Study on the Plugging Performance of Bilayer-Coating Microspheres

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Thermodynamics, Transport, and Fluid Mechanics

Study on the plugging performance of bilayer-coating microspheres for indepth conformance control: Experimental study and mathematical modeling Tingting Cheng, Jirui Hou, Yulong Yang, Zhenjiang You, Yang Liu, Fenglan Zhao, and Jun Li Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 25, 2019

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Industrial & Engineering Chemistry Research

1

Study on the plugging performance of bilayer-coating

2

microspheres for in-depth conformance control: Experimental

3

study and mathematical modeling

4

Tingting Chenga, Jirui Houa, Yulong Yang*a, Zhenjiang Youb, Yang Liuc,

5

Fenglan Zhaoa, Jun Lic

a Unconventional

6

Beijing, 102200, China

7

b School

8

of Chemical Engineering, The University of Queensland, Brisbane QLD 4072, Australia

9

10

Petroleum Research Institute, China University of Petroleum,

c College

of Petroleum Engineering, China University of Petroleum, Beijing, 102200, China

11

*

To whom all correspondence should be addressed.

Email: [email protected] (Yulong Yang)

1

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT

2

Microparticles covered with double-layered coatings are developed for in-depth

3

conformance control to enhance oil recovery within heterogeneous reservoirs. The

4

proposed bilayer-coating microspheres (BCMS) can transport deeply into porous media,

5

owing to the rigid outer layer designed for protecting the adhesive inner coating. The

6

objective of the present work is to characterize the adhesion property and the plugging

7

behavior of BCMS at reservoir temperature and fluid salinity. A series of static and

8

coreflood tests are conducted. BCMS exhibits resistance to high temperature and high

9

salinity and shows a great ability of deep transport into porous media. A mathematical

10

model for the deep-bed filtration of BCMS in porous media is developed, accounting

11

for the limited retention concentration and the velocity difference between the

12

suspended particles and the carrier fluid. Modeling results match the measured pressure

13

drop histories in coreflood tests with high accuracy, which validates the proposed

14

analytical model. BCMS shows promising potential for application in production

15

enhancement in hydrocarbon reservoirs.

16

1. INTRODUCTION

17

Reservoir heterogeneity may result in an undesirable water channeling and early water

18

breakthrough during water flooding in enhanced oil recovery, leading to a reduction in

19

hydrocarbon production and an increasing cost caused by scale, corrosion, water/oil

20

separation, etc.1-3 Microspheres are widely applied within a heterogeneous formation

21

to reduce the permeability of layers with high permeability and divert the injected fluid

22

into the untapped-oil zone with relatively low permeability (so-called “conformance

23

control”).4-7

24

The injected particles can be captured in porous media by several mechanisms,8-9 for

25

example, straining (size exclusion), attachment, bridging, sedimentation, etc. (Figure

26

1). It is recognized that strained or bridged particles cause more severe permeability

27

reduction of porous media, compared with particles attached to the surface.10-12

28

Therefore, the effectiveness of particle plugging at pores or fractures under reservoir 2


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1

conditions is one of the crucial factors to the success of conformance control

2

technologies.

3 4

Figure 1. Schematic of particle capturing mechanisms: straining, bridging, and

5

attachment.

6

Polymer spheres are considered economical and practical (easy for pumping and

7

injection) candidates for hindering water production from high-perm layers by forming

8

a physical barrier in porous media.13-17 Yet, in many field cases, water producing zones

9

also produce hydrocarbons, and polymer spheres cannot target water producing zones

10

without influencing hydrocarbon production in this region.18 Researchers have

11

developed polymers that are capable of preferentially decreasing the relative

12

permeability to water.19 Besides, inorganic particles have been designed and

13

successfully applied for conformance control in naturally fractured reservoirs.20,21

14

However, few products can satisfy the requirement of high temperature and salt

15

resistance in oil reservoirs. Zhao et al..22 developed plugging particles coated with a

16

layer of modified epoxide resin. These particles exhibited good performance in

17

conformance control under high-salinity and high-temperature environment. However,

18

the particles cannot migrate deeply into porous media due to lack of protection to the

19

coating layer. Aggregation of particles occurred shortly after being injected into a core, 3



Page 4 of 41

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and therefore, plugging showed up close to the entrance.

2

Several mathematical models for deep-bed filtration of particles in porous media have

3

been developed. The classic filtration theory assumes particles migrate with the average

4

fluid velocity,23-26 which contradicts with various experimental results. Numerous

5

experimental studies have shown either an early breakthrough of particles,27,28 or a

6

significant delay.29,30 Yang and Bedrikovetsky31 introduced a drift delay factor  in

7

order to characterize the velocity difference between particles and fluid. ‘Faster’

8

particle migration, i.e.,   1 , is explained by the division of porous space into fractions

9

that are accessible and inaccessible to finite-size (non-zero) particles.32,33 While ‘slower’

10

particle movement, i.e.,   1 , is attributed to the tortuosity of pores32 and the rolling

11

or sliding of particles near the rock surface where the velocity is lower compared with

12

the average fluid velocity.34,35

13

Another assumption of the classic model is that the retained particle volume is

14

negligible compared to the pore volume, i.e., low retention concentration, and therefore,

15

the maximum retention concentration is never reached. The latter is questionable in the

16

case of limited particle retention. Santos and Araujo36 derived exact solutions for deep-

17

bed filtration accounting for the moving boundary of the maximum retention

18

concentration. However, their model did not account for the velocity difference

19

between particles and fluid.

20

Stochastic models have been derived accounting for pore- and particle-size

21

distributions.32,36-38 Santos and Barros39 proposed a statistical filtration model taking

22

multiple capture mechanisms into account. Guedes et al..40 proved that an aggregated

23

single filtration coefficient can represent multiple capture mechanisms, and the multi-

24

capture model can be reduced to a single-mechanism deep-bed filtration model. Yuan

25

and Shapiro41 derived mathematical models incorporating both the distribution of

26

filtration coefficients and the distributed particle flight time to characterize the effect of

27

core heterogeneity. 4


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1

In the present work, to mitigate the near-wellbore damage caused by the early

2

aggregation of traditional microparticles and achieve the in-depth conformance control,

3

the bilayer-coating microspheres with high temperature and salt resistance are

4

developed. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is used to

5

calculate interactions between particles, and a series of corefloods are conducted to

6

study the plugging behavior of BCMS in porous media. Mathematical model and

7

analytical solutions are derived to characterize the deep-bed filtration of BCMS. The

8

introduction of the drift delay factor into the model allows explaining the phenomenon

9

of earlier or later arrival of the suspending particles at a certain position compared to

10

the fluid. The maximum retention concentration of particles is also taken into account.

