Improving water injectivity and enhancing oil recovery by wettability ...

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Amott. (1959) studied the effect of wettability on residual oil by carrying out .... value or capillary pressure d. Deposition e. Entrainment fe. Flow efficiency pt.
Journal of Petroleum Science and Engineering 86–87 (2012) 206–216

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Improving water injectivity and enhancing oil recovery by wettability control using nanopowders Binshan Ju a, b,⁎, Tailiang Fan a, b, Zhiping Li a a b

School of Energy Resources, China University of Geosciences, Beijing, China Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Accumulation Mechanism, Ministry of Education, China University of Geosciences, Beijing, China

a r t i c l e

i n f o

Article history: Received 27 September 2011 Accepted 15 March 2012 Available online 25 March 2012 Keywords: wettability control chemical agents enhanced oil recovery numerical simulator wettability index

a b s t r a c t Wettability of porous media plays an important role in effecting multiphase flow, which provides a clue to modify percolating process in porous media. The objective of this work is to study the effects of wettability on fluids flow and its applications in oil fields. Firstly, the effect of wettability on oil recovery was analyzed by experimental data. Secondly, the wettability alteration induced by wettability control agents was studied by experimental approach. Thirdly, a two-phase flow mathematical model considering wettability control by chemical agents is presented. Finally, a numerical simulator considering wettability control was developed and oil field examples were run on the simulator and the percolation behaviors of two-phase flow were predicted. Numerical simulations show that the treatment of increasing water-wetting wettability control agent (IWWCA) leads to 15.38% more in oil recovery than that of normal water displacement. Increasing oilwetting wettability control agent (IOWCA) improves 60% to 80% more in water injection rates. It was found that the concentration of IWWCA has an obvious effect on oil recovery when IWWCA concentration is less than 0.02. IOWCA treatments of 6 oil-field injection wells show that average water injection capacity increases up to 2.75 times of their initial injection capacity. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Wettability plays an important role in a number of industrial applications (Singhal and Dranchuk, 1975) and has a dominant effect on the microscopic distribution of wetting phase and non-wetting phase in rock pores and controls the percolating process of multiphase flow. Therefore, the displacement behavior of two phases in an oil reservoir is bound to be influenced by wettability. The strong interest attracting oil reservoir engineers lies in the fact that wettability of an oil formation effects residual oil and final oil recovery. Amott (1959) studied the effect of wettability on residual oil by carrying out four kinds of displacements for the rock-water–oil system. Experimental study of the effects of wettability on two-phase displacement has been conducted in the lab (Morrow and McCaffery, 1973). Anderson (1987a) gave a detailed analysis on the relations between the wettability and fluid location in pores for multiphase flow. The effects of wettability on oil recovery displaced by water in oil reservoirs have been reported in the references (Anderson, 1987b; Guo and Abbas, 2003; Ju et al., 2002; 2006). However, they haven't arrived at

⁎ Corresponding author at: School of Energy Resources, China University of Geosciences (Beijing), Xueyuan Road No.29, Haidian district, Beijing 100083, China. Tel.:+ 86 10 82320972. E-mail address: [email protected] (B. Ju). 0920-4105/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2012.03.022

agreements on the effects of wettability on ultimate oil recovery flooded by water. The results (Han et al., 2006; Morrow, 1990) showed that the ultimate oil recovery obtained by water flooding is the highest for intermediate wetting reservoir among water, intermediate and oil wetting reservoirs, which is supported by their experimental data. Ultra low capillary force in intermediate porous media (Morrow, 1990) eliminates the flow rate difference in large and small pores, which extends water swept volume. The results from other references (Donaldson and Alam, 2008; Guo et al., 2001; Zhao, 2008) show that the stronger the water-wetting oil formation is, the higher oil recovery is for water flooding reservoirs. Their conclusion was drawn from the fact that the oil can be displaced by high capillarity in the thin pores in strong water-wetting systems. Previous research results show that the wettabilities of porous media undoubtedly have a noticeable effect on the fluids flow performance and oil recovery of oil reservoirs. It indicates that two-phase displacement behaviors can be changed by artificial wettability control. Li and Firoozabadi (2000) presented the results that the wettability of porous media was altered from preferential liquid-wetness to preferential gas-wetness after chemical agent treatment in the laboratory. Their intention is to improve recovery of condensing gas reservoirs by gas-wetting control. Yao and Li (2007) published their results on the relations of wettability alterations and alteration agents by experimental approach in laboratory. And their experimental results show that oil recovery performance is improved by wettability control agent treatment.

