Impact of chemical osmosis on water leakoff and flowback behavior from hydraulically fractured gas shale

Journal of Petroleum Science and Engineering (xxxx) xxxx–xxxx

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Impact of chemical osmosis on water leakoff and flowback behavior from hydraulically fractured gas shale ⁎

Fei Wang , Ziqing Pan, Shicheng Zhang China University of Petroleum, Beijing, China

A R T I C L E I N F O

A BS T RAC T

Keywords: Shale Chemical osmosis Fracturing-fluid Leakoff Flowback

In this paper, the development of a comprehensive multi-mechanistic multi-porosity water/gas/salt flow model to investigate the leakoff and flowback behavior of the fracturing fluid from hydraulically fractured shale gas wells is presented. The multi-mechanistic model takes into account water transport induced by hydraulic pressure driven convection, osmosis pressure driven convection and capillary imbibition, gas transport induced by both hydraulic pressure driven convection and desorption, and salt transport induced by advection and concentration driven diffusion. In the multi-porosity model, hydraulic fractures are considered as a interconnected continuum embedded in shale matrix, where organic shale is interspersed within vast inorganic shale. The organic matrix is thus considered disconnected in the entire reservoir. The water saturation profiles for chemical osmosis-induced, capillary pressure-induced and hydraulic pressure-induced cases are compared, revealing a region of saturation that effectively is immobile even though irreducible saturation has not been reached. In sensitivity analyses, cases with different hydraulic pressure, injected fluid salinity and salt diffusion coefficient are considered.The results indicate that chemical osmosis intensifies water leakoff and hinders water flowback. Further, chemical osmosis is a key mechanism for water retention after the treatment of hydraulic fracturing and should not be ignored especially in flowback data analysis of hydraulically fractured shale gas wells.

1. Introduction As an important unconvectional natural gas resource, shale has received much attention. The United States and Canada have successfully commercially exploited many shale basins (Ahmed, 2015). Slickwater fracturing is one of the key technologies for realizing fracturing stimulation in shale gas reservoirs (Thompson et al., 2010). Comparing with crosslinked water-based fracturing-fluids, the slickwater fracturing-fluid has several advantages, including low cost (because the water ratio can be as high as 99.5%), less formation damage and ease of creating complex fracture networks (Schein, 2004; Cipolla et al., 2009; Cheng, 2012). One of the concerns with slickwater is that most of the water pumped during the treatment is retained in the shale reservoir. In practice, it is common that only a small fraction of pumped water, typically 10–20%, can be recovered during the process of flowback for cleanup of the loaded fluid. In many studies, this water retention phenomenon is attributed to two mechanisms: fracture closure and water leakoff. However, there is no proven explanation of which of the two mechanisms is predominant. Some researchers believe that water trapped in the fracture network

⁎

might be the major mechanism responsible for water retention. They consider that because of the low permeability of shale matrix, most of the pumped water will remain either in fractures as an immobile “propping” phase or in “non-communicating” fractures that were initiated by the treatment but become disconnected from the well after fracture closing (Fan et al., 2010; Ehlig-Economides and Economides, 2011; Sharma and Agrawal, 2013). Other researchers consider that water leaked into shale matrix might be the major mechanism responsible for water retention (Roychaudhuri et al., 2011; Dehghanpour et al., 2012, 2013; Makhanov et al., 2012; Lan et al., 2014). Besides the forced leakoff driven by pressure difference between hydraulic pressure and formation pore pressure, spontaneous imbibition driven by capillary pressure is a widely reported effect that induce extra water invasion. A vast amount of experimental and mathematical studies have been conducted to investigate the spontaneous imbibition of water into shale matrix. Several single-porosity or dual-porosity gas/ water flow models are established to simulate fracturing fluid flowback and analyze fracture parameters (Michel et al., 2012; Jurus et al., 2013; Ilk et al., 2010; Lee and Karpyn, 2012; Ezulike et al., 2013; Clarkson and Kovacs, 2013; Almulhim et al., 2014; Xu et al., 2015). In these

Corresponding author. E-mail address: [email protected] (F. Wang).

http://dx.doi.org/10.1016/j.petrol.2017.01.018 Received 20 July 2016; Received in revised form 29 December 2016; Accepted 5 January 2017 0920-4105/ © 2017 Elsevier B.V. All rights reserved.

Please cite this article as: Wang, F., Journal of Petroleum Science and Engineering (2017), http://dx.doi.org/10.1016/j.petrol.2017.01.018

