shale gas report mscthesis
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Shale Gas enginereing master workTRANSCRIPT
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AES/PE/11-38 Numerical modeling of well performance in
shale gas reservoirs:
The impact of fracture spacing on
production of adsorbed gas.
A.E.Kalantarli
September 26, 2011
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Title : Numerical modeling of well performance in shale gas reservoirs: The impact of fracture spacing on production of adsorbed gas. Author(s) : A.E.Kalantarli Date : September 2011 Professor(s) : Prof. dr. P.L.J. Zitha Supervisor(s) : Dr. C.J. de Pater, Stratagen Prof. dr. P.L.J. Zitha TA Report number : AES/PE/11-38 Postal Address : Section for Petroleum Engineering Department of Applied Earth Sciences Delft University of Technology P.O. Box 5028 The Netherlands Telephone : (31) 15 2781328 (secretary) Telefax : (31) 15 2781189 Copyright ©2011 Section for Petroleum Engineering All rights reserved. No parts of this publication may be reproduced, Stored in a retrieval system, or transmitted, In any form or by any means, electronic, Mechanical, photocopying, recording, or otherwise, Without the prior written permission of the Section for Petroleum Engineering
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Abstract
Shale gas became an important source of natural gas in the United States and is expected to
contribute significantly to worldwide energy supply. This has been the main motivation for the
research and development on shale gas.
Shale gas is found in extremely low permeable organic rich formations that are either a source
rock or a reservoir. Such formations are porous and contain gas, but have almost no matrix
permeability. Shale gas reservoirs from different places have significant differences in structural
environment, mineralogical composition, in depth of deposition and in the thickness of the
productive layer. Besides, each of the shale gas properties vary substantially within the same
producing area. The variability of shale gas properties greatly influences the well performance
that should be taken into account for optimizing gas production.
The focus of this thesis is to investigate the main factors influencing well performance in shale
gas reservoirs: the complexity and conductivity of the fracture network, the proppant
distribution within the complex fracture network, the impact of closure stress on un-propped
and partially propped fracture conductivity, and finally the factor which is intrinsic to shale gas
reservoirs -adsorbed gas. Based on a literature survey, the most important factors prioritized
and numerical simulation models constructed for further investigation of prioritized factors.
The main challenge in development of shale reservoirs is that in order to reach economically
viable production it is indispensible to implement stimulation treatment, such as artificial
hydraulic fractures to connect the natural fractures within the shale rock and to create pathway
for gas to flow into the wellbore.
Shale gas reservoirs are typically comprised of two distinct porous media: the shale matrix
containing the majority of gas storage in the formation but with a very low permeability, and
the fracture network with a higher permeability but low storage capacity. The gas in the
fractures is produced immediately, the adsorbed gas is released as the formation pressure is
drawn down by the well.
The aim of this thesis work is to conduct theoretical research of the influence of above
mentioned factors on well productivity, to prioritize the most crucial factors, and then
numerically model them for two different real cases from shale gas reservoirs of North America,
in order to investigate the effect of specific parameters on well performance, with the further
prospective to model European shale gas reservoirs, as found in the Vienna basin, Northern
Germany, Poland, Southern Sweden , the UK, Brabant, Netherlands.
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Acknowledgements
This report presents my final thesis work as part of MSc study of Petroleum Engineering and
Geosciences specialization track at the department of Geotechnology of the Delft University of
Technology.
The project is performed in cooperation with Fenix Consultancy Delft, an engineering consulting
company. Fenix Consultancy offers range of services, including fracture and reservoir studies,
fracture treatment design and onsite treatment supervision.
First of all, I would like to thank my supervisor at TU Delft Prof. dr. P.L.J Zitha deeply for his
guidance during this project and for willingness to share his expertise on reservoir engineering
with me.
I am grateful to my supervisor Dr. Hans de Pater, manager of Fenix Consultancy Delft, for the
possibility to do my research on this interesting topic in cooperation with Fenix Consultancy.
Special thanks for all of his advice and that he has been willing to share his knowledge and
expertise with me.
Special thanks to Josef Shaoul, for his support on software programmes I used for this thesis
and for sharing his ideas and expertise on modeling hydraulic fractures.
I would like to thank the committee members for their interest in my work and their willingness
to be part of my graduation committee.
Finally, I would like to deeply thank my family and friends for their support and understanding.
Thank you!
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Table of contents
ABSTRACT ............................................................................................................................. 5
ACKNOWLEDGEMENTS .......................................................................................................... 7
1 INTRODUCTION ................................................................................................................ 11
1.1 SHALE GAS RESERVOIRS .............................................................................................................. 11
1.2 SCOPE OF THE THESIS ................................................................................................................. 12
1.3 STRUCTURE OF THESIS ................................................................................................................ 12
2 LITERATURE SURVEY ......................................................................................................... 14
2.1 FRACTURE CONDUCTIVITY ........................................................................................................... 14
2.2 PRIMARY FRACTURE SPACING ...................................................................................................... 15
2.3 MATRIX PERMEABILITY EFFECT ..................................................................................................... 16
2.4 COMPLEXITY OF FRACTURE NETWORK ........................................................................................... 16
2.5 EFFECT OF CARRIER FLUID VISCOSITY ............................................................................................. 17
2.6 IMPACT OF STRESS DEPENDENT NETWORK FRACTURE PERMEABILITY .................................................. 18
2.7 EFFECT OF ADSORBED GAS .......................................................................................................... 19
3 THEORY ............................................................................................................................ 20
3.1 CONDUCTIVITY ......................................................................................................................... 20
3.2 WELL PERFORMANCE ................................................................................................................. 20
3.2.1 Flow regimes ................................................................................................................. 21
3.2.2 End of pseudolinear flow regime .................................................................................. 22
3.3 ADSORPTION ASSESSMENT ......................................................................................................... 23
3.4 IMPACT OF GAS DESORPTION ON THE LONG TERM DRAWDOWN BEHAVIOR ......................................... 25
3.5 CONSTANT PRESSURE FLOW RATE FOR SINGLE TRANSVERSE FRACTURE IN HORIZONTAL WELLS ................... 27
4 SENSITIVITY ANALYSIS ...................................................................................................... 28
4.1 DURATION OF PSEUDOLINEAR FLOW REGIME .................................................................................. 29
4.1.1 Model equation ............................................................................................................ 29
4.1.2 Effect of the physical parameters ................................................................................. 30
4.2 WELL PERFORMANCE ................................................................................................................. 32
4.2.1 The impact of permeability ........................................................................................... 32
4.2.2 Effect of fracture half-length on cumulative production ............................................. 34
4.2.3 Impact of adsorbed gas. .............................................................................................. 35
4.3 SUMMARY ............................................................................................................................... 36
5 MODELING OF SHALE GAS RESERVOIRS ............................................................................. 40
5.1 SIMULATION MODEL SETUP ........................................................................................................ 40
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5.1.1 Shale gas properties ..................................................................................................... 40
5.1.2 Grid, well and hydraulic fracture properties ................................................................. 41
5.2 SINGLE POROSITY MODEL .......................................................................................................... 43
5.2.1 Single porosity model without hydraulic fracture ........................................................ 43
5.2.2 Single porosity model with hydraulic fracture .............................................................. 46
5.2.3 Single porosity multi stage fracturing .......................................................................... 48
5.3 DUAL POROSITY SYSTEM........................................................................................................ 51
5.3.1 Dual porosity without adsorbed gas............................................................................. 52
5.3.2 Dual porosity model with adsorbed gas, coal bed methane option. ............................ 54
5.3.3 Dual porosity model Haynesville case. ......................................................................... 55
5.3.3.1 Comparison with analytical model results ........................................................... 58
5.3.3.2 Multistage fracturing ............................................................................................. 60
5.3.4 Dual porosity model New Albany case. ...................................................................... 67
5.3.4.1 Multistage fracturing ............................................................................................. 70
5.4 ECONOMICS ........................................................................................................................... 75
5.5 SUMMARY ............................................................................................................................. 76
6 CONCLUSION AND RECOMMENDATIONS .......................................................................... 79
6.1 CONCLUSIONS .......................................................................................................................... 79
6.2 RECOMMENDATIONS ................................................................................................................. 81
7 BIBLIOGRAPHY ................................................................................................................. 82
7.1 BOOKS AND ARTICLES ................................................................................................................ 82
7.2 SOFTWARE .............................................................................................................................. 84
8 APPENDIX – FLOW CALCULATION IN ANALYTICAL MODEL ....................................... 85
9 APPENDIX- FLOW CALCULATIONS IN NUMERICAL SIMULATOR................................ 89
10 APPENDIX- GRID REFINEMENT .................................................................................. 92
11 APPENDIX- DUAL POROSITY OPTION ........................................................................ 94
12 APPENDIX – INTRODUCTION OF ECLIPSE300 COMPOSITIONAL MODE .................. 96
13 APPENDIX- ADSORPTION MODEL IN ECLIPSE300 .................................................... 98
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1 Introduction
1.1 Shale gas reservoirs
The global conventional hydrocarbon resources are rapidly declining and will not be able to
meet the future demand of energy. Huge amount of hydrocarbon reserves are still present in
tremendously large, ultra-low matrix permeability unconventional shale gas reservoirs. The
exploitation of shale gas reservoirs have launched a new period of hydrocarbon exploration and
production in the energy industry worldwide. The recent advancements in drilling and
stimulation techniques have made the production from shale gas reservoirs economically viable
(Fazelipour, 2011).
The further development of unconventional gas reservoirs will definitely contribute to the
future energy supply. However, their economic viability depends on the effectiveness of
stimulation treatments. Cost effective production from unconventional shale can be achieved
by multi-stage hydraulic fracturing combined with extended horizontal wells. Hydraulic
fracturing is a stimulation technique where a viscous fluid is pumped into the reservoir together
with sand or ceramic proppant, at downhole pressures exceeding the formation stress. This
causes the formation to break and split apart in the direction perpendicular to the minimum
stress. Such an induced fracture improves the well productivity by creating a conductive
pathway within the rock that provides much better contact between well and reservoir (van
Zelm, 2010; Economides and Nolte, 2000).
The goal of hydraulic fracturing stimulation in shale gas reservoirs is to induce a very complex
fracture network, which is indispensable to achieve economically viable production. This can be
achieved by using large volumes of low viscosity fluids to give an incentive to fracture
complexity and place very low concentrations of small proppant, which differs from
conventional approach of using high viscosity fluid with high concentrations of proppant
(Cipolla et al. 2009).
One of the distinctive features of shale gas reservoirs is the presence of significant amounts of
free and adsorbed gas. Free gas is stored in the pore spaces and the adsorbed gas is attached
on the matrix particle surface (Montgomery et al. 2005; Lewis, 2007). The contribution of the
adsorbed gas to the total production increases over time. Depending on reservoir
characteristics, it may become significant in the later life of the well, when the reservoir
pressure is so low that this induce desorption of the adsorbed gas.
Understanding the performance of such ultra-low permeable media creates new challenges to
scientists. The primary issues in modeling the production of shale gas: (1) accurately describing
gas flow from tight shale matrix into the conductive fracture, (2) properly characterizing the
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matrix block size and the conductivity of the network fractures, (3) evaluating the impact of
stress dependent network fracture conductivity and gas desorption (Cipolla et al., 2009).
Several analytical models were developed for fluid flow in naturally fractured shale gas
reservoirs (Cipolla et al., 2009). However, most of the existing analytical models cannot capture
properly the very long transient behavior in the matrix blocks, which is a key feature for shale
gas due to the ultra-low permeability of the matrix and the presence of adsorbed gas. On that
way, the numerical techniques are more appropriate to model the transient behavior of matrix
blocks. An accurate numerical modeling of fluid flow behavior in shale-gas reservoirs requires a
proper representation of the geological heterogeneities of the formation including complex
fracture network (natural fractures, primary fractures, secondary fracture network), shale
matrix and adsorbed gas. In this project commercial numerical simulator Eclipse2011
(Schlumberger) was used to investigate the production benefit from fractured shale gas
reservoirs.
1.2 Scope of the thesis
The initial objective of the thesis was to conduct a detailed literature survey to identify the
factors affecting well performance in shale gas reservoirs. Afterwards, an analytical model was
constructed to gain further insights of well performance in hydraulically fractured shale
reservoirs, with the aim to make final prioritization of the main factor to be used for further
numerical investigation. Base on the outcome of the literature survey and analytical modeling,
was decided to conduct numerical simulation studies focusing on the effect of primary spacing
on the desorption process. The final aim of the project was to test the impact of desorbed gas
on cumulative production with decreasing pressures and variation of fracture spacing for the
case of horizontal well with single and multi-transverse fractures. On that way, single and dual
porosity numerical models were constructed for two shale gas reservoir cases of North America
(Haynesville shale and New Albany shale) with the further prospective to model European shale
gas reservoirs, as found in the Vienna basin, Northern Germany, Poland, Southern Sweden and
the UK.
1.3 Structure of thesis
This thesis consists of 6 main chapters, starting with the introduction to the general problem
and objectives of thesis in Chapter 1. Next, Chapter 2 provides a literature overview of some
crucial parameters of rock properties as well as the parameters of stimulation treatment design
affecting the well performance in shale gas reservoirs. Chapter 3 includes some theoretical
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background on fluid flow in a reservoir towards a hydraulically fractured well and the basics of
fluid flow regimes.
Chapter 4 considers the sensitivity analysis of pressure interference time between the primary
fractures and of the well performance to different factors in shale gas reservoir using analytical
model discussed in Chapter 3.
Chapter 5 considers the effect of primary spacing on desorption of adsorbed gas on the cases of
Haynesville and New Albany shale gas reservoirs. In this chapter the models were constructed
for single porosity and dual porosity systems using commercial numerical simulator Eclipse2011
(Schlumberger).
Chapter 6 concludes with the main findings of the thesis and provides recommendations for
further research.
Finally, after the thesis bibliography (Chapter 7), a total of 6 appendices are included in the back
of this thesis report (Chapters 8 to 13). The listed chapters provide background information on
the simulations and on decisions made in the project.
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2 Literature survey
In the following chapter, an overview of some crucial rock properties as well as the parameters
of stimulation treatment design is given, for the evaluation of well performance in shale gas
reservoirs using the hydraulic fracture stimulation treatment. The section was mainly focused
on investigation of the following parameters: conductivity of primary fracture and fracture
network, the proppant distribution within the complex fracture network, the effect of fluid
filtrate and the impact of adsorbed gas phenomenon. The results of literature survey in
combination with analytical model were used for numerical simulations in Chapter 5.
2.1 Fracture conductivity
A crucial factor that influences the production profile in fractured reservoirs is the conductivity
of the hydraulic fracture system, which in turn depends on proppant distribution in the fracture
network. Therefore, one of the requirements when modeling production from unconventional
gas reservoirs is to characterize the flow capacity or conductivity of the fracture network and
primary hydraulic fracture (if present). Additionally, the propagation of the proppant within the
complex fracture network and the conductivity of the primary or main fracture (if present) play
a significant role in well performance (Cipolla et al. 2009).
Cipolla et al. (2009) compared the effects of two proppant distribution scenarios in fracture
network, on well performance: (1) when the proppant is evenly distributed through the
fracture network and (2) when the proppant is concentrated in the dominant primary fracture.
In the latter scenario the dominant primary fracture connects to un-propped fracture network.
In that case the production may be controlled by the conductivity of un-propped network.
When the fracture network is evenly propped the concentration of proppant is low and not
sufficient for the cost effective production. Therefore, the un-propped fracture conductivity
may dominate the well productivity, otherwise for efficient even distribution a huge amount of
proppant is required. However, when the proppant is confined within the dominant primary
fracture the average proppant concentration is high in the primary fracture. The result is much
higher conductivity of primary fracture and better connection between the fracture network
and the wellbore, which could significantly improve productivity.
Numerical simulation studies for different ranges of network fracture conductivity have shown
that, reservoirs with a very tight matrix cannot be drained efficiently when the network fracture
conductivity is too low (Cipolla et al. 2009). A drastic increase in gas production was for fracture
network conductivities larger than to 50 md-ft. It was therefore concluded that, for tight
fractured formations with matrix permeabilities in the range of 0,1 µd, fracture network
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conductivities equal or larger than 50 md-ft are required to maximize the production rate.
Cipolla et al. 2009b also highlighted the effect of primary fracture conductivity on production
profile. In the case when sufficiently propped primary fracture exists, the drainage from ultra-
tight matrix can be very efficient. Gas recovery can be significantly accelerated when the
primary fracture conductivity is 20 md-ft, whereas the primary conductivity above 100 md-ft
provides minimal incremental benefits. However, in most cases it may not even be possible to
generate such high conductivity throughout the entire network with low viscosity fluid. On the
contrary when the primary fracture conductivity is not high, the drainage is much less effective
and the reservoir pressure remains significantly higher, indicating poor gas recovery.
Finally, it has to be noticed that when the network fracture conductivity increases up to 500
md-ft, the production signature becomes very similar to that of a high conductivity primary
fracture connected to low conductivity fracture network (Cipola and Lolon, 2009).
2.2 Primary fracture spacing
The primary fracture spacing is controlled by the number of fracture treatment stages, where
increase of number of stages results in closer spacing of primary fractures. As already discussed
in previous section, if the primary high conductive fracture can be created, then the effect of
primary fracture spacing becomes insignificant (Cipolla and Lolon, 2009). Otherwise, the
reduction of the primary fracture spacing, by increasing the number of fracture treatment
stages will positively affect production rates and gas recovery (Cipolla and Lolon, 2009).
The impact of primary fracture spacing on the production profiles was investigated numerically
and compared to production data from two Barnett shale horizontal wells with fracture spacing
of 500-600 ft (Cipolla and Lolon, 2009). The production trend from these wells was similar to
that of 2md-ft uniform conductivity network and the primary fracture spacing 500-600 ft. This
example shows that in reality most of the time it is impossible to reach high conductive primary
and the uniformly conductive network contributes to production. Consequently, the primary
fracture spacing becomes an important issue in order to achieve preferable production rates
and gas recovery. It has to be reminded that Chapter 5 is mainly focused on fracture spacing
variation effect on production of adsorbed gas on case of Haynesville and New Albany shale gas
reservoirs.
