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URTeC 1582144
Compositional Modeling of Liquid-Rich Shales Considering
Adsorption, Non-Darcy Flow Effects and Pore Proximity Effects on
Phase Behavior
X. Xiong, D. Devegowda, F. Civan, University of Oklahoma, R.F. Sigal, Consultant, A.
Jamili, University of Oklahoma
Copyright 2013, Unconventional Resources Technology Conference (URTeC)
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Denver, Colorado, USA, 12-14 August 2013.
The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper
have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is
subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not
necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper without the written consent of URTeC is prohibited.
Summary
Impact of pore proximity on transport of gas in nano-scale organic and inorganic pores is investigated by
consideration of several effects, including the fractioning of different hydrocarbon species causing the composition
of the non-adsorbed fluid phase to vary during transport through the reservoir, alteration of the hydrocarbon phase
behavior and permeability by the pore proximity effects, and the influence of the adsorbed layer and non-Darcy flow
effects in the non-adsorbed fluid. This is accomplished by developing a compositional model that accounts for all
the phenomena necessary to quantify transport in organic and inorganic pores in shales and the permeability
multiplier curves appropriate for non-adsorptive and adsorptive nanoporous media. The significance of the pore
proximity and adsorptive phase correction to the critical properties and the apparent permeability on gas and
condensate production over a wide range of pressure is demontrated. These additional corrections made to the phase
behavior and PVT properties are shown to substantially influence the well production trends. These modifications
indicate that the production of valuable components is underestimated in conventional simulation approaches and oil
prouduction will last for a longer period in extremely tight formations. However, the heavier components in organic
pores are more difficult to recover than dry gas methane from organic pores. Further, we show that effective gas
permeability could be 10 times as much as effective oil permeability.
Introduction
Although liquids-rich shale plays are economically producible, the existing conventional reservoir simulation
technology fails to include many of the production phenomena encountered in liquids-rich plays. Xiong et al.(2012)
pointed out the complex transport issues involved in the presence of adsorptive layer and non-Darcy flow conditions.
The free and adsorptive transport model of Xiong et al.(2012) is only applicable to gas comprising of a single gas
component. A multi-component transport model is necessary to correctly model the fluid system that consists of
multiple gas species or phases.
Freeman et al.(2009) extended the mean free path of a single component gas to each component in a mixture of
variable species. The non-Darcy flow effects and the total apparent gas permeability of the mixture are different in
the presence of the interactions with other species. Further, the liquids reduce the pore space available for gas flow
through the pores. The loss in pore space reduces the apparent permeability for gas, but not as much as in a
conventional reservoir as the smaller pore size increases the non-Darcy term in the permeability expression.
Moreover, because the oil is less mobile than gas in nano pores, the flowing fluid composition changes along the
trasnsport path. In nanometer scale pores fluid phase diagrams are a function of pore size(Singh et al, 2011,
Devegowda et al, 2012). Conventional PVT analysis assuming bulk fluid behavior is inadequate for pore sizes found
in liquids-rich shale reservoirs, which range from a few to a hundred nanometers. This paper presents a
comprehensive modeling approach to address the fluid phase behavior under confined condition and flowing
compositional dynamics in consideration of adsorption, non-Darcy flow, and pore pore proximity effects.
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2
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Phase Behavior in Nano-pores
The liquids-rich shale reservoirs are extremely tight having pore sizes in orders of nanometers. The hydrocarbon
fluids confined in nano pores exhibit different phase behavior from the bulk fluid conditions assumed in
conventional PVT modeling. Devegowda et al. (2012) indicated pore morphology and pore surface-fluid attraction
(Singh et al., 2011) affect the critical properties of fluids confined in pore sizes of 4-50 molecular diameters. Critical
properties of fluids confined in nano pores deviate significantly from that of bulk fluids in pore sizes that range up to
an order of magnitude larger than the molecular size. Critical temperature of confined fluids becomes smaller with
decreasing pore sizes in both attractive and non-attractive cylindrical pores, and approaches bulk values with
increase in pore diameter. Critical pressure behavior is similar to that of critical temperature, with the exception that
for attractive pore walls it overshoots the bulk fluid value before approaching the value for the bulk system. The
different behavior in attractive pores reflects that adsorption alters the vapor-liquid equilibrium in nano pores. The
shifted phase behavior in nano pores distinguishes PVT analysis of liquids-rich shale from the conventional
modeling approach. The pore proximity effects on critical properties are delineated for 4, 6, 10, and 20 nm diameter
non-attractive and attractive cylindrical pores in Table.1 and Table.2, respectively. The critical properties are
computed for each species using the ratio of critical properties in confined nano pores to that in the bulk from for
different pore width and molecular size ratios Singh et al. (2011), assuming the average size of 0.4nm for molecules.
