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A New Approach for the Simulation of Fluid Flow in UnconventionalReservoirs through Multiple Permeability ModelingBicheng Yan, SPE, Masoud Alfi, SPE, Yuhe Wang, SPE, John E. Killough, SPE, Texas A&M University

Copyright 2013, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September2 October 2013.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohi bited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

AbstractShale reservoirs are characterized by ultra-low permeability, multiple porosity types, and complex fluid storage and flow

mechanisms. Consequentially the feasibility of performing simulations using conventional Dual Porosity Models based on

Darcy flow has been frequently challenged. Additionally, tracking of water in shale continues to be controversial and

mysterious. In organic-rich shale, kerogen is generally dispersed in the inorganic matter. Kerogen is different from any other

shale constituents because it tends to be hydrocarbon-wet, abundant in nanopores, fairly porous and capable of adsorbing gas.

However, the inorganic matter is usually water wet with low porosity such that capillary pressure becomes the dominant

driving mechanism for water flow, especially during hydraulic fracturing operations. This work presents a technique of

subdividing shale matrices and capturing different mechanisms including Darcy flow, gas diffusion and desorption, and

capillary pressure. The extension of this technique forms a solid and comprehensive basis for a specially-designed simulator

for fractured shale reservoirs at the micro-scale.

Through the use of this unique simulator, this paper presents a micro-scale two-phase flow model which covers three

continua (organic matter, inorganic matter and natural fractures) and considers the complex dynamics in shale. In the model,

TOC is an indispensable parameter to characterize the kerogen in the shale. A unique tool for general multiple porositysystems is used so that several porosity systems can be tied to each other through arbitrary connections. The new model

allows us to better understand the complex flow mechanisms and to observe the water transfer behavior between shale

matrices and fractures under a microscopic view. Sensitivity analysis studies on the contributions of different flow

mechanisms, kerogen properties, water saturation and capillary pressure are also presented.

Introduction

In recent years, unconventional resources have played a significant part to balance between the increasing energy demand

and the shortage of production from the conventional reservoirs in the United States (Wei et al. 2013). Hydrocarbon from

organic rich shale is one of the most significant unconventional resources. The successful development of shale reservoirs is

greatly attributed to horizontal well drilling and hydraulic fracturing operations. In industry, effective hydraulic fracturing for

shale wells is performed mainly through injecting slickwater under high pressure. However, generally the recovery of

fracturing fluid is quite low.King (2012)suggested that the water might be trapped in the small pores and the micro-fractures

of shale. Besides, evidence shows that there is a high concentration of chloride salts in the flowback fluid, while it cannot beexplained either from the composition of fracturing fluid (mostly fresh water) or from the constituents of shale and the

salinity of formation brine (King 2012).Wang and Reed (2009)propose that there exist four pore systems in the organic-rich

shale: inorganic matter, organic matter (kerogen), natural fractures and hydraulic fractures. It is also suggested that the

organic matter is oil wet and that single oil or gas phase flow without residual water is dominated in kerogen fragments.

However, the inorganic matrix is mostly considered as water-wet (Kalakkadu et al. 2013). Through the approach of

Molecular Dynamics Simulation and with the initial condition of water and NaCl,Hu et al. (2013)suggested that water could

be filled in the larger pores in the kerogen through capillary condensation but no water enters the smaller 0.9 nm kerogen

pores. Water exists in the inorganic MgO pores in the liquid phase; meanwhile, there is a much higher ionic concentration in

the inorganic matter than that in the kerogen.

In shale gas reservoirs, the source of shale gas can be thermogenic, biogenic or combined source (Darishchev et al. 2013).

Natural gas is usually considered to exist in three forms: compressed gas in pores and fissures, adsorbed gas in the organic

and inorganic matter, and dissolved gas in the kerogen (Javadpour 2009;Zhang et al. 2012). Usually it might be reasonable

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that the sorbed gas in the inorganics be neglected, because under moisture conditions methane molecules are preferentially

sorbed on the walls of hydrophobic pores in the kerogen. In the inorganic matter, water molecules might either block the

hydrophilic pores or occupy those sorption sites (Ji et al. 2012; Zhang et al. 2012). Using gas solution and diffusion

parameters from bitumen,Swami and Settari (2012)considered gas solution in the kerogen through an ideal model with a

cylindrical nanotube surrounded by the kerogen solid bulk and observed the difference caused by solution gas. However, it

might not be pragmatic to isolate nanopores in the kerogen from the kerogen solid bulk in a conventional simulation based on

porous media, unless it can be upscaled properly.