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2.3 Matrix permeability effect
Many authors have investigated the effect of matrix permeability on production profile from
shale gas reservoirs (Cipolla et al. 2009). Numerical simulations have shown that the effect of
matrix permeability diminishes with decrease of the network block size. For the block size 50 ft
the increase of the production is only 10% for a 10-fold change in matrix permeability after 15
years production simulation (Cipolla and Lolon, 2009). This is indication that tight matrix blocks
can only be effectively drained if very complex fracture networks created.
The ultra-low matrix permeability also may have effect on flow regimes in shale gas wells. As
production continues in multi fractured wells, the pressure waves travel further into formation.
At some point pressure waves from adjacent transverse fractures will touch each other and the
pressure interference will occur, which defines the time of change of pseudo linear flow regime
to pseudo steady-state flow (Bo Song, 2010). Low matrix permeability tremendously delays the
time of interference between adjacent fractures. The interference occurs earlier with increasing
permeability. That is the reason why often in ultra-low permeability reservoirs the depletion
occurs before reaching the pseudo steady-state conditions.
2.4 Complexity of fracture network
As already mentioned, one of the requirements for cost effective production in shale
formations is the generation of a complex fracture network. The recovery with simple planar
network instead of complex network is possible in nano-Darcy reservoirs, but the recovery will
be a small fraction of the gas in place in any reasonable time period (Warpinski et al. 2009).
Presently the propagation of fracture network can be observed via mapping. Even the best
mapping services provide just general idea of the network that has been created, such as
information on Stimulated Reservoir Volume (SRV) (Warpinski, Mayerhofer et al. 2009).
Although, the recent advances in Microseismic Mapping improved understanding of complex
fracture growth and propagation of proppant in shale gas reservoirs, the overall effectiveness
of stimulation treatments is still difficult to determine. The main difficulty is that the
propagation of proppant and distribution of the conductivity within the facture network cannot
be measured, which are extremely critical parameters that control well performance (Cipolla
and Lolon, 2009).
The effect of fracture network size on production profile assessed by numerical simulation
studies (Cipolla et al. 2009; Mayerhofer et al. 2008). The main conclusion of those simulations is
that gas recovery can be significantly accelerated and drainage markedly improved if more
complex fracture networks (smaller network fracture spacing) can be created instead of simple
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planar fractures. Insights gained from reservoir modeling leads to the development strategies
of shale gas by maximizing fracture complexity, decreasing the spacing between primary
fractures and more fracture treatments in horizontal wells. This can be achieved by using small
proppants to propagate treatment fluid and create new fractures at higher injection rates.
2.5 Effect of carrier fluid viscosity
The hydraulic fracturing treatments in conventional gas reservoirs use high viscosity fluids to
reduce fracture complexity and promote planar fractures. This allows the placement of high
concentrations of proppant needed for economically viable production. However, in shale gas
reservoirs the approach is rather different. Stimulation treatments in shale gas reservoirs use
large volume of low viscosity fluids to promote fracture complexity and to place very low
concentrations of proppant. Low viscosity requires higher pump rates to transport proppant
into the fracture. Furthermore, in shale formations, the conventional treatments are often
uneconomic due to the cost of polymers used to viscosify the fracturing fluids, and to the
damage resulting from polymer retention in such low permeability formations (Cipolla and
Lolon, 2009).
Hydraulic fracturing in shale gas reservoirs in most cases implemented with low viscosity slick
water. Slick water utilized for fracturing shale formations uses much less polymer and have a
viscosity slightly higher than water. It mainly consists of water that is “slickened” with some
additives in order to reduce the friction in the wellbore (Kostenuk, 2010). The use of low
viscosity fluids leads to formation of extended narrow fractures in the reservoir without the
excessive height growth that often observed in fracturing with high viscosity cross-linked fluids
(Zahid et al. 2007). The disadvantage of these low viscosity fluids is in poor proppant
transportation properties. On the other hand, fracturing with low viscosity fluids can decrease
the effective fracture half-length because of phase trapping in the formation.
Many previous researches have been focused on improvement of proppant propagation by
either reducing proppant size or density (both factors lower proppant settling rates according
to Stoke’s law). However using smaller proppant sizes either expensive or can result in lower
fracture conductivities.
Recently, a new method of proppant transportation for slick water fracturing that involves
transformation modifier additive to the slick water fluid was proposed (Kostenuk, 2010). The
additive changes the proppant to an airphilic state and creates micro-bubbles around each
proppant grain. That micro-bubbles change the buoyancy of the proppant allowing it to be
transported in slick water without the use of viscosity or turbulent flow. The new transport
method significantly reduces the proppant settling and proppant banking in slick water shale
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fracturing treatments. With that new method the proppant in slick water is traveling further
distances into the formation without settling (Kostenuk, 2010).
Cipolla and Lolon (2009) conducted the evaluation of production data from Barnett shale
including fracture and re-fracture treatments. The evaluation was performed on wells
stimulated with water–fracs and cross-linked (XL) gel treatment. Although, the XL gel treatment
showed production signatures indicating higher fracture conductivity than the water-fracs re-
fracs, all of the water-fracs re-fracs significantly improved gas production. Water-fracs re-
stimulation treatment forms larger and more complex fracture networks, containing much
more reservoir surface area which explains higher production despite the lower fracture
conductivity (Cipolla and Lolon, 2009).
2.6 Impact of Stress Dependent Network Fracture Permeability
There is high probability that large part of the fracture networks created during stimulation
treatment may be un-propped or only partially propped.
Estimation of the impact of closure stress and Young’s modulus on un-propped fracture
conductivity have shown a dramatic decrease in fracture conductivity as closure stress
increases and Young’s modulus decreases (Cipolla and Lolon, 2009). Numerical simulations
were performed for different fracture spacing including the effect of desorbed gas. The
outcome is higher initial production rates for small sized blocks, while there is very little impact
on the initial production profile when block sizes are larger. In all cases stress dependent
fracture conductivity reduces gas production, as the drawdown in the fracture network
continues to increase throughout the well life (Cipolla and Lolon, 2009).
As a next goal, the effect of Young’s modulus on production profile was investigated. As Young’s
modulus decreases (softer rock), the impact of increasing closure stress on un-propped or
partially propped fracture conductivity becomes more severe (Cipolla and Lolon, 2009). At
lower modulus, the fracture conductivity is reduced significantly as the pressure drop in the
fracture network increases with time, resulting in poor drainage of the tight matrix rock and
significantly lower gas recovery. However, the severity of stress dependent fracture
conductivity may not be critical at early stages of production (Cipolla and Lolon, 2009).
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2.7 Effect of adsorbed gas
As already discussed in previous sections the coexistence of adsorbed with free makes shale gas
reservoirs unique. Because adsorption is related to unconventional mode of gas storage, its
effect was usually not included in conventional reservoir engineering analyses. However, in
some practical reports indicated that adsorbed gas might account for up to over 80% of gas
storage in some shale gas plays (Bo Song, 2010). Consequently, desorption of gas might
significantly contribute to cumulative production and effect the pressure transient behavior in
shale gas reservoirs. It appears to be very important to include adsorbed gas in modeling shale
gas reservoirs. However, in most cases it is extremely difficult to desorb adsorbed gas due to
ultra-tight permeability of matrix.
Figure 2.7.1: Storage mechanism of shale gas reservoirs (Bo Song, Economides, 2011)
Cipolla et al. (2009) performed a series of reservoir simulations based on reservoir properties
typical to Barnett shale to investigate the impact gas desorption on well performance.
According to investigations, at higher pressures more gas is stored in the matrix porosity and
the gas porosity will contribute more to production than desorption. Furthermore, the impact
of flowing buttomhole pressure also has been investigated. It became clear that decreasing the
flowing bottomhole pressure will have insignificant impact on desorption and production of
adsorbed gas.
Little research work has been devoted to the adsorbed gas in shale gas reservoirs. The effects
of the adsorbed gas are poorly understood except that it tends to increase production and
ultimate recovery.
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3 Theory
This chapter provides the theoretical background of gas flow and production in shale gas
reservoirs. Equations for production rates developed incorporating fracture parameters in the
diffusivity based solutions for transient flow regime. The performance of a hydraulic fracture
treatment is evaluated based on cumulative production, which is a function of the production
profile over a period of time. The main objective is to perform sensitivity analysis with the
derived analytical model on some of the parameters discussed in previous chapter, in order to
find out the input parameter for numerical simulations to further detailed analysis.
3.1 Conductivity
Placing the required amount and type of proppant in the fracture is critical for achieving the
goal of a hydraulic fracturing treatment. Several factors including proppant properties
(strength, particle size, roundness), closure stress, fracturing fluid viscosity, damage from fluid
additivies, embedment and the effective fracture width all affect the fracture conductivity. The
conductivity of the fracture can be expressed as a product of proppant permeability and
propped fracture width ( ) (Economides, Martin, 2007). Typically the conductivity of fracture
is measured in millidarcy-feet (md-ft) and one of the key design parameters. The unit of
permeability is length squared and fracture width is unit length. So, the conductivity can be
thought as a volumetric capacity of the fracture to transmit reservoir fluids (Economides,
Martin, 2007).
The most common way to define conductivity is as the dimensionless conductivity ( )
Eq.3.1.1
where k is formation permeability, is the fracture permeability in md, is the propped
fracture width in feet, the fracture half-length in feet.
3.2 Well performance
The well productivity index represents the well rate as a function of pressure drop in the
reservoir and depends on several reservoir properties as well as the flow regime under which
the well is producing. The production of gas in a fractured wells exhibits several flow regimes:
bilinear flow regime, linear flow regime, elliptical flow regime. All of these flow regimes may
not be important and may not last for a very long period (Kelkar, 2008). In this section, the
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importance and duration of different flow regimes will be briefly discussed and the typical flow
regimes for shale gas reservoirs will be emphasized.
3.2.1 Flow regimes
As production starts and the pressure difference between the bottomhole of the well and the
reservoir initiate the flow of the gas into the wellbore, the pressure near the wellbore starts
rapidly decreasing towards the wellbore pressure. Thus, the initial decrease in pressure is
referred to as the ‘transient period’ (van Zelm, 2010; Lake, 2003).
The transient regime consists of several sub-regimes. At very early times, there is flow only
inside the fracture due to expansion of fluid in the fracture as shown in the figure 3.2.1. This
flow regime lasts for a short time and is very difficult to detect (Kelkar, 2008).
Figure 3.2.1 fracture linear flow (Kelkar, 2008)
At slightly later times, bilinear flow regime begins as shown in figure 3.2.2. The first flow regime
which may be observed in very tight or shale gas wells. This flow regime ends when the fracture
tips start affecting the response of the well. During that regime the flow in reservoir becomes
two-dimensional (Kelkar, 2008).
Figure 3.2.2 Bilinear flow (Kelkar, 2008)
At intermediate times the linear flow regime starts, which might be the only flow regime in
ultra-tight shale gas reservoirs. During this flow regime each fracture produces independently
with the reservoir fluid flowing mainly in perpendicularly to the fracture plane with a small
fraction of the flow coming to the fracture tips. The duration of the linear flow regime is
governed by the diffusivity coefficient for the shale gas reservoirs. For very tight reservoirs the
linear flow can extend for several years and it can be the most important flow regime during
production (Kelkar, 2008).
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Figure 3.2.3 Formation linear flow (Kelkar, 2008)
After a transient period the pressure starts to decline with time at a stable rate throughout the
reservoir. That period is named either ‘steady state’ or ‘pseudo-steady state’, depending on
either the boundary is transparent (steady state) or sealing (pseudo-steady state) (van Zelm,
2010; Lake 2003). This flow regime is usually called elliptical, because the equipotential lines are
ellipses. In this flow regime there is interference of the pressure disturbances from adjacent
fractures (Kelkar, 2008).
Figure 3.2.4 Elliptical flow regime (Kelkar, 2008).
3.2.2 End of pseudolinear flow regime
The consideration of appropriate flow condition is an important issue in modeling production
from shale gas reservoirs. In conventional gas reservoirs, the pseudo steady-state flow
condition dominates the production life of a well, and therefore modeling of production profile
considering this flow condition only may be sufficient. The case is different in tight gas
reservoirs, where in the early production period the transient flow is dominant, whereas the
later period governed by the pseudo steady-state condition (Rahman, Rahman , 2001).
However, in ultra-tight shale gas reservoirs the only flow regime might be pseudolinear flow of
the transient period. In this project the analytical solution will concern the pseudolinear flow
regime. The question then arises, how long one should continue to assume transient flow
condition and then switch to the pseudosteady state flow condition, or is it even necessary to
switch to another flow condition.
Bo Song (2011) in his paper expressed equation for end of pseudolinear flow incorporating the
fracture spacing but without taking into account the adsorption factor. That equation defines
the time when the pressure disturbances from two adjacent fractures interfere.
23
2948 ( / 2)
4
t sepfl
c xt
k
[Field units] Eq.3.2.1
A similar equation can also be written in SI units:
20.2666 ( / 2)
4
t sepfl
c xt
k
[SI units] Eq.3.2.2
where k is the reservoir permeability, Xs is the fracture spacing, and ɸ is the porosity. The fluid
properties including μ (viscosity) and Ct (total compressibility) are the average values.
However, in reality the properties of gas changes apparently as pressure changes. In MTFHWs
(Multi Transverse Fractured Horizontal Wells), if we know the fracture spacing, we can estimate
the time when pressure interference between two adjacent transverse fractures occurs, to be
precise the time when the pseudolinear flow ends.
However, it has to be mentioned that in shale gas reservoir, gas desorption also impacts the
pressure investigation time. For the same pressure investigation depth, the corresponding
interference time with the prevalence of gas desorption will be larger than that without gas
desorption (Bo Song, 2010). Therefore, the estimation of interference time should take gas
desorption impact into account. The estimate of interference time with the consideration of gas
desorption can be done by combining the pressure investigation depth calculation and time
shift calculation due the adsorbed gas factor (will be discussed in the following section). If we
know the permeability and fracture spacing, we can apply equations 3.2.1 and 3.2.2 to calculate
a time which of interference which doesn’t take gas desorption into account.
3.3 Adsorption assessment
The most accurate method for determining the adsorbed gas in a formation is through core
sampling and analysis. Depending on the depositional conditions, the adsorbed gas can
represent a large percentage of the gas in place and may have a considerable impact on
production.
Gas adsorption is a surface phenomenon and is a physical bond caused by attractive inter-
molecular forces i.e., Van der Waals forces (Rushing et al., 2008, Bo Song, 2010), while
desorption is the opposite process of adsorption.
Nowadays, the most common used model for quantifying gas adsorption/desorption is the
Langmuir model which is in field units.
24
Lads
L
V pV
p p
Eq.3.3.1
Where, , [scf/ton], the gas volume can be adsorbed by a rock of unit mass, , [scf],
Langmuir volume, the maximum gas volume can be adsorbed, , [psi], Langmuir pressure, at
which half of Langmuir volume gas can be adsorbed, p, [psi], random pressure (Bo Song ,2010).
When using the Langmuir adsorption model the temperature is assumed to be constant and,
for this reason, the plot of the Langmuir formula is called a “Sorption Isotherm” (Bo Song,
2010). This assumption is reasonable when the reservoir flow processes are practically
isothermal but it should be kept in mind that using the Langmuir isotherm for thermal process
can lead to large errors. A typical Langmuir isotherm is illustrated in figure 3.3.1. The adsorbed
gas starts to be desorbed when pressure decreases to a point called the “critical pressure” (Bo
Song, 2010).
Figure 3.3.1: Sorption isotherm. Gas storage capacity is the gas volume that adsorbed by rock of unit mass. Langmuir volume is the maximum gas volume can be adsorbed. Langmuir pressure- at which half of the Langmuir volume can be adsorbed (Boyer, Kieschnick, 2006).
25
3.4 Impact of Gas Desorption on the Long Term Drawdown Behavior
The main effect of gas desorption on the production profile is to delay the pressure decline by
providing an extra gas supply besides the free gas. This is illustrated by a time shift on a log-log
diagnosis plot by making comparison between a drawdown behavior including gas desorption
and without desorption (figure 3.4.1) (Bo Song, 2010).
Figure 3.4.1: Time shift on log –log diagnostic plot due to effect of desorption (Bo Song, 2010). Purple line demonstrates the drawdown behavior including the desorption and green line without desorption. Gas desorption results in an apparent time shift in the early linear flow.
Bo Song (2010) considered that time shift due to gas desorption, and labeled it as the
adsorption index, (the ratio of investigation time with gas desorption to that without gas
desorption). The adsorption index depends on several parameters: , , and
/ads ads noadsI t t
Eq.3.4.1
where is the time including adsorption and the time without adsorption.
26
Bo Song (2010) constructed program for determination of time shift, adsorption index. A large
number of simulations were run to establish the following correlation for the adsorption index
as function of adsorption parameters and reservoir properties:
1ads ads adsI C
Eq.3.4.2
where adsC is the adsorption coefficient:
2
2
log ( / )1( , , ) exp( )
22
L iads i L c
p pC C p p A
Eq.3.4.3
1.0215(6875.34 / 2.4298 0.1992)c i iA p p
Eq.3.4.4
Where is the initial reservoir pressure, - the Langmuir pressure, σ- the adsorption index
correlation coefficient, - correlation coefficient, ɸ- porosity. However, the above correlation
applies only for the range of parameters represented in Table 3.4.1. If the parameters are
outside of the given range, then it is recommended to run new simulation to determine
adsorption index.
Table 3.4.1: The range of parameters for which correlations can be used.
0.01 0.1
0.01 (g/cc) ads 0.1(g/cc)
1000 psi ip 10000 psi
/10ip Lp 10 ip
27
3.5 Constant pressure flow rate for single transverse fracture in horizontal
wells
Bo Song and Economides (2011) presented simplified model for each transverse fracture in
horizontal wells considering only two flow regimes: pesudolinear flow until the time of inter-
fracture interference and pseudosteady state flow after interference. In this work, we only
consider pseudolinear flow regime, taking into account the fact that for very tight reservoirs the
linear flow can extend for several years and which in most cases might be the only essential
regime governing the gas production. The following assumptions have been made : the model
considers single-phase production in single-porosity system from multi transverse fractured
horizontal well, the pressures throughout the production are assumed to be constant and
incorporated using pseudopressure variables, the production from single transverse fracture
and the adsorbed gas is introduced by the adsorbed index.
Applying those assumptions the approximate rate decline behavior for horizontal shale gas well
with equally spaced fractures for a given fracture half-length and given reservoir and adsorption
properties can be calculated (Bo Song, Economides, 2011). The below expression represents the
rate decline behavior of the gas flow rate from a single transverse fracture in single phase
single-porosity system.