Table.1 Critical temperature of bulk and confined fluid
Tc,°F
Component
Bulk
Nonattractive
cylinder
pore
Attractive
cylinder
pore
4nm
6nm
10nm
20nm
4nm
6nm
10nm
20nm
Component
Bulk
Nonattractive
cylinder
pore
Attractive
cylinder
pore
4nm
6nm
10nm
20nm
4nm
6nm
10nm
20nm
C1
-116.7
-152.7
-135.8
-124.5
-120.0
-183.0
-155.3
-134.2
-127.0
C1
666.4
393.7
495.4
567.1
657.8
2025.0
2175.6
1849.5
989.9
C2
89.9
32.2
59.3
77.3
84.6
-16.3
28.1
61.8
73.4
C3
206.1
136.1
168.9
190.8
199.6
77.3
131.2
172.0
186.1
n-C4
305.6
225.2
262.9
288.1
298.2
157.7
219.5
266.4
282.7
n-C5
385.8
296.9
338.6
366.4
377.6
222.3
290.7
342.5
360.4
Table.2 Critical pressure of bulk and confined fluid
Pc, psia
C2
C3
n-C4
n-C5
706.5
616.4
550.6
488.6
417.4
364.2
325.3
288.7
525.2
458.2
409.3
363.2
601.2
524.6
468.6
415.8
697.3
608.4
543.5
482.3
2146.8
1873.1
1673.1
1484.7
2306.5
2012.4
1797.5
1595.1
1960.7
1710.7
1528.1
1356.0
1049.5
nt915.7
817.9
725.8
C6
453.6
357.6
402.6
432.7
444.7
277.0
350.9
406.8
426.2
C7+
729.3
604.4
663.0
702.1
717.8
499.4
595.6
668.5
693.7
C10
652.0
535.2
590.0
626.5
641.2
437.1
526.9
595.1
618.6
C6
483.0
285.4
359.1
411.0
476.7
1467.7
1576.9
1340.5
717.5
C7+
318.4
188.1
236.7
271.0
314.3
967.5
1039.5
883.7
473.0
C10
305.2
180.3
226.9
259.7
301.2
927.4
996.4
847.0
453.4
Phase diagrams for synthetic and black oil in non-attractive and attractive cylindrical pores are shown in Fig.1 and
Fig.2. The dashed straight lines represent reservoir temperature and the reservoir fluids are produced at isothermal
conditions. A synthetic oil case and a black oil case are studied, with each fluid composition and reservoir
temperature specification given in Table.3. Conventional PVT models, which don’t account for the fluid properties
shifts in confined space, fail to capture the correct phase behavior under the pore proximity effect. We studied the
phase diagrams for synthetic oil and black oil for both non-attractive and attractive cylindrical pores.
The pore confinement effect significantly alters the phase envelops and critical points of the reservoir fluids bearing
in ultra-tight formations, as illustrated in Fig.1. At typical reservoir pressures reservoir fluids start out in a single oil
phase. As pressure drops the transition to a two-phase occurs at lower and lower pressures as pore size decreases.
This will improve oil production rates and more importantly production of the more valuable components. In
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URTeC 1582144
3
attractive confined nano pores, the interaction between the wall and fluid causes the phase envelop to change
dramatically, shown in Fig.2. The two phase region occurs at lower temperature but at higher pressures as pore size
decreases. Fluid ordinary in liquid state at initial reservoir condition goes into two-phase zone. Liquids and gas are
produced at the same time with the initialization of pressure dropdown in the organic pores. In Fig.3, the liquid takes
up from 0.5 to 0.84 in mole percentage in adsorptive pores and increases with increment in pore width. In presence
of increasing vapor fraction in the fluid mixture in smaller organic pores, the heavier components become more
difficult to recover compared to only oil flow, because heavier components have tendency to be in the liquid.