Because the permeability in the organic rich shale is extremely low and the pore size in the shale is in the nanometerscale, some non-Darcian mechanisms including gas diffusion, desorption and slippage flow have been brought into

consideration in order to explain the profitable gas rate in shale reservoirs (Civan et al. 2011; Ertekin et al. 1986; Freeman et

al. 2012; Javadpour 2009; Javadpour et al. 2007; Shabro et al. 2011; Shabro et al. 2012). A common approach for those

authors is to use an apparent permeability either based on mechanisms or through a condition function of Knudsen number.

Matrix subdivision due to the difference between the kerogen and the inorganic matter is generally not taken into account,

and the complexity of the connectivities between different pore systems cannot be properly represented. Therefore, it might

be difficult to observe the dynamics of fluid flow from the shale matrix to outer fractures through those models.

Previously we have established a single gas phase Micro-Scale Model (Yan 2013; Yan et al. 2013b; Yan et al. 2013a). It

subdivided the shale matrix into the inorganic matrix and the organic matrix with different pore geometries. The issue of

connectivities between different continua is solved through the random distribution of kerogen units. The model also

considers adsorbed gas and gas diffusion in the kerogen and a petrophysical parameter - the content of total organic carbon

(TOC, wt%). It demonstrates that desorption can maintain a high gas in place level and diffusive flow is quite significant to

gas rate with permeability down to nanoDarcy magnitude.

This work is based on our previous research, with the same structure in the micro model (Yan 2013; Yan et al. 2013a), but

gas and water two phase flow with mixed wettability in the shale matrix is implemented. The effect of high capillary pressure

is also taken into account here. The work is motivated to interpret the dynamics of gas and water flow at the micro-scale

level. Case analysis is introduced to evaluate the influence of different mechanisms or parameters on the gas and water flow

in the model.

Model Description

To better catch the dynamics of complex processes during hydrocarbon production from unconventional reservoirs, we have

used a multiple porosity model previously offered by the authors (Yan et al. 2013a). Supported by different petrophysical and

geological data, this new model allows us to understand the complex mechanisms and eventually to better predict ultimate

recovery from shale reservoirs.

In this paper, four different pore systems are considered with distinctive characteristics. To account for the presence of

induced or natural fractures in the shale, we have divided the media into fracture (representing natural fractures in thereservoir) and bulk matrix blocks. Characterized by their high permeability, natural fractures serve as pathways to connect

low permeability shale matrix blocks with the induced fracture network or the well-bore. Based on the difference between the

kerogen and the inorganic matter in the shale matrix, the matrix bulk is further divided into two sub-media: the organic and

the inorganic matter (Wang and Reed 2009). As reflected in the geological data (Fig. 1andFig. 2), the presence of different

pore sizes has inspired us to further subdivide the organic matter into kerogen with micropores and kerogen with nanopores.

This further subdivision will help us to better understand the effect of different transportation mechanisms in each sub-

continuum.

Fig. 1Different pore geometry in shale, especially in kerogen, large and small pores can be observed (InGrain 2010).

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Fig. 2Local pore distribution in kerogen, smaller pores reside on the wall of larger pores (Curtis et al. 2010).

Considering that shale matrices are surrounded by fractures,Yan et al. (2013a)proposed a configuration of different pore

systems in a Micro-Scale Model. Specifically each block of kerogen with nanopores is surrounded by six blocks of kerogen

with micropores in an attempt to mimic the effect that kerogen with micropores ties kerogen with nanopores to any other

non-kerogen pore systems. This type of grid configuration is supported by the geological and petrophysical data from shale

rocks, which indicates that in the kerogen those nanopores are located through the wall of the larger pores (Fig. 2). Kerogen

units are randomly distributed in the matrix bulk through a rigorous Monte Carlo algorithm, and their abundance depends on

different factors such as TOC and different media properties (Fig. 3). Based on the grid configuration, kerogen with

nanopores can only connect to kerogen with micropores. In the larger pore sizes, fluid in kerogen with micropores, inorganic

matter, and natural fractures can either flow in themselves or among each other. Therefore, there should be seven types of

connections for those pore systems mentioned above (Fig. 4).

