Numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes

Accepted Manuscript Numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes Huijuan Chen, Qinfeng di, Feng Ye, Chunyuan Gu, Jingnan Zhang PII:

S1875-5100(16)30700-4

DOI:

10.1016/j.jngse.2016.09.060

Reference:

JNGSE 1836

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 26 March 2016 Revised Date:

22 September 2016

Accepted Date: 22 September 2016

Please cite this article as: Chen, H., di, Q., Ye, F., Gu, C., Zhang, J., Numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes, Journal of Natural Gas Science & Engineering (2016), doi: 10.1016/j.jngse.2016.09.060. 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.

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40 Before injecting the HNPs

After injecting the HNPs

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Pressure/MPa

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Simulated BHP Measured WHP

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Calculated BHP

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Time/month

Nanoparticles adsorption on the rock surface

Water injection pressure decreases by 12.5MPa after the nanoparticles adsorption

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Numerical simulation results agree well with the measured data

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Numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes Huijuan Chen a, b, Qinfeng Di a, b,*, Feng Ye a, b, Chunyuan Gu a, b,*, Jingnan Zhang a, b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

b

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a

Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China [email protected] (Huijuan Chen) [email protected] (Qinfeng Di)

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[email protected] (Feng Ye) [email protected] (Chunyuan Gu)

*Corresponding authors

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[email protected] (Jingnan Zhang)

Tel.: +86-21-56333256 (Qinfeng Di) Fax: +86-21-56331961 (Qinfeng Di) Email: [email protected] (Qinfeng Di)

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Address: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 149 Yanchang Road, Shanghai, 200072, China Tel.: +86-13482354545 (Chunyuan Gu) Fax: +86-21-56331961 (Chunyuan Gu)

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Email: [email protected] (Chunyuan Gu) Address: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,

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149 Yanchang Road, Shanghai, 200072, China

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Abstract: The drag reduction technology by nanoparticles adsorption method has been developed to effectively reduce the water injection pressure, enhance the injection rate, and partially protect the formation from the damage during water flooding processes of low permeability reservoirs. However, there is a lack of an effective method to simulate the drag reduction effects on the scale of oilfields. In this study, the slip velocity model in the reservoir microchannels caused by nanoparticles adsorption onto the porous wall is firstly presented based on fluid dynamics theory. The relationship between the effective permeability of water phase and the slip length is established by combining the slip velocity model with Darcy’s law. Then, a three-dimensional, two-phase model (water, oil) is developed to simulate the drag reduction effects, and the procedures for solving this model are described. Based on a water injection well pattern in Jiangsu oilfield, experimental tests on the adsorption behavior of hydrophobic nanoparticles (HNPs), the wettability changes on the core surface, and the core displacement as well as the numerical simulation of the drag reduction effects of the HNPs adsorption method are conducted. The experimental results show that HNPs can be adsorbed tightly onto the surface of the sample slice of the core from the oilfield, and the surface wettability of the sample slice is changed from hydrophilic to hydrophobic. The effective permeability of water phase increases by 130% after the nanoparticles are adsorbed onto the porous walls of the core sample’s microchannels. The field test shows that the operation pressure of the water injection well decreases by 12.5 MPa and the effective period of the nanoparticles adsorption method is approximately 12 months. The simulation results show that the method promoted in this paper can be used effectively to simulate the drag reduction effect and agree well with the field test results during the whole water injection process when the formation damage near the wellbore is taken into account in the numerical simulation. Moreover, the adsorption of HNPs onto the porous wall slows down the formation damage to some extent. This work may serve as an efficient tool for simulating drag reduction effects owing to the adsorption of HNPs on the oilfield scale. Keywords: drag reduction, hydrophobic nanoparticles adsorption, slip effect, numerical simulation, water flooding

1. Introduction

Water flooding is the main method used in the development of low permeability reservoirs and it has been used widely in China. The prevailing problem is that a lot of injection wells face to high injection pressure in a given injection rate or a low injection rate in the designed injection pressure. One reason is that the reservoir formation in the vicinity of the injection well is always damaged due to the poor quality of the injection water, velocity sensitivity, and water sensitivity, etc., which may block the pores or throats by filling them with solid particles, resulting in a decrease in the reservoir permeability and an increase in the injection pressure. To efficiently solve this problem, well stimulations, such as acidification and fracturing, have been used to remove blockages near the wellbore to eliminate the formation damage, but the effective period of these stimulations are short. Another reason is that