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Qwf-m

Nomenclature

Bw Cf Cm C inj C0f C0m C fm

D1 D2 fr hf H lf L kf krw km krg mg pwf pwf pwm pgm pwm pgf pgm pcgw pL

qgfW qgmf qwfW qwmf QwW-f

Qwf-W

water-phase volume factor, non-dimensional salt concentration of fluid in the hydraulic fracture, ppm salt concentration of fluid in the matrix, ppm salt concentration of the injected fluid, ppm initial salt concentration of fluid in the hydraulic fracture, ppm initial salt concentration of fluid in the matrix, ppm salt concentration of fluid transferring between the hydraulic fracture and matrix, ppm diffusion coefficient of salt ions between the hydraulic fracture and matrix, cm2/s diffusion coefficient of salt ions within the matrix, cm2/s water load recovery of the well, % height of the hydraulic fracture, m height of the shale reservoir, m half-length of the hydraulic fracture, m length of the shale reservoir, m hydraulic fracture permeability, μm2 relative permeability of water, non-dimensional permeability of the matrix, μm2 relative permeability of gas, non-dimensional mass of adsorbed gas in formation volume, g/cm3 water-phase pressure in the hydraulic fracture, bar flowing pressure in the bottom hole, bar water-phase pressure in the matrix, bar gas-phase pressure in the matrix, bar water-phase pressure in the matrix, bar gas-phase pressure in the hydraulic fracture, bar gas-phase pressure in the matrix, bar capillary pressure in the matrix, bar Langmuir's pressure, the pressure at which 50% of the gas is adsorbed, bar gas-phase transfer rate between the fracture and wellbore, g/cm3 s gas-phase transfer rate between the fracture and matrix, g/cm3 s water-phase transfer rate between the fracture and wellbore, g/cm3 s water-phase transfer rate between the fracture and matrix, g/cm3 s accumulated injection volume of water from the wellbore to fracture, m3

Qwf-m

Vw VE VL wf W R Swf Sgf Swm Sgm Swm0 Swf0

Sk T xm xf

α δ ρw ρg ρR ρgsc ηw ηg ϕf ϕm Fsadv Fsdiff n Γ

accumulated leakoff volume of water from the fracture to matrix, m3 accumulated flowback volume of water from the fracture to wellbore, m3 accumulated flowback volume of water from the matrix to fracture, m3 partial molar volume of water, 10 m3/kmol standard gas volume adsorbed per unit rock mass, cm3/g Langmuir's volume, cm3/g width of the hydraulic fracture, cm width of the shale reservoir, m ideal gas constant, 0.008314 MPa m3 /(kmol K) water saturation in the hydraulic fracture, non-dimensional gas saturation in the hydraulic fracture, non-dimensional water saturation in the matrix, non-dimensional gas saturation in the matrix, non-dimensional initial water saturation in the matrix, non-dimensional initial water saturation in the hydraulic fracture, nondimensional volume proportion of source rock temperature, K molar fraction of water in the matrix, non-dimensional molar fraction of water in the hydraulic fracture, nondimensional shape factor between the hydraulic fracture and matrix, cm−2 shape factor between the wellbore and the hydraulic fracture, cm−2 density of water, g/cm3 density of gas, g/cm3 source rock density, g/cm3 gas density at standard condition, g/cm3 viscosity of water, mPa s viscosity of gas, mPa s hydraulic fracture porosity, non-dimensional matrix porosity, non-dimensional salt transfer terms between the hydraulic fracture and matrix by advection, 10−6 s−1 salt transfer terms between the hydraulic fracture and matrix by diffusion, 10−6 s−1 normal direction of the outer boundary outer boundary of a shale reservoir

salinity of slickwater is low, approximately 1000 ppm. Therefore, in a hydraulic fracturing treatment, the significant salinity difference between the injected slickwater and formation brine inevitably results in a considerable chemical potential difference, eventually causing the osmotic migration phenomenon of water molecules. Despite all previous studies, analyzing leakoff and flowback behaviors of the fracturing fluid driven by various mechanisms, especially chemical osmosis on gas/water/salt flow in shale remains largely unexplored. In this study, a comprehensive multi-mechanistic multiporosity water/gas/salt flow model is developed. Then, a numerical model is built to accurately simulate and predict water flow behavior in hydraulically fractured gas shale. Sensitivity analyses are performed to further investigate the chemical osmosis, capillarity and hydraulic pressure respectively on the water saturation distribution and migration front progression. The results would help to understand the impact of shale properties on the water leakoff and flowback as well as provide detailed quantitative information for the simulation and prediction of multiphase flow in hydraulically fractured gas shale.

models, gas/water relative permeability, formation stress sensitivity, capillary pressure, gravity and other physical factors are considered. Shale is composed of fine-grained sediments with strong heterogeneity; it mainly contains kerogen, clay, quartz, feldspar and pyrite. Compared with convectional reservoirs, a shale reservoir has a relatively high clay content, reaching up to 80% (Bohacs et al., 2013). High-clay shale formations could behave as a semi-permeable membrane, thus causing osmotic water molecules permeate the membrane and migrate, that is, water molecules migrate from the low-salinity side of the semi-permeable membrane to the high-salinity side (Lomba et al., 2000; Rahman et al., 2005; Al-Bazali et al., 2009; Fakcharoenphol et al., 2014; Wang and Raham, 2015). A shale matrix contains a certain amount of formation water. As a result of the water drainage during the tectonic compaction process (Bredehoeft et al., 1963) and the water consumption during the hydrogen generation process (Schimmelmann et al., 2001; Mastalerz and Schimmelmann, 2002), the original formation water has extremely high salinity (Fang et al., 2014). Haluszczak et al. (2012) showed that the brine salinity of the shale reservoir is high, reaching up to 280000 ppm. Generally, the

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2. Leakoff and flowback: flow mechanism model