Fig. 3A representative micro-model with random kerogen distribution (green grids: kerogen, other empty space in the cuboid:inorganic matter)(Yan et al. 2013b)

Fig. 4Schematic of connectivities in the Micro-Scale Model

Advective flow

Diffusive flow

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In the Micro-Scale Model, the previous single gas phase flow (Yan et al. 2013a)has been extended to two phase gas

water flow according to the characteristics of each pore system. As the mean free path of gas molecules becomes somehow

comparable to the pore diameter, in addition to viscous flow (Darcys law), molecule/walls interactions will play a more

significant effect so that diffusive flow cannot be neglected. According to Ficks law, the mass flux is p roportional to the

concentration gradient. Considering the nanometer pore size in kerogen, diffusive flow is considered there. Since the mean

pore diameter in the kerogen with nanopores is very small, Darcy flow is not considerable there. Therefore, in kerogen with

nanopores, diffusive flow is assumed to be the only flow mechanism. On the other hand, Darcy flow exists in kerogen with

micropores, the inorganic matter and the fracture network. Diffusive flow is considered to only occur in the gas phase; waterflow takes place only through Darcy flow.

Unlike conventional gas reservoirs, the gas storage mechanism in shale reservoirs is not limited to compressed gas;

adsorbed gas is also important. As we previously mentioned, in a gas-water two phase system, considering the different

wettability of the inorganic matter and the kerogen, gas adsorption in the kerogen should be considered, however, gas

adsorption in the inorganic matter might be so weak as to be neglected under moisture conditions. As reservoir pressure

decreases, adsorbed gas in the kerogen will be gradually desorbed as free gas and flow into fractures. Therefore, the

desorption process actually increases the gas accumulation within the kerogen grids in this model. A popular form of

desorption modeling is the Langmuir isotherm (Cui et al. 2009), which has been used in this paper as well.

In addition to fluid flow and storage mechanisms, in two phase water and gas flow, wettability, relative permeability and

capillary pressure further increase the complexity of the model. Particularly, capillary pressure might play a significant effect

due to the small pore size in the shale matrix. Pore systems in the kerogen (micro- and nano-pores) are considered to be gas

wet (Passey et al. 2010;Wang and Reed 2009)and gas can flow within the kerogen in a continuous phase. However, in the

inorganic matter, especially the siliclastic minerals are water-wet so that water can be layered on the grain surfaces (Passey et

al. 2010). Water dynamics in the shale reservoir are important during hydraulic fracturing and the early gas production

period. Because of its affinity to the inorganic matter and the high capillary pressure between the gas and water phases, water

is likely to be imbibed into the shale matrix. Although a large quantity of research has studied different aspects of capillary

pressure in shale reservoirs, this phenomenon still stays ambiguous due to the complex interactions of water molecules with

extremely small scale pores in the tight gas and shale gas reservoirs. These ultra-small pore sizes, however, can be interpreted

as a medium with high capillary pressure (Wang et al. 2013). In this paper, the Brooks and Corey formulation (Brooks and

Corey 1964)is used to calculate capillary pressure.

c

ee

P

PS (1)

Wherewr

wrw

e S

SS

S

1

Fig. 5 shows the capillary pressure curve used for the base case simulation in this paper. Due to extremely low absolute

permeability of shale, it is difficult to physically measure the actual relative permeability in this type of reservoirs. For our

simulation purposes, Eq. (2) and (3) are used to build non-wetting phase relative permeability curves for the drainage and

imbibition process. For the wetting phase, however, we have assumed no hysteresis occurs, which means that we can use the

same formula (Eq. (4)) for both drainage and imbibition cases (Dacy 2010; Molina 1980). Fig. 6 shows the imbibition

relative permeability curve we have incorporated into our simulator, and Table 1 represents the values used to calculate

hydraulic properties of the base case or default values.

nwdn

wcnwnwc

wcnwwrnwd

SS

SSk

1

1 (2)

nwin

nwtwi

wiwrnwi

SS

SSk

11 (3)

wn

wcw

wcwwrw

S

SSk

1 (4)

Considering that water molecules are just present in the aqueous phase and hydrocarbon molecules can be found only in

the gaseous phase (solubility of hydrocarbon molecules in the aqueous phase is considered to be negligible in this work), the

gas phase mass balance equation can be used for the hydrocarbon component and the aqueous phase mass balance can be

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used for the water component. Therefore, the mass balance equations for the two phase micro model can be written as Eq. (5)

and (6).

