Theoretical Research in Laboratory and Field Trial of Micro-Nano-Oil Displacement System Conformance Control Technology

With the rapid development of economy, the consumption demand for energy, especially oil resources, has been increasing year after year, which brings potential risks to energy security. Enhanced oil recovery technology by chemical flooding has become an important way of resource utilization and sustainable development. Due to low cost and simple operation, polymer flooding technology has been widely used as an effective method for enhancing oil recovery and obtained good results in increasing oil production and decreasing water cut (L. F. [1]). But for strongly heterogeneous reservoirs, the development effect of polymer flooding becomes worse in the late stage. Due to the reservoir heterogeneity and polymer retention characteristic, the phenomenon of “entry profile inversion” occurs, which is not favorable for further expanding the swept volume and enhancing oil production. At the same time, the water cut of producing wells becomes higher again and the polymer utilization rate decreases. Consequently, the above factors have a negative impact on the development effect of polymer flooding [2]. Fortunately, a new enhanced oil recovery (EOR) technology, using dispersion system as oil displacement agent, has been developed to solve the above problems. In recently years, different methods are adopted to synthesize small elastic particles with different sizes, in order to match with pore throat [3]. Pu et al. evaluated the micro morphology and particle size distribution of self-made polymer microsphere PM1 in laboratory, then tested the core throat distribution by core mercury injection method, and carried out a series of core physical simulation experiments [4]. Bao et al. prepared AMPST polymer microspheres by two inverse emulsion polymerization methods and optimized the synthesis process of microspheres. The structure and properties of AMPST microspheres were characterized by FTIR, GPC, optical microscope, SEM, TG, rheological analyzer, and core plugging experiment [5]. Dai et al. studied the matching law of elastic gel dispersion (DPG) particles and reservoir pore throat through indoor physical simulation experiment and proposed the deep control mechanism of gel dispersion particles in the core pore throat [6]. Inspired by the remarkable underwater wet adhesion of mussel byssus, Liu et al. found that hydrogel particles which can adhere stably on the fracture rock surface in reservoir conditions could achieve long-lasting reservoir control effect. They prepared the size-controllable biomimetic functional hydrogel particles by mechanical shearing after bulk hydrogel was constructed by catechol-functionalized polyacrylamide and phenolic resin crosslinking agent and then investigated the influence of solution salinity on the aggregation and adhesion of hydrogel particles via scanning electron microscope (SEM), colloidal probe atomic force microscope (AFM), and quartz crystal microbalance with dissipation (QCM-D) [3].

Although progress has been made in performance evaluation and oil displacement effect of the dispersed system, there are still many problems [7–11]. In particular, most of the above systems are limited to indoor synthesis and evaluation [4, 12–15]. Very few field applications have been carried out. In order to solve this problem, we proposed a micro-nano-oil displacement system (MNS), used as displacing phase, to adjust the permeability of different parts of reservoir and improve sweep efficiency for conformance control. This can enhance oil recovery by working jointly with water. This system has the characteristics of good elasticity, strong deformation ability, and narrow particle distribution. After entering into the porous media, it can migrate, be captured, and pass through the throat by deformation, which can significantly expand the swept volume. In particular, in recent years, field tests of micro-nano-oil displacement system have been carried out in many oilfields with different conditions, which contains the reservoir temperature from 24 to 126°C, crude oil viscosity from 1.36 to 156 mPa·s, water cut from 81.4% to 97.5%, and recovery degree from 9.55% to 64.4%. The results show that they all obtain good technical and economic effect, with the lowest input-output ratio of 2.33 and the highest of 14.37 [16–19].

However, compared with its field test and application status, the reservoir adaptability evaluation and oil displacement mechanism are still in the initial stage. It is urgent to study on the related methods and action mechanism. Therefore, theoretically guided by reservoir engineering, physical chemistry, and biological fluid mechanics, by means of macroscopic physical simulation and microfluidic technology, this paper researched its physicochemical properties, reservoir adaptability, transport and deep fluid diversion ability, and oil displacement mechanism. The research results provide theoretical basis and technical support for the popularization and application of micro-nano-oil displacement system conformance control technology, which may also provide some reference for oil companies to make investment decision in low oil price period. Furthermore, the security of energy supply can be fully guaranteed.

