Modeling fracturing-fluid flowback behavior in hydraulically fractured shale gas under chemical potential dominated conditions

Accepted Manuscript Modeling fracturing-fluid flowback behavior in hydraulically fractured shale gas under chemical potential dominated conditions Fei Wang, Ziqing Pan, Shicheng Zhang PII:

S0883-2927(16)30154-8

DOI:

10.1016/j.apgeochem.2016.10.008

Reference:

AG 3729

To appear in:

Applied Geochemistry

Received Date: 21 July 2016 Revised Date:

26 September 2016

Accepted Date: 9 October 2016

Please cite this article as: Wang, F., Pan, Z., Zhang, S., Modeling fracturing-fluid flowback behavior in hydraulically fractured shale gas under chemical potential dominated conditions, Applied Geochemistry (2016), doi: 10.1016/j.apgeochem.2016.10.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Modeling Fracturing-fluid Flowback Behavior in Hydraulically Fractured Shale Gas under Chemical Potential Dominated Conditions Fei Wang*, Ziqing Pan, Shicheng Zhang

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Institute of Petroleum Engineering, China University of Petroleum, Beijing *Corresponding author: Fei Wang, Institute of Petroleum Engineering, China University of Petroleum, No. 18, Fu Xue Road, Changping District, Beijing 102200. Phone number: (86)15201682026. Email address: [email protected]

1. Introduction

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Abstract: Shale with high clay content has caused instability from hydration during the hydraulic fracturing process. Macro-level migration phenomenon of water molecules is induced by the chemical potential difference between low-salinity fracturing fluid and high-salinity formation brine. This study aims to establish the equation for the chemical potential difference between fracturing fluid and formation brine by theoretical deduction in order to investigate the effect of the aforementioned phenomenon on fracturing flowback. Accordingly, a mathematical model was established for the gas–water two-phase flow which driven by the chemical potential difference. Viscous force, capillarity and chemiosmosis were considered as the driving forces. A numerical simulation of fracturing fluid flowback with or without considering of the effect of chemiosmosis was performed. A simulation analysis of the water saturation and salinity profiles was also conducted. Results show that capillarity and chemiosmosis hinder fracturing fluid flowback in different degrees. As the condition worsens, they inhibit more than 80% of water to flow back out of the formation, forming a permanent water lock. This study contributes to improvement of the theory on shale gas–water two-phase flow, establishment of a flowback model that suitable for shale gas wells, and accurate evaluation of the fracturing treatment. Keywords: shale; hydration; chemical potential; flowback; chemiosmosis

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Shale gas has received much attention as an important unconventional natural gas resource. The United States and Canada have commercially exploited a number of basins. Massive slickwater fracturing is one of the key technologies for realizing the fracturing stimulation in shale gas reservoirs. A large liquid measurement and displacement mode must be adopted to realize the large volume of stimulation and to meet the required sand-carrying capacity (Vera and Ehlig-Economides, 2014). Studies on fracturing stimulation in shale gas reservoirs in China and other countries show that fracturing fluid flowback rate is generally low (Chekani et al., 2010; Penny et al., 2006). In the United States, fracturing fluid flowback rate is within the range of 20%–40%. The flowback rate in a portion of Fuling shale gas wells in China is even lower, reaching only 5%–10% (Zhong, 2011). Previous studies had proven that this phenomenon is attributed to capillary imbibition or natural crack closure (Cheng, 2012; Ehlig-Economides et al., 2011; Ehlig-Economides et al., 2012; Fan et al., 2010). Shale is composed of fine-grained sediments with strong heterogeneity. Shale mainly contains kerogen, clay, quartz, feldspar and pyrite. A shale reservoir has a relatively high clay content reaching up to 80% when compared with conventional reservoirs (Bohacs et al., 2013). In the formation process, shale with high clay content acts as a semipermeable membrane, causing osmotic water molecules permeate the membrane and migrate from the low-salinity side of the semipermeable membrane to the high-salinity side (Lomba et al, 2000; Rahman et al, 2005; Fakcharoenphol et al., 2014; Wang and Rahman, 2015). A shale matrix contains a certain amount of formation water. The original