Table. 3 Fluid compositions for synthetic oil and black oil studies
Mole fraction, %
Molecular
Acentric factor
Black Oil
weight, lb/mole
Synthetic Oil
(McCain, 1933)
Component
(modified after
(McCain, 1933)
(McCain, 1933)
McCain, 1933)
Case
Reservoir
temperature, °F
250
150
-
-
C1
C2
C3
n-C4
n-C5
C6
C7+
C10
53
11
36
37.54
9.67
6.95
5.37
2.85
4.33
33.29
-
16.043
30.070
44.097
58.123
72.150
86.177
218.000
142.285
0.0104
0.0979
0.1522
0.1995
0.2514
0.2994
0.3493
0.4898
(a) Synthetic oil
(b) Black oil
Fig. 1 Phase diagram for synthetic and black oil in hard cylindrical pores
(a) Synthetic oil
(b) Black oil
Fig.2 Phase diagram for synthetic and black oil in attractive cylindrical pores
URTeC 2013
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4
1.0
1.0
0.8
0.8
Moles of Liquid
Moles of Liquid
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URTeC 1582144
0.6
0.4
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.2
0.0
0
500
1000
1500
2000
2500
0.6
0.4
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.2
0.0
3000
0
500
1000
1500
Pressure, psia
Pressure, psia
(a) Synthetic oil
(b) Black oil
2000
Fig.3 Moles of liquid for fluid in the bulk and fluid confined in attractive cylindrical pores
Non-Darcy Flow Model
The pore proximity and pore wall interactions with fluids do not only effect the produced gas composition. The
slippage of gas molecules at different velocities in nano pores can also contribute to the varying producing fluid
composition with time. Xiong et al. (2012) proposed an apparent permeability correction in organic pores for single
component. The apparent permeability varies with different hydrocarbon species. For the liquids-rich shale
reservoirs, the apparent permeability correction for multi-component mixtures should be made by using a mean free
path j which differs for each component in the mixture. Freeman et al. (2009) proposed the mean free path of a
single species labeled as 1 in a n-component gas mixture using the ideal gas law as:
1 
v1
n
 d1d i
i 1
v12

vi2
(1)
N A Pi
RT
where Pi - partial pressure of component i , Pa , N A - Avogadro constant, mol 1 , R - gas constant, J ( K  mol ) ,
T - temperature, K , d i - Lennard-Jones potential parameter, m , and vi - average velocity of a single component in
gas mixture, m / s , given by:
8RT
(2)
M
The Lennard-Jones potential diameters are defined where the potential is zero. Table. 4 gives their values for C1
through C7 and C10.
v
Table. 4 Lennard-Jones potential parameter
Component
C1
C2
C3
n-C4
n-C5
C6
C7
C10
L-J parameter(Å)
4
4.8
5.5
6.1
6.7
7.3
7.9
9.6
In pores with both gas and liquid phase, the hydraulic radius will change with the volume available to gas flow. The
effective hydraulic radius in two phase flow region is modified according to the saturation of gas.
Reff  R S g
(3)
Each species has a Knudsen number corresponding to its mean free path,
Kni 
i
Reff
(4)
with a Knudsen correction, given as
4 Kni
)
1  Kni
The producing gas composition is influenced by fractioning effect of Knudsen diffusion velocity for different
species. Thus, define the flowing gas composition as:
f ( Kni )  (1   ( Kni ) Kni )(1 
(5)
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5
y f ( Kni )
~
yi  n i
 yi f ( Kni )
(6)
y i is the phase equilibrium composition of component i in mole fractions in the vapor phase.
The molar flux of the multi-component mixture n is the summation of molar flux of each component,
in which
n
n 
 nvi K  f ( Kni )
i 1

P
(7)
The apparent permeability for multi-component gas mixture K ai is given in the formula below
n  nv
K amix

P
(8)
Equating above two equations yields,
n
K amix  K   yi f ( Kni )
(9)
i 1
in which yi  ni nv .
The effective gas permeability K g in two phase flow
K g  KamixSg
(10)
The effective oil permeability K o in two phase flow
K o  K  So
(11)
We define the permeability multiplier of each phase by diving effective permeability of oil and gas with absolute permeability.
