Impact of Capillary Pressure and Nanopore Confinement on Phase

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Impact of Capillary Pressure and Nanopore Confinement on Phase Behaviors of Shale Gas and Oil Julian Youxiang Zuo, Xuqiang Guo, Yansheng Liu, Shu Pan, Jesus A Canas, and Oliver C. Mullins Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03975 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 21, 2018

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Impact of Capillary Pressure and Nanopore Confinement on Phase Behaviors of Shale Gas and Oil Julian Y. Zuoa, Xuqiang Guob, Yansheng Liub, Shu Panc, Jesus, Canasc, Oliver C. Mullinsc a

Corresponding author, FMG, Canada, [email protected]

b

China University of Petroleum_Beijing at Karamay, China

c

Schlumberger, Houston, TX, USA

Abstract In this paper, a general framework of theoretical models and algorithm is developed to predict phase envelopes (saturation points) and quality lines of shale gas and oil in nanopores. The equation of state (EOS) and the modified Young-Laplace equation are used to take into consideration the effect of phase behavior and capillary pressure on phase envelopes, respectively. The Zuo and Stenby parachor model is applied to determine interfacial tensions between the vapor and liquid phases. In addition, critical property shift of pure components is utilized to account for the impact of nanopore confinement on phase envelopes. The algorithm has proven to be robust for generating phase envelopes including critical points, cricondentherms (maximum temperatures) and cricondenbars (maximum pressures) for a variety of fluids at different compositions, vapor mole fractions (quality lines) and pore sizes. The models and algorithm are then used to explain the recently measured data of normal boiling point or bubble point temperatures for pure n-heptane in type I kerogen, binary mixtures of n-pentane + n-hexane and n-pentane + n-heptane and a ternary mixture of n-pentane + n-hexane + n-heptane in the nanofluidic devices. For pure n-heptane in type I kerogen, with a presumption of nanopores being completely wetted by the liquid phase, the models agree well with the experimental data within a reasonable range of type I kerogen nanopore distributions in the presence of capillary pressure effect only as well as both capillary pressure and nanopore confinement effects. However, for the binary and ternary mixtures in the nanofluidic devices, the complete wettability assumption seems no longer valid. The wetting fluid-wall interaction parameter (λ) is then adjusted to match the experimental data at the nanopore radius of 5 nm. The adjusted parameters are λ = -142.2 ~ -167.5 and λ = -14.0 for the three-tested binary and ternary mixtures in the presence of capillary pressure effect only as well as both capillary pressure and nanopore confinement effects, respectively. The models provide not only good predictions at other radii but also a correct trend for the mixtures in the presence of capillary pressure effect only but a wrong trend against the experimental data in the presence of both capillary pressure and nanopore confinement effects. In addition, in the presence of both capillary pressure and confinement effects, a decrease in bubble and dew point pressures with decreasing pore radius is observed for shale gas and oil. For gas condensate mixtures, field production data show that produced liquid and gas ratios decrease even at reservoir pressures above bulk retrograde dew points. It is obvious that the model with critical property shift contradicts the field observation. More research activities in this area are required. Whereas, in the presence of capillary pressure effect only, a decrease in bubble point pressures is estimated for shale oil while an increase in dew point pressures is predicted for shale gas with decreasing pore radius. Keywords: Shale gas and oil, phase envelope, capillary pressure, confinement, nanopore, interfacial tension Introduction Shale and tight gas and oil are enormous energy resources all over the world. In the past decades, the industry has made considerable efforts to produce gas and oil economically from unconventional shale

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and tight reservoirs using new technology such as horizontal well drilling and hydraulic fracturing. These unconventional reservoirs generally have ultra-low permeability (in the order of 1 to 100 nd) and extremely small pore sizes (a few nanometers to 100 nm) compared with conventional reservoirs. [1] Such small pore sizes give rise to high capillary pressure and spatial confinement, thus yielding different fluid phase behaviors than conventional reservoir fluids. Phase behaviors and properties of reservoir fluids play a key role throughout the entire production processes of reservoir fluids. Therefore, it is of great importance to develop an effective and reliable method to model and predict the phase behaviors of gas and oil in shale or tight formations and investigate the effects of some key factors on phase behaviors. Experimental investigation on fluid phase behaviors in unconventional reservoirs is very difficult and of high uncertainty owing to their unconventional characteristics. Some researchers experimentally studied the effects of pore sizes on phase behaviors. In 1966, Tindy and Raynal [2] measured the bubble point pressures of two reservoir crude oils in both a PVT cell and a porous medium with grain sizes in the range of 160 to 200 micros. The bubble point pressures of two crude oils were a few percent higher in the porous media than those in a conventional PVT cell. Later, Trebin and Zadora [3] reported that there was a 10-15% increase in the dew point pressure of gas condensate mixtures in the porous media. On the contrary, Tindy and Raynal [2] could not observe any considerable difference for saturation pressure in the porous media when dealing with the mixture of methane and n-heptane in the same phase equilibrium cells. Sigmund et al. [4] measured the dew point and bubble point pressures for methane + n-butane and methane + n-pentane mixtures with 30-40 US mesh bead size in the Constant Composition Expansion (CCE) process. They concluded that there was no effect of porous media on the saturation pressure. Recently, Pathak et al. [5] measured the boiling point temperatures and bubble point temperatures in type I kerogen for pure components such as n-heptane, nitrobenzene and ethanol and the light sweet Wyoming crude using Differential Scanning Calorimetry (DSC). Alfi et al. [6] measured the bubble point temperatures of n-pentane + n-hexane, n-pentane + n-heptane and n-pentane + n-hexane + n-heptane mixtures using the nanofluidic devices at pore sizes of 10, 50 and 100 nm. Their results indicated that the boiling point and bubble point temperatures increase with a decrease in nanopore radius at atmospheric pressure. Molecular simulation and molecular thermodynamics methods have been used to fundamentally study fluid properties under spatial confinement. Those studies revealed that in theory critical pressure and temperature considerably deviate from those in the bulk when pore sizes are less than 10 nm. Zarragoicoechea and Kuz investigated the critical property change for some pure components in nanopores using a generalized van der Waals equation of state (EOS) and derived the equations for critical temperature and pressure changes related to the ratio of the Lennard-Jones potential parameters to pore radius [7]. Vishnyakov et al. [8] investigated the critical properties of the Lennard-Jones fluid in slitlike pores using Gibbs ensemble Monte Carlo simulation and lattice gas models. It was found that the critical temperature linearly depends on the inverse pore size and strongly on the strength of the fluid-wall interactions. Hamada et al. used the grand canonical Monte Carlo simulation to study properties of confined particles in slit and cylindrical pore systems [9]. Singh et al. also employed the grand canonical Monte Carlo simulation to investigate the phase behavior of methane, n-butane and n-octane in slits. They found that the shifted critical properties rely on both pore sizes and surface types [10, 11]. Alharthy et al. [12] further correlated shifted critical properties based on the simulation results from Singh et al. However, their correlations cannot be reduced to the bulk phase if the porous medium is removed. Additionally, the calculated bubble points can be higher or lower than those in the bulk, whereas the dew points are lower than those in the bulk phase, which contradicts the notion introduced by experimental data.