2.2. Chemical osmosis-induced leakoff and flowback

2.1. Chemical osmosis

Several million gallons of water are required to pumped into the target formation in a multistage hydraulic fracturing treatment of horizontal wells. Once the low-salinity slickwater fracturing fluid and shale matrix, which contains high-salinity brine, are in contact during the treatment of hydraulic fracturing, a osmosis pressure is occurred. Based on Eq. (2.3), the osmosis pressure between the formation brine and slickwater can be expressed by

Chemical osmosis has been recognized as a means to induce water molecules flow in and out of a shale by adjusting the water activity of injected fluids (Ewy and Stankovich, 2000). This mechanism is initially developed in drilling fluid/shale interactions (Chenevert, 1970), because water flow in and out of shale formations plays a major role in the alteration of the physicochemical and mechanical properties of a shale thus leading to wellbore instability problems (Al-Bazali et al., 2009). By definition, the chemical potential ( μi ) of a component i is related to its water activity (ai ) by the equation:

μi = μiΘ + RT ln(ai )

Pπ =

(2.1)

a w, shale RT ln Vw a w, mud

(2.2)

where Pπ refers to osmotic pressure; Vw refers to the partial molar volume of water; a w, shale and a w, mud respectively refer to the water activity of shale formation brine and the drilling fluid. According to the definition of water activity, it is the ratio of fugacity of salt solution to fugacity of pure water (Yan, 2001). And the fugacity of the particular component under a certain temperature and pressure is directly proportional to its mole fraction (Chen et al., 2009). So Eq. (2.2) can be rearranged as

Pπ = −

fw, shale a w, shale x w, shale RT RT RT ln = ln = ln Vw a w, mud Vw fw, mud Vw x w, mud

(2.4)

where x f and xm respectively refer to the molar fraction of the water molecule in the slickwater and shale formation brine. In the situation of hydraulic fracturing, x f > xm , Pπ becomes a positive driving force, driving water molecules to flow into the shale matrix. Besides, there are three main driving forces, i.e. hydraulic pressure (Pf), pore pressure (Pp) and capillary pressure (Pc), which drive water to flow in and out of a fractured gas shale. Fig. 1 depicts the forced situation of leakoff water from a hydraulic fracture into the shale matrix during the processes of fracturing injection and flowback. In the process of fracturing fluid injection (Fig. 1a), water flows into the hydraulic fracture from the wellbore under the hydraulic pressure difference( ΔPf = Pf − Pp ), and then tends to enter the inorganic matrix under the integrated pressure ( ΔPf + Pc + Pπ ). Because there is no inorganic clay in the organic matrix and the capillarity inside is negative. Due to the existence of a adsorption layer on the surface of organic matrix, the gas in the matrix is continuously adsorbed on the surface of organic matrix with the increasing of reservoir pressure during the injection process; In the process of fracturing fluid flowback (Fig. 1b), the water in the hydraulic fracture flows into the wellbore under the hydraulic pressure difference( ΔP′f = Pp − Pf ), and simultaneously the water in the inorganic matrix flows into the hydraulic fracture as compensation under the integrated pressure(ΔP′f − Pc − Pπ ). With the decreasing of reservoir pressure during the flowback process, gas is gradually desorbed out of the organic matrix and released into the inorganic shale. Generally, clay-rich sediments (such as shale) show a non-ideal semipermeable membrane, allowing ions to pass through by diffusion (Schlemmer et al., 2003). Because the salt concentration of shale formation brine is much higher than that of fracturing fluids, the concentration gradient dominated salt ions diffusion is always in a direction opposite to that of the water molecules osmosis during the treatment of hydraulic fracturing.

where μi is the chemical potential of the particular component at temperature T and pressure P ; μiΘ is the chemical potential of the particular component at standard condition; R represents the ideal gas constant, and T is the temperature. By considering shale as a semi-permeable membrane that allows the migration of water and restricts the migration of ions, Low and Anderson (1958) presented an osmotic pressure equation, which indicates osmosis as a mechanism explaining the migration of water during interactions between shale and drilling fluids. Using thermodynamic principle and classical concept of an osmotic cell, Low and Anderson (1958) derived the following equation to determine the osmotic pressure that could develop between shale formation brine and the drilling fluid.

Pπ = −

xf RT ln Vw xm

(2.3)

where fw, shale and fw, mud respectively refer to the water fugacity of shale formation brine and the drilling fluid;x w, shale and x w, mud respectively refer to the molar fraction of the water molecule in shale formation brine and the drilling fluid. And the following cases can be highlighted from Eq. (2.3):

2.3. Flow mechanism model development Based on the understanding of shale structure and water driving forces, a comprehensive multi-mechanistic multi-porosity(MM) model is proposed, shown in Fig. 2. Three interconnected domains are established in the reservoir simulation of three flow regions in shale: organic matrix, inorganic matrix and hydraulic fractures. Due to the content of organic matter is much less than that of inorganic matter, and the organic matter is generally considered disconnected to each other. Therefore, in the MM model, organic

(1) x w, shale < x w, mud , chemical osmosis induces water molecules to flow into the shale; (2) x w, shale = x w, mud , no aqueous chemical osmosis-induced flow; and (3) x w, shale > x w, mud , chemical osmosis induces water molecules to flow out of the shale.

Fig. 1. Schematic of force interactions during the treatment of hydraulic fracturing.

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Fig. 2. Schematic diagram of the MM model.