Therefore the permeability multipliers for gas and oil are as below
K rg  K amixS g K 
(12)
K ro  So
(13)
Case Studies – Synthetic Oil
Synthetic oil is produced at 250°F with pressure depleting from 3000psia to 200 psia. For the sake of convenience,
all the phase-equilibria calculations are performed on the basis of one mole of the hydrocarbon mixture.The molar
fraction of each species or total number of moles in the vapor phase out of the entire mixture is modeled using
conventional PVT mode for bulk fluids. In the scenaios of fluids confined in nano pores, conventional approach is
modified using shifted critical temperatures and pressures in non-attractive and attractive pores. The corresponding
compositional dynamics are shown in Fig.4, Fig.5 and Fig.6 for methane, n-butane and decane.
Methane
0.8
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.6
0.4
0.2
0.0
Mole Fraction of C1 in the Vapor
Phase
Mole Fraction of C1 in the Vapor
Phase
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i 1
Methane
0.8
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.6
0.4
0.2
0.0
-0.2
-0.2
0
500
1000
1500
2000
Pressure, psia
(a) Static fluid in non-attractive pores
2500
3000
0
500
1000
1500
2000
Pressure, psia
2500
3000
(b) Flowing fluid in attractive pores
URTeC 2013
Page 2380
Mole Fraction of C1 int eh Vapor
Phase
Mole Fraction of C1 in the Vapor
Phase
6
Methane
0.8
0.6
0.4
0.2
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.0
-0.2
0
500
1000
Methane
0.8
0.6
0.4
0.2
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.0
-0.2
1500
2000
Pressure, psia
2500
3000
0
(c) Static fluid in attractive pores
500
1000
1500
2000
Pressure, psia
2500
3000
(d) Flowing fluid in attractive pores
n-Butane
0.14
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.12
0.10
0.08
0.06
0.04
0.02
0.00
n-Butane
0.14
Mole Fraction of C1 inthe Vapor
Phase
Mole Fraction of C1 in the Vapor
Phase
Fig.4 Molar percentage of methane in the vapor phase in synthetic oil
-0.02
Static
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
0
500
1000
1500
2000
Pressure, psia
2500
3000
0
n-Butane
0.14
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.12
0.10
0.08
500
1000
1500
2000
Pressure, psia
2500
3000
(b) Flowing fluid in attractive pores
0.06
0.04
0.02
0.00
-0.02
Mole Fraction of NC4 in the Vapor
Phase
(a) Static fluid in non-attractive pores
Mole Fraction of NC4 in the Vapor
Phase
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URTeC 1582144
n-Butane
0.14
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
0
500
1000
1500
2000
Pressure, psia
2500
(c) Static fluid in attractive pores
3000
0
500
1000
1500
2000
Pressure, psia
2500
3000
(d) Flowing fluid in attractive pores
Fig.5 Molar percentage of n-butane in the vapor phase in synthetic oil
The pore proximity effect suppressed the occurrence of gas bubbles. The length of oil production only increases
with decreasing pore size. In organic pores, two phase flow starts in the beginning of pressure depletion. In the
vapor phase, molar percentage of methane increases more quickly than that of decane, indicating more decane left in
the liquid. The different velocities among species are reflected in the difference between the number of moles of the
flowing gas and phase equilibrium bulk fluid. The lighter component has a larger mean free path, then a larger
Knudsen correction, and thus moves faster. The non-Darcy flow effect contributes to enhanced flowing composition
of dry gas methane at low pressures. The differential velocities for various species in the mixture eliminate the
amount of flowing vapor of heavier components, n-butane and decane, as shown in Fig.5 and Fig.6. In attractive
pores, the total number of moles of each hydrocarbon species in vapor phase increases significantly at in-situ
pressure, especially decane. The mole fraction of flowing methane increases greatly even at initial reservoir pressure
URTeC 2013
Page 2381
URTeC 1582144
7
Decane
0.04
Mole Fraction of C10 in the Vapor
Phase
Mole Fraction of C10 in the Vapor
Phase
The flowing vapor composition is shown different from phase equilibrium vapor composition. And the composition
of hydrocarbons stored in inorganic pores also differs from that stored in organic pores. By simply using PVT data
obtained in the lab, we overlook the effect of pore confinement and fractioning effect between dry gas and liquids.
The percentage of fluid coming from pores in organic matters also adds complexity to the fluid composition both
underground and what we are producing.