B. Ju et al. / Journal of Petroleum Science and Engineering 86–87 (2012) 206–216

Nomenclature A AWI B c d Cl Dl f k kr Kro Krw kf n OWI p pc PV PVW PVWCA q Rl S Sor Sspo Sspw Swc s

sv t ul ulc V Vp Vw, inj WWI x z α β γ ϕ μ ν νl νl* θ σ ω

Area, m 2 Amott wettability index Volume factor of fluid Concentration of wettability control agent, m3⋅m− 3 Diameter of WCA particles, m Volume concentration of WCA in phase l, m 3⋅ m − 3 Dispersion coefficient of WCA in fluid, m 2⋅ s − 1 Flow efficiency factor Absolute permeability of porous media, m 2 Relative permeability Relative permeability of oil phase Relative permeability of water phase Constant for fluid seepage allowed by the plugged pores Coefficient for the relation between porosity and permeability Oil-wetting index Pressure, Pa Capillary force, Pa Pore volume of injection Pore volume of water injection Pore volume of wettability control agent injected Injection rate or production rate, m 3⋅ s − 1 Volume changing rate of WCA in fluid per unit bulk volume of the porous media m 3⋅m − 3⋅s − 1 Saturation Residual oil saturation Spontaneous oil imbibition saturation Spontaneous water imbibition saturation Connate water saturation Total surface area in contact with fluids for all particles of WCA per unit bulk volume of the porous media, m 2⋅ m − 3 Specific area of sand core, m 2⋅ m − 3 Time, s Flow velocity for liquid phase in porous media, m⋅s − 1 Critical velocity for liquid phase, m⋅s − 1 Volume, m 3 Total pore volume of sandstone, m 3 Accumulated volume of water injection, m 3 Water-wetting index Distance, m Distance from reference level Rate constant, m − 1 Surface area coefficient Specific gravity of fluids Porosity of porous media Viscosity of fluid, Pa·s Volume of retention of WCA per unit bulk volume of the porous media, m 3⋅ m − 3 Volume of WCA available on pore surfaces per unit bulk volume of the porous media, m 3⋅m − 3 Volume of WCA entrapped in pore throats per unit bulk volume of the porous media, m 3⋅m − 3 Wetting angle Interfacial tension between wetting and non-wetting phases N/m Coefficient for calculating specific area

Subscripts 0 Initial value c Critical value or capillary pressure d Deposition

e fe pt o w

207

Entrainment Flow efficiency Pore throat Oil Water

For the time being, there are few published papers addressing the applications of wettability alteration in oil fields. The adsorption of Wettability control agents (WCA) on pore walls and its influences on wettability alteration and two-phase flow performance are not well understood yet. There are no comprehensive mathematical models considering wettability control by WCA displacement and predicting WCA transport, wettability alteration and its effects on two-phase flow behaviors in porous media. The purpose of this work is to study the effects of wettability on two-phase flow in porous media and its applications in enhanced oil recovery and improving water injection by wettability modification with two kinds of WAC treatments. We preliminarily focus on experimental studies on wettability modification with WCA treatments by measuring wetting angles, the relations of oil recovery and wettability, wettability alteration with two kinds of WCA treatments for enhanced oil recovery and improving water injection in oil fields. The one-dimensional numerical simulation of increasing waterwetting wettability control agent (IWWCA) slugs injected shows that oil recovery is up to 66.41% with IWWCA treatment (c = 0.02) and the recovery is 15.38% more than that of normal water injection. However, for an actual reservoir, the enhanced recovery may be lower than 15.38% due to a low volumetric sweep and reservoir heterogeneity. The numerical results of W1-3 have good agreements with field data, which validates the mathematical model. The field tests of 6 injection wells indicate that it is feasible to enhance water injection by increasing oil-wetting wettability control agent (IOWCA) treatment.

2. Effects of wettability on oil recovery Since wettability is a major factor in controlling the fluid location, flow and distribution in pores of oil reservoirs, it plays an important role in the oil recovery of a petroleum reservoir. To verify the wettability of sandstone cores to have effects on the recovery by imbibition, 28 sandstone core samples obtained from H.Z.J oil field, east China, were used for imbibition experiments. The core samples located the formation from 1748.51 m to 2506.36 m in depth before they were drilled and brought onto the surface. Table 1 gives the description of these core samples. The wettabilities of these cores and recoveries by water spontaneous imbibitions were obtained by experimental approach in the laboratory. The imbibition experimental procedure is: (1) A core sample is chosen and saturated with oil. The oilsaturated sample is then placed in an imbibition cell surrounded by water. The water is allowed to imbibe into the core sample displacing oil out of the sample until equilibrium is reached. The volume (Vwi) of water imbibed is measured. (2) The core sample is then removed and the remaining oil in the sample is forced down to residual saturation by displacement with water by pump in a sealed core holder. The volume (Vod) of oil displaced may be measured. (3) A core sample is chosen and saturated with water at residual oil saturation, is placed in an imbibition cell and surrounded by oil. The oil is allowed to imbibe into the core displacing

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Table 1 Description of the core samples. Sample

Core description and location

Core size

Core no.

