A Refined Numerical Simulation Method for Amine-Ether Gemini Surfactant Emulsion Flooding

Abstract

The physicochemical mechanisms and numerical characterization of amine-ether gemini surfactant emulsion flooding remain insufficient, limiting its field application in low-permeability reservoirs. This study developed a refined numerical simulation method that integrates full-process emulsion kinetics, including generation, coalescence, dispersion-assisted oil displacement, and demulsification, with graded emulsion characterization using the differentiated inaccessible pore volume (IPV) and residual resistance factor (RRF). Core-flooding validation demonstrated that the model accurately reproduced the key dynamic responses of water cut reduction and oil production increase, with a relative error of about 3.0%. Mechanistic analysis showed that the enhanced oil recovery performance arose from the combined effects of ultralow interfacial tension and emulsion-induced profile control. Relative to conventional surfactant flooding, emulsion flooding increased oil recovery by an additional 4.8–5.0% and lowered water cut by about 12 percentage points. For the Shengli Oilfield pilot block, the optimized injection design involved a surfactant concentration of 1.2 wt.%, an injection rate of 60 m³/d, a slug size of 0.01 PV, an injection–production ratio of 0.95, and a stepwise concentration-decline strategy. The field pilot further confirmed the applicability of the method: daily oil production of the well group increased by 46.5%, while comprehensive water cut decreased by 8.6 percentage points. These results demonstrate the value of the proposed method for both mechanistic characterization and field design of amine-ether gemini surfactant emulsion flooding in heterogeneous low-permeability reservoirs.

1. Introduction

Low-permeability and ultra-low-permeability reservoirs commonly face major development challenges, including strong heterogeneity, high threshold pressure for water injection, and limited reservoir energy replenishment, which together result in poor injectivity and insufficient production. Conventional stimulation and flow-control methods often fail to provide adequate injectivity in microporous formations [1,2].

To address these challenges, previous studies have developed surfactant-enhanced waterflooding systems based on amine-ether gemini surfactants. Owing to the combined structural characteristics of ionic and nonionic surfactants, these agents exhibit strong interfacial activity together with good temperature and salinity tolerance [3,4], enabling ultralow oil–water interfacial tension. In addition, emulsions generated during the displacement process can selectively block preferential flow channels and promote flow redistribution through interactions with residual oil, thereby improving sweep efficiency and oil recovery in low-permeability reservoirs.

However, as a relatively new chemical flooding process, amine-ether gemini surfactant emulsion flooding is still not fully understood, and its numerical description remains limited. As a result, the reliable optimization of injection parameters remains difficult, limiting effective field application.

At present, a series of numerical simulation methods has been developed for surfactant-based flooding processes. Zhang et al. [5] considered pressure reduction, injectivity improvement, changes in relative permeability, and surfactant adsorption and retention in the formation, establishing a three-dimensional, two-phase, three-component model. On this basis, Li et al. [6] incorporated non-Darcy flow behavior, threshold pressure gradient, and the convection, diffusion, and adsorption of surfactants in low-permeability reservoirs, significantly improving prediction accuracy. Daripa et al. [7] focused on oil–water interfacial tension reduction and proposed a mathematical model in which interfacial tension varies dynamically with surfactant concentration. This model was incorporated into an incompressible immiscible two-phase flow framework, providing a useful approach for numerical simulations under complex reservoir conditions. Kumar et al. [8] used the capillary number correlation interpolation method to modify relative permeability curves, thereby characterizing wettability alteration and interfacial tension reduction in numerical simulations. Meanwhile, by introducing the Langmuir adsorption model, they described the influence of adsorption and retention on the effective concentration of the surfactant system. Ahmadi et al. [9] established a multiphase, multicomponent seepage model and, by integrating an improved Stone II relative permeability model with an interfacial tension function, further improved the physicochemical characterization of the displacement process.

Conventional studies have generally attributed the enhanced oil recovery effect of surfactant systems in low-permeability and ultra-low-permeability reservoirs primarily to oil–water interfacial tension reduction. However, recent experimental studies have shown that surfactants can also generate stable emulsions, which improve fluid distribution in porous media and suppress the formation of preferential flow channels [10,11,12,13]. Therefore, coupled numerical characterization of interfacial tension reduction and emulsification-related flow behavior has become an important issue in this field.

Several studies have also investigated emulsification mechanisms and their numerical modeling. Pu et al. [14] established a theoretical framework for synergistic oil displacement involving interfacial tension reduction and emulsification and dynamically quantified the emulsification rate using a chemical reaction kinetics approach. By introducing interfacial tension effects and emulsification reactions as two independent parameters, their model improved the mechanistic representation of the process. Cao et al. [15] developed a mathematical model for emulsion flow and physicochemical properties based on the matching relationship between droplet size and pore-throat size, advancing the quantitative characterization of profile-control performance in emulsification systems. Alade et al. [16] established a three-phase flow model for oil, water, and emulsion and coupled the mass conservation and momentum equations to achieve relatively accurate predictions of oil recovery under different injection conditions. Du et al. [17] investigated microscopic flow mechanisms and revealed the effects of surfactant-induced emulsion generation and fluid-configuration evolution on displacement efficiency, providing an important theoretical basis for modeling emulsification-related flow behavior.

Although previous studies have advanced the mechanistic understanding and numerical characterization of emulsification in surfactant systems, important limitations remain for amine-ether gemini surfactant emulsion flooding. Most existing models are confined to oil–water–surfactant three-phase relative permeability formulations [18,19] or treat emulsification as a microemulsion displacement process; therefore, they cannot dynamically capture the full emulsion life cycle, including generation, coalescence, migration, retention-induced plugging, and demulsification. In addition, the contribution of emulsification to enhanced oil recovery is commonly interpreted mainly in terms of viscosity modification and mobility control, whereas its role in selectively plugging dominant flow channels, redistributing the flow field, and improving sweep efficiency has not been adequately represented. Available models have mainly been developed for conventional surfactant systems and are therefore not directly applicable to amine-ether gemini surfactant systems, where ultralow interfacial tension and emulsion-induced profile control coexist. Furthermore, current research has remained largely at the laboratory scale, and a field-oriented numerical framework integrating emulsification kinetics, profile-control behavior, and injection–production parameters is still lacking.

To address these limitations, this study develops an improved numerical simulation method for amine-ether gemini surfactant emulsion flooding in low-permeability reservoirs by incorporating emulsification reactions and emulsion-induced profile control into the numerical framework. The method is intended to provide a more refined description and performance evaluation of the displacement process. Specifically, it (i) establishes a reaction kinetics-based framework to characterize emulsion generation, dispersion-assisted oil displacement, coalescence-induced profile control, and demulsification; (ii) introduces the inaccessible pore volume (IPV) and residual resistance factor (RRF), based on the permeability–pore-throat matching relationship, to capture the distinct roles of emulsions with different droplet sizes in migration, selective plugging, and dispersion-assisted displacement; and (iii) uses core-flooding experimental data to calibrate and validate the model, quantify the synergistic contribution of ultralow interfacial tension reduction and emulsion-induced profile control, and support the optimization of field development parameters and injection strategy design.