3.2. Mathematical model

matrix grid is embedded in the inorganic matrix grid and its function is simulated by the source-sink term. Hydraulic fractures are considered as a interconnected continuum embedded in shale matrix. Hydraulic fractures are represented by a set of high-permeability matrix grids. Specifically, in organic matrix, only the gas phase is considered. The adsorption and desorption of gas occur with the reservoir pressure change. The adsorption and desorption of gas are assumed to be an instantaneous equilibrium process and can be described by the Langmuir equation; In inorganic matrix, due to the presence of clay surface membrane, water transport is induced by hydraulic pressure driven convection, osmosis pressure driven convection and capillary imbibition, simultaneously carrying dissolved salt ions. Besides, gas transport is induced by hydraulic pressure driven convection, while salt ions transport is induced by advection and concentration driven diffusion; In hydraulic fractures, the transport of both water and gas is induced by hydraulic pressure driven convection. The whole mass transfer is a continuous process, shown in Fig. 3.

The mass transport equations for water, gas and salt in the fracturematrix system of fractured shale reservoirs are given below. Fracture water mass transport:

⎞ ⎛ k f krw ρ ∂ w (ϕ f Swf ρw ) = ∇ ⎜ ∇pwf ⎟ − qwfm + qwWf ∂t ⎠ ⎝ ηw

(3.1)

where refers to the water-phase source-sink term (g/cm3 s), representing the injection/production rate between the wellbore and fracture; qwfm refers to the water-phase transfer term between the hydraulic fracture and matrix (g/cm3 s) (Kazemi and Gilman, 1993) and is extended to chemical osmosis-induced mass transport in this model as

qwWf

qwfm =

αρw k f krw f ( pw − pwm + σpπ ) ηw

(3.2)

qwfm

where the water-phase mass transfer term is induced by hydraulic pressure difference between the hydraulic fracture and matrix and osmotic pressure pπ , defined in Eq. (2.4); σ is the osmotic efficiency coefficient, which depends on several factors, such as clay/shale type and porosity, salt concentration of formation brine, injected fluid composition (Schlemmer et al., 2003). Neuzil and Provost (2009) presented experimental data indicating that the osmotic efficiency coefficient of shale is less than 5%. Fracture gas mass transport:

3. Leakoff and flowback: mathematical model 3.1. Assumptions and considerations Base on the MM model, the following assumptions and considerations are made: (1) The effect of stress-dependent permeability is considered; (2) The effect of capillarity is considered. (3) The effect of chemical osmosis is considered. (4) The effect of gas adsorption and desorption is considered; (5) The diffusion of salt ions is considered; (6) The temperature gradient between the fluids in the fracture and matrix is neglected and isothermal flow is assumed; (7) Consider a twodimensional flow (including convection, advection and diffusion) within the fracture and matrix, respectively. The effect of gravity is disregarded. (8) Fluid is slightly compressible.

⎛ k f krg ρ ⎞ ∂ g (ϕ f Sgf ρg ) = ∇ ⎜⎜ ∇pgf ⎟⎟ − qgfm + qgWf ∂t ⎝ ηg ⎠

(3.3)

where qgWf denotes the gas-phase source-sink term(g/cm3 s), representing only the production rate between the wellbore and fracture since there is no gas injection during the treatment; qgfm denotes the gasphase mass transfer term between the hydraulic fracture and matrix (g/cm3 s) and is defined as

Fig. 3. Mass transfer representation of the MM model.

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qgfm =

αρg k f krg ηg

( pgf − pgm )

⎞ ⎛ C mk mkrw ∂ m m m (C ϕ Sw ) = ∇ ⎜ ∇pwm ⎟ + Fsadv + Fsdiff + ∇(D2 ∇C m ) ∂t ⎠ ⎝ ηw

(3.4)

where the term of ∇(D2 ∇C m ) refers to the salt diffusion due to the concentration gradient within the matrix based on the Fick's second law (Shabro et al., 2012); D2 refers to the diffusion coefficient of salt ions within the matrix (cm2/s). Initial and boundary conditions for pressure, saturation and concentration in fracture-matrix system are given below. Initial condition of hydraulic fracture:

Due to the macropore and high-conductivity of the hydraulic fracture (Sun et al., 2015), the gas-phase mass transport through the hydraulic fracture is only considered as hydraulic pressure driven convection. Fracture salt mass transport:

⎞ ⎛ C f k f krw q Wf ∂ (C f ϕ f Swf ) = ∇ ⎜ ∇pwf ⎟ − Fsadv − Fsdiff + C inj w ∂t ρw ⎠ ⎝ ηw Fsadv

(3.5)

pgf (x, y, t )

Fsdiff

and refer to the salt transfer terms between the where hydraulic fracture and matrix by advection and diffusion, respectively. Based on conservation of mass and Fick's first law (Bird et al., 2002), Fsadv and Fsdiff are defined below

F adv = C fmqwfm / ρw

(3.6)

F diff = αD1 (C f − C m )

(3.7)

(3.14) (3.15)

C f (x, y, t ) t =0 = C0f

(3.16)

