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Conceptual study of thermal stimulation in shale gas formations
HanYi Wang a , *, Omobola Ajao b , Michael J. Economides a , 1
a University of Houston, United Statesb EPT International, United States
a r t i c l e i n f o
Article history:
Received 8 September 2014
Received in revised form
11 October 2014
Accepted 13 October 2014
Available online 30 October 2014
Keywords:
Shale gas
Adsorption
Desorption
Thermal recovery
Hydraulic fracture
Stimulation
a b s t r a c t
Shale gas formations have become a major source of energy in recent years. Developments in hydraulic
fracturing technology have made these reservoirs more accessible and productive. Apart from otherdissimilarities from conventional gas reservoirs, one major difference is that a considerable amount of
gas produced from these shale gas formations comes from desorption. Up to 85% of the total gas within
shale can be found as an adsorbed phase on clay and kerogen, so how much adsorbed gas can be pro-
duced will have signicant impact on ultimate gas recovery. The Langmuir isotherm has been widely
used in industry to describe the pressure dependence of adsorbed gas. However, temperature dependent
adsorption behavior and its major implications for evaluating thermal stimulation as a recovery method
for shale reservoirs have not been thoroughly explored. Therefore, in order to design and analyze the
thermal treatment of shale gas formations successfully, it is crucial to understand the effects of fracture
heating on the shale gas adsorption and desorption phenomenon, and how can we exploit such effects to
enhance shale gas recovery from hydraulically fractured reservoirs. Even though numerous research
efforts have been focused on thermal recovery of shale oil, its possible application to shale gas has not
been investigated.
In this research, we propose a method to evaluate desorbed gas as a function of pressure and tem-
perature in shale formations, by regression of a Bi-Langmuir model on Langmuir isotherm data. We have
developed a fully coupled unconventional reservoir simulator, which is capable of capturing real gas ow
in the shale matrix and in the hydraulic fracture by accounting for the effects of gas desorption anddiffusion, as well as the temperature diffusion process within the matrix. This simulator enables us to
investigate the effects of fracture heating on the shale gas desorption phenomenon on the global well
performance and recovery. The results of this study show, for the rst time in a rigorous way, that by
increasing the temperature within the fracture, shale gas recovery can be improved.
We have rationalized and quantied relations between the adsorption/desorption fundamental phe-
nomena and stimulation temperature, fracture spacing, reservoir permeability and bottom hole pressure.
The thermal properties of shale formations only have limited impacts on long term production. The
results of this study can provide a guidance to develop a strategy to design thermal treatment in hy-
draulically fractured shale formations and propose the degree of thermal stimulation temperature
required in a fracture to promote an economically viable return on production.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Unconventional gas reservoirs are expectedto play a vital role in
satisfying the global demand for gas in the future. The major
component of unconventional gas reservoirs comprises of shale
gas. Shales and silts are the most abundant sedimentary rocks in
the earth's crust and it is evident from the recent year's activities in
shale gas plays that in the future shale gas will constitute the largest
component in gas production globally. Unlike conventional gas
reservoirs, shale gas reservoirs have very low permeability, and are
economical only when hydraulically fractured. The key techniques
that allow extracting shale gas commercially such as horizontal
drilling and hydraulic fracturing, are expected to improve with
time; however as better stimulation techniques are becoming
attainable, it is important to have better understanding of shale gas
reservoir behavior in order to apply these techniques in an ef cient
fashion. One important aspect of shale gas reservoirs which needs
special consideration is the adsorption/desorption phenomenon.* Corresponding author.
E-mail address: Hanrry@spemail.org (H. Wang).1 Deceased.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c om / l o c a t e / j n g s e
http://dx.doi.org/10.1016/j.jngse.2014.10.015
1875-5100/©
2014 Elsevier B.V. All rights reserved.
Journal of Natural Gas Science and Engineering 21 (2014) 874e885
mailto:Hanrry@spemail.orghttp://www.sciencedirect.com/science/journal/18755100http://www.elsevier.com/locate/jngsehttp://dx.doi.org/10.1016/j.jngse.2014.10.015http://dx.doi.org/10.1016/j.jngse.2014.10.015http://dx.doi.org/10.1016/j.jngse.2014.10.015http://dx.doi.org/10.1016/j.jngse.2014.10.015http://dx.doi.org/10.1016/j.jngse.2014.10.015http://dx.doi.org/10.1016/j.jngse.2014.10.015http://www.elsevier.com/locate/jngsehttp://www.sciencedirect.com/science/journal/18755100http://crossmark.crossref.org/dialog/?doi=10.1016/j.jngse.2014.10.015&domain=pdfmailto:Hanrry@spemail.org
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In organic porous media, gas can be stored as compressed uid
inside the pores or it can be adsorbed by the solid matrix. Similar to
surface tension, adsorption is a consequence of surface energy
(Gregg and Sing, 1982), which causes gas molecules to get bounded
to the surface of the rock grains. The gas adsorption in shale-gas
system is primarily controlled by the presence of organic matter
and the gas adsorption capacity depends on TOC (Total Organic
Carbon), organic matter type, thermal maturity and clay minerals
(Ambrose et al., 2010; Chalmers and Bustin, 2008; Hill et al., 2007;
Jarvie et al., 2007; Jenkins and Boyer, 2008; Passey et al., 2010; Ross
and Bustin, 2008). Generally, the higher the TOC content, the
greater the gas adsorption capacity (Zhang et al., 2013). In addition,
a large number of nanopores lead to signicant nanoporosity in
shale formations, which increases the gas adsorption surface area
substantially ( Javadpour et al., 2007). The amount of adsorbed gas
varies from 35 to 58% (Barnett Shale, USA) up to 60e85% (Lewis
Shale, USA) of total gas initial in-place ( Darishchev et al., 2013).
