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Permeability Reduction of Berea Cores Owing to Nanoparticles Adsorption onto the Pore Surface: Mechanistic Modeling and Experimental Work Bin Yuan, Wendong Wang, Rouzbeh Ghanbarnezhad Moghanloo, Yuliang Su, Kai Wang, and Miaolun Jiang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02108 • Publication Date (Web): 14 Nov 2016 Downloaded from http://pubs.acs.org on December 4, 2016

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Energy & Fuels

Permeability Reduction of Berea Cores Owing to Nanoparticles Adsorption onto the Pore Surface: Mechanistic Modeling and Experimental Work Bin Yuan, *† Wendong Wang, ξ Rouzbeh G. Moghanloo, † Yuliang Su, ξ Kai Wang†, and Miaolun Jiang, ξ † Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma, Norman, OK 73019, USA. ξ School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, P. R. China

ABSTACT This paper examines an integrated approach to study the permeability alteration resulting from nanofluid flow through porous media. Hydrophilic Nano-structure particles (NSP) are dispersed in the brine stream at 0.05, 0.2 and 0.5wt% concentrations, and injected into several oil-wet Berea sandstones. The pressure drops across the cores, and the effluent nanoparticles concentrations are monitored. To quantify the nanoparticles adsorption/detachment and straining behavior and associated effects on formation permeability, analytical mechanistic models are derived using the method of characteristics. The interplay between nanoparticles and rocks is described by the classical particles filtration theory coupled with the maximum adsorption concentration model. All the necessary parameters, e.g., the maximum adsorption concentrations, reversible or detachment adsorption concentrations, nanoparticles adsorption and straining rates, and the corresponding formation damage coefficients are characterized. The experimental results indicate that nanoparticles adsorption and straining, (i.e., the maximum adsorption concentration, nanoparticles adsorption straining rates) are enhanced along with the increase of nanoparticles injection concentration. As results, the breakthrough of injected nanoparticles is delayed, the steady-state effluent concentration decreases, and the pressure drop increases more rapidly. The nanoparticles adsorption consists of reversible and irreversible adsorption. During post-flush, the reversible nanoparticles concentrations are enhanced by the increase of nanoparticles concentrations. In practice, this paper contributes to the following applications: 1) apply lab experiments to highlight the effects of nanoparticles adsorption, straining, and detachment behaviors on the formation damage. 2) The analytical mechanistic model provides physical insights to quantify nanofluid flow performance, and can be extended to optimize the treatment of nanofluid application (e.g., injection concentrations) while considering both the loss of nanoparticles and their induced formation damage. INTRODUCTION Recently, Nanofluid have been widely reported in diverse potential applications in the oil and gas industry, including formation damage mitigation, assisted surfactant/alkaline/low salinity/gas flooding, functional nanoparticles used as tracers or sensors to detect certain reservoir rock and fluid properties, and fracturing fluid additives in unconventional reservoirs (Patra, 2008). The types of nanoparticles mainly include Al2O3, MgO, ZrO2, CeO2, TiO2, ZnO and Fe2O3.Nanofluids can exhibit unique electrical, magnetic, and chemical properties. Achinta et al. (2016) reviewed the applications of nanoparticles and nano-dispersion in the upstream of oil industry, including oilfield exploration, reservoir characterization, drilling and completion, and enhanced oil recovery etc. Song et al (2007) proposed hyperpolarized silicon nanoparticles to be applied to take image of hydrocarbon reserves. Nano-sensor and nanoidentification techniques have been proposed to identify the physical and chemical properties, fluid flow type, rock mechanical characteristics (Kapusta et al., 2011; Abousleiman et al. 2009; Berlin et al., 2011; Jahagirdar, 2008). The designed nanoparticles have been in drilling or completion fluids for clay stabilization (McDonald, 2012), fluid loss control (Contreras et al., 2014), viscosity alternation (Gurluk et al., 2013), wellbore stability (Zhang et al., 2015), drag and torque friction (Sharma et al., 2012), cementation additives (Santra et al., 2012; Pang et al., 2014; Van Zanten et al., 2010) and fracturing fluid purposes (Crews et al., 2008). In addition, nanotechnology has been extensively applied into enhanced oil recovery using laboratory experiments related to wettability alteration (Li et al., 2013, Li et ACS Paragon Plus Environment