(x, y, t ) t =0 =

is the initial water saturation in the hydraulic fracture; C0f is where the initial salt concentration of fluid in the hydraulic fracture (ppm). Initial condition of matrix:

pgm (x, y, t ) Swm (x,

C m (x ,

t =0

= pi

y, t ) t =0 =

Swm0

y, t ) t =0 =

C0m

Swm0

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

∂p ∂n

(3.17) (3.18) (3.19)

C0m

=0

is the initial

(3.20)

Γ

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

where k m denotes the permeability of the matrix (μm2). During the hydraulic fracturing treatment, the permeability of the formation near the surface of the hydraulic fracture is expressed by an exponential function in a simple form varying with pressure (Jurus et al., 2013):

qwWf =

δρw k f krw ( pwf − pwf ) ηw Bw

(3.21)

where pwf denotes the flowing pressure in the bottom hole (bar); Bw denotes the water-phase volume factor; δ denotes the shape factor between the wellbore and the hydraulic fracture (cm−2). Constraint conditions are provided below for solving the partial differential equations. Constraint condition of hydraulic fracture:

(3.9)

where kom refers to the initial permeability of the matrix (μm2); pnet refers to the net pressure (bar) and is equal to the difference between the cell pressure, pcell , and the initial reservoir pressure, pi ; m refers to permeability change coefficient(1/bar). Matrix gas mass transport:

⎛ k mkrg ρ ⎞ ∂ m m g (ϕ Sg ρg + mg ) = ∇ ⎜⎜ ∇pgm ⎟⎟ + qgfm ∂t ⎝ ηg ⎠

= pi

Swf0

(3.8)

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

t =0

Swf0

Swf

where C fm represents the salt concentration of fluid transferring between the hydraulic fracture and matrix (ppm), which is equal to C f when transferring from the fracture to the matrix or C m when transferring from the matrix to the fracture, respectively; D1 represents the diffusion coefficient between the hydraulic fracture and matrix (cm2/s), which should be a temperature dependent value. While in this model, it is constant since no temperature gradient between the fluids in the fracture and matrix is assumed. Matrix water mass transport:

⎞ ⎛ k mkrw ρ ∂ m m w (ϕ Sw ρw ) = ∇ ⎜ ∇pwm ⎟ + qwfm ∂t ⎠ ⎝ ηw

(3.13)

Swf + Sgf = 1

(3.22)

pgf = pwf

(3.23)

(3.10)

Constraint condition of matrix:

where mg refers to the mass of adsorbed gas in formation volume(g/ cm3), involved in the matrix model as a sink-source term. mg is described (Silin and Kneafsey, 2012):

Swm + Sgm = 1

(3.24)

pgm

(3.25)

mg = ρR ρgsc VE Sk

where pcgw is the capillary pressure in the matrix (bar).

(3.11) 3

where ρR is the source rock density (g/cm ); ρgsc is the gas density at standard condition (g/cm3); Sk is the volume 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 the Langmuir isotherm(Langumuir, 1916), the dependency of adsorbed gas volume on pressure at constant temperature is given below,

VE = VL

= pcgw

3.3. Model solution Fully implicit finite difference scheme is used to solve the mathematical model. Fig. 4 shows a simplified flow chart of our programming code. The fully implicit algorithm is composed of four parts: (1) discretize the equation system according to fully implicit method; (2) compute the transmissibility term by using upwind scheme. There are some transmissibility terms in the discrete equation system, such as ⎛ Hk mρm ⎞ . The principle of upwind scheme is to determine the ⎜ η ⎟ ⎝ w ⎠i, j +1/2 parameter values according to the source direction of the fluid, i.e. if ⎛ Hk mρm ⎞ ⎛ Hk mρm ⎞ =⎜ pi, j +1 > pi, j , then , else ⎟ ⎜ η ⎟ ⎝ w ⎠i, j +1/2 ⎝ ηw ⎠i . j +1

pgm pgm + pL

−

pwm

(3.12)

where VL is the Langmuir's volume in cm3/g; pL is the Langmuir's pressure (bar), the pressure at which 50% of the gas is adsorbed. Matrix salt mass transport: 5

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The numerical values of MBw, MBg, MBc are computed after each Newton iteration and the material balance errors are considered to be sufficiently small if they are all less than 1.0–7. The thermodynamics consistency of the model has also been investigated as presented in Appendix A. 4. Leakoff and flowback simulation 4.1. Simulation model description A horizontal well with a lateral length of 1200 m is considered in this study. It is completed with a fifteen-stage hydraulic fracturing treatment. In each single stage, four transverse fractures are created along the horizontal wellbore with a fracture spacing of 20 m, and the fracture half-length is considered to be 180 m for each of them. The height, length and width of the shale reservoir are 42, 1500 and 600 m respectively. Basic reservoir, fluid and fracture properties used (Chen et al., 2010; Brodie and Jerauld, 2014) are given in Table 1. 4.2. Simulation analysis In this model, the gas-water relative permeability and the capillary pressure curves of shale are set according to the core experimental data in a previous study, as shown in Fig. 5. The pumping of slickwater is simulated as a water-injection process. The injection speed and injection volume are controlled by adjusting the permeability change coefficient (m). The stress-sensitivity curve of permeability after the adjustment is shown in Fig. 6. In order to facilitate modeling, the mineral salt in formation brine and slickwater is assumed to be sodium chloride. The simulation is initialized by continuously injecting slickwater for one hour into the hydraulic fractures through the horizontal wellbore. The bottom-hole flowing pressure is set to 50 MPa. In the injection process, the water enters the reservoir matrix by hydraulic pressure difference from the hydraulic fractures. Subsequently, the well is shut in for half an hour, allowing the invaded water to imbibe into a deeper matrix spontaneously. Finally, the well is re-opened to cause the fracturing fluid flowback. The flowback duration is set to 5 days and the bottom-hole flowing pressure is set to 5 MPa.