Lithology

Formation depth (m)

Diameter (cm)

Length (cm)

Porosity (%)

Parameter Permeability (10− 12 × m2)

Quartz (%)

Mineralogy Feldspar (%)

Clay and other's (%)

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

Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Medium standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone Medium standstone Fine standstone Fine standstone Fine standstone Fine standstone Medium standstone Fine standstone Medium standstone Fine standstone Fine standstone Fine standstone Fine standstone Fine standstone

1748.51 1762.46 1813.16 1856.06 1866.60 1889.36 1903.14 2198.22 2205.76 2208.18 2211.68 2217.07 2219.00 2220.00 2242.15 2278.45 2287.90 2309.67 2318.69 2332.88 2335.79 2338.52 2340.80 2342.98 2432.81 2476.26 2488.18 2506.36

2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.49 2.50 2.48 2.49 2.49 2.49 2.49 2.50 2.49 2.49 2.48 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.48

5.93 6.02 4.07 3.95 3.99 4.03 4.15 5.3 5.84 5.57 4.11 5.39 3.85 6.19 4.19 4.24 5.21 5.75 4.13 4.23 4.27 5.02 5.41 5.8 3.99 4.63 5.66 5.48

24.40 22.70 24.7 23.3 24.9 22.9 25.1 21.40 29.30 24.90 22.10 24.70 20.60 23.4 22.1 29.00 20.50 25.10 20.10 25.9 29.1 26.9 29.5 24.4 25.90 26.90 22.90 23.30

0.996 0.437 0.682 0.455 0.598 0.275 1.013 0.470 1.341 0.598 0.293 0.682 0.212 0.766 0.293 1.247 0.319 0.933 0.241 0.951 1.247 1.307 1.541 0.996 0.951 1.407 0.275 0.455

56.90 52.02 – – – 57.85 – – – – 53.27 61.81 51.64 54.10 63.93 – – 72.90 75.09 70.35 73.71 – 71.14 71.12 – – – 70.99

10.34 12.40 – – – 12.40 – – – – 17.49 11.02 12.30 18.03 10.66 – – 4.67 3.43 2.83 1.14 – 6.00 7.00 – – – 3.42

32.76 35.58 – – – 29.75 – – – – 29.24 27.17 36.07 27.87 25.41 – – 22.43 21.48 26.81 25.14 – 22.86 21.88 – – – 25.59

–: No data.

water out of the sample. The volume (Voi) of water displaced is measured (equal to volume of oil imbibed). (4) The core is removed from the cell after equilibrium is reached, and remaining water in the core is forced out by displacement in a centrifuge. The volume (Vwd) of water displaced is measured. Wettability index is used to specify quantitatively the wettability of a material. The water-wetting index is defined as

WWI ¼

Sspw −Swc V oi ¼ ; 1−Swc −Sor V oi þ V od

ð1Þ

where Sspwis spontaneous water imbibition saturation, Swc is connate water saturation, and Sor is residual oil saturation. The value of WWI is from 0.0 to 1.0. The greater is WWI, the stronger is the water wetness.

Similarly, the oil-wetting index is defined as OWI ¼

Sspo −Sor V wi ¼ ; 1−Swc −Sor V wi þ V wd

ð2Þ

where Sspo is spontaneous oil imbibition saturation. The value of OWI is also from 0.0 to 1.0. The greater is OWI, the stronger is the oil wetness. The experimental data are shown in Fig. 1. It indicates that oil recovery by spontaneous imbibition increases exponentially with water-wetting index. Donaldson and Thomas (1971) studied the effects of wettability of sandstone on oil recovery and relative permeability of water and oil phases by core water flooding experimental approach in the laboratory. According to their experimental data, we analyzed the relations between wettability index and oil recovery by water flooding (see Fig. 2). In this figure, Amott wettability index (AWI) is defined as AWI ¼ WWI−OWI

Fig. 1. The relations between oil recoveries and water-wetting index.

ð3Þ

B. Ju et al. / Journal of Petroleum Science and Engineering 86–87 (2012) 206–216

209

Fig. 2. The relations between oil recoveries and Amott wettability index.

AWI is from −1.0 to 1.0 according to the definition of water-wetting and oil-wetting indices. Pore volume of water injection is defined as PV ¼

V w;inj p ; Vp

ð4Þ

where Vw, inj is the accumulated volume of water injected, and Vp is the total pore volume of sandstone core. Fig. 2 shows that oil recovery by water flooding strongly depends on Amott wettability index at the same pore volume of water injected (according to experimental data (Donaldson and Alam, 2008). More oil is displaced from the strong water-wetting sandstone core at the same water injection volume. Both the recovery obtained by spontaneous imbibition and the recovery flooded by water indicate that wettability of porous media has an effect on oil recovery. It provides the theoretical and practical evidences to change flow performances of two or more phase flow in porous media by wettability control. The next section will focus on the wettability modification by wettability-control agent. 3. Experimental study on wettability modification with WCA treatments The objective of this experiment is to study the wettability change of sandstone surface after WCA treatment. The measurement of wetting angles was conducted to recognize the wettability of the surface of sandstone samples with WCA treatment. 3.1. The description of WCA used in this work The WCA used in the experiment is a nanometer scaled powder that could change the wettability of the porous surfaces, in which the main component is SiO2, obtained by adding an additive activatable by γray, is a kind of modified ultra-fine powder with the average size of

80 nm. The bulk density of WCA is 0.060 g/ml. According to the surface wettability of the particles, WCA can be classified into three types: (1) hydrophilic, (2) neutral wettable, and (3) lipophilic WCA. IOWCA belongs to the first type and IWWCA belongs to the last type.

