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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: [email protected] (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:[email protected]://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:[email protected]

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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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