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Impact of nanoporosity on hydrocarbon transport in shales’ organic matter Amaël Obliger, Franz-Josef Ulm, and Roland J.-M. Pellenq Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04079 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018
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Nano Letters
Impact of nanoporosity on hydrocarbon transport in shales’ organic matter Ama¨el Obliger,†,‡ Franz-Josef Ulm,†,‡ and Roland Pellenq∗,†,‡,¶ †MultiScale Materials Science for Energy and Environment (MSE 2 ), The joint CNRS-MIT Laboratory, UMI CNRS 3466, Massachusetts Institute of Technology, Cambridge 02139 MA, USA ‡Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge 02139 MA, USA ¶CINaM-Aix Marseille Universit´e-CNRS, Campus de Luminy, 13288 Marseille cedex 09, France E-mail:
[email protected] Abstract In a context of growing attention for shale gas, the precise impact of organic matter (kerogen) on hydrocarbon recovery from unconventional reservoirs still has to be assessed. Kerogen’s microstructure is characterized by a very disordered pore network that greatly affects hydrocarbon transport. The specific structure and texture of this organic matter at the nanoscale is highly dependent on its origin. In this study, by the use of statistical physics and molecular dynamics, we shed some new lights on hydrocarbon transport through realistic molecular models of kerogen at different level of maturity [Bousige et al., Nature Materials 15, 576, 2016]. Despite the apparent complexity, severe confinement effects controlled by the porosity of the various kerogens allow linear alkanes (from methane to dodecane) transport to be studied only via the self-diffusion coefficients of the species. The decrease of the transport coefficients with the amount of adsorbed fluid can be described by a free volume theory. Ultimately, the transport coefficients of hydrocarbons can be expressed simply as function of the porosity (volume fraction of void) of the microstructure, thus paving the way for shale gas recovery predictions.
Keywords kerogen, microporosity, diffusion, hydrocarbons, shales Hydrocarbon recovery from shale gas reserare trapped in nanoporous organic matter voirs enhanced by hydrofracking 1 is a very comcalled kerogen that produces oil and gas durplex process that exhibits specific features coming a very slow decomposition process. 6 This pared to the recovery process from conventional kerogen is characterized by a severely confinreservoirs that plagues any forecasting attempts ing (pore sizes d < 2 nm) and disordered pore of the wells’ productivity. In particular, strong space where hydrocarbon transport is thus hinoutput flow’s declines are observed from differdered by very strong adsoption effects. 5,7 Other ent reservoirs 2–4 along with very low permeabilphenomenon may influence the recovery pro5 ities. cess as well such as interfacial effects between In unconventional reservoirs, hydrocarbons the fractures and the organic matter, 8 swelling ACS Paragon Plus Environment
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upon desorption, and fracture clogging. As shown by previous molecular dynamics studies 9–11 hydrocarbon transport in kerogen is purely diffusive, concentration dependent and mostly driven by strong solid/fluid interactions leading to transport coefficients that scale with the reciprocal of the alkane length. In this case, the usual models for hydrocarbon recovery in conventional reservoirs relying on hydrodynamics and Darcy’s law are not relevant. Indeed, these methods can be improved by including some mechanisms occuring at the nanoscale (adsorption, wetting, Knudsen diffusion etc.) 8,12–27 or by correcting Darcy’s law (slippage, Klinkenberg effect). 7,28–33 However, a specific description for transport in the amorphous microporosity (pore size below 2 nm) of the kerogen is still needed. For instance, in the case of sandstones where pores are well connected with pore size of several micrometers, the permeability can be evaluated directly from the porosity via the Kozeny-Carman model. 