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.03
0.02
0.01
0.00
-0.01
0
500
1000
1500
2000
Pressure, psia
2500
0.02
0.01
0.00
-0.01
0
Mole Fraction of C10 inthe Vapor
Phase
Mole Fraction of C10 in the Vapor
Phase
0.2
500
1000
1500
2000
Pressure, psia
2500
3000
(b) Flowing fluid in attractive pores
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.3
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.03
3000
Decane
0.4
Decane
0.04
(a) Static fluid in non-attractive pores
0.1
0.0
-0.1
Decane
0.4
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.3
0.2
0.1
0.0
-0.1
0
500
1000
1500
2000
Pressure, psia
2500
3000
0
(c) Static fluid in attractive pores
500
1000
1500
2000
Pressure, psia
2500
3000
(d) Flowing fluid in attractive pores
Fig.6 Molar percentage of decane in the vapor phase in synthetic oil
16
16
Kro
Krg(4nm)
Krg(6nm)
Krg(10nm)
Krg(20nm)
12
Kro
Krg(4nm)
Krg(6nm)
Krg(10nm)
Krg(20nm)
14
Permeability Multiplier
14
Permeability Multiplier
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due to fractioning effect of differential non-Darcy velocities. While the mole fraction of flowing n-butane and
decane decreases.
10
8
6
4
12
10
8
6
4
2
2
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
So
0.4
0.6
0.8
1
So
(a) In hard pores
(b) In attractive pores
Fig.7 Permeability multiplier of confined synthetic oil
URTeC 2013
Page 2382
8
The permeability multiplier of synthetic oil is shown in Fig.7. The gas permeability multiplier goes beyond that of
oil due to flow enhancement of gas slippage at the interface between oil and gas. Gas moves at a faster speed in
smaller pores. The enhancement of gas permeability could be as high as 15 times of absolute permeability in 4nm
pore at low oil saturation. The gas permeability doesn’t start to shoot up until the gas bubbles accumulate to certain
level. When liquid volume drops below certain point, oil is no longer movable and fluid flow becomes gas flow. The
valuable components are more likely to be left behind in the ultra-tight formations.
Methane
0.5
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.4
0.3
0.2
0.1
0.0
Methane
0.5
Mole Fraction of C1 in the Vapor
Phase
Mole Fraction of C1 in the Vapor
Phase
Case Studies – Black Oil
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.4
0.3
0.2
0.1
0.0
-0.1
-0.1
0
500
1000
1500
0
2000
500
1000
Methane
0.4
0.3
0.2
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.1
0.0
0
500
1500
2000
Methane
0.5
0.4
0.3
0.2
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.1
0.0
1000
Pressure, psia
2000
(b) Flowing fluid in hard pores
Mole Fraction of C1 in the Vapor
Phase
Mole Fraction of C1 in the Vapor
Phase
(a) Static fluid in hard pores
0.5
1500
Pressure, psia
Pressure, psia
1500
2000
0
(c) Static fluid in attractive pores
500
1000
Pressure, psia
(d) Flowing fluid in attractive pores
Fig.8 Molar percentage of methane in the vapor phase in black oil
n-Butane
0.05
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.04
0.03
0.02
0.01
0.00
-0.01
0
500
1000
1500
Pressure, psia
(a) Static fluid in hard pores
2000
Mole Fraction fo NC4 in the Vapor
Phase
Mole Fraction of NC4 in the Vapor
Phase
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URTeC 1582144
n-Butane
0.05
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.04
0.03
0.02
0.01
0.00
-0.01
0
500
1000
1500
2000
Pressure, psia
(b) Flowing fluid in hard pores
URTeC 2013
Page 2383
URTeC 1582144
9
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.04
0.03
0.02
0.01
0.00
Mole Fraction of NC4 in the Vapor
Phase
Mole Fraction of NC4 in the Vapor
Phase
n-Butane
-0.01
0.05
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.04
0.03
0.02
0.01
0.00
-0.01
0
500
1000
Pressure, psia
1500
2000
0
500
(c) Static fluid in attractive pores
1000
Pressure, psia
1500
2000
(d) Flowing fluid in attractive pores
Heptane+
0.020
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.015
0.010
0.005
0.000
-0.005
0
500
1000
1500
Mole Fraction of C7+ in the Vapor
Phase
Mole Fraction of C7+ in hte Vapor
Phase
Fig.9 Molar percentage of n-butane in the vapor phase in black oil
Heptane+
0.020
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.015
0.010
0.005
0.000
-0.005
0
2000
500
(a) Static fluid in hard pores
0.005
0.000
500
1000
Pressure, psia
1500