2. Methods

2.1. Basic Model Assumptions

The amine-ether gemini surfactant emulsion flooding process is inherently a complex system involving the coupling of multiphase flow, multicomponent transport, and multiple physicochemical mechanisms. The process includes surfactant transport, interfacial adsorption, emulsion generation and breakdown, emulsion transport, and profile control. Because of the large number of components and the complexity of the underlying physicochemical interactions, it is difficult to describe the system rigorously using a single reaction equation. Therefore, to develop a mathematical model that retains the essential mechanisms while remaining computationally tractable, the following assumptions are adopted:

(1)

The amine-ether gemini surfactant is assumed to follow the same constitutive relationships as those used in conventional surfactant flooding models for the characterization of physicochemical properties, including adsorption isotherms, interfacial tension, and capillary pressure effects [20,21,22].

(2)

The reservoir is assumed to be isothermal, the solid phase is stationary, solute transport is governed by Fickian dispersion, fluid mixing is ideal, and seepage flow follows Darcy’s law. The generation, transport, retention, and loss of surfactant and emulsion components are governed by mass conservation. The model considers both the rheological behavior of the injected chemicals and their interactions with reservoir rock and in situ fluids.

(3)

The developed numerical simulation model is based on a two-phase, multicomponent oil–water flow system, in which the aqueous phase comprises water, surfactant, and an oil-in-water (O/W) emulsion component.

2.2. Refined Characterization of Emulsification Mechanism

The emulsification–reaction model developed in this study for amine-ether gemini surfactant emulsion flooding consists of two parts: an emulsion mass conservation model and an emulsification kinetics model. Based on stoichiometric relationships and Arrhenius-type kinetic concepts, the model was used to quantitatively characterize emulsion generation, evolution, and breakdown during surfactant flooding.

2.2.1. Fundamentals of Reaction Kinetics

In chemical kinetics, the Arrhenius equation is widely used to describe the dependence of reaction rate on temperature and reactant concentrations. Its general form is given by Equation (1) [23]:

$$r_i = r_{rk}·\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{E_a}{RT}})\cdot {\displaystyle \prod _{i=1}^{n_c}}{c}_i^{ni}$$

(1)

where r_i is the reaction rate of component i, expressed as the amount of substance consumed or generated per unit volume per unit time, mol/(m³·s); r_rk is the reaction kinetic constant; E_a is the activation energy, J/mol; R is the universal gas constant, 8.314 J/(mol·K); T is the absolute temperature, K; and c_i is the concentration factor of reactant i, mol/m³.

2.2.2. Four Key Mechanisms of Emulsification Reaction

To characterize the formation and evolution of emulsions during amine-ether gemini surfactant emulsion flooding, emulsion generation and migration are treated as a complex kinetic process involving multiple mechanisms. In this study, this process is represented by the following four key mechanisms.

(1)

Emulsion generation mechanism

Owing to its amphiphilic molecular structure, the amine-ether gemini surfactant adsorbs at the oil–water interface and forms a dense and stable interfacial film, thereby reducing interfacial energy and promoting the formation of oil-in-water (O/W) emulsions [24,25]. Its stability is regulated by surfactant concentration, adsorption kinetics, and interfacial rheological properties. The process is shown in Figure 1.

The generation process of emulsion droplets conforms to a first-order kinetic reaction, and its kinetic equation is defined as follows:

$$\mathrm{Water} + \mathrm{Surfactant} + \mathrm{Oil} \stackrel{r_i}{\to } \mathrm{Emulsion}$$

(2)

This expression is used as a simplified phenomenological representation of emulsion formation for kinetic modeling, rather than a strict molecular-level reaction equation. The same applies to the following expressions.

(2)

Emulsion coalescence and plugging mechanism

With the increase of surfactant injection volume, the emulsification effect is continuously enhanced. A high concentration of emulsion droplets may accumulate and amplify the Jamin effect, which can lead to an increase in local flow resistance, thereby playing a role in regulating microscopic mobility. The accumulation and plugging of emulsions in the main seepage channels will cause an increase in seepage resistance (trapped emulsion), thereby redirecting local flow. This phenomenon is shown in Figure 2. The kinetic behavior of this process can be described by the following Equation (3):

$$\mathrm{Emulsion} \stackrel{r_i}{\to } \mathrm{Trapped} \mathrm{Emulsion}$$

(3)

Figure 2. Experimental observation of emulsion accumulation, coalescence, and plugging during surfactant flooding.

Figure 2. Experimental observation of emulsion accumulation, coalescence, and plugging during surfactant flooding.

(3)

Emulsion dispersion and oil-displacement mechanism

When large-particle-size emulsions migrate in low-permeability porous media, they are subjected to strong shear action while flowing through micropore throats, thereby forming small-particle-size emulsion droplets. In addition, large-particle-size emulsions can usually only exert a temporary plugging effect on relatively high-permeability zones; as the injection pressure increases, these large-particle-size emulsion droplets will further undergo breakup and dispersion, and also transform into small-particle-size emulsion droplets. Through continuous accumulation and extrusion in the pore space, the small-particle-size emulsion droplets can promote the mobilization of residual oil, converting it from an immobile state to a mobile state, which is then transported under the carrying of the fluid flow. This process can be referred to as the residual-oil entrainment and mobilization mechanism [26], is shown in Figure 3. Its kinetic equation can be defined as follows:

$$\mathrm{Emulsion} + \mathrm{Trapped} \mathrm{Emulsion} \stackrel{r_i}{\to } \mathrm{Emulsion}$$

(4)

(4)

Emulsion depletion and demulsification mechanism

During the emulsion flooding process, the amine-ether gemini surfactant will undergo adsorption and retention in porous media, and at the same time, its concentration gradually decreases due to the dilution effect of injected water. When the concentration of the amine-ether gemini surfactant drops below the critical micelle concentration (CMC) [27], the oil–water interfacial tension rises significantly, which destroys the interfacial stability of the emulsion, leading to emulsion destabilization and demulsification, separating into oil and water phases, which then continue to migrate through the porous medium. This process is shown in Figure 4. Its kinetic equation is defined as follows:

$$\mathrm{Emulsion} + \mathrm{Trapped} \mathrm{Emulsion} \stackrel{r_j}{\to } \mathrm{Water} + \mathrm{Oil}$$

(5)

2.3. Mathematical Model Formulation

2.3.1. Emulsion Transport Model

Based on the control-volume method and the law of mass conservation, a balance model was established for a two-phase, multicomponent system consisting of the oil phase, aqueous phase, surfactant, and emulsion pseudo-component [28]. The distribution of each component in porous media satisfies the following component conservation equation:

$$\varphi \sum _j{c}_{i,j}{S}_j = V_i$$

(6)

where ϕ is the porosity; S_j is the saturation of phase j; c_i,j is the concentration of component i in phase j; and V_i is the amount of component i within the representative control volume.