Chemical reagents include Tween 80, Span 80, polyvinyl alcohol, dilute hydrochloric acid, formaldehyde, acrylamide, ammonium persulfate, and N,N$′$-methylene bisacrylamide. The reagents used in the experiment are all analytically pure.

The polymer was partially hydrolyzed polyacrylamide (HPAM) powder, with a relative molecular mass of $2500×104$ and solid content of 90%. The dyeing agent was sodium fluorescein, produced by Tianjin Damao Chemical Reagent Factory. The experimental oil and water were all from SZ Oilfield. The viscosity of crude oil was 45 mPa·s at 60°C. Water quality analysis is listed in Table 1.

The preparation method of the micro-nano-oil displacement system was simple. The inverse emulsion polymerization of a one-step reaction in situ crosslinking was adopted. This system was a two-component interpenetrating network structure formed by main molecules and auxiliary molecules. It has long-term stability at 120~160°C. In addition, this system has flexibility and expansibility. It can be directly injected into the oil layer, and it has good oil displacement performance. The specific preparation method was as follows:

• (1)

  120 parts of dispersant and 40 parts of Tween 80-Span 80 composite emulsifier were mixed at room temperature to obtain solution A, and in the composite emulsifier, the mass ratio of Tween 80 and Span 80 was 1 : 1

• (2)

  40 parts of aqueous solution of polyvinyl alcohol, 10 parts of dilute hydrochloric acid, and 10 parts of diluted aqueous solution of formaldehyde were mixed to obtain solution B. The degree of polymerization of polyvinyl alcohol was 200~6000, and its weight percentage in the aqueous solution was 10%. The solution concentration of dilute hydrochloric acid and diluted aqueous solution of formaldehyde was 5%

• (3)

  16 parts of acrylamide, 0.01 parts of ammonium persulfate, 0.2 parts of N,N$′$-methylene bisacrylamide, and 10 parts of water were mixed to obtain solution C

• (4)

  At the stirring speed of 100 r/min, solution C was added to solution B. Stir evenly at room temperature to form a transparent and clear solution, and continue stirring for 20 minutes to obtain solution D

• (5)

  At the stirring speed of 1000 r/min, solution D was added to solution A. The mixture was emulsified at room temperature for 10 minutes to obtain solution E

• (6)

  At the stirring speed of 350 r/min, solution E was placed in 75°C water bath to conduct the crosslinking polymerization of in situ two-component interpenetrating. The polymerization can take 5 hours to obtain the micro-nano-oil displacement system

By using the scanning electron microscope, it was found that the system was a three-dimensional directional interpenetrating network structure with spherical appearance.

The core was made of quartz sand cemented by epoxy resin. Compared with other core-making technology, this method has certain advantages and is widely used in the performance evaluation of oil displacement agent. For more details, see Chinese patent 200510063665.8.

• (1)

  Columnar core: 10 cm length and 2.5 cm diameter, with permeability from 150 to $6000×10−3μm2$⁠, used to test the reservoir adaptability of MNS (see Figure 1)

• (2)

  “Five-spot” simulation model: $4.5cmheight×30cmwidth×30cmlength$ with three layers, each layer with permeabilities of $300×10−3μm2$⁠, $800×10−3μm2$⁠, and $2400×10−3μm2$ from bottom to top, used to test its deep fluid diversion ability (see Figure 2)

Long core, 18 m length with 7 pressure measuring points [20, 21], with permeability of $5000×10−3μm2$⁠, was used to test its migration ability (see Figure 3).

Micro models can be used to observe the micro transport and oil displacement mechanism of MNS. For more details, see Chinese patent 201410153168.6.