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al., 2014, Bera et al., 2015), IFT reduction (Moghadam et al., 2014), enhanced adsorption of injected chemicals (Esmaeilzadeh et al., 2011), enhanced stability of emulsion (Aminzadeh et al., 2012), foam stability (Yu et al., 2012; Adkins et al. 2007, Gonzenbach et al. 2007, Prigiobbe et al. 2016), channels plugging, and emulsification (Ogolo et al. 2012; Abdelrahman et al.,2015; Ju et al., 2006; Ju et al, 2009). Particles migration within reservoirs and subsequent permeability reduction have been regarded as a significant cause of well impairment (Sarkar, 1990; Zeinijahromi et al., 2012 and 2013;). Core flooding experiments recognized that fluid salinity, flow rates, pH, temperature, rock and fluid polarity influence fines migration within reservoirs (Ezeukwu, 1998). The application of nanoparticles to control fines migration has been previously investigated (Assef, 2014; Yuan, 2016). Nanoparticles with extremely high surface areas of approximately 200m3/g are suitable to help fixate mobile formation fines by altering the surface potential of fines particles or grain surfaces and effectively reduce the double layer repulsive forces between fine particles and rock grains (Huang, 2008; Ju, 2006). Mathematical modelling and lab experiments have also demonstrated that a very small concentration of nanoparticles coated with fracture proppants can greatly help prevent fines migration and subsequent formation damage (Yuan, 2015 and 2016). The successful applications of silica nanoparticles to mitigate fines migration in sand packs saturated with nC60 have also been reported under the high salinity condition (Cheng, 2005; Ju, 2009; Yu, 2012). In past decades, the efficiency of nanofluid stability, transport, adsorption and desorption during water flooding has been studied by means of a limited number of lab experiments (Keller et al. 2010). However, under certain conditions, nanoparticles could be also adsorbed and plugged in pore-throats, resulting in permeability impairment, which offsets their positive effects to mitigate fines migration and enhancing oil recovery (Kartic et al., 1999; Zhang et al., 2013; Yuan et al., 2016). Laboratory experiments have demonstrated that the equilibrium adsorption of silica nanoparticles on sandstone, limestone, and dolomite are different (Yu et al., 2012, Huang et al.2015). The higher concentration of nanofluids could block the pore throats and result in permeability impairment and wettability alteration (Li et al., 2015a,b). Many laboratory experiments and phenomenon observation have been provided serving as proof of concept, however, the evaluation of nanoparticles adsorption and detachment has yet to be addressed. Therefore, a comprehensive study of nanoparticles adsorption/detachment behavior is essential to provide an essential foundation for the numerous benefits of nanoparticles. The aim of this paper is to better understand nanofluid effects on permeability impairment using both lab experiments and mathematical modelling works. In view that hydrophilic nanoparticles adsorption can lead to the alteration of rock wettability from oil-wet toward water-wet, which is preferable for enhanced oil recovery, it is desirable to study the hydrophilic Nanofluid flow with dynamic adsorption/detachment behavior, and its negative effects on the permeability of initially oil-wet cores in purpose of EOR. The hydrophilic silica Nano-structure Particles (NSP) (particles sized in nanoscale) are chosen because they consist of more than 90% silicon oxide, which is the main constituent of sandstone reservoirs; hence, they refrain from negatively effecting the environment (Hendraininggrat et al. 2012 and 2015). NSP has average particles sizes of 7 nm, and specific area of 300m2/g, but they can aggregate to form bigger particles which might be bigger than 100nm. In the core-flooding, the effluent nanoparticles concentrations and pressure drops across the cores are recorded to estimate nanoparticles adsorption and retention behavior, as well as particles detachment during brine post-flush. This paper extends a mathematical approach presented by (Yuan et al. 2016) for nanoparticles application. To quantify nanoparticles adsorption, straining and detachment behaviors, and associated formation damage effects, mechanistic analytical solutions are derived using the method of characteristics. This paper also provides insights on the importance of proper nanoparticles treatment design (e.g., different injection concentration of nanoparticles) by considering both the loss of nanoparticles and their induced formation damage. NANOPARTICLES AND EXPERIMENTAL METHODS ACS Paragon Plus Environment