34,35 We may then wonder if systematic relations between transport coefficients and porosity also exist in the case of kerogen. Following the recent work of Falk et al., 9 by using molecular simulations and statistical physics for transport in a disordered nanoporous carbon, Obliger et al. 11 showed that, owing to negligible velocity crosscorrelations in amorphous and ultraconfined environments, the transport coefficients of linear alkanes involved in hydrocarbon mixtures can be estimated from simple parameters using a free volume theory (chain length, adsorbed amount, and friction coefficient at low loading). These previous studies focused on similar carbon microstructures, reconstructed after pyrolized activated saccharose 9 or after pyrobitumen. 11 The free volume theory has not been investigated yet for different structures. Thus, we lack insights on the evolution of the transport coefficients with the properties of the kerogens’ microstructures. In this letter, we use statistical mechanics including equilibrium molecular dynamics to investigate the transport of linear alkanes (from methane to dodecane) in realistic models of kerogen. 36 Here we take advantage of the fact
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that, in such ultraconfing media, transport properties of alkane mixtures can be captured by a free volume theory involving parameters that can be predicted from the pure component case. 11 We show that the same free volume theory holds for the diffusive transport of alkanes in a broad diversity of kerogens with very different structures and textures. We highlight that the parameters involved in this free volume theory are mainly controlled by the porosity of the microstructures. Furthermore, it is found that the dependence of these parameters on the porosity follows simple relations leading to a better understanding of the transport mechanism in disordered microporous structures. This model provides a very convenient parametrization for transport coefficients of hydrocarbons in kerogens’ microporosity that can be used in multi-scale simulations able to account for the complexity of unconventional reservoirs at larger scales to make progress toward production forecasting of shale-gas reservoirs. The molecular models of kerogens 36 were obtained from hybrid Reverse Monte Carlo simulations which generate structures satisfying experimental properties (density, chemical hybridization, composition, vibrational/mechanical properties, pair distribution function and adsorption isotherms). 36–39 These structures cover a broad range of kerogens from immature to very mature kerogens and are mainly composed of carbon but also hydrogen and oxygen atoms (Fig. 1). Kerogen from different maturity and geological origins are considered: an immature kerogen from the Middle East (MEK), an immature kerogen from the Eagle Ford field (EFK), a mature kerogen from the Marcellus field (MarK) and a very mature kerogen mature from Russia (PY02). Although the latter one can be seen as an overmature kerogen very close to a pyrobitumen. The structures exhibit disordered pore space with pore sizes from few ˚ A to ∼16 ˚ A. For the alkanes, we use a coarse grained united atom model where each CHx (x = 2, 3) is a Lennard-Jones sphere. 40 Hydrocarbon transport in the kerogen models was investigated using configurational biased Grand Canonical Monte Carlo 41,42 and
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Figure 1: a) Logarithm of the rescaled self diffusion coefficients ni Di , with the alkane length 0 ni , versus the free volume fraction Vfree /Vfree . The latter is calculated independently for a given adsorbed amount Γ. The colors indicate the alkane type: methane (black), propane (blue), hexane (green) and dodecane (red). The solid lines are the predictions of the free volume theory ln(ni D(s) ) ∝ 0 1 − Vfree /Vfree where the parameters α and ξ0 are fitted against all the data for each microstructure. Symbols denote different microstructures: pyrobitumen at 0.8 g/cm−3 (dots), Middle-East kerogen at 0.8 g/cm−3 (triangles), Eagle-Ford kerogen at 1 g/cm−3 (squares). For clarity, only the results for these three kerogens are reported here. Snapshots of pyrobitumen at 0.8 g/cm−3 (b) and EagleFord kerogen at 1 g/cm−3 (c) are shown. The grey, red and white sticks on the snapshots are the covalent bonds between carbon, oxygen and hydrogen atoms in kerogen. The box volume is 5×5× 5 nm3 with periodic boundary condition in each direction. molecular dynamics simulations at temperature and pressures relevant to shale reservoirs (T = 423 K and P < 100 MPa). Details are provided in the Supporting Informations. In the following, we recall the general picture for the transport of linear alkane’s mixtures. For mixtures of hydrocarbons composed of ` different types of n-alkanes at a molecular density ρ = N/V with molecular fractions xi = Ni /N , with Ni the number of molecules of component i and N the P` total number of molecules in the mixture ( i=1 xi = 1), we define for a component i ; its monomer length ni , its number density ρi = Ni /V , its chemical potential µi and its centre of mass velocity vi . The following linear response law at steady-state vi = −Ki ∇P