2[ ( ) ( )] ( )
0.000264 ( )1424
2
i wf t i f
g
ads
kh m p m p c xq
k tIT
(MSCF/day) Eq.3.5.1
A similar equation can be written in SI units:
7 2 (1/2)
8
7.6326*10 [ ( ) ( )] ( )[ ]6.95*10
i wf t i f
g
ads
kh m p m p C xq
T ktI
(S Eq.3.5.2
28
4 Sensitivity analysis
To demonstrate the long term production behavior of MTFHW (Multi Transverse Fractured
Horizontal Well) in shale gas reservoirs, series of sensitivities were studied using the analytical
model described in previous chapter. Sensitivities are performed to permeability, fracture
spacing, adsorption and fracture half-length. The analytical simulations focused on horizontal
completions, as the majority of shale gas reservoirs are being developed using horizontal wells
with multiple fracture treatment stages. The base case model is designed to capture the typical
characteristics of a producing shale gas field. The list of reservoir, well and fluid properties used
for the base case model are presented in Table 4.1. The model inputs for this project represent
properties approximately similar to reported values for Haynesville shale (Bo Song,
Economides, 2011).
Table 4.1: Reservoir, well and fluid properties for base case model. Properties SI units Field units
, Viscosity 0.000019 Pa*sec 0.019 cp
, specific gravity 0.6 0.6
Pi, reservoir pressure, 62 MPa 9000 Psi
PL, Langmuir pressure, 10.3 MPa 1500 Psi
T, reservoir temperature 140 Celsius 284 F
, porosity 5 % 5 %
k, permeability, 1.5E-19 0.152 µD
, Adsorption density 100 kg/ 0.1 g/cc
Total compressibility 3.2* 0.0002
h, pay zone thickness 60 m 196 ft
Well length 1000 m 3280 ft
Number of fractures 8 8
, fracture half-length 100 m 330 ft
, fracture spacing 92 m 300 ft
m(Pi), pseudo pressure 2.8E+19 Pa/s 5.9*10^8
m(Pwf), pseudo pressure 9.6E+17 Pa/s 2.03*10^7
, initial water saturation
30 % 30 %
Adsorption index 2.38 2.38
29
4.1 Duration of pseudolinear flow regime
4.1.1 Model equation
As stated in the previous chapter, considering the appropriate flow regime is important for
modeling production from shale gas reservoirs. In ultra-tight shale gas reservoirs the only flow
regime observed might be pseudolinear flow of the transient period. There are several reasons
for this and the most important are the effects of adsorbed gas and the low matrix
permeability.
The MTFHW in shale gas reservoirs may produce gas only within a small distance around
transverse fractures so that we will not even see the pressure interference between two
adjacent fractures and the linear flow regime may extend for many decades (Bo Song, 2010).
The focus of the analytical solution of this project will be based on investigation of pseudolinear
flow regime in shale gas reservoirs. The first step is to estimate the duration of the transient
flow regime in order to see the life cycle of reservoir for further sensitivity studies.
20.2666 ( / 2)
4
t sepfl
c xt
k
[SI units) Eq.4.1.1
This equation takes into account the spacing between the fractures ( ), assuming that the
fractures are equally spaced. For the base case model, the reservoir, well and fluid parameters
listed in Table 4.1 were treated. The fluid properties including viscosity ( μ ) and total
compressibility were used as the average values, even though in reality the fluid properties
of gas changes as the pressure changes.
Using the Equation 4.1.1 with fracture spacing of 92 meters, the time of pressure interference
between two adjacent transverse fractures for the base case permeability 1.5E-19 (0.152µd)
is approximately 1.1 years. But, the above equation does not incorporate the effect of adsorbed
gas, which may cause crucial delay of pressure interference. In order to incorporate the effect
of adsorbed gas, the adsorption index was defined. Considering the specific reservoir
properties, =0.05; ip =9000 psi ( 62 MPa); Lp =1500 psi ( 10.3MPa); ads = 0.1 g/cc (100 kg / 3m ),
adsorption index was found to be 2.38 (Bo Song, 2010). Therefore, if gas desorption is taken
into account, the real time of interference should be 1.1 years multiplied by 2.38, which is
around 2.6 years. It means that during first 2.6 years of production each fracture will produce
independently with the reservoir fluid flowing mainly perpendicular to the fracture and only by
30
the end of that time the pressure interference between two adjacent transverse fractures will
occur.
4.1.2 Effect of the physical parameters
Three parameters have an important effect on interference time between two adjacent
transverse fractures: spacing of the fractures, permeability of shale and adsorbed gas. In the
following section the sensitivity of interference time to above mentioned parameters is
considered.
By knowing the fracture spacing, we can estimate the time of pressure interference between
two adjacent transverse fractures (Bo Song, 2010). On that purpose the analytical sensitivity
was performed. The variations of fracture spacing used in the sensitivity analysis are presented
in Table 4.1.2
Table 4.1.2: The impact of fracture spacing variation on duration of pseudolinear flow regime. Adsorption causes substantial delay in pressure interference time.
Xs (fracture spacing)
t_eplf (end of linear flow)
t_eplf (end of linear flow)
t_eplf (end of linear flow)
m Days Years (without
adsorption) Years (with adsorption)
43 85 0.2 0.6
92 399 1.1 2.6
152 1088 3.0 7.1
244 2785 7.6 18.2
As can be seen from Table 4.1.2, the interference time drops from 2.6 years (including adsorbed
gas) to 0.6 years as the fracture spacing decreases from 92 meters to 43 meters. However, if we
increase the fracture spacing, the interference time increases. For example, if the spacing is
increased to 244 meters compared to base case 92 meters, then the end of the pseudolinear
flow will be extended to 18.2 years, meaning that during this time the fractures will produce
independently from each other and the pseudolinear flow will dominate. This shows that the
design of stimulation treatment affects the duration of flow regimes and controlling the
production throughout the well life in shale gas reservoirs.
Another important factor influencing the pressure interference time is the presence of
adsorbed gas. That is why the estimation of interference time should take gas desorption
impact into account. In the following part the effect of the time shift (due to adsorption) on the
duration of pseudolinear flow regime was investigated. The base case model was used for
variation of adsorption indexes presented in Table 4.1.3. The values for adsorption index were
31
used from Bo Song (2010) referring to the program that was made to calculate the time shift,
according to the specific properties: , , and .
Table 4.1.3: The impact of adsorption index variation on pressure interference time.
Adsorption index t_eplf
(-) Years(with adsorption)
1.5 1.6
2.38 2.6
2.65 2.9
3.1 3.4
In the case of adsorption index of 1.5 (extremely low amount of adsorbed gas) the pressure
interference occurs after 1.6 years, however if that index is increased to 3.1 then the
interference time is shifting to 3.4 years.
Finally, the last but not least reason of extended transient period in shale gas reservoirs is the
ultra-low matrix permeability of shale. Different ranges of permeability represented in Table
4.1.4 were used to perform sensitivity investigation of the influence of permeability to the
pressure interference from two adjacent fractures.
Table 4.1.4: The impact of permeability variation on duration of pseudolinear flow regime for the cases with and without adsorbed gas. The pressure interference occurs increasingly earlier with increasing permeability.
k t_eplf t_eplf
Years (without adsorption) Years (with adsorption)
1.5E-19 ( 0.152 µd ) 1.1 2.6
1.9E-19 ( 0.19 µd) 0.9 2.1
2.95E-19 (0.3µd) 0.6 1.3
9.86E-19 (1µd) 0.2 0.4
As long as the permeability increases the duration of pseudolinear flow regime is constantly
shortening. For the case of permeability 1.5E-19 (0.152µd), typical permeability for shale
reservoirs, the duration of pseudolinear flow regime extends to 2.6 years. However, for the
case of 9.86E-19 (1µd) the duration of pseudolinear flow is tremendously decreased to 0.4
years.
There are might be several reasons for comparable short duration of linear flow in this case.
The first reason is high initial reservoir pressure in Haynesville reservoir, which allows the
production at a high initial drawdown, serving for acceleration of pressure wave extension in
reservoir. In many other cases the shale gas reservoirs are shallow depositions with low initial
reservoir pressure, confining production at low drawdowns. The second reason might be the
32
fact that adsorption, representing 12-14% of gas in place, the minor component in Haynesville
case. The impact of that small amount of adsorbed gas on pressure interference time should
not be high. Those two reasons might be the only explanations for shortened pressure
interference time in case of Haynesville shale reservoir. Later in Chapter 5 the numerical
simulations will be performed for the case of Haynesville shale, with high initial reservoir
pressure, small amounts of adsorbed gas and for the case of New Albany shale, where the
initial reservoir pressure is low and the adsorbed gas constitutes about 70% of gas in place, in
order to compare the results of both cases and to validate our assumptions.
4.2 Well performance
In this section the performance of a hydraulic fracture treatment is evaluated based on
cumulative production, which is a function of the production profile over a period of time. The
sensitivities were performed for variety of reservoir and fracture treatment properties affecting
the well performance. Each of those factors may influence well performance that could be used
for optimizing gas production. The rate decline equation for pseudolinear single transverse
fracture, which is discussed in previous chapter, was treated for the purposes of the analytical
modeling.
4.2.1 The impact of permeability
In this section the impact of formation permeability on cumulative production in fractured
horizontal wells was evaluated. The base case model comprises the permeability of 1.5E-19
(0.152µd) the typical value for most of the shale gas reservoirs. In this specific case, the fracture
half-length extends for 100 meters. Based on reservoir, well and fluid properties presented in
Table 4.1 the analytical model for the case of single transverse fracture under constant pressure
was constructed and presented in Figure 4.2.1.
Even though the early production starts with high flow rates, 504 , this production
rate drops quickly and most of the well life the production continues at almost constant low
rates, with just small drops towards the end of 10 years. This is due to low matrix permeability
of the shale, which on its turn does not allow the efficient drainage of the reservoir and only a
small area in the vicinity of the induced fracture can be efficiently drained. For this case the
cumulative production from single transverse fracture after 10 years is 23 ( 819 MMScf).
For validation purposes the results is compared with the similar setup numerical model in
Chapter 5.
33
Figure 4.2.1 shows a significant increase in cumulative production for higher values of
permeability. Each time we increase permeability, the cumulative production is positively
affected. For instance, the increase of permeability to 1.87E-19 (0.19 µd) (red line) will
affect the outcome by additional 26% after 10 years of production. However, the impact is
more severe for 2.95E-19 (0.3µd) permeability. In that case the production from single
transverse fracture reaches the point of 33 M (1150 MMScf) (green line), which is extra 40%
compared to the base case results. Finally, for the case of 9.86E-19 (1µd) permeability
(purple line), the typical range for conventional gas reservoir, the cumulative production is
increased to 60 M (2110 MMScf).
It becomes obvious that even small variability of reservoir permeability affects the production
profile in fractured wells and may have the major impact on cumulative production. In fact the
the modeled range of permeability variability is inherent to shale reservoirs due to different
depositional environments of each individual shale reservoir. For every specific shale gas case,
this reservoir property should be taken under serious consideration. Based on outcome of the
analysis the right fracture treatment design has to be chosen, in order to reach the cost
effective production and the efficient drainage of the reservoir.
Figure 4.2.1: Cumulative gas productions from single transverse fracture for different ranges of permeability. The increase of permeability value has positive impact on outcome of cumulative production for the same fracture treatment design.
0
10
20
30
40
50
60
70
0 1000 2000 3000 4000
Gp
(MSm
3)
time( days)
Gas cumulative production vs time
k=1.5E-19 m^2(0.00015md)
k=1.87E-19 m^2( 0.00019 md)
k=2.98E-19 m^2(0.0003md)
k=9.86E-19 m^2(0.001md)
34
4.2.2 Effect of fracture half-length on cumulative production
We now focus on the impact of fracture half-length on the outcome of 10 years production
simulation in fractured horizontal wells. The aim is to determine to which extent that design
characteristic affects the production profile in ultra-tight shale reservoirs and, how the
improvement of fracture treatment design may have effect on cumulative production. Figure
4.2.2 shows the cumulative gas production profile for different ranges of fracture half-length.
For the base case the fracture half-length extends to 100 m. For this case the cumulative
production from single transverse fracture constitute 23 M (819 MMScf). The decrease of
fracture half-length (depends on the amount of injected proppant) to 70 m diminishes the
cumulative production to 16 (574 MMScf), which is 30% less than the cumulative
production of the base case. Further decrease of the fracture half-length to 45 m will have
larger negative impact on cumulative production. In that case the cumulative production will be
almost 10.5 (374 MMScf), which is 65% decrease compared to the base case results. For
the final run, the fracture half-length is decreased to 15 m. In that case the cumulative
production after 10 years tremendously decreased to 3.5 M (124 MMScf), 15% of cumulative
production of the base case.
Figure 4.2.2: Cumulative gas productions from single transverse fracture for different ranges of fracture half-length. The extension of fracture half-length has significant contribution of gas supply to cumulative production.
0
5
10
15
20
25
0 500 1000 1500 2000 2500 3000 3500 4000
Gp
(MSm
3)
time(days)
Cumulative production vs time
xf=15m
xf=46m
xf=70m
xf=100m
35
The simulation runs for different fracture half-length ranges show that the increase of fracture
half-length from 15 m to 100 m provides 19.5 M (695 MMScf) extra gas supply. The
extension of the fracture half-length is the function of fracturing fluid amount pumped during
treatment. This depends on fracture treatment design and varies from reservoir to reservoir.
The optimization of this property can improve the production economics from shale gas
reservoirs.
4.2.3 Impact of adsorbed gas.
Figure 4.2.3 show analytically the impact of adsorbed gas on cumulative gas production for
typical fractured horizontal shale gas completion. The adsorption factor is incorporated in rate
decline equation as adsorption index, the ratio of investigation time with gas desorption to that
without gas desorption. The list of reservoir, well and fluid properties used in base case model
are presented in Table 4.1. Increase of adsorption index means increase of the ratio of
investigation time with gas adsorption to that without adsorption, which on its turn means
increase of presence of adsorbed gas in the reservoir.
Figure 4.2.3: Cumulative gas productions from single transverse fracture for different values of reservoir permeability.
0
5
10
15
20
25
30
35
40
0 500 1000 1500 2000 2500 3000 3500 4000
Gp
(MM
Sm3
)
time(days)
Cumulative production vs time
No adsorbtion
Iads=1.5
Iads=2.38
Iads=2.7
Iads=3.1
Iads=3.7
36
In the base model the cumulative production from single transverse fracture reaches 23 M
(819 MMScf). In the next run we used adsorption index equal to 1 meaning that no adsorbed
gas is present in the model. In that case the entire gas in place is stored in matrix pores. In this
case, the cumulative production after 10 years becomes 36 M (1263 MMScf) which is 54%
higher than cumulative production of the base case. As a next, the adsorption index 1.5 is
treated, which means the increase of the amount of adsorbed gas in the reservoir in
comparison to no adsorption case. For this case the cumulative production of the analytical
model becomes 25% higher than the base case production (red line).
Finally the cases with adsorption index higher than the base case index were investigated. In
the beginning the adsorption index value was increased to 2.7 (means that adsorbed gas
constitute 16% of gas in place). In that case the cumulative production after 10 years becomes
22 M (776 MMScf), which is 5% less than the cumulative production of the base case. Further
increase of adsorption index to 3.1 and 3.7, leads to cumulative productions 20 M (717
MMScf) and 18 M (656 MMScf) respectively.
4.3 Summary
A series of analytical computations were performed to gain insight into gas production from
horizontal wells completed with hydraulic fracture treatments in shale gas reservoirs. The
analytical modeling proved that the productivity of shale gas reservoirs has significantly
affected by the following factors: the permeability of shale, the presence of adsorbed gas, the
extension of fracture half-length and the primary fracture spacing. Each of those factors may
influence well performance that could be used for optimizing gas production.
Another way to represent the influence of input parameters that can be used in the sensitivity
analysis is the tornado plot. A tornado plot of the analytical evaluation of productivity of low
permeability reservoirs is shown in Figure 4.3.1. The tornado plot presents the sensitivity of the
computed value, in this case cumulative production, to the input parameters, sorted according
to the difference between the low output and the high output. It may not be immediately clear
which parameter has the largest influence. This is caused by the fact that a relatively large
difference in high and low input will always result in a large difference between both outputs,
even if the parameter itself is not the most influencive one. Therefore, the range of input
parameters should reflect realistic differences that will occur in practice. With that purpose the
range of parameters used in sensitivity analysis is taken from practical cases: Barnett–
Woodford shales, Fayetteville shale, Coney shale, Floyd shale (Alabama), Lewis/Mancos shales,
Haynesville shale, New Albany shale.
37
Figure 4.3.1: Tornado plot of analytical evaluation of productivity of shale gas reservoirs.
According to Tornado plot the reservoir permeability is one of the main factors that controls
the production profile in fractured wells and may have the major impact on cumulative
production in ultra-tight gas reservoirs. The variation of permeability from 1.5E-19 (0.1 µd)
(typical permeability for shale gas) to 9.86E-19 (1 µd) has incremental effect on cumulative
production up to additional 37 M . Moreover, the permeability of rock also has crucial effect
on duration of transient flow period. The pressure interference between two adjacent fractures
occurs increasingly earlier with increasing permeability. Most of the time, due to ultra-low
permeability the depletion in shale reservoirs occurs before reaching the pseudo steady-state
conditions. In this case transient solution should be considered as the main flow regime during
the life of the well in ultra-tight gas reservoirs.
In that way another factor having huge influence on production in shale gas reservoirs is the
extension of fracture half-length. The fracture half-length is stimulation treatment property
that directly depends on fracture treatment design. In our model the variation of that property
from 15 m to 100 m reflects on increase of cumulative production after 10 years up to
additional 33M . The fracture half-length in shale gas can be optimized with the use large
volume of low viscosity fluids to promote fracture complexity and place very low
concentrations of small proppant, which is completely different approach from that used in
conventional gas reservoirs. In fact, the right choice of fluid filtrate viscosity and the
optimization of the fracture half-length in unconventional reservoir may have incremental
effect on production profile and play one of the major roles in increase of the recovery factor.
