Earlier studies show that huff-n-puff injection is preferred to continuous gas flooding to improve liquid oil production in shale oil reservoirs. Compared to gas flooding, huff-n-puff has more operational parameters to optimize so that liquid oil production can be maximized. This paper is to discuss the optimum huff-n-puff times, number of cycles and soaking time under practical operational and reservoir conditions. The operational and reservoir conditions dictate the maximum injection and production rates, and the maximum injection pressure and minimum production pressure.
James J. Sheng
Texas Tech University, P.O. Box 43111, Lubbock, TX 79409, USA. Southwest Petroleum University, Chengdu 610500, China
Received 16 December 2016- Accepted 28 March 2017
The numerical simulation results and discussions show that the optimum huff time is so long that the pressure near the wellbore reaches the set maximum injection pressure during the huff period; and the optimum puff time is the time required for the pressure near the wellbore to reach the set minimum production pressure during the puff period. The benefits of soaking may not compensate the loss in injection and production due to the time lost in the soaking period. Therefore, soaking may not be necessary during the huff-n-puff gas injection in shale oil reservoirs. The number of huff-n-puff cycles is determined when an economic rate cut-off is reached.
It is well known that primary depletion using horizontal wells with multistage fracturing can only produce a few percent of the oil in shale reservoirs. The question how to produce the remaining oil needs to be answered sooner or later. Probably answering this question becomes more important in the current low oil price, as high-cost drilling, fracturing and completion have to be minimized. Thus using existing wellbores to improve remaining oil production becomes more important. Considering different enhanced oil recovery methods, gas injection is probably most feasible method , . Since Wan et al.  first proposed cyclic gas injection (huff-n-puff) to improve oil recovery in shale oil reservoirs, many papers have been published on the subject, as reviewed by Sheng .
Sheng and Chen  used simulation approach to show that cyclic gas injection has the highest potential to enhance oil recovery (EOR) in shale oil reservoirs. Chen et al.  used compositional fluid models of a Bakken formation to simulate CO2 huff-n-puff. Their results show that the final recovery factor in the huff-n-puff process is lower than that in the primary recovery, because the incremental recovery in the production stage is unable to compensate the loss in the injection and shut-in stages. In their models, the huff-n-puff process are from 300 days to 1000 days; the bottom-hole injection pressure is 4000 psi and the producing pressure is 3000 psi. Using his model, Sheng  was able to repeat Chen et al.  results (the huff-n-puff recovery is lower than the primary recovery).
However, his model shows that all the oil recovery factors at the end of 30, 50 and 70 years from the huff-n-puff process are higher than those from the primary depletion, when the injection pressure of 7000 psi is used. Therefore, Chen et al.’s results are caused by the low injection pressure of 4000 psi which is lower than the initial reservoir pressure of 6840 psi. The injection pressure in the high-pressure reservoir should be raised. From this example, we can see that optimization of huff-n-puff is very important because sometimes a wrong conclusion could be made without optimization. This paper is to discuss the optimization of huff-n-puff gas injection, focusing on shale oil reservoirs. The parameters to be investigated are huff time, puff time and soaking time. Simulation approach is used combined with some laboratory results.
Setup of a base simulation model
Several authors ,  built models using the Middle Bakken data. But their detailed models are not publically available. And no data which are more completed than the Bakken data are seen in the literature. Thus we will use the Bakken data to build a validated base model.
In this study, the compositional simulator, GEM, developed by Computer Modeling Group , is used. Because of flow symmetry, a half-fracture connected through a vertical well is simulated. In the Middle Bakken case, a horizontal well is fractured with 15 fracturing stages. It is assumed that only one fracture is generated at one stage. So the production data from this model represents the 30th of the actual production.
Fig. 1. Schematic of the base model.
The simulation model (reservoir volume) includes two regions: the stimulated reservoir volume and un-stimulated reservoir volume. The schematic is shown in Fig. 1. The model area is 296.25 ft wide in the I direction, 4724 ft in the J direction with 724 ft in the stimulated reservoir volume (SRV) area, and 50 ft in the K direction (not shown in the figure). In this model, the half-fracture spacing is 296.25 ft in the I direction, the fracture length is 724 ft in the J direction, and the fracture height is 50 ft in the K direction. The half-hydraulic fracture width is 0.5 ft. The detailed block sizes of this base model are as follows.