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Materials The materials used to conduct the experiments include: Nanofluid, Berea sandstone, and laboratory prepared NaCl, diluted with 3wt% to the desired concentration. The Berea sandstone, measuring 8cm in length and 3.83cm in diameter, are used as core samples. The core permeability before and after Nanofluid injection are inversed by the results of pressure drop using Darcy flow model, respectively. To address some problems in reservoir formations, hydrophilic silica Nano-Structure Particles (NSP) are dispersed in different concentrations. The diameters of these nanoparticles are in the order of nanometers. The Transmission Electron Microscope (TEM) images of NSP is shown in Table 1. Table 1 Properties of the Nano-Structure Particles used in the experiment Type of Nanoparticles

Particle Size, nm

Surface areas, m2/g

Nano-Structure Particles (NSP)

7

300

TEM images

Nanofluid

Density, g/cm3

Viscosity, cP

NaCl Brine, 3 wt. %

1.022

1.0026

NSP Nanofluid 0.05 wt. %

1.021

1.0858


1.022

1.1550


1.022

1.5627

Experimental Procedures Prior to the flooding experiments, the core plugs are saturated with 3wt% NaCl brine using a vacuum pump to ensure no trapped air left inside the cores. The hydrophilic silica Nano-Structure Particles (NSP) dispersion is diluted as three different concentrations (0.05 wt. %, 0.2 wt. % and 0.5 wt. %) into 3wt% NaCl solutions. The density and viscosity of the nanofluids at different concentrations are also measured, as shown in Table.1. The experiment process is started with the core plug being exposed to sets of experiments conducted under confining pressures, up to 20 bars. The flow rates in all experiments are kept constant as 2 ml/min. At the beginning, 1 PV (about 16ml) of brine is injected to establish a base permeability. Then, a slug of 4 PV Nanofluid (NSP nanoparticles) is injected into one end of the core plug. After, a continuous 20 PV injection of brine is used as post-flush to ensure the desorption behavior occurred. The differential pressure across the core plugs is continuously recorded by a data gathering system. The effluent nanoparticles concentrations are measured in use of UV Spectrophometer, after collecting the effluent fluid sample every 1/4 PV. The detailed schematic of flooding setup is the same as described by Li et al. (2015a, b). MECHANISTIC MODEL Nanoparticles Transport Model During the nanoparticles transport in porous medium, the nanoparticles may be adsorbed and strained at the stagnant points on the pore-throat surfaces (Bedrikovetsky, 2011Zhang et al. 2013). Nanoparticles with low surface zeta potential can be adsorbed on the surface of fine particles/rock grains (Yuan, 2015). Meanwhile, particles collisions also occur when nanofluids flow through the pore-throats. ACS Paragon Plus Environment

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Consequently, nanoparticles can be blocked or stained at the entrance of the pore-throats. The previous analysis (Zhang et al. 2013) suggested that nanoparticles undergo both reversible and irreversible adsorption. In this paper, the different behaviors of nanoparticles, including adsorption, straining, and detachment are coupled into an analytical model. Some commonly used assumptions are listed as follows: (1) The porous medium (core plug) is one-dimensional (1D), uniform and homogeneous by ignoring heterogeneity, and the local thermodynamic equilibrium assumption applies; (2) Twocomponents exist (water, nanoparticles) and two-phase (one flowing and one stagnant) isothermal flow takes place; (3) Adsorption of nanoparticles are described with the classic filtration theory and the maximum adsorption concentration model (Yuan et al., 2016). (4) Flow velocity is sufficiently large to neglect the dispersion flow effects. Here, introducing dimensionless length and time: xD =

x , L

tD =

qinj t

φ AL

(1)

where xD is the dimensionless distance; tD is the dimensionless time; The mass-balance equation of nanoparticles flowing through the permeable medium, considering their deposition and straining on rock grains (Bedrikovetsky, 2014) can be written as, ∂CNP ∂CNP 1 ∂σ NP 1 ∂S NP + + + =0, ∂xD ∂t D φ ∂t D φ ∂t D

(2)

Nanoparticles straining and adsorption rate can be expressed by the particles filtration theory (Gued es et al. 2009; Massoudieh and Ginn 2010), ∂S NP ∂σ NP = λs CNPφ L , = λad CNPφ L , ∂t D ∂tD



when, σ NP < σ NP ,max , σ NP ,max1 = 1 − ( 

(3)

