Injection rate
Surfactant solution with concentration of 0.01 g/cm3 is injected into the fracture, and oil and surfactant solution are produced at the same rate as injection rate from the top of the fracture. The injection rates are listed in Table 7. The pressure drop between the injector and producer is increasing with the increase in injection rate. But because the matrix size is small, the pressure drop is only 0.727 atm even when the injection rate is 5.34 cm3/h.
Table 7 Injection rate of surfactant solution and the steady pressure drop between injector and producer Figure 9 shows all the injection rates leads to the same ultimate oil recovery which is around 80% and that the oil recovery is increasing with the increase in injection rate when the injection rate is smaller than 0.027 cm3/h (i.e., 0.001 PV/h). When the injection rate is higher than 0.027 cm3/h, the oil recovery is almost the same. After 80 days of surfactant injection, the oil recovery is about 70%. And the oil recovery rate is slower afterwards. The oil recovery reaches the plateau after 500 days of surfactant flooding. Figure 10 shows that the higher injection rate results in a lower oil recovery after injecting a certain amount of surfactant solution. Because of the small size of the matrix, most the injected fluid could be produced directly without any contribution to oil recovery when the injection rate is large. When the injection volume is 2 PV, the surfactant flooding time is about 83 days and the oil recovery is about 70% for the injection rate of 0.027 cm3/h. Figure 11 shows that the ultimate oil recovery increases slower when the injection rate is lower than 0.027 cm3/h, and the ultimate oil recovery has a power function relation with injection rate when the injection rate is higher than 0.027 cm3/h. Considering the surfactant flooding time, the injection volume, and the oil recovery, the proper injection rate for the model is 0.027 cm3/h.
Even though the pressure drop increases with the increase in injection rate, the ultimate oil recovery does not change, which implies that the pressure drop does not have significant effect on oil recovery. When the injection rate is lower than 0.027 cm3/h, the injection rate is smaller than the imbibition rate, so the oil recovery rate is decided by the injection rate. But when the injection rate is higher than 0.027 cm3/h, the injection rate is larger than the imbibition rate; thus, the oil recovery rate depends on the imbibition rate. The surfactant imbibition into matrix could be affected by the surfactant diffusion and the fracture properties. Therefore, some contrastive simulations have been done to study these parameters.
Effect of surfactant diffusion
In the base case, the surfactant diffusion is 5 × 10−4 cm2/h. In order to study the effect of surfactant diffusion on surfactant EOR, the surfactant diffusion is set to zero in the contrastive simulation. The summary of the simulation results are listed in Table 8. Figure 12 shows that the injection rate has a dramatic effect on the oil recovery when the surfactant diffusion is zero, especially after 100 days’ injection. When the surfactant diffusion is ignored, surfactant is imbibed into the matrix by capillary pressure, gravity and the pressure difference between fracture and matrix. But the capillary force is decreased with the increase in the water saturation in the matrix and in this matrix the gravity force is very small (about 0.001 atm). In addition, the surfactant concentration will be diluted by the water in matrix and the adsorption, so surfactant efficiency is reducing with the imbibition distance into the matrix. When the capillary force is decrease to zero, the surfactant imbibition will depend on the pressure difference between fracture and matrix, which is increasing with the increase in the injection rate. Therefore, when the capillary imbibition stops (about 100 days in this case), the oil recovery is varying with injection rate. Comparing the oil recovery between the base case and the contrastive case (Fig. 13), it is obvious that surfactant diffusion could significantly increase the oil recovery. One reason could be that because the matrix size is very small, surfactant could diffuse into the whole matrix in a relatively short time. Another reason is that the matrix is homogeneous, so the sweep efficiency is not improved by the pressure difference, and fluid could be easily flow through the fracture system which makes it difficult to result in a large pressure drop between injector and producer. In reality, the reservoir is very complicated, so the injection rate may lead to a high pressure difference thus improve the sweep efficiency. The large size of the matrix in reservoir could decrease the relative efficiency of surfactant diffusion.