3.2. The function of WCA and mechanism of wettability modification When WCA is injected into porous media, four phenomena will occur: adsorption, desorption, blocking and migration with flowing fluid. When the force between the WCA particle and pore walls is attractive, it, in turn, leads to adsorption of WCA on the pore wall. Otherwise, the desorption of WCA from the pore wall will occur for the repulsion. The dynamic equilibrium of adsorption and desorption is controlled by the force type between particle and pore wall. Blocking will take place if the diameter of WCA particles is larger than the size of the pore throat, or when several WCA particles smaller than the pore size bridge at the pore throat. The migration of WCA in porous media is governed by diffusion and convection. Wettability will alter for adsorption of different wetting WCA. The wettability alteration of pore walls in the reservoir rock leads to the change in flow resistance of oil and water, which induce the changes in oil and water relative permeability. IOWCA treatment in pore media will lead to the increase in the relative permeability of the oil-phase (Kro). The treatment can be used for enhancing oil recovery. IWWCA treatment in porous media will lead to the increase in the relative permeability of the water-phase (Krw), which can be used for enhancing water injection for water injection wells. The advantage of WCA treatment lies in the fact that the relative mobilities of water and oil phase can be modified by treatment with different types of WCA. However, the disadvantage of WCA treatment is formation damage (reductions in absolute permeability (K) and porosity) caused by WCA adsorption on pore walls and blocking at pore throats. Thus a successful treatment depends on effective permeability (Krei = K × Kri) of one phase. If the relative permeability (Kri) of one

Fig. 3. Wettability change with WCA treatment. (A: Wetting angle without any WCA treatment; B: Wetting angle after IWWCA treatment; C: Wetting angle after IOWCA treatment).

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phase increases obviously and absolute permeability reduces slightly by a treatment, it leads to a successful treatment. 3.3. The procedure of contact angle measurement Contact angle is a feasible approach to understand the wettability of rock surface. The imaging method (Singhal and Dranchuk, 1975) is used to measure the contact angle. First, three sandstone core samples were cut from a block of sandstone and then furbished with ultra-fine sand paper; then, a drop of pure water was placed on the rock surface which has previously been submerged in an oil-filled transparent cell. The enlarged image of the water drop is obtained by photographing. The dimensions of the drop image are used to calculate the contact angle (θN) in the system. The angle (θN) is approximately equal to π/2, which indicates the surface of this sandstone core is almost neutral wetting (Fig. 3A). The other two sandstone core samples were immersed in suspensions of IWWCA and IOWCA respectively for 5 h and then were taken out to measure the wetting angles. The wetting angle (θWW) became much less than π/2 after IWWCA treatment (Fig. 3B), which implies the wettability of the sandstone turned into strong water-wetness (high affinity for water (Takata et al., 2005) from neutral wetness. The wetting angle (θOW) (Fig. 3C) became far greater than π/2 after IOWCA treatment, which implies the wettability of the sandstone turned into strong oilwetness from neutral wetness. 4. Mathematical model for describing WCA transport in porous media 4.1. Assumptions The mathematical model simulating two-phase flow with WCA is based on the following assumptions: (1) The flow is in isothermal condition. (2) Both sandstone (one type of porous media) and fluids are supposed to be compressible. (3) The porous media is heterogeneous. (4) The fluid flow in porous media follow Darcy's law. (5) The gravity force is considered. (6) The viscosity and density of oil and water are constant and they are Newtonian fluids. 4.2. Transport of fluids with WCA in porous media Since the fluid flow in porous media follow Darcy's law, the governing equations for slightly compressible multiphase flow and Newtonian fluids are given by the following equations:  div

k⋅krw gradΦw Bw ⋅μ w

 þ qw ¼

Fig. 4. The relative permeability curves of oil and water of a sandstone at original state and after IWWCA treatment.

  k⋅kro ∂ div gradΦo þ qo ¼ ðϕ⋅So =Bo Þ; Bo ⋅μ o ∂t

ð6Þ

Φo ¼ po þ γo ⋅z;

ð7Þ

Φw ¼ pw þ γw ⋅z ¼ po þ pcwo þ γ w ⋅z;

ð8Þ

where t is time, ϕ is the porosity of porous media, S, μ and p are saturation, viscosity, and pressure of fluids, respectively, k is absolute permeability, kr is relative permeability, B is the volume factor of fluid, q is the production or injection rate of fluid, γ is the specific gravity of fluids, z is the distance from reference level, and pc is the capillary force. For saturated flow of the oil and water phases, the sum of saturations of oil and water is equal to 1. 4.3. Transport of WCA in porous media Since WCA have wettabilities, water-wetting WCA exists in the water, and oil-wetting WCA exists in the oil phase. Inasmuch as the sizes of WCA are in nanometer scale, Brownian diffusion should be considered. Thus, the governing equation for WCA transport in porous media can be expressed as ∂ðϕSl C l Þ ∂C ∂C ∂C þ ulx l þ uly l þ ulz l − ∂x ∂z  ∂t  ∂y   ; ∂ ∂C l ∂ ∂C l ∂ ∂C þ þ þ Rl ¼ 0 ϕSl Dlx ϕSl Dly ϕSl Dlz l ∂x ∂y ∂y ∂x ∂y ∂x

ð9Þ

The initial condition for Eq. (9) is given by C l ¼ 0; t ¼ 0;

ð10Þ

Boundary condition at well injection site is

∂ ðϕ⋅Sw =Bw Þ; ∂t

ð5Þ

C l ¼ C l;inj ;

ð11Þ

where Cl is the volume concentration of WCA in phase l, Dl is the dispersion coefficient of WCA in phase l, Rl is the net loss rate of WCA in phase l, and Cl, injis the concentration of WCA in the injected fluids.