nections with the more general Onsager framework, we proposed Green-Kubo relations between the permeances and the Onsager coefficients. 11 Also, in such confining and disordered materials, transport is mainly driven by strong adsorption effects. As a consequence, the effect of cross-correlations between fluid molecules (linear alkanes) on transport can be neglected and the permeances can be simply written as 11 : (s)
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so that the transport properties investigation can be reduced to the study of the self diffusion coefficients. The numerical study of this work is focused on these latter quantities computed from equilibrium molecular dynamics simulations. We aim now at giving a molecular description of the self diffusivities for hydrocarbon mixtures in very confining porous media. Recently, it has been demonstrated that the free
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0 Figure 2: (a) Free volume fraction Vfree /Vfree versus the loading Γ = ρCHx /ρmax i,CHx for different alkanes (black: methane, blue: propane, green: hexane, ornage: nonane and red: dodecane) in various microstructures (crosses: PY02 at 0.8 g/cm3 , squares: EFK at 1.0 g/cm3 and empty circles: MEK 0 = 1 − βΓ for PY02 at at 1.2 g/cm3 ). The solid and the dashed lines are linear fits such as Vfree /Vfree 3 3 0.8 g/cm and EFK at 1.0 g/cm respectively. The dotted lines are similar linear fits with packing efficiency depending on the alkane length due to the disconnected pore space. a,b,c) Adsorption isotherms for different alkanes (methane: black, propane: blue, hexane: green, nonane: orange, and dodecane: red) in (b) PY02 at 0.8 g/cm3 , (c) EFK at 1 g/cm3 and (d) MEK at 1.2 g/cm3 at T = 423 K. Adsorbed amounts ρCHx are plotted as the number of CHx groups in mmol per g of kerogen as a function of pressure P . The solid lines are fits against the Langmuir equation Γ = κi P/(1 + κi P ) where the κi ’s are the Henry constants for the different alkanes considered. Except for the MEK at 1.2 g/cm3 that has a disconnected porous space, the maximun density ρmax i,CHx does not depend significantly on the alkane length.
volume theory 43,44 is succesfull to describe the transport properties of alkane mixtures through microporous carbons. 9,11 Whitin this free volume approach that we investigate further in this study, the self diffusivities of alkanes are then expressed as : Vfluid (s) (s) (3) Di = Di,0 exp −α Vfree
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kB T . ni ξ0
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P where Vfluid = `j=1 Nj Vj is the total volume occupied by the mixture in the system with Vj the (s) volume of a molecule of type j, Di,0 = µmob i,0 kB T is the self diffusivity at infinite dilution whith µmob i,0 the mobility of the species i. In this picture inspired by the Rouse model for polymer diffusion, 45 the influence of the membrane on a molecule of ni monomers is modeled by a friction force Fv = −ni ξ0 v = −v/µmob proi,0 portional to the centre of mass velocity of the molecule where ξ0 is a friction coefficient defined for a single monomer. The mobility is thus µmob = (ni ξ0 )−1 so that we have for the i,0
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volume of void, Eq. 3 can be rewritten as : 0 Vfree kB T (s) exp α 1 − . (5) Di = ni ξ0 Vfree
When the microporosity is disconnected, the Toth adsorption model 47 gives in fact better results (not shown). In the following we address the question of the links between the overlap and the friction parameters as well as the packing efficiency and the characteristics of the kerogen’s nanostructure. Despite of some fundamental differences between these materials, (chemistry, texture, density and structure) numerical results (Fig. 3) clearly indicate that a single parameter, the porosity, controls the transport properties of hydrocarbon fluids adsorbed in such microporous materials. Fig. 3 displays the values of the transport parameters α and the logarithm of ξ0 for all the matrices considered in this work as function of the porosity. More precisely, Fig. 3a displays