11

Close agreement between the measured and predicted data validates the analytical

12

model.

13

The structure of the paper is as follows. Section 2 presents the laboratory study,

14

including materials, laboratory setup and methodology. Section 3 derives exact

15

solutions for deep-bed filtration with limited particle retention concentration. The

16

particle moving velocity is also involved. Section 4 discusses the experimental results

17

for physical properties and the plugging performance of microspheres. The treatments

18

for pressure drop data using the developed analytical model are presented in this section.

19

Section 5 concludes the paper.

20

2. EXPERIMENTAL SECTION

21

In this section, we briefly demonstrate the preparation of materials (Section 2.1),

22

experimental setup (Section 2.2) and methodology (Section 2.3).

23

2.1. Materials and preparation

24

2.1.1. Microspheres

25

Bilayer-coating microspheres are designed for in-depth conformance control. Figure

26

2(a) presents the photo of BCMS. The microspheres consist of an internal core and two

27

coated layers, as demonstrated in Figure 2(b). The internal core is made of ultralight 5



Page 6 of 41

1

ceramsite, with a bulk density less than 1.25g/cm3 and a roundness of 0.9. The breakage

2

rate of the ceramsite is 18% under 52MPa pressure as reported by Beijing Qisintal New

3

Material Co., Ltd, China. Materials containing bisphenol A epoxy resin and curing

4

agents are sprayed on top of a functional inner coating, forming the rigid outer layer.

5

The hot molten inner layer with a critical adhesion temperature is made of cardanol

6

modified thermosetting phenolic resin. Both layers of coatings are with thicknesses

7

varying from 1.5μm to 2.0μm (Figure 3). The particle size distribution (Figure 4) is

8

measured using Zetasizer Nano ZS (ZS-3600, Malvern Instruments Ltd.,

9

Worcestershire, UK). The average diameter of the particles is 117μm.

10 11 12 13

(a)

(b)

Figure 2. Bilayer-coating microspheres: (a) photos of BCMS; (b) schematic of particle structure: the rigid internal core, the functional coating layer, and the external protection layer.

14 15

Figure 3. The thickness of the external rigid layer. 6


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1

The rigid outer layer works as a protection layer to the inner coating. Particles do not

2

interact with each other at room temperature and atmospheric pressure, which avoids

3

near-wellbore damage to some extent. As particles migrate in porous media, external

4

layers are torn due to shearing and friction, and the inner functional layers are gradually

5

exposed to the reservoir environment. When reservoir temperature reaches a critical

6

value, the exposed functional coating layers start to melt, and particles tend to bond

7

with each other as a result of interactions between inner coatings. To be specific, the

8

interactions refer to the physical hydrogen bonding. Bonding particles with different

9

sizes bridge at pore throats and fractures, pushing the fluid flow into the bypassed zones.

10

Moreover, the broken external coatings fill in the pores of bridging particles, which

11

enhances the plugging intensity.

12

Figure 4. Particle size distribution of BCMS.

13 14

2.1.2. Quartz sands

15

The quartz sands used in the present study have a SiO2 content of over 99%. Sands are

16

first sieved to constrain particle sizes, assisting the reproducibility of core properties.

17

The procedures for sand washing are described in Russell et al..42

18

2.1.3. Cores and fluids 7



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Sand-pack models filled with quartz sands of 10-40 mesh are used to construct porous

2

media with permeability 3000 to 30000 millidarcys (mD) (Bohai oil field, China). The

3

diameter and length of the packed column are 2.5cm and 50cm, respectively. Wet

4

packing procedures are used for quartz sand compaction to create artificial porous

5

media.43 By adjusting the mixing ratio of quartz sands with different sizes and the

6

degree of compaction, we obtain cores with targeted permeabilities. The porosity is

7

determined using water saturation method,44 and the obtained values range from 0.37

8

to 0.39 for cores with variant permeabilities.

9

Table 1. Ionic compositions for artificial formation water Ions

Ion concentrations, mg/L

Ca2+ Mg2+ Na+ HCO3ClSO42Total

629.29 251.70 2700.04 183.52 5899.58 29.75 9693.88

10

Microparticles are dispersed in solutions with the same ionic composition as the

11

formation fluid in the studied reservoir. The measurements of pH of BCMS-based

12

solutions are carried out with pH-100B meter (Shanghai Lichen Instrument Equipment

13

Co. Ltd., China). The key ionic components of the prepared artificial formation water

14

(AFW) are presented in Table 1. Deionized ultrapure water (Millipore Corporation,

15

USA) with an electrical resistivity of 1.82105 Ω·m at 25C is used for the preparation

16

of BCMS-based suspensions. The fluids are deaerated for one hour to prevent dissolved

17

air from damaging the core permeability.42 The low density of BCMS (1.06-1.20g/cm3)

18

yields low particle sedimentation rate in the carrier fluid.

19

2.2. Laboratory setup

20

Experimental apparatus for real-time permeability measurements are assembled and

21

employed in the present study. A schematic diagram of the laboratory setup are 8


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1

illustrated in Figure 5.

2 3

Figure 5. Experimental setup for coreflooding tests: (a) schematic: 1- syringe pump, 2-

4

salt water, 3- microparticle, 4- sandpack, 5- six-way valve, 6,7,8,9,10- control valves,

5

11- test tube, 12,13,14,15- pressure transducers, 16- data acquisition system, 17- PC

6

with LabView.

7

The fluid delivery system includes a syringe pump 1 equipped with two 90mL stainless

8

steel syringes (100DX, Teledyne ISCO, USA). This system is used for delivering salt

9

water 2 or microparticle suspension 3 to the sand pack 4. Quartz sands are fixed inside

10

the column. A six-port valve 5 and five one-way valves 6-10 are used to connect

11

apparatus, ensuring continuous fluid injection into sand pack. Valves 9 and 10 separate

12

the sand pack from other parts of the system, eliminating fluid leakage during system

13

assembly. Effluents are collected at the outlet of the sand pack by test tube 11. Pressure

14

transmitters 12-15 spaced 10cm apart from each other are employed to measure

15

pressure at four different points along the sand pack. The obtained data are transmitted

16

to the data collection system 16 and 17.