Table 8 Summary of the surfactant flooding with different injection rate when the surfactant diffusion is zero Effect of fracture porosity
The fracture width has effect on fracture porosity, fracture permeability and drop pressure between the injector and producer. Thus, in the contrastive case, the fracture width is reduced to 0.0034 cm. The fracture porosity and absolute permeability are calculated with Eqs. 2 and 3 separately. The properties of fracture are listed in Table 9.
$$\phi_{\text{f}} = \frac{{V_{\text{f}} }}{{V_{\text{t}} }} = \frac{b}{{L_{\text{t}} }}$$
(2)
$$K_{f} = C\frac{{b^{2} }}{12}$$
(3)
where \(\phi_{\text{f}}\) is fracture porosity, fraction; \(V_{f}\) is fracture volume, cm3; \(V_{\text{t}}\) is total volume, cm3; \(b\) is fracture width, cm; \(L_{\text{t}}\) is block length, cm; \(K_{\text{f}}\) is fracture absolute permeability, mD; \(C\) is unit convert coefficient, 1011.
Table 9 Fracture properties in the base case and contrastive case Comparing the ultimate oil recovery in two cases, Fig. 14 tells that the ultimate oil recovery is slightly smaller (about 0.3% OOIP) for the contrastive case with 0.1% fracture porosity when the injection rate is lower than 0.53 cm3/h, but the ultimate oil recovery is larger for the contrastive case when the injection rate is higher than 0.53 cm3/h. When the injection rate is 53.4 cm3/h, the ultimate oil recovery in the contrastive case is larger than the base case by 4% OOIP. The ultimate oil recovery is about 0.796 OOIP in the base case, but it starts to increase when the injection rate is higher than 2.67 cm3/h in the contrastive case, which indicates that the increase in the injection rate is more efficient to increase the pressure difference between fracture and matrix in the system with lower fracture porosity. The pressure drop between injector and producer does not have big difference between the two cases for all the injection rates, but Fig. 15 shows that when the fracture porosity is 0.1%, the ultimate oil recovery has obvious increase with the increase in the pressure drop when the pressure drop exceeds 0.4 atm, which implies that the pressure difference between fracture and matrix cannot be obtained from the pressure drop between injector and producer.
When the injection rate is higher than 0.027 cm3/h, the oil recovery curves are almost the same for the base case. However, for the contrastive case, the final oil recovery time to obtain the ultimate oil recovery is dramatically decreasing with the increase in injection rate (Fig. 16). The final oil recovery time is about 500 days when the injection rate is 0.01 PV/h. And it is reduced to 50 and 5 days when the injection rate is increased to 5.34 and 53.4 cm3/h separately. The results reveal that the oil recovery rate is enhanced by the increase in pressure difference between fracture and matrix which results from the fracture properties and injection rate. For the base case, the required injection volume to obtain the ultimate oil recovery is increasing with the increase in injection rate, which will lead to a higher cost. But for the contrastive case, the required injection volume is the same for the injection rate of 5.34 and 53.4 cm3/h (Fig. 17). Hence, for the contrastive case, the high injection rate (53.4 cm3/h) could be a good choice considering the oil recovery rate, the final oil recovery time, and the injection volume.
When the injection rate is smaller than 0.53 cm3/h, the pressure difference between the fracture and matrix is still too weak to impetus the oil recovery. So the main parameters of surfactant oil recovery are the same for both cases, which are capillary pressure and surfactant diffusion. On the contrary, when the high injection rate is applied, the brine or surfactant solution could be high-efficiently pushed into the matrix by the pressure difference, so the fluids flow faster in the matrix, which increases the capillary number. Therefore, the ultimate oil recovery is increased. At the same time, because of the increased influence of pressure difference, the relative contribution of surfactant diffusion to the oil recovery becomes smaller.