The block sizes in feet in the I direction from I = 1 to I = 11 are:
0.5 0.257312051 0.522150017 1.059571985 2.150134547 4.363156667 8.85392783 17.96681715 36.45913142 73.98462696 150.1331714
The block sizes in feet in the J direction with total 31 blocks are:
5*200 187.1636568 90.39505341 43.65839939 21.08584226 10.18389932 4.918551703 2.375529264 1.147317264 0.554123632 0.267626932 0.5 0.267626932 0.554123632 1.147317264 2.375529264 4.918551703 10.18389932 21.08584226 43.65839939 90.39505341 187.1636568 5*200
One block is used in the K direction with its size 50 feet.
We tried to use the data of the Middle Bakken formation presented by Kurtoglu . Table 1 summarizes the input matrix and fracture properties in the Non-SRV and SRV regions in the Middle Bakken shale. The dual permeability model was used to simulate the naturally and hydraulically fractured shale reservoirs. The shale matrix permeability is 0.0003 mD. The natural fracture effective permeability in the SRV is 0.0313 mD. The natural fracture permeability in the un-stimulated reservoir region is 0.00216 mD that is much lower than the stimulated region.
Table 1. Matrix and Fracture properties.
The reservoir fluid composition and the Peng-Robinson EOS parameters are from Yu et al.  as re-presented in Table 2, and the binary interaction coefficients are shown in Table 3. In Table 2, Pc, Tc and Vc are critical pressure, critical temperature and critical volume, respectively, and MW is molecular weight. The reservoir temperature is 245 °F, and the initial reservoir pressure is 7800 psi. The initial water saturation is 0.4. The history-matched relative permeabilities are presented in Fig. 2, Fig. 3.
Table 2. Peng-Robinson EOS fluid description of the Bakken oil.
Table 3. Binary interaction coefficients for Bakken oil.
Fig. 2. Water and oil relative permeabilities.
Fig. 3. Gas and oil relative permeabilities.
The above model is actually the history-matched model. During history matching (1.2 years production history), the stock-tank oil rate is imposed, and effort is made to match gas rate and well bottom-hole pressure by adjusting model parameters. Fig. 4 compares the simulated well bottom-hole pressure (line) with the actual data (dotted points). They are reasonably matched. The oil rate is exactly matched because it is input to the model. The gas rate from the model is lower than the actual data, but follows the same trend of actual data. We believe it is caused by the imperfect representation of PVT data by the EOS model used. Therefore, the model is reasonably calibrated.
Fig. 4. Well bottom-hole pressure (dot points are actual data, and line is simulated data).
The effect of grid sensitivity is also checked. The number of grid blocks in each direction are doubled and reduced by half. The oil rate, gas rate and their cumulative values are closely overlapped, except that the bottom hole pressure data are slightly deviated from each other at later times (10%), as shown in Fig. 5. Such difference is acceptable in engineering.
Fig. 5. Effect of grid block sizes on well bottom-hole pressure.
To optimize a process, we need to first define what is the objective function or parameter. Probably, net present value is a good parameter. To calculate this parameter, many parameters are needed such as equipment cost, operational cost, royalty tax, and interest rate. These parameters are very case-dependent. It will be very difficult to use this parameter to work out general criteria for optimization that is the objective of this paper. Considering investment and operational costs are similar, we choose to use oil recovery factor as the objective function. Improving oil recovery is the main motivation to employ the huff-n-puff process.
Compared with gas flooding, three important times are huff time, puff time and soaking time. These parameters are related to injection and production pressures, and injection and production rates. Therefore, these pressures and rates need to be first addressed. These parameters are governed by the facility constraints, e.g., compressor, safety and operational constraint, and a maximum-profit parameters like net present value. They are case-specific. But we need to use typical values to build a base model. In this study, the maximum injection pressure is set to be the initial reservoir pressure that is 7800 psi.
This is a typical practice for pressure maintenance. The maximum injection rate for the whole fractured horizontal well is set to be 9 MMSCF/D. For this model, we only simulate a half-fracture for a 15-stage well. So the maximum rate in the model is 300 MSCF/D.
Sheng and Chen  showed that a higher oil recovery is obtained if a lower bottom-hole flowing pressure (BHFP) is used, even though the flowing pressure is lower than the bubble point pressure. Thus the minimum bottom-hole flowing pressure is set at 500 psi. The maximum producing oil rate is 1500 STB/D or 50 STB/D in the model. The maximum producing gas rate is 9 MMSCF/D or 300 MSCF/D in the model. Before gas injection, the primary depletion is extended from 1.2 years to about 3 years (1000 days) under the constraint of the minimum flowing pressure of 500 psi. The injection is continued until 10,950 days (total about 30 years). The injected gas is methane.