Table 2 Main parameters used the numerical simulation example. Parameters

Values

Number of grid Grid size, dx/m Cross-sectional area/10− 4 m2 Original porosity, Original permeability/μm2 Original saturation of oil Viscosity of reservoir oil/mPa⋅s Viscosity of injection water/mPa⋅s Injection rate of water/10− 8m3⋅ s− 1 Production rate of fluid/10− 8m3⋅ s− 1

50 0.02 10.0 0.25 0.85 0.78 8.50 0.61 1.50 1.50

Table 3 Main parameters and their values. Parameters Rate coefficients for surface retention of WCA in the phase l αd, 1, m Rate coefficients for entrainment of WCA in the phase l αe, 1, m− 1 A coefficient for pore throat blocking ,αp, 1, m− 1 The critical velocity for the phase l to entrain particles ,μlc, m·s− 1 Dispersion coefficient of WCA in fluid, m2⋅s− 1, Dl A constant for fluid seepage allowed by the plugged pores, kf

Value −1

0.06 0.02 0.01 0.00052 0.0008 0.35

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211

Fig. 5. The distribution of IWWCA concentration during injection of IWWCA slug (injection source at the inlet, where dimensionless distance is 0.0).

4.4. Net loss rate of WCA in transport process

The rate equation for the entrapment of WCA in pore throats in phase l can be written as

The pore spaces in sandstone mainly consist of interconnected pore bodies and pore throats. During the WCA transport carried by fluid stream in the porous media, two types WCA retention in the pore spaces may occur: deposition on pore surfaces and blockage in pore throats. For the retained WCA on pore surfaces, they may be desorbed for hydrodynamic forces, and then possibly adsorbed on other sites of the pore bodies or entrapped at other pore throats. By modifying the Ju's model (Ju et al., 2002), Rl in Eq. (9) is given by Rl ¼

∂ν l ∂νl þ ; ∂t ∂t

ð12Þ

where vl is the volume of WCA adsorbed on the pore surfaces per unit bulk volume of sandstone, vl* is the volume of WCA entrapped in pore throats from phase l per unit bulk volume of sandstone due to plugging and bridging. According to the results (Gruesbeck and Collins, 1982), there exists a critical flow velocity for surface deposition of WCA, below which only WCA retention occurs and above which retention and entrainment of WCA take place simultaneously. A modified Gruesbeck and Collins's model for the surface deposition is expressed by ∂ν l ¼ ∂t



α d;l ul C l ; when ul bulc α d;l ul C l −α e;l ν l ðul −ulc Þ ; when

ul > ulc

:

ð13Þ

In Eq. (13), αd, l andαe, l are rate coefficients for surface retention and entrainment respectively of WCA in the phase l, and μlcis the critical flow velocity for the phase l to entrain particles.



∂νl ¼ α p;l ul C l ; ∂t

ð14Þ

where αp, l is a constant for pore throat blocking. 4.5. Changes in porosity and absolute permeability Both the deposition of WCA on the pore surfaces and the blockage of WCA in pore throats may lead to the reductions in porosity and permeability. The instantaneous porosity is expressed by ϕ ¼ ðϕ0 −∑ΔϕÞ;

ð15Þ

where ΣΔϕ denotes the variation of porosity by release and retention of WCA in the porous media, and it is expressed by 

∑Δϕ ¼ vl þ vl :

ð16Þ

According to Ju's model (Ju et al., 2002), the expression for calculating instantaneous permeability due to the deposition and blocking of particles can thus be written as h in k ¼ k0 ð1−f Þkf þ f ϕ=ϕ0 ;

ð17Þ

where k0 and ϕ0 are initial permeability and porosity, k and ϕ are instantaneous local permeability and porosity of the porous media, kf is

Fig. 6. The distribution of IWWCA after injection of IWWCA slug.

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a constant for fluid seepage allowed by the plugged pores, and f is the fraction of the original cross-sectional area open to flow. 4.6. Evaluating the effect of WCA on capillary force The existence of WCA in fluid may lead to the change in capillary force due to the change of interfacial tension, which will affect the flow behaviors of two-phase displacement (Grunde et al., 2005). For two phases, capillary force for an ideal thin tube with equal diameters can be expressed as pc ¼

