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# Integrating Embedded Discrete Fracture and Dual-Porosity, Dual-Permeability Methods to Simulate Fluid Flow in Shale Oil Reservoirs

## Model Validation

As mentioned by Ţene et al. [17], using EDFM for fractures with very low permeability may create inaccurate results. So only permeable fractures are considered in this study. In this section, we present a three-dimensional (3D) case with two sets of permeable fractures. The hybrid EDFM-DPDP approach is compared to EDFM, DFM, and dual-porosity approaches to verify the accuracy of the hybrid EDFM-DPDP method in modeling fracture networks. Figure 4 shows the dimensions of the reservoir and the positions of fracture planes. Figure 4a shows the fracture system used in this study. Figure 4b is the DFM with 213,810 cells.

Figure 4c is the DPDP model, with a flow-based method used to homogenize all of the fractures in the upscaling process. Figure 4d is the EDFM, explicitly showing the fractures. Figure 4e shows the hybrid EDFM-DPDP method, picturing one set of fractures by dual porosity and the other set of fractures by EDFM. In the hybrid EDFM-DPDP method, small- and medium-scale fractures are upscaled by a flow-based method.

Figure 4. Fracture model. (a) Fracture model; (b) DFM; (c) Dual-porosity model; (d) EDFM; and, (e) hybrid EDFM-DPDP method.

The reservoir dimensions are 1000 × 1000 × 20 ft. The fractures fully penetrate the reservoir vertically (with a height of 20 ft from the top to the bottom of the reservoir). The width and permeability of the fractures is 0.01 ft and 500 md, respectively. As a result, the fracture conductivity is 5 md-ft. A uniform 50 × 50 × 2 matrix grid is defined in dual-porosity, EDFM, and hybrid EDFM-DPDP methods. The dimensions of the matrix cells are 20 × 20 × 10 ft. Five vertical wells are defined in the reservoir: one is a water injector located at the reservoir center, with an injection rate of 200 stb/day and limited bottomhole pressure (BHP) no more than 5000 psi; the other four wells are oil producers located at the corner, with oil rates of 50 stb/day and limited BHP no less than 500 psi.

This example is for water injection of a low-permeability oil reservoir. The reservoir is isotropic as the permeabilities in the X, Y, and Z directions are the same. The Corey model was used for the relative permeability curve for both matrix and fracture. Peaceman’s model was applied to calculate the well indices. The detailed reservoir and fluid properties are summarized in Table 1.

Table 1. Reservoir and Fluid Properties.

Figure 5 shows the well oil production rates and the cumulative oil production of different models. The results of EDFM and DFM are highly consistent in these plots, and the dual-porosity model is significantly different among these methods, while curves from the hybrid EDFM-DPDP method are between that from dual-porosity and DFM methods, indicating that EDFM improves the accuracy and verifying of the the EDFM. The upscaling method and grid refinement are considered as other ways to improve accuracy of the dual-porosity model.

In this study, we also run five cases with different upscaling methods (Oda method and flow-based method with different boundaries: linear, constant pressure, no-flow, and periodic) and three cases with different grid sizes from 5 to 20 for dual porosity. The comparison among different upscaling methods with the EDFM method is shown in Figure 6. Figure 6a indicates that different upscaling methods reach similar results for water flooding, and Figure 6b shows the difference between the Oda method and other upscaling methods for gas flooding. Meanwhile, the figure also shows a significant difference between these upscaling methods and EDFM.

Figure 5. Comparison of production for different models. (a) Well “Prod_1” oil rate; (b) Well “Prod_2” oil rate; (c) Well “Prod_3” oil rate; (d) Well “Prod_4” oil rate; and, (e) Field cumulative oil.

Figure 6. Simulation results for different models. (a) water flooding; (b) gas flooding.

Capillary pressure plays an important role in fractured reservoir. In this study, different methods with capillary pressure for water flooding are studied. As shown in Figure 7, the difference between EDFM and DP methods is about 3.5–4.0%. While the difference is 1.5% between EDFM and hybrid EDFM and DP methods.

Figure 7. Simulation results for different models with capillary pressure for water flooding.