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Attempts were also made in modeling the phase behaviors of gas and oil in shale or tight formations. The equations of state have been used as the tool to study the effects of capillary pressure, confinement, adsorption, and so on. [13-25] Brusilorsky developed a theoretical model to study the influence of capillary pressure on phase equilibria for natural multicomponent systems. [13] He concluded that capillary pressure made the dew point increase and the bubble point decrease. Guo et al. took into account the adsorption influence on the dewpoint pressure of gas condensate and found that adsorption decreases the retrograde dewpoint pressure, opposite to the influence of capillarity. [14] Pang et al. studied the effect of capillary pressure on phase behaviors for oil and gas condensate in shale and tight reservoirs. [15] Nojabaei et al. used the Peng-Robinson EOS [26] and the Macleod and Sugden parachor correlation [27, 28] to calculate phase behaviors of hydrocarbons in tight porous media. [16] Wang et al. investigated the impact of pore size distributions on the phase transition of hydrocarbon mixtures in nanoporous media. [17] Sandoval et al. developed an algorithm to generate phase envelopes of gas and oil in nanopores by considering capillary pressure influence. [18] All these authors concluded that capillary pressure changed phase envelopes everywhere except critical points, by decreasing the bubble point pressures of crude oil and increasing the retrograde dew point pressures of gas condensate. Most of them showed that phase envelopes do not change at the cricondentherm, which is incorrect. Li and Sheng took into account the effect of both capillary pressure and critical property changes on phase behaviors of hydrocarbons under confinement. [19] Shapiro and Stenby derived the Kelvin equation to determine condensate saturation by incorporating the Young-Laplace equation for multicomponent mixtures. [20, 21] Travalloni et al. extended the van der Waals EOS for the critical behavior of pure confined fluids [22] and then the PengRobinson EOS for the phase equilibria of fluids confined in porous media. [23] Dong et al. took into account the effects of capillary pressure, adsorption film and critical property shift on phase equilibria in nanopores. [24] A comprehensive review was made by Barsotti et al. on capillary condensation in nanoporous media. [25] It was noticed that many of the published modelling work directly implemented interfacial tension (IFT) models without validating them against experimental data for the mixtures under their studies. It was also noticed that the impacts of critical property shift in additional to capillary pressure haven’t been fully explored. In the current work, we make some efforts on these two aspects by interpreting some of the recently measured data for pure and multicomponent hydrocarbons. In this paper, a general framework of theoretical models and algorithm has been developed to predict the phase envelopes and quality lines of shale gas and oil in nanopores. The IFT model used for capillary pressure estimation has been compared with the experimental data of pure and binary hydrocarbon mixtures to better understand the modeling uncertainty. The developed models and algorithm have been used to successfully generate phase envelopes and quality lines for pure and multicomponent hydrocarbon mixtures including critical points, cricondentherms and cricondenbars. Effects of capillary pressure and critical property shift due to confinement on phase envelopes have been studied for different types of fluids, particularly for some pure and multicomponent hydrocarbons with recently measured data. General Framework of Theoretic Models and Numerical Algorithms According to thermodynamics, the phase equilibrium criterion for an N-component mixture is given by [29]

(

)

(

f iV T V , PV , y = f i L T L , P L , x

)

(1)

where superscripts V and L represent the vapor and liquid phases. T, P, fi, y and x are the temperature, pressure, fugacity of component i, mole fractions in the vapor and liquid phases, respectively. Because the fugacity can be calculated by the equation of state, Eq. (1) is rewritten as


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(

)

(

yi PV ϕ iV T V , PV , y = xi P Lϕ iL T L , P L , x

)

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(2)

Owing to the effect of capillary pressure in nanopores, pressures in the vapor and liquid phases are different unlike in conventional reservoirs. In this work, it is presumed that liquid is the wetting phase. The capillary pressure is calculated by the Young-Laplace equation:

P C = PV − P L =

2σ cosθ r

(3)

where r is the radius of cylindrical nanopores and θ is the contact angle between the surface of the wetting phase and nanopores. If θ is zero, nanopores are completely wetted by the liquid phase. σ denotes the interfacial tension (IFT) between the vapor and liquid phases. A modified Young-Laplace equation can be used as well [30]:

P C = PV − P L =

2σ r (1 − λ )

(4)

where λ is a parameter related to the interaction between fluid and pore material. The value of λ can be determined from experimental data. Negative λ (λ < 0) decreases capillary pressure while positive λ (0 < λ < 1) increases capillary pressure. As suggested by Barsotti et al. [25], the actual effects are well represented by this approach by taking into account fluid-wall interactions. Consequently, the EOS has a strong predictability in modeling confined fluid mixtures given the bulk behavior of the system. It should be noted that adjustment of λ is equivalent to tuning contact angle θ in Eq. (3) numerically, but θ may not be meaningful anymore. With hydrocarbons being adsorbed onto the wall of nanopores to form an adsorption film, effective nanopore radius is reduced to: [24]

re = r − t − σ ss / 2

(5)

where r stands for the original pore radius. t denotes the thickness of the equilibrium adsorption layer, which can be derived from the adsorption isotherm. σss is the diameter of the solid wall molecule. The IFT in mN/m can be estimated by the parachor model modified by Zuo and Stenby [31]

  σ = ∑ Π i xi ρ L − yi ρ V   i 

(

)

3.6

(6)

where ρ and Πi stand for the density of the vapor or liquid phase in mol/cm3 and the parachor of component i in cm3/mol⋅(mN/m)1/3.6, respectively. The density and fugacity coefficients are calculated by the Soave- Redlich-Kwong (SRK) EOS in this work because the parachor model of Zuo and Stenby used the SRK EOS. [32] In addition, nanopore confinement lowers the critical temperature and pressure of pure components. This effect is also taken into account in this work. The changes of critical properties are calculated by the model of Zarragoicoechea and Kuz [7]:

∆Tc =

Tcb − Tcp Tcb

σ LJ

σ  = 1 − 0.9409 + 0.2415 LJ  r  r 

2


(7)

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∆Pc =

Pcb − Pcp Pcb

= 1 − 0.9409

σ LJ

σ  + 0.2415 LJ  r  r 

2

(8)

The Lennard-Jones (LJ) parameter in nm is estimated by 1/ 3

σ LJ

T  = 0.244 cb   Pcb 

(9)

where Tcb and Tcp are the critical temperature of pure component in the bulk phase and nanopores in K; Pcb and Pcp are the critical pressure of pure component in the bulk phase and nanopores in atm. It should be noted that Zarragoicoechea and Kuz [7] used the mean field theory in the van der Waals equation of state to derive the aforementioned critical property shift correlations assuming neutral walls of nanopores. The correlations were compared with the experimental data of simple fluids like Ar, CO2, N2, Xe, O2, and C2H4. The upper boundary of Eqs. (7) and (8) is σLJ/r ≤ 0.37. For large molecules, σLJ/r may be greater than 0.37 in particular when r becomes very small. Ma et al. and Jin et al. developed the correlations which are also dependent on σLJ/r and applicable for σLJ/r > 0.37 [33, 34, 19]. In this work, because σLJ of the heaviest component < 1 nm, the calculated minimum pore radius is about 2.7 nm based on the upper limit of Eqs. (7) and (8). Since nanopore radius is equal to and greater than 5 nm in this work, Eqs. (7) and (8) are still applicable. In addition, Alharthy et al. [12] correlated shifted critical properties based on the simulation results from Singh et al. [10,11] However, their correlations cannot be reduced to the bulk phase if the porous medium is removed. Additionally, the calculated bubble points can be higher or lower than those in the bulk, whereas the dew points are lower than those in the bulk, which contradicts the notion introduced by experimental data. Because convergence issues often occur in the vicinity of the critical point and it is difficult to determine the cricondentherm and cricondenbar, Michelsen’s phase envelope algorithm [35] is extended to calculate phase envelopes in the presence of capillary pressure and/or confinement in nanopores. The effect of nanopore confinement is taken into account through the critical property shift of pure components. That is, different critical properties are assigned to pure components in nanopores of certain effective nanopore radius. The influence of interactions between the wetting phase and the wall of nanopores is accounted for by tuning λ to match one or more point(s) of experimental data. Therefore, we have N + 3 nonlinear equations:

[

(

)] [

(

)]

 Fi (α, β ) = ln K i + ln PV ϕiV T , PV , y − ln P LϕiL T , P L , x = 0,  N  F (α, β ) = ( y − x ) = 0  N +1 ∑ i i  i =1  F (α, β ) = P L − PV + P C T , PV , P L , y, x = 0  N +2  FN +3 (α, β ) = α s − S = 0

(

)

i = 1,..., N (10)

where Ki= yi/xi is the vapor-liquid equilibrium value dependent on temperature, pressure and compositions, estimated by the EOS. The mole fractions of component i in the liquid and vapor phases are calculated by the following equations

xi =

zi , 1 + β (K i − 1)

yi =

zi K i 1 + β (K i − 1)


(11)

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where β is the vapor phase mole fraction. β = 0 corresponding to the bubble point whereas β = 1 corresponding to the dew point. The first to the Nth equations correspond to the phase equilibrium equations. The (N+1)th equation is the Rachford-Rice equation. The (N+2)th equation is the pressure equilibrium criterion under capillary pressure. The (N+3)th equation is the specification equation. The vector of dependent variables is given by

(

α T = ln K 1 , ln K 2 ,..., ln K N , ln T , ln P V , ln P L

)

(12)

When the Newton-Raphson method is used to solve the set of nonlinear equations, good initial guesses are required for each of the points on the phase envelopes or quality lines. The same extrapolation method is utilized as Michelsen. [35] A polynomial extrapolation is used to obtain a good initial estimation for kth iteration α k (S ) = α k 0 + α k 1 S + α k 2 S 2 + α k 3 S 3

(13)

where akj, j = 0,1, ... ,3, are the coefficients of the polynomial regressed from the information of the last two points. We select the first point at low pressure of the liquid phase, e.g., PL = 1 atm, using a converged point without capillary pressure as initial guesses. Unlike Sandoval et al. [18], we choose lnPL and lnPV instead of PL and PV as dependent variables to avoid negative pressure (either PL or PV) during the numerical process in search of the solutions. The current algorithm can be straightly implemented into the existing phase envelope algorithm of bulk fluids. It should be noted that this method can automatically determine critical points, cricondentherms (maximum temperature) and cricondenbars (maximum pressure) on phase envelopes. For a pure component, the equilibrium criterion and capillary pressure equations reduce to

( F (T , P

) )= P

(

)

(

)

F1 T , PV , P L = ln PV + ln ϕ V T , PV − ln P L − ln ϕ L T , P L = 0

(14)

(

(15)

2

V

, PL

L

)

− PV + P C T , PV , P L = 0

When one of T, PV and PL is specified, the remaining variables can be solved from Eqs. (14) and (15) by the Newton-Raphson method. The initial values can be obtained without considering capillary pressure impact. As it has been long recognized that the SRK EOS can give good vapor pressure results for pure components outside the vicinity of the critical point, we don’t conduct further validation and simply use it for the vapor pressure calculations in this work. Results and Discussions The aforementioned framework has been implemented to calculate phase envelopes for various fluids at different pore sizes and vapor mole fractions in the presence of capillary pressure only and of both capillary pressure and confinement due to critical property shift. In addition, it is reasonable to ignore the effects of adsorption and solid wall molecules on the reduction of pore radii because pore radii are equal to and greater than 5 nm in our calculations, which is considerably greater than the thickness of adsorption layers and solid wall molecules. [24] Pure Components


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Pure n-pentane and n-heptane were taken as examples to validate the current modelling framework, with relevant experimental data available in the literature. First of all, the IFT model was tested against the experimental data in the bulk in Figure 1. The IFT predicted by the Zuo and Stenby parachor model [31] has shown good agreement with the experimental data [36]. This ensures the accuracy of IFT calculations for capillary pressure estimation. 25 Exp. (n-C5 + n-C7)

Interfacial Tension, mN/m

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Bubble point (n-C5+n-C7) Dew point (n-C5+n-C7)

