It is widely accepted that foam flooding can significantly enhance oil recovery^[1,2,3], but it is difficult to figure out the oil displacement mechanism of foam because the flow characteristics of fluid inside the core cannot be observed directly from conventional core flooding devices. At present, the microscopic mechanism of foam flooding is primarily studied by microscopic microscopy technique. But this method require that the thin section model must be less than 3 mm thick to ensure its light transmission^[4,5], it can only simulate two-dimensional flow and can’t truly reflect the flow characteristics in reservoir because it restricts the flow of fluid along the model thickness direction^[6]. In addition, the stability of foam is a key factor affecting the flooding efficiency of foam^[7]. The conventional methods evaluating foam stability include the volume method, conductivity method and pressure method^[8]. The volume method is commonly used in evaluating foam stability due to its simple operation and wide adaptability, and it is further divided into the Ross-Miles method, oscillation method and Waring-Blender method^[9,10,11]. However, it is difficult to quantitatively describe the performance of the foam by the volume method for the large manual error in the actual operation process. Conductivity method and pressure method have high sensitivity, but the experimental devices are complicated and not easy to operate with high cost^[12]. Moreover, the methods above all belong to the static category because it is used to evaluate the stability of foam in a standing container. The foam flooding in a porous medium is a dynamic process of continuous collapse and regeneration of foam, so static evaluation method without porous medium cannot truly reflect the stability of the foam in the reservoir^[6,13]. Few methods have been developed to study dynamic stability of the foam during flooding process. The resistance factor can reflect the plugging ability of the foam in the porous medium and the dynamic stability of foam to some extent. But the resistance factor is mainly based on the pressure change caused by Jamin effect during the foam flooding process^[14]. In the experimental process, the pressure is affected by many factors and difficult to reach a stable value, a large amount of foam needs to be injected to make the pressure stable^[15], therefore, it is necessary to establish a new method to evaluate foam dynamic stability.

In this study, the NMR experiments on foam flooding were conducted by combining NMR technology with traditional core flooding method. The average size of pores where the fluid locate and the mass change of the fluid in the core can be reflected by the T₂ spectrum^[16,17], and the displacement characteristics of foam in the core can be visually observed from the NMR images. At the same time, a new method evaluating the dynamic stability of foam in the core has been established based on the NMR T₂ spectrum and the law of mass conservation. The displacement characteristics and dynamic stability of the two kinds of foam systems were studied by adopting two different displacement modes (directly foam flooding and foam flooding after water flooding).

The movement of liquid molecules in the core causes the molecules to collide with the wall of the microchannel in the rock many times, and the two relaxation processes occurred during each collision (longitudinal relaxation and transverse relaxation). In core NMR tests, the transverse relaxation is tested usually as the longitudinal relaxation has a longer measurement time and fewer measurement points. The transverse relaxation involves three different relaxation mechanisms, free relaxation, surface relaxation and diffusion relaxation^[18]. The effects of the three relaxation mechanisms on the relaxation time mainly depend on the type of fluid, pore size, and surface relaxation strength, etc., so the NMR relaxation time can be used to analyze a series of physical properties of the sample^[19]. The T₂ value in the transverse relaxation curve is proportional to the size of the pore where the liquid locates, and the peak area enclosed by the signal amplitude and relaxation time is proportional to the liquid mass in the core^[20]. The spatial localization of the nuclear magnetic signal is realized by applying three mutually perpendicular controllable linear gradient magnetic fields on the target object. The receiving device acquires the amplitude of nuclear magnetic resonance signal and corresponding spatial position information, then the NMR image is obtained after processing^[17].