Figure 8 shows the cumulative oil and time consumption vs. different models. We can find that the refinement grid from 20 to 5 m for the dual-porosity model doesn’t improve accuracy in this study, and time consumption increases from 25 to 2927 s when grid number increases from 5000 to 16,000 in the DP models. The figure also points out that DFM consumes 4322 s, EDFM takes 268 seconds, and the hybrid EDFM-DPDP method takes 55 s. All of the simulations were performed on a 2.6 GHz, Intel CoreDuo CPU. The time consumption of the hybrid EDFM-DPDP method is only 1/80 that of the DFM method and 1/5 that of the EDFM method. From the study, we conclude that EDFM maintains accuracy and saves CPU time.

Figure 8. Simulation results for different models. (a) Cumulative oil for different models; (b) Time consumption for different models.

## Comprehensive Sensitivity Studies

There is high uncertainty in shale oil formations because of many uncertain parameters, such as reservoir permeability, fracture half-length, number of fractures, and fracture conductivity. In addition, parameters related to CO2 huff-and-puff are also uncertain, such as CO2 injection rate, injection time, and soaking time, and the number of cycles of CO2 huff-and-puff. Accordingly, in the subsequent simulation study, we perform a series of simulations to investigate the impacts of these uncertain parameters related to the CO2 huff-and-puff process.

### Reservoir Model

As shown in Figure 9, a base model is constructed to perform simulation studies for a single horizontal well with natural fractures and multiple hydraulic fractures in a shale oil reservoir. Several reservoir and fracture parameters are analyzed, including natural fracture permeability, hydraulic fracture permeability, hydraulic fracture half-length, hydraulic fracture stages, and so on.

Figure 9. Natural fracture, hydraulic fracture distribution in reservoir.

The parameters assumed for the model are summarized in Table 2. The properties of the components used for the simulation studies are shown in Table 3.

Table 2. Parameters of the base model.

Table 3. Live oil composition and properties.

In huff-and-puff recovery, we maintain injection pressure to be higher than the minimum miscibility pressure. In this study, the minimum miscibility pressure is estimated to be 3000 psi based on experiment and slim-tube simulation. Therefore, well BHP is set to 4000 psi during production and well BHP is set to 6000 psi during the CO2 injection. During the injection process, pure CO2 is injected into the reservoir. Specifically, the well pressure is fixed at 4000 psi from day 1 to 300 to carry out primary recovery.

Then, the well is operated as an injection well from day 301 to 360 at a fixed pressure of 4000 psi. During this period, pure CO2 is injected into the reservoir. From day 361 to 390, the well is closed, letting the CO2 mix with oil in the reservoir. From day 391 to 480, the well is reopened to produce hydrocarbons at a fixed pressure of 4000 psi. The same CO2 huff-and-puff steps are repeated until day 1200, giving rise to five cycles of CO2 huff-and-puff. Detailed steps are listed in Table 4.

Table 4. CO2 huff-and-puff steps.

### Large Natural Fracture Permeability

A sensitivity study was conducted on large natural fracture permeability for 0.02, 0.2, and 2 md with 16 hydraulic fractures. Figure 10a shows that the oil rate depletes from 40 to 2.4 m3/day for the first 300 days, with primary recovery being only 0.62%. After 60 days of gas injection and 10 days of soaking, oil rate increases to 40 m3/day and decreases to 7 m3/day at the end of the first cycle. Figure 10b shows the oil recovery increase from 3.51 to 3.95% when natural fracture permeability increases from 0.02 to 2.0 md, which means a 12.5% improvement.

The results illustrate that using gas huff-and-puff could significantly improve production and remarkably impact the permeability of the cumulative oil production. Higher natural fracture permeability can provide higher flow conductivity and result in higher oil recovery.

Figure 10. Simulation results for different natural fracture permeabilities. (a) Oil rate of different natural fracture permeabilities; (b) Recovery of different natural fracture permeabilities.

### Hydraulic Fracture Permeability, Length, and Stages

A simulation study is performed on hydraulic fracture permeability for 2, 20, 100, 500, and 5000 md, with natural fracture permeability of 0.02 md, number of hydraulic stages of 16, and a half-length of 400 ft. Figure 11 shows the simulation results of five different hydraulic fracture permeabilities. The Figure illustrates that a higher hydraulic fracture permeability results in a higher recovery.