Presently, the only method for accurately determining the
adsorbed gas in a formation is through core sampling and analysis.
However, understanding the effects that initial adsorption, and
moreover, desorption has on gas production will increase the
effectiveness of reservoir management in these challenging
environments.In shale formations, the total gas in-place (GIP) is determined by
free gas in-place and adsorbed gas inplace. Adsorbed gas can be the
dominant in-place resource in highly organically rich shales. Free
gas becomes the dominant in-place resource in high clastic content
shales. The calculation of free gas in-place for a given areal extent is
governed, to a large extent, by pressure, temperature, gas-lled
porosity and net organically-rich shale thickness. A Langmuir
isotherm (1916) can be established for a prospective area of shale
basin using available data on TOC and on thermal maturity to
establish the Langmuir volume (V L) and the Langmuir pressure (P L).
Adsorbed gas in-place is then calculated using the formula below:
mad ¼ r
mr
g 0V L
P
P þ P L (1)
where mad is the gas adsorption mass per unit volume of formation
(kg m3), rm is shale matrix density (kg m3), r g 0 is gas density at
standard condition (kg/scf). In general, Langmuir volume V L (scf/
ton) is a function of the organic richness and thermal maturity of
the shale and the Langmuir pressure P L(Pa) is a function of how
readily the gas can be adsorbed on the organics in the shale matrix
and how readily it is released as a function of a nite decrease in
pressure.
The Langmuir isotherm (Fig. 1) gives us an idea of how the
adsorbed gas, free gas and total gas capacity of the shale reservoir
relates with the pressure in terms of gas content. We can also
deduce that the reservoir pressure must be suf ciently low to
liberate the adsorbed gas and the ultimate recoverable amount of
gas is largely a function of the adsorbed gas that can be released
(desorbed) in organically rich shales. Because most adsorbed gas
can only be released at low reservoir pressure, due to the extremely
low permeability in shale matrix, even with hydraulic fracturing, it
would take considerable production time for the average pressure
within the drainage area to drop to a level where most of the
adsorbed gas can be liberated, and the production rate may have
already reached the economical shut-in limits by then.
Thermal stimulation techniques that can increase the formation
temperature around the hydraulic fracture during production can
be utilized as a potential method to enhance ultimate recovery
from shale gas reservoir by altering shale gas desorption behavior.
This will enhance desorption rate and recovery of a larger amount
of gas prior to reaching reservoir pressure economic limits.
Numerous authors have investigated how to enhance hydro-
carbon recovery through thermal treatment, such as in-situ com-
bustion (Hascakir et al., 2013), using electromagnetic materials
(Yahya et al., 2012), injecting uids including CO2 or steam through
created hydraulic fractures (Biglarbigi et al., 2007; Thoram et al.,
2011).
Symington et al. (2006) proposed an electric heating method for
converting oil shale to producible oil and gas through heating theoil shale in situ by hydraulically fracturing the oil shale and lling
the fracture with electrically conductive material to form a heating
element. The temperature in the hydraulic fracture could be stim-
ulated up to a temperature of 400 C (752 F).