Fig. 4. Simulator flow chart.

⎛ Hk mρ ⎞ ⎛ Hk mρm ⎞ = ⎜ η m ⎟ . (3) Solve the difference equation. By introdu⎜ η ⎟ w ⎠i, j +1/2 ⎝ w ⎠i . j ⎝ cing initial conditions and boundary conditions, coefficients of the variables (p, Sw, C) can be obtained and coefficient matrix is formed. Then, the values of the variables at each time step can be calculated. (4) After obtaining the reasonable values of each variable, move to next time step and return to part (2) to continue the computation. The convergence criteria are primarily based on material balance. If the residuals are summed over all cells in the reservoir, the flow term cancel, because the flow out of one cell is always equal and opposite in sign to the corresponding flow into its neighboring cell. Thus the sum of the residuals for each phase corresponds to the net mass accumulation within the reservoir less the net influx through wells. Take water phase as an example:

⎛ ∂m w ⎞ ⎟ + ∂t ⎠

∑ (Rw )i = ∑ ⎜⎝ i

i

i

∑ (qwWf )i i

4.3. Simulation results Fig. 7a display the pore pressure profiles in the near-hydraulicfracture region with time. Pore pressure in reservoir matrix increases significantly. After 1 h water injecting, the pore pressures are increased to 45.42 MPa in the matrix at the fracture face. While during the well shut-in and flowback, the matrix pore pressure continuously decreases. At the end of 5 days flowback, the pore pressures at the fracture face decrease to 10.6 MPa and the pressure transient has been reached to 1000 cm. Fig. 7b displays the dynamic profiles of water saturation in the near-hydraulic-fracture region with time. The simulation result indicates that, at the end of pumping, the water fills the hydraulic fracture. And a high-water-saturation region surrounding the hydraulic

(3.26)

where (Rw)i refers to the water residual in cell i. Then the material balance errors are converted to MB values.

⎫ ⎧ ⎞⎪ ⎞⎛ ⎛ ⎪ ⎜⎜∑ (Rw )i ⎟⎟ / ⎜⎜∑ (PV )i ⎟⎟ ⎬ MBw = Bw dt ⎨ ⎪ ⎪ ⎠⎭ ⎠⎝ i ⎩⎝ i

(3.27)

where Bw is the water formation factor and (PV)i is the pore volume in cell i. Table 1 Basic reservoir, fluid and fracture properties. Initial reservoir pressure Matrix porosity Hydraulic fracture conductivity Viscosity of the pumped slickwater Source rock density Volume proportion of source rock Formation brine salinity Gas density at standard condition Slickwater density at standard condition Partial molar volume of water

26 MPa 0.08 6.5 D cm 1 m Pa s 2.56×103 kg/m3 0.06 280000 ppm 0.77 kg/m3 1000 kg/m3 18.02×10−6 m3/mol

Reservoir temperature Matrix permeability Initial water saturation Viscosity of gas Osmotic efficiency coefficient Salt diffusion coefficient Water compressibility Slickwater salinity Langmuir's volume Langmuir's pressure

6

324 K 300 nd 0.2 0.022 m Pa s 0.05 3×10−10 m2/s 5×10−4 MPa−1 1000 ppm 3.32×10−3 m3/kg 5.8 MPa

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fracture is formed due to the forced water leakoff. The water leakoff front is approximately 75 cm away from the hydraulic fracture face. Saturation values are 0.2 in the rest of the matrix where the leakoff water has not reached. After a half-hour shut-in, the high-watersaturation region grows flat as water imbibes farther into the matrix. During the flowback process, a similar pattern in the growth of the saturation profile is seen with an increase in time. A fraction of water returns back to the wellbore and a small fraction of water imbibes into the deeper matrix. After 5 days flowback, the water saturation drops considerably near the hydraulic fracture and the leakoff front is approaching 105 cm. Because the water flowback rate is almost zero at his point, this saturation region effectively becomes immobile even though irreducible saturation has not been reached. Fig. 7c presents the dynamic salinity profiles in the region near the hydraulic fracture. The simulation result indicates that, during the well shut-in, salt concentrations near the hydraulic fracture increased a little bit as hydrated salt ions in the matrix continuously diffuse to the hydraulic fracture. With the continuous flowback of water, salt concentrations near the hydraulic fracture is increasing. On day 5 of the flowback, the matrix salt concentration at the fracture surface increases to approximately 130000 ppm, from 80000 ppm at the end of the pumping. The water flowback rate and load recovery in the fractured horizontal well is demonstrated in Fig. 7d. The initial peak of flowback rate is 273 m3/d. subsequently, the flowback rate rapidly decreases and is approaching zero after 5 days. The accumulated load recovery at this point is only 32%, which means a large quantity of water is retained in the reservoir. Fig. 8a–c provide the comparisons of pore pressure, water leakoff and flowback profiles, respectively, from only hydraulic pressureinduced, (hydraulic pressure+osmosis)-induced and (hydraulic pressure+capillarity)-induced cases. The simulation result indicates that the difference on matrix pressure of the aforementioned cases is not

Fig. 5. Gas-water relative permeability and capillary pressure.