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the initial oil-wet microchannels of the reservoir near the water injection well may become water-wet and lead the injection pressure to increase during the water flooding process. In this case, the surface modification methods including drag reduction by surfactants and by hydrophobic nanoparticles (HNPs) can be applied to decrease the water injection pressure and enhance the water injection rate, thereby preventing the formation from damage by modifying the wettability of the reservoir rocks. In recent years, the applications of nanotechnology in enhancing oil recovery have drawn much attention. The capabilities of nanoparticles to alter the wettability of the reservoir rock and reduce the interfacial tension between crude oil and brine phase have been actively investigated (Ju et al., 2002; Ju and Fan, 2009; Roustaei et al., 2013; Parvazdavani et al., 2014; Zargartalebi et al., 2015; Moradi et al., 2015). Ju et al. (2002) and Ju and Fan (2009) considered that the mechanism for enhancing water injection came from improving the relative permeability of water phase by changing the wettability induced by the adsorption of polysilicon onto the porous surface of sandstone. On this basis, they presented a one-dimensional, two-phase mathematical model with consideration of the migration and adsorption of hydrophobic and lipophilic polysilicon and the change of wettability in reservoir rock. Onyekonwu and Ogolo (2010) studied the capabilities of three different polysilicon nanoparticles as agents for wettability alteration and oil recovery. El-Amin et al. (2012, 2013 a, b, c, 2015) developed a mathematical model and numerical simulation to describe the imbibition of nanoparticles-water suspension into two-phase flow in a porous medium. The model included general formulae for both positive/negative capillary pressure and mixed relative permeability correlations to fit with the mixed-wet system. Moreover, buoyancy and capillary forces, as well as Brownian diffusion and mechanical dispersion, were also included in the mathematical model. Ryoo et al. (2012) performed a theoretical and experimental investigation of the motion of multiphase fluids containing paramagnetic nanoparticles in porous media. Roustaei et al. (2013) evaluated the efficiency of modified silica nanoparticles in enhancing oil recovery of light and intermediate oil reservoirs by experiment. They found that the modified silica nano-fluid improved oil recovery principally through the mechanisms of interfacial tension reduction and wettability alteration toward oil-wet condition. Salama et al. (2015) used the multipoint flux approximation to numerically investigate the transport of nanoparticles in anisotropic porous media. Yuan et al. (2015, 2016 a, b, c, d) developed an analytical model to study the interplay between adsorption of nanoparticles and their geochemical effects on fines migration and the consequent sand production. Gu et al. (2007) and Di et al. (2010) conducted a series of experiments on the adsorption and distribution of HNPs at the core surface under a scanning electron microscope (SEM) as well as on changes in the surface wettability and core permeability. Based on these results, they proposed that the decompression and enhancement of water injection resulted from the considerable slippage effects of the super-hydrophobic nanomaterial layer induced by the adsorption of HNPs. In their work, the slip effect, which was proposed by Navier early in 1823, was found to be the important mechanism of the drag reduction.

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2. Model description

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Many researchers studied the slip effect with experimental and simulation methods. Choi et al. (2003) experimentally investigated the slip effects of water flow in hydrophilic and hydrophobic microchannels, and found the slip length varied approximately linearly with the flow shear rate. Zhu et al. (2005) described the numerical simulation of the fluid slip on hydrophobic microchannel walls using the single phase lattice Boltzmann method. Zhang et al. (2010, 2012) and Di et al. (2015) used the lattice Boltzmann method and the support-vector machine algorithm to calculate the drag reduction and slip length induced by HNPs adsorption. However, the drag reduction effects on the oilfield scale caused by nanoparticles adsorption were not investigated in the above studies and there is a lack of methods for simulating such a problem. The main objective of this work is to develop a novel simulation method to evaluate the drag reduction effects of the nanoparticles adsorption method on the scale of oilfields. We first briefly described the mechanism of the drag reduction effect caused by nanoparticles adsorption onto the porous wall, and then the relationship between the effective permeability of water phase and the slip length was established. A three-dimensional, two-phase model (water, oil) was developed to simulate the drag reduction effects. Based on a water injection well pattern in China’s Jiangsu oilfield, a series of experiments were firstly conducted to validate the mechanism, and then the drag reduction effect of the injection well was simulated through the proposed method.