20

Model (Pure n-C5) Exp. (Pure n-C5) 15

Model (Pure n-C7) Exp. (Pure n-C7)

10

5

0 250

300

350

400

450

500

550

Temperature, K

Figure 1. Comparison of IFT predicted by the parachor model [31] with the experimental data [36] for pure n-pentane, n-heptane and a binary mixture of n-pentane (55.8 mol%) + n-heptane (44.2mol%). The parachor model matches the experimental data well. The framework described previously was then used to predict saturation pressure in the vapor and liquid phases of bulk fluids, and fluids in nanopores with capillary pressure effect only as well as with the effects of both capillary pressure and nanopore confinement due to critical property (CP) shift at nanopore radii of 50 and 10 nm. The predicted results are illustrated in Figure 2. At pore radius of 50 nm without CP shift, saturation pressure in the vapor phase [Vapor (No CP shift, r = 50 nm)] is almost the same as that in the bulk. In the presence of capillary pressure effect only ((No CP shift), although the critical point is not affected because of zero capillary pressure, the saturated pressure (PL) curves in the liquid phase [Liquid (No CP shift)] move toward the higher temperature range, particularly at low pressure owing to large capillary pressure. The smaller pore radius, the lower saturation pressure in the liquid phase at a specified temperature or the higher saturation temperature in the liquid phase at a specified pressure. On the other hand, nanopore confinement due to CP shift moves saturation pressure curves in the liquid phase [Liquid (CP shift)] toward the lower temperature range at higher pressure because nanopore confinement decreases the critical temperature and pressure of a pure component. The model with the effects of both capillary pressure and confinement predicts the boiling point temperatures higher than those in the bulk at lower pressures whereas lower than those in the bulk at higher pressures. The model with the effect of capillary pressure only predicts the boiling point temperatures always higher than those in the bulk except at the critical point. These observations need further validation from future experimental study.


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Figure 2. Predicted saturation pressure in the vapor and liquid phases versus temperature with and without the effects of capillary pressure and/or nanopore confinement due to pure critical property (CP) shift. (a) n-Pentane at r = 50 and 10 nm; (b) n-Heptane at r = 50 and 10 nm. λ = 0. Notations: Vapor = saturation pressure in the vapor phase; Liquid = saturation pressure in the liquid phase; CP shift = confinement due to critical property shift. Recently, Pathak et al. [5] measured the variation of normal boiling point temperatures of pure components and bubble point temperatures of the light sweet Wyoming crude oil in kerogen using Differential Scanning Calorimetry (DSC). For pure n-heptane, the measured normal boiling point temperature is 429.15 K (about 60 K higher than the bulk normal boiling point temperature). It is assumed that the aforementioned model can predict boiling points of pure components. Then we can check at which pore radii the predictions of boiling points from the models match the measured data. Therefore, the aforementioned models were used to predict boiling point temperatures for n-pentane and n-heptane at atmospheric pressure at different pore radii. The results are shown in Figure 3. In the presence of capillary pressure effect only, the boiling point temperature predicted by the model at the pore radius of 13 nm matches the experimental data for pure n-heptane. In addition, if both capillary pressure and confinement effects are considered, the boiling point temperature predicted by the model matches the experimental data at the two pore radii of 5.5 and 32 nm for pure n-heptane. Because Pathak et al. did not report the pore size distributions of type I kerogen in their paper, it is hard to determine which case is closer to the actual situation. It seems that both cases provide reasonable predictions since the obtained pore radii are in a reasonable range for type I kerogen pore size distributions. It is interestingly observed that in the presence of both capillary pressure and confinement effects the predicted normal boiling point temperatures for pure n-pentane and n-heptane increase with a decrease in pore radius, then reaches a maximum value around 10 nm and decrease afterward. Whereas if only capillary pressure effect is present, the predicted normal boiling point temperatures for pure n-pentane and n-heptane monotonically increase with a decrease in pore radius. For multicomponent mixtures, the model with effects of both capillary pressure and confinement gives similar behavior to that for pure components. Thus, we will explain why the maximum value occurs in the next section. Actually, the model with effects of both capillary pressure and confinement predicts a wrong trend against the experimental data.


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Boiling point temperature, K

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480

n-C5 (No CP shift)

460

n-C5 (CP shift) n-C7 (No CP shift)

440

n-C7 (CP shift)

420

Exp. (n-Heptane)

400 380 360 340 320 300 1

10

100

1000

10000

Pore radius, nm

Figure 3. Variations of normal boiling point temperature predicted by the models with pore radius for pure n-pentane and n-heptane. The boiling point temperature predicted by the models at reasonable pore radii matches the experimental data for n-heptane. The experimental data [5] are drawn as constant – an average value for all pore radii for simplicity. λ = 0. Multi-Component Mixtures The parachor IFT model of Zuo and Stenby [31] was utilized to predict IFT for the n-pentane (55.8 mol%) + n-heptane (44.2 mol%) mixture. The IFT results are also shown in Figure 1. The predicted IFT is in good agreement with the experimental data. [36] It was observed that the IFT values are in between those of pure n-pentane and n-heptane. This observation suggests that the IFT model can give reliable IFT predictions for the n-pentane + n-heptane mixture. The aforementioned framework and algorithm were then used to predict phase envelopes for this binary mixture. The new algorithm can generate this narrow bubble-dew point phase envelopes successfully as shown in Figure 4. In the absence of nanopore confinement effect (no CP shift, i.e. capillary pressure only) at r = 10 nm, dew point pressure is just slightly lower than bulk dew point pressure whereas bubble point pressure is much lower than bulk bubble pressure at a given temperature. In other words, dew point temperature is just slightly higher than bulk dew point temperature whereas bubble point temperature is much higher than bulk bubble point temperature at a given pressure. On the other hand, if we account for both capillary pressure and nanopore confinement effects (CP shift) at r = 10 nm, the critical temperature and pressure of the mixture are lower than those in the bulk. The phase envelope looks like a shift from that of considering capillary pressure effect only toward the lower temperature side. The bubble and dew point pressures are higher than those in the bulk in the higher-pressure region, whereas the bubble point pressures are lower than those in the bulk in the lower-pressure region like the pure components shown in Figure 2.