Gas phase:

t

q

t

SzgP

KKPDC a

gg

gg

g

rg

gg

))1(()()(

(5)

Aqueous phase:

t

SzgP

KK wwww

w

rww

)()(

(6)

Where 1 gw SS

For Eq. (5) and (6), the left hand side refers to the difference between the mass flux into and out of the system. Mass

transfer in the gaseous phase occurs either through diffusive flow or Darcy flow. However, we will neglect the diffusive term

in the mass balance equation of the aqueous phase, because in the liquid its effect is negligible compared to that of Darcy

flow. On the other hand, the right hand side represents the accumulation of the gas and aqueous phase. For gas we consider

both compression (the first term) and desorption (the second term). However, we just consider the compressibility of the

aqueous phase in the mass accumulation.

Fig. 5Capillary curve used for the base case

Fig. 6Relative permeability curve used for the Micro-Scale Model

0

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Pc,psi

Pc,MPa

Water Saturation

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0 0.2 0.4 0.6 0.8 1

Kr

Kr

Water Saturation

Krg_drainage

Krg_imbibition (used in this paper)

Krw_imbibition (used in this paper)

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Table 1Hydraulic properties of the base model

Parameter Value

1.5

eP , MPa 4.0

wrS 0.2

wcnwS 0.25

nwcS 0.05

wiS 0.25

nw tS 0.25

wcwS 0.2

nwdn 3

nw in 3.5

wn 4

In this work, a 50508 model (20,000 total grid blocks) is used to represent a single matrix bulk surrounded by a layerof fracture grids outside. The dimensions are 482 m482 m 62 m with matrix cubes of 10 m length and fracture

aperture of 1 m. The number of the kerogen and the inorganic blocks are specified based on the TOC value. For the base

case simulation, TOC is 9.0 wt%, which means 2625 randomly distributed kerogen grid blocks (including kerogen with

micro- and nano-pores), 11199 inorganic blocks, and 6176 fracture blocks. Table 2provides more details about the properties

of each pore system for the base case.

In the micro model, the fracture pressure is constant at 8.6 MPa; the initial matrix pressure is set to be 17.2 MPa. The

average matrix pressure changes with time as hydrocarbon flows from the matrix to fracture and water is imbibed into the

matrix bulk. Initial saturation in different media varies based on their characteristics. Kerogen with micropores and nanopores

(gas-wet pore system) are considered to have very high initial gas saturation (S g= 0.99). On the other hand, we consider the

fracture media to be mostly saturated with water (Sw> 0.99). During the simulation, water imbibition occurs from the fracture

into the matrix so that hydrocarbon gas flows out of the matrix. Initial water saturation in the inorganic matter can vary

depending on the situation from 0.25 to 0.65 (Hill and Nelson 2000). For the base case, the initial water saturation in the

inorganic matter is considered to be 0.30. Note that the provided mesh data, TOC and media properties (Table 2),wettabilities, capillary pressure and relative permeability correlations (Table 1), initial pressure, and initial water saturation

values in different pore systems are used as the default in this paper, if not specified.

Table 2Parameters for the base model

Porosity system Fracture InorganicKerogen

micropores nanoporesDensity, Kg/m

3 -- 2.610

31.3510

3 1.410

3

Porosity 1.0 0.02 0.2 0.25

Permeability, nD 84 50 50 --

Diffusivity, m2/s -- -- 8.2110

-5 2.0110

-6

DesorptionLangmuir pressure, MPa -- -- 10.342 10.342

Langmuir volume, m3/Kg -- -- 1.638710

-2 1.794810

-2

Results Analysis

Before any simulation results are shown, we should note that the model is quite small in a magnitude of 1.010 -10m3, and

through observation the dynamics in such a micro model start from1.010 -7second and deplete to final steady state after 0.1

second. Therefore, to make the simulation results readable in a time-scale, a dimensionless time is defined as a ratio of the

simulation time to the minimum time step size (1.010-7). Additionally, grid pressure (pressure of the non-wetting phase) is

always plotted for different media.

