Sensitivity Analysis and Multiobjective Optimization of CO2 Huff- N-Puff Process after Water Flooding in Natural Fractured Tight Oil Reservoirs

The CO2 huff-n-puff is an effective substitute technology to further improve oil recovery of natural fractured tight oil reservoirs after water flooding, for its high displacement efficiency and superior injectivity. The CO2 huff-n-puff process is influenced by many factors, such as miscible degree, complex fracture networks, and production schemes. What is worse, those influence facts affect each other making the process more complex. Many researchers concentrated on mechanisms and single sensitivity analysis of CO2 huff-n-puff process, whereas few optimized this process with the consideration of all influence factors and multiobjective to get favorable performance. We built multiobjective consisted of miscible degree, oil recovery, and gas replacing oil rate considering the aspects of CO2 flooding special characteristic, technical effectiveness, and economic feasibility, respectively. We have taken Yuan 284 tight oil block as a case, firstly investigated sensitivity analysis, and then optimized CO2 huff-n-puff process using orthogonal experiment design with multifactors and multiobjectives. The optimization results show CO2 huff-n-puff can significantly improve oil recovery by 8.87% original oil in place (OOIP) compared with water flooding, which offers guidelines for field operations.


Introduction
For tight oil reservoirs with natural fractures, the development performance varies due to the influence of natural fractures. Water flooding becomes feasible for natural fractures to provide a high permeability flow path [1]. However, the nature fracture also brings adverse effects at later development stage. The injected water flows along natural fractures and breaks through early, reducing the sweep efficiency of water flooding severely. The more injected water becomes invalid, and the more oil in matrix is left without effective recovery. Vertical wells were used instead of multiple fractured horizontal wells (MFHWs), because once MFHWs suffer water breakthrough, it is hard to conduct water plugging [2].
To further improve oil recovery after water flooding, CO 2 huff-n-puff is proposed. This is because CO 2 huff-n-puff can take the advantages of natural fractures and avoid their bad effects. CO 2 huff-n-puff fully uses the enormous areas provided by nature fractures to get contact with oil, and only extracts oil around injection wells unlike CO 2 continuous flooding suffers gas breakthrough [3]. The studied Yuan 284 block is rich in natural fractures [4,5]; based on these aforementioned facts, CO 2 huff-n-puff is proposed as a substitute technology after water flooding to further improve oil recovery.
The oil recovery of CO 2 huff-n-pull is affected by many factors; what is worse, multifactors affect each other making the process more complex. Both good and bad results were obtained on site, and the process optimization has become an imperative issue needed to be settled. Many researchers have investigated the mechanisms and single sensitivity analysis of CO 2 huff-n-puff process in the literature.
Fracture density and fracture geometry influence huff-npuff performance significantly, because fractures provide CO 2 with high conductive flow paths and enormous contact areas with oil [6][7][8]. Fractures also impair CO 2 and oil miscible degree by influencing pressure maintenance [9,10]. Miscible degree promotes oil recovery by improving displacement efficiency, so injection pressure higher than minimum miscible pressure (MMP) is needed [11]. CO 2 molecular diffusion plays an important role in enhancing oil recovery during CO 2 soaking time and promotes the mixture of CO 2 with matric oil swelling oil volume and reducing oil viscosity [9]. CO 2 molecular diffusion needs enough soaking time to fully act its role, but soaking time is not the longer the better, and there is an optimal point [12,13]. The reopen production bottom hole pressure affects oil recovery significantly by influencing drive mechanisms. It was found that CO 2 solution drive due to low bottom hole pressure plays a more important role than CO 2 miscible driver with high bottom hole pressure [14]. Other researchers also investigated the interaction of multifactors and found that primary depletion time, CO 2 injection time, and reopen production time have obvious influence on each other [15].
Unfortunately, few optimized the CO 2 huff-n-puff process considering multiple factors effects and the interactions between them. In this research, Yuan 284 block of Changqing oil field was taken as a case, and firstly single factor sensitivity analysis was conducted to investigate the influence rule on huff-n-puff performance. Then, multiobjective goal consisted of miscible degree, oil recovery, and gas replacing oil rate was built. It fully considered CO 2 flooding special characteristic, technical effectiveness, and economic feasibility. Orthogonal experimental design is a widely used multifactor optimal method, for it can select the optimal project without calculating all possible schemes, reducing the calculated scheme number and computational cost [16,17]. Based on the orthogonal experimental design method, the CO 2 huff-n-puff process with multifactors influence and multiobjective goal was optimized, which provides guidelines for treatments on site.

