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Scientific RepoRts | 6:36673 | DOI: 10.1038/srep36673
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A Comprehensive Model for Real
Gas Transport in Shale Formations
with Complex Non-planar Fracture
Networks
Ruiyue Yang
1
, Zhongwei Huang
1
, Wei Yu
2
, Gensheng Li
1
, Wenxi Ren
1
, Lihua Zuo
2
, Xiaosi Ta n
2
,
Kamy Sepehrnoori
3
, Shouceng Tian
1
& Mao Sheng
1
A complex fracture network is generally generated during the hydraulic fracturing treatment in shale
gas reservoirs. Numerous eorts have been made to model the ow behavior of such fracture networks.
However, it is still challenging to predict the impacts of various gas transport mechanisms on well
performance with arbitrary fracture geometry in a computationally ecient manner. We develop a
robust and comprehensive model for real gas transport in shales with complex non-planar fracture
network. Contributions of gas transport mechanisms and fracture complexity to well productivity and
rate transient behavior are systematically analyzed. The major ndings are: simple planar fracture
can overestimate gas production than non-planar fracture due to less fracture interference. A “hump”
that occurs in the transition period and formation linear ow with a slope less than 1/2 can infer
the appearance of natural fractures. The sharpness of the “hump” can indicate the complexity and
irregularity of the fracture networks. Gas ow mechanisms can extend the transition ow period. The
gas desorption could make the “hump” more profound. The Knudsen diusion and slippage eect play
a dominant role in the later production time. Maximizing the fracture complexity through generating
large connected networks is an eective way to increase shale gas production.
Large-scale shale gas production began in 2000, when horizontal drilling and hydraulic fracturing techniques
provided access to commercial volumes of shale gas. According to recent EIA report, 43 billion cubic feet of gas
per day is produced from shales in the US
1
. Hydraulic fracturing in shale formations is oen associated with com-
plex fracture networks
2–6
. e occurrence of complex non-planar fracture network is much more common than
initially anticipated, especially in unconventional reservoirs
6
. e complexity and non-planarity is caused by the
interaction of hydraulic fractures with pre-existing natural fractures, ssures or cleat
4
.
Signicant eorts have been made to numerically model shale gas production in complex fracture networks.
e dual continuum model (dual porosity and dual permeability)
7–11
and discrete fracture models (DFM)
12–14
are the two most common methods to handle complex fracture networks and to study ow in fractured reser-
voirs (with natural fractures and/or induced fractures). Cipolla et al. (2011) developed automated unstructured
gridding algorithms to numerically simulate well performance from the complex fractures
15
. Li and Lee (2008),
Moinfar (2014), used embedded discrete fracture models (EDFM) to treat the matrix as structured grids and dis-
cretize the complex fractures into a number of segments
16,17
. Sheng et al. (2012) integrated a shale-gas transport
model with extended nite element method (XFEM) to study the main ow gas mechanism of shale in complex
fracture network
18
. Jiang and Younis (2015) proposed two hybrid approaches: one is the coupling EDFM with
multiple interacting continua (MINC), the other is the coupling of unstructured DFM with continuum-type
approaches
19
. However, these numerical methods are still challenging to apply due to complicated gridding issues,
an expensive computational cost, and complexities in development of computational codes.
1
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, P.R.
China.
2
Department of Petroleum Engineering, Texas A&M University, Collage Station, TX, 77843, USA.
3
Department
of Petroleum and Geosystems Engineering, University of Texas at Austin, Austin, TX, 78712, USA. Correspondence
and requests for materials should be addressed to Z.H. (email: huangzw@cup.edu.cn) or W.Y. (email: yuwei127@
gmail.com)
Received: 23 June 2016
Accepted: 19 October 2016
Published: 07 November 2016
OPEN
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Scientific RepoRts | 6:36673 | DOI: 10.1038/srep36673
Analytical and semi-analytical approaches have also been developed to investigate the well performance in
complex fracture networks. Zhou et al. (2013) proposed a semi-analytical model by combining an analytical
reservoir solution with a numerical solution on a discretized fracture panels
20
. However, the model did not incor-
porate the main gas transport mechanisms in shale gas formations. Yu et al. (2015) developed a comprehensive
semi-analytical model for gas transport in shale formation with complex fracture geometry
21
. e model consid-
ered the complex non-planar fractures with varying fracture width and fracture permeability, and the gas trans-
port mechanisms in shale. However, there is no systematic studies for the eects of various gas ow mechanisms
on the production. Besides, the complex fracture network due to the interconnection of hydraulic fracture and
natural fractures has not been considered. Jia et al. (2015) adopted the Star-Delta transformation to solve the
interplay of ow between the interconnected fractures in their semi-analytical model
22
. However, the method is
based on the discrete fracture network simulation and the fracture ow is numerically solved by the method of
nite dierence method, which is also related to gridding problem and computational cost. Moreover, most of the
recent models only solved the orthogonal fracture network without considering the arbitrary fracture orientation
and geometry
22,23
.