Fig. 6. Stress-dependent permeability.

Fig. 7. Results of base case. (a) Pore pressure profiles; (b) Water-saturation profiles; (c) Salt concentration profiles and (d) Water flowback rate and load recovery.

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Fig. 8. Comparison of cases with different driving forces. (a) Pore pressure profiles; (b) Water leakoff profiles; (c) Water flowback profiles and (d) Water load recoveries.

pressure increasing from 50 to 60 MPa, makes the accumulated injection volume of water from the wellbore to fracture, QwW-f, and the accumulated flowback volume of water from the fracture to the wellbore, Qwf-W evidently increase, but the accumulated leakoff loss of water between the fracture and the matrix, (Qwf-m−Qwm-f), is also increased significantly, which leads to a even lower load recovery. That indicates the increase of pf can contribute to the well injection capacity, but unfortunately it can aggravate the water leakoff and retention as well. Injected slickwater salinity increasing from 1000 to 100000 ppm, makes the accumulated injection volume of water decrease by 312 m3, and the flowback volume of water increased by 196.7 m3. That indicates high salinity fluid contributes to reduce water leakoff and retention during the treatment, although it loses some injection capacity. The ion diffusion coefficient decreases from 3×10−10 to 5×10– 13 m2/s, which is the experimental data arrange measured from a variety of shale samples (Brodie and Jerauld, 2014), however, not only the increased accumulated injection and leakoff volumes, but also the decreased flowback volume and load recovery of water are all very small. That suggests ion diffusion coefficient is not an important factor to both the water leak-off and the flowback during the treatment of hydraulic fracturing under this simulation condition.

significant. However, capillarity and chemical osmosis both drive extra water flow into the shale matrix, as a result, the created high-watersaturation regions with capillarity and chemical osmosis considered respectively, distribute more flat and the corresponding leakoff fronts are farther away from the fracture face than the only hydraulic pressure-induced case. In this case, chemical osmosis influences more obviously than capillarity, although they both intensify water leakoff and hinder water flowback. Fig. 8d demonstrates the comparison of water load recoveries from the aforementioned cases. In the only hydraulic pressure-induced case, the initial peak of flowback rate is 349 m3/d and the water load recovery after 5 days is as much as 44%. While, with chemical osmosis considered, the water load recovery is approximately 33.5%. The comparison indicates that chemical osmosis leads to an extra 10.5% fluid retention during the treatment of hydraulic fracturing. To investigate the role of hydraulic pressure (pf), fracturing-fluid salinity (Cinj) and salt diffusion coefficient (D), on water leak-off and flowback during the treatment of hydraulic fracturing, three groups of sensitivity simulation cases were run. Each group of cases simulated the change of one variable and kept the other variables consistent with the base case, which is (hydraulic pressure+chemical osmosis)-induced one. The simulation results are listed in Table 2. The simulation results indicate that the bottom-hole flowing Table 2 Simulation results of three sensitivity parameters.

QwW-f (m3) Qwf-m (m3) Qwf-W (m3) Qwm-f (m3) fr (%)

Base case

pf=55 MPa

pf=60 MPa

Cinj=10000

Cinj=100000

D=10–12 m2/s

D=5×10–13 m2/s

11686.1 8190.4 3915.8 1704.1 33.5

18100.1 13795.9 5587.4 3105.6 30.9

27777 22538.4 7605.2 4885.9 27.4

11665.2 8159 3935.5 1713.6 33.7

11374.1 7814.9 4112.5 1804.5 36.2

11694 8198.9 3905.3 1694.2 33.4

11701.9 8210.2 3895 1684.7 33.3

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and the values of D in x and y directions are the same. Precise modeling of salt diffusion in different domains with temperature-dependent diffusion coefficients is currently under consideration and will be reported in the future work.

5. Discussion Chemical osmosis-induced flow has long been recognized in drilling fluid/shale interactions and properly used to deal with drilling fluid selection and wellbore instability problems. However, chemical osmosis has been overlooked as a possible mechanism for leakoff and retention of the fracturing fluid during the treatment of hydraulic fracturing, since there is a considerable salinity difference between the fracturing-fluid and the shale formation brine. To address this issue, a comparative simulation has been performed to analyze the combined influence of hydraulic pressure, capillary pressure and osmotic pressure on the water leakoff and flowback during the treatment of hydraulic fracturing. Such analysis provides an intuitive information of the influence weight of each driving force under given reservoir and fluid conditions. The result indicates that hydraulic pressure is still the main controlling factor. Thus, to further investigate the importance of chemical osmosis during water flow in hydraulic fracturing, the leakoff and flowback have been simulated with different hydraulic pressure. The simulation results indicate that under the condition of higher hydraulic pressure injection, the water retention becomes even more severe. Therefore, chemical osmosis as a key mechanism for water retention should not be neglected during the post-treatment evaluation of hydraulic fracturing. Moreover, a sensitivity simulation has been performed then for a quantitative analysis of the influence of the competitive parameter Cinj on chemical osmosis. Since the salinity contrast between the injected fluid and the formation brine is a directly influence factor of the osmotic pressure. The simulation result is useful for fracturing-fluid optimization in the design phase. From the perspective of leakoff minimization and flowback maximization, high-salinity fracturing fluid is a good choice. It coincides with those low-salinity fluids, which are designed to achieve flooding maximization, such as low-salinity EOR technology (Sandengen et al., 2016). The influence of another competitive parameter D on chemical osmosis has also been investigated. The diffusion of salt ions can counteract a proportion of water flow induced by chemical potential gradient, and therefore affects the chemical osmosis in indirect way. We validated this argument with a D-sensitive simulation. However, there is some limitations of the work. Only concentration driven diffusion is considered, although based on the Stokes-Einstein equation (Okazawa, 2007), D should be temperature-dependent. However, since the temperature gradient is neglected in the model, the temperature influence on diffusion is neglected as well. Besides, D1=D2 is assumed