Reservoir Model Description
In this section, the pilot test reservoir model of Yuan 284 block was described, including geometry model, fluid model, relative permeability curve, and history match. It provided the basic simulation model for further sensitivity analysis and multiobjective optimization.
The average permeability and porosity of Yuan 284 block are 0.41 mD and 11.08%, and it belongs to tight oil reservoirs. The target reservoir bury depth is 2100 m, and reservoir temperature and initial pressure are 70.6°C and 15.1 MPa. The target reservoir has four well groups, and they are all inverted nine-point diamond-shaped patterns. The bubble map of production rates and water injection rates in August 2012 were shown in Figure 1. It indicates that the reservoir has serious heterogeneity for water cut of several wells are extremely higher than the others. The CO 2 huff-n-pull was proposed to further improve oil recovery. The water injection well in the center of each well group as before and the other production wells as CO 2 huff-n-pull wells are considering reservoir pressure maintenance and remaining oil distribution.
For this target reservoir with natural fractures, the simulation of natural fractures is very important, and we used high permeability channels to mimic natural fractures. The high permeability channels were determined by history match, that is, we modified the high permeability channels until the history data and calculated data achieve good match, and their distributions before and after history match are different as shown in Figure 2. The oil and water production total achieved good match with the real data after history match as shown in Figure 3, because natural fractures were appropriately simulated by changed high permeability channels.
We used the compositional fluid model to describe the complex interaction of CO 2 and crude oil. To improve computational efficiency, we grouped all compositions of CO 2 and oil fluid system into 9 pseudocomponents in Table 1, according to the composition's properties and expert experience. We used RP3-EOS to describe the phase behavior of CO 2 and oil system, and the parameters of EOS were determined for further fluid simulation. We turned and determined the RP3-EOS parameters by fitting the simulation results and experimental results. The determined EOS parameters were shown in Table 1. What is more, the MMP was also determined by slim-tube experiment, when the pressure is higher than the MMP 16.8 MPa, the miscible condition is achieved and the process gets a favorable displacement efficiency.
Relative permeability curves accounting for dynamic interaction of reservoir fluids and rock media were measured by core flooding experiments according to Darcy's law as Figure 4 shows. The residual oil saturation of water flooding is 0.31, and the ideal displacement efficiency of water flooding is only 44.7% OOIP, which is far below CO 2 flooding displacement efficiency, and this is the main reason why CO 2 flooding is proposed as the substantial EOR technology after water flooding.