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35

Critical point

30

Bulk phase Bubble point (No CP shift, r=10 nm)

25 Pressure, atm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Dew point (No CP shift, r=10 nm) 20

Dew point (CP shift, r=10 nm) Bubble point (CP shift, r=10 nm)

15 10 5 0 250

300

350

400 Temperature, K

450

500

550

Figure 4. P-T diagram for binary n-pentane (55.8 mol%) + n-heptane (44.2 mol%) mixture in the presence and absence of capillary pressure and nanopore confinement at r = 10 nm. λ = 0. Recently, Alfi et al. [6] employed their nanofluidic devices to measure bubble point temperatures at three different nanopore sizes and atmospheric pressure for three binary and ternary mixtures. The aforementioned framework and algorithm were employed to predict bubble point temperatures and compared with the experimental data for these mixtures. The first binary mixture is the n-pentane (50 mol%) + n- heptane (50 mol%). This mixture is similar to the mixture in Figure 4. The predicted variations of bubble point temperatures versus pore radius at atmospheric pressure are depicted in Figure 5(a).

Figure 5. Bubble point variations for the n-pentane (50 mol%) + n-heptane (50 mol%) mixture. (a) Variation of bubble point temperatures vs. nanopore radius at atmospheric pressure with and without tuning λ; (b) Variation of bubble point curves in the presence of nanopore confinement (CP shift) at different nanopore sizes without tuning λ. Experimental data are taken from [6].


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If it is presumed that the liquid phase is completely wetted on the wall of nanopores in the nanofluidic devices, i.e., λ = 0 (or the contact angle θ = 0), the bubble point temperatures predicted by the model in the presence of capillary pressure effect only as well as both capillary pressure and nanopore confinement effects are much higher than the experimental values [6]. It should be noted that the same models satisfactorily predicted the boiling point temperature of pure n-heptane in type I kerogen as described previously with the complete wettability presumption. Why do the same models significantly over-predict bubble point temperatures by adding the equal mole of n-pentane that is similar to n-heptane? One can only make some conjectures since the authors [6] did not report what the nanochannels of the nanofluidic devices are made of. One possibility is the adsorption effect. If hydrocarbons were adsorbed on the surface of nanopores, this adsorption may lead to: (1) narrower pore radii and (2) composition changes in the liquid phase. Let’s look at the narrowed pore size due to adsorption first. The narrowed pore radii give rise to higher capillary effect according to the Young-Laplace equation, thus yielding an increase in bubble point temperatures. This is opposite to the observation and makes the difference between the experimental data and predicted values even bigger. Then let’s look at the composition variation. If liquid composition becomes lighter and in the extreme case the liquid becomes pure n-pentane, we can see from Figure 3 that the predicted boiling point temperatures of pure n-pentane are 414.0 K and 371.4 K in the presence of capillary pressure effect only as well as both capillary pressure and nanopore confinement effects at r = 5 nm. These values are still much higher than the experimental value of 338.6 K. On the other hand, if liquid composition becomes heavier and in the extreme case the liquid becomes n-heptane, the predicted boiling point temperatures of pure n-heptane are even higher than those of pure n-pentane as shown in Figure 3. Therefore, these two factors should not result in such a small influence on bubble point temperature. Other explanations could be that the wall of nanopores in the nanofluidic devices may not be fully wetted by the mixtures of n-pentane and n-heptane or that weak interactions between the wetting phase and the wall of nanopores tend to significantly reduce the influence of capillary pressure. In this study, λ was then adjusted to match the experimental data at r = 5 nm as suggested by Barsotti. [25] The calculated results after tuning are also illustrated in the lower part of Figure 5(a). It can be seen that the model with capillary pressure effect only (λ = -145.9) matches the experimental data well with an average deviation of 0.8 K. Whereas the model with both capillary pressure and nanopore confinement effects (λ = -14.0) gives a larger average deviation of ~6 K and even a wrong trend in contradiction to the experiment. Similar to those results of pure components shown in Figure 3, the bubble point temperatures at atmospheric pressure predicted by the model with both capillary pressure and nanopore confinement effects increase to achieve a maximum value and then decrease with decreasing pore radius. Figure 5(b) depicts the variations of bubble point curves in phase envelopes with pore radius predicted by the model in the presence of both capillary pressure and nanopore confinement effects without tuning λ. The bubble point curves cross over in the lower temperature and pressure region. Pure components have similar behavior. This explains why a maximum value can be observed in Figure 5(a) for the mixture and Figure 3 for pure components. This behavior results from the critical property shift only and causes a wrong trend against experiments. Figure 6 illustrates the physical property variations for the n-pentane (50 mol%) + n-heptane (50 mol%) mixture in the presence of capillary pressure effect only with and without tuning λ. Liquid density significantly decreases and vapor density increases with decreasing pore radius when λ = 0 as shown in Figure 6(b) because bubble point temperatures increase with a decrease in pore radius as shown in Figure 5(a). This gives rise to a significant decrease in IFT with a decrease in pore radius as depicted in Figure 6(a). On the other hand, according to the Young-Laplace equation, reduction of pore radius and IFT results in opposite effects on capillary pressure. Contribution of pore radius reduction to capillary


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pressure is much bigger than that of IFT reduction. Therefore, capillary pressure considerably rises with a decrease in pore radius as illustrated in Figure 6(a). After tuning λ = -145.9, liquid density decreases and vapor density increases very slightly with a reduction in pore radius as given in Figure 6(b). Because bubble point temperatures are low and far away from the critical point, IFT values in Figure 6(a) change slightly from 14.7 to 13.7 mN/m when pore radius changes from 1000 to 5 nm, which are much higher than those (from 14.7 to 3 mN/m) without tuning λ. Hence, λ = -145.9 is needed to match the experimental data, which corresponds to weak wettability.

Figure 6. Physical property variations for the n-pentane (50 mol%) + n-heptane (50 mol%) mixture in the presence of capillary pressure effect only. (a) Variation of capillary pressure and interfacial tensions with pore radius at atmospheric pressure with and without tuning λ; (b) Variation of liquid and vapor densities with pore radius at atmospheric pressure with and without tuning λ. In the presence of both capillary pressure and confinement effects, because of CP shift, IFT values become lower. Thus, a lower λ value is required to match the measured data. Alfi et al. [6] also measured bubble point temperatures for the n-pentane (50 mol%) + n-hexane (50 mol%) mixture and the n-pentane (40 mol%) + n-hexane (30 mol%) + n-heptane (30 mol%) mixture. We compared the calculated bubble point temperatures with the experimental data for the two mixtures as shown in Figure 7. The results are similar to those of the n-pentane (50 mol%) + n-heptane (50 mol%) mixture. The adjusted parameters are very close for the three mixtures, λ = -142.2 ~ -167.5 in the presence of capillary pressure effect only and is a constant (λ = -14.0) in the presence of both capillary pressure and confinement effects. The model with capillary pressure effect only and partial wettability presumption matches the experimental data satisfactorily. Whereas the model with the effects of both capillary pressure and confinement gives an incorrect trend against the experimental data. It implies that only changing critical properties of pure components in the cubic EOS may not be sufficient. Further investigation is required.