0.15 µD
15 m
3.7
1 µD
100 m
1
0 10 20 30 40 50 60 70
Permeability
Half-length
Adsorbtion
Cumulative gas production (Mm3)
38
Another fracture treatment property that may have significant influence on production in shale
gas reservoirs is fracture spacing. Although, this property is not incorporated in our analytical
model, but the effect of spacing has been included in calculations of the duration of
pseudolinear flow. As a result of sensitivity analysis, it was determined that, the design of
stimulation treatment might be a crucial factor effecting the duration of the well life in shale
gas reservoir. The fracture spacing influences the desorption process and thus, has effect on
cumulative production. The impact of desorption on cumulative production increases when the
fracture spacing is smaller. By reduction of the spacing between primary fractures and pumping
more fracture treatment stages will speed up the pressure interference time and thus will
contribute to effective drainage of the reservoir.
Among all of the investigated factors the most interesting and mostly less investigated one is
adsorbed gas. Experimental measurements have indicated that more than 50% of the total gas
in place in shale may exist as an adsorbed phase (Xiao-Chun Lu et al., 1995). Analytical
sensitivity determined that depending on depositional environment, the adsorbed gas might
have an impact on well performance. Furthermore, the adsorbed gas may have significant
effect on pressure transient behavior in shale gas reservoirs. For the same pressure
investigation depth, the corresponding investigation time with the existence of gas desorption
will be longer than that without gas desorption. Therefore, the estimation of interference time
should take gas desorption impact into account.
Even though, in the Tornado plot the impact of the adsorbed gas on well performance is less
noticeable, taking into account the fact that adsorbed gas might account for up to over 80% of
gas storage in some shale gas plays (Bo Song, 2010) it can moderately contribute to the
cumulative gas production from unconventional shale reservoirs. Although, it is extremely
difficult to desorb adsorbed gas due to ultra-tight permeability. The desorption can allow for
significantly larger quantities of gas to be produced. With depletion of conventional gas
reservoirs, the optimization of the desorption of adsorbed gas can contribute to global energy
supply.
To determine the impact of adsorbed gas in multi transverse fractures horizontal wells, the
further detailed numerical investigations are required. That is because, the analytical model is
simplified, it comprises only single phase production and does not incorporate some fracture,
reservoir and fluid properties which are playing crucial role in well performance. Additionally
the analytical model does not incorporate the natural fractures within the shale reservoir,
which is inherent factor to this kind of reservoirs and might influence significantly to the
production. On that way, it is important to construct numerical model and make sensitivity
39
analysis of production profile to adsorbed gas and the influence of desorption on cumulative
production. In the next section the numerical models for shale gas including the adsorption
factor will be presented. Initially, simplified single porosity models will be presented and later
on elaborated dual-porosity models including adsorbed gas will be considered. The main
objective of numerical sensitivity analysis will be the investigation of the effect of desorption on
cumulative production, for variations in fracture spacing on the example of Haynesville and
New Albany shale reservoirs.
40
5 Modeling of Shale Gas Reservoirs
This chapter focuses on modeling well performance in shale-gas reservoirs using numerical
simulations. The special attention is paid on contribution of adsorbed gas production for variety
of fracture stages on the example of two real shale gas cases: Haynesville shale and New Albany
shale. In case of Haynesville shale, the adsorbed gas is a minor factor, while in New Albany case
the adsorbed gas dominate and might constitute up to 70% of gas in place.
Section 5.1 presents the model setup: grid, well and hydraulic fracture properties. Section 5.2 is
focused on single-porosity model of various cases, and section 5.3 discusses the dual-porosity
model, on the example of Haynesville and New Albany shale cases, where adsorption and
natural fractures are included, which are typical characteristics of shale gas reservoirs. Finally,
section 5.4 considers some economic calculations followed by section 5.5 with the main
findings during numerical modeling.
5.1 Simulation Model Setup
5.1.1 Shale gas properties
The recovery in shale gas is determined by a number of factors, including the: permeability of
rock, artificial stimulation (hydraulic fracturing), reservoir pressure and drainage area of a well,
presence of a natural fracture system in the formation. In the following models all of the above
mentioned factors will be analyzed to some extent. On that way, the base case model is
designed to capture the typical characteristics of a producing shale gas field. The parameters in
Table 5.1 are chosen for the following model cases.
Table 5.1: Model parameters.
Depth to reservoir 3500 m
Model size(L-W-H) 400-153-65 m
Reservoir pressure 620 bars
Porosity 5 %
Permeability 0.152 µD
Water Saturation 0.3 -
Fracture 100 m
As it already discussed in previous chapters, shale gas reservoir have unique geological and
operational characteristics: tight rock matrix in nano-darcy range permeabilities, gas adsorbed
on matrix surface, natural fractures and induced hydraulic fractures. Thus, each of the listed
factors complicates the modeling of shale gas reservoirs.
41
The base case model has a matrix permeability of 0.152 µd. The model is assumed to be
uniform in all its properties, so the horizontal and vertical permeabilities are both 0.152 µd.
Typical shale gas reservoirs exhibit porosity of 4-8%, as it shown in studies of Barnett Shale
(Cipolla et al., 2009). Therefore, in the base case model, the average porosity of 5% was chosen
and it is uniform throughout the reservoir.
The initial reservoir pressure for the base case model was chosen to be 620 bars, based on the
study from Haynesville shale (Bo Song, 2011). However, it is difficult to relate this range to
typical shale gas reservoir, because shale gas reservoirs have significant differences from place
to place, as they can be shallow or deep, high-pressured or low-pressured, high-temperature or
low-temperature.
For the cases of two-phase modeling (gas-water), a uniform water saturation of 0.3 is assumed
throughout the reservoir, and gravity/capillary effects in the vertical direction are not included
to the initial water distribution. Two saturations zones were defined in the model, the first one
for matrix and the second zone for induced fracture. It should be noted, that in reality due to
low matrix permeability, the production from shale gas reservoirs is not so sensitive to
saturation and PVT curves, and it is not a big issue for the type of study that we conduct in this
work. The standard simple saturation curves for shale gas reservoirs were used for the
following single and dual porosity models. The reservoir gas PVT properties and saturation
tables are taken from a similar ultra-tight matrix modeling study (David H et al. 2002).
5.1.2 Grid, well and hydraulic fracture properties
For single-porosity system cases, the commercial black oil reservoir simulator Eclipse2011
(Schlumberger) was used to model the factors affecting the well performance in hydraulically
fractured horizontal well. The simulation model comprises the reservoir as a number of discrete
units in 3D and the modeling executed by the progression of fluid fronts through space and
time, in series of discrete steps (Schlumberger, 2005).
The synthetic reservoir model is a rectangular block, shown in Figure 5.1, with a length of 400
m, a width of 153 m and thickness of 50 m. The base case grid consists of 81 cells in x-direction
(length), 51 cells in y-direction (width) and 15 cells in z-direction (height). In fact the shale
reservoirs can extend for kilometers in length, but in this work, for simplicity purposes just 400
m long reservoir was modeled.
Simulations focused on horizontal completions with transverse fractures, as the majority of
shale gas reservoirs being developed using horizontal wells with multiple fracture treatment
stages. Transverse fracture means that the main or primary fracture representing the propped
42
fracture is connected to the wellbore in a perpendicular direction. The horizontal section of the
well is placed in the middle of z- direction at the edge of grid block ( grid cell in y-direction).
The vertical length of the well from surface to the top of the reservoir is 3500 m, after which
the reservoir continues for 65 m. The well has a production tubing of inner diameter 7.67 cm (3
inch).
Figure 5.1.: Synthetic reservoir model.
In view of symmetry only half of the reservoir block drained by the well was used in this study,
which means that only 1/2 of the model was modeled and the well is located at the edge (51th
grid cell in y-direction) of the grid block. Due to this symmetry, the simulated well rates are 50%
of the actual values.
The hydraulic fracture is designed as an induced zone of enhanced permeability and porosity in
y-direction of the grid. The extension of the induced zone was treated as the propped fracture
half-length, which is extends to 100 m. In order to model the same fracture storage space and
transmissibility as in the real fracture, the porosity and permeability of the fracture is scaled
down proportionately. This procedure is standard in hydraulic fracture modeling and results in
sufficiently accurate simulations (Shaoul et al., 2006).
In this thesis work, the host grid refinement option is chosen for the reservoir model. The grid
contains a refinement in the x-direction, in that part where the hydraulic fracture was induced.
The width of the refined grid cell is treated as the width of induced fracture. As it referred
earlier, the refined cells belong to induce fracture zone, where the fluids from the lower
43
permeability matrix, where pressure and saturation changes are small, transfers into the high-
permeability fracture. This discontinuity requires good grid resolution, and therefore smaller
grid blocks and small time steps (van Zelm, 2010). More information about the refinement
option used in this study can be found in Appendix 10.
5.2 Single porosity model
The numerical simulations of shale gas reservoir performance can be categorized in two main
systems: single porosity and dual porosity. The single porosity approach does not effectively
depict the shale gas reservoirs, as some important characteristics like adsorbed gas and natural
fractures within the reservoir cannot be captured. However, for sensitivity analysis purposes
both of these approaches will be considered and systematically compared in this work.
5.2.1 Single porosity model without hydraulic fracture
In this section, as a first step a simplified case with single porosity system is considered. In this
approach the reservoir is discretized and the induced fractures are represented with grid cells
as single planar planes (in x or y-direction) (Cipolla et al. 2009). Using single porosity system no
natural fractures and no adsorption gas are considered, which are typical properties for shale
gas reservoirs. In single-porosity approach the model grid was initially discretized with
permeability of 0.152 d and afterwards the induced fracture with scaled permeability and
porosity was introduced. As a first, the single porosity single-phase (gas) and two-phase (gas-
water) models without hydraulic fractures were simulated, to verify that the cost effective
production cannot be achieved in absence of stimulation treatment. For these models the
parameters listed in Table 5.1 were used. In the cases of single phase model it was assumed
that the reservoir is fully saturated with gas and no other phase is presented, which is far away
from reality, because water always present phase in any reservoir, at least at a level of connate
water. For the cases of two-phase modeling (gas-water), a uniform water saturation of 0.3 is
assumed throughout the reservoir. For current simplified cases the production was simulated
from horizontal well for 2 years. The well was put under bottom-hole pressure control with
constant BHP of 160 bars throughout the production with the initial drawdown of 460 bars.
Such a big drawdown is a usual practical case for most of the shale gas reservoirs all over the
world due to critically low permeability of the shale. Furthermore, as the low pressure is the
primary issue for the release of adsorbed gas, in most cases it is necessary to go to possibly high
drawdown in order to desorb adsorbed gas.
44
At this point, in order to establish the reference level for the production from shale gas
reservoirs, the normalized production term is introduced. Normalized production can be
achieved by division of acquired production by reservoir quality/drawdown or by production of
a vertical well with single fracture stage. For the type of study that we conduct, it is more
appropriate to use the vertical single fracture case for normalization, as the unstimulated case
is unsuitable.
Rough estimates were also made to establish economic cut-off. The cost of single horizontal
well with single transverse fracture treatment is used as a reference level for economic cut-off.
The design assumes $425k/1000m (US price) for drilling the vertical segment and $720k/1000m
(US price) for the horizontal segment (Bo Song and Economides, 2011). The gas price is
assumed to be $0.15/ (US price), 15% royalties and 4% discount rate. The single fracture
stimulation treatment is assumed to cost in average $100,000 (US price). According to rough
estimates, the single horizontal well with single transverse fracture for the base case reservoir
properties costs $1,750,000 (US price). Approximately 12.5 M of produced gas payouts that
cost at 15% royalties and 4% discount rate after 10 years of production. Due to the half
symmetry of the synthetic reservoir model that was treated in this study, only 50% of that value
should be used for the comparison purposes. The production of 6.25 M will be the reference
level for the following simulation cases, and any production below that point will be accounted
out of economic interest.
The following simulations were performed for 4 different matrix permeabilities, starting with 10
µd reservoir permeability and ending up with the permeabilities inherent to unconventional
shale reservoirs. The results of simulations are depicted on figures 5.2.1 and 5.2.2. Table 5.2.1
shows the gas production after 2 years, both as a normalized and the numeric gas volume.
Some minor production can be reached with the permeability of 10µd (red line). Even in the
case of permeability 1 µd (blue line), the value typical for tight gas reservoirs, some amount of
gas can be produced without stimulation treatment. However, in the case of permeability
k=0.152 µd (green line) and k=0.01 µd (orange line) hardly any production can be achieved
without stimulation treatment. This caused by the lowered normalized gas production after 2
years; resp. 0.0002 and 0.00007 compared to 0.01 for the 10 µd permeability model. In the case
of very low permeable matrix the gas phase is immobile within the rock, and there is no
conductive pathway for gas to flow inside the wellbore. In that case, the reservoir pressure
throughout the production remains almost the same as initial reservoir pressure and hardly any
production can be reached.
45
Figure 5.2.1: Single porosity model. Single (gas) phase simulations without stimulation treatment for various ranges of matrix
permeability. In case of 0.152 and 0.01 µD permeability it is hardly possible to achieve any production without stimulations
treatment.
Figure 5.2.2: Cumulative gas production after 2 years of production without stimulation treatment, for various ranges of matrix permeability. The plot shows that the unstimulated production is not cost effective.
0
20
40
60
80
100
120
140
kSm
^3
After 2 years of production
Cumulative gas production
k=10 microdarcy
k=1 microdarcy
k=0.152 microdarcy
k=0.01 microdarcy
46
Table 5.2.1: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
These simulation cases prove the fact that the tight shale matrix cannot be effectively drained
without presence of conductive pathway for gas to flow inside the wellbore. Therefore, almost
every well in a shale gas reservoir must be hydraulically stimulated (fractured) to achieve
economical production.
5.2.2 Single porosity model with hydraulic fracture
For the following cases an hydraulic fracture of 100 m half-length (assumed as propped fracture
half-length) was introduced as an induced zone of high permeability and porosity in y-direction
of the grid. As it already discussed in previous section, the model grid was refined in x-direction
at the place where hydraulic fracture is induced. In this case the fracture is placed on cell
in x-direction (in the middle of grid length) and the fracture half-lengths extends in y- direction
capturing 40 grid cells (100 meters). The porosity and permeability of the fracture is scaled
down proportionately to 0.5% and 500 mD respectively. As in previous cases, the simulations
were performed for single and two phase models for two permeability values, k=0.152µd and
k=0.01µd. The production was simulated for 10 years and the results of simulations are shown
in the following graphs (figures 5.2.3 and 5.2.4).
The simulations show that the induced fracture of 100 m half-length has positive effect on
production profile in ultra-tight matrix models. If without induced fracture the production from
tight matrix was not viable, in case with induced fracture of 100 m half-length the production
becomes more or less attractive. Of course, these models do not capture some important
characteristics of shale gas, like adsorbed gas and natural fractures, which in fact have
contribution on cumulative production from shale gas reservoirs.
Simulation scenario
Normalized production
(2years)
Numeric production
(2 years)
(-) Ksm^3
k=10 µD 0.01 125
k=1 µD 0.002 14
k=0.152 µD 0.0002 2.5
k=0.01 µD 0.00007 0.8
47
Figure 5.2.3: Cumulative gas production after 10 years of production simulation, for k=0.152 µd and k=0.01 µd. Single and
two phase models.
In the case of k=0.152 µd the cumulative production for single-phase and two-phase models
reaches 8.6 and 4.2 respectively, recovering 12% and 6% percent of gas in place.
In case of single-phase model the cumulative production is higher than that for case of two-
phase. The reason is that in single-phase models the reservoir block including the induced
fracture is initially fully saturated just only with gas phase, and well only produces gas.
However, in case of two-phase simulations a uniform water saturation of 0.3 is assumed
throughout the reservoir, and along with gas the water phase is produced which on its turn has
effect on cumulative production. It can be seen, that the production from the two-phase single-
fracture model is 3% less than the economic cut-off and thus, that recovery does not even
payout the well costs and cannot be economically attractive. If we pay attention to the lower
permeability case k=0.01 µd, which is typical for some gas shale reservoirs of North America,
we can obviously see the effect of low matrix permeability on cumulative gas production. In
case of single-phase model the production decreased to 2.4 compared to 8.6 and
in case of two-phase model the production deteriorated to 1.2 . The recovery
tremendously decreased to 3.5% and 2.5% respectively. This example shows that at the same
model setup one fold change of matrix permeability has 70% effect on cumulative production
of both simulation models. This caused by the lowered normalized gas production after 10
years; resp. 0.21 and 0.11 compared to 0.71 and 0.38 for one fold higher permeability models
(Table 5.2.2).
48
Figure 5.2.4: Cumulative gas production after 10 years.
Table 5.2.2: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation scenario
Normalized production (10 years)
Numeric production (10 years)
(-) Msm^3
k=0.152 µD 1-phase 0.71 8.5
k=0.152 µD 2-phase 0.38 4.5
k=0.01 µD 1-phase 0.21 2.5
k=0.01 µD 2-phase 0.11 1.3
As a result, none of models can even reach the point of economic cut-off and cannot be
considered as economically viable. In most cases the production is not economically viable with
single fracture stimulation treatment and, in order to reach the cost effective production the
multi stage treatments should be applied.
5.2.3 Single porosity multi stage fracturing
In this approach the reservoir is fractured in multiple sections with a specific distance between
the fractures. The actual goal of this work is to determine how fracture spacing design has the
effect on production of adsorbed gas in shale gas reservoirs. But, before considering the case
with all the characteristics typical to shale gas reservoirs, it is useful to treat multi-frac cases
12% recovery
6% recovery
3.5% recovery
2.6% recovery
Economic cut-off 6.25 MSm^3
0
1
2
3
4
5
6
7
8
9
MSm
^3
Production after 10 years from single transverse fracture
Cumulative gas production
k=0.152 microdarcy 1-phase
k=0.152 microdarcy 2-phase
k=0.01 microdarcy 1-phase
k=0.01 microdarcy 2-phase
49
with simplified single porosity system, to see how the matrix permeability effects the pressure
interference time between two adjacent fractures.
Thus, in order to alter the fracture spacing the number of fracture stages has to be changed. In
the following cases, two simulation models with different numbers of fracture stages were
treated. In the first case, the model with 2 hydraulic factures and 200 m spacing in between
was simulated. However, the second case comprises 6 fracture stages with fracture spacing of
66 m. Both cases were simulated for k=0.152 µd and k=0.01 µd. In these runs the distance
(spacing) between primary fractures is varied but the lateral length is kept the same for all the
cases (the distance in x-direction is always 400 meters). All simulations assume that the main
fracture is 100% effectively propped. The simulation results are presented on figures 5.2.5,
5.2.6 and 5.2.7. Table 5.2.3 shows the gas production after 10 years, both as a normalized and
the numeric gas volume.