 )2  φ (1 − Sor ) . 2φ rP Fe,max y  2 µ rNP U

Prior to the nanoparticles adsorption reaches maximum limits, we apply the classic particles capture kinetics equation to quantify the attachment rates of nanoparticles (Vafai, 2005); λad and λs are filtration coefficients for adsorption and straining, respectively. Usually, they are assumed as constants. Initially, there are no nanoparticles saturated in cores, and the injected nanoparticles concentrations are kept as constant, hence, the initial and boundary conditions are as follows:  C NP ( x D , 0) = 0  σ NP ( x D , 0) = 0  S NP ( x D , 0) = 0   C (0, t ) = C D NP , inject = C 0  NP σ NP ( 0, t D ) = λ ad φ LC 0 t D   S NP ( 0, t D ) = λ s φ LC 0 t D

(4)

During post-flush of brine, as indicated by (Zhang et al., 2013), the absorbed nanoparticles might detach from the pore surfaces due to the changes of flowing fluid properties. Inferred from the maximum retention concentration of nanoparticles Yuan et al., (2015), we assume that it is the changes of drag-electrostatic force ratio lead to the decrease of nanoparticles adsorption, as follows: 

σ NP ,max (U ) = 1 − ( 

2 µ rNP U 2 ) φ 2φ rP Fe y 

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(5)

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y= f(

χ ρ Fe 4π rNP3 , ∆ρ g ) µ 3Fe

(6)

In view that there are no changes o the injected fluid salinity, it can be understood that the changes of drag-electrostatic force ratio (Eq.6) are not attributed to alteration of salinity, but only be caused by the decrease of fluid density changing with injected nanofluid concentration. The density of injected fluid can be expressed as weighted average of nanoparticles and carrier water density: ρ = ρw (1 − CNP ) + ρNPCNP = ρw + CNP ( ρNP − ρw )

(7)

Hence, the maximum retention concentration of nanoparticles becomes a function of injected nanoparticles concentration. We assume the detachment of nanoparticles occurs instantly after the abrupt change of nanoparticles concentration. Thus, the mass balance equation of nanoparticles during the post-flush of brine is expressed, as follows: ∂CNP  1 σ NP ,max1 − σ NP,max 2  ∂CNP + 1 + =0  CNP ∂xD  φ  ∂t D

(8)

Before the post-flush of brine, there are already amounts of absorbed nanoparticles, and hence the initial conditions for the post-flush process are as follows: (9) C NP (0, t D ) = 0; σ NP ( 0, t D ) = σ NP , max 2 Where, σ NP,max1 is the maximum retention concentration of nanoparticles at the phase of nanoparticles injection, and σ NP,max 2 is the maximum retention concentration of nanoparticles at the phase of post-flush. Method of Characteristic (MOC) Solutions

Substituting the particles capture kinetics equation Eq.2 into mass balance equation Eq.1, yields: Suspended Nanoparticles:

∂CNP ∂CNP + + ( λad + λs ) CNP L = 0 ∂xD ∂tD

(10)

Nanoparticles Adsorption:

∂σ NP ∂σ NP + + ( λad + λs ) σ NP L = 0 ∂xD ∂tD

(11)

Nanoparticles Straining:

∂S NP ∂S NP + + ( λad + λs ) S NP L = 0 ∂xD ∂t D

(12)

Appling the approach of MOC, the following ordinary differential equations can be obtained, along characteristic line

dxD = 1, dt D

dCNP dσ NP dS NP = − ( λad + λs ) CNP L, = − ( λad + λs ) Lσ NP , = − ( λad + λs ) LS NP dt D dtD dt D

(13)

Fig.1 shows the distance-time diagram with different lines representing the propagation of different nanofluid concentration conditions along the 1-D cores at different time. Combined with the boundary condition, Eq.4, we obtain the solution of suspended nanoparticles and retained nanoparticles concentration in Zone I and Zone II, when 0 ＜ tD ＜ tDc. Time tDc is the moment when the retained nanoparticles concentration on rock grains at the inlet reaches the maximum value, σ NP,max1 : t Dc =

σ NP ,max 1 λad φ L (1 − S or )C0

C NP ( xD , t D ) = 0  (xD > t D ), Zone I: σ NP ( xD , t D ) = 0 S ( x , t ) = 0  NP D D

C NP ( xD , t D ) = C0 exp ( − ( λad + λs ) LxD )  (xD < t D ), Zone II: σ NP ( xD , t D ) = λadφ LC0 ( t D − xD )  exp ( − ( λad + λs ) LxD )   S NP ( xD , t D ) = λsφ LC0 ( t D − xD )  exp ( − ( λad + λs ) LxD )