It is necessary to clearly distinguish the water, foam and oil both in spectral line and image of T₂ in order to visually study the oil displacement characteristics of foam. The nuclear magnetic signals of the oil and water cannot be clearly distinguished in water flooding due to the overlap of the nuclear magnetic resonance relaxation time of oil and water. So the oil peaks and water peaks cannot be distinguished in the T₂ spectrum, and the oil and water can’t be distinguished in the NMR image either. When the MnCl₂ aqueous solution is used for flooding, the direct contact of Mn²⁺ with H protons would cause spin exchange, make the relaxation and decay of H protons in water accelerate^[21], so the relaxation time of oil and water don’t overlap anymore, and the NMR signals of the two can be distinguished from each other. Results of several experiments show that replacing water with MnCl₂ aqueous solution of 0.5wt% in water flooding can best distinguish oil and water NMR signals^[22]. In foam flooding, the gas phase in the foam does not produce nuclear magnetic signal, and the nuclear magnetic resonance relaxation time of the water phase in the foam also overlaps with relaxation time of oil. The nuclear magnetic signals of the foam and oil can also be distinguished by adding 0.5wt% MnCl₂ to the foaming liquid. But the premise of this method is to ensure the performance of the foam wouldn’t be affected by adding MnCl₂. Therefore, the performance of the foam before and after 0.5wt% MnCl₂ was added (S-2 and S-NP-2) was evaluated by the Waring-Blender method. Each experiment was repeated three times and the average values were calculated. The experiment results are shown in Table 1.

The results (Table 1) show that the stability of the foam with 0.5wt% MnCl₂ is close to the stability of the foam without MnCl₂, so the 0.5wt% MnCl₂ aqueous solution was used in foam preparation and water flooding instead of water in this study.

Materials used in the experiments included distilled water, manganese chloride (MnCl₂), simulated oil (formulated by filtered diesel and crude oil in a mass ratio of 10:1, with a viscosity of 2.50 mPa·s at 25 °C), nitrogen, core (artificial, physical properties are shown in Table 2), foam of S-2 (the main component is sodium lauryl sulfate with a concentration of 3wt %), and S-NP-2 (the main component is sodium lauryl sulfate with a concentration of 3wt% and silicon dioxide nanoparticles with a concentration of 0.5wt%). It is worth noting that the foam of S-NP-2 is a stable foaming system obtained through a large number of repeated experiments in which nanoparticles of different particle sizes, different modifiers and different wettability were added to foam of S-2. The evaluating results of the foam stability by the Waring-Blender method are shown in Table 1. The stability of the foam of S-NP-2 is better than that of S-2.

A visual displacement experimental setup based on nuclear magnetic resonance is shown in Fig. 1. It includes ISCO pumps, intermediate containers, a foam generator, a special core holder, a nuclear magnetic resonance unit, a control unit, and a metering unit, etc. The experimental procedure is as follows: (1) Detecting the substances such as iron which is not allowed to contain in the core because it can interfere with the magnetic field. (2) Testing the properties of the core. (3) Saturating the core with water by vacuuming and applying pressure. (4) Debugging parameters of NMR. (5) Establishing the bound water by flooding water with oil and aging for 48 hours after the effluent liquid with no water. (6) Water flooding: water is injected at a constant rate of 0.5 mL/min until the water cut is greater than 98% at the back pressure of 0 MPa. (7) Foam flooding: the gas-liquid ratio of the foam is 1:1, the injection speed is 0.5 mL/min, and the displacement is stopped after the water cut is greater than 98% at the back pressure of 0 MPa. (8) Injection pressure and liquid output are recorded during the injection process, and nuclear magnetic resonance T₂ spectra and image are obtained.

Four experiments using core 1#-4# were conducted in this study to find out the flooding characteristics and oil recovery of the directly foam flooding (displacement mode 1) and foam flooding after water flooding (displacement mode 2) with S-2 and S-NP-2. Among them, core 1# and core 2# were flooded by displacement mode 1, core 3# and core 4# were flooded by displacement mode 2. Core 1# and core 3# were flooded with S-2, core 2# and core 4# were flooded with S-NP-2.

The oil displacement efficiency and water cut of the foam flooding with the pore volumes are shown in Fig. 2 to Fig. 5.