During surfactant flooding, component transport is governed mainly by convection and dispersion [29]. Therefore, the flux of component i in phase j can be written as follows:

$$J_{i,j} = {\rho }_j\cdot x_{i,j}\cdot u_j - D_{i,j}\nabla ({\rho }_j\cdot x_{i,j})$$

(7)

where J_i,j is the transport flux of component i in phase j; u_j is the Darcy velocity of phase j; ρ_j is the phase density; x_i,j is the mole fraction of component i in phase j; and D_i,j is the diffusion coefficient (or dispersion tensor) of component i in phase j.

Based on Equations (6) and (7), the governing conservation equation for component i can be written as follows:

$${\displaystyle \frac{\partial (\varphi S_w·c_{em})}{\partial t}} + \nabla \cdot \left(u_w·c_{em}-\varnothing S_w{D}_{em}\nabla c_{em}\right) = \left(r_i-r_j\right) + q_{em}$$

(8)

where c_em is the concentration of the emulsion component in the aqueous phase, mol/m³; D_em is the dispersion coefficient (or tensor) of the emulsion component; r_i is the emulsion generation rate, mol/(m³·s); r_j is the emulsion demulsification rate, mol/(m³·s); and q_em is the well-related source/sink term.

In Equation (8):

• The first term is the accumulation term, which represents the temporal variation of emulsion concentration within the control volume and reflects the accumulation or depletion of emulsion in porous media.
• The second term is the convection–diffusion term, which describes the transport and spatial redistribution of emulsion within the pore space. Specifically, the dispersive effect is represented by the spatial gradient of the emulsion component concentration, whereas the convective transport of the emulsion component is governed by the aqueous-phase flow velocity, reflecting the co-transport behavior of the emulsion with the aqueous phase.

2.3.2. Emulsification Kinetic Model

To describe emulsion generation during amine-ether gemini surfactant emulsion flooding, an emulsification kinetic model was established based on core-flooding observations and reservoir flow characteristics [30]. In this model, the emulsion is treated as an aqueous-phase component, and its generation rate is assumed to depend on water saturation, surfactant concentration, and the current emulsion concentration. The kinetic expression is written as follows:

$$r_i = k_c\varphi S_w{\left({\displaystyle \frac{c_s}{\mathrm{C}\mathrm{M}\mathrm{C}}}-1\right)}^n\left(1-{\displaystyle \frac{c_{em}}{c_{em}^{max}}}\right), c_s\ge \mathrm{C}\mathrm{M}\mathrm{C}$$

(9)

and,

$$r_i \approx 0, c_s<\mathrm{C}\mathrm{M}\mathrm{C}$$

(10)

where r_i is the emulsion generation rate; k_c is the effective emulsification kinetic coefficient obtained by history matching of core-flooding data; c_s is the surfactant concentration in the aqueous phase; n is the apparent reaction order; and c_em is the concentration of the emulsion component in the aqueous phase.

The term (c_s/CMC-1)ⁿ reflects the dependence of emulsification on the surfactant concentration above the CMC, and the last term imposes an upper limit on emulsion generation. Since the present model is isothermal, the temperature dependence of the kinetic coefficient is neglected, and k_c is treated as an effective fitting parameter.

The functional form was selected to reflect the dependence of emulsification on water availability, surfactant effectiveness above the CMC, and a finite upper bound on emulsion concentration, and it was calibrated using core-flooding data. This model incorporates the key physicochemical mechanisms governing emulsification during amine-ether gemini surfactant emulsion flooding. The main considerations are summarized as follows.

(1)

Reaction kinetic parameters

In general, the kinetic parameters can be expressed as a function of temperature according to the Arrhenius equation [31]:

$$k_c = A\cdot \mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{E_a}{RT}})$$

(11)

where A is the pre-exponential factor associated with the molecular structure of the surfactant, d⁻¹. In the present study, the flooding process was assumed to be isothermal; therefore, the temperature dependence of the emulsification reaction rate was neglected. Accordingly, the exponential term in Equation (11) was taken as constant, and k_c was treated as an effective constant kinetic parameter to be determined through model calibration.

(2)

Critical micelle concentration (CMC)

In this model, the CMC is introduced as a key threshold parameter to define the concentration range over which the amine-ether gemini surfactant exhibits effective emulsification performance [32]. The CMC corresponds to the critical concentration at which the oil–water interfacial tension reaches its minimum value and serves as an important indicator of the interfacial activity and emulsification capability of the surfactant.

Figure 5 presents the relationship between surfactant concentration and oil–water interfacial tension. As the surfactant concentration increased from 0.1 wt.% to 0.3 wt.%, the oil–water interfacial tension decreased significantly, reaching its minimum at 0.3 wt.%. A lower oil–water interfacial tension reduces the thermodynamic free energy required for emulsification, making emulsion formation easier and resulting in the strongest emulsification capacity of the system. Therefore, under the experimental and field application conditions considered in this study, the CMC of the investigated amine-ether gemini surfactant system was set to 0.3 wt.% and used for model development and parameter calibration. It should be noted that the CMC is not a fixed value and may vary with temperature, salinity, and surfactant formulation. Therefore, under different reservoir conditions, the CMC should be re-determined experimentally, and the model parameters should be adjusted and recalibrated accordingly.

2.3.3. Emulsification Profile Control Model

The amine-ether gemini surfactant can form a stable emulsion system in low-permeability reservoirs. Its profile-control effect is mainly attributed to the selective plugging of dominant flow channels by emulsion droplets and the increased flow resistance in high-permeability channels caused by the Jamin effect. As a result, the subsequent displacing fluid is diverted into low-permeability, unswept regions, which increases sweep efficiency and improves oil recovery. To quantitatively characterize these coupled effects, the inaccessible pore volume (IPV) [33,34,35] and residual resistance factor (RRF) [36] were introduced as two key parameters in the emulsion profile-control model. These two parameters were selected because they characterize, respectively, the effective action range and the flow-resistance variation of the emulsion in porous media, thereby providing a practical description of its transport, retention, and profile-control and flow-diversion behaviors in low-permeability reservoirs. Specifically, IPV reflects the accessibility of the emulsion to pore space. Owing to droplet-size effects, pore-throat sieving, and local retention, the emulsion cannot access the entire pore volume; therefore, IPV is used to parameterize the physically accessible pore space available for emulsion transport. By contrast, RRF reflects the additional flow resistance induced by emulsion transport, including droplet retention, adsorption, coalescence, local plugging, and mobility control, and is therefore used to quantify the corresponding profile-control and flow-diversion capacities.

(1)

Matching Relationship Between Emulsion Droplet Size and Pore-Throat Size

The transport behavior and profile-control performance of emulsions in porous media largely depend on the size compatibility between emulsion droplets and pore throats. When the droplet size is comparable to or larger than the pore-throat size, droplets are prone to retention or cause local plugging, significantly increasing flow resistance. By contrast, when the droplet size is much smaller than the pore-throat size, the emulsion can readily pass through the pore space with the flowing fluid, mainly contributing to oil displacement through dispersion. Therefore, establishing a proper size-matching criterion is crucial for modeling the transport behavior of emulsions in low-permeability reservoirs [37,38,39].