Another possible way to heat the hydraulic fracture directly is to
use nanoparticles forincreased coal seam gas, shale gasand oilshale
production via enhanced electromagnetic heating of hydrocarbon
deposits. Already, microwave applications in oil sands bitumen and
shale oil production and in petroleum upgrading are gaining
considerable interest in recent years. Energy companies and petro-
leum researchers have been working on a variety of unconventional
technologies such as microwave and radio frequency (RF) energies
torecoveroil and gas from oil shale (Mutyala et al., 2010). Underthe
oil shale extraction scenario,auxiliary wellsare drilled intothe shalestrata usingstandardoil-industry equipment, and then RF antennas,
or transmitters, are lowered into wells. The antennas then transmit
RF energy to heat the buried shale rock. This results in the volatili-
zation of water, which in turn, results in the micro-fracturing of the
formation, enhancing product recovery uniformly. Microwaves can
generate heat faster than convection heating and it is observed that
shale can be adequately heated to extract oil within a month or two
of beginning production activities, rather than the year or longer for
other methods. Nanoparticles in the form of nanouids have been
used for enhanced oil recovery applications and it has shown that
due to absorption of electromagnetic waves by the cobalt ferrite
nanoparticles that were used, oil viscosity was reduced resulting in
an increase of oil recovery (Yahya et al., 2012). However, all of these
studies only focus on improving heavy oil/shale oil recovery byincreasing formation temperature to convert kerogen into oil/gas
andreduce oilviscosity. Few studies have exploredthe possibility of
enhancing shale gas recovery with similar techniques. Now the
question arises: Can these thermal treatments be applied to shale
gas reservoirs? If we can increase the temperature within the hy-
draulicfracture with similar methods,how much will itaffectthegas
desorption mechanism in shale matrix and the ultimate recoverable
amount of gas?
In this study, we proposed a method to evaluate shale gas
adsorption/desorption capacity as a function of pressure and tem-
perature through regression of a Bi-Langmuir model based on data
from Langmuir isotherm. An unconventional, fully coupled, hy-
draulic fractured shale gas reservoir simulator was developed to
investigate how the fracture temperature will impact the shale gasFig. 1. Combining free and adsorbed gas for total gas in-place (Kuuskraa et al., 2011).
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production and what main factors can determine whether increase
formation temperature can be successful. The volume of the
reservoir that realizes an effect of the thermal stimulation will be
referred to herein as the Stimulated Reservoir Volume (SRV) for the
purposes of this paper. The results of this study can provide a
foundation for future research efforts on cost-effective thermal
stimulation techniques to enhance the ultimate shale gas recovery.
2. Thermodynamic casting of shale gas adsorption/
desorption
Traditionally, Langmuir isotherms are widely used to model
adsorption of coal bed methane and shale gas at a constant tem-
perature, by measuring crushed rock samples in laboratory to
describe the amount of adsorbed gas as a function of its pressure at
constant temperature (Vasilache, 2010). This model is a simplied
model of gas/solid adsorption which is based on four assumptions
(Czepirski et al., 2000):
1. All of the adsorption sites are equivalent and each site can only
accommodate one molecule.
2. The surface is energetically homogeneous and adsorbed mole-cules do not interact.
3. There are no phase transitions.
4. At the maximum adsorption, only a monolayer is formed.
Adsorption only occurs on localized sites on the surface, not
with other adsorbates.
With these assumptions, the Langmuir isotherm equation can
be rigorously derived from the theory of kinetics and thermody-
namics, and is commonly written as (Adamson, 1982; Ruthven,
1984):
mad ¼ rmr g 0V LK ðT ÞP
1 þ K ðT ÞP (2)
K (T ) is the adsorption equilibrium constant (1/Pa), which can be
considered as temperature dependent:
K ðT Þ ¼ k0T 12e
E RT (3)
where k0 is a pre-exponential constant independent of temperature
(1/Pa), T is temperature in Kelvin, E is the characteristic adsorption
energy (J/mol) and R is the universal gas constant (8.3145 J/mol K).
However, regardless that this Langmuir model can describe
monolayer gas adsorption on a homogeneous adsorbent well
enough, it may not be suitable for gas/shale systems because
different materials may contribute to gas adsorption. Lu et al.
(1995) investigated temperature dependent adsorption curves on
shale samples and proposed a Bi-Langmuir model that can account
for gas adsorption on both clay minerals and kerogen:
mad ¼ rmr g 0V L
f 1
K 1ðT ÞP
1 þ K 1ðT ÞP þ f 2
K 2ðT ÞP
1 þ K 2ðT ÞP
(4 e1)
where f i is dened as the ratio of the amount of the ith type of
adsorption at monolayer coverage to the total amount adsorbed at
monolayer coverage and each adsorption site is assumed to follow
the Langmuir equation. For two types of adsorption sites we have:
f 1 þ f 2 ¼ 1 (4 e2)
K 1ðT Þ ¼ k1T 12e
E 1RT (4 e3)
K 2ðT Þ ¼ k2T 12e
E 2RT (4 e4)
The study indicated that the Bi-Langmuir model can t the
experimental data better than the Langmuir model when extrap-
olating isotherms to desired temperatures. Even though the as-sumptions behind the Langmuir isotherm model may not always
fully depict the real phenomenon, it is still the most common
isotherm equation to use in industry due to its simplicity and its
ability to t a variety of adsorption data.