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formation water has extremely high salinity as a result of compaction and water drainage during the tectonic process, and water consumption in hydrogen generation during the shale gas generation process (Fang et al., 2014). Haluszczak et al. (2013) reported that brine salinity of the shale reservoir is high, reaching up to 280,000 ppm. Generally, the salinity of slickwater fracturing fluid is approximately 1,000 ppm. In a hydraulic fracturing process, the significant salinity difference between injected water and formation water inevitably results in a considerable chemical potential difference, which driving the fracturing fluid to migrate from the hydraulic fracture to the shale matrix. Fracturing flowback is generally regarded as an immiscible displacement process. Some researchers have established single-porosity and dual-porosity gas–water two-phase flow models, simulated numerically fracturing fluid flowback and analyzed fracture parameters (Almulhim et al., 2014; Clarkson and Kovacs, 2013; Ezulike et al., 2013; Ilk et al., 2010; Lee and Karpyn, 2012; Xu et al., 2015). Assumptions of the conditions in flowback models are classified into two types: one type is water flowing into the fracture, while another type is water flowing into the matrix and fracture simultaneously. Gas–water relative permeability, formation stress sensitivity, capillary force, gravity and other control factors are considered in a sensitivity analysis. However, previous studies on the driving forces of water migration only focused at the physical level and disregarded the chemical osmosis process. In present study, the concept of chemical potential difference is introduced in the mathematical model to show the comprehensive effects of conventional viscous force, capillary force and chemiosmotic force during fracturing fluid flowback. This study aims to provide a better understanding of the mechanism of migration and retention of slickwater fracturing fluid in shale gas reservoirs and the mechanism of shale gas recovery.

2. Chemical potential difference

2.1 Derivation of chemical potential difference for different solutions For a multicomponent solution system, the differential formula for the chemical potential of component B can be

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expressed as (Han et al., 2009)

dµ B = − S B ,m dT + VB ,m dp

(2.1)

where µ B refers to the chemical potential of component B; SB,m and VB,m refer to the partial molar entropy and partial

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molar volume of component B, respectively; T and p refer to the temperature and pressure of the system, respectively. (2.1):

That is,

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Under an isothermal condition, the chemical potential of component B can be derived from the direct integration of Eq. p

p

∫ dµB = ∫ VB,m dp p

Θ

p

(2.2)

Θ

µ B (T , p, aq ) = µ B (T , p , aq ) + ∫ V B,mdp p

Θ

(2.3)

pΘ

where µ B (T , p, aq ) denotes the chemical potential of component B in the solution; aq denotes the solution system; p

(

Θ

)

denotes the standard pressure; µ B T , p Θ ,aq denotes the standard chemical potential of component B in the solution. If solution B is an ideal solution, the chemical potential of solution B can also be expressed as

µ B (T , p, aq ) = µ B (T , p, l ) + RT ln x B

(2.4)

ACCEPTED MANUSCRIPT where µ B (T , p, l ) represents the chemical potential of the pure solution; R represents the ideal gas constant, i.e. 8.314 J/(mol·K); xB represents the molar fraction of water molecule in solution B. On the basis of Eq. (2.4), the chemical potential difference of solution B between two different contents, x1and x2, under different pressures, p1 and p2, can be presented as

µB (T , p1 , x1 , aq ) − µB (T , p2 , x2 , aq ) = µB (T , p1 , l ) + RT ln x1 − [µB (T , p2 , l ) + RT ln x2 ] (2.5)

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Eq. (2.6) is derived by combining Eq. (2.5) and Eq. (2.3):

µ B (T , p1 , x1 , aq ) − µ B (T , p2 , x2 , aq ) =  µ B (T , p Θ , l ) + ∫ VB dp  −  µ B (T , p Θ , l ) + ∫ VB dp  + RT ln p1



p

Θ

p2

 

Then,

µB (T , p1 , x1 , aq ) − µB (T , p2 , x2 , aq ) = ∫ VB dp + RT ln

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p1

p2

pΘ

x1 x2



x1 (2.6) x2

(2.7)

different solutions can be written as follows:

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If the partial molar volume fraction does not change with pressure, the chemical potential difference between