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Figure 7. Variation of bubble point temperatures with pore radius at atmospheric pressure with and without tuning λ. (a) Binary n-pentane (50 mol%) + n-hexane (50 mol%) mixture; (b) Ternary n-pentane (40 mol%) + n-hexane (30 mol%) + n-heptane (30 mol%) mixture. Experimental data are taken from [6]. The model with capillary pressure only and partial wettability presumption matches the experimental data satisfactorily. Reservoir Fluids We chose two unconventional reservoir fluids: Eagle Ford shale gas [25] and Wolfcamp shale oil [19] to test the aforementioned framework and algorithm. The characterization procedure of Zuo and Zhang [37] and Zuo et al. [38] was utilized to characterize the reservoir fluids and the SKR EOS was used to describe the phase behavior of the reservoir fluids. The characterized compositions and critical properties of the reservoir fluids are given in the Appendix. The phase envelopes including the critical point, cricondentherm and cricondenbar were generated by the aforementioned framework and algorithm. The results are shown in Figure 8 for the Eagle Ford shale gas. Figure 8(a) shows that in the presence of capillary pressure effect only, the predicted bubble point pressures are slightly lower than those in the bulk at a specified temperature whereas the predicted retrograde dew point pressures are slightly higher than those in the bulk. The difference between the bulk and nanopores increases with a decrease in pore radius (not shown in Figure 8(a)), in particular in the low-pressure region where capillary pressure are often large. The algorithm can be easily implemented to generate quality-lines as shown in Figure 8(a) where the fixed vapor mole fraction (β) lines of β = 0.5, β = 0.8 (0.2) and β = 0.9 (0.1) are given. On the other hand, if both capillary pressure and confinement effects are present, the results are quite different from those in the presence of capillary pressure effect only as shown in Figure 8(b). Critical points move toward the lower temperature and pressure region with pore radius decreasing. The dew point curves change significantly for small pore radius. The dew point pressure is much lower than that in the bulk at a specified temperature, even fully disappears. For example, if we take a typical Eagle Ford reservoir temperature of 441.5 K, when r = 3 nm, no phase change will occur to this fluid at any pressure. Figure 8(b) also depicts the variations of cricondentherms and cricondenbars with pore radius. The quality-lines were also smoothly generated in the case of r = 5 nm at the fixed vapor mole fraction (β) of β = 0.5, β = 0.2 (0.8) and β = 0.1 (0.9) as shown in Figure 8(b). For gas condensate mixtures, field production data show that produced liquid and gas ratios decrease even at reservoir pressures above bulk retrograde dew points. However, predictions from the model with CP


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shift point to a different direction. This obviously contradicts the field observation. Therefore, a great deal of research activities in this area are required.

Figure 8 Phase envelopes predicted by the models for the Eagle Ford shale gas in the presence of capillary pressure only as well as both capillary pressure and confinement. (a) Effect of capillary pressure only; (b) Effect of capillary pressure and confinement. λ = 0.

Figure 9 compares the variations of the dew point pressures predicted by the models in the presence of capillary pressure effect only as well as in the presence of both capillary pressure and confinement effects with pore radius at reservoir temperature of 441.5 K. At smaller pore sizes, the effects of both capillary pressure and confinement on dew point pressures appears to be significant. Capillary pressure and confinement oppositely influence dew point pressures while the latter seems to be dominant.


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Figure 9 Variations of the dew point pressures predicted by the models in the presence of capillary pressure effect only as well as both capillary pressure and confinement effects at 441.5 K for the Eagle Ford shale gas. Capillary pressure and confinement oppositely influence dew point pressures. λ = 0.

Figure 10 depicts the phase envelopes predicted by the models in the presence of capillary pressure effect only as well as in the presence of both capillary pressure and confinement effects for the Wolfcamp shale oil. In the presence of capillary pressure only, the predicted bubble point pressures are lower than those in the bulk at a specified temperature whereas the predicted retrograde dew point pressures are slightly higher than those in the bulk. In the presence of both capillary pressure and confinement, the bubble point pressures are shown to be considerably lower than those in the bulk at a given temperature, particularly when pore radius is very small. It may change fluid types from oil to gas condensate in very small pores. The ground truth deserves deeper investigation in the future.


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Figure 10 Phase envelopes predicted by the models for the Wolfcamp shale oil in the presence of capillary pressure only as well as both capillary pressure and confinement. (a) Effect of capillary pressure only; (b) Effect of capillary pressure and confinement. λ = 0.

Figure 11 compares the variations of the bubble point pressures predicted by the models in the presence of capillary pressure effect only as well as in the presence of both capillary pressure and confinement effects with nanopore radius at reservoir temperature of 397 K. In very small nanopores, the effects of both capillary pressure and confinement are significant. Both capillary pressure and confinement decrease bubble point pressures.


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160

Bubble point pressure, atm

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140

Bubble P (CP shift) 120 Bubble P (no CP shift) 100

Bulk bubble P

80 0

20

40

60

80

100

Pore radius, nm

Figure 11 Comparison of variations of bubble point pressures predicted by the models in the presence of capillary pressure only as well as both capillary pressure and confinement at 397 K for the Wolfcamp shale oil. Both capillary pressure and confinement decrease bubble point pressures. λ = 0.