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Water flooding in low permeability reservoirs can be regarded as the displacement of the oil by water, and this process has always been conducted for a period before the HNPs are injected, so the mobile oil near the water injection well has almost been displaced away. Therefore, there only exists water flow in the vicinity of the water injection well after HNPs are injected into the formation and adsorbed onto the porous walls. The adsorption of HNPs forms a stronger hydrophobic nanoparticles layer that exerts a slip effect on the fluid flow, resulting in a large increase in the flow velocity and flow rate (Gu et al., 2007; Di et al., 2010; Yu et al., 2015). Based on this mechanism, we firstly present a slip velocity model in the reservoir microchannels caused by nanoparticles adsorption according to fluid dynamics theory. Subsequently, the relationship between the effective permeability of water phase and the slip length is established by combining the slip velocity model with Darcy’s law. On this basis, a three-dimensional, two-phase model (water, oil) to simulate the drag reduction induced by the nanoparticles adsorption is developed. The procedures for solving this model are also described. 2.1 Slip velocity model The reservoir microchannels can be approximated as capillary tubes with the same diameters. Fluid velocity models of a single capillary tube before and after HNPs adsorption are shown in Fig. 1. Note that u and uh indicate the fluid velocity before and after HNPs adsorption, and r0 and r0λ indicate the radius of the capillary tube before and after HNPs adsorption. Before HNPs adsorption, the fluid velocity on the boundary is zero as shown in Fig. 1 (a). As HNPs with a diameter dp are absorbed

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onto the porous walls, the slip effect occurs and the boundary velocity changes to a nonzero value. This nonzero velocity is termed the slip velocity, denoted by u0; accordingly, the zero velocity boundaries are extended. The enlarged radius is termed the slip length and denoted by λ (Botan et al., 2011; Bhushan, 2011; Wang et al., 2016), as shown in Fig.1 (b).

uh x

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(a) Before HNPs adsorption (b) After HNPs adsorption Fig. 1 Sketch of the velocity model before and after HNPs adsorption

The fluid flow in the reservoir microchannels can be described by fluid dynamics. Based on Hagen-Poiseuille theory, the flow velocity and flow rate before HNPs adsorption can be respectively expressed as follows: ∇P 2 u=− r0 − r 2 (1) 4µ

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q = ∫ A udA = −

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πr04 ∇P 8µ

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where P is the pressure. µ is the fluid viscosity. r0 is the radius of the capillary tube before HNPs adsorption. q is the fluid flow rate before HNPs adsorption, and A is the cross-sectional area of the capillary tube before HNPs adsorption. After HNPs adsorption, the radius of the capillary tube changes to r0λ, and can be written as

r0λ = r0 - dp

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where dp is the average diameter of the nanoparticles. Because of the slip effect, the slip velocity is nonzero and the flow rate after the adsorption of HNPs can be given as πr04λ qh = ∫ Ah u h dAh = − ∇P + πr02λ u0 (4) 8µ where qh is the fluid flow rate after HNPs adsorption, and Ah is the cross-sectional area of the capillary tube after HNPs adsorption. Furthermore, the zero boundary after HNPs adsorption enlarges to r0λ + λ as a result of the slip effect. The slip velocity can be expressed as (Yu et al., 2015)

u0 = u r =r0 λ = −λ

∂u ∂r

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r0λ λ ∇P 2µ

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Substituting Eq. (5) into Eq. (4), the flow rate after HNPs adsorption can be

ACCEPTED MANUSCRIPT obtained. Thus, the increase in the flow rate of the multi-capillary tubes, ∆Q, can be calculated by ∆Q = n∆q = n(qh − q )

 πr 4  λπr03λ πr 4 = n − 0λ ∇P − ∇P + 0 ∇P  (6) 2µ 8µ  8µ  nπ =− ∇P r04λ + 4λr03λ − r04 8µ where n is the number of capillary tubes. The radius of the sorption area for nanoparticles adsorption method is only about 2-3 m in the vicinity of the water injection well. The mobile oil in this area has been displaced away, and there mainly exists water flow which can be described by Darcy’s law. Therefore, the increased flow rate can be given by  k nπr 2  k nπr 2 ∆Q = − rw 0 ∇P −  − rw 0λ ∇P  (7) µφ µφ h   where kw and kwh indicate the effective permeability of water phase before and