µB (T , p1 , x1 , aq ) − µB (T , p2 , x2 , aq ) = VB ( p1 − p2 ) + RT ln

x1 x2

(2.8)

2.2 Chemical potential difference between fracturing fluid and formation water

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Approximately 10,000 m3 fracturing fluid is pumped into the formation during a massive hydraulic fracturing construction. However, the salinity of original water in the shale reservoir is extremely high, resulting in a chemical potential difference between high-salinity original water and low-salinity fracturing fluid. If the fracturing fluid enters the shale matrix through hydraulic fracture and original water exists in the matrix, the chemical potential difference between original water and fracturing fluid is expressed by

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µ wf − µ wm = Vw ( pwf − pwm ) + RT ln

xf xm

(2.9)

where µw and µw refer to the chemical potential of fracturing fluid and formation water in the matrix, respectively; f

m

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Vw refers to the partial molar volume of water; pwf and pwm refer to the pore pressures in the fracture and the matrix, respectively; x f and xm refer to the molar fraction of water molecule in the fracturing fluid and the formation water, respectively. The molar fraction of water molecule in the salt solution can be calculated with mineral salts and their concentrations. A comparison of the chemical potential difference and the pressure difference shows that they are both driving forces of water migration and ∆µ/ V has a dimensional pressure. Therefore, Eq. (2.9) can be expressed as

µ wf − µ wm Vw

= pwf − pwm +

RT x f ln Vw xm

(2.10)

As shown in Eq. (2.10), the chemical potential of the solution is not only related to the components of solution and the contents of substances but also related to pressure. When the salinity difference between formation water and injected water is disregarded, the driving force is the pressure difference, p f − pm , that is, the conventional viscous

ACCEPTED MANUSCRIPT force equation. By contrast, if the difference between salinities of both types of water is considered, the driving force is the right side of Eq. (2.10). Amongst all the terms on this side,

RT x f refers to the chemiosmotic force caused by ln Vw xm

the difference in the molar fraction of water, that is, the force that drives water to flow from the low-salinity side to the high-salinity side. The pores of shale are extremely wide in scale and distributed unevenly in the shale reservoir. Thus, inorganic clay

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on the surface shows a non-ideal semipermeable membrane and also allows ions to pass through by diffusion. Generally, membrane efficiency, λ , is adopted to indicate the selective capacity of a semipermeable membrane. Neuzil and Provost (2009) presented experimental data indicating that the efficiency of semipermeable membrane of shale is less than 5%. Therefore, the force driving the fracturing fluid from fracture to matrix can be expressed as

Vw

= pwf − pwm + λ

3.1 Assumptions and physical model

(2.11)

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3 Flowback mathematical model and solution

RT x f ln Vw xm

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µ wf − µ wm

This study adopts the following assumptions and considerations: 1) The shale reservoir is composed of a matrix and hydraulic fractures; 2) The matrix is considered as a homogeneous system with simple permeability anisotropy; 3) The hydraulic fracture is a symmetric two-wing fracture with height equals to thickness of the reservoir; 4) Isothermal percolation is assumed with the effect of gravity disregarded; 5) The effect of stress sensitivity on permeability is considered; 6) The effect of capillary force is considered; 7) The effect of chemiosmosis is considered; 8)The effect of

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desorption gas is considered; 9) During pumping of the fracturing fluid, water enters the matrix through the hydraulic fracture, while during the fracturing flowback process, the gas–water enters a horizontal wellbore through the hydraulic fracture.

According to these assumptions and considerations, the shale reservoir can be simplified into a combination of two independent systems, namely, hydraulic fracture and matrix. Flowrate, pressure and salinity in the matrix–fracture

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interface are used to continuously couple the matrix and the fracture. For a horizontal well with three transverse fractures, cell partition of the matrix and the fracture is shown in Fig. 1, where i, j and k indicate three directions of the

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shale reservoir. The size of each matrix cell is represented by ∆xi, ∆yj and ∆zk. With the flow of fracture cell in the direction of the fracture width is ignored, i and k are uniformly used to present the direction of the 2D fracture cell block.