In the presence of both capillary pressure and confinement effects, the aforementioned predictions imply that both shale gas or oil have phase changes in turn in the bulk, big pores, and then small pores during depressurization. However, in the presence of capillary pressure effect only, shale gas has opposite behavior, i.e., phase changes occur sequentially in small pores, big pores, and then the bulk phase. Future experimental study is in demand to identify the more realistic mechanism between these two assumptions. Conclusions A general framework of theoretical models and algorithm has been developed to predict phase envelopes of shale gas and oil in nanopores, including critical points, cricondentherms and cricondenbars. The SRK EOS has been used for phase behavior calculations and the parachor IFT model of Zuo and Stenby was employed for interfacial tensions in capillary pressure estimation. The impact of nanopore confinement has been accounted for by the critical property shifts of pure components. The algorithm has proven to be robust for generating phase envelopes for a variety of fluids at different compositions, vapor mole fractions (quality lines) and nanopore sizes. The models and algorithm have been used to elucidate the recently measured data of normal boiling point or bubble point temperatures for pure n-heptane in type I kerogen, binary n-pentane (50 mol%) + n-hexane (50 mol%) and n-pentane (50 mol%) + n-heptane (50 mol%) and ternary n-pentane (40 mol%) + n-hexane (30 mol%) + n-heptane (30 mol%) mixtures in the nanofluidic devices. For pure n-heptane in type I kerogen, by assuming nanopores are completely wetted by the liquid phase, the model predictions agree with the experimental data and a reasonable range of type I kerogen nanopore distributions were obtained in the presence of capillary pressure effect only as well as both capillary pressure and nanopore confinement effects. However, for the binary and ternary mixtures in the nanofluidic devices, the completely wetting assumption seems no longer valid. The fluid-wall interaction parameter (λ ) has been adjusted to match the experimental data. The adjusted parameters for the three-tested binary and ternary mixtures are: λ = -142.2 ~ -167.5 in the presence of capillary pressure effect only and λ = -14.0 in the presence of both capillary pressure and confinement effects. The models


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give a correct trend for the mixtures in the presence of capillary pressure effect only but a wrong trend against the measured data in the presence of both capillary pressure and nanopore confinement effects. In the presence of both capillary pressure and confinement effects, the model predicts a decrease in bubble and dew point pressures with decreasing pore radius for shale gas and oil, i.e., both shale gas and oil in turn have phase changes in the bulk, big pores, and then small pores during depressurization. However, in the presence of capillary pressure effect only, the model predicts a decrease in bubble point pressures for shale oil while an increase in dew point pressures for shale gas with decreasing nanopore radius. In shale gas, phase changes occur sequentially in small pores, big pores, and then the bulk phase if only capillary pressure is present. For gas condensate mixtures, field production data show that produced liquid and gas ratios decrease even at reservoir pressures above bulk retrograde dew points. It is obvious that the model with critical property shift contradicts the field observation. Therefore, a great deal of research activities in this area are required.

References [1] Pitakbunkate, T., Balbuena, P.B., Moridis, G.J., Blasingame, T.A., “Effect of Confinement on Pressure/Volume/Temperature Properties of Hydrocarbons in Shale Reservoirs”, J. SPE, April, 621-634 (2016). [2] Tindy, R., Raynal, M., “Are Test-Cell Saturation Pressures Accurate Enough?” Oil and Gas Journal, 1966, 64(126). [3] Trebin, F. A. et al., “Experimental Study of the Effect of a Porous Media on Phase Change in Gas Condensate System”, Neft' i Gaz, 1968, 8(37). [4] Sigmund, P.M., Dranchuk, P.M., Morrow, N.R., Purvis, R.A., “Retrograde Condensation in Porous Media”, SPE J. 93-105 (1973). SPE# 3476 https://doi.org/10.2118/3476-PA [5] Pathak, M., Velasco, R., Panja, P., Deo, M.D., “Experimental Verification of Changing Bubble Points of Oils in Shales: Effect of Preferential Absorption by Kerogen and Confinement of Fluids”, SPE# 187067-MS, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9-11 October, 2017. [6] Alfi, M., Nasrabadi, H., Banerjee, D., “Effect of Confinement on Bubble Point Temperature Shift of Hydrocarbon Mixtures: Experimental Investigation Using Nanofluidic Devices”, SPE#187057-MS presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9-11 October, 2017. [7] Zarragoicoechea, G.J., Kuz, V.A., “Critical Shift of a Confined Fluid in a Nanopore”, Fluid Phase Equilibria 220, 7-9 (2004). [8] Vishnyakov, A.; Piotrovskaya, E. M.; Brodskaya, E. N.; Votyakov, E. V.; Tovbin, Yu.K. Critical Properties of Lennard-Jones Fluids in Narrow Slit-Shaped Pores. Langmuir 2001, 17, 4451-4458. [9] Hamada, Y., Koga, K., Tanaka, H., “Phase Equilibria and Interfacial Tension of Fluids Confined in Narrow Pores”, J. Chem. Physics, 127 (8), 084908 (2007). https://doi.org/10.1063/1.2759926 [10] Singh, S.K., Sinha, A., Deo, G., Singh, J.K., “Vapor-Liquid Phase Coexistence, Critical Properties, and Surface Tension of Confined Alkanes”, J. Phys. Chem. C, 113, 7170-7180 (2009). [11] Singh S.K., Singh, J.K., “Effect of Pore Morphology on Vapor-Liquid Phase Transition and Crossover Behavior of Critical Properties from 3D to 2D”, Fluid Phase Equilibria , 300 182-187 (2011). [12] Alharthy NS, Nguyen TN, Kazemi H, Teklu TW, Graves RM. Multiphase compositional modeling in small-scale pores of unconventional shale reservoirs. In: SPE annual technical conference on exhibition. New Orleans (Louisiana, USA): Society of Petroleum Engineers; 2013. p. 1–20. http://dx.doi.org/10.2118/166306-MS. [13] Brusilovsky, A. I., “Mathematical Simulation of Phase Behavior of Natural Multicomponent Systems at High Pressures with an Equation of State”, SPE Reservoir Engineering 7(1), 117-122 (1992).