(14) (15)

(16)

As the distance-time diagram, or motion of particles concentration fronts in plane of xD-tD shown in ACS Paragon Plus Environment

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Fig.1, there exists an “attached front,” the retained and suspended nanoparticles concentration along the characteristic line in Fig. 1 can be obtained when tD=tDc, then we have:  C ( x , t ) = C exp ( − ( λ + λ ) Lx ) 0 ad s D  NP D D  (17) σ NP ( xD , tD ) = σ NP ,max1 exp ( − ( λad + λs ) LxD )   S ( x , t ) = λs σ NP ,max1 exp ( − ( λad + λs ) LxD )  NP D D λad Based on the continuity condition around the “attached front,” C + = C − = C0 (Bedrikovetsky, 2011),

the following differential equations can be derived: ∂σ NP = λadφ LC0 ∂t D

(18)

∂σ NP = −λad φ LC0 − L ( λad + λs ) σ NP,max1 ∂xD

(19)

dxcr λad φ LC0 = = const. dtD λad φ LC0 + L ( λad + λs ) σ NP,max1

(20)

The moving trajectory of nanoparticles “attached front” can be represented by: σ NP,max1   λad φ LC0  tD −  (a) λad φ LC0 + L ( λad + λs ) σ NP ,max1  λad φ LC0 

Distance form :

xcr =

Time form :

λad φ LC0 + L ( λad + λs ) σ NP ,max1 σ NP,max1 tcr = xcr + λad φ LC0 λad φ LC0

(21)

(b)

Because the slopes of characteristic lines in Zone III are in unity, the lines which start from any intersection points at the “attached front” can be obtain by: Line III: xD − xcr = t D − tcr (22) According to Eq.21 and Eq.22, the start points on the “attached front” at Zone III is given by, Distance form: xcr 0 = ( tD − xD )

λad φ C0 1 − ( λad + λs ) σ NP ,max1 ( λad + λs ) L

(23)

 λad φ C0 + ( λad + λs ) σ NP ,max1  1  − ( λad + λs ) σ NP ,max1   ( λad + λs ) L

Time form: tcr 0 = ( tD − xD ) 

(24)

The retained and suspended nanoparticles concentration at Zone III and Zone IV are given as:     λad φ C0 1 σ NP = σ NP ,max1 exp  − ( λad + λs ) L  x D − ( t D − xD ) +   ,   + + L λ λ σ λ λ ( ) ( )  ad s NP ,max1 ad s         λad φ C0 1 + , C NP = C 0 exp  − ( λad + λs ) L  x D − ( t D − x D ) ( λad + λs ) σ NP ,max1 ( λad + λs ) L        S NP = λ s C0φ L ( t D − xD ) exp ( − ( λad + λs ) LxD )  

(a)

(b)

(25)

(c)

After t ＞ tcr (XD=1), all of intervals along the permeable medium have reached the maximum retention concentration of fine particles, then in Zone IV, the retained nanoparticles concentration would be constant, σ NP,max1 . Since then, the suspended nanoparticles would become steady state. σ NP ( xD , t D ) = σ NP ,max1  Zone IV: C NP ( xD , t D ) = C0 exp ( −λs LxD )   S NP = λs C0φ L ( t D − xD ) exp ( −λs LxD ) φ C + σ NP,max1 σ tcr ( xD = 1) = 0 xD xD =1 + NP ,max1 φ C0 λadφ LC0

(a) (b) (c)

After tD1 we start the post-flush of brine, and the initial conditions of post-flush are as follows: ACS Paragon Plus Environment

(26) (27)

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C NP ( x D , t D 1 ) = C 0 exp ( − λ s Lx D )

(28)

σ NP ( x D , t D1 ) = σ NP ,max 1 S NP ( x D , t D 1 ) = λ s C 0φ L ( t D1 − x D ) exp ( − λ s Lx D )

Applying the approach of MOC for the mass-balance equation (Eq.8), we obtain the following ordinary differential equations. dt D 1 σ NP ,max1 − σ NP ,max 2 = 1+ φ dxD C NP

Along the characteristic line,

(29)

Analytical solutions for suspended nanoparticles and absorbed nanoparticles can be derived as:  0 < xD < 1  , ZoneV:  1 σ NP ,max1 − σ NP , max 2    x D + t D1 t D >  1 + φ C NP   