Furthermore, the common methods for analysis of dierent gas ow regimes is mainly focused on the tran-
sient pressure behavior under constant ow rate
24–26
, because most of these models are within the Laplace domain,
which are proved to be acceptable for fractures with innite conductivity. However, shale-gas wells with low per-
meability and nite ow capacity fractures are generally produced at constant bottomhole pressure rather than
constant ow rate
27,28
. Accordingly, type curves under constant bottomhole pressure, i.e. rate transient analysis, is
especially more useful to identify the ow regime and deserves more interest to estimate the fracture properties.
In this paper, we develop a comprehensive and ecient semi-analytical model by incorporating the main shale
gas ow mechanisms, including gas diusion, gas desorption, gas slippage, and non-Darcy’s ow in the com-
plex fracture network. An innovative approach dened as “Correction of Flow Performance at Interconnected
Nodes” is introduced to consider the interplay of ow between the interconnected fractures. en, we verify the
semi-analytical model against a numerical model and an analytical model. Subsequently, the eects of various
gas ow mechanisms and fracture network complexities on well performance and rate transient behavior with
the constraint of constant bottomhole pressure are studied systematically. Furthermore, we apply the model to
perform history matching and production forecasting in an actual vertical fractured well from Marcellus shale.
e semi-analytical model we present is simple-yet-rigorous to deal with complex fracture network with arbitrary
orientation, geometry, various properties and interconnections between fractures. Besides, by use of the varying
time step automatically according to the changing speed of gas ow rate, the model is computationally ecient.
To best of our knowledge, this work is the rst study that presents the impacts of gas transport mechanisms on
well performance and rate transient analysis in shale formations with the complex non-planar fracture network.
Results
Model validation. e accuracy of the semi-analytical model is conrmed by comparing the results with the
numerical simulation (CMG, 2015) and an analytical solution (Kappa, 2015). e reservoir and fracture prop-
erties are as follows: initial reservoir pressure is 5,000 psi, reservoir temperature is 130 °F, reservoir permeability
is 500 nd, reservoir porosity is 7%, reservoir thickness is 150 , rock compressibility is 1 × 10
−6
psi
−1
, fracture
width is 0.01 , fracture half-length is 350 , fracture conductivity is 50 md-, Langmuir pressure is 1,300 psi,
Langmuir volume is 140 scf/ton, and shale bulk density is 2.5 g/cm
3
. e constant bottomhole pressure of 500 psi
is used for simulation constraint and the simulation time is 30 years. Figure1 shows a good match of gas ow rate
and cumulative gas production between the semi-analytical model and numerical model and analytical model.
Eects of gas ow mechanisms. Shale gas is natural gas produced from shale sequences
29
. Due to low
permeability of the shale rock (nano-Darcy scales) and organic matter as a medium of gas source and storage, the
gas transport mechanism is signicantly dierent from conventional natural gas
30
. We will investigate the physical
aspects of gas production from shale with a single bi-wing fracture in the following sections.
Gas diusion. According to Javadpour et al. (2007), the gas evolution process from shale has four dierent
transport processes: (1) gas ow in micro-pores, i.e. gas ow in fractures, which can be described by Fickian
Figure 1. Model validation with numerical model and analytical model.
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Scientific RepoRts | 6:36673 | DOI: 10.1038/srep36673
diusion and/or Darcy’s law depending on the original pressure; (2) gas ow in nano-pores, i.e. gas ow in
shale matrix, where a Knudsen diusion is the dominant diusion process; (3) Gas desorption from the sur-
face of the kerogen/clays to the pore networks; (4) Gas molecule diusion from the kerogen bulk or clays to the
exposed surfaces
29
. Besides, the experimental studies show that the diusion coecient for Knudsen diusion
is 4 × 10
−2
cm
2
/s and the diusion coecient for gas molecule transport in the kerogen bulk is 2 × 10
−6
cm
2
/s
29
.