Injection timing
In this section, the injection timing of surfactant is studied to try to find out if surfactant should be applied at the secondary or tertiary recovery stage and whether surfactant could be used at the area swept by brine. Based on the previous study, the injection rate of 0.0005 PV/h is used. There are seven scenarios of surfactant injection following the pre-water flooding with volume of 0.4, 0.9, 1.3, 1.8, 2, 4, and 11 PV, and the results are compared with the results of surfactant flooding and water flooding (Fig. 18). The ultimate oil recovery is 80% OOIP for all the scenarios, which means the surfactant is imbibed into the whole matrix. Since the capillary pressure is zero after completed water flooding, and the gravity is very small in this model, the surfactant diffusion is the key parameter that let the surfactant go into the matrix and then change the matrix wettability and reduce the IFT, thus improve the oil recovery, which is proved by the contrastive case where the surfactant diffusion is neglected. When the surfactant diffusion is neglected, the ultimate oil recovery is about 0.5 OOIP for the surfactant flooding, and it decreases with the increase in the pre-water flooding volume (Fig. 19). The surfactant enhanced oil recovery is about 1.7% OOIP after injecting 15 PV surfactant solution for the scenario with 11 PV pre-water injection, which illustrates that the surfactant with poor diffusion efficiency should not be used after water flooding.
For the base case, the oil recovery rate is becoming slower after recovering about 90% of ultimate oil recovery, which is about 0.72 OOIP (Fig. 18). Plot the total injection volume of brine and surfactant solution and the injection volume of surfactant solution when the oil recovery is 0.72 OOIP in Fig. 20. It shows that the total volume has a linear relation with the pre-water flooding volume. And the required surfactant volume also increases with the increase in pre-water flooding volume. So even if the surfactant has high-efficient diffusion, the early surfactant application could reduce the time cost and surfactant consumption.
Surfactant slug size
The surfactant assumption is an important influence factor of the economy. The goal is to achieve the largest oil recovery in a reasonable cost of surfactant. In this section, the surfactant is injected before water flooding. And the surfactant injection volume is varying from 0.2 to 4 PV. The surfactant concentration in the base case is 0.01 g/cm3. Another injection concentration of 0.005 g/cm3 is used as the contrastive case. The relationship between injection volume of surfactant solution and the ultimate oil recovery is plotted in Fig. 21. After injecting 1.3 PV surfactant solution with concentration of 0.01 g/cm3, the ultimate oil recovery (about 0.8 OOIP) is obtained. But the ultimate oil recovery is about 0.5 OOIP for the contrastive case with surfactant concentration of 0.005 g/cm3. Besides, it requires much more surfactant solution to obtain the maximum oil recovery. The critical micelle concentration of the surfactant (C12TAB) is about 0.004 g/cm3 and required concentration to change the wettability to strongly water wet is no less than 0.005 g/cm3. When the surfactant is moving into the matrix, the concentration is diluted and becomes smaller and smaller with the distance into the matrix. For the small concentration, the dilution has a large negative effect on the surfactant efficiency. Therefore, the lower concentration results in a smaller oil recovery with the same surfactant slug size. The relationship between the injection mass of surfactant and the ultimate oil recovery (Fig. 22) shows that even injecting the same amount of surfactant, the ultimate oil recovery is smaller in the case with a lower surfactant concentration, which implies that the surfactant efficiency is decreasing with the decrease in surfactant concentration. The relationship between surfactant mass in matrix and the ultimate oil recovery are similar for both cases, and the ultimate oil recovery has a strong positive linear function relation with the surfactant mass in matrix (Fig. 23), which means the ultimate oil recovery depends on how much the surfactant goes into the matrix. This also implies that less surfactant can be imbibed into the matrix for the lower surfactant concentration; hence, the surfactant efficiency is reduced. Based on the previous analysis, it can be concluded that it needs less surfactant to obtain the maximum oil recovery with the application of higher surfactant concentration, so under the condition of injection safety, the relatively higher surfactant concentration is a better choice.