C NP ( xD , t D ) = 0  σ NP ( x D , t D ) = σ NP ,max 2

(30)

We can obtain the maximum retention concentration of nanoparticles during the post-flush phase, σ NP ,max 2 by identifying the time of breakthrough, ∆t D1 .  1  − 1  φ C NP  ∆ t D1 

σ NP ,max 2 = σ NP ,max 1 − 

(31)

Table.2 summarizes the solutions of nanoparticles adsorption, straining and detachment for different zone in distance-time diagram, Fig.1. In the case with constant injection rates, the pressure drop along 1-D permeable medium would increase with particulates attachment and straining. The decrease of permeability has been proposed as empirical formulas to characterize the effects of particulates adsorption and straining by various past investigations (Sharma 1987, Bedrikovetsky 2011). The modified Darcy’s flow equation considering the decrease of formation permeability is written as, U=

k0

L µ (1 + β aσ NP

dp + β s S NP ) dxD

(32)

The pressure drop can be obtained by integrating Eq.30 along the whole along the whole core. 1

∆p ( t D ) = ∫ 0

ULµ (1 + β aσ NP + β s S NP ) k0

dxD

(33)

RESULTS AND DISCUSSIONS Experimental Results The core-flood pressure drops of nanofluid injection is presented in Fig.2. NSP nanoparticles with different injection concentrations have different tendencies. Caused by the adsorption and straining of nanoparticles, the pressure drops increases rapidly after the start of nanofluid injection. This may be attributed to the multilayer adsorption of nanoparticles, and gradual straining effects, which leads to the reduction of pore-throat sizes and the escalation of pressure drop. The higher the injected nanoparticles concentration is, the more rapid and significant the pressure drop increases. During the post-flush of brine, the pressure drop decreases gradually. It may be attributed to the enlargement of porosity caused by detachment of those adsorbed nanoparticles. After several PV of post-flush, the pressure drop reaches steady-state. Since then, no more detachment and straining of nanoparticles occur.


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Fig.1 Distance–time diagram or motion of nanoparticles concentration fronts in the plane of xD-tD Table.2 The summary of suspended, attached and strained nanoparticles concentration along 1-D permea ble medium at the different zones in distance-time diagram Zone

Suspended concentration

Attached concentration σ NP

Strained concentration S NP

I

0

0

0

II

C0 exp ( − ( λad + λs ) LxD )

λa C0φ L ( t D − xD ) exp ( − ( λad + λs ) LxD )

III

 − ( λad + λs ) L ×               xD − ( tD − xD )   x t x − −      D ( D D ) λ φ C 0 ad   σ NP,max1 exp  − ( λad + λs ) L  ×  C0 exp   λadφC0    ( λad + λs ) σ NP,max1    ×      ( λad + λs ) σ NP,max1   1      + 1  (λ + λ ) L     + ad s        ( λad + λs ) L    

λs C0φ L ( t D − xD ) exp ( − ( λad + λs ) LxD )

λs C0φ L ( tD − xD ) exp ( − ( λad + λs ) LxD )

IV

C0 exp ( −λs LxD )

σ NP ,max1

λs C0φ L ( tD − xD ) exp ( −λs LxD )

V

0

σ NP ,max 2

λs C0φ L ( t D1 − xD ) exp ( −λs LxD )


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Fig.3 shows the effluent history of dimensionless NSP nanoparticles concentrations, which is defined as the ratio of effluent nanoparticles concentration to the injected concentration. First, the case with 0.05 wt.% NSP has the earliest breakthrough of nanofluid, reaches the steady state of nanofluid effluent. The 0.05 wt. % case has the least amounts of NSP nanoparticles loss caused by the adsorption and straining effects of nanoparticles. Indicated by the different levels of effluent concentration at the steady-state plateau, as the injected nanoparticles concentration increases, there are more nanoparticles to be retained by the pore surfaces, and the breakthrough of nanofluid is also delayed. A “tail” of nanofluid effulent curve during post-flush of brine indicates the detachment of absorbed nanoparticles, also referred as reversible nanoparticles adsorption. Moreover, the non-symmetric features of nanofluid effluent history between the early injection phase and the later post-flush phase indicates that there are limited amounts of absorbed nanoparticles to detach during post-flush of brine.