2σ cosθ r

ð18Þ

where σ is the interfacial tension between wetting and non-wetting phases N/m; θ is the wetting angle; r is the radius of the capillary. During the treatment with WCA, the existence of WCA in the fluid will change interfacial tension (σ) on one hand, and the adsorption of WCA on pore walls will lead to the change in wetting angle (θ) for wettability alteration on the other hand. Therefore the interfacial tension can be regarded as the concentration of WCA in the fluid and the wetting angle is expressed as the function of the retention of WCA on porous walls. In porous media such as sandstone, the capillary force is obtained by mercury injection experiments in laboratory and it is regarded as a function of the saturation of wetting phase if wettability doesn't change. Considering the wettability alteration caused by WCA treatment and the heterogeneity of sandstone, the capillary force can be regarded as    pc ¼ f Sw ; C l ; νl þ ν

ð19Þ

4.7. Evaluating the effects of WCA on relative permeability The wettability of pore surfaces is the major factor affecting the relative permeability of two phases in porous media. The WCA adsorbed on pore surfaces may induce wettability changes and further lead to the change in shape of the relative permeability curve. Supposing the spherical particles of WCA are touching each other in the form of point contact and using the real volume of particles as the denominator, the specific area of the particles is 6/d (Qin and Li, 2001) in which d is the diameter of the particles. Since vl is the WCA volume adsorbed on the pore surfaces and vl* is the volume of WCA entrapped in pore throats per unit bulk volume of the porous media, WCA adhered to the pore walls first spreads as a single layer. The surface area for particles of WCA is given by     6 : s ¼ νl þ ν l sb ¼ ν l þ ν l d

ð20Þ

occupied by WCA, the relative permeabilities of water and oil phases are taken as k′rwj and k′roj respectively. The relative permeabilities of water and oil phases are taken as a function of the surfaces covered by WCA, and the relative permeabilities of water and oil are given by

0 0 krwjp ¼ krwj þ krwj −krjw :Rs

ð23Þ

and

0 0 krojp ¼ kroj þ kroj −krjo :Rs ;

Rs ¼

s : sv

ð24Þ

ð25Þ

When s ≥ sv, the total surfaces per unit bulk volume of the porous media are completely covered by WCA adsorbed on pore body surfaces or entrapped in pore throats, and wettability is determined by WCA (Rs = 1). 5. The solution procedure to the mathematical model The mathematical model is a nonlinear system that includes the continuity equations of oil (o) and water (w) phases (Eqs. (5),(6)), the convection–diffusion–adsorption equation (Eq. (9)), and a series of auxiliary equations. The finite-difference method is adopted to transform the nonlinear partial equations into linear algebraic equation. The Implicit-Pressure /Explicit-Saturation (IMPES) technique was used to solve the pressure-saturation equation (Eq. (5),(6)) and an explicit method was employed to solve the convection–diffusion–adsorption equation (Eq. (9)). The procedures are: (1) First, the pressure distribution is obtained by solving the pressure-saturation equation (Eq. (5),(6)), then the pressure derivative for each phase at each dimension can be calculated by using the pressure distribution. The velocity of each phase (ulx,uly and ulz) can be calculated by Darcy's law when the pressure derivative is known. These velocities are used to solve Eq. (9). (2) The WCA concentration distribution is obtained by solving the convection–diffusion–adsorption equation (Eq. (9)) using explicit iterative technique. (3) The updated porosity ϕ, absolute permeability k, and relative permeabilities of oil and water phases for each grid are calculated by using Eqs. (15), (17), (23) and (24); and then return to the first step if maximum simulated time is not reached.

Considering the irregularity of WCA particles and characteristics of WCA adsorption, the surface area for particles can be modified as   6 ; s ¼ β νl þ νl d

ð21Þ

where β is the surface area coefficient. The reference (Qin and Li, 2001) gives an equation to calculate specific area of porous media, and in this work a modified equation to calculate specific area of porous media is, sv ¼ 7000ϕ

rffiffiffiffiffiffiffi ϕ ; ωk

ð22Þ

where ω is a coefficient for calculating specific area. We suppose that the relative permeabilities of water and oil phases are, respectively, krwj and kroj at a water saturation, Swj before WCA treatment. When the surfaces per unit bulk volume of the porous media are completely

Fig. 7. The relations between water cut and the concentrations of IWWCA slug injected (c is volume concentration of IWWCA in water injected).

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213

Fig. 8. The relations between oil recovery and the concentrations of IWWCA slug injected.

6. Application examples and discussion This section gives two application examples for modifying percolating performance by WCA treatment. The first example is that IWWCA is used in an oil reservoir to improve oil recovery. The second one is that IOWCA is used in a low permeability oil reservoir to enhance water injection capacity.

6.1. Improving oil recovery by IWWCA treatment For the mature oil field, improving oil recovery is a major task. Since IWWCA treatment can increase the tendency of strong water-wetness by adsorbing IWWCA on porous surfaces, it can be used to improve oil recovery in the oil fields by water flooding. The following simulation of a one-dimensional example is conducted to predict production performance with injection of an IWWCA slug. The injection and production process is: (1) Keeping a constant production rate at the outlet of the one-dimensional porous media model during the whole production process. (2) Injecting water at the inlet at the same rate of production rate until the accumulated water injection volume is up to 1.0 pore volume (PV) of the model. (3) Injecting a 1.0 PV IWWCA slug. (4) Injecting 2.0 PV water after the IWWCA slug is injected. The main parameters such as grid size, fluid and rock properties used in the numerical simulation runs are shown in Table 2. The proposed model has some sensitive parameters such as rate coefficients for surface retention of WCA and dispersion coefficient. Some parameters are difficult to be obtained for the complexity. The approaches for identifying these parameters are obtained by numerical matches and modification in the range of experiential value. These parameters used in this work were listed in Table 3. The two-phase relative permeability curves of before and after IWWCA treatment are shown in Fig. 4.