Kim et al. (2015) presented that the Fick diusion coecient remains 5.068 × 10
−4
cm
2
/s and is independent
of the pore radius
31
. erefore, in this study, the range of diusion coecient is determined from 1 × 10
−2
to
1 × 10
−4
cm
2
/s.
e simulation results show that the higher the diusion coecient, the greater the diusion eect is, espe-
cially when it is larger than 1 × 10
−3
cm
2
/s, the impact increases drastically (Fig.2a). For the diusion coecient
of 1 × 10
−2
cm
2
/s, which is within the scope of Knudsen diusion, the contribution to cumulative production is
up to 54%. Hence, Knudsen diusion plays a dominant role in the gas production. When the diusion coecient
is lower than 1 × 10
−4
cm
2
/s, the gas diusion plays a negligible role in well performance and the contribution to
well performance is only 0.01%.
Gas desorption. Gas adsorption and desorption is an important process in organic rich shale reservoirs
32
.
e organic matter has a strong adsorption ability because of the large surface area and anity to methane
21
. Gas
is supposed to rst desorb from the surface of nano-pores to matrix then transport into fractures. Dierent gases
have dierent Langmuir adsorption capacities
32
.
e eects of dierent Langmuir adsorption capabilities on well performance are shown in Fig.2b. It suggests
that the gas desorption contributes to 10–27% increase of cumulative gas production at 30 years. is is because
gas desorption increases the eective pore diameter for ow, reduces tortuosity and causes extra slippage at the
boundary, thereby increases the matrix permeability manifold
33
. In addition, the production is higher with a
larger value of Langmuir volume. e reason is that the Langmuir volume reects the capacity of adsorbed gas
in the reservoir. e larger the value, the more adsorbed gas in the reservoir, and the more gas could desorb from
matrix to fractures when well produces at a constant bottomhole pressure.
Gas slippage. Gas ows through shale matrix with pore size ranging from nanometers (1 nm = 10
−9
m) to
micrometers (1 µ m = 10
−6
m)
29
. e velocity of gas molecules at pore walls is referred to the gas slip velocity.
Because of the comparable dimensions of pore size in a shale reservoir to the mean free path of molecules, the
slip velocity is not zero
34
. is phenomenon is known as gas slippage eect or Klinkenberg eect
35
. Small pore
Figure 2. Eects of three gas transport mechanisms on cumulative gas production. (a) Eect of gas
diusion with dierent gas diusion coecients. (b) Eect of gas desorption with dierent Langmuir volumes.
(c) Eect of gas slippage with dierent pore diameters.
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Scientific RepoRts | 6:36673 | DOI: 10.1038/srep36673
size enhances gas slippage along pore walls and needs to be quantied
36
. To illustrate the gas slippage eect on
cumulative gas production and rate transient behavior, the range of pore size from 5 nm to 500 nm is studied.
Simulation results indicate that the smaller the pore size is, the more important the gas slippage eect (Fig.2c).
When the pore size is 5 nm, the slippage eect could contribute to 37% of increase in cumulative gas production.
When the pore size approaches 500 nm, the gas slippage eect becomes negligible, which contributes only 0.69%
of the increase in cumulative gas production.
e reason is that the smaller pore size results in a higher Knudsen number under the same pressure and per-
meability condition. A higher Knudsen number indicates the distances between gas molecules are comparable
to the pore dimension, resulting in rareed gas
34,37
, thus more gas production could be obtained. Besides, the
slippage eect could accelerate the gas molecules transport speed because there is less drag or no stationary layer
to slow them
34
. erefore, slippage eect, acting as an enhancement of apparent permeability, could increase the
shale gas production.
Eects of fracture complexity. e eects of complex fracture networks on well performance are studied.
e fractures are simulated from simple to complex. Six cases are investigated to illustrate the fracture complexity
(Fig.3). Case 1 is simple planar hydraulic fracture without considering natural fractures. Case 2 is non-planar
hydraulic fracture without considering natural fractures. Case 3 is non-planar hydraulic fracture interconnected
with simple planar natural fractures. Case 4 is non-planar hydraulic fracture interconnected with non-planar
natural fractures. Case 5 is based on Case 3, but with more complicated natural fracture networks, i.e. the planar
natural fractures are also interconnected with each other. Case 6 is based on Case 5, the planar natural fractures
are treated as non-planar natural fractures. e natural fracture properties are as follows: fracture half-length is
180 for the ones interconnected with hydraulic fracture and 100 for natural fractures in the network. Fracture
width and fracture conductivity is 0.01 and 1 md- for both of the natural fracture systems.