Fig. 2 Pressure drop of NSP during nanofluid and post-flush brine injection

Fig. 3 Effluent concentrations of nanoparticles NSP curves for oil-wet cores

The calculated values of permeability from pressure drops both before the nanofluid injection and after post-flush of brine are compared in Table.3. The permeability reduction is characterized by a ratio between those two values for the cases of different injection concentrations. As the injected ACS Paragon Plus Environment

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nanoparticles concentration increases, the damage of core permeability is enhanced. The last column of Table.3 lists the values of permeability damage using analytical solutions. The comparisons between the last two columns indicates the accuracy of the mechanistic models. Table. 3 Permeability of core plugs during NSP nanofluid injection Concentration, wt.%

Lab experimental results

Analytical model

Pre-injection K1, mD

After post-flush, K2, mD

K2/K1

K2/K1

0.05

327

86

0.263

0.212

0.2

362

42

0.116

0.010

0.5

526

33

0.063

0.068

Quantification of Nanoparticles Adsorption, Straining and Detachment Behavior To quantify the nanoparticles adsorption behavior, we first follow the workflow described in Fig.4: Indicated by the nanoparticles effluent history (Fig.3), we find the λs by using the peak value of nanoparticles concentration(Eq.28). We can directly combine Eq. 21b into Eq.25b and have just one unknown parameter tcr left in Eq.34. The tcr can also easily be determined by the infection points from the effluent history. To obtain the only unknown, λad, a trial and error algorithm is applied by calculating Eq.34 to best-fit effluent history.  C NP ,eff   L ( λad + λs ) + 1 1 (34) = exp  − ( λad + λs ) L  xD − ( tD − xD ) +   C NP , inj L ( λad + λs )( tcr − 1) ( λad + λs ) L     Followed by, σmax1 during nanoparticles injection can be quantified by substituting both λad and λs into Eq.25b. The σmax2 during post-flush is determined using Eq.31 after knowing the breakthrough time of post-flush brine, ∆t2 . In addition, nanoparticles adsorption will not increase any more tcr. Hence, in the range of time, ∆t1, the increase of pressure drop can only be attributed to the nanoparticles straining effects. Substituting Eq.28 into Eq.33, we can obtain the increase of pressure drop for the range of ∆t1, as shown in Eq.35. Using Eq.35, the formation damage coefficient βs is determined, and then find βa by matching Eq.33 with the pressure drop curve. Fig.5 compares the results of nanoparticles effluent concentration history and pressure drop calculated from analytical models and lab experiment results, respectively. The excellent agreement with lab experiment results help quantify the mechanistic parameters for nanoparticles adsorption, straining and detachment behaviors. Finally, we determine series of parameters which describe nanoparticles adsorption, straining and detachment behavior, including the maximum adsorption, reversible adsorption, nanoparticles adsorption and straining rates, formation damage coefficients βa and βs, as summarized in Table.4. 1

∆p1 = ∫ 0

ULµβ s λs C0φ L∆t D exp ( −λs L )

( kintrinsic krw )0

dxD


(35)

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Fig.4 Workflow to quantify nanoparticles adsorption & detachment behavior using analytical model and experimental data

Fig. 5 The match between nanoparticles effluent history obtained from analytical models with experimental results


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Fig. 6 Comparison between nanoparticles pressure drop obtained from analytical models and lab experimental results

Indicated by Table.4, as the injected nanoparticles concentration increases, the maximum nanoparticles adsorption amounts are enhanced (the solid line in Fig.7). The detachment of reversible adsorbed nanoparticles occurs during the post-flush of brine. The amount of reversible adsorption also increases along with the increase of the injected nanoparticles injection concentration (the dash line in Fig.7). In addition, the average percentage of reversible adsorption is approximately 30% of the maximum adsorption. In other words, there is only 70% of nanoparticles adsorption amount to be retained in a stable manner. As shown in Fig.8, moreover, the nanoparticles adsorption and straining rates are also functions of injected nanoparticles concentrations. The higher the injected nanoparticles concentration is, the larger the nanoparticles adsorption and straining rates will be. In general, the adsorption rates of nanoparticles are larger than nanoparticles straining rates.