Based on the above principles, optimum huff time, puff time and soaking time are determined, and the number of cycles is discussed.
Optimum huff-n-puff times
First the literature information is reviewed. Kurtoglu  used 60 days of injection, 10 days of soaking and 120 days of production in her simulation work. Shoaib and Hoffman  used three months in each of injection, soak and production periods. Wang et al.  simulated the EOR potential in the tight (0.04–2.5 mD) Bakken formation in Saskatchewan. In their models, one cyclic process includes 10 years of CO2 injection, 5 years of soaking time, and 5 years of production time. The literature information here shows that the huff-n-puff times are very different. What should the huff-n-puff times be?
Table 4. Effect of huff-n-puff times.
Table 4 shows the effect of huff-n-puff times on oil recovery factor. When the huff time is increased from 100 days (Case H100P300) to 300 days (Case H300P300), the oil recovery factor increases by 6.15% from 15.05% to 21.2%, with the same puff time of 300 days. This comparison indicates that the huff time is important. Why?
Fig. 6. Near-wellbore block pressures when the huff time is 100 days (left) and 300 days (right), all puff time 300 days.
Fig. 6 compares the block pressures near the injection well for 100 days of huff time (the left figure) with the pressure for 300 days of huff time (in the right figure). It shows that the pressure for 100 day huff time is less than 4000 psi, while the pressure for 300 day huff time reaches around 7800 psi. Then the drawdown pressure used to produce oil from the former case is almost half of that for the latter case. It can be understood that the huff time of 100 days is not long enough.
However, when the production time is increased from 100 days (Case H100P100) to 300 days (Case H100P300) with the same huff time of 100 days, the oil recovery factor decreases by 0.07% from 15.12% to 15.05%. It indicates that the puff time is not important. Why? When the huff time is 100 days, the pressure near the well is not high. Then the drawdown during the puff period will be low and the oil rate will be low as well. In such case, the rate at later puff period will be low (not productive). Thus the longer puff time cannot produce significantly more oil in the single cycle. It is even worse that more productive time is lost when the longer puff time is used.
From the above two sets of cases, it can be seen that the pressure buildup near the well during the huff period is important. Is the pressure drawdown during the puff period important?
Two cases are compared. One case is H300P300 in which both huff-n-puff times are 300 days. In the other case, the huff time is kept at 300 days, but the puff time is changed to 100 days (Case H300P100). The oil recovery factors decrease from 21.2% to 15.38%. The well-bottom pressure in H300P100 is shown in Fig. 7.
Fig. 7. Near-well block pressure when the huff time is 300 days but the puff time is100 days (Case H300P100).
It reveals that the pressure is not depleted to the set minimum production pressure of 500 psi at the end of 100 days of puff. By this time, the well is switched to the huff mode. Then the effective production is lost. To further confirm this result, another case with the huff time 300 days and puff time 200 days, H300P200, is simulated. The oil recovery factor is 19.49%, lower than that from H300P300 but higher than that from H300P100.
Will the oil recovery increase when the puff time is further increased? Three more cases with the same huff time of 300 but the puff times extended to 350, 450 and 600 days, H300P350, H300P450 and H300P600, are simulated. The oil recovery factors are 20.95%, 20.57% and 20.12%, respectively (see Table 4), all lower than that from H300P300. The near-wellbore block pressures during the huff-n-puff are slightly lower than those in H300P300 (data not shown here to shorten the paper). Also, the oil rate after 300 days are very small so that extended production may not be effective.
From the above discussion, it may be concluded that the optimum huff time is when the block pressure near-wellbore reaches to the set maximum injection pressure, and the optimum puff time is when the block pressure near-wellbore reaches to the set minimum production pressure.
To support the above conclusion, additional cases are simulated. Based on Case H100P100, another case H100P100qx3 is simulated. In this case, the maximum injection rate and maximum production rate are increased by three times. What is expected from this case is that the near-wellbore block pressure will reach the maximum set injection pressure during the huff period and the set minimum production pressure during the puff period. Fig. 8 shows the expected result. According to the conclusion, the expected oil recovery factor from this case should be close to that from Case H300P300 (21.2%). The actual oil recovery factor from this case is 23.3%, which supports the conclusion.
Fig. 8. Near-wellbore block pressure when the huff-n-puff time are 100 days but high rate (Case H100P100qx3).