Fig. 5 shows the wave travel process of the dimensionless concentration of IWWCA in water phase along the dimensionless distance during the injection of an IWWCA slug. The concentration increases with the increase in volume of IWWCA injected and the concentration wave of IWWCA travels toward the outlet (dimensionless distance is 1.0) during an IWWCA injection. The decline of IWWCA concentration along the distance is caused by its adsorption on the pore surfaces, entrapment at pore throats and diffusion. Fig. 6 demonstrates the traveling behaviors of the concentration wave of IWWCA during fresh water injection following an IWWCA slug injection. It indicates that the IWWCA concentration decreases gradually and travels toward to the outlet and only a small percentage of IWWCA in water is in the vicinity of the outlet after injection of 0.5 PV water. The IWWCA slug is gradually displaced out by water injected from inlet. Fig. 7 gives the water cut (water cut is defined as the percentage of water in production fluid) of production fluid changing during the whole injection and production period. The water cut of production fluid is zero before the 0.12 PV water is injected and then water cut increases dramatically after the water break through at the outlet. The water cut increases to 93.5% when 1.0 PV water is injected. The water cut doesn't decrease immediately after IWWCA injection for the reason that water cut is controlled by two-phase flow behavior at the outlet and needs time for IWWCA sweeping to the outlet. When the injected IWWCA sweeps the vicinity of the outlet and leads to wettability alteration, which, in turn, reduces water cut of the production fluid from the outlet. The water cut decreases earlier and lower for the higher concentration of IWWCA injected. Water cut decreases down to 68.1% after injection of 0.8 PV of IWWCA slug (c = 0.04) (1.0 PV water and 0.8 PV IWWCA). Fig. 8 shows the effect of concentration of IWWCA on oil recovery. When 1.0 PV of water is injected, the oil recovery is 40.2%. The oil recovery isn't improved immediately after the beginning of the

Fig. 9. The relations between final oil recovery and the concentrations of IWWCA slug injected after 4.0 PV of water and IWWCA was injected.

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Table 4 Main parameters of the samples and evaluation on heterogeneity (1 md = 10− 15 m2). Type

Sample number

Average porosity

Average permeability/md

Variation coefficient

Dykstra–Parsons coefficient

A B C

32 41 13

0.221 0.199 0.166

39.8 12.5 1.7

0.726 0.821 0.634

0.745 0.834 0.676

IWWCA injection. When the 1.0 PV of IWWCA slug injection is finished, the oil recovery improves for the slug with concentration of 0.02 and 0.04. Comparing with water flooding, oil recovery continues to increase after the IWWCA slug injection is finished. When total injection of 4.0 PV of water and IWWCA finished, the relations of oil recovery and concentration of IWWCA slug are shown in Fig. 9. The simulation results have a good match with experimental data, which validates the mathematical model. It shows the final oil recovery is from 51.03% (IWWCA concentration = 0.00) to 67.17% (IWWCA concentration = 0.04). The recovery is 66.41% with IWWCA treatment ((IWWCA concentration = 0.02) and oil recovery is improved up to 15.38% in comparison to normal water injection. It implies that the increase in the concentration of the IWWCA slug leads to dramatic increase in oil recovery when the concentration of the IWWCA slug is less than 0.02. However, when the concentration of the IWWCA slug is larger than 0.02, the further increase of the concentration has a slight effect on oil recovery. It indicates that the

injection of 1.0 PV IWWCA with the concentration of 0.02 is enough to lead to pore surfaces fully covered by IWWCA. Overmuch adsorption of IWWCA on pore surfaces does not further change the wettability of pore surfaces. Therefore, the increase in concentration (> 0.02) doesn't obviously improve oil recovery. In addition, multilayer adsorption of IWWCA on pore walls will cause the reduction in porosity and blocking at narrow pore throats, which leads to formation damage. Both the simulation and experimental results indicate the improvement in oil recovery and the decrease in water-cut obtained by IWWCA treat are obviously desirable at pore level in onedimensional model. However, for an actual reservoir, the oil recovery depends on displacement efficiency (DE) as well as volumetric sweep efficiency (VSE). While the core-scale experiments and 1D simulation validate an obvious increase in DE treated by IWWCA, the recovery for actual reservoirs is lower than that of the model used in this study due to VSE less than 1.0. For most reservoirs, the range of VSE is about 0.40–0.60. Therefore, it may be deduced that the EOR obtained by IWWCA treatment for actual oils is about 5.35 to 8.03% (based on 15.38% of oil improved). 6.2. Enhancing water injection by IOWCA treatment This example demonstrates that the IOWCA treatment enhances water injection for a low permeability oilfield (N.Zh oil field, Bohai

Fig. 10. (A) Well locations and the contours of the depth of formation C1. (B) The fence diagram of the five wells. (W1-3 is IOWCA treatment well).