• (1)

  Microfluidic chip: $0.5cmheight×1cmwidth×4cmlength$⁠, made by PMMA (acrylic), including the “straight channel” model with 10-50 μm pores and “curved channel” model with 10-30 μm pore. They were used to observe its micro oil displacement mechanism (see Figure 4)

• (2)

  Three-layer heterogeneous micro model: $4.5cmheight×4.5cmwidth×4.5cmlength$⁠, composed of quartz sand with three different sizes, used to observe its deep fluid diversion mechanism (see Figure 5)

A three-mesh metallographic microscope, Germany Leica Company DM1750m, was used to observe the morphology of MNS. A laser particle size analyzer, Microtrac Inc. S3500, was used to measure the size distribution of MNS particles before and after expansion. An interfacial tension instrument, STX-500H, was used to test the interfacial tension between the displacement agent and crude oil. Visual micro experimental equipment: including stereomicroscope, image acquisition and processing system, digital injection pump, and microfluidic chip. The stereomicroscope is used to observe images with magnification up to 7-50 times. The image acquisition and processing are completed by a computer. The visual microexperimental process is shown in Figure 6(a). Core flooding experimental equipment: including a constant-flux pump, a pressure sensor, a core holder, a hand pump, and an intermediate container. All the apparatuses except the constant-flux pump and the hand pump are kept in a 60°C thermostat. The core flooding experimental process is shown in Figure 6(b).

The research ideas and technical route of this paper are given in Figure 7.

During the experimental process, the injection rate is 0.3 mL/min, and pressure recording interval is 30 minutes. The range of core permeability is from 150 to $6000×10−3μm2$⁠.

• (1)

  Specific experimental steps of transport ability test: first, inject 0.3 PV MNS solution, and then, perform subsequent water flooding until the pressure at each pressure measuring point reaches steady. Second, let stand the core for 3 days, and perform the second subsequent water flooding. Third, let stand the core for another 3 days, and perform the third subsequent water flooding. During the experimental process, the injection rate is 0.5 mL/min, and MNS solution is injected into the core immediately after preparation

• (2)

  Oil displacement effect evaluation: the oil displacement experimental scheme is shown in Table 2 

The visual microexperimental scheme is shown in Table 3.

According to the preparation method, MNS with a series of particle sizes in different sizes (from nanometer to micrometer) can be obtained. And it has good expansion ability. By using the three-mesh metallographic microscope, MNS in different sizes before and after expansion is shown in Figure 8.

As shown in Figure 8, the appearance of MNS is spherical and its distribution in solvents is uniform. MNS are spherical polymer colloids with 3D network structure. This special structure not only makes MNS insoluble in water but also has good water absorption and expansion performance. In addition, the particle size of MNS2 is larger than that of MNS1. Through FTIR test, the comparison between MNS and PAM is given as follows in Figure 9.

From Figure 9, the FTIR spectrum shows that the main component of MNS is partially hydrolyzed crosslinked polyacrylamide, which contains alkane sulfonate surfactant. And the existence of strong hydrophilic group of carboxylic acid or sulfonate is the possible reason for its rapid expansion in water.

Furthermore, take MNS2 as an example; by using laser particle size analyzer, the size of MNS2 before and after expansion is shown in Figures 10(a) and 10(b), respectively.

As shown in Figure 10(a), the median value (⁠$d50$⁠) is 15.62 μm and that in Figure 10(b) is 63.73 μm. Therefore, according to formula (1), the expansion multiple is 4.08. As for MNS1, the median value (⁠$d50$⁠) of the initial particle size is 2.36 μm and the expansion multiple is 7.18. Furthermore, its size distribution is narrow and relatively concentrated compared with the traditional displacement agent (polymer solution). For polymer solution, it is a continuous phase system, and its particle size distribution range is wide. Therefore, under the action of Brown force, polymer solution enters different sizes of pores indiscriminately, resulting in irreversible blockage in small pores. However, the inaccessible pore volume of MNS is larger. MNS particles preferentially enter high-permeability layer and plug the larger pores, causing little damage in the low-permeability layer. On the other hand, its carrier fluid turns into the low-permeability layer and displaces oil more efficiently.

The effect of temperature and salinity on MNS expansion ability is further analyzed. Firstly, at different temperatures, the relationship between expansion multiple and salinity is shown in Figure 11(a). Secondly, at different salinity, the relationship between expansion multiple and temperature is shown in Figure 11(b).