For the base case with the default parameters in the model, the results are shown in Fig. 7, Fig. 8, and Fig. 9. The

dynamics in the inorganic matter are shown inFig. 7.In the inorganic matter, water saturation increases from the initial level

0.30 to the final level 0.74. In the inorganic matter, gas is the non-wetting phase. Due to the initial high capillary pressure in

the inorganic matter (Fig. 5), water is imbibed but gas is drained out. In consequence, the inorganic matter is downstream for

water flow but upstream for gas flow a counter-current imbibition process. Reviewing the relative permeability curve in

Fig. 6,in the Swrange of 0.3 to 0.42, the relative permeability of gas (imbibition) is very high but that of water is close to

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zero; therefore, during this period, the water flowing in to the inorganic matter is limited to fracture (upstream)-inorganic

connections at the outer part of shale matrix (Fig. 10(b)), however, the gas flowing out from the inorganic matter is supported

by fracture-inorganic, inorganic-inorganic, and inorganic-organic (single phase) connections. The combined effect of gas

flow-out and water flow-in is that pressure in the inorganic matter decreases. After Swbecomes greater than 0.42 (Fig. 6), the

inorganic-inorganic connection also joins in the water flow process so that water can easily get into the inner shale matrix.

When Swin the inorganic matter reaches to 0.64, gas relative permeability in the inorganic matter is close to zero but that of

water keeps increasing. In consequence, in the inorganic matter, water flow-in is enhanced but gas is trapped there.

Therefore, when Swis greater than about 0.64, pressure in the inorganic matter increases and finally reaches to a steady level(Fig. 7). On the other hand, through the Swchange in the inorganic matter, the water imbibition into the inorganic matrix is

extremely active with an increase of about 0.44 pore volume (that of inorganic pore system) of water imbibed.

Fig. 7Dynamics in the inorganic matter including average Swand average pressure

Fig. 8Dynamics in the kerogen including average Swand average pressure

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WaterSaturation

Pressure,MPa

Dimensionless Time

Gas Pressure in the Inorganic Matter

Sw in the Inorganic Matter

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WaterSaturation

Pressure,MPa

Dimensionless Time

Pressure in the Kerogen

Sw in the Kerogen

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Fig. 9Gas recovery from shale matrix to surrounding fractures

The dynamics in the kerogen are shown in Fig. 8. Kerogen is gas-wetting and upstream for water flow. With Sw

approximately constant at 0.01 in the kerogen (Fig. 8), water cannot flow out from the kerogen and consequently only singlegas phase flows there. Therefore, pressure change in the kerogen is only caused by gas flow through the kerogen. At the early

production period, gas flows from the inorganic matter into the kerogen, and simultaneously gas also flows from the kerogen

into the fracture system. These two gas flow pathways have the opposite effect on average pressure change in the kerogen.

Initially they compensate each other and thus an approximately constant level of pressure at the early production period is

observed in Fig. 8. Since water continues to imbibe into the inorganic matter, in the inorganic matter water saturation

increases and gas relative permeability decreases. Therefore, at a later production period, gas flowing from the inorganic

matter to the kerogen gradually becomes weak but gas keeps flowing out from the kerogen to the fractures, and thus the

pressure decreases in the kerogen. Finally, a steady state in the kerogen is reached when the micro model is in equilibrium.

The gas recovery from the shale matrix into the surrounding fracture system is plotted inFig. 9.The ultimate gas recovery

is about 30%. In this case, there are 6 horizontal layers of matrix in the micro model. Here the second layer of matrix is taken

as an example, and the grid map is shown inFig. 11.Those yellow grids are the inorganic grids, and the blue crosses here are

kerogen with micropores and kerogen with nanopores, and the brown grids surrounding the matrix square are the fracture

grids. The kerogen grids are randomly distributed within this layer.Fig. 10 shows grid pressure and water saturation changesin this layer in a time sequence. InFig. 10(a), the pressure in the inorganic matter drops because it is predominated by the gas

release, yet the water saturation in the inorganics exhibits little change; in the kerogen the pressure stays high and S wthere is

at 0.01.Fig. 10(b) shows the dynamics afterFig. 10(a). The pressure in the inorganics mostly further decrease, and S win the

inorganic matter neighboring fractures increases; in the kerogen, the pressure decreases moderately and water saturation is

still 0.01. Fig. 10(c) is the final time step of the simulation. S w in the inorganic matter increases to a high level and the

pressure there also builds up and is higher than that in the kerogen.

Sensitivity Analysis

In this part, the effects of desorption, diffusion, TOC, initial Sw and capillary pressure curve in the inorganic matter are

analyzed. Those corresponding parameters are sensitized here and any other inputs for the simulation are the same as that in

the base case in the last section. To better compare with the base case, cumulative gas production in all the cases below is

normalized by the gas in place in the base case, namely normalized cumulative gas production.