In this study, we only investigate the thermal stimulation effects
based on the Bi-Langmuir model obtained using regression from
Langmuir isotherm data, we also assume the gas adsorption and
desorption curves coincide without hysteresis. For a more complex
adsorption model that can be applied to a specic case, which
needs to consider the effects of multiple hydrocarbon components,
multi-layer adsorption, nonhomogeneous adsorbents and phase
change behavior, the reader should refer to various other ap-
proaches that have been proposed by numerous authors (Ambrose
et al., 2011; Das et al., 2012; Fathi and Akkutlu, 2009; Hartman et al.,
2011; Ji et al., 2012; Leahy-Dios et al., 2011; Li et al., 2013; Zhang
et al., 2013).
The ve unknown independent parameters f 1, k1, k2, E 1 and E 2can be determined from a Langmuir isotherm curve at provided
temperature condition by regression. Thus, the temperature effects
can be included to describe shale gas adsorption capacity. Fig. 2
shows an example of temperature effects on gas adsorption ca-
pacity: the original Langmuir isotherm is provided at the temper-
ature of 150 F with Langmuir volume of 400 scf/ton and Langmuir
pressure of 500 psi, and the adsorption capacity is extrapolated to
the temperature of 400 F by tting Eq. (4) against Eq. (1). It can
also be observed that with increasedtemperature, large amounts of
extra gas can be released even at high pressure. Table 1 shows the
estimation of parameters in the Bi-Langmuir model based on the
provided Langmuir isotherm curve.
3. Mathematical model
The physical process of thermal treatment for shale gas reser-
voirs involves uid ow within the formation matrix and hydraulic
fracture, shale gas adsorption and desorption as a function of
pressure and temperature, real gas properties affected by pressure
Fig. 2. Gas adsorption capacity with different temperatures.
Table 1
Estimates of parameters in Bi-Langmuir model.
f 1 k1 (1/psi) E 1 (kcal/mol) k2 (1/psi) E 2 (kcal/mol)
0.4017 0.0014 2.2032 0.000022262 5.0015
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and temperature, and heat transfer process between the hydraulic
fracture and shale formation.
Many shale gas reservoirs can have matrix permeability values
in the range of tens to hundreds of nanodarcies. Due to the ultra-
ne pore structure, non-Darcy ow mechanisms such as Knudsen
diffusion and/or gas slippage effects may affect matrix perme-
ability, depending on a combination of pressure-temperature
conditions, pore structure and gas properties. Even though a vari-
ety of correlations and models have been proposed in recent years
to account for the apparent permeability enhancement in nanopore
structures (Florence et al., 2007; Javadpouret al., 2007; Civan, 2010;
Michel et al., 2011; Fathi et al., 2012; Sakhaee-Pour and Bryant,
2012), given that our main objectiveis to characterize the enhanced
recovery in shale formations by heating through hydraulic frac-
tures, this study will still be based on Darcy's Law to determine gas
ow rate in shale matrix.
q g ¼ k g m g
$VP (5)
where q g is velocity vector of gas phase (m/s),k g is gas permeability
vector (md), and m g is gas viscosity (Pa s).The continuity equation in shale formation is:
vm
vt þ V$
r g q g
¼ Q m (6)
where m is total gas content per unit volume (kg m3), r g is local gas
density (kg m3), Q m is the source term (kg m3 s1) and t is time
(s).
The total gas content m is a combination of two parts:
m ¼ r g ∅m þ mad (7)
r g Øm is free gas mass in shale pore space (kg m3), and adsorption
gas mad
can be determined by Eq. (4) at given temperature and
pressure.
In situ gas density can be calculated by the real gas law:
r g ¼ PM
ZRT (8)
where M is average molecular weight of mixed gas (kg/mol) and Z-
factor can be calculated with pseudo reduced pressure ( p pr ) and
pseudo reduced temperature (T pr ) of mixed gas by the correlation
(Mahmoud, 2013):
Z ¼ð0:702e2:5T pr Þð p2 pr Þ ð5:524e2:5T pr Þð p pr Þ
þ ð0:044T 2 pr 0:164T pr þ 1:15Þ(9)
Among all gas properties, gas viscosity, which is usually char-
acterized by some available correlations, still remains uncertain.
Values of gas viscosities are used to model gas mobility in reser-
voirs and have a signicant impact on reserves estimation during
eld development planning. 1% error in gas viscosity can lead to 1%
error in gas ow rate prediction, which in a large scale of gas
production may severely underestimate or overestimate recovery
(Davani et al., 2009). Lee et al. (1966) proposed a correlation to
calculate gas viscosity at temperatures from 100 to 340 F and
pressure from 100 to 8000 psi. Viswanathan (2007) measured the
viscosity of pure methane at pressure from 5000 to 30,000 psi and
temperatures from 100 to 400 F, and modied the correlation by
Lee et al. (1966). Based on measurements and results of
Viswanathan (2007):
m g ¼ 104Ke X r
Y g (10 e1)
where
K ¼ ð5:0512 0:2888M ÞT 1:832
443:8 þ 12:9M þ T (10 e2)
X ¼ 6:1166 þ
3084:9437
T
þ 0:3938M (10 e3)
Y ¼ 0:5893 þ 0:1563 X (10 e4)
Tangential derivatives (Chen et al., 2013) are used to dene the
ow along the interior boundary representing a hydraulic fracture
within the porous medium. Since a hydraulic fracture itself is lled
with proppant and the gas ow rate is relatively slow due to
extremely low formation permeability, ow behavior inside the
hydraulic fracture can be described by Darcy's Law:
q f ¼ k f m g
$d f VT P (11)
where q f is the volume ow rate vector per unit length in the
fracture (m3/s m), k f is fracture permeability vector (md), VTP is
pressure gradient tangent to fracture surface.