17

2.3. Methodology

18

2.3.1. SEM imaging of BCMS micromorphology

19

Scanning electron microscope (GeminiSEM 300, ZEISS, Germany) is used to analyze

20

the micromorphology of BCMS at 65°C. Particles, quartz sands, and the prepared 9



Page 10 of 41

1

artificial formation fluid with a salinity of 9693mg/L are well blended in a glass bottle.

2

The mixture is stirred at a constant speed of 400rpm for 30 minutes to break outer

3

coatings at room temperature and then placed in a 65°C thermostat to bond particles

4

with the molten inner layers. Gold is sprayed on a representative sample of the mixture

5

at 10mA to make particles conductive. Afterwards, the sample is put into the vacuum

6

chamber of SEM. A secondary electronic probe is employed to observe particle surface

7

morphology in more detail.

8

2.3.2. Measurements of Zeta potential, refractive indexes, and dielectric constants

9

Electrophoretic mobility for BCMS is measured with Zetasizer Nano ZS (ZS-3600,

10

Malvern Instruments Ltd., Worcestershire, UK). Refractive indexes and dielectric

11

constants of particles, quartz, and fluid solution are measured with Rudolph

12

Refractometers (J457, Rudolph Research Corporation, USA) and Precise Dielectric

13

Constant Apparatus (ZJ-3J, NanjingDuozhu Science and Technology Corporation,

14

CHN), respectively. Ionic strengths of the fluids used for measurements are similar to

15

those used in coreflood experiments with pH≈7. Refractive indexes and dielectric

16

constants are used to calculate the Hamaker constant according to the Lifshitz theory.45

17

All measurements are performed in a 65°C environment.

18

2.3.3. Tests for heat and salt resistance of particles

19

2.3.3.1 Heat resistance tests

20

A muffle furnace together with a high-temperature and high-pressure reaction kettle is

21

used to test the thermal stability and salt resistance of the inner coatings of particles.

22

We add 50g particles to 50ml of the prepared artificial formation fluid. The solution is

23

stirred until the outer coatings are worn out and the inner layers are exposed to the liquid.

24

The well-blended mixture is put inside the reaction kettle. The kettle is pressurized to

25

10MPa for one minute by injecting N2 and is then placed in a muffle furnace with a

26

given temperature. The packing column is taken out after 48 hours, and the status of

27

particle adhesion is observed. 10


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1

The above procedure is repeated at temperatures 65°C, 90°C, 100°C, and 120°C. To

2

test the long-term adhesion of BCMS particles, the packing column is placed at 90°C

3

for 12 months.

4

2.3.3.2 Salt resistance test

5

The salt resistance test follows the heat resistance test. All the tests are performed at

6

65°C, and the same experimental procedure is repeated for the variant salinities of

7

artificial water, i.e., 9693mg/L, 19386mg/L, and 29079mg/L. In the latter two solutions,

8

the ionic concentration of each component for AFW listed in Table 1 is doubled and

9

tripled, respectively.

10

2.3.4. Coreflooding tests

11

Coreflooding tests are carried out to evaluate the plugging performance of BCMS and

12

the consequent permeability reduction of artificial cores. The flow rate of the prepared

13

BCMS-based suspensions containing 0.05PV particles is maintained at 1.0mL/min

14

throughout the experiment. Partially hydrolyzed polyacrylamide (PHPA) with a

15

molecular weight of 25 million Daltons is added to the suspension to enhance the

16

suspendability and particle-carrying capacity of the fluid. PHPA accounts for 0.05wt%

17

of the solution. The core is aged for 48 hours after flooding. Corefloods are repeated

18

for injection of fluids with different particle concentrations (2%, 3%, and 5%) into cores

19

with permeabilities of around 10000mD and for 5% particle suspension injection into

20

cores with various permeabilities (3028mD, 6314mD, 9153mD, 15136mD, 20917mD,

21

and 31811mD).

22

3. MATHEMATICAL MODELING FOR DEEP BED FILTRATION OF

23

MICROPARTICLES

24

This section presents the mathematical model for depth filtration of microparticles in

25

porous media with limited retention concentration. Section 3.1 introduces the system

26

of governing equations. Section 3.2 derives exact solutions in a characteristic

27

coordinate. Formula for pressure drop calculation based on the derived exact solutions 11



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1

is given in Section 3.3.

2

3.1. Governing equations

3

The main assumptions of the model include:

4



The fluid is incompressible;

5



Hydrodynamic dispersion and porosity variation are neglected;

6



Particle retention rate is proportional to the flux of suspended particles;

7



The filtration coefficient depends only on the retained particle concentration.

8

The governing system, including a mass balance equation for transport of

9

microparticles in porous media, a kinetic equation for particle capturing, and a modified

10

Darcy’s law, is applied to describe permeability reduction due to deep-bed filtration of

11

the injected microparticles:10,33,40,41

12

- Mass Balance Equation

13

 c    c  Us 0 t x

14 15 16 17

(1)

- Kinetic equation for particle capturing     U s c t

(2)

- Modified Darcy’s Equation U 

k   dp  dx

(3)

18

where  is the porosity, Us is the particle velocity, c is the suspended particle

19

concentration,  is the retained particle concentration,  is the filtration function, k is

20

the permeability,  is the fluid viscosity, and p is the pressure.

21

The particle moving velocity Us is involved in the mass balance equation and the kinetic

22

equation for particle capturing, indicating that particles are moving in a different

23

velocity with the carrier fluid. The dependency of permeability on the particle retention

24

concentration is obtained by neglecting the second- and higher-order terms in Taylor’s 12


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1

2

series for function k0 k   :40,48

k   

k0 1  

(4)

3

where k0 denotes the initial core permeability before particle injection, and  is the

4

formation damage coefficient.