Effect of Desorption

The effect of desorption is analyzed by changing the Langmuir desorption parameters in the kerogen (Table 3), with other

inputs for the simulation the same as the default. Here five cases with an increase of adsorption gas in the kerogen are

analyzed. The results for each case are plotted inFig. 12 andFig. 13.Note that in the plot the average Langmuir parameters

are shown. InFig. 12 andFig. 13,with an increase in the Langmuir desorption in the kerogen, the gas production increases

correspondingly. However, here there is not much significant increase. We consider that gas production is determined by the

Langmuir curves and the pressure drop in the kerogen (Fig. 13). InFig. 13, the pressure drops in the kerogen for the five

cases are almost the same. The average pressure in the kerogen is always greater than the Langmuir pressure in the kerogen

(10.342 MPa). Because the Langmuir pressure is the pressure corresponding to half of the Langmuir volume, in all of those

cases the desorbed gas in the kerogen is less than half of the Langmuir volume. Therefore, only small increases in gas

production can be expected after desorption is introduced.

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0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 3.5E+05 4.0E+05

GasRecovery,%

GasRecovery,%

Dimensionless Time

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(a) Early time

(b) Later time

(c) Final time

Fig. 10Pressure and water saturation in different time steps

Fig. 11Grid map for the matrix layer, blue crosses are the kerogen grids; yellow grids are the inorganic grids; brown grids are thefracture grids.

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Table 3Parameters for the desorption analysis (Case 4-Base Case)

Case NO.

Kerogen with micropores Kerogen with nanopores

Langmuirpressure, MPa

Langmuirvolume, m

3/Kg

Langmuirpressure, MPa

Langmuirvolume, m

3/Kg

Case 1 NA NA NA NA

Case 2 10.342 1.041510-2 10.342 1.170510

-2

Case 3 10.342 1.326610-2 10.342 1.482710

-2

Case 4 10.342 1.638710-2 10.342 1.794810

-2

Case 5 10.342 1.950910-2 10.342 2.106910

-2

Fig. 12Gas production for cases with different Langmuir parameters in the kerogen

Fig. 13

Average pressure in the kerogen for cases with different Langmuir parameters

Effect of Diffusion

Diffusion occurs in the kerogen in the micro model. Through changing the diffusion coefficient shown in Table 4, the

effect of diffusion is also analyzed with the other inputs for the simulation the same as the default. Here five cases with an

increase of the diffusion coefficient in the kerogen are analyzed. The results are plotted inFig. 14 andFig. 15.InFig. 14,the

normalized cumulative gas production in Case 1 is far lower than other cases (2 to 5), and the normalized cumulative gas

productions in Case 2 to 5 are all the same (30.0%). Since diffusion is deactivated in Case 1, gas production in Case 1 is only

through Darcy flow. As diffusion occurs only in the kerogen, the gap of cumulative production between Case 1 and other

cases implies the importance of kerogen to the gas production process. In addition to that, lower gas production in Case 1

shows the indispensable role of diffusion, besides Darcy flow, as a main production mechanism in the kerogen network. The

separation of Case 1 and other cases after the early production period in Fig. 14 also indicates that diffusion occurs following

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NormalizedCumulativeGasProduction,%


Dimensionless Time

Case 1-No Desorption

Case 2-VL = 1.09E-2 m/Kg, PL = 10.34 MPa




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Pressure,MPa

Pressure,MPa

Dimensionless Time

Case 1-No Desorption





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Darcy flow. Further, with diffusion considered in Case 2 to 5, the ultimate cumulative gas production is almost the same.

This implies that different diffusion coefficients can actually accelerate the gas production process, but do not change the

ultimate production. Fig. 15 shows the average pressure in the kerogen. In Case 1, pressure changes little in the kerogen

because diffusion is not considered. In Cases 2 to 5, diffusion is considered and it is clearly helpful in accelerating the

pressure depletion in the kerogen.

Table 4Parameters for the diffusion analysis (Case 4-Base Case)

Case NO. Diffusion Coefficientin Kerogen with micropores, m2/s Diffusion Coefficientin Kerogen with nanopores, m

2/s

Case 1 NA NA

Case 2 8.2110-7 2.0110

-8

Case 3 8.2110-6 2.0110

-7

Case 4 8.2110-5 2.0110

-6

Case 5 8.2110-4 2.0110

-5

Fig. 14Gas production in the kerogen for cases with different diffusion coefficient

Fig. 15Average pressure in the kerogen for cases with different diffusion coefficient

Effect of TOC

TOC (wt %) is a necessary parameter to the discretized the micro model because it controls the number of kerogen grids

(Yan et al. 2013b; Yan et al. 2013a). Here four TOC values are compared, 3.0 wt%, 6.0 wt%, 9.0 wt% (base case), 12.0 wt%.

