The document discusses modelling fluid flow in shale reservoirs. It describes the complex porous network in shales which includes multiple gas storage and transport mechanisms. Effective modelling requires accounting for different porosity systems including the organic matrix, inorganic pores and natural fractures. Common modelling approaches for fractured reservoirs like dual porosity and dual permeability models are discussed as well as their limitations for modelling low permeability shales. More advanced models like MINC (Multiple INteracting Continua) and locally refined dual permeability models are presented to better represent transient fluid flow in shales. Key shale properties affecting gas production including adsorbed gas, non-Darcy flow, and fracture properties are also summarized.

1. ERA Shale Gas Joint Programme
Technical seminar
Modelling of fluid flow in shales
Faculty of Drilling, Oil and Gas
Department of Natural Gas Engineering
Gdańsk, 8-9.10.2014
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2. shale gas = unconventional gas (why?)
shale gas - natural gas that is trapped within fine-grained
sedimentary rocks (called shale or mudstone), that can be source
rocks for hydrocarbons
„unconventional reservoirs” are those that cannot be produced
at economic flow rates without massive stimulation treatments or
special recovery processes and technologies
the term „unconventional” reflects current level of techniques
and technologies, the knowledge and experience applied to
recover hydrocarbons from such type of reservoirs
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3. shale gas resources
• important contribution to the U.S. „energy cocktail”
• shale gas resources are of high interest; expected to be future
source of hydrocarbons
• economically efficient development achieved by
intensive multi-stage hydraulic fracturing
World shale gas in place ~690 Tcm
Technically recoverable resources ~ 190 Tcm
Conventional natural gas proved reserves ~210 Tcm
According to Energy Information Agency (EIA, 2013)
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4. shale rock properties
• variety of shale rock types => different types of shale gas
reservoirs
• four important characteristics :
1. maturity of organic matter
(vitrinite reflectance [%Ro]; > 1% Ro)
2. type of gas generated and stored in the reservoir
(thermogenic or biogenic)
3. TOC content of the strata (min. 1.0 wt%)
4. permeability of the reservoir
(0.00001-0.001mD = 10-1000 nD)
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5. modelling „problems”
• complex porous system and
interaction between its elements
• multiple gas storage and
transport mechanisms
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6. 4-porosity system
• three different natural porous systems:
1. gas-wet organic porosity
2. water-wet (primarly) inorganic porosity
3. system of natural fractures
• one human-made pore system – hydraulicaly induced
fractures
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7. tank representation
of the quad-porosity model
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Hudson, 2011
•the solid tanks represent four different porosity systems
•the dashed small tanks represent internal physical phenomena
•the valves represent the connectivity between each system

8. quad-porosity model in parallel
with cross-flow
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9. quad-porosity model in parallel
without cross-flow
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10. quad-porosity model in series
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11. how do we model naturally fractured rocks?
• Dual Porosity model (DP)
• Dual Permeability model (DK)
• Multi INteracting Continua
(MINC)
• fractures orthogonal in three directions (fracture spacing in i,j,k),
act as boundaries for matrix elements
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12. standard Dual Porosity model
• two porosity systems: matrix and fracture porosity
• own porosity, permeability and other properties
(e.g. water saturation) values for each porosity system
• matrix connected only to the fracture in the same grid
block
• fluid flows through the fracture network; matrix blocks
act as source and sink terms
• no direct matrix-matrix flow
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13. Dual Permeability model
• main difference – each matrix block is connected to both
the fracture blocks and the surrounding matrix blocks
• fluid flows both through the fracture network as well as
through the matrix
• where to use?
– in cases where there is capillary continuity
– when vertical (K direction) matrix-matrix mass
transfer is important
– matrix-matrix flow can be controlled (or even set to
zero) by matrix transmissibility multipliers
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14. • one-dimensional nested
discretization of matrix
blocks – allows for better
representation of matrix-fracture
transfer
• very efficient
representation of the
transient fluid regime
• can represent the
pressure, viscous and
capillary forces; the
gravity force is not
considered in this nested,
one-dimensional matrix
refinement
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15. DK vs MINC – what to choose?
• DK – normally used when simulating naturally fractured
reservoirs
• MINC – accounts for transient flow from matrix to
fracture; useful for low permeability systems where
pressure drop between fracture and shale is very large
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16. solution: LS-LR-DK model
(Logarithmically Spaced – Locally Refined – Dual Permeability)
simple local grid refinement (LGR) based model gridded similarly to
MINC but without its limitations of lack of matrix-matrix flow
MINC LS-LR-DK
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17. hydraulic fracures/SRV
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18. shale rock modelling - coclusions
• the standard Dual Perm model is unable to properly
model very low permeable fractured shales
• the MINC model is able to approximately reproduce the
flow in very low permeability fractured shales, but
cannot be used in higher permeability shale gas models
• the LGR based logarithmically spaced dual permeability
(LS-LR-DK) grid overcomes limitations of both DK and
MINC grids
• together with non-Darcy flow permeability based
correction factor (Kcorr) non-Darcy flow effects can be
accurately modelled in hydraulic fracture blocks as wide
as 2 ft
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19. gas storage mechanisms
three types of gas storing mechanisms:
1. free gas – gas stored in matrix pore volume (pores and
natural fractures)
2. adsorbed gas – gas adsorbed onto surface of the shale
formation and solid organic material
3. gas dissolved in organic material
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20. adsorbed gas
• amount of adsorbed gas varies between reservoirs - from
15% up to 60% (even 85%), of gas initially in place
• sufficient pressure decrease necessary to liberate the
adsorbed gas
• modeled with use of Langmuir isoterm, which relates the
volume of adsorbed gas (Vads) to reservoir pressure (P)
= ´
ads L
• VL and PL – Langmuir’s characteristic volume and pressure;
depend on TOC
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L
V V P
P +
P

21. pressure drop/desorption extent
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22. adsorbed gas contribution
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23. Knudsen diffusion number and flow regimes
• viscous flow Kn ≤ 0.001
(the mean free path of gas molecules
is negligible compared to pore throat size)
• slip flow 0.001 ≤ Kn ≤ 0.1
p m l
´ ´ ´ ´
(flow velocity at pore boundary is not zero; mean free
path becomes significant compared with pore throat size
and collisions with pore walls start to become important)
• transition flow regime 0.1 ≤ Kn ≤ 10
(most difficult; most of shales fall in this region)
• free molecular regime Kn > 10
(modelled using Knudsen diffusion)
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1
2
2.82
n
pore
R T
K P M
r k
f
= =

24. Klinkenberg effect
= æ + ö çè ø¸
( )
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1
1 1 4 1
1
a
n
n
n
k k b
P
b a
K K
P K
¥
æ ´ ö = - ´ ´ç + ¸- è + ø

25. how do we model gas flow in shales?
• gas flow through the shale matrix
• viscous flow (Darcy flow)
• diffusion
▪ gas flow in fractures
• Darcy flow
• non-Darcy flow
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26. Thank you!
stanislaw.nagy@agh.edu.pl
lukasz.klimkowski@agh.edu.pl
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27. natural fracture spacing effect
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28. primary fracture conductivity effect
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29. primary fracture permeability gradient effect
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30. primary fracture permeability gradient effect
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31. SRV extent effect
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