The continuity equation along the fracture reects the material
balance:
d f v∅ f r g
vt þ VT $
r g q f
¼ d f Q f (12)
where d f is hydraulic fracture width, Øf is the fracture porosity, and
Q f is the mass source term (kg m3 s1), which can be calculated by
adding mass ow rate per unit volume from two fracture walls (left
and right) by:
Q f ¼ Q f lef t
þ Q f right
(13 e1)
Q f left
¼ k g u g
vP leftvnleft
(13 e2)
Q f right
¼ k g u g
vP rightvnright
(13 e3)
where n is the vector perpendicular to fracture surface.
When the hydraulic fracture is directly heated, the fracture
surface is considered as a constant temperature boundary condi-
tion. Heat transfer between the hydraulic fracture and formation
matrix is governed by a thermal diffusion equation in an isotropic
porous medium; radiative effects, viscous dissipation, and the work
done by pressure changes are negligible. Considering an elemental
volume of a porous medium we have, for the matrix:
ð1 ∅mÞrmC mvT mvt
þ ð1 ∅mÞV$ðk mVT mÞ ¼ ð1 ∅mÞQ m
(14)
and for the gas phase:
∅mr g C p; g vT g vt
þ∅mV$
k g VT g
þ r g C p; g q g $VT g ¼ ∅mQ g (15)
where r is the density (kg m3), C m is the heat capacity of the rock
matrix, C p, g is heat capacity at constant pressure of the gas phase (J/
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temperature is imposed along the hydraulic fracture. The combi-
nationof input parameters is designed to reecta relatively high gas
adsorption level,so that nearly80% of initial gasin-place comesfrom
adsorbed gas, this can be the case in organic rich shale formations
such as Devonian shales (Schettler and Parmely, 1991).
5. Results and analysis
In this section, we present results of the analysis to demonstrate
howheating a hydraulic fracture canimpact the release of adsorbed
gas in a given SRV and what factors can inuence long term pro-
duction performance. Each SRV has its own fracture, each with an
equal geometry of half-length and permeability.
Fig. 4(a) shows the temperature, pressure, viscosity and density
proles in the simulated SRV, all of which are time-space depen-
dent during production. After 1 year's production, the front edge of
temperature diffusion has reached the virtual SRV boundary while
the pressure propagation has not touched the boundary and the
ow regime still exhibits transient linear ow. Gas viscosity and
density values are lowest in the high temperature and low pressure
zone around the hydraulic fracture.
Fig. 4(b) shows the same proles without thermal stimula-
tion. Comparing these results with the ones in Fig. 4(a), it can
be observed that the gas density is higher and the viscosity is
slightly lower in the pressure depleted zone due to lower
formation temperature. More important, it can be also noticed
that the pressure propagation has reached the virtual SRV
boundary and the fracture started to deplete its SRV under
pseudo-steady state after 1 year's production. This indicates
that the extra adsorbed gas released within the thermally
stimulated zone provides a self-induced pressure maintenance
effect.
Fig. 4. (a). Temperature-pressure-viscosity-density distribution after 1 year of production with thermal stimulation. (b). Temperature-pressure-viscosity-density distribution after
1 year of production without thermal stimulation.
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Fig. 5 shows the percentage of adsorbed gas produced after 10
years' production with and without thermal treatment. In the case
without thermal stimulation, nearly 45 percent of original adsor-
bed gas has been released from the vicinity near to the hydraulic
fracture (within a distance of 15 ft). When the hydraulic fracture is
heated up to 400 F, nearly 85 percent of original adsorbed gas can
be released from this near fracture region.
Fig. 6 shows total production rate from the simulated horizontalwell with an assumed count of 20 transverse hydraulic fractures,
throughout therst ve years of production. It can be observed that
even though the thermal stimulation production rate is higher than
that without thermal stimulation, both rates decline rapidly during
the rst year of production. The thermal treatment does not pre-
vent substantial reduction in production rate in early stages, as can
be observed in both cases, where production rate decreased nearly
80% over the rst 2 years of production.