6. Conclusions In this paper, the development of a comprehensive multi-mechanistic multi-porosity water/gas/salt flow model is presented based on the shale properties of semipermeable membrane, pore structure and fluid salinity. A numerical simulation of fracturing fluid leakoff and flowback in a hydraulically fractured shale gas well is also conducted using the proposed MM model. The main conclusions are as follows. 1. A high-water-saturation region surrounding the hydraulic fracture is formed during the process of fracturing fluid pumping due to the leakoff mechanism, which includes three positive driving forces, i.e. osmotic, capillary and hydraulic pressures. 2. The high-water-saturation region grows flat during the flowback process as a fraction of water returns back to the wellbore and a small fraction of water imbibes into the deeper reservoir. At the end of the flowback (when the water flowback rate is almost zero), this saturation region effectively becomes immobile even though irreducible saturation has not been reached. The water flowback is driven by a hydraulic pressure difference and two opposite forces driven by chemical osmosis and capillarity. 3. Chemical osmosis intensifies water leakoff and hinders water flowback, which leads to an extra-low load recovery. It can be inferred that chemical osmosis is a key mechanism for fluid retention during the treatment and should not be ignored especially for significant fracturing fluid/shale salinity difference cases. 4. This work provides a basis for shale gas/water flow, post-treatment prediction and flowback data analysis of hydraulically fractured shale gas wells. Acknowledgments The authors would like to acknowledge the National Natural Science Foundation of China (No. 51504266), Beijing Natural Science Foundation (No. 3154038), and Science Foundation of China University of Petroleum, Beijing (No. 2462015YQ0212) for their financial support.

Appendix A This appendix presents the energy balance equations of the model which are based on those reported by Zheng et al. (2011) for a heating and hydration process in clay- fluid interactions. The formulation assumes that all phases and species are at local thermal equilibrium and therefore they are all at the same temperature. Hence, the energy balance is described in terms of an equation of internal energy which is defined by the following balance of enthalpy:

∂h + ∇(−Λ⋅∇T + I e ) = 0 ∂t

(A1)

where h is the enthalpy of the gas-liquid mixture (kJ) which is given by:

h = ϕρw S whw + ϕρw S wChs + ϕρ g S ghg w

g

(A2)

s

where h , h and h are the specific enthalpies of water, gas and salt ions, respectively. The density of dilute solution is assumed to be equal to the density of pure water. Λ is the bulk thermal conductivity tensor, which is given by: (A3)

Λ = Λl + Λg where Λl and Λg are the thermal conductivities of liquid and gas, respectively, J/(cm s °C). ∇I e is the convective energy flux which is given by:

∇I e = q whw + q gh g + q shs

(A4)

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where qw, qg and qs are the mass fluxes of water, gas and salt ions, respectively. Taking the matrix grid cell which is close to the hydraulic fracture as an example, then qw, qg and qs can be described by:

⎛ k mkrw ρ ⎞ w qw = ∇ ⎜ ∇pwm ⎟ + qwfm η ⎝ ⎠ w

(A5)

⎛ k mkrg ρ ⎞ ∂mg g ∇pgm ⎟⎟ + qgfm − q g = ∇ ⎜⎜ ∂t ⎝ ηg ⎠

(A6)

⎞ ⎛ C mk mkrw ρ w qs = ∇ ⎜ ∇pwm ⎟ + αρw D1 (C f − C m ) + ρw ∇(D2 ∇C m ) ηw ⎠ ⎝

(A7)

Due to the isothermal flow, which is assumed during the fluid transport, the thermal conductivity term in Eq. (A1) is 0, i.e. (A8)

∇(−Λ⋅∇T ) = 0 and combined with the conservation of mass, the conservation of energy extended by the following equation is achieved. ∂h ∂t

∂h ∂ + ∇I e = ∂t [ϕ mρw Swm hw ∂t ∂ hs [ ∂t (C mϕ mSwm ρw )] = 0

+ ∇(−Λ⋅∇T + I e ) = ∂

+ h g [ ∂t (ϕ mSgm ρg )] +

∂

+ ϕ mρw Swm C mhs + ϕ mρg Sgm h g] + hw [ ∂t (ϕ mSwm ρw )] (A9)

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