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Horizontal well

∆yj

Matrix/fracture interface

∆zk

z

x

Fractures

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y

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∆xi

Fig. 1.Diagram of matrix and fracture cell.

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3.2 Mathematical model Matrix water mass transport:

 k m krw ρ w  ∂ m m ∇pwm  − qwmf φ S w ρ w = ∇ ∂t  ηw 

(

)

(3.1)

φ m denotes the matrix porosity (non-dimensional); S wm denotes the water saturation in the matrix (non-dimensional); ρ w denotes the density of water (g/cm3); k m denotes the permeability of the matrix (µm2); krw m denotes the relative permeability of water (non-dimensional); η w denotes the viscosity of water (mPa·s); pw denotes

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where

mf

the water-phase pressure in the matrix cell block (10-1 MPa); qw denotes the water-phase crossflow rate between matrix cell and fracture cell (cm3/s), and is defined as

ρ w k m k rw  µ wm − µ wf  η w  Vw

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qwmf = α

 RT xm  ρ k m k rw  m  = α w pw − pwf + λ ln Vw x f  η w  

(3.2)

where pw represents the water-phase pressure in the fracture cell block (10-1 MPa); λ represents the membrane f

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efficiency (non-dimensional); Vw represents the partial molar volume of water (10 m3/kmol); R represents the ideal gas constant, i.e. 8.314 J/(mol·K); T represents the temperature (K); xm represents the molar fraction of water in the matrix cell block (non-dimensional); xf represents the molar fraction of water in the fracture cell block (non-dimensional);

α

represents the shape factor between fracture cell and matrix cell (cm-2), and is equal to

α=

2 ∆ y j ( ∆ y j + w)

where ∆y j represents the size of the cell in y direction (cm); Matrix gas mass transport:

w represents the fracture width (cm).

(3.3)

ACCEPTED MANUSCRIPT  k m krg ρ g  ∂ m m φ S g ρ g + mg = ∇ ∇p gm  − q gmf  ∂t  ηg 

(

)

(3.4)

where S gm refers to the gas saturation in the matrix (non-dimensional); ρ g refers to the density of gas (g/cm3); k rg refers to the relative permeability to gas (non-dimensional); η g refers to the viscosity of gas (mPa·s); p gm refers to the

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gas-phase pressure in the matrix cell block (10-1 MPa); mg refers to the mass of adsorbed gas in formation volume (g/cm3) and is described as (Silin and Kneafsey, 2012)

m g = ρ R ρ gscVE S k

(3.5)

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where ρ R is the source rock density (g/cm3); ρ gsc is the gas density at standard condition (g/cm3); S k is the volume

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proportion of source rock; VE is the standard gas volume adsorbed per unit rock mass (cm3/g). If the adsorbed gas terms can be represented by Langmuir (1916) isotherm, the dependency of adsorbed gas volume on pressure at constant temperature is given below,

VE = VL

p gm

p gm + p L

(3.6)

Where V L is the Langmuir’s volume in cm3/g; p L is the Langmuir’s pressure, the pressure at which 50% of the gas is

(cm3/s), and is expressed as

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adsorbed (10-1 MPa). In Eq. (3.4), q gmf refers to the gas-phase crossflow rate between matrix cell and fracture cell

q

mf g

ρ g k m k rg m ( =α p g − pgf ) ηg

(3.7)

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where p gf refers to the gas-phase pressure in the fracture cell block (10-1 MPa).

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Matrix salt mass transport:

 C m k m krw ρ w  ∂ m m m C φ S w ρ w = ∇ ∇pwm  ηw ∂t  

(

)

(3.8)

where C m refers to the salt concentration of fluid in the matrix (ppm). During the hydraulic fracturing process, permeability of formation near the wall surface of the fracture is expressed by an exponential function in a simple form varying with pressure (Jurus et al., 2013)

k m / kom = 10mpnet = 10 m ( pcell − pi ) (3.9) m

where ko refers to the initial permeability of the matrix (µm2); pnet refers to the net pressure (10-1 MPa) and is equal

ACCEPTED MANUSCRIPT to the difference between cell pressure, pcell , and original reservoir pressure, pi ; m refers to the permeability change coefficient (1/bar). In consideration of gas–water two-phase flow, the following auxiliary equations should be added as supplements:

S wm + S gm = 1 (3.10)

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p gm − pwm = pcgw where Pcgw refers to the capillary force (10-1 MPa). Fracture water mass transport:

(

)

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 k f krw ρ w  ∂ f f φ S w ρ w = ∇ ∇pwf  + qwmf − qwfW ∂t  ηw 

(3.11)

(3.12)

where φ refers to the fracture porosity (non-dimensional); S w refers to the water saturation in the fracture f

f

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f

fW

(non-dimensional); k refers to the fracture permeability (µm2); q w refers to the water crossflow rate between fracture cell and wellbore (cm3/s). Fracture gas mass transport:

 k f k rg ρ g ∂ f f φ S g ρ g = ∇ ∇pgf ∂t  ηg

)

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(

 mf  + qg − q gfW  

(3.13)

where S gf refers to the gas saturation in the fracture (non-dimensional); q gfW refers to the gas-phase crossflow rate between fracture cell and wellbore (cm3/s).

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Fracture salt mass transport:

 C f k f krw f  inj qwfW ∂ f f f C φ Sw = ∇ ∇pw  − C ∂t η ρw w  

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(

)

(3.14)

where C f refers to the salt concentration of fluid in the fracture (ppm); C inj refers to the salt concentration of injected fluid (ppm).

In consideration of gas–water two-phase flow, the constraint equation with saturation is added as a supplement:

S wf + S gf = 1 (3.15)

Moreover, owing to the relatively high permeability of the fracture, the capillary force in the fracture is approximated to 0, and the phase pressure in the fracture is expressed as

pwf = p gf (3.16) Initial condition of matrix:

ACCEPTED MANUSCRIPT p gm (x, y, z , t ) S wm ( x, y, z, t ) C m ( x, y , z , t )

t =0

= pi

(3.17)

= S wm0

(3.18)

= C0m

(3.19)

t =0

m

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m

t =0

where S w 0 is the initial water saturation in the matrix; C0 is the initial salt concentration of fluid in the matrix (ppm). Initial condition of fracture:

S wf (x, z , t )

t =0

t =0

= S wf 0

f

t =0

(3.20)

(3.21)

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C f ( x, z , t )

= pi

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p gf (x, z , t )

= C0f

(3.22)

f

where S w0 is the initial water saturation in the fracture; C0 is the initial salt concentration of fluid in the fracture (ppm). Outer boundary condition:

∂p Γ=0 ∂n

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(3.23)

where Γ is the outer boundary of a shale reservoir; n is the normal direction of the outer boundary. Inner boundary condition:

fW

fW

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It refers to the crossflow rate between wellbore and hydraulic fracture, i.e. q w in Eq. (3.12) and q g in Eq. (3.13). fW

fW

as

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Given that the fluid flows radially into a horizontal wellbore from the hydraulic fracture, q w and q g are expressed

q

fW w

2πρ w k f k rw = ( pwf − pwf ) ∆xi ∆zkη w ln(re / rw )

qgfW =

2πρ g k f krg ∆xi ∆z kη g ln(re / rw )

(3.24)

( pgf − pwf ) (3.25)

where ∆xi and ∆zk denote the size of the cell in x and z directions (cm); pwf denotes the flowing pressure in the bottom hole (10-1 MPa); re denotes the equivalent radius of the cell block where wellbore is located (cm); rw denotes the radius of the wellbore (cm).

ACCEPTED MANUSCRIPT 3.3 Model solution Fully implicit method is used to solve the flowback mathematical model after difference discretization. Fig. 2 shows a simplified flow chart of our programming code. The algorithm is composed of six parts: Discretize the equation system according to fully implicit method. Initialize the pressure, water saturation and salinity in matrix as well as the hydraulic fracture. Compute phase mobility and transmissibility at each timestep.

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Solve the discretized equation system according to initial and boundary conditions to update variables. If the equation residuals and the primary variables converge but set time does not elapse, it moves to compute phase mobility and transmissibility at next timestep. Otherwise, it cycles back to compute phase mobility and transmissibility until it converges at current timestep.

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If set time elapses, the program ends and output the results of each timestep.

