, TOC, ρf, ρad, and T into eq 20, we fitted the unknown parameters, no, εs/k, A0, and A1. The absolute methane adsorption estimation algorithm was developed as follows nabs = (0.879 + 0.359 × TOC)· 2ρ [1 − exp( −873.96/T )]
f ρf × 23.13 23.13 − ρf
(21)
where nabs is the absolute methane adsorption capacity, ρf is the molar density of free methane determined by pressure and temperature, T is the absolute temperature, and TOC is the abundance of organic matter. 4.4. Estimation of Geological GIP. Geological parameters, such as geothermal gradient and pressure gradient, were determined based on previously reported studies.56−60 The current geothermal gradient in southeast Chongqing is approximately 22 °C/km with a nominal surface temperature of 15 °C. The shale reservoir is considered as a hydrostatic system under a pressure gradient of 9.8 MPa/km.61 We assumed a shale porosity of 6% and a gas saturation of 70%, referring to the previously reported studies.61 The profiles of absolute methane adsorption capacities versus depth were established by eq 21. Due to the comprehensive influences of increasing pressure and temperature, the relationship of methane adsorption capacity with depth is not monotonic. As shown in Figure 7, methane adsorption increases rapidly with depth initially because of the dominant effect of pressure at shallow depths, reaches its maximum around 1000 m, and then gradually declines with the effect of temperature becoming dominant, instead of pressure. Figure 7 also shows that, with higher TOC content, shales are prone to present larger gas adsorption capacities. In addition, the maximum of adsorption capacity also turns to a deeper depth with TOC increasing. GIP of Longmaxi shale summing of adsorbed and free gas contents can be expressed as
Figure 8. Geological GIP of the Longmaxi shale with the increasing depth determined by eq 22. Estimation of GIP is exampled by sample #4-64 with the TOC content of 4.07%, a total porosity of 6%, and a gas saturation of 70% with the geothermal gradient of 22 °C/km and the pressure gradient of 9.8 MPa/km.
dramatically higher than that of the Lower Ganchaigou shale at the same temperature. This phenomenon is because the Longmaxi shale has a larger TOC content than Lower Ganchaigou shale, supporting that TOC content could be one dominant controlling factor of the methane adsorption capacity of shale.1,2,15,63 4.3. Estimation of Absolute Methane Adsorption. The adsorption process in shale is comprehensively controlled by multiple geological factors, consisting of inherent characteristics, such as geochemistry properties and mineralogical composition, and exogenic characteristics, such as pressure and temperature.2 As discussed above, TOC content is the primary inherent parameter influencing methane adsorption. Combined with pressure and temperature, the dominant factors controlling methane adsorption at a given geological condition were optimized. The impact of TOC, pressure, and temperature on methane adsorption can be quantitatively expressed by fitting the Ono−Kondo parameters at a given geological condition. As Figure 5A illustrated, a regression formula is used to relate the monolayer saturated methane adsorption to TOC content. We express the formula using linear regression
n0 = A 0 + A1·TOC
+ 23.13 × exp( −873.96/T )
GIP =
(19)
φ·Sg
P·Tsc · + (0.879 + 0.359 × TOC)· ρshale Psc·Z·T 2ρ [1 − exp( −873.96/T )]
f ρf × 23.13
where n0 is the saturated methane adsorption capacity of the monolayer, TOC is the abundance of organic matter, and A0 and A1 are constants. Considering temperature and pressure, the estimation algorithm of methane adsorption was established under the actual geological settings. The exogenic factors follow the Ono−Kondo function eq 12. When eq 19 is substituted into eq 12, a function of shale gas adsorption capacity under the reservoir conditions can be expressed as follows:
23.13 − ρf
· + 23.13 × exp( −873.96/T )
ρf ⎞ ⎛ ⎜1 − ⎟ ⎝ 23.13 ⎠
(22)
The estimation of GIP is considered not only the pressure and temperature but also the internal factors, TOC, porosity, and gas saturation. Combined with the content of adsorbed gas, the profile of GIP versus depth is established, taking the sample G
DOI: 10.1021/acs.energyfuels.6b03425 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
Figure 9. Organic matter abundance, density, porosity, gas saturation, and the gas content of Longmaxi shale of well CQ-2.
#4-64 as an example (Figure 8). The trends of free gas content, adsorbed gas content, and GIP with increasing depth are shown in Figure 8: (1) free gas content increases rapidly first and then gently; (2) adsorbed gas content initially increases rapidly at depths less than 1000 m, reaches the maximum of adsorption capacity, and then gradually decreases with the increasing depth; and (3) GIP rapidly increases at shallower depths and then relatively more gently at depths greater than 1000 m. The patterns of methane adsorption capacity and GIP with increasing depth are in agreement with other investigators,31,61,62 and significant to better understanding of the variation of GIP and methane adsorption in terms of the burial time over geological periods. In addition, the estimation algorithms were applied to estimate the adsorbed gas content and GIP of an exploratory well (CQ-2) in Qianjiang Block. The geological data were collected from Chongqing Institute of Geology and Mineral Resources. TOCs of well CQ-2 range from 0.47 to 4.4 wt %, presenting higher TOC contents on the bottom. The porosities range from 1.76% to 6.24%, and the gas saturations range from 26.68% to 85.17%. Substituting the data into eqs 21 and 22, the adsorbed gas content, free gas content, and GIP can be obtained, which are 1.09−2.98, 0.11−1.00, and 1.01−3.91 m3/t, respectively (Figure 9). Therefore, the estimation algorithms of adsorbed gas content and GIP proposed in this study can be
used to estimate the actual shale gas content. This research is significant to better understand the assessments of the exploration and development of shale gas.
5. CONCLUSION On the basis of the experimental results of organic and inorganic matters, and the collected data of methane adsorption isotherms of the Longmaxi shale in southeast Chongqing, China, how organic and inorganic matters affect methane adsorption was investigated. Meanwhile, the estimation algorithms of methane adsorption and GIP under specific geological conditions were established. The main conclusions drawn from this study are summarized as follows: (1) One excess adsorption function was proposed to fit the collected methane adsorption isotherms to obtain the unknown parameters in absolute adsorption function based on the Ono−Kondo model. Thus, the excess adsorption was successfully corrected into absolute adsorption. (2) The saturated adsorption of the monolayer presents a greatly positive relationship with TOC and a negative relationship with clay due to the predominant influence of organic matter on the methane adsorption. (3) Methane adsorption increases with increasing pressure and decreases with temperature. On the basis of the H
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relationships, an estimation function was established to calculate actual methane adsorption capacity in terms of the TOC, pressure, and temperature based on the Ono− Kondo model. GIP calculated based on the sum of adsorbed gas and free gas was determined under the actual geological settings. (4) The profiles of gas content and adsorption capacity as a function of depth show that methane adsorption increases rapidly with depth initially because of the dominant effect of pressure at shallow depths, reaches its maximum around 1000 m, and then gradually declines with the effect of temperature becoming dominant, instead of pressure. With higher TOC content, shales are prone to present larger gas adsorption capacities. In addition, the maximum of adsorption capacity also turns to a deeper depth with TOC increasing.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
He Bi: 0000-0003-1890-166X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the National Science and Technology Major Project (2016ZX05046). The authors wish to acknowledge the Chongqing Institute of Geology and Mineral Resources for providing the shale cores and experimental data used in this study.
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