5.1. Impact of stimulation temperature
In order to investigate how the magnitude of stimulation tem-
perature can impact the long term production, a constant tem-
perature applied along the hydraulic fracture was modeled from200 F to 400 F with intervals of 50 F for a reservoir with initial
temperature of 150 F.
The simulation results are shown in Fig. 7 and it can be observed
that by increasing the stimulation temperature along the hydraulic
fracture, long term cumulative production can be enhanced. The
larger the temperature difference between the stimulation tem-
perature and initial reservoir temperature, larger is the volume of
desorbed gas that can be recovered. With 400 F of stimulation
temperature, more than 20% additional gas can be recovered after
20 years of production.
5.2. Impact of shale thermal properties
The formation thermal properties such as heat capacity and heat
conductivity used in Eq. (17) may impact the ef ciency of thermal
stimulation. These properties are a function of several parameters
of a particular shale formation, including composition, porosity,
water content, clay content and even changes with temperature
and pressure. Gilliam and Morgan (1987) conducted laboratory
experiments and a systematic study on shale samples form Devo-
nian shale, Pierre shale and Green River shale formation and
Railsback (2011) compiled data of thermal conductivity of sedi-
mentary rocks as shown in Fig. 8.Based on their work and the ranges of temperature and
pressure investigated in this study, the heat capacity in our
model was set from 500 J/(kg K) to 1500 J/(kg K) and heat con-
ductivity was set from 1 W/(m K) to 6 W/(m K), to reect the
possible ranges of these thermal properties in shale and the in-
uence of laminated interbeded formations or layers of sands
and carbonate.
Fig. 9 shows that the formation heat capacity has limited
impact in the early stages of production and has negligible im-
pacts on thermal stimulation effects after 20 years of production,
because the whole SRV region will be heated up to a desired
temperature regardless of formation heat capacity if given enough
time for the heat diffusion process to occur. It should be
mentioned however, that even though the formation heat ca-pacity will not make much difference in the cumulative produc-
tion while the fracture temperature is kept constant, it has a huge
impact on how much energy is required to heat up the formation.
The smaller the heat capacity, the less input energy is required for
heating the formation.
Fig. 10 demonstrates that heat conductivity impacts the cumu-
lative production, especially in the 2e12 years window. The smaller
the heat conductivity, the faster the SRV region can be heated up to
the desired temperature. After the whole SRV area reaches the
stimulation temperature, the heat conductivity becomes less
important.
Fig. 5. Percentage of adsorbed gas produced after 10 years of production.
Fig. 6. Production rate decline during 5 years of production. Fig. 7. Cumulative production with different stimulation Temperature T f .
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5.3. Impact of fracture spacing
The spacing between perforations and the number and orien-
tation of transverse fractures have a major impact on well pro-
duction, and the fracture spacing should avoid stress interference
between transverse fractures in order to obtain optimal fracture
geometry (Roussel and Sharma, 2011; Morrill and Miskimins, 2012;
Wang, H et al., 2014). Hydraulic fracture spacing is a critical
parameter in the design of multi-stage transverse fractures in
horizontal wells. Here we investigate how fracture spacing will
impact the thermal stimulation, starting from our previously
studied base case, i.e. a horizontal well with 20 transverse hydraulic
fractures with 120 ft fracturing spacing.
Fig. 11 shows the cumulative production under different fracturespacing, keeping constant the total reservoir drainage area, with
and without thermal stimulation. It is not surprising that the
smaller the fracture spacing (i.e., the larger number of transverse
hydraulic fractures in the drainage area), and the larger the thermal
stimulation input, the more gas is recovered. Appropriate fracture
spacing should therefore be designed based on the impact of geo-
mechanical effects (stress interference effects) and economic ef-
fects (Net Present Value of heating vs. production).
5.4. Impact of formation permeability
Permeability is one of the most fundamental properties of any
reservoir rock required for modeling hydrocarbon production and
the optimal hydraulic fracture design is also highly dependent on
the reservoir permeability (Economides et al., 2002). Many shale
gas reservoirs have extremely low matrix permeability values in
the range of tens to hundreds of nanodarcies, and the low forma-
tion permeability can adversely impact the pressure diffusion
process so that the transient ow in SRV may dominate the entireproduction life and the average pressure in the SRV will not be able
to decline to a level that allows suf cient desorption before pro-
duction rates reach economical limits.
Fig. 12 shows the cumulative production under different for-
mation permeability scenarios with and without thermal stimula-
tion. It can be observed that the formation permeability seems to
have a negligible impact on how much extra gas (around 2.8 BSCF
for all cases) can be produced after 20 years of production, but the
ratio of cumulative production under heating to cumulative pro-
duction without heating decreases as formation permeability
increases.
5.5. Impact of bottom hole pressure
In order to mimic possible surface production conditions and
constraints on wellhead owing pressure, the corresponding bot-
tom hole pressure (BHP), which is a function of the hydrostatic
pressure difference and the frictional pressure losses in the tubing
string, is also subject to constraints.