It can be seen from Figs. 2 and 3, for core 1# and core 2#, outlet end begin to produce water when foam is flooded to 0.4 PV, then the water cut increases quickly while oil displacement efficiency tending to be mild. When foam is flooded to 1.0 PV, the outlet water cut is more than 98% with the oil displacement efficiency values for core 1# and core 2# are 50.80% and 55.80% respectively. It can be seen from Figs. 4 and 5, for core 3# and core 4#, outlet water cut is more than 98% when water is flooded to 1.0 PV with the oil displacement efficiency values are 45.67% and 41.82% respectively. Then use foam flooding and outlet water cut increases slowly after obvious drop, stop flooding until the water cut is larger than 98%, the oil displacement efficiency values are 63.72% and 67.50% for core 3# and core 4#.

It can be seen from Table 3 that the oil displacement efficiency of core 1# and core 2# are lower than that of core 3# and core 4#, indicating that displacement mode 2 can recover more oil than displacement mode 1. The oil displacement efficiency of core 2# and core 4# is higher than that of core 1# and core 3#, respectively, indicating that the oil displacement effect obtained by using foam of S-NP-2 under the same displacement modes is better. After water flooding, the foam flooding was used and the oil displacement efficiency of core 3# increased by 18.05%, and the oil displacement efficiency of core 4# increased by 25.68%. It can be seen that the displacement mode 2 can significantly enhance oil displacement efficiency and the foam of S-NP-2 can get better effect.

The resistance factor is the ratio of the pressure difference between two ends of the core in foam flooding when the pressure stabilizes to that in water flooding under same conditions. It is an important index to evaluate the plugging ability of the foam^[23]. Since when the image and T₂ spectrum were taken during the experiments, the injection of foam needs to be stopped, so it is difficult to obtain a complete continuous pressure monitoring curve throughout the whole displacement process compared with the conventional foam flooding experiment without NMR experiment. In order to obtain the stable pressure difference during the foam injection process, the foam was continuously injected until the pressure was stable after the last image and T₂ spectrum were tested, and the pressure difference at this point was recorded as the foam flooding pressure difference.

It can be seen from Table 4, the foam had a good plugging effect in all the four groups of experiments. And the resistance factors of core 1# and core 2# are less than the resistance factors of core 3# and core 4#, respectively, which indicates that the displacement mode 2 can achieve better plugging performance. The resistance factors of core 2# and core 4# are larger than those of core 1# and core 3#, respectively, suggesting that the plugging ability of foam S-NP-2 is better than S-2 in the same displacement mode.

The nuclear magnetic resonance images of the foam flooding experiments are shown in Figs. 6 and 7. The black area represents the water or foam and the remaining colored part represents oil.

It can be seen from Fig. 6 that when direct foam flooding (mode 1) is taken, the displacement front appeared when the foam of 0.5 PV was injected and the remaining oil was concentrated in front of the displacement front (right part in the core). A small amount of residual oil was behind the displacement front. When the foam of 1.0 PV was injected, there was no obvious residual oil enrichment area, and a small amount of residual oil was distributed throughout the core, indicating that the sweep efficiency is high and the washing effect is remarkable. It can be seen from Fig. 7 that the oil saturation in the core after the water of 1.0 PV was injected significantly reduced, but a large amount of residual oil was left throughout the core after water flooding due to the relatively poor washing effect of the water. The oil displacement characteristics using S-2 and S-NP-2 by adopting flooding mode 1 and mode 2 are similar. Only a small amount of residual oil was left in the core after the foam of 1.0 PV was injected, which shows that the displacement efficiency of foam flooding is more remarkable.

In summary, the nuclear magnetic resonance image can be used to visually observe the oil displacement characteristics, but it is difficult to reflect the differences between the two kinds of foam systems in different cores.

The nuclear magnetic resonance T₂ spectrum of the two kinds of foam systems by adopting displacement mode 1 are shown in Figs. 8 and 9, and the nuclear magnetic resonance T₂ spectrum of them by adopting displacement mode 2 are shown in Figs. 10 and 11. The peak with a shorter relaxation time on the left side is water peak and the peak with a longer relaxation time on the right side is oil peak.