Fig. 2. Simulator flow chart.

4 Flowback simulation

4.1 Description of simulation model The basic parameters of the simulation model for the shale gas reservoir are as follows: thickness, length and width of the shale reservoir are 42 m, 1,500 m and 600 m, respectively; length of the horizontal wellbore is 1,000 m; original reservoir pressure is 26 MPa; temperature in the formation is 324 K; original water saturation is 0.2; matrix porosity is 8%; matrix permeability is 300 nD; matrix compressibility is 4.4×10−4 MPa−1; half-length of the hydraulic fracture is 120 m; conductivity of the hydraulic fracture is 6.5 D·cm; number of fracture segments are 20, with 4 clusters in each segment; viscosity of gas is 0.022 mPa·s; viscosity of the injected slickwater is 1 mPa·s; original

ACCEPTED MANUSCRIPT salinity of slickwater is 1,000 ppm and formation water salinity is 280,000 ppm; efficiency of the clay membrane is 0.05; and partial molar volume is 18.02×10−6 m3/mol. In this model, the relative permeability to gas–water and the capillary force curve of shale are set according to the core experimental data in a previous study, as shown in Figs. 3 and 4 (Dacy, 2010). The pumping of fracturing fluid is simulated as a water-injection process. The injection volume is controlled by adjusting the permeability change coefficient. The stress-sensitivity curve of permeability after the adjustment is shown in Fig. 5. The pertinent simulation model for the shale gas well.

4.2 Simulation results and analysis

Fig. 4. Capillary force.

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Fig. 3. Gas-water relative permeability.

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program developed for simulation analysis is conducted based on the aforementioned fracturing flowback simulation

Fig. 5. Stress-dependent permeability.

Initially, slickwater is continuously pumped for 30 min into the fractures through perforation tunnels in the horizontal wellbore. The bottom-hole flowing pressure during the injection is set to 55 MPa. In the pumping process, water enters the matrix through the leakoff mechanism from the fracture. Subsequently, water is allowed to be imbibed

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into the matrix spontaneously. After pumping, the well is immediately opened to cause a fracturing fluid flowback. The flowback simulation production length of the model is set to 7 days and the bottom-hole flowing pressure is 5 MPa. Fig. 6 shows the water saturation profile at different distances away from the fracture surface along the y axis. It reflects that change in water saturation in the region near the fracture monitored from the beginning of the flowback to

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the end. The simulation result shows that water fills the fracture at the end of pumping. As a result of leakoff and spontaneous imbibition, the region 20 cm away from the fracture is invaded by water. During the flowback process, water saturation in the region near the fracture (within 13 cm) has continuously decreased. Furthermore, water

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saturation in the region distant (13 m away) from the fracture has gradually increased. These results indicate that local pressure drop in water-phase in the matrix is less than the chemiosmotic force. Slickwater will migrate to the deep portion of shale formation even during the flowback process. As shown in Fig. 6, water front migrates by 40 cm, from 20 cm at the beginning of flowback (0 h) to 60 cm by the end of flowback (168 h). Fig. 7 shows the salinity profile at different distances away from the fracture surface along the y axis. The simulation result shows that high-concentration salt ions in the matrix have continuously migrated to the fracture by diffusion and flowed back to the ground surface along with water during the flowback process. The salt concentration in the fracture surface increases by 8,410 ppm from 1,000 ppm at the beginning of flowback (0 h) to 9,410 ppm by the end of flowback (168 h). Water flowback rate and water load recovery in the fractured horizontal well are shown in Fig. 8. As shown in Fig. 8, the yield of water in this well has rapidly decreased. The initial peak of flowback rate is 1.15×105 m3/d and the yield of water after 24 h is almost zero. Seven days later, the accumulated load recovery is only 13%. Fig. 9 shows the comparison of water load recoveries from case 1 considering viscous and capillary forces, case 2 considering viscous

ACCEPTED MANUSCRIPT and chemiosmosis forces, and case 3 considering viscous force only. Without chemiosmosis, water load recovery is approaching 29%. Meanwhile, without capillarity, water load recovery is 19.6%. Without chemiosmosis and capillarity, water load recovery after seven days is as much as 41%. Flowback with chemiosmosis considered is significantly different from that when chemiosmosis is disregarded. Therefore, the effect of chemiosmosis should be considered in

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fracturing flowback simulations and fracturing treatment evaluation.