From the above formulae, when the system is stable, the systematic chemical potential (⁠$ΔF$⁠) and elastic free energy (⁠$ΔFel$⁠) are both zero. The effect of salinity on the expansion multiple demands on the change of $ΔFel$⁠. After absorbing water, there are many dissociable groups on the polymer molecular chains of MNS, which produce positive cations and macromolecular negative ions. Furthermore, with the increase of cation concentration, the interaction between polymer molecules becomes weak and the elastic free energy reduces. Therefore, the system tends to be more stable, and its expansion ability decreases accordingly.

On the basis, from Figure 11(a), when the solvent water salinity is from 0 to 5000 mg/L, the maximum range of expansion multiple is 3.56 at 65°C. Therefore, at high temperature, the effect of salinity on the expansion ability of MNS is more obvious. In Figure 11(b), when the temperature is from 25°C to 65°C, the maximum linear slope is 0.098 with water salinity of 729 mg/L. So the effect of temperature on the expansion ability is more obvious at low-salinity condition. In conclusion, at high temperature, the salinity plays a dominant role in the expansion ability of MNS. At lower salinity, its expansion ability is more sensitive to temperature.

According to the core flow experiment, $FR$ and $FRR$ of MNS1 and MNS2 are shown in Table 4.

As shown in Table 4, the MNS concentration and core permeability both have effect on $FR$ and $FRR$⁠. At the same concentration, $FR$ and $FRR$ decrease with the increase of core permeability. This is because when core permeability increases, the pore throat size becomes larger. And MNS particles are easier to pass through the core. So the seepage resistance decreases, and the fluid diversion effect becomes worse.

Based on formula (8), the influence laws of MNS particle sizes, solution concentration, and core permeability on its seepage characteristics and reservoir adaptability are further explored, which are shown in Figure 12.

As shown in Figure 12, when MNS particle size and solution concentration increase, as well as core permeability decreases, $FR$ shows the continuous rising trend, which indicates that synergistic effects exist between the three influencing factors. As a result, the probability of particle bridge blocking becomes larger, which changes the pore space in porous media and reduces the flow channels. Therefore, MNS effectively block the large pores and increase the seepage resistance and thus realize deep fluid diversion and expand sweep volume, which is conducive to further enhancing oil recovery.

Through literature research, the previous studies on the reservoir adaptability of MNS were mainly focused on the median value of sizes between particles and pore throat [23–25]. Therefore, it is necessary to further quantitatively analyze the matching relationship of size distributions between MNS particles and pore throat.

According to formula (9) and the reservoir adaptability evaluation result (see Table 4), the matching coefficient plates of MNS1 and MNS2 at different permeabilities are obtained, which are shown in Figures 14(a) and 14(b), and the corresponding values are given in Table 5.

As shown in Figure 14 and Table 5, at the same permeability, the five matching coefficients $x1$⁠, $x2$⁠, $x3$⁠, $x4$⁠, and $x5$ gradually increase, while with the increase of permeability, the matching coefficients decrease. Furthermore, according to the plugging rate, the migration and plugging modes of MNS are divided into 3 modes: efficient, normal, and inefficient plugging. The variable range of matching coefficients for different modes is shown in Table 6.

As shown in Table 6, firstly, the efficient plugging mode is mainly used for profile control near wellbore in the strong heterogeneity reservoirs. Secondly, the normal plugging mode can both realize the goal of deep profile control and oil displacement, because it can not only adjust profile effectively in the early stage of injection but also migrate to the deep reservoir, which increases the injection pressure and enhances oil recovery significantly. Thirdly, in the inefficient plugging mode, the particle size of MNS is too small to form effective plugging in large pore.

The pressure gradient at each pressure measuring point during different flooding stages is shown in Table 7.

As shown in Table 7, during the injection process of MNS into the 18 m length core, as the injection pore volume increases, the pressures of measuring points 1, 2, 3, and 4 increase in turn and MNS particles transport gradually to these points, while the pressure changes of measuring points 5, 6, and 7 are not obvious, which indicates that MNS has not yet migrated to these areas. For the 1^st, 2^nd, and 3^rd subsequent water flooding, the pressures of measuring points 5, 6, and 7 increase gradually, which shows that the size of MNS particles becomes larger after absorbing water and the number of retained particles in porous media increases. Therefore, the probability of particles bridging and plugging also increases, resulting in the continuous increase of seepage resistance and injection pressure. Then, MNS has moved to the back area of the core, which shows MNS has good transport ability.