Non-planar hydraulic fracture. To illustrate the eect of non-planar hydraulic fracture on gas production,
Cases 1 and 2 are compared. In this situation, only one single bi-wing hydraulic fracture is considered. e total
fracture length is the same for both cases. e dierence is that Case 1 is a straight hydraulic fracture, while Case
2 has an arbitrary geometry.
As illustrated by Fig.4a, there is 5% higher of cumulative gas production for the simple planar hydraulic frac-
ture. Hence, the planar hydraulic fracture could overestimate the cumulative gas production. e possible reason
could be that fracture segments in non-planar fracture have a larger production interference and competition
with each other, which could be regarded as a reduction of fracture conductivity. e pressure distribution aer
10 days production suggests that the drainage area of the non-planar fracture is smaller than the simple planar
fracture, resulting in the smaller pressure drop, thus less gas production was obtained.
Non-planar natural fracture. Shale gas reservoir is the naturally fractured formation. e interaction
between hydraulic fracture and natural fractures is common. Cases 3 and 4 are compared to study the eect of
non-planar natural fractures.
As indicated in Fig.4b, hydraulic fracture interconnected with simple planar natural fractures could overesti-
mate about 12% of cumulative gas production. Similar with the eect of non-planar hydraulic fracture, with the
appearance of interconnection between hydraulic fracture and natural fractures, the signicance of non-planar
natural fracture becomes more pronounced. e reason could be attributed to the occurrence of more production
interference among the fractures including hydraulic fracture with natural fractures and natural fractures with
each other.
Figure 3. Six dierent complex fracture networks. Case 1 is the simple planar hydraulic fracture; Case 2 is
the non-planar hydraulic fracture; Case 3 is the simple planar natural fracture; Case 4 is the non-planar natural
fracture; Case 5 is the simple planar natural fracture network; Case 6 is the non-planar natural fracture network.
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Scientific RepoRts | 6:36673 | DOI: 10.1038/srep36673
Non-planar fracture network. In this simulation case, the natural fractures are also interconnected with
each other, the eect of non-planar natural fracture networks is studied.
As shown in Fig.4c, hydraulic fracture is interconnected with simple planar natural fracture networks could
overestimate about 21% of cumulative gas production. Similarly, the signicance of non-planar natural fracture
network is increasingly noteworthy. erefore, with the increasing complexity of the fracture network, the impact
of non-planar fracture increases, indicating that it is important to accurately characterize the realistic complexity
of the fracture network in actual eld application.
e results show that the more complex the fracture network is, the higher the production could be obtained.
e hydraulic fracture interconnected with natural fracture networks could achieve the highest gas recovery at
the end of production. Comparing Case 2 with Case 4, the natural fracture contributes to 17% of cumulative gas
production. Comparing Case 4 with Case 6, the natural fracture network could contribute to 36% of cumulative
gas production. erefore, increasing the fracture complexity and the interconnections between hydraulic frac-
ture and natural fractures could improve the gas production signicantly.
Maximizing the fracture complexity through generating large fracture networks is an eective way to increase
shale gas production. is can be done through pumping large volumes of low viscosity uid, for example, slick
water. In addition, low viscous uid could improve the clean-up behavior
4
.
Field application. One vertical well in Marcellus shale is selected to perform history matching and further
illustrate the application of this semi-analytical model. e reservoir and fracture properties are as follows: the
initial reservoir pressure is 4,917 psi, the reservoir temperature is 130 °F, the reservoir porosity is 6.8%, the res-
ervoir thickness is 80 , the rock compressibility is 3 × 10
−6
psi
−1
, the initial gas saturation is 75%, and the gas
gravity is 0.59.
Based on the given parameters, the semi-analytical model is used to perform history matching and production
forecasting. e bottomhole pressure of 500 psi is used for simulation constraint and cumulative gas production
is the history-matching variable. Complexity of fracture networks, fracture half-length, fracture conductivity, and
matrix permeability are tuning parameters to perform history matching. e Langmuir volume is 140 scf/ton, the
average pore size is 10 nm, and the diusivity coecient is 4 × 10
−2
cm
2
/s.
Because the history-matching process usually leads to non-unique solutions. In other words, dierent sets of
values can achieve satisfactory match results. Due to lack of data for this well such as microseismic monitoring,
advanced sonic logs, 3D-seismic interpretation of curvature stress and natural-fracture orientation, two pos-
sible history-matching results are generated below: one is the planar fracture network and the other one is the
Figure 4. Eects of fracture complexity on gas production and pressure distribution aer 10 days. (a) Eect
of non-planar hydraulic fracture; (b) Eect of non-planar natural fracture; (c) Eect of non-planar natural
fracture network.