(c) Static fluid in attractive pores
2000
Mole Fraction of C7+ in the Vapor
Phase
0.010
0
2000
Heptane+
Bulk Fluid
Confined in 4nm
Confined in 6nm
Confined in 10nm
Confined in 20nm
0.015
1500
(b) Flowing fluid in hard pores
Heptane+
0.020
1000
Pressure, psia
Pressure, psia
Mole Fraction of C7+ in the Vapor
Phase
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n-Butane
0.05
0.020
Bulk Fluid
Flow(4nm)
Flow(6nm)
Flow(10nm)
Flow(20nm)
0.015
0.010
0.005
0.000
0
500
1000
Pressure, psia
1500
2000
(d) Flowing fluid in attractive pores
Fig.10 Molar percentage of heptane+ in the vapor phase in black oil
Black oil is produced at 150°F with pressure drwandown from 2000psia to 200 psia. The mole fractions of vapor
phase of methane, n-butane and heptane plus out of the entire black oil are illustrated in Fig.8, Fig.9 and Fig.10.
Similar phenomenon are observed with repect to sythetic oil. Vapor fraction of each hydrocarbon component
diminished under pore confinement effect. The flowing vapor fraction of dry gas methane however is elevated due
to a favorable Knudsen diffusion velocity compared with other species like n-butane and heptane plus. In attractive
pores, the increment of vapor phase is considerable. The combination impact of adsorption and pore proximity
results in higher percentage of vapor methane, but the molar percentage of heptane plus is less than orignial
composition.
The permeabilities multipliers of black oil in non-attractive and attractive pores are given in Fig.11.
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10
12
Kro
Krg(4nm)
Krg(6nm)
Krg(10nm)
Krg(20nm)
10
8
Permeability Multiplier
Permeability Multiplier
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12
6
4
2
Kro
Krg(4nm)
Krg(6nm)
Krg(10nm)
Krg(20nm)
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
0
0
0.2
0.4
0.6
0.8
1
So
So
(a) In hard pores
(b) In attractive pores
Fig.11 Permeability multiplier of confined black oil
Conclusions
In this work, we proposed apparent permeability for multi-component gas mixture and recommended the possible
permeability multiplier for two-phase flow. The conventional PVT modeling is demonstrated insufficient to predict
the fluid phase behavior in the confined spaces and in adsorptive organic porous media. Compositional modeling
based on altered critical pressures and temperatures in hard and attractive pores are used to evaluate the composition
change throughout the pressure depletion.
 Pore proximity effect improve the production of more valuable components by keeping fluids in single liquid
phase. The appearance of gas bubbles is put off to lower pressures with decreasing pore sizes.
 Reservoir fluids transport is mainly two-phase flow in adsorptive porous media. Moles of fluid dimishes with
decreaing pore width. Heavier components are more difficult to recover than dry gas methane in adsorptive
porous media.
 The composition of hydrocarbon species changes with the fluid flow through the reservoir. Composition of
methane in the vapor phase will increase, while the heavier components in the vapor phase will decrease
compared to their orginial storage composition.
 The permeability of gas is about 10 times higher than that of oil in two-phase flow region.
References
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Pore Proximity Effects: Implications for Transport, Reserves and Well Productivity. Paper SPE 160099 presented at
the 2012 SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA. 8-10 October.
McCain, W.D. 1933. The Properties of Petroleum Fluids. Second edition. PennWell Publishing Company: Tulsa.
Singh, S.K., Singh, J.K., 2011. Effect of Pore Morphology on Vapor-liquid Phase Transition and Crossover
Behavior of Critical Properties from 3D to 2D. Fluid Phase Equilibria. 300(2011): 182-187.
Xiong, X., Devegowda, D., Michel, G.G., Sigal, R.F., Civan, F. 2012. A Fully-Coupled Free and Adsorptive Phase
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2012 SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA. 8-10 October.
Acknowledgments
We gratefully acknowledge the funding from RPSEA (The University of Oklahoma Subcontract No. 09122-11) and
operating and service companies in our consortium who provide support for the work done here.
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