As shown in Figure 15, from the comparison of pressure increase amplitude at each pressure measuring point, the difference is very small, which further shows that MNS has strong transport ability in the core pore. During the subsequent water flooding stage, the pressure at each pressure measuring point increases firstly, then decreases, and finally tends to balance. This is because MNS particles absorb water gradually, the sizes increase, and the plugging effect improves. Furthermore, with the increase times of subsequent water flooding, the MNS particles move forward. As a result, the pressures in the front area of the core decreases, while those in the back area increase gradually.

(1) The Experimental Results of Oil Recovery Rate. In runs 1-1 and 1-2, by the injection method of constant pressure, the contrast results of EOR between polymer solution and MNS are shown in Table 8.

As shown in Table 8, the ultimate oil recovery rate of polymer flooding in run 1-1 is 26.14%, and that of MNS flooding in run 1-2 is 33.11%. Therefore, the oil recovery increment of MNS flooding is greater than that of polymer flooding, which indicates that MNS has good oil displacement effect.

(2) Dynamic Characteristics. In runs 1-1 and 1-2, the dynamic characteristic curves in the experimental process are shown in Figure 16.

As shown in Figure 16, under the condition of the same agent type, composition, and slug size, the oil increment and water reduction effect of MNS flooding is greater than that of polymer flooding. This is because due to the strong retention capacity of polymer solution, the cross section in core pore reduces and the flow resistance increases, which causes the injection ability and liquid production speed decrease greatly (see Figure 16(a)). And these have a significant negative impact on the oil recovery increment (see Figures 16(b) and 16(c)). Meanwhile, compared with the injection method of constant speed, the injection method of constant pressure used in this experiment is much closer to the actual situation of the field trial, because the specified injection pressure must not exceed the fracture pressure of the reservoir rock and it is also limited by the rated working pressure of injection equipment. Therefore, the constant pressure experiment can more truly reflect the oil increment and water reduction effect of oil displacement system.

The reason why MNS have the above-mentioned good performances is its advanced mechanism. The expanded MNS particles are prone to generate elastic deformation and gather towards the channel center, due to the fluid shear force. Therefore, MNS particles preferentially enter the large pores in the high-permeability layer and have little impact on the low-permeability layer, which do not cause damage. So the particle phase separation phenomenon is easy to occur (see Figure 17), which make MNS show the properties of “plugging large pores while leaving small ones open” when migrating in porous media. Furthermore, the division of labor between MNS particles and their carrier fluid jointly improve sweep efficiency and achieve the remarkable effect of oil increment and water reduction.

This phase separation phenomenon is validated from the straight channel and curved channel, respectively, which is shown as follows.

In biophysical fluid mechanics, when blood cells flow through branch areas of capillaries during the blood circulation process, they tend to flow into the larger branch while little enter into the smaller branch. This phenomenon is called the “Fahraeus-Lindqvist” or “Zweifach-Fung” effect. And this can be used to separate blood cells and plasma (in Figure 17, fluid enters from the entrance on the left and flows out from the two outlets on the right).

On this basis, the microfluidic technology is used to observe the migration characteristics of MNS and polymer in different channels, and the flow state photos in microfluidic chips are shown in Figures 18(a) and 18(b). It can be seen that, when the particle size is larger than 1 μm, MNS gather at the channel center and choose to enter the main channel with low resistance and high velocity, due to the action of fluid shear force, while most carrier liquid flows out from the side channel.

On the contrary, there is great difference between the particle migration of MNS and polymer solution. For polymer solution, its molecular coil size is larger than 1 μm. So due to Brownian motion, it enters into large and small pores indiscriminately, resulting in irreversible blockage of small pores. And this is also the primary cause for the different effects of the two agents on the “entry profile inversion.”

When fluid flows in a curved channel, the situation is more complex. According to the mass conservation law, a pair of counterrotating and symmetrical eddies are formed in the vertical direction of fluid flow. These are located at the upper and lower parts of the cross section, respectively, which are called Dean vortices (see Figure 19). The Dean vortices exert drag force on particles in the fluid, called Dean drag force (⁠$FD$⁠).