Oil recovery increases from 3.51 to 4.51% when hydraulic fracture permeability increases from 2 to 100 md. However, oil recovery only increases 0.20% when permeability increases from 100 to 5000 md. The results illustrate that there exists an optimum value of hydraulic fracture permeability. Over the optimum value (100 md in this case), increasing hydraulic fracture permeability has a slight impact on oil recovery.

Figure 11. Recovery of different hydraulic fracture permeabilities.

A comparison of oil recovery factor with different hydraulic fracture lengths is shown in Figure 12. In this study, half-hydraulic-fracture-lengths for three cases are 200, 300, and 400 m. In the Figure, we can find that more oil can be produced with a longer hydraulic fracture. This is because longer hydraulic fractures yield more connections with natural fractures and matrix, resulting in higher oil recovery.

Figure 12. Recovery of different hydraulic fracture lengths.

The hydraulic fracture stage is one important parameter with a significant impact on the CO2 huff-and-puff process in shale oil. In this case, we run five cases with different numbers of stages from 8 to 24. Figure 13 shows the recovery and oil rate vs. time at different fracture stages. When the stage increases from 8 to 24, oil recovery increases from 2.70 to 3.90%, which means recovery improved by 44% for the case at stage number 8.

Figure 13. Simulation results for different hydraulic fracture stages. (a) Recovery of different hydraulic fracture stages; (b) Oil rate of different hydraulic fracture stages.

### Capillary Pressure

Capillary pressure is one of the important parameters for fractured reservoir, especially when water flooding and gas flooding processes are involved. In this study, we run three cases with different capillary pressure curves. Figure 14a shows capillary pressure curves used in the study and Figure 14b shows the recovery for different curves. Recovery decreases with capillary pressure increases, and the case without capillary pressure reach higher recovery.

Figure 14. Simulation results for different capillary pressure. (a) Three capillary pressure curves (b) Recovery of different capillary pressure curves.

### Huff-And-Puff Scenario

In order to investigate the effect of the huff-and-puff scenario on the CO2 estimated oil recovery (EOR) process, several parameters are modified from the base model set up previously (the others remain unchanged). We compare three cases to determine the better injection strategy for the huff-and-puff scenario. The huff-and-puff patterns are summarized in Table 5. We fix the total production and injection periods with different combinations. Figure 15 shows the impact of different strategies on cumulative oil production. The Figure also shows that a reduced cycle length and increased cycles could increase the oil production.

Figure 15. Cumulative oil production of different injection pattern times.

Table 5. Simulation patterns.

## Conclusions

In this work, we implement a novel simulation method that integrates EDFM and dual-continuum methods to successfully simulate a complex fracture network with multiple orientations and length-scales induced by hydraulic fracturing treatment. The hybrid model could explicitly describe the dominant role of large-scale fractures on flow conduits, as well as offer computationally efficient simulations without employing unstructured gridding and mesh refinement near fractures.

The small and medium natural fracture networks connecting the global flow are simulated by the dual-continuum model. The proposed numerical model is designed and compared with DFM, EDFM, and dual-porosity methods, and comprehensive modeling studies are conducted to understand the key reservoir and fracture properties that affect production performance and to investigate the feasibility of CO2 huff-and-puff in shale oil reservoirs. We obtain the following conclusions from the simulation results:

(1)    The study verifies that this new EDFM-DPDP method can save time and maintain high accuracy.

(2)    Increasing hydraulic fracture permeability and enhancing hydraulic fracture intersection with an extensive network of natural fractures is the key to improving well productivity.

(3)    Incremental oil is sensitive to natural fracture permeability, hydraulic fracture permeability, number of stages, cycling length, and number of cycles.

### Acknowledgments

The authors are grateful for financial support from the State Major Science and Technology Special Project of China during the 13th Five-Year Plan (Grant No. 2016ZX05014-004, 2016ZX05025-003-007 and 2016ZX05034-001-007) and Major Project of China National Petroleum Corporation (Grant No.RIPED-2017-JS-236) .

### Author Contributions

Weirong Li and Zhenzhen Dong conceived of the presented idea. Weirong Li developed the theory and performed the computations. Zhenzhen Dong and Gang Lei verified the methods. Zhenzhen Dong encouraged Weirong Li to investigate CO2 Huff and Puff in shale oil with new model and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript.

#### Conflicts of Interest

There are no conflicts of interest.

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Correspondence to the authors:

[email protected] (W.L.);  [email protected] (Z.D.); [email protected] (G.L.)