5

We inject fluid with particle concentration c0, and the core is clean before particle

6

injection. Therefore, the boundary and initial conditions for suspended and retained

7

concentrations are given by

8

c  x , t  x 0  c 0

(5)

9

c  x, t  t 0  0,   x, t  t 0  0

(6)

10 11 12 13 14

Introducing dimensionless parameters into Eqs. (1, 2, 5) X

x Ut c  U ,T  , C  0 , S  0 ,   s ,   L L L c c U

(7)

yields the following dimensionless form of governing system C C S   0 T X T S   S C T

(8) (9)

15

C  X , T  X 0  1

(10)

16

C  X , T  T 0  0, S  X , T  T 0  0

(11)

17 18 19

Let us introduce the characteristic variable

 T  X 

(12)

then the governing system in the domain R  0  X  1,    X /   takes the form

20

C   S C  0 X

(13)

21

S   S C  0 

(14)

13



Page 14 of 41

1

C  X , T  X 0  1

(15)

2

C  X , T    X   0, S  X , T    X   0

(16)

3

3.2. Exact solutions

4

From Eq. (14), one obtains

5 6 7

C

1 S  S  

(17)

At X=0, according to the boundary condition (15), the integration of Eq. (17) gives



1



S 0 , 

 0

S  S 

(18)

8

We denote  0*  T0* as the moment when the maximum retention concentration Sm is

9

reached at X=0. Therefore,

10

 0*  T0* 

1



Sm

S

  S 

(19)

0

11

A linear Langmuir blocking filtration function is usually applied as the expression for

12

the dependency of filtration coefficient on the retention concentration40

13

 S    S    0 1  Sm  

(20)

14

However, the integral function in Eq. (19) diverges if the filtration function (20) is

15

applied. It implies that the retention concentration can asymptotically approach the

16

maximum value of retention concentration, yet never reach it.43 This contradicts the

17

occurrence of a plateau of pressure drop shown in Section 4. Therefore, we implement

18

the following formula43,49

19

 S    0 1 

S Sm

(21)

20

At the moment when the maximum retention concentration is reached, the probability

21

of particle retention becomes zero, i.e.,  S   0 .

22

Substituting Eq. (21) into Eq. (19), one obtains 14


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1 2

T0* 

2 Sm  0

(22)

We denote S

3

4 5 6 7

8 9 10 11 12

du  u  0



then the suspension concentration can be expressed as

C

 

(24)

Substituting Eq. (24) into Eq. (13) and changing the order of differentiation yield

 

 1 S    S  X

 S 0    

(25)

Therefore, S   S S  const X

(26)

From the initial condition (16), we obtain S   S S  0 X

(27)

Integrating (27) by separation of variables leads to S 0 , 

13

(23)

dS

X      S S

(28)

S X,

14

where S 0,   represents the retention concentration at the characteristic X  0 at the

15

moment  .

16

Combining Eqs. (13) and (27), we have

17 18

19

20

 ln C S  0 X

(29)

Thus, from boundary condition (15) one obtains

C  X ,  

C 0,   1 S  X ,   S  X ,  S 0,   S 0,  

(30)

The plane  X ,   is divided into four regions (see Figure 6): 15



Page 16 of 41

R0 :  X ,  ; 0  X  1,   0 1

R1 :  X ,  ; 0  X  1, 0     0* 

(31)

R2 :  X ,  ; 0  X  1,  0*     *X  R3 :  X ,  ; 0  X  1,    *X 

2

Below we derive exact solutions in each region.

3 4

Figure 6. Schematic of region divisions and the corresponding characteristic lines on

5

X-ζ plate.

6

I. Exact solution in region R0

7

In R0, the particle moving front is behind a certain X, which means C=0 at X. Thus we

8

can also obtain S=0 from Eq. (14).

9

II. Exact solution in region R1

10

Substituting Eq. (21) into Eq. (18) allows obtaining the expression for retention

11

concentration at X=0

12

13

      2  S 0,    Sm 2 *    *     T0   T0  

The retention concentration for any X is determined from Eqs. (21), (28) and (32). 4e

14

(32)

S  X ,    Sm

0 X

      2  2 *    *   T T   0   0  



 0 X  1  e 0 X 1  e 



S 0,    1  Sm 

2

(33)

16


Page 17 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 2

Substituting Eq. (33) into Eq. (30) results in

C  X ,  

4e   0 X



 0 X  1  e 0 X 1  e 



S 0,    1  Sm 

2

(34)

3

III. Exact solution in region R3

4

In R3, the particle retention concentration reaches its maximum, i.e., S=Sm. Moving

5

particles are no longer captured in this region, and therefore, the suspension

6

concentration equals one, i.e., C=1.

7

IV. Exact solution in region R2

8

In region R2, integration of Eq. (27) starts from a moving boundary X '  X '   between

9

regions R2 and R3, along which S=Sm (see Figure 6). S

10 11 12

du S  u u   X  X ' m

(35)

Eq. (30) turns into the form

C  X ,  

1 S  X ,  Sm

(36)

13

Now let us determine X '   .

14

Differentiating both sides of Eq. (35) with respect to ζ leads to

15 16 17

18 19

20

S dX '   S S  d

(37)

Substituting Eq. (36) into Eq. (14) yields

S S   S   Sm

(38)

Combining Eqs. (37) and (38) allows obtaining

dX '   d S m

(39)

At T  T0* , we have X '  0 . Thus, the initial condition of (39) is given by 17



1 2 3

4 5 6 7 8 9

X '   T0*   0

Page 18 of 41

(40)

From Eqs. (39) and (40), one obtains

X '

    T0*  Sm

(41)

As seen in Figure 6, it is easy to conclude

X ' X ,  *X   X

(42)

and therefore, we get

 *X 

Sm



X  T0*

(43)

Furthermore, from (12) and (43), one obtains TX*  1  Sm 

X



 T0*

(44)

10

Substituting (41) into (35) results in the expression of retention concentration in region

11

R2

12

13

14

S  X ,    Sm

4e   0  X  X ' 

1  e

0  X  X ' 



2

 Sm

4e

   *  0  X     T0    Sm  

  * 0 X      T0    Sm  1  e   

2

(45)

From (36), we obtain the expression of suspension concentration in this region

C  X ,  

4e

   *  0  X     T0    Sm  

   *   0  X     T0     S  1  e  m   

2

(46)

15

Substituting (12) back into Eqs. (33), (34), (45) and (46) yields exact solutions in (X,T)

16

plane. Expressions written in (X,T) plane are summarized in Table 2.