Sensitivity Analysis
We investigated the effects of CO 2 injection volume, injection time, soaking time, production bottom hole pressure, reopen production time, and huff-n-puff cycle number on the oil recovery. The parameters of the basic model were as follows: one cycle CO 2 huff-n-puff process consists of 10 days CO 2 injection time, 5 days soaking time and 200 days reopen production time. The one cycle CO 2 injection volume is 988.5 t, the production bottom hole pressure is     3 Geofluids 7 MPa, and the total cycle number is 5. When we studied the effect of a single factor on oil recovery, the other factors were kept the same as the basic model set.
We first investigated the effect of CO 2 injection volume on oil recovery. As Figure 5(a) shows the oil recovery increases with the increased injection volume from 197.7 t to 988.5 t, the increased CO 2 injection volume increases the amount of CO 2 dissolved in the matrix oil, and more oil swells and easily flows out for decreased viscosity. What is more, the increased CO 2 volume increases the pressure around injection wells, which improves CO 2 and oil miscible degree and displacement efficiency obviously. However, after a point, the oil recovery stops increasing from 988.5 t to 1383.9 t and even decreases with the increased injection volume from 1383.9 t to 1779.3 t, because the excessive injected CO 2 is not fully utilized and even expels the oil away from the well, which impairs the reopen production performance. Figure 5(b) shows the oil recovery increases with the increased CO 2 injection time, indicating that slow CO 2 injection rate is favorable to oil recovery. This is because the injected CO 2 with a lower injection rate has more time to propagate forward and mix with oil, which increases the contacted oil amount and gets more favorable mixing effect. Figure 6(a) shows the oil recovery increases with the increased soaking time, but after a point slightly decreases with the increased soaking time. This is because due to the extremely low permeability of a tight oil reservoir, CO 2 molecular diffusion needs a certain time to mix with matric oil and achieve better performance. However, too long soaking time leads to the gravity separation of CO 2 and oil in fractures, which results in the slightly decreased oil recovery. Figure 6(b) shows the oil recovery significantly increases with the decreased bottom hole pressure. The decreased bottom hole pressure increases the potential of dissolved CO 2 releases from oil and increases the CO 2 solution driver proportion. However, it decreases CO 2 and oil miscible degree and displacement efficiency, and CO 2 miscible drive proportion decreases. It illustrates that for CO 2 huff-n-puff process, the CO 2 solution drive contributes more on oil recovery than CO 2 miscible drive. Figure 7(a) shows the oil recovery significantly increases with the increased reopen production time from 7.75% OOIP to 14.63% OOIP. This illustrates that increasing reopen production time leads to favorable oil recovery, for it fully mines the potential of the injected CO 2 during the huff process. Figure 7(b) shows the oil recovery increases with the increased huff-n-puff number, while the gas replacing oil rate decreases as the cycle number increases. This is because more oil around the huff-n-puff well was extracted by injected CO 2 with the increased cycle number, so the oil recovery increases. However, the oil saturation around the huff-n-puff well decreases with the increased cycle number, and the injected CO 2 efficiency decreases resulting in the decreased gas replacing oil rate.

Multiobjective Optimization
For CO 2 huff-n-puff process optimization, the optimization objective determination is very important. The optimization objective should comprehensively consider the aspects of CO 2 flooding special characteristic, technical effectiveness, and economic feasibility. In this research, multiobjectives consisted of miscible degree, oil recovery, and gas replacing oil rate were used to describe these aspects comprehensively. Since the miscible degree is significantly affected by pressure, the average pressure was used to describe the miscible degree for convenience. What is more, we adopted the orthogonal experimental design method to optimize the CO 2 huff-npuff process considering multifactor influences and multiobjective goals.
In Section 3, we investigated the effect of a single factor on oil recovery. However, the optimization design process cannot be determined by sensitivity analysis, because the oil recovery is simultaneously influenced by many factors. We selected CO 2 injection volume, injection time, soaking time, production bottom hole pressure, reopen production time, and cycle number as influencing factors, and each influencing factor has 5 levels. If we use the full experimental design method, all possible schemes 7776 are needed to test for optimization, and the computational cost is very high. To avoid   Table 2.
Multiobjective optimization designs were conducted, and the three objective indices were transformed into one comprehensive objective to facilitate evaluation. The comprehensive objective scores were calculated by formula (1). The multiplied weights were determined by expert experience