It can be seen from Figs. 8 to 11 that the oil peaks gradually decrease with the injection of the displacement agent, indicating that the foam is effective for flooding oil. The oil peak didn’t shift obviously during decline when the core 1# and core 2# were flooded by foam directly, indicating the pores of various sizes produce oil uniformly in this mode of flooding. Core 3# and core 4# were flooded by foam after water flooding, and the oil peak of the T₂ spectrum shifted to the left by 46.29 ms and 23.94 ms in core 3# and core 4#, respectively. This is because that in water flooding, the large pores produce more oil, so the relaxation time decreases and the oil peak shifts to the left. When the core was turned to foam flooding after water flooding, the oil peak shifted to the right by 71.96 ms and 77.14 ms in the core 3# and core 4#, respectively, suggesting that the foam has a certain profile control effect. More oil was produced from small pores in this period, so the corresponding relaxation time increased, and the oil peak shifted to the right.

A new method to evaluate the dynamic stability of foam in the process of oil displacement has been established in this study based on NMR T₂ spectrum and mass conservation law.

3.1.1. Mass conservation equation

During foam flooding, water and gas were injected into the core from the inlet end, and oil, gas and water flow out from the outlet (Fig. 12). The mass change of the core is equal to the fluid mass difference between the inflow and the outflow within a certain period of time according to the law of conservation of mass^[24]. And the mass conservation equation for foam flooding is established as follows.

3.1.2. Conversion of the gas-liquid volume ratio and gas- liquid mass ratio

In order to substitute the mass conservation equation, the gas-liquid volume ratio needs to be converted into mass ratio. The gas-liquid mass ratio and volume ratio at the inlet of the core are:

Substituting the gas state equilibrium equation into the density formula:

The density of water phase must be strictly tested according to the density measurement method described in《GB/T 2013-2010》as surfactant is added to the water phase.

3.1.3. Mass change of oil and water during foam flooding

The peak area formed by the water peak curve and the oil peak curve with the abscissa can be obtained by integration in nuclear magnetic resonance T₂ spectrum. The peak area is in proportion with the corresponding mass of the fluid in the core, so the mass change of the oil and water during the foam flooding process can be obtained from the T₂ spectrum.

3.1.4. Dynamic instability factor of the foam

Substituting equations (5)-(7) into equation (1)

When the water cut is more than 98% with continuous foam in outlet end, the foam gas-liquid ratio inside the core is expressed as

Make

Then

Wang et al. found that the gas-liquid ratio reflected the stability of the foam to a certain extent by observing a large number of nitrogen foam flooding experiments, when the gas-liquid ratio of the foam was relatively low, the foam was slowly generated and small in amount, so the pressure was low and the resistance factor was small during the foam flooding; when the gas-liquid ratio was high, the foams generated were large in size and sparse, easy to break, so the resistance factor was also smaller^[25].

The “s” in equation (11) reflects the variation degree of gas-liquid ratio after foam is injected to the core. When s=0, then, n_m=n_m,in, which indicates that the gas-liquid ratio of the foam in the core doesn’t change and the break speed and generation speed of the foam reaches a dynamic equilibrium, which is an ideal stable state. When s>0, then, n_m>n_m,in, which indicates that gas-liquid ration increases after foam is injected, the proportion of liquid in the core reduces, and the foam drainage occurs. When s<0, then, n_m<n_m,in, which indicates gas-liquid ration decreases after foam is injected that the proportion of gas in the core decreases and the foam is broken. The smaller the $\left| s \right|$ value, the smaller the varation degree of gas-liquid ratio after foam is injected is and the closer the foam is to the ideal stable state, and the better the stability of foam is. Therefore, define the dynamic instability factor as:

The larger the f, the poorer the dynamic stability of the foam; the smaller the f, the greater the dynamic stability of the foam.