18


Page 19 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Table 2. Exact solutions of microparticle retention concentration and suspension

2

concentration in porous media Regions

R0: 0  T 

Notations

Expressions

Retention

S X ,T   0

X

concentration, S



Suspension concentration, C

R1:

X



T T  * 0

X



 * 2 Sm   T0   0  

R2: T0* 

X



 T  TX*

X  * *  TX  1  Sm   T0    

Retention concentration, S

Suspension concentration, C

Retention concentration, S Suspension concentration, C Retention

R3: T  TX*

concentration, S Suspension concentration, C

CX ,T   0  T  X   T  X       4e 0 X 2 * *   T0   T0  S  X , T   Sm 2  S  0 X  1  e 0 X 1  1  e  S m  



CX ,T  

  



4e  0 X  0 X  1  e 0 X 1  e 



S  X , T   Sm

CX ,T  

2

4e  0  X  X ' 

1  e

4e  0  X  X ' 

1  e



0  X  X 1  2

,



1

S   Sm 

2

where X ' 

  X *  T   T0   Sm  



0  X  X '  2

S  X , T   Sm

CX ,T   1

3

The evolution profiles for the concentrations of retained and suspended particles at four

4

instants T1, T2, T3, and T4 are presented in Figure 7(a) and (b), respectively. The

5

suspended concentration profiles are given by equations listed in column 3 of lines 2,

6

4, 6, and 8, Table 2, exhibiting discontinuity at the constant-speed front. It is zero ahead

7

of the front since the particle front has not arrived yet. The suspension concentration

8

decreases with distance monotonously behind the front at moments T1 and T2 when the

9

maximum value of retention concentration is not reached at X=0. While at moments T3 19



Page 20 of 41

1

and T4 the decline of suspension concentration starts from a certain position X, behind

2

which the suspension concentration equals one as suspended particles are no longer

3

captured there. The certain position X is determined from Eq. (44). The retention

4

concentration profiles are expressed by equations listed in column 3 of lines 1, 3, 5, and

5

7, Table 2, showing a weak discontinuity at the front. It is zero ahead of the front and

6

accumulates with time behind the front. When a limited retention concentration is

7

reached at a position X, the retention concentration reaches its maximum value Sm

8

behind X.

9 10

Figure 7. Schematic of retention and suspension profiles at four instants T1, T2, T3, and

11

T4: (a) retention profiles; (b) suspension profiles.

12

3.3 Pressure drops along each core section

13

Substituting dimensionless form of x and σ in Eq. (7) into Eq. (3) leads to the formula

14

of pressure drop pw along the core section with a certain length wL

15 16

pw 

UL w 1  c0S dX k0 0

(47)

where w is the dimensionless distance of a measuring point from the core inlet, w  [0,1] . 20


Page 21 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Substituting exact solutions of particle retention concentration allows deriving the

2

pressure drop across a core section.

3

4. RESULTS AND DISCUSSIONS

4

This section presents the results and discussions for the laboratory study described in

5

Section 2 and the treatment of experimental data using the analytical model derived in

6

Section 3. Section 4.1 shows SEM images for the micromorphology of BCMS before

7

and after the external coating exposed to the artificial formation water. Section 4.2

8

analyzes the DLVO interaction characteristics between two particles. Section 4.3

9

characterizes the heat and salt resistance of BCMS. Section 4.4 presents the pressure

10

drop data from coreflooding tests and data matching by the analytical model. The

11

sensitivity analysis of the proposed model is presented in Section 4.5.

12

4.1. Micromorphology of BCMS

13

SEM images of BCMS are exhibited in Figure 8. Figure 8(a) shows the appearance of

14

an unworn particle. Under shearing and friction, the outer coating of BCMS is gradually

15

torn, and the functional inner coating is exposed to the fluid with a temperature higher

16

than the melting point of the inner layer. The magnified appearance of a worn particle

17

is illustrated in Figure 8(b). Figure 8(c) shows the adhesion status of BCMS, with inner

18

layers exposed to a high-temperature environment. SEM imaging analysis clearly

19

demonstrates the feasibility of BCMS as a candidate for in-depth conformance control

20

in a heterogeneous porous media.

21

21



Page 22 of 41

(a)

1

(b)

(c)

2 3

Figure 8. SEM images of BCMS status: (a) the unworn BCMS; (b) the worn BCMS;

4

(c) the adhesion status of the peeled BCMS.

5

4.2. DLVO analysis

6

Interactions between particles are quantitatively described by the DLVO theory.

7

Formulae used in our calculation follow You et al..50 The DLVO interaction is the sum

8

of potential energies arising from the attractive long-range London-van der Waals force,

9

the short-range repulsive/attractive electrical double layer force, and the Born repulsion

10

force.

11

The measured value of the outer surface zeta potential for microparticles suspended in

12

AFW at 65°C is -25.2mV. Refractive indexes for particles and fluids are 1.347 and

13

1.342, respectively. Dielectric constants for particles and fluids are 7.020 and 60.848,

14

separately. Other parameters used for DLVO calculation are adopted from You et al..50

15

The obtained total interaction energy curve with respect to an average particle radius of

16

50μm is shown in Figure 9 (blue curve). The absence of the primary energy minimum 22


Page 23 of 41

1

is observed. The inflection point on the energy curve with an appreciably high value of

2

interaction potential energy about 19000 kBT at 0.4nm distance indicates a significant

3

energy barrier when two particles approach each other, which hinders particle

4

aggregation. A sensitivity analysis regarding the particle size effect on the particle-

5

particle interaction is also performed. The red and black curves plotted in Figure 9

6

represent calculation results for 10μm and 100μm particles, respectively, showing that

7

larger particle size intensifies particle-particle repulsion. 6

10 4 rs=100 m

5

rs=50 m rs=10 m

4 Energy, KB T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 2 1 0 -1 10 -10

8

10 -9

10 -8

10 -7

Separation distance (m)

9

Figure 9. Particle-particle interaction energy curves calculated by DLVO theory.

10

The above DLVO analysis approves the effectiveness of protection to the inner layers

11

provided by the outer ones under the experimental condition.

12

4.3. Heat and salt resistance of BCMS

13

Microparticle adhesion occurs if the environment temperature is higher than the melting

14

point of the functional inner coating. The stability of particle adhesion under high

15

temperature and high salinity is essential to the performance of conformance control.

16

Therefore, tests for heat and salt resistance are carried out.