Therefore, four mesh maps are generated with different numbers of kerogen grids and input into the simulator. The results are

0.0

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

NormalizedCumulativeGas

Production,%

NormalizedCumulativeGas

Production,%

Dimensionless Time

Case 1-No DiffusionCase 2-D_micro = 8.21E-7 m/s, D_nano = 2.01E-8 m/s

Case 3-D_micro = 8.21E-6 m/s, D_nano = 2.01E-7 m/sCase 4-D_micro = 8.21E-5 m/s, D_nano = 2.01E-6 m/s

Case 5-D_micro = 8.21E-4 m/s, D_nano = 2.01E-5 m/s

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

Pressure,MPa

Pressure,MPa

Dimensionless Time

Case 1- No Diffusion





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plotted inFig. 16.The figure shows that the higher the TOC, the greater the ultimate gas cumulative production. TOC is the

weight percentage of organic carbon (kerogen) in shale matrix. In the kerogen in the micro model, desorption occurs and

there is also considerable free gas. Therefore, higher TOC content means more kerogen in the shale matrix and thus more gas

in place provided for gas production (Yan et al. 2013a).Fig. 16 clearly shows that the higher the TOC, the higher the ultimate

gas cumulative production. In addition, the slopes of gas cumulative production curves are actually determined by the

production rate. Fig. 16 shows that the higher the TOC value, the larger the slope of the curve of the gas cumulative

production during the main production period because of an increasing effect of diffusion.

Fig. 16Gas production for cases with TOC value in the shale matrix

Fig. 17Gas production for cases with different initial Swin the inorganic matter

Effect of Initial Water Saturation in the Inorganic Matter

In the micro model, the inorganic matter is water wet, and gas in this pore system is easily blocked by water, shown as Krg

imbibition curve inFig. 6.Therefore, initial water saturation (Sw) may influence the gas production and water imbibition in

the inorganic matter. Here five initial Sw values in the inorganic matter are sensitized, 0.21 (slightly higher than the

irreducible water saturation 0.20), 0.3 (base case), 0.4, 0.5, and 0.6. The results are plotted in Fig. 17 andFig. 18.Higher

initial Swhere means lower gas saturation in the inorganic matter. Therefore, with the same initial pressure and temperature,

cases with higher initial water saturation should have moderately lower gas in place even though porosity in the inorganic

matter is relatively low. Therefore, we observe that higher initial Swin the inorganic matter brings lower gas production in the

shale matrix (Fig. 17). InFig. 18,the average Swin the inorganic matter is plotted. Those cases with higher initial S whave

less water imbibition capacity and all of them finally reach a final saturation of about 0.73.

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06


Norm

alizedCumulativeGasProduction,%

Dimensionless Time

Case 1- TOC = 3.0 wt%




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Dimensionless Time

Case 1- Sw = 0.21Case 2- Sw = 0.30Case 3- Sw = 0.40Case 4- Sw = 0.50Case 5- Sw =0.60

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Fig. 18Average Swin the inorganic matter for cases with different initial Swin the inorganic matter

Effect of Capillary Pressure Curve in the Inorganic MatterTo better investigate the effect of capillary forces, as an important factor during spontaneous imbibition, we have

analyzed three different capillary pressure scenarios (Fig. 19). Case 1 represents a system with fairly even distribution of the

pore sizes and relatively small entry pressure, which serves as the low capillary pressure case here. Case 2 (the base case),

has higher capillary entry pressure but same pore size distribution. Case 3, on the other hand, has a slightly lower pore size

distribution factor (pore sizes are distributed more widely) with a higher entry pressure that results in higher capillary

pressure values (capillary pressures in the inorganic blocks for cases 1 to 3 are 6, 16 and 37 MPa respectively, at the initial Sw

of 0.3). To better analyze the imbibition process and see the effect of inorganic network on gas production, capillary pressure

parameters in the organic grids will be considered constant and the changes will be imposed solely upon the inorganic grids.