For the emulsion generated by the amine-ether gemini surfactant system, the droplet radius is denoted by r_p. Its size is jointly affected by surfactant concentration, oil–water volume ratio, shear intensity, and formation temperature, and it can be experimentally measured using a laser particle size analyzer. The average pore-throat radius in low-permeability reservoirs is strongly correlated with permeability. In this study, the average pore-throat radius is characterized using a classical empirical permeability–pore-throat radius relationship [40]:

$$r_h={0.9232k}^{-0.81}$$

(12)

where r_h is the average reservoir pore-throat radius, μm; and k is the absolute permeability, μm².

For the emulsion generated by the amine-ether gemini surfactant system, the droplet radius (r_p) is jointly governed by surfactant concentration, oil–water volume ratio, shear intensity, and formation temperature. Experimental measurements of the emulsified system using a laser particle size analyzer revealed that the emulsion droplets exhibit a relatively wide radius distribution, ranging from 2.5 to 7.5 μm.

Based on these observed droplet characteristics, a graded matching relationship between the emulsion droplet radius (r_p) and pore-throat radius (r_h) is introduced to represent its transport behavior. This framework is established by referencing the well-documented profile-control mechanisms of nano/micron polymer particle dispersions [41]. This reference framework is appropriate because both methodologies rely on the inaccessible pore volume (IPV) and residual resistance factor (RRF) to quantitatively evaluate profile-control efficacy. By adapting this mature paradigm and incorporating the unique physicochemical properties of emulsion droplets—namely, their deformability and high coalescence tendency—along with mechanisms such as dispersion for oil displacement and selective profile control, a four-level matching criterion is proposed:

• When r_p/r_h ≤ 0.15, the emulsion droplets can pass freely through the pore throats with the flowing fluid, causing almost no Jamin effect or additional flow resistance and exerting little influence on reservoir-seepage behavior;
• When 0.15 < r_p/r_h ≤ 1, the emulsion droplets are affected by the Jamin effect as well as adsorption and retention in porous media, resulting in temporary plugging of relatively high-permeability flow channels and thereby improving sweep efficiency;
• When 1 < r_p/r_h < 1.5, the emulsion droplets can pass through pore throats by interfacial deformation once the injection pressure exceeds a critical value, although considerable additional flow resistance still exists during the passage process;
• When r_p/r_h ≥ 1.5, the emulsion droplets are more likely to undergo coalescence and retention at pore throats, leading to persistent plugging and a significant reduction in the effective permeability of the reservoir.

The theoretical rationality of this graded relationship lies in its direct mapping to the heterogeneous permeability profile of the reservoir. By inversely calculating the permeability boundaries based on the experimental droplet radii, the selective plugging mechanism becomes highly evident. For instance, for the lower-bound droplet radius (r_p = 2.5 μm), the emulsion exhibits weak or no plugging in formations where k > 3.43 μm² (r_p/r_h < 1) but initiates persistent plugging in zones where k ≤ 2.08 μm² (r_p/r_h ≥ 1.5). Conversely, larger droplets (e.g., the upper-bound radius r_p = 7.5 μm) will cause persistent plugging (r_p/r_h ≥ 1.5) even in relatively high-permeability zones (k ≤ 8.08 μm²). This quantitatively demonstrates the differentiated profile-control roles of droplets within a single emulsion system: larger droplets preferentially plug dominant high-permeability channels, whereas smaller droplets migrate deeper into lower-permeability matrices to enhance oil displacement.

(2)

Inaccessible Pore Volume (IPV) Model

The IPV is used to quantitatively describe the pore space that can be accessed by the emulsion in porous media. Physically, it is defined as the fraction of the total pore volume that cannot be invaded by the emulsion. The mathematical expression is given by:

$${\varnothing }_p = \left(1-\mathrm{I}\mathrm{P}\mathrm{V}\right)·\varnothing$$

(13)

Only pore throats satisfying r_p/r_h ≤ 1.5 are considered accessible to the emulsion, whereas the remaining pore space is treated as inaccessible. In this way, the emulsion droplet size directly controls the swept pore space.

(3)

Residual Resistance Factor (RRF) Model

Adsorption of the amine-ether gemini surfactant and emulsion on the rock surface reduces water-phase permeability and is therefore a key factor affecting the profile-control performance. When 0.15 < r_p/r_h ≤ 1, the emulsion induces Jamin plugging and causes a reduction in reservoir permeability. This change is quantitatively described by the permeability reduction coefficient R_k [42,43,44]:

$$R_k=1+(\mathrm{R}\mathrm{R}\mathrm{F}-1)\times {\displaystyle \frac{{Ad}_{cell}}{A{d}_{max}}}$$

(14)

In this model, adsorption and retention on the rock surface are described by the Langmuir adsorption isotherm [45]:

$$A{d}_{cell}={\displaystyle \frac{A{d}_{max}\cdot c_{i,j}}{(1+K_{ad}·c_{i,j})}}$$

(15)

where Ad_cell is the adsorption amount of injected chemicals on the rock surface, mol/m²; Ad_max is the maximum adsorption capacity, mol/m²; and K_ad is the Langmuir adsorption constant, m³/mol.

The RRF, obtained from core-flooding experiments, is used to characterize this effect. It is defined as the ratio of water-phase mobility before and after emulsion flooding:

$$\mathrm{R}\mathrm{R}\mathrm{F}={\displaystyle \frac{{\lambda }_w}{{\lambda }_e}}={\displaystyle \frac{(k/\mu {)}_w}{(k/\mu {)}_e}}={\displaystyle \frac{Q_w}{Q_e}}\times {\displaystyle \frac{\mathsf{\Delta }{p}_e}{\mathsf{\Delta }{p}_w}}$$

(16)

where λ is the mobility, μm²/(mPa·s); k is the effective permeability, μm²; μ is viscosity; Q is the flow rate, cm³/s; and p is the displacement pressure drop, MPa. The subscript w denotes water, and the subscript e denotes emulsion.

The values of these two parameters were jointly determined through experimental characterization and history matching. IPV was measured using the two-slug concentration-profile method to characterize the accessible pore volume of the emulsion in porous media, whereas RRF was obtained mainly from constant-flow-rate pressure-drop experiments to quantify the increase in flow resistance caused by emulsion action. These experimentally derived values were used as initial constraints in the numerical simulation and were subsequently refined through history matching and parameter inversion to obtain parameter values applicable to the target reservoir conditions.

3. Results

3.1. Core Flooding-Based Validation of the Proposed Method

To evaluate the oil-displacement performance of the amine-ether gemini surfactant system and to investigate its mechanism for enhancing residual-oil recovery, a laboratory core-flooding experiment was carried out. During the experiment, the cumulative produced fluid, cumulative oil production, and cumulative water production were continuously recorded to characterize the displacement performance of the system in low-permeability cores. The main experimental conditions, as well as the core and fluid properties, are listed in

Table 1. Statistical summary of the main parameters used in the core-scale numerical simulation model.