Figure 5.2.5: Gas cumulative production after 10 years, for variation of fracture stages.
As it was supposed the case with 6 fractures and 66 m fractures spacing contributes more to
the cumulative gas production, than the case with 2 fractures and 200 m fracture spacing. In
the case of k=0.152 µd, both fracture spacing variations have recovery overpassing the
economic cut-off point, with the highest recovery of 36% in the case of 6 fracture treatment
stages. However, the case of 2 fracture stages and 200 m fracture spacing just payouts the
production costs calculated as economic cut-off. For the models with k=0.152 µd, the pressure
50
interference between two adjacent fractures, for the case of 6 fracture stages, is captured after
4 months of production. In the case of 2 fractures stages the interference time is delayed up to
2.2 years.
Figure 5.2.6: Cumulative gas production after 10 years, for different ranges of fracture stage and matrix permeability.
Table 5.2.3: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation scenario
Normalized production (10 years)
Numeric production (10 years)
(-) Msm^3
k=0.152 µd 6 fracs 1.26 15
k=0.152 µd 2 fracs 0.66 7.8
k=0.01 µd 6 fracs 0.55 6.5
k=0.01 µd 2 fracs 0.21 2.5
The decrease of matrix permeability to k=0.01 µd results in significant drop of cumulative
production. In the case of 6 fractures stages the production might be accepted as economically
viable, exceeding the economic cut-off for 3.5%. However, the case is different for the fracture
spacing of 200 m. In that case the recovery is 6% of gas in place, and is not even sufficient to
payout the well costs. One fold permeability decrease delays the pressure interference time up
to 2 years in the case of 6 fracture stages. In the case of 2 fractures stages the interference time
even cannot be captured after 10 years of production simulation.
36% recovery
16% recovery
19% recovery
6% recovery
Economic cut-off 6.25 MSm^3
0
2
4
6
8
10
12
14
16
M S
m^3
After 10 years of production
Cumulative gas production
6 fracs 66m spacingk=0.152 microdarcy
6 fracs 66m spacingk=0.01 microdarcy
2 fracs 200m spacingk=0.152 microdarcy
2 fracs 200m spacingk=0.01 microdarcy
51
As a conclusion, it has to be noted that one fold change of matrix permeability has huge effect
on production profile and the duration of flow regimes in unconventional gas reservoirs.
Figure 5.2.7: Pressure distribution in the reservoir after 10 years of production. Upper picture corresponds to k=0.152µd and the bottom picture to k=0.01µd. One fold decrease of matrix permeability significantly delays pressure interference time between adjacent fractures.
5.3 Dual porosity system
Shale gas reservoirs present numerous challenges to analysis that conventional reservoirs
simply do not provide. The first of these challenges to be discussed is the dual porosity nature
of these reservoirs. Shale gas reservoirs almost always have two different storages, the rock
matrix and the natural fractures (Gale et al. 2007; Lewis, 2007). The natural fractures are
generally closed due to the pressure of the overburden rock (Gale et al. 2007; Lewis, 2007). In
order to model such reservoirs the dual/multi porosity option can be used together with the
coal bed methane option. Dual porosity system is usually standard practice to hydraulically
fracture shale gas reservoirs in order to achieve economically sustainable flow rates.
52
5.3.1 Dual porosity without adsorbed gas
As a first, the simplified dual porosity case without adsorption is considered. In a dual porosity
reservoir, fluids exist in two interconnected systems: the rock matrix, which usually provides
the bulk of the reservoir volume and the highly permeable rock fractures. To model such
systems, two simulation cells are associated with each block in the geometric grid, representing
the matrix and fracture volumes of the cell (Schlumberger, 2011).Unlike a dual porosity oil
reservoir model, in which the matrix has both an associated pressure and an oil saturation, only
the gas concentration in the shale is tracked. In the fracture system, however, the standard
flow equations are solved (Schlumberger, 2011). A matrix-fracture coupling transmissibility is
constructed automatically by Eclipse (Schlumberger) to simulate flow between the two
systems. The detailed description of dual porosity model features is presented in Appendix 12.
The rock compaction tables were used to model the collapse of pore channels due decrease of
fluid pressure. Two saturations zones were defined in the model, the first one for matrix and
natural fractures and the second zone for induced fracture. It is practical issue for dual porosity
modeling to define matrix and natural fracture as single saturation zone. It should be noted,
that in reality due to low matrix permeability the production from shale gas reservoirs is not so
sensible to saturation curves. As in the case of single porosity models the standard simple
saturation curves for shale gas reservoirs were used for the following dual porosity system.
The hydraulic fracture of 100 m half-length (assumed as propped fracture half-length) was
introduced as an induced zone of high permeability and porosity in y-direction of the grid. As it
already discussed in previous sections, host grid refinement option was used. The model grid
was refined in x-direction at the place where hydraulic fracture is induced.
Table 5.3.1: The dual porosity model setup.
Reservoir pressure, bar 620
Model size(L-W-D), meters 400-153-50
Depth to reservoir, meters 3500
Rock density, kg/ 2650
Matrix 1-6 cells (in z-direction)
Porosity, % 5%
Permeability, µD 0.152
Fracture 7-12 cells( in z-direction)
Porosity, % 0.05
Permeability, µD 0.152
Induced fracture
Porosity, % 0.5
Permeability, mD 500
Fracture half-length , m 100
53
For dual porosity modeling Eclipse300 compositional mode was used instead of Eclipse
100.More information about the differences between two simulators and the reason why it was
switched to compositional mode can be found in Appendix 13.
As a first, the base case model for dual porosity system was simulated. The model setup is
shown in Table 5.3.1. The production simulated for 10 years and the results of simulations are
shown on Figures 5.3.1 and 5.3.2.
Figure 5.3.1: Base case cumulative gas production after 10 years.
With dual porosity single fracture model the production after 10 years reaches the point of 11.6
MS . In comparison to single –fracture single-porosity model, this value is much higher due to
contribution of the gas stored in the natural fractures. The recovery with single fracture stage
reaches 18% of gas in place and exceeding the economic cut-off point for 8%. The reservoir
pressure after 10 years production simulation with constant BHP of 160 bars drops to 451 bars.
The pressure distribution in reservoir after 10 years of production is shown on Figure 5.3.3. As it
can be seen from pressure distribution profile, with the single fracture of 100 m half-length only
a small area in the vicinity of induced fracture is effectively drained. The reservoir pressure with
the distance from induced fracture is still high, which means that those zones are still
ineffectively drained. For more effective drainage of the reservoir, the introduction of multi-
stage fracturing might be necessary.
18% recovery
10% recovery
0
2
4
6
8
10
12
14
MSm
^3
After 10 years of production
Cumulative gas production
Single-fracture
Economic cut-off
54
Figure 5.3.2: Base case gas cumulative production from single transverse fracture.
Figure 5.3.3: The pressure distribution in the reservoir after 10 years of production. Only the area in the vicinity of induced
fracture is effectively drained.
5.3.2 Dual porosity model with adsorbed gas, coal bed methane option.
One of the major characteristics of shale gas reservoirs is the presence of adsorbed gas. In
order to introduce the adsorbed gas factor into dual porosity system the available coal bed
methane option in Eclipse2011 should be treated. For that purpose, modified Warren and Root
model used to describe the physical processes in a typical shale gas project.
The Extended Langmuir isotherm, which is already discussed in previous chapter, is used to
describe the shale sorption for the different components. For each component two constant
55
parameters need to be input, the Langmuir volume ( ) and the Langmuir pressure ( ). These
parameters are typical determined from experiments. In the following cases Langmuir volume
and Langmuir pressure parameters will be used typical for Haynesville and New Albany shale
reservoirs. More detailed information about CBM option is presented in Appendix 14.
5.3.3 Dual porosity model Haynesville case.
In the following simulations the parameters typical to Haynesville shale gas reservoir will be
treated. In reality Haynesville shale basin extends over 5.5 million acres. It is one of the largest
shale plays in US. It has the following properties: highly mature rock with less than 3% of total
organic carbon (TOC), system with very high pore pressure (the reservoir pressure reaches 620
bars), formation depth up to 3500m true vertical depth (TVD) with high temperature in average
around 140 , free gas in place dominates and constitutes up to 70-80% of gas in place, most
natural fractures are calcitized (Fan and Thompson, 2010). The synthetic reservoir model as
rectangular block, with a length of 400 m, a width of 150 m and thickness of 60 m was used for
modeling purposes of Haynesville shale. In the following cases the grid consists of 81 cells in x-
direction (length), 51 cells in y-direction (width) and 12 cells in z-direction (height).
Single fracture models with adsorbed gas and with only free gas were treated to compare the
contribution of adsorbed gas after 10 years of production simulation. The parameters used for
the following models are shown in Table 5.3.2.
Table 5.3.2: Model setup
Reservoir pressure, bars 620
Model size(L-W-D), meters 400-153-50
Depth to reservoir, meters 3500
Rock density, kg/ 2650
Matrix 1-6 cells (in z-direction)
Porosity, % 5%
Permeability, µD 0.152
Fracture 7-12 cells( in z-direction)
Porosity, % 0.05
Permeability, µD 0.152
Induced fracture
Porosity, % 0.5
Permeability, mD 500
Fracture half-length , m 100
Adsorption parameters
Langmuir volume ( ), /kg 0.0015
Langmuir pressure ( ), bar 103
Reservoir temperature, 140
56
The long term production simulations including adsorbed gas and without adsorbed gas factor
were performed in order to see the effect of that unique property to the production profiles. As
it can be seen from figures 5.3.4 and 5.3.5, in the case of single fracture treatment, there is
small contribution of adsorbed gas (1.2% extra gas) after first 2 years of production simulation
and, after 10 years of production simulation the contribution of adsorbed gas increases to extra
4.5% in comparison to the case with only free gas in place. It is clear that the desorbed gas
contribution is insignificant at early stage of well life, within the first 5 years of production (less
than 2%) and thus, not likely to materially impact production economics. At a later stages of
production, the reduced pressure in the reservoir allows gas desorption from the surface of the
shale to the fracture. Gas diffuses from the matrix of the shale towards the induced fracture
surface, thus providing additional gas supply to the production. But, still because the adsorbed
gas constitutes the minor amount of gas in Haynesville shale reservoir, its impact on production
profile is insignificant.
Figure 5.3.4: Cumulative gas production with adsorbed gas (solid line) and without adsorbed gas (dotted line). Undetectable impact of desorbed gas at early stages of production. At a later stages of well life the contribution of desorbed gas is still minor.
57
Figure 5.3.5: Cumulative gas production at early stages of well life and after 10 years of production simulation. The recovery factors are related only for the cases with adsorbed gas.
Table 5.3.3: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation scenario
Normalized production
(2 years)
Numeric production
(2 years)
Normalized production
( 10 years)
Numeric production
(10 years)
(-) Msm^3 (-) Msm^3
Single-frac
No adsorption
0.98 4.75 0.96 11.35
Single-frac
Adsorption
1 4.81 1 11.85
The pressure distribution profiles, figure 5.3.6, depict the fact that with single transverse
fracture the pressure drop in reservoir is very small. Even though, the pressure wave extends all
over the reservoir, the drop is visibly higher in the vicinity of induced fracture. Which means,
that with single fracture it is only possible to effectively drain the area in the vicinity of induced
fracture. Meanwhile, the pressure at other parts of reservoir still high and the reservoir remains
ineffectively drained. However, the production from single fracture including adsorbed gas
factor after 10 years exceeds the economic cut-off point for 7.5% and can be considered as
economically viable. Table 5.3.3 shows the gas production after 2 and 10 years, both as a
normalized and the numeric gas volume. This example shows the fact that most of the time it is
1.2% extra
6.5% recovery
4.5% extra 16% recovery
Economic cut-off 8.5% recovery
0
2
4
6
8
10
12
14
MSm
^3
After 2 years of production After 10years of production
Cumulative gas production
Without adsorbed gas
With adsorbed gas
Economic cut-off
58
economically unprofitable to exploit the ultra-low permeable reservoirs with only single
transverse fractures. Thus, currently the multiple transverse fracture treatment is the most
popular way to effectively drain tight matrix and to reach the cost effective production in shale
gas reservoirs.
Figure 5.3.6: Pressure distribution in the reservoir (in bars) after 10 years of production simulation for the case with adsorbed gas (right picture) and without adsorption (left picture).
5.3.3.1 Comparison with analytical model results
In this section the base case analytical model presented in Chapter 4 was compared with the
similar case numerical model. It should be reminded once again that the data used for the base
case analytical model is also typical for Haynesville shale reservoir.
It has to be mentioned that the analytical model was constructed on the base of the rate
decline equation for pseudolinear flow regime in horizontal well with single transverse fracture,
and only considers the single porosity system. However, the numerical model was constructed
on the base of Warren and Root model, and considers the dual porosity system. Both models,
considers adsorbed gas factor. The analytical model incorporates the adsorbed gas using the
adsorption index term, discussed in Chapter 3. The numerical case models the adsorption gas
using the extended Langmuir isotherm, and defines the adsorption capacity as a function of the
pressure and the free gas phase composition. Both models consider the single phase gas
production after 10 years of production simulation. For comparison purposes the numerical
model for this case was changed from two-phase to single-phase. In the case of single phase
model it was assumed that the reservoir is fully saturated with gas and no other phase is
presented. As previously mentioned, for the numerical simulation purposes half symmetry
model was treated, which means that only 1/2 of the synthetic reservoir was modeled. Due to
this symmetry, numerically simulated well rates are regarded as 50% of the actual values.
59
Figure 5.3.7: Plot of cumulative gas production of analytical versus numerical models. Small discrepancy between the
models, which results in 0.3 M gas production in the case of numerical model.
Figure 5.3.8: Comparison of the analytical and numerical models.
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12
MSm
^3
Time( years)
Cumulative gas production
Analyticalbase vase
Numericalbase case
11.6 11.9
6.25
0
2
4
6
8
10
12
14
MSm
^3
After 10 years of production
Cumulative gas production
Analytical case
Numerical case
Economic cut-off
60
Table 5.3.4: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation
scenario Normalized
production ( 10 years)
Numeric
production (10 years)
(-) Msm^3 Analytical model 0.98 11.6 Numerical model 1.008 11.9
The figures 5.3.7 and 5.3.8 show the results of two models after 10 years of production
simulation. The cumulative production lines of two models are almost aligning along the
production profile. There is small discrepancy between the analytical and numerical models
along the production profile, which results in extra 0.3 M gas production in the case of
numerical model, after 10 years of production simulation. Table 5.3.4 shows the gas production
after 10 years, both as a normalized and the numeric gas volume. The extra gas production in
the case of numerical model is anticipated due to dual porosity character of the model, that
captures the presence of natural fractures in the model. However, that excess in production is
much less than expected and might be related to inaccuracy of the analytical model. Plus, the
analytical model was constructed using constant pressure terminal equation, assuming
constant reservoir pressure and BHP throughout the production, which of course affects the
production rates. And finally, due to high pressure nature of Haynesville reservoir the natural
fractures might be compacted, thus store less amount of free gas.
5.3.3.2 Multistage fracturing
With introduction of multistage stimulation treatment the primary fracture spacing appears to
be an important factor impacting the well performance. There is a very small research was
conducted on the impact of primary fracture spacing on desorption of adsorbed gas in shale gas
reservoirs. That is why, the main goal of this work is to investigate the fracture spacing variation
effect on desorption of adsorbed gas on two shale gas cases (Haynesville shale and New Albany
shale).
The main issue in this type of spacing variations is keeping the symmetry on both sides of the
grid. As our synthetic model extends 400m in length, the following variation of fracture spacing
is used:
61
Table 5.3.5: Variation of fracture stages.
The simulation results show that for the Case1 there is almost no contribution of adsorbed gas
on production profile at early stage of well life (first 3 years) because the pressure drop in
reservoir quite low to initiate desorption of adsorbed gas. However, even at later stages of well
life, when pressure wave extends for whole reservoir the contribution of adsorbed gas is
miserable, just 3.3% extra gas production, exceeding the economic cut-off for 9%. Despite of
low contribution of adsorbed gas, even with two transverse fractures the cumulative
production after 10 years is quite high. The reason for that is the possibility to perform
production at initial high drawdown (the difference between the reservoir and flowing
buttomhole pressure (460 bars), due to high pressure nature of the reservoir. The high
drawdown factor on its turn might be the reason for early pressure interference time and high
production rates at early stages of the well life. However, the situation is not the same for other
shale gas reservoirs. For instance, in the case with New Albany shale, the initial reservoir
pressure is 50 bars and in that case the production is possible with only small drawdown.
If we look at reservoir pressure drop profile, we can see that in Case1 the reservoir pressure at
constant BHP 160 bars drops to 350 bars after 10 years of production. However, it seems that
this quite high drop of reservoir pressure is insufficient for efficient desorption of adsorbed gas.
The pressure interference between the fractures occurs after 3 years of production for the case
without adsorbed gas. In the case including the adsorbed gas factor there is 6 months delay in
pressure interference. This fact shows that pseudo linear flow regime in reservoir, when
fractures independently produce from each other, lasts just 3.6 years. That time period
corresponds to “no contribution” time of adsorbed gas to total gas production (figure 5.3.9).
Number of fractures Spacing, meters
Case 1 2 200
Case 2 4 100
Case 3 6 66
Case 4 8 50
Case 5 10 40
62
Table 5.3.6: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation scenario Normalized production Adsorption
Numeric production Adsorption
Normalized production
No adsorption
Numeric production
No adsorption
(-) Msm^3 (-) Msm^3
2 fracs adsorption 1.82 21.6 1.76 20.9
4 fracs adsorption 2.65 31.3 2.5 29.6
6 fracs adsorption 3.08 36.6 2.9 34.5
8 fracs adsorption 3.20 38 2.95 35
10 fracs adsorption 3.3 39.2 3 36
Figure 5.3.9: The graph of cumulative production versus time for different fracture stages and fracture spacings. Case1: 2 fractures, 200m spacing, with adsorption (red line) and without adsorption (dotted red line). Case2: 4 fractures, 100m spacing, with adsorption (blue line) and without adsorption (dotted blue line). Case3: 6 fractures, 66m spacing, with adsorption (green line) and without adsorption (dotted green line). Case4: 8 fractures, 50m spacing, with adsorption (orange line) and without adsorption (dotted orange line). Case5: 10 fractures, 40m spacing, with adsorption (purple line) and without adsorption (dotted purple line).