the overlap coefficient against the porosity where we clearly see that it follows a linear trend for porosities larger than a threshold values ϕc = 23% below which its value goes to zero. Due to the nature of the overlap coefficient α, which is a correction factor to take into account the overlap of the free volume per molecule, its value naturally decreases when the porosity decreases and tend to zero when the pore space of the material is not connected (ϕ < ϕc ). Note that this is to be understood as a limit because no transport occurs in this situation. In very confining situation such as in the kerogen microstructure, this situation coincides with pore sizes equivalent to the molecules size. The coefficients evaluated for EFK and MEK at 1.2g/cm3 correspond to vibrations of independent molecules trapped in closed pores. The exponential decrease of the transport properties as function of the loading highlighted by the free volume model depends on pore size effects. This is in fact simply controled by the porosity that acts as an order parameter for α near a percolation threshold ϕc = 23%. As a result, when the pore space is connected the overlap coefficient can be expressed as:
Fig. 1 shows that this free volume scaling can correctly describe the loading dependence of the self diffusivities of linear alkanes in very different microstructures. These numerical results allow us to simply evaluate the transport coefficients α and ξ0 for the different kerogen structures. Additionally, this free volume theory has been expressed in the Maxwell-Stefan framework using the generalized Darken equation recently obtained by Liu et al. 46 (see S.I.). The free volume term can be expressed as funcmax tion of the loading Γ = ρCHx /ρmax CHx where ρCHx is the maximum density of monomers that can be adsorbed by the use of the linear relation 0 Vfree /Vfree = 1 − βΓ (Fig 2a), thus giving αβΓ kB T (s) exp − . (6) Di = ni ξ0 1 − βΓ Here β is the packing efficiency of linear alkanes confined in the structures and does not depend on the alkane length when the pore space is connected (Fig. 2a). This is not the case when the pore space is not connected; because of pore size effects, small molecules can be adsorbed in some pores while it is not possible for longer molecules thus changing the maximum adsorbable quantity and the packing efficiency with the alkane length. For large porosities, typically 40-60%, the maximum density of monomers is the same regardless of the alkane length (Fig. 2b). This can be considered as a fair approximation for porosities larger than 20 % (Fig. 2c). Whereas, this is no longer valid for lower porosities (Fig. 2d) and the adsorption isotherms for different alkanes are thus crossing each other. These features are the consequences of a disconnected pore space where some pores can be filled by small molecules only. 42 For all of these microstructures, the maximum adsorbed quantity decreases when the porous volume decreases. We also notice that the adsorption isotherms are described less accurately by the Langmuir model when the confinement increases (i.e. when the porosity decreases).
α = α0 (ϕ − ϕc ) ,
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Figure 3: (a) Overlap coefficient α and (b) friction coefficient ξ0 as function of the porosity ϕ (in percentage) for hydrocarbon fluids (from methane to dodecane) confined in various kerogens with different structural, textural and chemical characteristics. Shapes indicate different structure densities (squares: 0.8 g/cm3 , dots: 1.0 g/cm3 , triangles: 1.2/g cm3 ) and colors indicate different kerogen types (black: PY02, green: MarK, blue: EFK, orange: MEK). (a) The solid line is a linear fit α0 (ϕ − ϕc ) with the threshold porosity ϕc = 23 % and the slope α0 = 8.57 10−2 . (b) The solid line is a linear fit ln(ξ0max /ξ0 ) = α0 (ϕ − ϕc ) where the parameters α0 and ϕc are fixed to the previous values and ξ0max = 7.95 10−12 N s m−1 is a maximum friction coefficient obtained from the fitting procedure. (c) Packing efficiency β as function of the porosity ϕ, the solid line corresponds to 0.64 ϕ/100 with ϕ expressed in percentage. the porosity (Fig. 3b). When the porosity is decreasing, the pore size effects become more important leading to an increase of the friction coefficient. The friction coefficient then reaches a limit value ξ0max = 7.95 10−12 N s m−1 (ϕ ' ϕc ) because the number of atoms of the structure interacting with a molecule inside a pore is at its maximum. This is in fact a theroretical limit since the diffusion would be governed by hopping mechanisms when the pore space is barely connected (ϕ very close to ϕc ). When the pores are no longer connected (ϕ < ϕc ) the limiting case arises when there is no transport. Note that the values of ξ0 evaluated for EFK and MEK at 1.2 g/cm3 correspond to molecular vibrations evaluated at short times to obtain finite values and thus do not correspond to transport coefficients. Finally, when pores are connected the friction coefficient can be written as : ξ0 = ξ0max exp[−α0 (ϕ − ϕc )] , (8)