Fig.7 Effects of injected nanoparticles concentration on the maximum adsorption concentration, maximum-irreversible adsorption, and the reversible adsorption of nanoparticles


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Table.4 Summary of nanoparticles adsorption, straining & detachment behavior for the cases of different nanoparticles injected concentrations NSP 0.05 wt. % σ NP , max 1

4.5×10

σ NP , max 2

2.9×10-3 1.6×10-3 0.34 15~20 1.3 100 2500

σdetach Reversible adsorption ratio λad λs βa βs

-3

NSP 0.2 wt. %

NSP 0.5 wt. %

-2

7.7×10-2

1.4×10-3 0.7×10-2 0.33 20~25 1.9 20 900

5.8×10-2 1.9×10-2 0.26 25~30 2.8 20 250

2.1×10

Fig.9 shows the formation damage coefficients for both nanoparticles adsorption and straining effects. It explains the increase of pressure drop during the phase of nanoparticles injection. As the injected nanoparticles concentration increases, the filtration coefficients for both effects decrease, correspondingly. In opposite to the relations between nanoparticles adsorption and straining rate, the formation damage coefficient of nanoparticles straining is much larger than that of nanoparticles adsorption, and hence the nanoparticles straining dominates the increase of pressure drop.

Fig.8 Effects of injected nanoparticles concentration on the adsorption and straining rates

Fig.9 Effects of injected nanoparticles concentration on the formation damage coefficient attributed to nanoparticles adsoprtion and straining


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CONCLUSIONS AND SUMMARY This paper provides series of experimental studies and mathematical modeling works to quantify the reversible/irreversible adsorption and straining behaviors of hydrophilic nanoparticles and their effects on the properties of oil-wet cores. The main outcomes of this study include: • An analytical model coupled the classical filtration theory with the maximum retention concentration model is confirmed effectively to characterize nanoparticles adsorption and straining phenomenon. • As the injected nanoparticles concentration increases, the breakthrough of NSP Nanofluid is delayed, and the maximum/reversible adsorption of nanoparticles are enhanced. • There is a positive correlation between the rates of nanoparticles adsorption & straining and the injected nanoparticles concentrations. In general, the adsorption rates are larger than straining rates. • The formation damage coefficients of nanoparticles straining are usually larger than that of nanoparticles adsorption, and the decrease of formation permeability is dominated by nanoparticles straining leading to the increase of pressure drop. AUTHOR INFORMATION Corresponding author* E-mail: [email protected]; Telphone: +01-405-3975288 Notes: The authors declare no competing financial interest. ACKNOWLEDGEMENT The authors thank the lab and technical support from Norwegian University of Science and Technology, Norway and Coven energy LLC., USA. We gratefully appreciate Dr. Ole Torsæter and Dr. Shidong Li for their kind advising and contributions in the part of lab experiments, which lead to the substantial improvement of this paper. Garth McLoed provided editing services. NOMENCLATURE CNP = CNP,inject, C0 = SNP = λs = λad = φ = L= A= σ NP = σ NP ,max1 = σ NP ,max 2 = xD = tD = tDc = tD1 = rNP= µ= qinj = rNP= rp = Fe = y= χ=

Volumetric concentration of adsorbed nanoparticles with respect to pore volume, m3/m3 Volumetric concentration of injected nanoparticles with respect to pore volume, m3/m3 Volumetric concentration of Straining nanoparticles with respect to pore volume, m3/m3 Straining filtration coefficient Adsorption filtration coefficient Porosity of core plug Length of core plug Cross-section area of core plug Volumetric concentration of retained nanoparticles with respect to bulk volume, m3/m3 Maximum retention concentration of nanoparticles at the phase of nanoparticles injection, m3/m3 Maximum retention concentration of nanoparticles at the phase of post-flush, m3/m3 Dimensionless distance Dimensionless time or injected pore volume Dimensionless time or injected pore volume when reaching maximum nanoparticles concentration Dimensionless time or injected pore volume start to post-flush without nanoparticles Radius of nanoparticles, m Fluid viscosity, Pa.s Fluid injection rate, ml/min Radius of nanoparticles, m Pore radius, m Electrostatic forces, N Ratio between drag and electrostatic force Lifting force coefficient ACS Paragon Plus Environment

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ρ= ∆ρ = ρw = ρNP = ∆t D1 = K1,2 = β1 = βs = ∆p =

Fluid density, kg/m3 Density difference between particles and fliud, kg/m3 Water fluid density, kg/m3 Nanoparticles fluid density, kg/m3 Range of time for steady-state effluent nanoparticles concentration Intrinsic permeability of core plug before and after core-flood, mD Formation damage coefficient related to nanoparticles adsorption Formation damage coefficient related to nanoparticles straining Pressure drop, MPa

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