Furthermore, the microfluidic technology is used to observe the flow state of MNS and polymer solution in microchip at different flow velocities, which is shown in Figures 20 and 21.

As shown in Figures 20 and 21, the inertial focusing flow of particles does not occur at low velocity. However, as the flow velocity increases, a band of particles appears. When the flow velocity further increases, the band becomes wider and divergent, which causes the inertial focusing phenomenon gradually disappear. On the contrary, MNS still remain the inertial focusing phenomenon, and the focusing degree further improves. In analysis from the fluid mechanics aspect, the flow state of particles in a curved channel is determined by the ratio (⁠$Rf$⁠). In formula (10), the lift coefficient $fRc,xc$ is proportional to Reynolds number (⁠$Rc$⁠), that is, $fRc,xc∼Rcn,n<0$⁠. Therefore, $Rf$ can be written as $Rf∼1/δ×a/Dh×ρUmDh/μn,n<0$⁠. It can be seen from the above formulae that the flow velocity is an important factor affecting the flow state of particles. Furthermore, at the high flow rate, the inertial focusing flow of MNS does not disappear like the polymer solution. The reason is that the ratio $Rf$ is proportional to the cubic of particle diameter, so the inertial focusing of larger particles is more obvious. As a result, the phase separation phenomenon occurs.

In conclusion, due to the phase separation phenomenon of MNS particles, they preferentially enter the high-permeability layer and generate effective plugging, while little particles enter into small pores. So MNS has little damage on the low-permeability layer. Therefore, compared with polymer solution, MNS flooding technology can slow down the severity of profile reversal or delay the time of profile reversal.

In recent years, MNS conformance control technology has been widely applied in many reservoirs. Take 8 oil fields as examples; its geological reservoir conditions and technical-economic effect are shown in Table 9.

As shown in Table 9, MNS conformance control technology has obtained good technical and economic effect in the 8 oilfields, with the lowest input-output ratio of 1.67 and the highest of 14.37.

Furthermore, in order to further analyze the influencing factors of EOR, the relationship between EOR and permeability, porosity, temperature, salinity, crude oil viscosity, recovery degree, water cut, and injection pore volume is established, by means of principal component analysis. The actual data in Table 9 is fitted by multivariate linear regression using the professional statistical analysis software SPSS, and the fitting accuracy results are shown in Table 10.

According to formula (11), the effects of permeability, porosity, temperature, salinity, crude oil viscosity, recovery degree, water cut, and PV on EOR are analyzed in Figure 22.

As shown in Figure 22, the order of influence magnitude is as follows: permeability, temperature, PV, salinity, crude oil viscosity, water cut, recovery degree, and porosity. Therefore, before conducting MNS conformance control technology, permeability is the first major consideration. On this basis, the influence law of recovery degree, water cut, and PV on EOR can be further analyzed: with the increase of injection pore volume, the lower recovery degree and water cut, the EOR increases continuously. Therefore, in order to achieve the better oil increment and water reduction effect, these factors should be taken into consideration. Furthermore, with the application scope of MNS conformance control technology continues to be expanded, this technology has been continuously improved.

HBDY, a sandstone reservoir, is a complex fault block with high recovery degree (36.2%) and water cut (82.9%), which is given in Figure 23. The dominant channel is developed, and the corresponding injection production well pattern is not good. The average viscosity of underground crude oil is 6.3 MPa s. The reservoir temperature reaches 90°C, and the mineralization degree is 10701 mg/L. To further enhance oil recovery, MNS conformance control technology has been applied, and the technical and economic effect is successful.

The slug design is shown in Table 11, and the injection method of “front slug” + “main slug” is adopted. In addition, the oilfield sewage is used for injection, the cumulative injection volume is 0.06 PV (⁠$27.8×104m3$⁠), and the injection time is 463 days. Furthermore, the production curves of HBDY are given in Figure 24.