63
Figure 5.3.10: Cumulative gas production after 10 years. The recovery factors are related only for the cases with adsorbed gas.
In Case2, the production simulated with 4 perforation clusters and 100m fracture spacing. In
that case “no contribution” time of adsorbed gas at early stages of well life shortened to 8
months and the impact of adsorbed gas to cumulative production after 10 years is increased to
5.5% compared to no adsorption case. For this case the pressure wave extends for whole
reservoir and pressure drop in reservoir is higher compared to previous case, reaching 258 bars
after 10 years of production (92 bar difference compared to the Case 1). The slope of the
pressure curves at early stage of well life in the Case 2 is noticeably larger compared to the Case
1. Which means higher pressure drop in early stages of well life and the reason for the
shortened “no contribution” time of adsorbed gas in comparison to the Case 1, as the
desorption of adsorbed gas occurs with decrease of reservoir pressure. Further, if we take a
look at pressure distribution profiles, figure 5.3.12, we see that the pressure in reservoir
proportionally drops, and the effectiveness of reservoir drainage is much higher than in Case 1.
The pressure interference time between the fractures is also decreased to 10 months for no
adsorption case and 1 year for the case with adsorbed gas. As in previous case the adsorbed gas
causes the obvious delay in pressure interference between the fractures. But, most part of
linear flow regime there is no contribution of adsorbed gas to total production.
Extra 3.3%
29.5% recovery
Extra 5.5%
42% recovery
Extra 6%
50% recovery
Extra 8% 52% recovery
Extra 9% 53.5% recovery
15.5% recovery
0
5
10
15
20
25
30
35
40
45
MSm
^3
After 10 years of production
Cumulative gas production
2 fracs No adsorption
4 fracs No adsorption
6 fracs No adsorption
8 fracs No adsorption
10 fracs No adsorption
Adsorption
Economic cut-off
64
Figure 5.3.11: The pressure change in reservoir versus time for different fracture stages and fracture spacings. Case1: 2 fractures, 200m spacing, with adsorption (red line) and without adsorption (dotted red line). Case2: 4 fractures, 100m spacing, with adsorption (green line) and without adsorption (dotted green line). Case3: 6 fractures, 66m spacing, with adsorption (blue line) and without adsorption (dotted blue line). Case4: 8 fractures, 50m spacing, with adsorption (brown line) and without adsorption (dotted brown line). Case5: 10 fractures, 40m spacing, with adsorption (purple line) and without adsorption (dotted purple line).
In further simulations the fracture spacing is decreased to, 66m, 50m, 40m and the number of
fracture stages is increased to 6, 8, 10 respectively (Case3, Case4 and Case 5). In all the
following cases the decrease of fracture spacing and increase of fracture treatment stages
causes the higher drop of reservoir pressure. The slope of the pressure curves at early life stage
of the well increases every time we decrease the fracture spacing, which leads to increase of
desorption of adsorbed gas and shortening of the time of linear flow regime, thus shortening
“no contribution” time of the adsorbed gas contribution to the production at early stages of
well life. The pressure interference times for corresponding cases are depicted in Table 5.3.7.
In conclusion of Haynesville case study, it should be noticed once again that even though the
adsorbed gas is minor factor and constitutes just 12% of gas in place, in order to increase the
efficiency of the reservoir drainage and achieve the contribution of that minor adsorbed gas in
place, the fractures should be placed at a small distance between each other with the main goal
to increase the sufficient drop of reservoir pressure, as the adsorbed gas starts to desorb from
the bulk rock with decrease of pressure. Furthermore, the small fracture spacing is necessary to
accelerate the pressure interference time between adjacent fractures, after which every single
65
fracture starts contributing to each other’s production. This is desired situation for this type of
reservoirs, as low matrix permeability and adsorbed gas existence delay pressure interference
time for decades, thus delaying the desorption of adsorbed gas.
Table 5.3.7: Pressure interference time for various cases.
Pressure interference after 10 years
Without adsorbed gas With adsorbed gas
Case 1 3 years 3.6 years
Case 2 9 months 1 year
Case 3 5 months 7 months
Case 4 3 months 5 months
Case 5 1.5 months 3 months
66
Figure 5.3.12: Pressure distribution in the reservoir (in bars) after 10 years of production for the cases defined in Table 5.3.3. The left hand side figures correspond to the cases without adsorption. Right hand side figures correspond to the cases including adsorption.
67
5.3.4 Dual porosity model New Albany case.
New Albany shale is only 730m deep and is underpressured at 50 bars. The reservoir
temperature is very low due to shallow deposition environment. Unlike the Haynesville shale
case where adsorbed gas composes just 12 % of gas in place which is believed to play a little
impact on production, in case of Albany shale the adsorbed gas is essential factor reaching
about 70% of gas in place (Bo Song, Economides, 2010).
Because of underpressured nature of the reservoir it is impossible to launch the production at
high initial drawdown similar to the case of Haynesville shale. For the following models the well
put under the constant BHP control mode at constant minimum BHP 13 bars through the well
life. The well and reservoir parameters that were used for modeling of New Albany shale is
presented in Table 5.3.8. As in the previous case, first single fracture models were simulated
and the results of simulations are depicted on figures 5.3.13 and 5.3.15.
Table 5.3.8: The model setup.
Reservoir pressure, bar 50
Model size(L-W-D), meters 400-153-50
Depth to reservoir, meters 725
Rock density, kg/ 2650
Matrix 1-6 cells (in z-direction)
Porosity, % 5%
Permeability, µD 0.18
Fracture 7-12 cells( in z-direction)
Porosity, % 0.05
Permeability, µD 0.18
Induced fracture
Porosity, % 0.5
Permeability, md 500
Fracture half-length , m 100
Adsorption parameters
Langmuir volume ( ), /kg 0.0035
Langmuir pressure ( ), bar 71
Reservoir temperature, 31
As it can be seen from Figure 5.3.15, for the single fracture case, the desorbed gas contributes
much more compared to previous case study, reaching the value of 27% additional recovery
compared to no adsorption case after 10 years of production simulation. One noticeable fact is
that due to low pressures the adsorbed gas starts to desorb almost immediately after the start
of production, reacting even for a small reservoir pressure drop. It means that there is very
small “no contribution time” of desorbed gas to production at early stages of well life in
68
comparison to 3 years time in the case of Haynesville shale. The figure 5.3.13 also depicts the
pressure drop in reservoir after 10 years of production simulation. The drop of reservoir
pressure with constant BHP is very small reaching 49 bars after 10 years of production. The
figure 5.3.14 shows the pressure distribution in the reservoir after 10 years of production
simulation. The red areas in the figure denote original reservoir pressure and dark blue
represent flowing bottomhole pressure. In this case the pressure wave just spreads in the
vicinity of the fracture and does not reach the rest part of the reservoir. Just a small area near
the fracture experiences high drop of pressure. That is why the production of gas just limited to
the reservoir area directly adjacent to the fracture network and most part of the reservoir
remains ineffectively drained.
For this case we get extremely low production rates at maximum possible drawdown. The
cumulative production with single fracture reaches 2.5 % out of the total gas in place calculated
by simulator. If in the case of Haynesville shale we could reach to some extend cost effective
production with single transverse fracture, here in the case of underpressured reservoir it
becomes impossible. The only way to exploit such underpressured reservoirs is by performing
the multi stage fracture treatment which will be considered in the following section.
Figure 5.3.13: Left scale: Cumulative gas production versus time for single-fracture case. The case with adsorption (red line) and without adsorption (dotted red line). Right scale: Reservoir pressure change (in bars) versus time. The case with adsorption (green line) and without adsorption (dotted green line).
69
Figure 5.3.14: The pressure distribution in the reservoir (in bars) after 10 years of production simulation for the case with adsorbed gas (right picture) and without adsorption (left picture).
Figure 5.3.15: Cumulative gas production after 10 years. The recovery factor is related only for the case with adsorbed gas.
Table 5.3.9: Production comparison between the various models; the results have been normalized to the single-fracture model including adsorption.
Simulation scenario Normalized production ( 10 years)
Numeric production (10 years)
(-) Msm^3
Single-frac No adsorption
0.038 0.45
Single-frac Adsorption
0.05 0.64
2.7 % recovery
27% extra
8.7% recovery
0
0.5
1
1.5
2
2.5
MSm
^3
After 10 years of production
Cumulative production
Single fracture No adsorption
Single fracture Adsorption
Economic cut-off
70
5.3.4.1 Multistage fracturing
As in the case of Haynesville shale, the variation of fracture numbers and fracture spacing is
used from the Table 5.3.8. The production was simulated for 10 years for all of the shown
mentioned cases and the results are depicted on the following graphs.
The simulations show that for the Case1 (2 fracture stages and 200m fracture spacing) the
desorption starts much earlier compared to Haynesville case, after first 3 months and the
contribution of adsorbed gas on production profile at early stages of well life is noticeable,
reaching 33% additional gas production in comparison to the same case without adsorbed gas.
If we look at reservoir pressure profile (Figure 5.3.17), we can see that in Case1 the reservoir
pressure drop is insignificant compared to the initial reservoir pressure after 10 years of
production. The figure 5.3.15 shows the pressure distribution in the reservoir after 10 years of
production simulation. The red areas in the figure denote original reservoir pressure and dark
blue represent flowing bottomhole pressure. As in the case with single fracture model, the
pressure waves just cover very small area in the vicinity of each fracture. In case of two
fractures stages the pressure interference between the fractures does occur after 10 years of
production, and is not expected soon due to very slow pressure drop in reservoir. It means that
gas during this time period will be produced just within a small distance around transverse
fractures and the linear flow regime will dominate in reservoir. During that regime each
fracture will produce gas independently from others which is not preferable as if the pressure
interference occurs then the fractures will produce in combination with each other, which on
its turn will accelerate the pressure drop in reservoir, thus increase the desorption of adsorbed
gas. Furthermore, if we make comparison between the case with adsorption and without, we
can easily detect that there is not such a big difference in pressure distribution in reservoir after
10 years simulation time, due to extremely low matrix permeability of reservoir and due to low
drawdown through the production.
Table 5.3.10: Pressure interference time for variation of fracture spacing.
Pressure interference after 10 years
Without adsorbed gas With adsorbed gas
Case 1 No interference No interference
Case 2 Close to interference No interference
Case 3 6 years 10 years
Case 4 3 years 7 years
Case 5 2 years 4 years
71
Figure 5.3.16: The graph of cumulative production versus time for different fracture stages and fracture spacings. Case1: 2 fractures, 200m spacing, with adsorption (red line) and without adsorption (dotted red line). Case2: 4 fractures, 100m spacing, with adsorption (green line) and without adsorption (dotted green line). Case3: 6 fractures, 66m spacing, with adsorption (blue line) and without adsorption (dotted blue line). Case4: 8 fractures, 50m spacing, with adsorption (light blue line) and without adsorption (dotted light blue line). Case5: 10 fractures, 40m spacing, with adsorption (purple line) and without adsorption (dotted purple line).
In the next Case2, the production simulated with 4 perforations clusters and 100m fracture
spacing. In that case we can see that the contribution of desorbed gas at early stages of well life
is higher in comparison to the Case1 and the impact of adsorbed gas to cumulative production
after 10 years is increased up to 35% additional gas production compared to the case without
adsorbed gas. For this case the pressure drop in reservoir is a bit lower compared to the Case1
reaching 47.8 bars after 10 years of production. It should be noticed that a small pressure drop
in the reservoir in comparison to the previous case initiated a significant increase in production
of adsorbed gas. Further, if we take a look at pressure distribution profiles, figure 5.3.19, we
see that the pressure in reservoir starts dropping proportionally, and the effectiveness of
reservoir drainage is much higher than in Case 1. But still the pressure waves between the
fractures are far away from interference. If we compare the last case with the similar one but
without adsorbed gas, we can see that after 10 years of production simulation the pressure
waves are almost reaching interaction and the interference is expected very soon. This example
shows that existence of adsorbed gas in large amounts has dramatic effect on flow regime of
the reservoir, by delaying the pressure interference time between adjacent fractures. The
pressure interference is desired in such unconventional reservoirs, due to very low
72
permeability. When the interference occurs the fractures start contributing to each other’s
production thus increasing the drainage area of reservoir.
Figure 5.3.17: The pressure change in reservoir versus time for different fracture stages and fracture spacings. Case1: 2
fractures, 200m spacing, with adsorption (red line) and without adsorption (dotted red line). Case2: 4 fractures, 100m
spacing, with adsorption (green line) and without adsorption (dotted green line). Case3: 6 fractures, 66m spacing, with
adsorption (blue line) and without adsorption (dotted blue line). Case4: 8 fractures, 50m spacing, with adsorption (light blue
line) and without adsorption (dotted light blue line). Case5: 10 fractures, 40m spacing, with adsorption (purple line) and
without adsorption (dotted purple line).
Table 5.3.11: Production comparison between the various models; the results have been normalized to the single-frac model including adsorption.
Simulation scenario Normalized production Adsorption
Numeric production Adsorption
Normalized Production
No adsorption
Numeric Production
No adsorption
(-) Msm^3 (-) Msm^3
2 fracs adsorption 0.1 1.29 0.07 0.9
4 fracs adsorption 0.21 2.535 0.16 1.875
6 fracs adsorption 0.31 3.76 0.23 2.76
8 fracs adsorption 0.4 4.8 0.3 3.5
10 fracs adsorption 0.5 5.95 0.35 4.1
73
Figure 5.3.18: Cumulative gas production after 10 years. The recovery factors are related only for the cases with adsorbed gas.
In the following simulations the fracture spacing is further decreased to 66 m, 50 m, 40 m and
the number of fracture stages is increased to 6, 8, 10 respectively (Case3, Case4 and Case 5). In
all the cases the decrease of fracture spacing and increase of fracture treatment stages causes
the higher drop of reservoir pressure, thus much higher contribution of desorbed gas to
production especially at later stages of well life. The special attention should be paid to the case
with 10 fracture stages and fracture spacing of 40 m. In this case the contribution of adsorbed
gas is the highest, 45% additional gas compared to no adsorption case, after 10 years of
production simulation. The noticeable thing that the contribution of adsorbed gas starts with
early production. In all the cases with decrease of fracture spacing and increase of the number
of fracture treatment stages the pressure interference time is shortening (Table 5.3.10). The
minimal pressure interference time is achieved with densely placed fractures (Case5), where
after 4 years the fractures start to produce in combination with each other by increasing the
drainage area of the reservoir and thus decreasing the pressure in reservoir proportionally
which on its turn initiate the release of the adsorbed gas toward the induced fracture.
However, overall recoveries are low in all the cases compared to the Haynesville reservoir
models. In Case1, the recovery does not even reach economic cut-off point of 8.7%, and out of
economical interest. The Case2 hardly overpasses the payout recovery. Only Case3, Case5 and
Case5 exceed the cut-off recovery by 7%, 12% and 17 % respectively. As a result of
33% extra
5.6% rec
35% extra 11% rec
36% extra
16% rec
40% extra
21% rec
45% extra 26% rec
8.7% rec
0
1
2
3
4
5
6
7
MSm
^3
After 10 years of production
Cumulative gas production
2 fracs No adsorption
4 fracs No adsorption
6 fracs No adsorption
8 fracs No adsorption
10 fracs No adsorption
Adsorption
Economic cut-off
74
multifracture simulations it becomes clear that only with densely spaced fracture treatment
design the production from this type of reservoir becomes cost effective.
Figure 5.3.19: Pressure distribution in the reservoir (in bars) after 10 years of production for the cases defined in Table 5.3.5. The left hand side figures correspond to the cases without adsorption. Right hand side figures correspond to the cases including adsorption.
75
5.4 Economics
Rough economic calculations were done for worst and best cases of Haynesville and New
Albany reservoirs. The design assumes $425k/1000m (US price) for drilling the vertical segment
and $720k/1000m (US price) for the horizontal segment. Also the gas price is assumed to be
$0.15/ (US price), 15% royalties and 4% discount rate. The single fracture stimulation
treatment is assumed to cost in average $100,000 (US price).In the case of Haynesville shale the
vertical depth to the reservoir is 3500 m and then the well extends for 400m. However, in New
Albany case the vertical depth to the reservoir is 730 m and the horizontal section extends for
400m. According to rough estimates the single horizontal well with single transverse fracture in
the case of Haynesville shale after 10 years of production just payouts the costs without any
additional income. However, if the number of fracture stages increased to 10, $3.500.000 profit
can be reached after 10 years of production.
The situation is different for New Albany shale case. Here, the single fracture production even
does not payout the expenses. In the case of production with 10 fracture stages just $250.000
profit can be reached, which is also out of economic interest. In the case of New Albany Shale,
in order to reach sustainable production, more fracture stages has to be treated.
Table 5.3.12: The economic calculations for the worst and the best production cases of Haynesville and New Albany shale reservoirs.
Haynesville case
Drilling and production costs $ 1.775.000
Net income
Single- fracture Worst case Just payouts the costs, no profit
10 fractures Best case $ 3.500.000
New Albany case
Drilling and production costs $600.000
Net income
Single- fracture Worst case Does not payout the costs
10 fractures Best case $ 250.000
76
5.5 Summary
In the first part of this chapter the numerical simulations were run for a single-porosity system
models. That system excludes the adsorbed gas factor and natural fractures. The simulations
ignoring the stimulation treatment proved that production is almost impossible without any
stimulation in such ultra-tight reservoirs. The single fracture model changed the situation to the
positive side, acquiring the recoveries of 3.5% and 2.6% for k=0.152 µd and k=0.01 µd
respectively. However, even these recoveries are not cost effective, less than the economic cut-
off production of 6.25 MS (the recovery that payouts the drilling and production cost in a
horizontal single fractured well). In most cases the production with single stage treatment is
uneconomical. The models with 2 (200 m spacing) and 6 (66 m spacing) fracture stages, in
general positively reflected on recoveries. In the case of k=0.152 µd, both fracture spacing
variations have recovery overpassing the economic cut-off production point, with the maximum
recovery of 36% in the case of 6 fracture treatment stages. However, one fold decrease of
matrix permeability dramatically changes the situation. In that case the production is still cost
effective with 6 fracture treatment stages, but the case with 2 transverse fractures is not
economically viable anymore. One fold decrease of matrix permeability reflects on delay of the
pressure interference time up to 2 years in the case of 6 fracture stages and in the case of 2
fractures stages the interference time even cannot be captured after 10 years of production.