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[

after HNPs adsorption, respectively. φ and φh indicate the porosity before and after HNPs adsorption, respectively, which can also be described as nπr02 L φ= = Vf Vf Vp

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φh =

nπr02λ L Vf

(8)

(9)

where V p and Vph are the pore volume before and after HNPs adsorption,

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respectively. Vf is the total volume of the rock. L is the length of the capillary tube. Comparing Eqs. (8) and (9) yields the following equation: Vf nπr02 nπr02λ = = (10) L φ φh Substituting Eq. (10) into Eq. (7), the following expression can be obtained:

∆Q = −

(k wh − k w )nπr02 µφ

∇P

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Then the following equation can be got by comparing Eqs. (6) and (11) :

kwh − kw =

φ

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(12) 8r The permeability, as a function of the capillary tortuosity, can be described using the Kozeny–Carman equation (Kozeny, 1927; Carman, 1937) φr02 k= (13) 8τ where k is the absolute permeability of the reservoir, and τ is the tortuosity of the capillary tube with a value ranging from 1.5 to 2.5. Substituting Eq. (13) into Eq. (12) yields the effective permeability equation of the 2 0

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water phase after HNPs adsorption: τr 4 + 4τλr03λ − τr04  kw τr04λ + 4τλr03λ − τr04  k wh = kw + k  0λ = k +  w   (14) krw  r04 r04    = kw (1 + Ew ) where Ew is the ratio of the effective permeability changes of water phase after HNPs adsorption to that before HNPs adsorption. By Eq. (14), the microscopic parameters of the slip effect induced by nanoparticles adsorption method can be associated with the macroscopic parameters of the porous media. Thus, the drag reduction effect by the nanoparticles adsorption on the microscopic scale can be described by the improvement of the effective permeability of water phase at the macroscopic scale.

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2.2 Fluid transport model in porous media

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During water flooding process, the governing equations for the two-phase flow of water and oil are used for the fluid transport model in porous media. Considering the gravity effect, the fluid velocity equations for oil and water phases before the HNPs injection can be given by kk vo = − ro ∇(Po − ρ o gD) (15)

µo

vw = −

kkrw

µw

∇(Pw − ρ w gD)

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where vl represents the velocity of phase l. krl represents the relative permeability of phase l. µl represents the viscosity of phase l. Pl represents the pressure of phase l. ρl represents the density of phase l. g is the gravitational acceleration. D is the reservoir depth, and l = o or w represents the oil or water phases, respectively. The mass conservation equations for the oil and water phases can be written as ∂ (ρ o S oφ ) (17) div (ρ o v o ) + =0 ∂t ∂ (ρ w S w φ ) (18) div (ρ w v w ) + =0 ∂t where Sl represents the saturation of phase l. Substituting Eqs. (15) and (16) into Eqs. (17) and (18), respectively, and considering the source terms of the oil and water, the fluid transport equations before the HNPs injection can be obtained:  kk  ∂ ∇ ⋅  ρ o ro ∇(Po − ρ o gD ) + ρ o qo = (ρ o S oφ ) (19) µo ∂t  

  kk ∂ ∇ ⋅  ρ w rw ∇(Pw − ρ w gD ) + ρ w q w = (ρ w S w φ ) (20) µw ∂t   where ql represents the volumetric flow rate per unit volume of phase l. After injecting the HNPs into the porous media, the slip effect is induced by HNPs adsorption, and the effective permeability of water phase within the nanoparticles adsorption area is increased. Therefore, the fluid velocity equation for water phase becomes

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where vwh represents the velocity of water phase within the nanoparticles adsorption area. Substituting Eq. (21) into Eq. (18) yields the following transport equation for water phase within the nanoparticles adsorption area:   kk (1 + E w ) ∂ ∇ ⋅  ρ w rw ∇(Pw − ρ w gD ) + ρ w q w = (ρ w S w φ ) (22) µw ∂t  

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The fluid velocity and transport equation for oil phase within the nanoparticles adsorption area are still given by Eqs. (15) and (19). Moreover, Eqs. (19) and (20) also are used to describe the two-phase flow of oil and water outside of the nanoparticles adsorption area. The fluid saturation and the capillary pressure for water and oil are interrelated by S w + So = 1 (23)