As shown in Figure 24, the oil increment is 35154.4 t, which realize the income of 11469.0 KUSD. The operating cost for per barrel is $12.6, and the input-output ratio is 1 : 3.2. Even if the oil price is 30 USD/B, the input-output ratio of 1 : 2.4 can still be achieved, which proves the success of this conformance control technology.

• (1)

  MNS with a series of particle sizes can be obtained. And it has good expansion ability. For MNS1 and MNS2, the median value (⁠$d50$⁠) of the initial particle size is 2.36 μm and 15.62 μm, respectively. And the expansion multiple is 7.18 and 4.08, respectively. Furthermore, at high temperature, the salinity plays a dominant role in the expansion ability of MNS, while at lower salinity, its expansion ability is more sensitive to temperature

• (2)

  MNS concentration and core permeability both have effect on $FR$ and $FRR$⁠. The migration and plugging modes of MNS are divided to efficient, normal, and inefficient plugging modes. The corresponding particle size should be selected according to the target oilfield

• (3)

  After entering into porous media, MNS has strong transport ability. MNS particles absorb water gradually, the sizes increase, and the plugging effect improves. Under the condition of constant pressure injection, the same agent type, composition, and slug size, the oil increment and water reduction effect of MNS flooding is greater than that of polymer flooding, increasing by 6.96%

• (4)

  MNS conformance control technology has obtained good technical and economic effect in the 8 oilfields, with the lowest input-output ratio of 1.67 and the highest of 14.37, due to its good performances and advanced mechanism—unique particle phase separation phenomenon

$E$⁠:

Expansion multiple, dimensionless

$D1$⁠:

Median value (⁠$d50$⁠) of MNS particle size before expansion (μm)

$D2$⁠:

Median value (⁠$d50$⁠) of MNS particle size after expansion (μm)

$δP1$⁠:

Pressure difference during water flooding (MPa)

$δP2$⁠:

Pressure difference during MNS flooding (MPa)

$δP3$⁠:

Pressure difference during subsequent water flooding (MPa)

$K$⁠:

Core permeability, 10^-3 μm²

$K1$⁠:

Core permeability before MNS injection, 10^-3 μm²

$K2$⁠:

Core permeability after MNS injection, 10^-3 μm²

$D$⁠:

Particle size of MNS (nm)

$C$⁠:

Solution concentration (%)

$a,b,c,d$⁠:

Parameters of empirical model, dimensionless

$x1$⁠, $x2$⁠, $x3$⁠, $x4$⁠, $x5$⁠:

Matching coefficients on the distribution curve of MNS and pore throat, dimensionless

$Dp$⁠:

Particle sizes of MNS corresponding to cumulative probability of 10%, 30%, 50%, 70%, and 90% (μm)

$DR$⁠:

Pore throat sizes corresponding to cumulative probability of 10%, 30%, 50%, 70%, and 90% (μm)

$FL$⁠:

Inertia lift (N)

$μ$⁠:

Fluid viscosity (mPa·s)

$Rp$⁠:

Reynolds number of particles, $Rp=RcD2/Dh2=ρUmD2/μDh$⁠, dimensionless

$fcRc,xc$⁠:

Lift coefficient, its size depends on the Reynolds number of channel and particle position on the cross section, dimensionless

$Rc$⁠:

Reynolds number of channel, dimensionless

$ρ$⁠:

Fluid density (kg/m³)

$Um$⁠:

Maximum velocity in channel (μL/s)

$Dh$⁠:

Channel size (nm)

$FD$⁠:

Dean drag force (N)

$r$⁠:

Curvature radius of channel (nm)

$Rf$⁠:

Ratio of inertia lift and Dean drag force, dimensionless

$δ$⁠:

Curvature ratio, $δ=Dh/2r$⁠, dimensionless

EOR:

Enhanced oil recovery rate (%)

$ϕ$⁠:

Porosity (%)

$T$⁠:

Temperature (°C)

$C$⁠:

Salinity (mg/L)

$R$⁠:

Recovery degree, nondimensional

$fw$⁠:

Water cut (%)

PV:

Injection pore volume, nondimensional.

The author can provide supplementary materials of data for readers to download.

The authors declare that they have no conflicts of interest.

This work was financially supported by the National Natural Science Foundation of China (No. 52074347).