Fig. 13 shows the effects of heating shale formation with
different values of BHP. It can be observed that after 20 years pro-
duction, 50% extra gas can be produced when the BHP is 2000 psi
while 20% extra gas can be produced when the BHP is 500 psi. The
is because with higher BHP, the average pressure in the SRV will
never decline to a level that most adsorbed gas can be liberated, so
the temperature effects play a more important role in releasing
adsorbed gas at high BHP.
Fig. 8. Thermal conductivity of different sedimentary rocks (modied from Railsback,
2011).
Fig. 9. Cumulative production with different formation heat capacity C
m.
Fig. 10. Cumulative production with different formation heat conductivity k m.
Fig. 11. Cumulative production with different fracture spacing Y e.
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5.6. Impact of Langmuir volume
According to Eq. (4), Langmuir volume, V L, determines how
much gas can be ultimately adsorbed by the rock matrix, which
reects shale formation's intrinsic adsorption capacity. Altering the
value of Langmuir volume is equivalent to altering the amount of
adsorbed gas initially in place, but the value of Langmuir volume
will not impact the shape of the adsorption curve and the results of
the ve regression parameters of Bi-Langmuir model, as long as the
Langmuir pressure, P L, is xed. Fig. 14 shows the cumulative pro-
duction with different Langmuir volume. The results indicate that
there is considerable improvement in recovery (~30% at 400 scf/
ton) with higher Langmuir volumes, however with smaller
Langmuir volume, less adsorption gas is initially in place and less
extra recovery is achieved by heating the formation. When the
Langmuir volume decreases to 100 scf/ton, the additional gas
recovered by thermal stimulation is negligible.
5.7. Impact of Langmuir pressure
As discussed in the previous section, the Langmuir pressure, P L,
is a function of how readily the adsorbed gas on the organics in the
shale matrix is released as a function of a nite decrease in pres-sure. Different values of Langmuir pressure lead to different shapes
of gas adsorption curves. Table 3 shows the results of the regression
performed to determine the parameters in the Bi-Langmuir model
with different Langmuir pressures.
The larger the Langmuir pressure, the smoother the adsorption
curve will look, as shown in Fig.15. It can also be noticed that with
smaller Langmuir pressure, the pressure has to be suf ciently low
in order to release the majority of adsorption gas.
Fig. 16 demonstrates that in general, larger amounts of gas can
be produced with higher Langmuir pressure, due to the fact that
more gas will be desorbed even at relatively higher pressure. It can
also be observed that with higher Langmuir pressure, less gas will
be desorbed by effects of the thermal stimulation; this is because if
Fig.12. Cumulative production with different formation permeability k g , P L ¼ 500 psi.
Fig. 13. Cumulative production with different bottom hole pressure.
Fig. 14. Cumulative production with different Langmuir volume V L .
Table 3
Estimates of parameters in Bi-Langmuir model with different Langmuir pressures.
Langmuir
pressure
f 1 k1 (1/psi) E 1 (kcal/
mol)
k2 (1/psi) E 2 (kcal/
mol)
500 psi 0.4017 0.0014 2.2032 0.000022262 5.0015
1000 psi 0.4014 0.000941 2.0178 0.0000108 5.0004
2000 psi 0.2673 0.000695 1.7723 0.0000079036 4.7423
Fig. 15. Gas adsorption curve with different Langmuir pressures P L.
Fig. 16. Cumulative production with different Langmuir pressures P L .
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most gas can be released at a higher reservoir pressure, then the
stimulation temperature will become less important.
Fig. 17 shows the cumulative production with different forma-
tion permeability when Langmuir pressure is 2000 psi. When
compared to Fig. 12 where the Langmuir pressure is 500 psi, for-
mation permeability plays a more important role in the effective-
ness of thermal stimulation, the amount of extra gas recovered by
thermal stimulation decreases with increasing formation perme-
ability. This is because when the Langmuir pressure is high, more
adsorbed gas can be released at a higher pressure and the higher
formation permeability can promote the pressure diffusion process
which leads to more desorption due to pressure depletion rather
than temperature elevation.
6. Discussions
The fundamental rationale behind thermal stimulation of shale
gas reservoirs is to promote the desorption of the adsorbed gas by
increasing the formation temperature which alters gas desorption
behavior.
The most important parameters for the effectiveness of thermal
stimulation are Langmuir volume, Langmuir pressure, stimulationtemperature, fracture spacing, reservoir permeability and bottom
hole pressure. Langmuir volume and Langmuir pressure determine
the initial adsorbed gas in place and the shape of the desorption
curve. An ideal candidate for thermal stimulation should have large
Langmuir volume and relatively low Langmuir pressure. In this
study, stimulation temperature in the hydraulic fracture has been
modeled up to 400 F due to limited correlations for gas viscosity at
high temperature. Nevertheless, it was found that the higher the
stimulation temperature, the larger the ultimate recoverable vol-
ume of gas.