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Pcwo (S w ) = Po − Pw

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where Pcwo (S w ) represents the capillary pressure of the two-phase flow of water and oil. The initial pressure and saturation of the water and oil are defined by

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So t =0 = 1 − S wc

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The outer boundary condition is

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∂P (28) Γ = 0 ∂n The inner boundary condition refers to the well injection rate or production rate and can be expressed as Ql ( x , y , z , t ) x = x

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= Ql (t )

(29)

The equations presented above constitute the fluid transport model for the two-phase flow of oil and water in the porous media. The drag reduction effect by HNPs adsorption can be simulated.

2.3 Solution and simulation procedures In the above models, the parameter Ew is zero before HNPs adsorption, so the models are solved by the implicit-pressure-explicit-saturation (IMPES) method when the parameters of the reservoir and fluid are known. The bottom hole pressure, the reservoir pressure and the saturation of oil and water phases in water flooding process can then be obtained. After injecting the nanoparticles, the parameter Ew is not zero and the effective permeability of water phase increases. In this case, if the effective permeability of water phase after the nanoparticles adsorption is known, the models

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can also be solved by the IMPES method. Thus, a core displacement experiment must be conducted firstly to test the changes of the water phase permeability before and after the nanoparticles adsorption, and then the drag reduction effects of the nanoparticles adsorption method in water flooding process can be simulated. In addition, as the water flooding process is a continuous process, the simulation before and after the HNPs adsorption should be linked up. Therefore, the grid-refinement and restart techniques are introduced to take the nanoparticles adsorption area and the effective permeability changes of water phase into account in the water flooding process.

3. Results and discussion

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Based on a water injection well pattern of a low permeability reservoir in Jiangsu oilfield, the drag reduction effects of HNPs adsorption were investigated using the method mentioned above. The depth of the well pattern ranges from 2,378.2 m to 2,394.2 m, and the reservoir thickness is 16 m. Well-logging data indicate that the reservoir porosity is 10% and the permeability is 4.4 × 10-3 µm2. The water injection data show that the initial value of the injection pressure is 25 MPa, but it increases to 31.5 MPa after injection of 6 months, which is close to the design limit of the injection pressure, 32 MPa, of the pipe network. Thus, drag reduction technology is needed to maintain normal production. To solve the above problem, we performed a series of research on the preparation of the nanomaterials, the adsorption behavior and distribution properties of the HNPs, and the wettability changes on the core surface, as well as core displacement experiments. Pilot nanomaterials were also prepared and applied in a field test. The drag reduction effect induced by HNPs adsorption for the water injection well was simulated and the results were compared with the field test results.

3.1 Experimental results and discussion

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3.1.1 Adsorption behavior and distribution properties of the HNPs

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Experiments were performed to observe the adsorption behavior and distribution properties of HNPs on porous walls. The material of the nanoparticles is SiO2, and their average diameter is 10 nm. Nanoparticles were firstly dispersed evenly to the mixed lipophilic organic solvent containing some surfactant, and then water was added to the solvent to form the aqueous nano-fluid solution. The concentration of the nano-fluid is 0.1 wt.%. A natural sandstone core from the target formation of Jiangsu oilfield was used for the experimental study. The core was cut into slices with a thickness of 1.5–2 mm. A slice was chosen and its microstructure was observed under the SEM as shown in Fig. 2(a). Another slice was immersed in an aqueous nano-fluid solution for more than 24 hours at a constant temperature of 60 , and then removed to observe the microstructure under the SEM as shown in Fig. 2(b). Figs. 2(a) and 2 (b) are the microstructure pictures magnified 3000 and 40000 times, respectively. Fig. 2(a) shows that there are many sheets of clay minerals with clear edges and corners, and the surfaces of many partial areas seem to be smooth. As shown in Fig. 2(b), the HNP-adsorbed surface is entirely covered with ellipsoidal

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nanoparticles that are tightly connected to each other, and there are many continuous papillate dots on it. The HNPs adsorb on not only clays but also sandstone minerals.