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[14] Guo, P., Sun, L., Li, S. Sun, L., “A Theoretical Study of the Effect of Porous Media on the Dew Point Pressure of a Gas Condensate”, SPE# 35644-MS, presented at the SPE Gas Technology Symposium & Exhibition, Calgary, 28 April–1 May, 1996. https://doi.org/10.2118/35644-MS [15] Pang, J., Zuo, J.; Zhang, D.; Du, L., “Effect of Porous Media on Saturation Pressures of Shale Gas and Shale Oil”, IPTC# 16419-MS, presented at the International Petroleum Technology Conference, Beijing, China, 26-28 March 2013, pp 26-28. https://doi.org/10.2523/IPTC-16419-MS [16] Nojabaei, B.; Johns, R. T.; Chu, L. Effect of Capillary Pressure on Phase Behavior in Tight Rocks and Shales. SPE Reservoir Eval. Eng., 16, 281-289 (2013). [17] Wang, L., Yin, X., Neeves, K.B., Ozkan, E., “Effect of Pore-Size Distribution on Phase Transition of Hydrocarbon Mixtures in Nanoporous Media”, SPE J., December, 1981-1995 (2016). [18] Sandoval, D.R., Yan, W., Michelsen, M.L., Stenby, E.H., “The Phase Envelope of Multicomponent Mixtures in the Presence of a Capillary Pressure Difference”, Ind. Eng. Chem. Res., 55, 6530-6538(2016). [19] Li, L., Sheng, J.J., “Nanopore Confinement Effects on Phase Behavior and Capillary Pressure in a Wolfcamp Shale Reservoir” J. Taiwan Institute of Chem. Eng., 78, 317-328 (2017). [20] Shapiro, A.; Stenby, E.H., “Kelvin equation for a non-ideal multicomponent mixture”, Fluid Phase Equilibria, 134, 87-101 (1997). [21] Shapiro, A.; Stenby, E.H., “Thermodynamics of the multicomponent vapor - liquid equilibrium under capillary pressure difference”, Fluid Phase Equilibria, 178, 17-32 (2001). [22] Travalloni, L., Castier, M., Tavares, F.W., Sandler S.I., “Critical Behavior of Pure Confined Fluids from an Extension of the van der Waals Equation of State”, J. Supercritical Fluids, 55, 455-461 (2010). [23] Travalloni, L., Castier, M., Tavares, F.W., “Phase Equilibrium of Fluids Confined in Porous Media from an extended Peng-Robinson Equation of State”, Fluid Phase Equilibria, 362, 335-341 (2014). [24] Dong, X., Liu, H., Hou, J., Wu, K., Chen, Z., “Phase Equilibria of Confined Fluids in Nanopores of Tight and Shale Rocks Considering the Effect of Capillary Pressure and Adsorption Film”, Ind. Eng. Chem. Res., 55, 798-811 (2016). [25] Barsotti, E., Tan, S.P., Saraji, S., Piri, M., Chen, J.-H., “A review on capillary condensation in nanoporous media: Implications for hydrocarbon recovery from tight reservoirs”, Fuel, 184, 344-361 (2016). [26] Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59-64 (1976). [27] Macleod, D. B. On a relation between surface tension and density. Trans. Faraday Soc., 19, 38-41 (1923). [28] Sugden, S. A relation between surface tension, density, and chemical composition. J. Chem. Soc., Trans., 125, 1177-1189 (1924). [29] Michelsen, M.; Mollerup, J. Thermodynamic Models; Fundamentals and Computational Aspects; Tie-Line Publications: 1998. [30] Tan SP, Piri M. “Equation-of-state modeling of confined-fluid phase equilibria in nanopores”, Fluid Phase Equilibria, 393, 48–63 (2015). http://dx.doi.org/10.1016/j.fluid.2015.02.028. [31] Zuo, Y., and Stenby, E. H., “Corresponding-States and Parachor Models for the Calculation of Interfacial Tensions", Can. J. Chem. Eng., 75, 1130-1137 (1997). [32] Soave, G., “Equilibrium Constants from a Modified Redlich-Kwong Equation of State,” Chem. Eng. Sci., 27, 1197-1203 (1972). [33] Jin, L., Ma, Y., Jamili, A., “Investigating the Effect of Pore Proximity on Phase Behavior and Fluid Properties in Shale Formations”, SPE-166192-MS, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 30 September-2 October, 2013. [34] Ma, Y., Jin, L., Jamili, A., “Modifying van der Waals Equation of State to Consider Influence of Confinement on Phase Behavior”, SPE-16676-MS, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 30 September-2 October, 2013. [35] Michelsen, L. Calculation of phase envelopes and critical points for multicomponent mixtures. Fluid Phase Equilibria, 4, 1-10 (1980).


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[36] Abdulagatov, I.M., Adamov, A.P., Abdurakhmanov, I.M., “Surface tension coefficient of the npentane+n-heptane system near the “liquid-gas” critical point” J. Eng. Phys. & Thermophys., 63(6), 1193-1198 (1992). [37] Zuo, J.Y.; Zhang, D. “Plus Fraction Characterization and PVT Data Regression for Reservoir Fluids near Critical Conditions” SPE# 64520-MS, presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, Australia, 16-18 October, 2000. https://doi.org/10.2118/64520-MS [38]. Zuo, J.Y., Zhang, D., Dubost, F.X., Dong, C., Mullins, O. C., O'Keefe, M., Betancourt, S.S., “EOSBased Downhole Fluid Characterization”, SPE Journal, 16(1), 115–124 (2011).

Appendix The characterized compositions and critical properties of the Eagle Ford shale gas are given in Table A1. Table A1 Characterized compositions and critical properties of the Eagle Ford shale gas Component N2 CO2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7-C8 C9-C10 C11-C13 C14-C17 C18-C80

Molecular weight g/mol 28.01 44.01 16.04 30.07 44.1 58.12 58.12 72.15 72.15 84 100.79 127.21 158.91 209.38 304.09

Critical P kPa 3394.4 7381.5 4599 4872 4248 3648 3796 3380 3370 3010.3 2958.8 2477.6 2191.7 1944.7 1815.2

Critical T K 126.1 304.2 190.6 305.3 369.8 408.1 425.1 460.4 469.7 507.5 541.6 583.9 627.4 684.3 773

Acentric factor 0.0403 0.2276 0.0115 0.0995 0.1523 0.177 0.2002 0.2279 0.2515 0.299 0.4818 0.5573 0.6449 0.7765 0.9949

Composition mol % 0.10 0.22 27.80 11.85 10.30 5.55 1.58 2.99 1.70 4.21 7.90 6.40 7.42 6.01 5.97

The characterized compositions and critical properties of the Wolfcamp shale oil are given in Table A2.


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Table A2 Characterized compositions and critical properties of the Wolfcamp shale oil Component C1 C2 C3 C4 C5 C6 C7-C10 C11-C15 C16-C20 C21-C28 C29-C80

Molecular weight g/mol 16.04 30.07 44.10 58.12 72.15 84.00 112.62 172.36 246.49 330.46 512.27

Critical P kPa 4599.0 4872.0 4248.0 3796.0 3370.0 3010.3 2494.6 1908.8 1649.8 1568.9 1569.6

Critical T K 190.6 305.3 369.8 425.1 469.7 507.5 556.2 637.2 713.3 785.8 917.8


Acentric factor 0.01150 0.09950 0.15230 0.20020 0.25150 0.29900 0.51567 0.68063 0.86643 1.04787 1.31193

Composition mol % 33.84 8.80 9.69 6.01 4.25 4.57 12.35 9.13 5.06 3.85 2.45

Impact of Capillary Pressure and Nanopore Confinement on Phase

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