Fracture spacing determines how far the virtual boundary will
be away from the hydraulic fracture, the closer the fracture spacing
is, the faster the SRV can be heated upto a desired temperature. The
formation permeability determines how long the transient owregime in the SRV will last and how fast the average pressure will
decline. Its impact on thermal stimulation results depends on
Langmuir pressure as the higher the Langmuir pressure, the deeper
the inuence of formation permeability. Based on the gas adsorp-
tion curve, the value of the bottom hole pressure can determine the
pressure drop prole in the drainage area and affect how much
adsorbed gas can be ultimately produced due to pressure decline.
To a lesser degree, thermal properties of shale formations inuence
the production of thermally stimulated wells. Within the range of
possible values investigated in this study, the shale formation heat
capacity has negligible impacts on the production and heat con-
ductivity only has noticeable inuence on the effectiveness of
thermal stimulation at early years of production.
Overall, the effectiveness of thermal stimulation is largely
dependent on the volume of adsorbed gas that can be recovered by
pressure depletion alone. If the average pressure in the SRV can
drop to a suf ciently low level to allow gas desorption within a
reasonable time frame, then the rationale behind thermal stimu-
lation will primarily be to increase gas production rate to maximize
NPV of the assets. If the average pressure in the SRV cannot reach a
suf ciently low level to allow desorption, then thermal stimulation
has great potential to be used as an effective recovery method to
enhance ultimate recovery in shale reservoirs.
Future research efforts should target laboratory experiment to
explore pressure and temperature dependency, mixed gas
adsorption behavior in an isotropic formations, with laminated and
variable lithologyand the feasibility of using electrically conductive
material or nano-particle coated proppant to heat the shale for-
mation in-situ along created hydraulic fractures via electric or
electromagnetic heating. Additionally, shear induced fracture slip
and formation permeability alteration due to thermal stress should
also be investigated. It should be emphasized that this paper is not
intended to discuss the techniques of heating hydraulic fracture indetail or to determine when to start thermal stimulation process or
how long the stimulation process should last from an economical
point of view. The purpose of this paper is to provide a feasibility
study of enhanced shale gas recovery by heating along hydraulic
fractures, and the results of this study can be used as general
guidance for future research efforts on developing cost effective
thermal recovery method in shale formation.
7. Conclusions
In this study, we proposed a method to evaluate shale gas
desorption as a function of pressure and temperature, by regression
of a Bi-Langmuir model based on Langmuir isotherm data. A fully
coupled unconventional reservoir simulator was developed toinvestigate how thermal stimulation in hydraulically fractured
formations can impact shale gas recovery and what factors most
impact the effectiveness of thermal stimulation. The results of this
study show that thermal stimulation can promote gas recovery and
the production rate of the desorbed gas is primarily determined by
the gas desorption curve, stimulation temperature, fracture
spacing, reservoir permeability, and bottom hole pressure. A good
candidate shale gas reservoir for thermal treatment should have
large Langmuir volume, low Langmuir pressure, relatively small
heat capacity, and high thermal conductivity. On the operational
side, fracture spacing and stimulation temperature are the only two
variables that we can control during treatment design and
execution.
Nomenclature
C m Matrix heat capacity at constant pressure, J/(kg K)
d f Fracture width, m
E Characteristic adsorption energy, J/mol
H Net pay thickness, m
k0 Regression constant, 1/Pa
k f Fracture permeability vector, md
k g Gas permeability vector, md
k m Matrix thermal conductivity, W/(m K)
K (T ) Adsorption equilibrium constant, 1/Pa
m Total gas content, kg m3
mad Gas adsorption mass per unit volume, kg m3
M Average molecular weight, kg/molFig. 17. Cumulative production with formation permeability k
g , P L ¼
2000 psi.
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n Normal vector
p pr Pseudo reduced pressure
P Reservoir Pressure, Pa
P L Langmuir pressure, Pa
q f ow rate vector in the fracture, m3/s m
q g Velocity vector of gas phase, m/s
Q Heat source term in matrix, J m3 s1
Q f Mass source term in fracture, kg m3 s1
Q m Mass source term in matrix, kg m3 s1
R Universal gas constant, 8.3145 J/mol K
r w Well radius, m
sc Choke skin
T Reservoir temperature, K
T f Thermal stimulation temperature along hydraulic
fracture, K
T pr Pseudo reduced temperature
V L Langmuir volume, scf/ton
X e SRV length parallel to the hydraulic fracture, m
Y e Fracturing spacing, m
m g Gas viscosity, Pa s
r g Gas density, kg m3
r g 0 Gas density at standard condition, kg/scf
rm Matrix density, kg m3
Ø f Fracture porosity
Øm Matrix porosity
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