17

As shown in Figure 10, the pressurized particle column (5cm in length and 2.5cm in

18

diameter) maintains its integrity after 48 hours’ standing in a muffle furnace at

19

temperatures of 65°C, 90°C, and 100°C (Figure 10(a)-(c)), while the column crumbles 23



Page 24 of 41

1

to dust at 120°C (Figure 10(d)). The experimental results indicate that the adhesive

2

inner coating remains active at temperatures ranging from 65°C to 100°C, and particles

3

are steadily bonded. The packing column can maintain its shape after 12 months’

4

standing at 90°C, which confirms the long-term adhesion of BCMS particles. However,

5

the designed functional layer is devitalized at temperatures 120°C and above. It is worth

6

mentioning that by modifying the ratio of cardanol and phenolic resin as well as the

7

reaction temperature, a series of particles with variant bonding temperatures ranging

8

from 30°C to 150°C can be produced. In the present paper, we focus on the

9

characterization of microparticles applicable to reservoirs with temperatures varying

10

from 65°C to 100°C.

11

(a)

(b)

12

(c)

(d)

13

Figure 10. Tests for heat resistance: (a) 65°C; (b) 90°C; (c) 100°C; (d) 120°C.

14

Figure 11 demonstrates particle packing (5cm in length and 2.5cm in diameter) status

15

under variant salinities at 65°C. The column integrity indicates stable particle adhesion

16

property at salinities ranging from 9693mg/L to 29079mg/L.

24


Page 25 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

1

(b)

(c)

2

Figure 11. Tests for salt resistance: (a) 9693mg/L; (b) 19386mg/L; (c) 29079mg/L.

3

4.4. Pressure drop history in coreflooding tests and data matching by the

4

analytical model

5

Pressures at four locations of the artificial core are measured with transmitters 12-15

6

placed at 0.1m, 0.2m, 0.3m, and 0.4m from the core entrance (Figure 5). The whole

7

core is divided into five sections by the four pressure gauges. The five sections are

8

sequentially numbered as 1 to 5 from left to right. To elucidate influences of particle

9

plugging on permeability decline of the porous media, pressure drops between

10

transmitter 12 (0.1m from the inlet) and other transmitters 13-15 are plotted in Figures

11

12 and 13, which correspond to the effect of particle concentration and initial core

12

permeability, respectively. Red points present the pressure drop across core section 2

13

(between transmitter 12 and 13), green points show the pressure drop across core

14

sections 2 and 3 (between transmitters 12 and 14), and blue points exhibit the pressure

15

drop across core sections 2, 3, and 4 (between transmitters 12 and 15). Not surprisingly,

16

the pressure drop across core section 2 (red points) is the lowest during the filtration

17

process, and the summation of the pressure drops of core sections 2, 3, and 4 has the

18

highest value (blue points). The non-zero pressure drops at initial moments of particle

19

injection are attributed to the frictional loss.

20

The pressure drop histories of each section exhibit a similar tendency of three stages,

21

i.e., after an initial short-term gradual increase, there is a rapid rise of pressure then

22

followed by a plateau stage or another stage of slow growth. Core section 1 has a length

23

of 0.1m, accounting for 20% of the total core length. Consequently, it takes 0.2PVI 25



1

(pore volume injection) for injected particles to arrive at the position of transmitter 12

2

theoretically. However, experimental results usually show an earlier or later arrival in

3

comparison with the theoretical prediction. The discrepancy can be interpreted by the

4

velocity difference between particles and the carrier fluid. In the first stage of pressure

5

drop history, i.e. before the moment of particle arrival, pressure drops across sections

6

2-5 remain constant or grow slowly, due to the frictional loss In the second stage, after

7

the moment of particle arrival, due to size exclusion or bridging of aggregated particles,

8

the pores are plugged severely and the pressure drop exhibits a rapid increase. When

9

the maximum retention concentration is reached (the third stage), the pressure drop

10

across core sections behind the moving front of maximum retention arrives at a plateau,

11

while the pressure drop across core sections ahead of the moving front continues to

12

increase. 25

80

20 60

15

P, KPa

P, KPa

40

10

0

13

20

Experimental data, Section 2 Model, Section 2 Experimental data, Sections 2 and 3 Model, Sections 2 and 3 Experimental data, Sections 2, 3, and 4 Model, Sections 2, 3, and 4

5

0

0.2

0.4

0.6

0.8

T, PVI

1

0

(a)

Experimental data, Section 2 Model, Section 2 Experimental data, Sections 2 and 3 Model, Sections 2 and 3 Experimental data, Sections 2, 3 and 4 Model, Sections 2, 3 and 4

0

0.4

0.8

T, PVI

1.2

1.6

(b)

120

90

P, KPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 41

60

Experimental data, Section 2 Model, Section 2 Experimental data, Sections 2 and 3 Model, Sections 2 and 3 Experimental data, Sections 2, 3 and 4 Model, Sections 2,3 and 4

30

0

14

0

0.2

0.4

0.6

0.8

T, PVI

1

(c) 26


Page 27 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Figure 12. Experimental data and model tuning results of pressure drops across

2

different core sections for tests I, II and III with variant concentrations of micro-particle

3

injection: (a) 2% of microparticle injection into a core with a permeability of 10380mD;

4

(b) 3% of microparticle injection into a core with a permeability of 9750mD; (c) 5% of

5

microparticle injection into a core with a permeability of 10484mD.

6

Figure 12(a)-(c) show pressure drop data for particle injection with different particle

7

concentrations (2%, 3%, and 5%) into artificial cores of permeability around 10000mD.

8

Higher particle concentration results in a greater pressure drop along each section

9

throughout the injection periods, indicating a better plugging performance if the

10

suspension of 5% BCMS is injected into a 10000mD porous media, compared to 2%

11

and 3% of BCMS injection scenarios.