Further on, the dual-porosity system cases were modeled. Firstly, the comparison was made
between the analytical and numerical models. The cumulative production lines of two models
are almost aligning along the production profile with is small discrepancy, which results in extra
0.3 M gas production in the case of numerical model, after 10 years production simulation.
The extra gas production in the case of numerical model is anticipated due to dual porosity
character of the model. The extra gas supply in numerical model may be due to contribution of
the gas stored in the natural fractures. However, that excess in production is much less than
expected and might be related to inaccuracy of the analytical model or because of cementation
of the natural fractures due to high pressure nature of Haynesville shale. Additionally, the
analytical model was constructed using constant pressure terminal equation, assuming
constant reservoir pressure and BHP throughout the production, which of course affects the
production rates.
Single fracture models show substantially higher production in the case of Haynesville shale
despite of low contribution of desorbed gas throughout the well life. The main reason is
relatively high drawdown throughout the production, which leads to a large decrease of the
reservoir pressure and efficient drainage of the reservoir. However, in this case there is almost
no contribution of adsorbed gas at early stages of well life, and the miserable contribution at
77
the end of well life. In fact the pressure drop in the reservoir that is sufficient for production of
free gas is absolutely insufficient for production of adsorbed gas. However, in the case of New
Albany shale the total production is significantly lower but the contribution of desorbed gas is
noticeable, even at early stages of well life. From one side the low pressure nature of the
reservoir does not allow production at high drawdown, but from another side, because of low
pressure, even the small decrease of reservoir pressure initiates high amounts of adsorbed gas
to be desorbed.
In case of Haynesville shale substantial production can be reached even with long fracture
spacing at high drawdown, but mostly free gas in place will be produced. The pressure
interference time between the fractures is quite short, even for high spacing cases.
Consequently the duration of linear flow is short, and most of the well life the fractures
produce in combination with each other. But, in order to reach efficient drainage of the
reservoir, the desorption of available adsorbed gas in place, the fracture treatment stages
should be increased and the fracture should be densely placed.
According to performed simulations, if the fracture spacing decreased up to 40 meters, the
point of 9% extra gas production at the end of the 10 years can be reached.
In the case of New Albany shale is impossible to launch the production at high drawdown due
to low pressure nature of the reservoir. With production at maximum possible initial
drawdown, it is difficult to reach sufficient pressure drop in reservoir. However, even small
drop at early stages of well life effecting the production of adsorbed gas in place. In the case
with two transverse fractures the contribution of adsorbed gas is noticeable throughout the
well life, reaching 11% extra gas production compared to no adsorption case, at the end of 10
years. However, the production is not cost effective with small number of fracture treatment
stages. The pressure interference time is delayed and even cannot be captured after 10 years of
production in the case with small number of fracture stages (Table 5.3.10). In that case of
underpressured reservoir, it seems to be necessary requirement to densely place the fractures
by increasing the number of fracture treatment stages, in order to accelerate the pressure
interference time and to reach sufficient drop of the reservoir pressure, which is indispensible
in order to release the adsorbed gas. If the preferable drop of reservoir pressure could be
reached the desorbed gas will definitely contribute to production as it constitutes quite high
percentage of gas in place. The outcome of all the simulations performed in this chapter is
presented in Table 5.3.13.
78
Table 5.3.13: The outcome of all the simulations.
Simulation scenario Cumulative production Recovery(%)
Single porosity MSm^3
Single fracture
k=0.152 µD 1-phase 8.5 12
k=0.152 µD 2-phase 4.5 6
k=0.01 µD 1-phase 2.5 3.5
k=0.01 µD 2-phase 1.3 2.6
2 fractures
k=0.152 µD 2-phase
7.8
19
k=0.01 µD 2-phase
2.5
6
6 fractures
k=0.152 µD 2-phase
15
36
k=0.01 µD 2-phase
6.5
16
Dual porosity
Haynesville case
Single-frac No adsorption
k=0.152 µD 2-phase 11.35 19
Single-frac Adsorption
k=0.152 µD 2-phase 11.85 6.5
2 fracs no adsorption k=0.152 µD 2-phase 20.9 35
2 fracs adsorption k=0.152 µD 2-phase 21.6 29.5
4 fracs no adsorption k=0.152 µD 2-phase 29.6 49
4 fracs adsorption k=0.152 µD 2-phase 31.3 42
6 fracs no adsorption k=0.152 µD 2-phase 34.5 57
6 fracs adsorption k=0.152 µD 2-phase 36.6 50
8 fracs no adsorption k=0.152 µD 2-phase 35 58
8 fracs adsorption k=0.152 µD 2-phase 38 52
10 fracs no adsorption k=0.152 µD 2-phase 36 59.5
10 fracs adsorption k=0.152 µD 2-phase 39.2 53.5
New Albany case
Single-frac No adsorption
k=0.18 µD 2-phase 0.45 4.5
Single-frac Adsorption
k=0.18 µD 2-phase 0.62 2.6
2 fracs no adsorption k=0.18 µD 2-phase 0.9 9.5
2 fracs adsorption k=0.18 µD 2-phase 1.29 5.6
4 fracs no adsorption k=0.18 µD 2-phase 1.875 19.5
4 fracs adsorption k=0.18 µD 2-phase 2.535 11
6 fracs no adsorption k=0.18 µD 2-phase 2.76 29
6 fracs adsorption k=0.18 µD 2-phase 3.76 16
8 fracs no adsorption k=0.18 µD 2-phase 3.5 37
8 fracs adsorption k=0.18 µD 2-phase 4.8 21
10 fracs no adsorption k=0.18 µD 2-phase 4.1 43
10 fracs adsorption k=0.18 µD 2-phase 5.95 26
79
6 Conclusion and recommendations
6.1 Conclusions
Chapter 4 introduces the analytical model to demonstrate the long term production behavior of
Multi Transverse Fractured Horizontal Well in shale gas reservoirs. The main findings are as
follows.
Primary fracture spacing has significant influence on production in tight matrix reservoirs. The
design of stimulation is one of the crucial factors affecting the duration of the well life in shale
gas reservoir. Moreover, fracture spacing influences the desorption process and thus, has an
effect on cumulative production. The impact of desorption on cumulative production increases
when the fracture spacing is smaller. The reduction of the spacing between primary fractures
and pumping more fracture treatment stages will speed up the pressure interference time and
thus will contribute to effective drainage of the reservoir.
As a result of further analytical computations, it becomes obvious that the reservoir
permeability is one of the main factors that controls the production profile in fractured wells
and may have the major impact on cumulative production in ultra-tight gas reservoirs. The
variation of permeability from 1.5E-19 (0.15 µd) (typical permeability for shale gas) to
permeability 9.86E-19 (1 µd), at similar fracture treatment design, has incremental effect on
cumulative production up to additional 37 M . The permeability factor also has crucial effect
on duration of transient flow period. The pressure interference between two adjacent fractures
occurs increasingly earlier with increasing permeability. Most of the time, in ultra-low
permeability reservoirs the depletion occurs before reaching the pseudo steady-state
conditions. In this case transient solution should be considered as the main flow regime during
the life of the well in ultra-tight gas reservoirs.
Among all of the analytically investigated factors the most interesting and mostly less
investigated one is adsorbed gas. As a result of analytical sensitivity analysis it becomes obvious
that adsorbed gas might have impact on well performance. Furthermore, the analytical
computations show that adsorbed gas may have significant effect on pressure transient
behavior in shale gas reservoirs. For the same pressure investigation depth, the corresponding
investigation time with the existence of gas desorption will be longer than that without gas
desorption. Therefore, the estimation of interference time should take gas desorption impact
into account.
Chapter 5 focuses on modeling well performance in shale-gas reservoirs using numerical
simulations. Each of the shale gas reservoirs are unique and have variability within the
producing area. In the thesis work it was demonstrated on the cases of two shale gas
80
reservoirs: the Haynesville shale (overpressured reservoir) and New Albany shale
(underpressured reservoir). In the case of overpressured reservoir the adsorbed gas constitutes
12% of gas in place, but in underpressured reservoir that unique property is dominating and
reaching up to 70% gas in place. It was found out that the reservoir pressure has great
influence on production profile and depending on that the stimulation treatment should be
treated in a specific ways. High reservoir pressure makes it possible to start the production with
high drawdown, which on its turn contribute to the acceleration of pressure waves interference
time and thus, shortening the duration of pseudolinear flow. All of those factors lead to quite
efficient drainage of the reservoir. Even, in case of single fracture treatment, the production
overpasses the economic cut-of point. However, most of the produced gas is the free gas. Even
high drawdown is not sufficient for desorption of small amount of adsorbed gas in place in
comparison to high amount of free gas. The pressure interference time between the fractures is
short, even for high spacing cases. Consequently the duration of linear flow is short, and most
of the well life the fractures produce in combination with each other. The production of minor
adsorbed gas in place becomes possible only with the increase of number of fracture stages and
decrease of spacing between fractures. In this, the case with 10 fracture stages reaches the
maximum recovery, where 9% extra gas is produced due to decrease of the reservoir pressure
and contribution of adsorbed gas.
However, the situation is completely different in low pressured New Albany shale reservoir,
where the reservoir pressure reaches 50 bars. In that case the production is possible only at low
drawdown which makes it difficult to reach sufficient pressure drop in reservoir. But, even small
drop at early stages of well life effecting the production of adsorbed gas in place. It leads to
decrease of cumulative production to uneconomical point. In that case the model with single
fracture does not even payout the production and drilling costs. The pressure interference time
delayed because of two factors: the domination of adsorbed gas in place and the low pressure
drawdown. In the case with two transverse fractures the contribution of adsorbed gas is
noticeable throughout the well life, reaching 11% extra gas production at the end of 10 years.
However, the production is not cost effective with small number of fracture treatment stages.
The pressure interference time is delayed and even cannot be captured after 10 years of
production in the case with small number of fracture stages. As a result it becomes necessary
requirement to densely place the fractures, in order to accelerate pressure interference time,
consequently sufficient drop of the reservoir pressure in order release the adsorbed gas. If the
preferable drop of reservoir pressure could be reached the desorbed gas will definitely
contribute to production as it constitutes quite high percentage of gas in place.
As a conclusion to the project, is has to be mentioned that gas desorption has probably minor,
but not necessarily insignificant impact on well performance. The impact of adsorbed gas is
primarily at the later stages of well life, when pressures in tight matrix become low enough to
81
produce the meaningful amount of the adsorbed gas. However, as the spacing between the
fractures increases and the initial reservoir pressure decreases, the ability to produce adsorbed
gas becomes increasingly difficult. Especially, the adsorbed gas factor plays major role in low
pressured reservoirs by hugely delaying the pressure interference time between fractures,
extending the duration of linear flow and thus, affecting the production profiles. In this type of
reservoirs, economical production is only possible with densely spaced hydraulic fractures.
6.2 Recommendations
Some recommendations for future fracture treatment procedures and further research are
presented in this section.
In further investigations the fracture network should be modeled besides of the primary
fractures. The effect of network fracture spacing on production of adsorbed gas has to
be investigated.
An analytical solution that can handle both dual porosity effects and hydraulic fracture
effects would have been very useful in ascertaining the comparison with numerical
models, for the multiple stimulation jobs performed on this well.
Most of the investigations were done on reservoir properties relevant to North
American shale reservoirs, so further investigations should be applied for properties of
European shale reservoirs.
Nowadays, the stimulation treatments consider 20 to 30 fracture stages. Therefore, it
would be useful to construct the grid with more grid cells, which on its turn will enable
to simulate a large number of fractures stages.
Shale gas wells produce loads of condensate along with gas. For the future research it
would be useful to include the modeling of condensate production.
82
7 Bibliography
7.1 Books and articles
Bo Song, Texas A&M University; Economides, M.J. University of Houston; and
Christine Ehlig-Economides, Texas A&M University. 2011. Design of Transverse
Fracture Horizontal Wells in Shale Gas Reservoirs. Paper SPE 140555. The paper was
presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in
the Woodlands, Texas, USA, 24-26 January 2011. DOI: 10.2118/140555-MS
Bo Song, Texas A&M University. Pressure Transient Analysis and Production Analysis for New Albany Shale Gas Wells.
Boyer,C., Pittsburgh, Pennsylvania, USA; Kieshchnick, J. and Suarez-Rivera, J., Salt Lake
City, Utah,USA; Lewis,R.E. and Waters,G.,Oklahoma City, USA. Production Gas from its
Source. Autumn 2006.
Cipolla, C.L., Lolon, E.P. StrataGen Engineering, Erdle, J.C. and Rubin,B. CMG. 2009.
Reservoir Modeling in Shale-Gas Reservoirs. Paper SPE 125530. Paper was presented at
the 2009 SPE Eastern Regional Meeting held in Charleston, West Virginia, USA, 23–25
September 2009.DOI: 10.2118/125530-PA
Cipolla, C.L., Lolon, E.P. StrataGen Engineering, Erdle, J.C. and Tathed,V. CMG.2009.
Modeling Well Performance in Shale-Gas Reservoirs. Paper SPE125532. The paper was
presented at the SPE/EAGE Reservoir Characterization and Simulation Conference in
Abu Dhabi, UAE, 19-21, October 2009. DOI: 10.2118/125532-MS
Cipolla, C.L., Lolon, E.P., and Dzubin, B., StrataGen Engineering. Evaluating Stimulation
Effectiveness in Unconventional Gas Reservoirs. Paper SPE 124843-MS. The paper was
presented at the SPE Annual Technical Conference and Exhibition, 4-7 October 2009,
New Orleans, Louisiana. DOI: 10.2118/124843-MS
Cipolla, C.L. and Lolon, E. P., Carbo Ceramics, Mayerhofer, M.J. and Warpinski, N.R.,
Pinnacle Technologies. Fracture Design Considerations in Horizontal Wells Drilled in
Unconventional Gas Reservoirs. Paper SPE 119366. The paper was presented at the SPE
Hydraulic Fracturing Technology Conference, 19-21 January 2009, The Woodlands,
Texas. DOI: 0.2118/119366-MS
Cipolla, C.L., Carbo Ceramics, Lolon, E.P., StrataGen Engineering and Mayerhofer, M.J.,
Pinnacle, Halliburton Service. Reservoir Modeling and Production Evaluation in Shale-
Gas Reservoirs. Paper IPTC 13185-MS. The paper was presented at the International
Petroleum Technology Conference, 7-9 December 2009, Doha, Qatar. DOI:
10.2523/13185-MS
Cipolla, C.L., Warpinski, N.R., Mayerhofer, M.J. and Lolon, E.P., Pinnacle Technologies,
and Vincent, M.C., Carbo Ceramics. The Relationship Between Fracture Complexity,
83
Reservoir Properties, and Fracture Treatment Design. Paper SPE 115769. The paper was
presented at the SPE Annual Technical Conference and Exhibition, 21-24 September
2008, Denver, Colorado, USA. DOI: 10.2118/115769-MS
Dake, L.P. 1978. Fundamentals of Reservoir Engineering. Amsterdam: Elsevier.
Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, 3rd edition. Chichester:
John Wiley and Sons.
Ehrl, E. and Schueler, S.K. 2000. Simulation of a Tight Gas Reservoir with Horizontal
Multifractured Wells. Paper SPE 65108 presented at SPE European Petroleum
Conference, Paris, France, 24-25 October. DOI: 10.2118/65108-MS.
Economides, M.J., University of Houston; Martin,T., BJ services, 2007. Modern
fracturing, enhancing natural gas production.
Fazelipour,W., BeicipFranlab (IFP Group). Innovative Reservoir Modeling and
Simulation of Unconventional Shale Gas Reservoirs Powered by Microseismic Data.
Paper SPE 141877. The paper was presented at the SPE Middle East Unconventional Gas
Conference and Exhibition, 31 January-2 February 2011, Muscat, Oman. DOI:
10.2118/115769-MS
Gale, Julia F. W., Robert M. Reed, and Jon Holder: “Natural Fractures in the Barnett
Shale and their Importance for Hydraulic Fracture Treatments,” AAPG Bulletin, Vol. 91,
No. 4 (2007, April): 603-622.
Haward.D.S. Law, Alberta Research Council (ARC) Inc.; van der Meer, L.G.H., TNO-
NITG; Gunter, W.D., Alberta Research Council (ARC) Inc. Numerical Simulator
Comparison Study for Enhanced Coalbed Methane Recovery Processes, Part I: Pure
Carbon Dioxide Injection. Paper SPE 75669-MS. The paper was presented at SPE Gas
Technology Symposium, 30 April-2 May 2002, Calgary, Alberta, Canada. DOI:
10.2118/75669-MS
Kelkar,M. Natural Gas. ISBN 978-1-59370-017-1. 2008.
Kostenuk,N. SPE, Browne, D.J. SPE, Trican Well Service. Improved Proppant Transport
System for Slickwater Shale Fracturing. Paper SPE 137818-MS. Paper was presented at
the Canadian Unconventional Resources and International Petroleum Conference, 19-21
October 2010, Calgary, Alberta, Canada. DOI: 10.2118/137818-MS
Lewis, A.M. Luisiana University. December 2007. Production Data Analysis of Shale Gas
Reservoirs. MSc thesis report.
Lee, W. J. and R. A. Wattenbarger: Gas Reservoir Engineering. SPE Textbook Series Vol.
5 (1996).
Montgomery,S., Jarvie,D.M., Kent A. Bowker, and Richard M.Pollastro:“Mississippian
Barnett Shale, Fort Worth Basin, North-Central Texas: Gas-Shale Play with Multi-Trillion
Cubic Foot Potential,” AAPG Bulletin, Vol. 89, No. 2 (2005, February): 155-175.
84
Mayerhofer, M.J., et al. What Is Stimulated Reservoir Volume (SRV)? Paper SPE
119890. The paper was presented at the 2008 SPE Shale Gas Production Conference, 21-
24 November 2008, Fort Worth, Texas, USA. DOI: 10.2118/119890-PA
Rahman, M. K., Rahman, M. M. & Joardera, A. H. Analytical Production Modeling for
Hydraulically Fractured Gas Reservoirs. DOI:10.1080/10916460500411663
Schlumberger Information Solutions. Eclipse Black Oil Reservoir Simulation (Training
and exercise guide, version1).25 August 2005.