Looking at the average water saturation in the inorganic grid blocks (Fig. 20), it is apparent that higher capillary pressures

accelerate the imbibition process. In addition to that, average water saturation at the late times is slightly higher in high

capillary cases due to an improved water influx. On the other hand, when we look at the gas production graph (Fig. 21), we

see capillary pressure (in the inorganic network) does not have considerable effect on ultimate gas production. This can be

interpreted as the important effect of kerogen grid blocks and different production mechanisms there (i.e. diffusion) on gasproduction as it was also observed in the diffusion sensitivity analysis.

Fig. 19Three different capillary pressure curves for the inorganic matter

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

WaterSatu

ration

WaterSatu

ration

Dimensionless Time

Case 1- Sw = 0.21 Case 2- Sw = 0.30

Case 3- Sw = 0.40 Case 4- Sw = 0.50

Case 5- Sw = 0.60

0

1000

2000

3000

4000

5000

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0.0 0.2 0.4 0.6 0.8 1.0

Pc,psi

Pc,MPa

Water Saturation

Case 1 - = 1.5; Entry Pressure: 1.5 MPa



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Fig. 20Average Swin the inorganic matter for cases with different capillary pressure in the inorganic matter

Fig. 21Gas production for cases with different capillary pressure in the inorganic matter

Conclusions

A Micro-Scale Model considering multiple pore systems, different mechanisms and mixed wettability has beenestablished. This model allows the interpretation of different complex flow interactions in shale.

The dynamics in the Micro-Scale Model are complex, and might be controlled by multiple factors at the same time.

The capacity of water imbibition into the inorganic matter is considerable. Under high water saturation in theinorganic matter, gas is trapped there, and further water imbibition makes pressure in the inorganic matter increase.

Desorption can increase the gas in place in shale but its effect on gas production rates is not significant because ofthe limited pressure drop in the kerogen.

Diffusion, as a gas-phase transport mechanism in the kerogen, plays an important role in total gas production byfacilitating the gas flow from the hydrocarbon-rich organic matter to the fracture network.

TOC content in the kerogen can increase the gas production with a combined effect of diffusion, desorption and freegas storage.

Higher capillary pressure in the inorganic matter accelerates the water imbibition process but has little influence ongas production.

0.0

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

WaterSatu

ration

WaterSatu

ration

Dimensionless Time




0.0

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1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06



Dimensionless Time

Case 1 - = 1.5; Entry Pressure: 1.5 MPaCase 2 - = 1.5; Entry Pressure: 4.0 Mpa

Case 3 - = 1.15; Entry Pressure: 6.0 Mpa

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Nomenclature

gC = gas compressibility, 1/Pa;

D = diffusion coefficient, m2/second;g = the gravitational acceleration vector, m2/s;

K = media permeability, m2;

rgK = gas relative permeability, dimensionless;

rnwdK = non-wetting phase drainage relative permeability, dimensionless;

rnwiK = non-wetting phase imbibition relative permeability, dimensionless;

rwK = water relative permeability, or wetting phase drainage/imbibition relative permeability, dimensionless;

nwdn = non-wetting phase drainage exponent, dimensionless;

nw in = non-wetting phase imbibition exponent, dimensionless;

wn = wetting phase drainage/imbibition exponent, dimensionless;

P = grid pressure, Pa;

cP = capillary pressure, Pa;

eP = capillary entry pressure, Pa;

gP = gas phase pressure, Pa;

wP = water phase pressure, Pa;

aq = the mass of gas adsorbed on unit volume of media, kg/m3;

eS = effective wetting phase saturation, fraction;

gS = gas saturation, fraction;

nwcS = non-wetting phase critical saturation, fraction;

nwtS = non-wetting phase trapped saturation, fraction;

wS = water saturation, or wetting phase saturation, fraction;

wiS = initial wetting phase saturation, fraction;

wcnwS = critical wetting phase saturation with respect to the non-wetting phase, fraction;

wcwS = critical wetting phase saturation with respect to the wetting phase, fraction;

wrS = wetting phase residual saturation, fraction;

t = time, seconds;

TOC = weight percentage of Total Organic Carbon, wt%z = distance in the gravitational direction, m;

g = gas density at reservoir conditions, kg/m3;

w = water density at reservoir conditions, kg/m3;

g = gas viscosity, Pas;

w = water viscosity, Pas;

= the porosity of the porous media, fraction;

= pore size distribution index, fraction;

Acknowledgements

The authors wish to thank The Crisman Institute at Texas A&M University for funding this project.

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