According to the above method, the stability of the foam in the core during the four groups of foam flooding experiments was evaluated. The nitrogen with the molar mass of 0.028 kg/mol was used in the foam flooding experiments of this study. And the temperature was kept at 298.15 K and the gas-liquid volume ratio at 1.00 at the inlet of the core during the isothermal percolation process. The dynamic instability factors calculated are shown in Table 5.

It can be seen from Table 5, the stability of the same foam system is better in the displacement mode 2. This is because when the foam flooding directly in the displacement mode 1, the oil saturation is high and the foam liquid film forms a "fake emulsion film", which reduces the stability of the foam^[26]. At the same time, the effective surfactant concentration reduces and the ability to regenerate foam during subsequent flooding also reduces. In the displacement mode 2, the water flooding first significantly reduces the oil saturation, and the influence of high oil saturation is avoided in the subsequent foam flooding, so the displacement mode 2 can achieve higher oil displacement efficiency than the displacement mode 1.

The resistance factor can directly reflect the plugging ability of the foam in the porous medium. Because the stability of the foam determines the plugging effect, the resistance factor can reflect the stability of the foam in the core flooding process to some extent. The dynamic instability factors and resistance factors of the four groups of experiments were compared (Table 6).

It can be seen from Table 6 that the dynamic instability factor of the foam S-NP-2 is less than that of the foam S-2 and the resistance factor corresponding to the foam system S-NP-2 is also higher than that of the foam S-2. Therefore, the results got by both methods show that the stability of the foam S-NP-2 in the core flooding process is better than that of the foam S-2 in the same displacement mode. This indicates that the results obtained by the dynamic stability evaluation method established in this study are consistent with the results obtained by the resistance factor method, which indirectly verifies the reliability of the dynamic stability evaluation method proposed in this study.

A NMR experimental method of foam flooding has been developed, which can directly reflect the oil displacement characteristics of the foam with NMR images and T₂ spectrum. Under different displacement modes, the foam has good oil washing performance and high sweeping efficiency. The change of transverse relaxation time of the T₂ spectrum shows that the foam plays a certain profile control role in the foam flooding after water flooding.

The oil displacement efficiency reached 63.72% and 67.50% by using the S-2 and S-NP-2 respectively by foam flooding after water flooding, 18.05% and 25.68% higher than that of directly foam flooding.

A new method for evaluating the dynamic stability of the foam during displacement process has been established based on the nuclear magnetic resonance T₂ spectrum and mass conservation law. Study with this method shows the dynamic stability of S-NP-2 is better than that of S-2 under the same displacement mode.

Nomenclature

A_oi, A_wi—peak area formed by the water peak curve and oil peak curve with the abscissa in T₂ spectrum under the conditions of saturated oil and saturated water, dimensionless;

ΔA_o, ΔA_w—peak area change formed by the water peak curve and oil peak curve with the abscissa in T₂ spectrum , dimensionless;

f—dynamic instability factor of foam;

m_oi, m_wi—mass of oil and water in the core saturated with oil and water, kg;

Δm—mass change of the core, kg;

Δm_o, Δm_w—mass change of the oil and water in the core, kg;

m_g,in, m_w,in—quality of the gas phase and water phase injected into the core, kg;

m_g,out, m_o,out, m_w,out—mass of the gas phase, oil phase and water phase flowing out of the core, kg;

m_w—mass of the water phase in the core before foam flooding, kg;

M—molar mass, kg/mol;

n_m—gas-liquid ratio inside the core, dimensionless;

n_m,in, n_v,in—gas-liquid mass ratio and gas-liquid volume ratio at the inlet of the core, dimensionless;

p_in—pressure at the inlet, Pa;

R—ideal gas constant, 8.314 J/(mol·K);

T_in—temperature at the inlet, K;

V_g,in, V_w,in—volume of the water phase and gas phase at the inlet respectively, mL;

ρ_g,in—gas density at the inlet, kg/m³;

ρ_w,in—water density at the inlet, kg/m³.