12

Figure 13(a)-(f) compare pressure drop data of 5% particle injection into artificial cores

13

with different permeabilities (3028mD, 6314mD, 9153mD, 15136mD, 20917mD, and

14

31811mD). The relationship between the pressure drop along each core section and the

15

core permeability exhibits a non-monotonic characteristic, i.e., particle injection into

16

cores with intermediate permeabilities (6314mD, 9153mD, and 15136mD) yields

17

higher pressure drop, compared to that of cores with lower or higher permeabilities

18

(3028mD, 20917mD, and 31811mD). The non-monotonicity could be explained by the

19

compatibility of the injected particles with porous media. According to Kozney-

20

Carman equation,51 lower permeability generally correlates with smaller average pore

21

size. Therefore, fewer particles can penetrate deeply into cores of very low permeability,

22

i.e., most particles are captured at the core inlet due to size exclusion. This yields a low

23

particle retention concentration, and therefore, a low pressure drop across the rear core

24

sections. While in cores with very high permeability and large average pore sizes,

25

particles can be transported freely with a low probability of being captured at pore

26

throats, which also yields a low pressure drop. In the cores with intermediate

27

permeability, in-depth filtration of particles occurs, and more particles are captured in

28

a deeper part of the core, resulting in a greater pressure drop across sections 2-5. This 27



1

confirms the potential application of BCMS for in-depth conformance control in

2

heterogeneous reservoirs, including low-permeability reservoirs with the existence of

3

natural or artificial fractures. Unfortunately, we are unable to produce smaller BCMS

4

at the current stage due to technical limitations. To be specific, the aggregation of

5

particles with a small size impedes the formation of uniform coating layers and

6

decreases the dispersity. Future development aims at tackling this difficulty, to achieve

7

a better profile control in low-permeability reservoirs. 150

20

120

15

90

P, KPa

P, KPa

25

10

0


0

0.2

0.4

8

0.6

0.8

T, PVI

30

1

0

(a)

0.2

0.4

0.6

0.8

1

(b)

120 Experimental data, Section 2 Model, Section 2 Experimental data, Sections 2 and 3 Model, Sections 2 and 3 Experimental data, Sections 2, 3 and 4 Model, Sections 2, 3 and 4


90

P, KPa

90

60

30

0

0

T, PVI

120

9


60

5

P, KPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 41

60

30

0

0.25

0.5

T, PVI

0.75

1

0

(c)

0

0.2

0.4

0.6

T, PVI

0.8

1

(d)

28


Page 29 of 41

90

35


28

P, KPa

60

P, KPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


21

14 30 Experimental data, Section 2 Model, Section 2 Experimental data, Sections 2 and 3 Model, Sections 2 and 3 Experimental data, Sections 2, 3 and 4 Model, Sections 2, 3 and 4

7

0

1

0 0

0.2

0.4

0.6

T, PVI

0.8

1

(e)

0

0.2

0.4

0.6

T, PVI

0.8

1

(f)

2

Figure 13. Experimental data and model tuning results of pressure drops across

3

different core sections for tests I to VI of micro-particle injection into cores with variant

4

permeabilities: a) 5% of microparticle injection into a core with a permeability of

5

3028mD; b) 5% of microparticle injection into a core with a permeability of 6314mD;

6

c) 5% of microparticle injection into a core with a permeability of 9153mD; d) 5% of

7

microparticle injection into a core with a permeability of 15136mD; e) 5% of

8

microparticle injection into a core with a permeability of 20917mD; f) 5% of

9

microparticle injection into a core with a permeability of 31811mD.

10

The analytical model derived in Section 3 allows treating the laboratory pressure drop

11

data during the overall injection period of coreflooding tests. The three sets of pressure

12

drop data across different core sections are tuned simultaneously for each test, and five

13

parameters are considered as tuning parameters: the formation damage coefficient β,

14

the maximum retention concentration Sm, the initial filtration coefficient 0, the drift

15

delay factor α, and the fluid viscosity μ. The fluid viscosity is chosen as a parameter to

16

be optimized due to its dependency on shear effect and particle concentration.52 We

17

assume all the tuning parameters are constant during each test. Optimization is

18

performed within Matlab (MathWorks Inc, 2016) using a genetic least-squares

19

algorithm because of its great ability to avoid convergence to local minima.53 The

20

obtained values of tuning parameters are summarized in Table 3. The optimized

21

pressure drop curves are shown as solid curves in Figure 12 and 13. Blue curves in each 29



Page 30 of 41

1

figure represent modeled pressure drops across cores sections 2-4; Green curves

2

correspond to those across cores sections 2 and 3; Red curves correspond to those across

3

cores section 2. All experimental data are reasonably matched, showing high values of

4

the coefficient of variation R2 (from 0.82 to 0.92), except for cores with the lowest

5

permeability of 3028mD (Figure 13(a)) and highest permeabilities of 20917mD and

6

31811mD (Figure 13(e) and (f)). The low R2 is ascribed to the particle compatibility to

7

the porous media as we have discussed, i.e., BCMS do not present typical deep-bed

8

filtration behavior in cores with relatively low and high permeabilities.

9

Table 3. Tuning parameters for coreflooding tests Permeability mD 9750 10376 10484 3028 6314 9153 15136 20917 31811

BCMS concentration wt% 2 3 5 5 5 5 5 5 5

Tuning Parameters β

Sm

0

α

μ, Pa·s

2.35E4 9.03E4 8.07E3 1.43E5 2.53E3 2.25E3 3.01E3 3.36E4 1.73E5

0.0147 0.0216 0.1352 0.0007 0.3032 0.3585 0.4267 0.0342 0.0023

2.2500 0.1053 8.3853 3.9487 3.8011 3.1907 2.7017 9.6498 6.3326

1.1943 0.9646 1.6951 0.5965 0.9390 1.5450 1.7590 1.9677 1.9847

0.0012 0.0015 0.0027 0.0012 0.0084 0.0018 0.0029 0.0030 0.0060

10

Although good matches between laboratory data and mathematical modeling are

11

observed for cores compatible with the designed particles, the discrepancy cannot be

12

ignored. In the present model derivation, we assume the filtration coefficient  only

13

depends on the retention concentration, which may not be the case for BCMS due to

14

the existence of an external protection layer. With the abrasion of the outer coating and

15

the gradual exposure of the inner functional layer, the particle capture probability

16

increases with the degree of exposure, and therefore, the filtration coefficient also

17

depends on the exposed area of the inner coating. Deriving exact solutions accounting

18

for abrasion evolution of the external layer is our next step.

19

It should be noted that, in our study, the effluent particle concentration cannot be 30


Page 31 of 41

1

measured because it is below the measurement accuracy of the instrument. Most of the

2

injected microparticles are captured inside the porous media. To further validate the

3

developed analytical model, a longer injection period should be applied to provide data

4

for effluent particle concentration history as well as the particle retention concentration

5

profile along the porous media.