Schlumberger Information Solutions. Eclipse manual. 2011.
Schlumberger Information Solutions. Eclipse Compositional and PVTI. Abingdon
Technology Center Training, 12 December 2005.
Shaoul, J.R., Behr, A. and Mtchedlishvili, G. 2006. Automatic generation of 3D reservoir
simulation input files directly from a fracture simulation model. OIL and GAS European
Magazine 4: 176-182. SPE.
Xiao-Chun Lu, Fan-Chang Li, and Watson, A.T., SPE, Texas A&M U. Adsorption Studies
of Natural Gas Storage in Devonian Shales. Paper SPE 26632-PA. SPE Formation
Evaluation journal. p- 109-113. June 1995. DOI: 10.2118/26632-PA
Zahid,S., Bhatti, A.A., Khan, H.A. and Ahmad, T. University of Engineering &
Technology, Lahore, Pakistan. Development of Unconventional Gas Resources:
Stimulation Perspective. Paper SPE 107053-MS. The paper was presented at SPE
Production and Operations Symposium, 31 March-3 April 2007, Oklahoma City,
Oklahoma, U.S.A. DOI: 10.2118/107053-MS
Van Zelm, L. Evaluation of post-fracture production in tight gas reservoirs: The impact of
unconventional reservoir behaviour on production and well test interpretation. MSc
thesis report, 2010.
Wang,J., Denbury Natural resources; Liu,Y., Texas A&M Simulation based well
performance modeling in Haynesville Shale reservoir. Paper SPE 142740. The paper was
presented at SPE Production and Operations Symposium, 27-29 March 2011, Oklahoma
City, Oklahoma, USA. DOI: 10.2118/142740-MS
Fan,L., SPE; Thompson, J.W., SPE, Robinson, J.R., SPE, Schlumberger. Understanding
Gas Production Mechanism and Effectiveness of Well Stimulation in the Haynesville
Shale Through Reservoir Simulation. Paper SPE 136696. The paper was presented at
Canadian Unconventional Resources and International Petroleum Conference, 19-21
October 2010, Calgary, Alberta, Canada. DOI: 10.2118/136696-MS
7.2 Software
Eclipse 100 ; 300, 2011. Houston, Texas: Schlumberger Information Solutions.
85
8 Appendix – Flow calculation in analytical model
The bases of analytical analysis of production profile in shale gas reservoirs lie on diffusivity
equation. The diffusivity equation is a combination of three expressions: continuity equation,
the Darcy’s equation and the equation of state (real gas law). Below mathematical expressions
of continuity equation and Darcy’s law are given (Lee and Wattenbarger, 1996; Lewis, 2007).
( )1 ( )( )rr v
r r t
Eq. 8-1
where r is the drainage radius, ɸ- the porosity, ρ- density, υ- the velocity, t- the time. Under
the assumption of the absence of inertial effects and neglecting the gravity, the Darcy’s law can
be written in the following way:
r
k pv
r
Eq. 8-2
As it mentioned earlier, using real gas law as an equation of state, the density term can be
expressed in the following way:
M p M pRT
z RT z
Eq.8-3
Where k is the reservoir permeability, µ - the viscosity, p - the pressure, z - the compressibility
factor, T - the temperature, M- molecular weight, R-gas constant.
Combining all above expressed equations and making an assumption of homogeneous rock
with constant gas composition and temperature we get the next mathematical expression of
diffusivity equation. (Lee and Wattenbarger, 1996; Lewis, 2007)
1( ) ( )
k p p pr
r r z r t z
Eq.8-4
The right hand side of the above equation can be expanded (Lee and Wattenbarger, 1996)
1( ) ( ) ( ( ))
p p p p p z p
t z z t t z z t p p p z
Eq.8-5
Involving the expressions of isothermal formation and gas compressibility and substituting
them in equation 8-5 for compressibility part, yields equation 8-8:
86
1( )fc
p
Eq.8-6
( / )g
z p zc
p p
Eq.8-7
( ) ( )f g
p p pc c
t z z t
Eq.8-8
Where c is the compressibility. Placing back the equation 8-8 into diffusivity equation we get
the radial diffusivity equation for a single-phase compressible real gas in a homogeneous,
horizontal medium.
( )1( )
f g tc c cp p p p p p
rr r z r k z t k z t
Eq.8-9
In order to solve that equation, the fluid has to be treated as slightly compressible. To do this,
the changes in gas viscosity and compressibility must be taken into account. On that way two
new variables have to be introduced: the pseudopressure (m(p)) and the pseudotime (ta) (Lee
and Wattenbarger, 1996; Lewis, 2007).
( ) 2
b
p
p
pm p dp
z
Eq.8-10
0
( )
t
a t i
t
dtt c
c
Eq.8-11
Finally, involving all of the above expressions into diffusivity equation we get:
1 ( ) ( )( )
a
m p m pr
r r r k t
Eq.8-12
The above equation can be solved by setting the initial and boundary conditions (Lee and
Wattenbarger, (1996); Lewis, (2007)).
87
Dimensionless variables
The diffusivity equation presented earlier can be solved in dimensional space. But that
procedure is quite time consuming. That is why more simplified solution can be reached by
involving dimensionless expressions. The dimensionless variables are used to define the
important groups that control the equation by using simplified expressions. On that purpose
the following dimensionless equations are introduced: (dimensionless radius) and
(dimensionless time), (dimensionless pressure) (Lewis, 2007).
As follow, the diffusivity equation for a single-phase compressible fluid in a homogeneous,
horizontal medium is:
1( ) tcp pr
r r r k t
Eq.8-13
The next step is to combine the variables into dimensionless expressions. For instance, the
following equation for pressure has no units, and is the combination of all variables that have
an effect on pressure (Lewis, 2007).
( )i wf
d
kh p pp
q B
Eq.8-14
The next expressions are also dimensionless, and governed by variables that are influential to
time and radius (Lewis, 2007).
2d
t w
ktt
c r
Eq.8-15
d
w
rr
r
Eq.8-16
Combining all the dimensionless variables, the diffusivity equation can be re-written in
dimensionless form as:
1( )d d
d
d d d d
p pr
r r r t
Eq.8-17
88
Dimensionless time and dimensionless pressure are equations that allow the diffusivity
equation to be solved more easily. The next re-arrangement of dimensionless pressure and
dimensionless time is defined by Lewis, (2007). The following two equations compose the main
parts of the constant pressure flow rate equation from horizontal well single transverse
fracture, which have been discussed in Chapter 3.
[ ( ) ( )
1422
i wf
wd
kh m p m pp
Tq
Eq.8-19
2
0.00634
( )d
gi ti w
ktt
c r
Eq.8-20
89
9 Appendix- Flow calculations in numerical simulator
Reservoir Simulation is a form of numerical modeling which is used to capture the physical
properties. The process involves dividing the reservoir into a number of discrete units in three
dimensions and modeling the progression of fluid fronts through space and time in a number of
steps. The equation solved for each cell and each time step is a combination of Darcy’s Law and
the material balance equation.
kq P
Eq.9-1
( * )M Qt
Eq.9-2
Where:
M = Mass Flux (In-Out)
( * )t
= Accumulation
Q = Injection/Production
Combination of above equations gives simulator flow equation including the gravity term.
( * ) ( )Q
P zt
Eq.9-3
A fully implicit method was used to calculate the changes in pressure and saturation over time.
The properties of the state of the property are taking into consideration at both the current
time and the next time step. The equations used by Eclipse (Schlumberger 2011) are explained
briefly in this appendix.
As it already mentioned the starting equation is the mass balance equation solved for pressure
and saturation implicitly. The solution vector is referred as X, the residual vector as R and the
Jacobian J ( van Zelm, 2010). Here X is defined as:
90
o
w
g
P
X S
S
Eq.9-4
where solution for oil pressure and the saturations for water ( ) and gas ( ). As we are
modeling only gas-water, the primary parameter is out of use. The residual vector looks like:
o
w
g
R
R R
R
Eq.9-5
Each of these residuals is presented separately, by the following equation:
( , ) ( , )tfl t t t t
dMR F P S Q P S
dt
Eq.9-6
Where:
= non-linear residual, for each cell and each fluid
dM = mass, per unit surface density, accumulated during time step dt
F = net flow rate into neighboring grid blocks
Q = net flow rate into wells during the time step
By taking the derivative of the R to X the Jacobian can be calculated. The main goal of the
numerical method is to approach R = 0, by taking ‘small enough time steps’ throughout the
simulation. In order to solve the mass balance implicitly, the following equations for a gas-
water system are used (Eq. 9-7 and Eq. 9-8).
t dt tdM M M
Eq.9-7
*
w
w
g
g
S
BM PV
S
B
Eq.9-8
91
Where:
M = mass or volume of cell
t = time
dt = time change (time step)
PV = cell pore volume
= water formation volume factor
= gas formation volume factor
For the flow calculation, the time step and the location of the grid blocks in which direction the
equation is solved using down or upstream weighing are important (van Zelm, 2010). The flow
rate F into cell i from neighbouring cell n is calculated by the following equation:
0
0 0 *
0
v rgro
o o g g
oni
rwni ni wni
w w
gni
rgs ro
o o g g
R kk
B BdP
kF T dP
BdP
kR k
B B
Eq.9-9
For the system used in this thesis, the equation will simply be reduced to:
0 0 0
0 0 *
0 0
oni
rwni ni wni
w w
gni
rg
g g
dPk
F T dPB
dPk
B
Eq.9-10
Where:
= flow rate from cell n into cell i
= transmissibility between cell n and cell i
nidP = phase α potential difference between the cells
92
10 Appendix- Grid refinement
The hydraulic fracture is designed in Eclipse2011 (Schlumberger) as an induced zone of
enhanced permeability and porosity in y-direction of the grid. In this thesis work, the host grid
refinement option is chosen for the reservoir model. That option requires a grid refinement in
the near-fracture area and the update of the hydraulic fracture properties accordingly (Ehrl and
Schueler, 2000). The grid contains a refinement in the x-direction, in that part where the
hydraulic fracture was induced. The width of the refined grid cell is treated as the width of
induced fracture.
In host grid refinement procedure, the width of the surrounding cells are gradually refining in x-
direction towards the host cell (width of the fracture) and then the refinement is gradually
deteriorating with the distance from the host cell. As it referred earlier, the refined cells belong
to induce fracture zone, where the fluids flow from the lower permeability matrix, where
pressure and saturation changes are small, transfers into the high-permeability fracture. This
discontinuity requires sufficient grid resolution, and therefore smaller grid blocks and small
time steps, especially early in production. The top view of the refined zone is shown in Figure
10-1 and Figure10-2.
Figure 10-1: Host grid refinement in the reservoir model.
93
Figure 10-2: Host grid refinement in the reservoir model, zoomed in close to the fracture.
94
11 Appendix- Dual porosity option
In a dual porosity reservoir, fluids exist in two interconnected systems: the rock matrix, which
usually provides the bulk of the reservoir volume and the highly permeable rock fractures. To
model such systems, two simulation cells are associated with each block in the geometric grid,
representing the matrix and fracture volumes of the cell. Only the gas concentration in the coal
is tracked. In the fracture system, the standard flow equations are solved. A matrix-fracture
coupling transmissibility is constructed automatically by Eclipse (Schlumberger) to simulate flow
between the two systems due to fluid expansion, gravity drainage, capillary pressure etc. In a
dual porosity run the number of layers in the z-direction should be doubled. Eclipse associates
the first half of the host grid with the matrix blocks, and the second half with the fractures. In
such runs number of grid cells in z-direction must therefore be even. That is why, for Dual
porosity modeling purposes the number of grid cells in comparison to previous models has
changed to 12 (even number). The size of each grid cell in z-direction is defined to be 10
meters. By activating the dual porosity option, the model is automatically divided in two zones.
First half of the grid block (first 6 cells) in z-direction is related to the matrix and the second half
to the pore space.
Transmissibility calculations
For dual porosity modeling it is necessary to specify multiplier ( ) to be used in the
construction of fracture-matrix coupling transmissibilities. In Eclipse2011 fracture-matrix
coupling multiplier can be applied by using the keyword SIGMA. In this case the multiplier
should be defined for the whole grid block. This sigma factor may be related to the matrix block
size with the expression proposed by the Kazemi:
2 2 2
1 1 14( )
x y zI I I
Eq.12-1
where , ,x y zI I I , and are typical x, y and z dimensions of the matrix blocks. Using the above
expression it was calculated that 0.4 sigma value corresponds to our model grid block
dimensions. However, because in our model the host grid refinement was used, the size of grid
cells in x-direction is changing all the time for different cases. So, in above calculation only
averaged value of grid cell size was used which might have some effect on sigma factor.
However, to clarify once again the effect of small variation in sigma factor on production
profile, some sensitivity analysis was performed for different sigma values. Simulations
95
performed for the following sigma values: 0.0001, 0.001, 0.01, 0.4, 0.66, 1. The results of
sensitivity analysis are shown in Figure 12.1
Figure 11-1: Gas cumulative production profiles for different values of sigma factor.
As it can be seen from the graph above, for very small sigma values (0.0001 and 0.001)
simulations went wrong and no production was reached. For the cases of sigma 0.4, 0.66, 1 the
results are similar and the production lines absolutely align. For the case of sigma magnitude
0.01 the production after 10 years is 17% less than for previous cases. It was determined that
there is insignificant effect of sigma factor on production profiles for the values in between 0.1
and 1. So, some inaccuracy in sigma factor by using the average value of grid cell size in x-
direction cannot dramatically affect the simulation results.
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12 Appendix – Introduction of Eclipse300 Compositional mode
For dual porosity shale gas modeling, Eclipse300 compositional mode was utilized instead of
Eclipse100. Compositional simulation is required when the black oil approximation is unsuitable
(Schlumberger, 2005). Compositional simulators such as Eclipse300 perform the same fluid flow
calculations as a black oil simulator with additional computations. As it already discussed, in
modeling of shale reservoirs the adsorbed gas should be involved. Although, in Eclipse100 it is
possible to introduce adsorbed gas as a solvent, for enhanced coal bed methane (shale gas)
projects Eclipse 300 a full compositional treatment is more preferable. In this appendix the
main differences of two simulators are discussed.
Eclipse100 Blackoil Simulator assumes that oil and gas phases can each be represented as one
component through time. The component properties can change with pressure and
temperature, but the composition does not change. Blackoil simulators such as Eclipse100
cannot model compositional changes. For compositional modeling, the solution GOR ( ) and
vapor OGR ( ) has to be varied (Schlumberger, 2005). Then, the fluid properties are can be
represented by a set of tables of PVT properties as functions of pressure.
0
( )g
s
B
Bf p
R
Eq.12-1
The required input to black-oil simulator is therefore a table of physical properties versus
pressure. For example, a table of oil viscosity at different pressures.
The Eclipse300 Compositional Simulator tracks each component of the oil and gas in the
reservoir. The reservoir fluid is treated as a number of flowing pseudo components. Once the
fluid flows have been calculated each pseudo component must be flashed to equilibrium
conditions. Then a cubic equation of state (EoS) must be solved for each pseudo component.
Both calculations are performed at each time step in every grid cell. The flow calculations take
less than 50% of the computational time of a compositional simulation, and flash calculations
together with EoS solution take up the rest of the time (Schlumberger, 2005). This method is
used to model fluids near the critical point where changes in the pressure and temperature can
result in very different fluid behavior.
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Using Eclipse300, one component (methane) case was modeled as the gas component in
the reservoir. If there are both oil and gas phases, we have to calculate the composition of each
phase. For given compositions the physical properties have to be calculated, for instance the
gas viscosity.
( , , )
ii
i
i i
yK
x
f p x y
Eq.12-2
Furthermore, more variables are needed in compositional simulation.
, 1,....
w
i c
p
z
z i n
Eq.12-3
As in Eclipse100 the oil pressure is used, the water molar density instead of , and the molar
densities of each hydrocarbon component. If there are hydrocarbon components, then
there are + 2 variables to solve. For instance, if we model out hydrocarbon fluid with 2
components then we will have 4 variables, instead of 3 used in a black oil model. Therefore, this
is computationally more expensive.
The key difference between black-oil and compositional simulation is the PVT description of the
fluid. In black-oil we can fully describe the fluid properties with a table of property vs. pressure.
However, in compositional simulation we need to solve a flash equation and solve and Equation
of State.
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13 Appendix- Adsorption model in Eclipse300
In order to introduce the adsorbed gas factor into dual porosity system the available coal bed
methane option in Eclipse2011 should be used. The reduced pressure in the fractures allows
gas desorption from the surface of the shale to the fracture. Gas diffusion occurs from the
matrix of the shale towards the fracture surface. For dual porosity the Coal Bed Methane model
uses a modified Warren and Root model to describe the physical processes. As the main
objective of our project is related to modeling of adsorbed gas, we use Coal Bed Methane
option in Eclipse (Schlumberger) to model characteristics of shale gas system.
In order to activate CBM option in Eclipse300 the COAL keyword is used. In Coal Bed Methane
option the COALNUM keyword defines the regions with coal. The region number entered with
this keyword is used to determine the sorption of the coal. A zero value means there is no coal
and that the standard dual porosity fluid flow equations should be solved. In all dual porosity
models treated in this project the first 6 grid cells defined as coal (shale) with region number 1,
however the last 6 grid cells are defined with shale region number 0 ( no shale region).
The Extended Langmuir isotherm is used to describe the shale sorption for the different
components. Using LANGMEXT keyword the adsorption capacity is introduced for each
component to region with shale as a function of the pressure and the free gas phase
composition. For each component two constant parameters need to be input, the Langmuir
volume ( ) and the Langmuir pressure ( ). In this project, the Langmuir volume and Langmuir
pressure parameters were treated typical for Haynesville and New Albany shale reservoirs.
For the single component cases the adsorption capacity is calculated by:
( ) ( * )
1
s
s
pP PL p V
pRT
P
Eq.13-1
Where
sP =Pressure at standard conditions
= Scaling factor
T = Temperature at standard conditions
R = Universal gas constant
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V = Langmuir volume for single component
P = Langmuir pressure for single component
P = Pressure
where V is the maximum storage capacity for the gas, referred to as the Langmuir volume
constant, and P is the Langmuir pressure constant. As the Langmuir volume constant V is a
surface volume over shale weight, we translate this to moles over coal weight by the ideal gas
law (by the term s
s
P
RT ).
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