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215

Fig. 11. The water injection rate ratios change with time.

Bay Basin, East China). The field was discovered in 1966. Formation C is an abnormal high-pressure sandstone pay zones. The initial average pressure and temperature are 53.5 MPa and 123.6 °C respectively, and current pressure has fallen down to 31.5 MPa. The pay zones were classified into three types according to capillary force data and pore structures. Variation coefficient and Dykstra–Parsons coefficient (Dykstra and Parsons, 1950) are used for evaluation of heterogeneity of the permeability data. The main parameters of the pay zones for the treatment are shown in Table 4. The average permeabilities of the core samples are less than 50 md, which belongs to low permeability pay zones (McKay and Aidan, 1991). Due to formation damages caused by the blockage of the nanoparticles at small throats of oil formation, the permeability of the formation chosen for IOWCA treatment should be larger than 5 md. Therefore, the formation of Type A and B in Table 4 are candidates for IOWCA treatment in case of a failure induced by formation damage. Both variation coefficient and Dykstra–Parsons coefficient of the permeability indicate that the oil formation has a strong heterogeneity, which is unfavorable for the improvement in a swept volume. A five-point well pattern is used for numerical simulation of the treatment. The well locations and fence diagram are shown in Fig. 10. The injection treatment well (W1-3) locates in the center of the five well pattern. The data such as formation depth and thickness in the figure are obtained by well logging interpretation. Fig. 11 shows the changes in water injection ratios (Injection ratio is defined as the water injection rate using IOWCA treatment divided by water injection rate before IOWCA treatment. If the ratio is larger than 1.0, it indicates water injectivity is improved by the treatment). It implies that the injection rate is about 1.6–1.8 times of its original rate after IOWCA treatment. The numerical results have good matches with field data of the injection well. The numerical simulation was validated by well data.

Six injection wells (Four wells in Formation C) in the field were selected for field trials with IOWCA treatments for enhancing water injection during the past five years. The injection volume of IOWCA suspension is 1 m 3 per meter of the sand formation in thickness. And the average voluminal concentration of IOWCA is 0.21. The field data after treatments with IOWCA are shown in Fig. 12. It indicates that the injection rates of 6 injection wells for field tests are 1.1 to 4.4 times of their original rates after IOWCA treatment. The field tests indicate that it is feasible to enhance water injection by IOWCA treatment. 7. Conclusion (1) Experimental data obtained by imbibition show that the relation between the water-wetting index and oil recovery is an exponential correlation. Water flooding experimental data show that oil recoveries increase with the increase in Amott wettability indices. (2) The changes in wetting angles verify the wettability alteration by WCA treatment. IWWCA treatment leads to the wetting angle (θWW) much less than π/2 and IOWCA treatment causes the wetting angle (θOW) to become far larger than π/2. (3) A two-phase percolation flow mathematical model considering the wettability control by injecting WCA is presented and a new numerical simulator for simulating two-phase flow by wettability treatment is developed. (4) The numerical results by injection of IWWCA slugs shows that the concentration of IWWCA has a noticeable effect on watercut and oil recovery. Further increase in IWWCA concentration above 0.02 has a slight effect on final oil recovery. The recovery is up to 66.41% with IWWCA treatment (c = 0.02) and the recovery is more than 15.38% that of normal water injection.

Fig. 12. The water injection rate ratios of 6 wells after IOWCA treatment.

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(5) IOWCA treatments of 6 oil-field injection wells show that water injection capacity increases up to 1.1 to 4.4 times (average 2.75 times) of the capacity before treatment. (6) The numerical results of the well (W1-3) have good agreements with field data, which validates the mathematical model presented in this work. The field tests of the 6 injection wells indicate that it is feasible to enhance water injection by IOWCA treatment. Acknowledgments The work was supported by the “the Fundamental Research Funds for the Central Universities” and the national science and technology major projects 2011ZX05009-002, 2011ZX05009–006 and the Project-sponsored by SRF for ROCS, SEM, of which support are appreciated. The authors would like to thank Dr. Y.B. Xiong and the faculty in the core analysis lab, Research Institute of Exploration and Development, Z.Y. oil company, PetroChina, for their partial experimental work on the preparation for rock cores. The authors would also like to thank Dr. Yu-Shu Wu, Colorado School of Mines, for his advice on simulation and Dr. ED Holroyd, a research physical scientist for U.S. Bureau Reclamation, for his work on grammar correction and clarity. The editors and reviewers are cordially appreciated for their Guide and valid comments. References Amott, E., 1959. Observations relating to the wettability of porous rocks. Trans. AIME 215, 156–162. Anderson, W.W., 1987a. Wettability literature survey: Part 5—The effects of wettability on relative permeability. J. Petrol. Technol. 39 (11), 1453–1468. Anderson, W.W., 1987b. Wettability literature survey: Part 6—The effects of wettability on water flooding. J. Petrol. Technol. 39 (12), 1605–1622. Donaldson, E., Alam, W., 2008. Wettability. Gulf Publishing Company, Houston.

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