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Fig. 2(a) Surface of the raw slice under SEM (×3000 times) (b) Surface of the slice with HNPs adsorption under SEM (×40000 times)

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The reason lies in that the acting forces between the HNPs and the rock surface include multi-hydrogen-bond, Van-der-Waals and electrostatic forces. As a kind of attractive force, the multi-hydrogen-bond and Van-der-Waals force overwhelm the electrostatic forces, which performs the repulsive force (Gu et al, 2011). Therefore, the HNPs can be adsorbed tightly onto the porous wall and distributed continuously and densely on its surface. These features are beneficial for preventing the hydration and inflation of clay, by excluding water from the core, thus avoiding damage to the formation.

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3.1.2 Wettability changes in the core surface

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In order to study the wettability changes in the core surface, the wetting angles of the water drop on the raw slice and the HNP-adsorbed slice were measured at room temperature by an optic contact-angle machine (OCA15), and the results are shown in Fig. 3.

Fig. 3(a) Wetting angle of the raw slice

(b) Wetting angle of the slice with HNP adsorption

Fig. 3(a) shows that the wetting angle of the water drop on the raw slice is 28.8°, which indicates that the core surface is hydrophilic. However, the wetting angle of the water drop on the HNP-adsorbed slice is 137.7°, as shown in Fig. 3(b). This indicates that the wettability of the slice surface changes from hydrophilic to hydrophobic by the adsorption of the HNPs, which is beneficial for injecting water into the formation. 3.1.3 Core displacement experiment

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Many researchers proved that significant slippage occurs at the hydrophobic surface, and the slip length is larger in the hydrophobic surface with the micro-structure or nano-structure than that in smooth surface. (Fukuda et al., 2005; Zhu et al., 2002; Tretheway et al., 2002; Cottin-Bizonne et al., 2003; Choi et al., 2003; Jia et al., 2004). The adsorption of the nanoparticles and the wettability changes above provide the necessary condition for the occurring of slip effect, but they can not verify the drag reduction effect, which can be tested with a core-displacement experiment (CDE). Therefore, a CDE was conducted to investigate the changes of the effective permeability of water phase before and after the nanoparticles adsorption and also to evaluate whether the flow resistance decreased. Another natural sandstone core from the target formation of Jiangsu oilfield was used for the laboratory experiment, with a diameter of 25 mm and a length of 6.348 cm. Chinese industrial criterion of SY/T 5345-2007 named “Test method for two phase relative permeability in rock” was adopted, and the displacement apparatus was listed in our previous publication (Gong et al, 2013). The experimental process was conducted at the temperature of 50 and the procedures were as follows: (1) Extract the core by benzene until no hydrocarbons are present in it, and then dry it in the oven. (2) Saturate the core with 3 wt. % NH4Cl aqueous solution. (3) Drive diesel oil into the core until the outflow contains no water. (4) Drive deionized water into the core at a constant rate of 2.0 mL/min until the outflow contains no oil, and then record the fluid flow rate and overall differential pressure. (5) Drive an aqueous nano-fluid with ten times the pore volume (PV) into the core, and then stop this driving and shut all valves for approximately 24 hours. (6) Drive deionized water into the core, and then record the fluid flow rate and the overall differential pressure. The effective permeability of water phase was calculated by Darcy’s law. The results show that the effective permeability of water phase before and after nano-fluid injection are 1.58 × 10−3µm2 and 3.64 × 10−3µm2, respectively. The increased effective permeability of water phase divided by the effective permeability of water phase before nano-fluid injection, that is, the increased ratio of the effective permeability is about 130%, which indicates that the flow resistance in the rock’s microchannels decreases after the injection of HNPs. Based on the above experiments, further pilot nanomaterials were prepared and another core was selected for repeat experiments to validate the reliability of the results. Subsequently, the pilot nanomaterials were applied in the field test.

3.2 Field test A field test of a water injection well was performed based on the above experimental study and the procedures were as follows: (1) Design the amount of the nano-fluid solution and the acid. The treatment area is 3 m around the water injection well and the amount is its pore volume. (2) Inject the acid at a constant rate of 0.5 m3/min into the target formation to make

ACCEPTED MANUSCRIPT it pretreatment. (3) Inject clear water to displace the acid. (4) Inject the nano-fluid solution at a constant rate of 0.4 m3/min into the target formation. (5) Shut in the well for 2 days and then open it to inject water. The test results are recorded as shown in Fig. 4.