We see that the parameter β simply follows a linear trend β = βs ϕ (9) where βs ' 0.64/100 where 0.64 is the packing efficiency of a random packing of hard spheres. 48 Finally, using the free volume parameters α(ϕ), ξ0 (ϕ) and β(ϕ) (Eqs. 7, 8 and 9) in Eq. 6 allows us to write the transport coefficients as function of the porosity : 1 − 2βs ϕΓ kB T (s) exp α0 (ϕ − ϕc ) Di = ni ξ0max 1 − βs ϕΓ (10) with respect to the loading Γ. The transport of simple hydrocarbon fluids in disordered microporous carbons can be therefore rationalized as function of, the porosity ϕ and the loading Γ, and of fixed parameters, ξ0max , α0 , ϕc and βs that depend on the fluid type and on the fluidsolid interactions. Furthermore, the porosity of the microstructures can be estimated from the kerogen’s mass density ρk = (1 − ϕ)ρs with ρs ' rsp 2.2+(1−rsp )1.2 g/cm3 the mass density of the kerogen’s walls and rsp the sp2 /(sp2 +sp3 )
with ξ0max = 7.95 10−12 N s m−1 . Fig. 3c displays for all the kerogen’s microstructures considered in this study, the packing efficiency β as function of the porosity ϕ.
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ratio of the kerogen structure where the effective wall density ρs is approximated as an averaging between the contributions of the aromatic and the aliphatic carbons (see S.I.). On the contrary to porous media like sandstones with pore size about the micrometer and where the Kozeny-Carman permeabilityporosity relation holds, the solid-fluid interactions cannot be neglected here and are captured by ξ0max in the model. Since kerogens’ microstructures are amorphous with similar pore sizes for different structures, the specific details of the pore space do not play an important role and thus, the pore size effects are mainly controled by the porosity ϕ. However, the details of the morphology of the pore space can explain the discrepancies between the scalings of the model and the data. This study provides further insights into hydrocarbon transport through ultraconfining materials. We adressed the question of the evolution of the two parameters involved in the free volume theory as function of the intrinsic properties of microporous carbon based materials and showed that there exists unexpectedly simple expressions inspired by percolation theory between the overlap and friction parameters and the porosity. The latter, as an order parameter related to the severeness of the confinement, controls both the exponential decline of the transport coefficients with the increasing fluid concentration and the connectivity of the materials. Finally, the results gathered in this work permit an extremely convenient parametrization of the transport parameters requiring only the knowledge of the fluid concentration and the porosity of the kerogen’s microstructure. Our model can thus be used in multiscale fluid simulations such as homogenization techniques (pore networks, lattice models, etc. 29,49–51 ). This general framework that accounts for strong adsorption effects in a simple way can be useful for many applications involving transport in disordered microporous media.
gens. This material is available free of charge via the Internet at http://pubs.acs.org/. Acknowledgement This work was supported by the X-Shale project enabled through MIT’s Energy Initiative in collaboration with Shell and Schlumberger. Additional support was provided by the ICoME2 Labex (ANR11-LABX-0053) and the A∗ MIDEX projects (ANR-11-IDEX-0001-02) cofunded by the French programme ‘Investissements d’Avenir’ managed by ANR, the French National Research Agency. We also thank Benoit Coasne for useful discussions and Colin Bousige for providing us with the molecular models of kerogens’ microstructures. The authors declare no competing financial interests.
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Graphical TOC Entry
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