Parameter	Value
Number of grid blocks	25 × 5 × 3
Core length, cm	9.7
Porosity, %	12.3
Core density, g/cm3	2.1
Core height, cm	5.0
Temperature, °C	70.0
Formation water viscosity, mPa·s	0.4
Surfactant concentration, wt.%	0.3
Crude oil viscosity, mPa·s	6.8

, and the experimental displacement data are summarized in

Table 2. Core-flooding experimental data obtained during surfactant emulsion flooding.

Time (min)	PV	Fluid Volume (mL)	Oil Volume (mL)	Water Volume (mL)
0	0	0	0	0
10	0.259	0.5	0.497	0.002
30	1.037	1.25	1.167	0.082
50	1.555	2.5	1.993	0.506
70	2	2.7	2.004	0.695
90	2.592	6.5	2.334	4.165
110	3.111	17.5	2.924	14.575
130	3.629	21.5	3.092	18.407

.

Based on the above core-flooding experiment, a core-scale numerical model consistent with the experimental scale was established in CMG-STARS (version 2020.10) using the numerical simulation method described above (Figure 6). The model adopted the same core dimensions, initial saturation, permeability, injection conditions, and fluid properties as those used in the experiment to simulate the amine-ether gemini surfactant emulsion flooding process. The proposed numerical model represents the emulsification-assisted flooding process using four coupled kinetic reactions: emulsion generation, trapped-emulsion formation, remobilization with oil carrying, and demulsification. These reactions were introduced to capture the main dynamic processes observed in the core-flooding experiments, including emulsion formation, selective retention in dominant flow channels, flow redistribution, and emulsion release under changing flow conditions. The validation therefore focused on whether the model could reproduce the observed oil recovery and water cut responses throughout the displacement process.

Figure 7 compares the experimental and simulated oil recovery and water cut curves. Model performance was assessed based on the agreement in overall trends, key-stage responses, and representative point deviations. A point-by-point comparison between the experimental and simulated oil recovery and water cut data was also performed to quantitatively evaluate the fitting accuracy of the model, including deviations at key points, stage-wise variation trends, and the final discrepancy. The results show that during the waterflooding stage (0–2.0 PV), the numerical model successfully reproduced the continuous increase in oil recovery and the rapid rise in water cut. At the end of waterflooding (2.0 PV), the experimental oil recovery was 35.1%, while the simulated value was 35.8%, with only a small relative deviation, indicating that the model can accurately capture the displacement behavior during the waterflooding stage.

During the amine-ether gemini surfactant emulsion flooding stage, oil recovery increased further, while the water cut exhibited a dynamic response characterized by an initial decrease followed by a subsequent increase. The numerical model reproduced not only the overall trend of the experimental curves, but also the main features of enhanced oil recovery and water cut reduction during surfactant flooding. For example, at 2.333 PV, the experimental oil recovery was 47.37%, compared to a simulated value of 46.1%. At 2.852 PV, the experimental and simulated oil recoveries were 49.12% and 49.1%, respectively, showing good agreement. The model also provided a satisfactory match for the overall variation trend of water cut throughout the displacement process. At the end of waterflooding (2.0 PV), the experimental water cut was 95.0%, whereas the simulated value was 94.0%. At the late stage of flooding (3.629 PV), the experimental and simulated water cuts were 96.0% and 96.1%, respectively, further demonstrating the capability of the model to characterize the evolution of water cut.

Overall, the model achieved a high-quality history match over different displacement stages and was able to effectively describe the dynamic evolution of oil recovery and water cut, as well as identify the main response characteristics and key turning points during the flooding process. These results demonstrate the reliability of the proposed numerical method and support its use for quantitative analysis of displacement mechanisms in heterogeneous low-permeability reservoirs.

3.2. Analysis of the Enhanced Oil Recovery Mechanism

On the basis of the reliably validated numerical model in Section 3.1, a heterogeneous low-permeability reservoir conceptual model was constructed to quantitatively reveal the EOR mechanisms of amine-ether gemini surfactant emulsion flooding and to clarify the synergistic contribution of ultra-low interfacial tension reduction and emulsification profile control. The model adopted a well pattern consisting of one injector and six producers, consistent with the field development configuration (Figure 8). The basic reservoir parameters are as follows: burial depth, 3200–3320 m; initial reservoir pressure, 38.87 MPa; stock-tank crude oil density, 0.9054 g/cm³; stock-tank crude oil viscosity, 9.5 mPa·s; porosity, 13%; initial oil saturation, 80%; and water-phase viscosity, 0.7 mPa·s. The permeability from bottom to top was set as 0.05 × 10⁻³ μm², 0.25 × 10⁻³ μm², 1.25 × 10⁻³ μm², and 6 × 10⁻³ μm², respectively.

The parameters listed in

Table 3. Effective model parameters used for numerical simulation of the amine-ether gemini surfactant emulsion flooding.

Component	Density (kg/m3)	Viscosity (mPa·s)	Molecular Weight (g/mol)	IPV	RRF	Admax (mol/m2)
Amine-ether gemini surfactant	1100	2	300	0	1.0	0.3
Small-droplet emulsion	960	8	500	0.08	1.15	0.1
Large-droplet emulsion	920	15	800	0.16	1.48	0.03

were derived from core-flooding experimental data through parameter inversion and history matching. For the emulsion components, the assigned density, viscosity, IPV, RRF, and adsorption-related parameters are effective model parameters used to characterize their transport and plugging behavior in porous media. For numerical simulation, the emulsion was represented using two representative droplet classes, namely, small-droplet emulsion and large-droplet emulsion, based on the experimentally observed droplet-size characteristics and the corresponding differences in transport, retention, and profile-control behavior in porous media. The small-droplet emulsion was mainly used to describe the emulsification-assisted dispersion and mobilization of residual oil, owing to its relatively stronger accessibility and migration capacity in smaller pore channels. By contrast, the large-droplet emulsion was mainly used to characterize the profile-control effect of the emulsion, including selective retention, local plugging, and flow diversion in dominant seepage channels. These two representative droplet classes were not treated as isolated populations; instead, their behavior was coupled through the emulsification-related kinetic equations established in the model. In particular, large droplets may be retained or trapped in pore throats, while under shear and seepage they may also undergo breakup and redistribution, contributing to the generation of more mobile small droplets. In this way, the model captures the intrinsic linkage between emulsification-assisted oil displacement and emulsification-based profile control within a reservoir-scale simulation framework.

The adsorption and diffusion behaviors of chemical agents in porous media are influenced by pore structure and pore size. When polymer or surfactant solutions with the same concentration flow through rock pores of different sizes, differences in pore structure lead to variations in the adsorption and diffusion capacities of the chemical agents, resulting in a nonuniform concentration distribution. Such concentration heterogeneity may further cause variations in oil–water interfacial tension or aqueous-phase viscosity at the pore scale, thereby affecting the seepage characteristics of oil–water two-phase flow.