30

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25

25

After injecting the HNPs

20 Before injecting the HNPs

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Water injection rate/(m3/d)

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Injection pressure Water injection rate

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Fig. 4 Water injection performance before and after injection of the HNPs

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Fig. 4 shows that the injection pressure of the water injection well markedly reduces from 31.5 MPa to 19.0 MPa after the HNPs were injected into the microchannels of the target formation, and it then gradually increases as the water injection process continued. However, after the HNPs injection, the injection pressure over the next 12 months are all lower than that before the HNPs injection (month 6), whereas the water injection rates have no obvious changes and they are all almost 30 m3/d except an anomalous point at month 18, which is caused by many field factors. Moreover, the apparent water injectivity index (AWII), which is the ratio of the water injection rate divided by the injection pressure, was calculated as shown in Fig.5.

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1.4

After injecting the HNPs

1.2

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AWII/(m3/(d.MPa))

1.3

1.1 1.0

Before injecting the HNPs

0.9 0.8

0

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6

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10

12

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16

18

20

Time/month

Fig. 5 Apparent water injectivity index changes

Fig.5 shows that the apparent water injectivity index increases from 0.966 m /(d.MPa) to 1.256 m3/(d.MPa) after the HNPs injection, and the AWII over the next 12 months are all higher than that before HNPs adsorption (month 6) except an 3

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3.3 Numerical simulation

Water injection well

Oil well

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Oil well

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A reservoir numerical simulation model of the well pattern was established based on the pattern’s geological and development characteristics. The structure diagram of the well pattern is shown in Fig. 6. The simulated area of the pattern, which contains one water injection well and two oil production wells, is 430 m × 290 m × 16 m, and is discretized into 43 × 29 × 3 = 3,741 grid blocks in the (x, y, z) directions. Moreover, the distance between the water well and the two oil wells is 187 m and 237 m, respectively. The water injection and liquid production rates of the two oil wells are all set to the field test values.

Fig. 6 Structure diagram of the well pattern

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The grid in which the water-injection well is located was refined to contain 11 × 11 blocks in the (x, y) direction, to reflect the nanoparticles adsorption area, as shown in Fig. 7. The blue area represents the nanoparticles adsorption area. After injecting the HNPs into the formation, the effective permeability of water phase in the blue area increased by 130% according to the experiment results.

INJ

Fig. 7 Grid of the water injection well located in

During the water flooding process, reservoir formation in the vicinity of the

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injection well always be damaged as a result of the poor quality of the injection water, reservoir velocity, water-sensitivity phenomena, and so forth. Thus, in order to simulate the drag reduction effects and assess the impairment of the formation near the water injection well, two cases were simulated based on the numerical simulation model presented above. The effective permeability of water phase for the two cases all increased by 130% after injecting the HNPs into the formation through restart technology. However, in case 1, the formation damage near the injection well was not considered and the permeability near the wellbore was regarded as constant during the water injection process. In case 2, the permeability changes near the water injection well during the whole water injection process were considered, and were modified dynamically using the restart technique to enforce agreement between the simulation results and the field test results. The relative permeability curves of oil and water phases are shown in Fig. 8, and the permeability changes near the water injection well for the two cases are shown in Fig. 9. 1.0

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Fig. 8 Relative permeability curves of oil and water phases

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Permeability/(10-3µm2)

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Fig. 9 Permeability changes near the water injection well

The simulated bottom hole pressure (BHP) of the water injection well in case 1 is shown in Fig. 10. Based on the simulated BHP, the wellhead pressure (WHP) was calculated using vertical flow theory and the results were compared with the field test results, as shown in Fig. 10. The changes in permeability near the wellbore and the

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simulated results for case 2 are shown in Figs. 9 and 11. In Fig. 10, the calculated values of WHP for case 1 both before and after the injection of HNPs into the formation are all lower than the measured BHP, and the average error between the calculated results and field test results is 11.55%. However, the calculated values of WHP for case 2 agree well with the field test results during the whole water injection process, with an average error of 3.68%, as shown in Fig. 11. This indicates that formation damage near the wellbore should be taken into account in the numerical simulation. 60

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Fig. 10 Pressure variation of the water injection well (case 1) 60

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Fig. 11 Pressure variation of the water injection well (case 2)

Figs. 9 and 11 also show that the permeability near the water injection well decreases markedly with the increase in water injection time before injecting the nanoparticles into the formation, which indicates that the formation is severely damaged, resulting in increased bottom-hole pressure and wellhead pressure. After injecting the nanoparticles into the formation, the bottom-hole pressure and wellhead pressure all remarkably decrease by 12.5 MPa as a result of the slip effect and wettability changes in the pore wall surfaces of the formation induced by the nanoparticles adsorption. As the water injection proceeded, the reservoir permeability near the wellbore decreases once again, but the extent of the decrease is smaller than that before the injection of the nanoparticles, which indicates that the HNPs adsorption slows down the formation damage from the subsequent water injection to some extent.