Geofluids
and study goals. The comprehensive objective scores calculation results were shown in Table 2. It shows that the 7th scheme gets the maximum score of 57 and is the optimal design.
where COS is the comprehensive objective scores, OR is the oil recovery, GRO is the gas replacing oil rate, and P avg is the reservoir average pressure.
The range of average scores represents the influence degree of factors on target goal, and it can be concluded that the influence degree ranking of multifactors is the following: reopen production time, cycle number, injection time, bottom hole pressure, injection volume, and soaking time. The reopen production time has the most obvious effect on the comprehensive objective. The soaking time affects oil recovery by CO 2 molecular diffusion mechanism during the well shut period, but the effect of it is the least compared with other factors during the whole production period.
The optimal scheme was determined based on these aforementioned investigations, and the optimal factor combination of Yuan 284 block is that one cycle CO 2 injection volume is 197.70 t, the CO 2 injection time is 6 days, the soaking time is 15days, the reopen production time is 400 days, the production bottom hole pressure is 6 MPa, the cycle number is 7, and the total production time is about 8 years.
The selected optimal scheme was calculated, and the average reservoir pressure and oil production rate of the CO 2 huff-n-puff process were shown in Figure 8. For the optimal CO 2 huff-n-puff process, the average reservoir Ai is the ith index average scores; R is range of average scores. 6 Geofluids pressure and the oil production rate were maintained at a high level. The average pressure and the oil production rate have the same change trend during each cycle and gradually decrease with the increased cycle number. The 8 years oil recovery of CO 2 huff-n-puff and water flooding were 19.07% OOIP and 10.20% OOIP, respectively. The optimal CO 2 huff-n-puff can significantly improve oil recovery by 8.87% compared with water flooding. The selected optimal scheme was calculated, and the average reservoir pressure and oil production rate of CO 2 huff-n-puff process were shown in Figure 8. For the optimal CO 2 huff-n-puff process, the average reservoir pressure and the oil production rate were maintained at a high level. The average pressure and the oil production rate have the same change trend during each cycle and gradually decrease with the increased cycle number. The 8 years oil recovery of CO 2 huff-n-puff and water flooding were 19.07% OOIP and 10.20% OOIP, respectively. The optimal CO 2 huff-n-puff can significantly improve oil recovery by 8.87% compared with water flooding. Figure 9 shows the remaining oil saturation distributions before and after CO 2 huff-n-puff and water flooding. Comparing the remaining oil saturations before and after taking measurements, the remaining oil saturation after CO 2 huffn-puff is much less than that after water flooding. This obviously indicates that the displacement efficiency of CO 2 huffn-puff is superior to water flooding, which is the main reason why the CO 2 huff-n-puff process is taken.
The CO 2 huff-n-puff process also achieved good sweep efficiency, which also attributes to the good performance of this process. We used CO 2 saturation distributions to approximately illustrate the sweep efficiency degree as shown in Figure 10. With the increase of the CO 2 huff-npuff cycle, the CO 2 saturation increases but the increase  7 Geofluids degree decreases. However, the CO 2 only centralized distributes around the huff-n-puff production well and decreases dramatically away from the production well. This indicates that the CO 2 huff-n-puff process achieves good sweep efficiency only around the production well, where the remaining oil is rich. Thanks to the superior sweep efficiency of the CO 2 huff-n-puff process, the remaining oil around the production well achieves high oil recovery.

Conclusions
Sensitivity analysis and multiobjective optimization of CO 2 huff-n-puff process were conducted in this research, and the following conclusions can be drawn: Single factor sensitivity analyses were conducted, and the influence rules were achieved. The decreased bottom hole pressure results in the increased oil recovery. It indicates that CO 2 solution drive with low bottom hole pressure contributes more on oil recovery than miscible drive with high bottom hole pressure for CO 2 huff-n-puff process.
The single factor influence degree ranking is determined based on the range scores: reopen production time, cycle number, CO 2 injection time, bottom hole pressure, CO 2 injection volume, and soaking time. The contribution degree of soaking time is the least during the whole production period compared with other factors, though it increases oil recovery by CO 2 molecular diffusion mechanism during well shut period obviously.
The optimal CO 2 huff-n-puff scheme was determined using orthogonal experimental design with multifactor influences and multiobjective goals, and it can significantly improve oil recovery by 8.87% OOIP compared with water flooding.

Data Availability
The data used to support the findings of this study are included within the article.

Conflicts of Interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work; there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.