To characterize the differences in oil–water interfacial tension caused by different displacing agents, corresponding relative permeability curves must be assigned to each respective region. In numerical simulations, the relative permeability corresponding to a specific interfacial tension is typically determined using capillary number-based correlation functions. Therefore, the capillary number corresponding to different oil–water interfacial tensions must be calculated using the theoretical formula for capillary number. This theoretical relationship can be expressed by Equation (17) [46]:

$$N_c={\displaystyle \frac{{\mu }_a{v}_a}{{\sigma }_{wo}}}$$

(17)

where μ_a is the viscosity of the aqueous phase, mPa·s; v_a is the seepage velocity of the aqueous phase fluid, m/s; and σ_wo denotes the oil–water interfacial tension, mN/m. The corresponding relative permeability curves are shown in Figure 9.

The numerical simulation was also divided into three stages: waterflooding, amine-ether gemini surfactant emulsion flooding, and subsequent waterflooding. Specifically, waterflooding was first continued until the overall water cut reached 90%, followed by the injection of a 0.3 wt.% amine-ether gemini surfactant solution at a slug size of 0.1 PV. Subsequent waterflooding was then performed until the overall water cut reached 98%. The injection rate was uniformly set at 60 m³/d for all three stages.

The simulation results are shown in Figure 10, Figure 11 and Figure 12. As shown in Figure 10 and Figure 11, during oil displacement in low-permeability reservoirs, the amine-ether gemini surfactant system exhibits a synergistic enhancement mechanism involving interfacial tension reduction, mitigation of injection pressure and improved injectivity, and emulsification-based profile control. This synergy significantly improves sweep efficiency and displacement uniformity, thereby reducing water cut and enhancing oil production at the high-water-cut stage.

As shown in Figure 12, after the injection of the amine-ether gemini surfactant system, the oil–water interfacial tension decreases sharply from 14 mN/m at the end of waterflooding to 0.0037 mN/m, reaching an ultralow level. This substantial reduction weakens capillary forces, improves crude oil mobility, and facilitates the mobilization and displacement of residual oil trapped in pore spaces.

The injection of amine-ether gemini surfactant also effectively regulates the reservoir pressure field. The underlying mechanism can be explained from two perspectives. On the one hand, the surfactant substantially reduces oil–water interfacial tension, thereby lowering capillary resistance, decreasing the overall pressure gradient within the reservoir, and mobilizing the previously unswept residual oil. On the other hand, the selective plugging effect of emulsions in high-permeability dominant flow channels gives rise to a relative pressure increase in low-permeability zones. As a result, the subsequently injected fluids, including low-concentration surfactant solution, are diverted into low-permeability regions, which improves the flow distribution in heterogeneous reservoirs and enlarges the effective sweep volume.

The emulsion distribution further validates this regulatory mechanism. After amine-ether gemini surfactant injection, an obvious emulsification zone is formed in the low-permeability reservoir. As the injected slug size increases from 0.05 PV to 0.1 PV, more stable emulsions are generated under the ultralow interfacial tension condition. These emulsions are mainly concentrated in the main flow channels and near the displacement front, where they effectively plug the dominant channels and redirect the subsequent displacing fluids toward the previously unswept areas.

As shown in Figure 13, a comparative analysis of the development performance of conventional surfactant flooding and surfactant flooding considering emulsification was conducted to quantitatively evaluate the contribution of emulsification to enhanced oil recovery. The results show that, after surfactant slug injection, both schemes exhibited better oil-displacement performance than water flooding owing to the substantial reduction in oil–water interfacial tension. For conventional surfactant flooding without emulsification, the water cut remained nearly constant at 0.88–0.91, with only minor fluctuations, indicating limited effectiveness in water cut reduction and mobility control. By contrast, when emulsification was taken into account, the water cut decreased from approximately 95% to 83%, corresponding to a reduction of about 12 percentage points, and remained consistently lower than that of the conventional surfactant flooding scheme during the subsequent development stage. These results indicate that emulsification can effectively improve sweep conformance and enhance water-control performance.

The recovery results further confirm the incremental contribution of emulsification. Compared with water flooding, both surfactant flooding schemes increased oil recovery, while the scheme incorporating emulsification achieved an additional recovery increment of 4.8–5.0% over conventional surfactant flooding. This finding indicates that, in addition to the reduction in residual-oil saturation and improvement in microscopic displacement efficiency induced by ultralow interfacial tension, emulsification can further improve macroscopic sweep efficiency by redistributing flow between high- and low-permeability zones and enlarging the swept volume. Therefore, the enhanced recovery achieved by the amine-ether gemini surfactant emulsion flooding system results from the synergistic effect of ultralow-interfacial-tension oil displacement and emulsification-assisted profile control, with emulsification-assisted profile control making a distinct incremental contribution to the final recovery factor.

Furthermore, by incorporating emulsification kinetics and an emulsification-based profile control model into the numerical simulator, the generation, transport, and flow effects of emulsions in porous media can be described more accurately. The simulated emulsion concentration results show that, after the emulsification depletion mechanism was considered, emulsion stability gradually decreased during the displacement process, and the emulsion concentration dynamically decayed until demulsification eventually occurred. This dynamic evolution not only avoids permanent plugging and potential formation damage caused by long-term emulsion retention but also helps establish more favorable flow pathways for the subsequent waterflooding stage, thereby improving the sustainability and controllability of the displacement process. The simulation results are in good agreement with the actual displacement behavior of amine-ether gemini surfactant emulsion flooding, demonstrating that the proposed model has good applicability and physical consistency.

3.3. Field Case Application of the Proposed Method

3.3.1. Field-Scale Model Construction

Guided by the enhanced oil recovery mechanism identified in Section 3.2, a pilot block in the Shengli Oilfield was selected as the field case to evaluate the engineering applicability of the proposed numerical method. The target reservoir is a typical low-permeability and strongly heterogeneous formation, with porosity ranging from 1.2% to 14.3% and permeability ranging from 0.02 × 10⁻³ to 13.78 × 10⁻³ μm². The interlayer permeability contrast reaches 689, indicating pronounced vertical heterogeneity. The reservoir also exhibits abnormal high-pressure characteristics, with a pressure coefficient of 1.39–1.44, which leads to poor injectivity and considerable difficulty in water injection. In addition, the block is characterized by low single-well productivity, rapid water cut increase, and an overall recovery factor of only 3%, reflecting the limited effectiveness of conventional development under current reservoir conditions.

These reservoir characteristics are well aligned with the anticipated application conditions of amine-ether gemini surfactant emulsion flooding, particularly in terms of ultra-low-interfacial-tension oil displacement, injectivity improvement, and emulsification-assisted profile control in heterogeneous formations. The pilot block therefore provides a representative field case for assessing the applicability of the proposed method in low-permeability reservoirs.

A field-scale numerical model was then constructed based on the geological features and production performance data of the pilot block. The model consisted of 129,952 grid cells, including 44,109 active cells, with an areal grid resolution of 30 m × 30 m. As shown in Figure 14, the model captures the main spatial heterogeneity characteristics of the target reservoir.

Considering that overpressure water injection had previously been applied in this block, hydraulic fracturing treatment was implemented for the injection wells in the model to improve the injectivity of the near-wellbore reservoir. The fracture parameters were set as follows: half-fracture length, 150 m; fracture height, 36 m; and fracture width, 0.046 m.