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Fig. 6. Water-saturation distribution along the length of y axis for a flowback period of 7 days.

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Fig. 7. Salinity distribution along the length of y axis for a flowback period of 7 days.

Fig. 8. Water flowback rate and water load recovery.

Fig. 9. Comparison of water load recoveries from cases with different driving forces.

5 Conclusions

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(1) In this study, a mathematical model for the gas–water two-phase flow driven by chemical potential is established based on the semipermeable membrane properties of shale and high salinity of formation water. A numerical simulation of fracturing fluid flowback in a shale gas well is conducted based on the coupled matrix–fracture model. (2) The simulation result on water saturation profile of the formation shows that a high-water-saturation area near the wall surface of the fracture is formed through leakoff and imbibition during the process of pumping of fracturing fluid. During the flowback process, water still migrates to the deep portion of the reservoir, and this migration is driven by the chemical potential difference. After seven days of fracturing flowback, the water migration distance can be as large as 40 cm. (3) The simulation result on salinity profile of the formation shows that salt ions in the matrix continuously migrate to the fracture during the flowback process. After seven days of fracturing flowback, salt concentration in the fracture surface increases by 8,410 ppm. (4) Water load recovery in the fractured shale gas well is mainly affected by viscous pressure difference, capillary imbibition and chemiosmosis. Capillarity and chemiosmosis both hinder fracturing fluid flowback, while the inhibition effect of chemiosmosis is more obvious than that of capillarity. This observation may reflect that the difference between shale and conventional reservoirs can be attributed to high content of clay and high salinity of formation water. Flowback with chemiosmosis considered is significantly different from that with chemiosmosis disregarded. Therefore, chemiosmosis is a key factor that should be fully considered when evaluating the fracturing treatment on shale gas well. (5) The study on the mechanism of fluid flow at the chemical level and the establishment of a dynamic evaluation model for fracturing fluid flowback in shale gas reservoirs with chemical factors considered have important theoretical and realistic significance in improvement of the theory on shale gas–water two-phase flow, the numerical simulation and effect prediction of fracturing fluid flowback, and the scientific design of hydraulic fracturing.

Acknowledgments This work was supported by the National Natural Science Foundation [No.51504266], the Beijing Natural Science Foundation [No.3154038] and the Science Foundation of China University of Petroleum, Beijing [No.2462015YQ0212].

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23. Silin, D., Kneafsey, T.J., 2012. Shale gas: Nanometer-scale observations and well modeling. J. Can. Petrol. Technol. 51(6), 464– 475. http://dx.doi.org/10.2118/149489-PA. 24. Vera, F., Ehlig-Economides, C.A., 2014. Describing shale well performance using transient well analysis. The Way Ahead 10(2), 24–28. 25. Wang, J.J., Raham, S.S., 2015. An investigation of fluid leak-off due to osmotic and capillary effects and its impact on micro-fracture generation during hydraulic fracturing stimulation of gas shale. Paper SPE-174392-MS presented at the EUROPEC, 1–4 June 2015, Madrid, Spain. http:// dx.doi.org/10.2118/174392-MS. 26. Xu, Y., Fu, Y., Ezulike, D.O., Dehghanpour, H., Virues, C.J., 2015. Modeling two-phase flowback data using an open tank model. Paper 175923 presented at the SPE/CSUR Unconventional Resources Conference, 20–22 October, Calgary, Alberta, Canada. http://dx.doi.org/10.2118/175923-MS. 27. Zhong, H., 2011. Flow of gas and water in hydraulically fractured shale gas reservoirs. Paper presented at the EPA HF Workshop, 28–29 March, Arlington, Virginia, USA.

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Equation for gas-water two-phase flow driven by chemical potential was generated High-water-saturation area near fracture wall is formed by leakoff and imbibition Salt ions in matrix continuously migrate to fracture during flowback process Chemiosmosis is a key factor to evaluate fracturing treatment on shale gas well

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