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4. Conclusions

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(1) The relationship between the effective permeability of the water phase and the slip length is established, which effectively associates the microscopic parameters of the slip effect induced by nanoparticles adsorption with the macroscopic parameters of the porous media. (2) The experimental results show that HNPs could be adsorbed tightly onto the surface of the core slice, and the wettability of the sample surface changes from hydrophilic to hydrophobic after HNPs adsorption. The effective permeability of the water phase after injecting the nano-fluid into the microchannels is increased and the increased ratio is about 130%. (3) The mathematical model presented in this paper can be used to successfully simulate the drag reduction effects of HNPs adsorption, and the simulation results agree well with those of the field test with considering the damage to the formation near the wellbore. Both the simulation and the field test show that the water injection pressure decreases by 12.5 MPa and the effective period of the nanoparticles adsorption is approximately 12 months. (4) The adsorption of HNPs onto the porous wall of the formation can slow down the formation damage from the subsequent water injection to some extent.

Nomenclature

Ah D

kw

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g k

EP

dp Ew

kwh

kro krw L

n

cross-sectional area of the capillary tube before HNPs adsorption, m2 cross-sectional area of the capillary tube after HNPs adsorption, m2 depth, m nanoparticles diameter, m ratio of the effective permeability changes of the water phase after HNPs adsorption to that before the HNPs adsorption gravitational acceleration, m/s2 reservoir permeability before HNPs adsorption, 10-3µm2 effective permeability of water phase before HNPs adsorption, 10-3µm2 effective permeability of water phase after HNPs adsorption, 10-3µm2 relative permeability of oil, fraction relative permeability of water, fraction length of capillary tube, m number of the capillary tubes

TE D

A

Po Pw Pi q qh

oil pressure, Pa water pressure, Pa initial pressure of the reservoir, Pa fluid flow rate, m3/s fluid flow rate after the HNPs adsorption, m3/s ∆Q increased flow rate of the multi-capillary tubes after the HNPs adsorption, m3/s qo volumetric flow rate of oil per unit volume, m3/(s.m3) qw olumetric flow rate of water per unit volume, m3/(s.m3) r0 radius of the capillary tube before HNPs adsorption, m r0λ radius of the capillary tube after HNPs adsorption, m So oil saturation, fraction Sw water saturation, fraction Swc irreducible water saturation, fraction t time, s u fluid flow velocity before HNPs adsoption, m/s

u0 vo vw vwh Vf Vp Vph

fluid flow velocity after HNPs adsoption, m/s slip velocity, m/s oil velocity, m/s water velocity, m/s water velocity within the nanoparticles adsorption area, m/s total volume of the rock, m3 pore volume before HNPs 3 adsorption, m pore volume after HNPs adsorption, m3

Greek symbols porosity before HNPs adsorption, fraction

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φ

φ h porosity after HNPs adsorption,

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EP

TE D

fraction µ fluid viscosity, Pa.s µo oil viscosity, Pa.s µw water viscosity, Pa.s ρo oil density, kg/m3 ρw water density, kg/m3 τ tortuosity of capillary, 1.5-2.5

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Acknowledgements This research is supported partly by the National Science Funding of China (U1663205, 50874071, 51274136), the Key Program of Science and Technology Commission of Shanghai Municipality (071605102), Shanghai Leading Academic Discipline Project (S30106), and the Shanghai Municipal Education Commission (Peak Discipline Construction Program).

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Slip velocity model in reservoir microchannels caused by HNPs adsorption is presented. A 3D two-phase model is developed to simulate the drag reduction effects. Effective permeability of water phase after HNPs adsorption increases by 130%. Water injection pressure after nanoparticles adsorption decreases by 12.5 MPa. Nanoparticles adsorption onto the porous wall can slow down the formation damage.

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