3.3.2. Parameter Optimization Design

To meet the application requirements of amine-ether gemini surfactant emulsion flooding in the pilot block, an optimization study of the key injection parameters was conducted to establish a rational development scheme adapted to the reservoir characteristics. Numerical simulation was used to compare the development performance of different scenarios, with emphasis on optimizing surfactant injection concentration, injection rate, injected slug size, injection–production ratio, and slug combination pattern. The preferred parameter combination was determined comprehensively based on cumulative oil production, water cut, daily liquid production, and economic indicators, thereby providing a design basis for field implementation.

(1)

Injection Concentration Optimization

The surfactant concentration directly affects the interfacial tension reduction capacity, emulsification performance, and oil-displacement efficiency of the system. Considering field operational conditions and formation parameters, five injection concentration schemes were designed: 0.3, 0.6, 0.9, 1.2, and 1.5 wt.%. In all cases, the injection rate of a single well was maintained at 50 m³/d, with a cumulative injected volume of 0.01 PV. The variations in cumulative oil production and water cut under different concentration levels were then compared and analyzed, as shown in Figure 15 and Figure 16.

The results show that cumulative oil production increased and water cut decreased with increasing surfactant concentration, indicating that the amine-ether gemini surfactant effectively enhanced oil-displacement performance. As the concentration increased from 0.0 wt.% to 1.2 wt.%, oil recovery improved markedly, mainly because the reduction in oil–water interfacial tension and the enhancement of emulsification promoted residual-oil mobilization and improved sweep efficiency. Within this concentration range, stronger adsorption of surfactant molecules at the oil–water interface increased the emulsification capacity of the system, allowing larger oil droplets to be dispersed into smaller ones that could migrate more readily through pore throats.

When the concentration was further increased to 1.5 wt.%, the increment in cumulative oil production became much smaller, indicating a clear diminishing-return trend. This suggests that, beyond 1.2 wt.%, further enhancement in interfacial tension reduction and emulsion-assisted displacement was limited. Considering both recovery performance and chemical cost, 1.2 wt.% was identified as the optimal injection concentration for this block.

(2)

Injection Rate Optimization

With all other parameters kept constant, five single-well injection rates—40, 50, 60, and 70 m³/d—were evaluated. Cumulative oil production and water cut were used as the main performance indicators to compare the different injection-rate scenarios, as shown in Figure 17 and Figure 18.

The simulation results show that the injection rate had a significant impact on oil-displacement performance. Cumulative oil production first increased and then decreased as the injection rate increased, indicating the presence of an optimal injection-rate range. At low injection rates, the displacement intensity was insufficient and the swept volume of the system remained limited. At excessively high injection rates, reservoir heterogeneity in the low-permeability formation became more pronounced, and the chemical slug was more likely to channel through relatively high-permeability zones, thereby reducing chemical utilization efficiency. Based on the overall comparison of development performance under the different scenarios, 60 m³/d was identified as the optimum injection rate. This rate allowed the displacement system to perform effectively while maintaining displacement stability.

(3)

Injected Slug Size Optimization

To balance oil-displacement performance and project economics comprehensively, four injected slug sizes—0.0025, 0.005, 0.0075, and 0.01 PV—were designed for numerical simulation studies. Based on field investigation data, the crude oil price was set as 3804 CNY/t, the operating cost as 1171 CNY/t, and the amine-ether gemini surfactant price as 15,000 CNY/t. The economic indicators and input–output ratio for each case were then calculated, with the results presented in Figure 19.

The results indicate that cumulative oil production increased overall with the increase of injected slug size, while the incremental oil production gain gradually diminished, showing a clear diminishing-return trend. From an economic perspective, although a larger slug size improved oil production, the chemical agent cost increased correspondingly, resulting in a gradual decline in the input–output ratio. Considering both technical performance and economic indicators comprehensively, 0.01 PV was identified as the optimal injected slug size for amine-ether gemini surfactant emulsion flooding in this block.

(4)

Injection–Production Ratio Optimization

The injection–production ratio directly affects the level of reservoir energy supplement and the advancement characteristics of the displacement front, and is an important parameter influencing the development effect. Under the condition that other parameters remain unchanged, five groups of schemes with injection–production ratios of 0.90, 0.95, 1.00, 1.05, and 1.10 were designed to carry out numerical simulation of amine-ether gemini surfactant emulsion flooding. The daily liquid production and development effect under different injection–production ratio conditions were compared and analyzed, and the results are shown in Figure 20.

The results indicate that the injection–production ratio has a significant impact on the block-development effect. When the injection–production ratio is relatively low (<1.0), the injection volume is insufficient to compensate for the formation energy loss caused by produced fluids, leading to a rapid decline in reservoir pressure and insufficient displacement driving force. When the injection–production ratio is relatively high (>1.0), the injection pressure is excessively high, and the oil-displacement system is more likely to channel along high-permeability channels, which is not conducive to the mobilization of remaining oil in low-permeability zones.

Comprehensive analysis shows that an injection–production ratio of 0.95 better balances reservoir energy support and displacement stability, thereby achieving the best development performance. Therefore, 0.95 was selected as the optimal injection–production ratio for this block.

(5)

Slug Pattern Optimization

Due to the high cost of amine-ether gemini surfactants, using a single high-concentration system throughout the entire process would not only increase chemical expenditure but also lower utilization efficiency. Therefore, based on the optimized injection parameters, slug design was further optimized, and a stepwise concentration-reduction strategy was proposed to improve chemical allocation. This strategy involves injecting a high-concentration slug in the early stage to rapidly reduce interfacial tension and enhance emulsion-assisted oil displacement, followed by switching to a lower-concentration system when the water cut reaches 80% to maintain displacement performance while slowing the rise in water cut. Several low-concentration slug combinations were evaluated, including a single low-concentration slug, a steep drop slug, and a decreasing slug (

Table 4. Injection modes of the amine-ether gemini surfactant system.

Injection Modes	High-Concentration Slug	Water Flooding	Low-Concentration Slug	Follow-Up Water Flooding
1	1.2% × 0.01 PV slug	to 80% water cut	0.2% × 0.01 PV slug	to 90% water cut
2	1.2% × 0.01 PV slug	to 80% water cut	0.4% × 0.01 PV slug	to 90% water cut
3	1.2% × 0.01 PV slug	to 80% water cut	0.6% × 0.01 PV slug	to 90% water cut
4	1.2% × 0.01 PV slug	to 80% water cut	0.8% × 0.01 PV slug	to 90% water cut
5	1.2% × 0.01 PV slug	to 80% water cut	0.8% × 0.005 PV + 0.2% × 0.005 PV slug	to 90% water cut
6	1.2% × 0.01 PV slug	to 80% water cut	0.8% × 0.004 PV + 0.6% × 0.003 PV + 0.4% × 0.003 PV slug	to 90% water cut

).

The water cut evolution, cumulative oil production, and overall oil-displacement performance of these schemes were compared and analyzed (Figure 21, Figure 22 and Figure 23).