6

4.5. Sensitivity analysis of mathematical model

7

This section analyzes how the variation of each tuning parameter affects the pressure

8

drop curves. This analysis allows examining the reliability of the proposed model for

9

characterizing the system from the measured data with respect to parameter variation.

10

For all calculations, the tuning results for the test of 5% BCMS injection into a core

11

with a permeability of 10484mD are selected as the standard model parameters (listed

12

in Row 4, Table 3): β=8.07×103, Sm=0.1352, 0=8.3853, α=1.6951, and μ=0.0027 Pa·s.

13

Sensitivity analysis is performed by perturbing the standard values by  5% . 150

150

S m 5%

5% 120 100

90

P, KPa

P, KPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60 50

30

0

14

0

0.2

0.4

0.6

T, PVI

0.8

1

0

1.2

0

0.2

(a)

0.4

0.6

T, PVI

0.8

1

1.2

(b)

31



120

120

0

5%

5% 100

90 P, KPa

P, KPa

80

60

60 40

30 20

0

0

0.2

0.4

1

0.6

0.8

1

0

1.2

0

0.2

(c)

T, PVI

0.4

0.6

T, PVI

0.8

1

1.2

(d)

150

5% 120

P, KPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 41

90

60

30

0

2

0

0.2

0.4

0.6

T, PVI

0.8

1

1.2

(e)

3

Figure 14. Sensitivity analysis with respect to 5% variation of tuning parameters: (a)

4

formation damage coefficient; (b) the maximum retention concentration Sm; (c) the

5

initial filtration coefficient 0; (d) the drift delay factor α; (e) the fluid viscosity μ. The

6

solid lines represent the pressure drop curve calculated by the standard value of each

7

parameter; the dashed and dot lines correspond to the perturbation of one of the five

8

parameters by  5% .

9

Figure 14(a)-(e) present the pressure sensitivity regarding the parameters β, Sm, 0, α,

10

and μ, respectively. The solid lines represent the pressure drop calculated by the

11

standard value of each parameter; the dashed and dot lines correspond to the

12

perturbation of one of the five tuning parameters by  5% . As shown in Figure 14(a)

13

and (b), the increase of β or Sm give rise to a growth of pressure drop across core sections

14

2-4 after particles arrive at core section 2. However, β and Sm do not affect the initial 32


Page 33 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

constant pressure drop due to the absence of the plugged particles in these sections at

2

the initial stage. Figure 14(c) shows that the initial filtration coefficient is not sensitive

3

to a small perturbation. However, the initial parameter can cause a late or early arrival

4

of the maximum retention concentration if a more substantial perturbation is given.

5

Figure 14(d) shows the sensitivity of the drift delay factor. Lower drift delay factor

6

yields a delayed arrival of particles, as well as the delayed plateau stage of pressure

7

drop. Figure 14(e) illustrates that the increase of fluid viscosity results in a higher

8

pressure drop throughout the injection period, including the period before the arrival of

9

particles at the inlet of core section 2. The latter is induced by the higher friction loss

10

as viscosity increases.

11

5. CONCLUSIONS

12

Bilayer-coating microspheres with high temperature and salt resistance are developed

13

for conformance control in heterogeneous reservoirs. Laboratory study on adhesion

14

properties and plugging behavior of BCMS as well as data treatment with the proposed

15

mathematical model allow drawing the following conclusions:

16

DLVO calculation suggests a significant repulsion between the outer layers of BCMS,

17

which confirms the effectiveness of protection to the inner coatings provided by the

18

outer ones under the experimental condition.

19

The functional inner coating remains active at temperatures ranging from 65°C to

20

100°C, while it is deactivated at 120°C. A steady particle adhesion property is observed

21

for salinities ranging from 9693mg/L to 29079mg/L at 65°C. A series of BCMS with

22

variant bonding temperatures can be produced by modifying the ratio of cardanol and

23

phenolic resin as well as the reaction temperature.

24

Compared to the prediction by the classical deep-bed filtration theory, the late or early

25

arrival of the suspending particles at a certain position indicates that the transport

26

velocity of particles differs from that of the carrier fluid.

27

The exact solution exhibits close agreement with the laboratory coreflooding data of 33



Page 34 of 41

1

pressure drops across different core sections. However, precise measurements of the

2

effluent particle concentration and the retention profile are required to provide a more

3

detailed validation for the derived analytical model.

4

BCMS performs deep-bed filtration and can be transported deeply into porous media,

5

which indicates its potential application for in-depth conformance control.

6

Nomenclature

7

c

Suspended particle concentration, m-3

8

C

Dimensionless suspended particle concentration

9

k

Permeability, m2

10

L

Core length, m

11

p

Pressure, Pa

12

S

Dimensionless retained particle concentration

13

t

Time, s

14

T

Dimensionless time

15

U

Darcy’s velocity, ms-1

16

Us

Particle’s seepage velocity, ms-1

17

w

Dimensionless distance of a measuring point from the core inlet

18

x

Dimensional linear coordinate, m

19

X

Dimensionless linear coordinate

20

Greek symbols

21

α

Drift delay factor

22



Formation-damage coefficient

23



Porosity

24



Filtration coefficient, m-1

25



Dimensionless filtration coefficient, m-1

26



Dynamic viscosity, kgm-1s-1

27



Concentration of retained particles, m-3 34


Page 35 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

ζ

2

Subscripts and Superscripts

3

a

Attached (for fine particles)

4

f

Front

5

M

Maximum value

6

0

Initial or boundary value (for permeability, retention concentration, filtration coefficient)

8

*

The moment at which the maximum value is reached at a certain location

9

'

Moving boundary

7

Characteristic variable

10

Acknowledgement

11

The authors are grateful to Prof P Bedrikovetski (The University of Adelaide) and Prof

12

Y Osipov (Moscow State University of Civil Engineering) for discussion of the

13

analytical model. Financial supports from the National Natural Science Foundation of

14

China (Grant No. 51804316, Grant No. 51734010, and Grant No. U1762211), the

15

national major project (Grant No. 2017ZX05009), and the Science Foundation of China

16

University of Petroleum, Beijing (Grant No. ZX20180228) are greatly acknowledged.

17

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18

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40


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1

Table of Content (TOC) Graphic

2

41


Study on the Plugging Performance of Bilayer-Coating Microspheres

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