The simulation results show that compared with the single low-concentration slug, the concentration-decreasing slug combination can more effectively delay the rise in water cut, inhibit the channeling of high-permeability channels, and improve the final oil recovery. Among them, the gradually declining concentration–decreasing slug combination performs the best; it can not only provide strong displacement capacity in the early stage but also maintain a relatively stable emulsification-driving effect in the later stage, balancing technical effect and economy. This indicates that the scheme is more suitable for the reservoir conditions with strong heterogeneity in the pilot block and has good potential for field application.

3.3.3. Field Pilot Application and Effect Evaluation

Based on the optimal parameters obtained from numerical simulation, a field pilot test was implemented in the target well group, with an injection concentration of 1.2 wt.%, injection rate of 60 m³/d, and injection–production ratio of 0.95. Starting from 1 January 2025, the pilot well group began to implement the amine-ether gemini surfactant slug injection measure. As of 25 April, the cumulative injection of surfactant reached 82.8 t. The production data of the pilot well group before and after surfactant flooding are summarized in

Table 5. Production data of the pilot well group before and after surfactant flooding.

Parameter	Before Surfactant Injection			After Surfactant Injection			Comparison
	Daily Fluid (t)	Daily Oil (t)	Water Cut (%)	Daily Fluid (t)	Daily Oil (t)	Water Cut (%)	Daily Fluid (t)	Daily Oil (t)	Water Cut (%)
X1	0.9	0.1	82.2	9.0	3.0	66.06	8.1	2.9	−16.17
X5	6.1	3.8	37.5	5.5	3.6	33.75	−0.6	−0.2	−3.75
X4	11.8	4.7	60.0	13.2	6.0	54.0	1.4	1.3	−6.0

. The production performance of the pilot well group before and after surfactant injection is shown in Figure 24.

Field-production performance data demonstrate that following the implementation of the surfactant injection treatment, the daily oil production of the three wells in the pilot well group increased from 8.6 t to 12.6 t, corresponding to an increment rate of 46.5%. The average daily oil production per well rose from 2.9 t to 4.2 t, with an increment rate of 44.8%. Meanwhile, the comprehensive water cut of the well group decreased from 59.9% to 51.3%, representing a reduction of 8.6 percentage points, which indicates a remarkable effect in water cut reduction and oil increment. Analysis of individual well performance shows that Well X1 exhibited the most pronounced response to the treatment: its daily liquid production increased from 0.9 t to 9.0 t, daily oil production rose from 0.1 t to 3.0 t, and water cut decreased by 16.17 percentage points. These field results further validate the rationality and effectiveness of the numerical simulation method and the corresponding injection–production optimization scheme developed in this study. The findings indicate that the proposed method holds favorable application potential for water control and oil enhancement in high-water-cut, low-productivity wells, as well as for improving the mobilization degree of remaining oil in low-permeability reservoirs.

4. Discussion

Compared with conventional surfactant-flooding models that mainly emphasize interfacial tension reduction, the present model explicitly incorporates emulsification kinetics and emulsion-induced profile control. This distinction is important because the EOR behavior of the amine-ether gemini surfactant system is governed not only by ultra-low interfacial tension, but also by emulsion generation, migration, trapping, remobilization, and demulsification in porous media.

The main novelty of this study lies in representing emulsion as an independent pseudo-component and coupling four dynamic processes: generation, coalescence/trapping, remobilization with oil carrying, and demulsification. Previous studies have recognized the synergistic role of interfacial tension reduction and emulsification, and some have described emulsion transport or profile-control effects using simplified formulations. However, these models were typically not designed to represent the full emulsion life cycle within a unified simulation framework applicable to field-scale analysis. In addition, the present model assigns differentiated IPV and RRF values to representative droplet-size classes, allowing the simulator to capture both the deep migration of small droplets and the preferential plugging caused by larger droplets. This feature is particularly relevant for heterogeneous low-permeability reservoirs, where droplet–pore-throat matching strongly affects flow diversion and sweep efficiency. The model reproduced the recovery factor and water cut trends observed in the core-flooding experiments, with a relative error of about 3.0%, indicating that the main displacement mechanisms were reasonably captured. In particular, the simulated decline and subsequent rise in water cut suggest that the observed performance cannot be explained by interfacial tension reduction alone, but is more consistent with the coupled effects of emulsification, temporary plugging, and flow redistribution. Therefore, the proposed framework improves not only history-matching performance, but also the physical interpretability of surfactant-flooding behavior.

Several model simplifications should nevertheless be clarified. The model parameters were calibrated mainly using laboratory core-flooding experiments. Therefore, when the method is applied to reservoirs with significantly different heterogeneity or pore structures, reservoir-specific parameter adjustment is still required. The current formulation also assumes isothermal conditions and adopts a fixed CMC for the studied surfactant system. For reservoirs with different temperature, salinity, crude oil composition, or formation water chemistry, the relevant physicochemical and transport parameters should be re-evaluated before application. In addition, the droplet-size effect is represented using discrete classes rather than a full population-balance formulation, so the continuous evolution of droplet-size distribution is approximated in an effective manner. The pore-throat radius is further characterized using an empirical permeability–pore-throat relationship. For other reservoirs, this relationship, together with the droplet-size matching and permeability-modification expressions, may need to be revised according to the specific geological and fluid conditions.

Overall, the model extends surfactant-flooding simulation beyond a purely interfacial tension-centered description by linking emulsification dynamics, droplet size-dependent profile control, and field-scale development design. Although several effective simplifications were adopted, the proposed method provides a practical and extensible numerical framework for connecting laboratory-scale mechanism characterization with reservoir-scale simulation and optimization.

5. Conclusions

This study proposed a fine-characterization method for simulating amine-ether gemini surfactant emulsion flooding in low-permeability reservoirs. The method integrates emulsification reaction kinetics, graded emulsion representation, and emulsion-induced profile control into a unified numerical framework, enabling dynamic characterization of emulsion generation, migration, retention, blockage, remobilization, and demulsification during displacement. In addition, a graded characterization scheme was established for emulsions with different droplet sizes and their associated profile-control effects. With IPV- and RRF-based descriptions, the distinct roles of different emulsion size classes in migration capacity and preferential channel blockage can be identified. Compared with conventional surfactant-flooding models mainly focused on interfacial tension reduction, the proposed method provides a more mechanistic representation of emulsification behavior during the flooding process.

The model was validated through core-flooding experiments and reasonably reproduced the main dynamic responses of the amine-ether gemini surfactant emulsion flooding process, confirming that the EOR performance of the studied system is governed by the synergistic effects of ultra-low interfacial tension and emulsion-induced profile control. The proposed method was further applied to field-scale parameter optimization and development design. By considering block-specific reservoir conditions, a stepwise concentration-decline injection strategy was developed, achieving a favorable balance between recovery improvement and chemical cost. Overall, the method provides a more mechanistically grounded and practically applicable tool for mechanism analysis, parameter optimization, and field implementation of amine-ether gemini surfactant emulsion flooding.