We think that this direct upscaling methodology is so optimistic due to that the laboratory cores have higher contact area and longer exposure time to CO2 than what might happen in the real conditions of unconventional reservoirs. As a result, both of previous simulation studies and experimental works might be too optimistic to predict a quick improvement in oil recovery from injecting CO2 in these tight formations.
And, this explains why the previous simulation studies have a clear gap with CO2 pilot tests performance. It is true that the molecular mechanism is more dominated in naturally fractured reservoirs due to two main reasons (Da Silva and Belery,1989): (1) dispersive flux through fractures rapidly increase the contact area for diffusion, (2) this mechanism needs small spacing for natural fractures which is so possible to exist in naturally fractured reservoirs.
However, the effective diffusion rate in the reported laboratory conditions is much faster than in the field scale conditions due to the difference in the contact area and the exposure time. This gap in the effective diffusion rates would clearly happen between the laboratory scale and the field scale of shale oil reservoirs.
The majority of the previous diffusion models were developed based on the single-porosity model which requires a tremendous grid refinement to represent an intensely fractured shale oil reservoir (Wan and Sheng 2015). In this simulation study, the LS-LR-DK (logarithmically spaced, locally refined, and dual permeability) model is used. It has been reported that the LS-LR-DK method can accurately capture the physics of the fluid flow in fractured tight reservoirs. Also, an advanced general equation-of-state compositional simulator has been used to build an equation-of-state model for Bakken oil. Then, both models have been combined to simulate compositional effects of reservoir fluid during primary and enhanced oil recovery processes.
Furthermore, implementation of a diffusion model in the LS-LR-DK (logarithmically spaced, locally refined, and dual permeability) model has been conducted. Moreover, the counter-current mechanism of molecular diffusion for CO2-EOR, which has been reported by the experimental work for Hawthorne et al. (2013), is simulated in this work. In this study, we tried to build a numerical model which has the typical fluid and rock properties of Bakken formation, one of the most productive unconventional formations in the US. In this model, we injected three different EOR-miscible gases including CO2, lean gas, and rich gas in separated scenarios as huff-n-puff protocol through hydraulically fractured well.
All the mechanisms which were proposed in Table 1 have been also incorporated in this model. In this field case study, the production well was stimulated with 5 hydraulic fractures. The spacing between the hydraulic fractures is 200 ft. The simulation model includes two regions which are stimulated reservoir volume (SRV) and un-stimulated reservoir volume (USRV) as shown in Fig. 5.
Fig. 5 a Average pressure in a depleted well in Bakken. b A closed view for SRV of production well.
The dimensions of the reservoir model are 2000 ft × 2000ft × 42 ft, which corresponds to length, width, and thickness, respectively. The dimensions of the hydraulically fractured region are 5 fractures with half-length of 350 ft in J direction, width 0.001 ft in I direction, and fracture height of 42 ft in K direction. Fracture conductivity is 15 md ft. The other model input parameters are shown in Table 2.
Table 2 Model input parameters for the base case.
Compositional model for the formation fluids
The typical Bakken oil has been simulated in this study. The oil which was used in this model has 42 APIo, 725 SCF/STB, and 1850 psi as oil gravity, gas oil ratio, and bubble point pressure, respectively. It is known that compositional models are the most time-consumed models due to the number of components in the typical reservoir oil. In our model, we have 34 components so that would take a long time for the simulator to complete running one scenario. The common practice in numerical simulation for such situation is the careful lump of reservoir oil components into a short representative list of pseudo-components.
These pseudo-components would be acceptable if they match the laboratory-measured phase behavior data. The supplied data for reservoir oil need to have a description of associated single carbon numbers and their fractions, saturation pressure test results, separator results, constant composition expansion test results, differential liberation test results, and swelling test results. All the available data can be used for tuning the EOS to match the actual fluid behavior.
In our simulation study, we lumped the original 34 components into 7 pseudo-components as shown in Table 3 by using WinProp-CMG. WinProp is an equation‐of‐state (EOS)‐based fluid behavior and PVT modeling package. In WinProp, laboratory data for fluids can be imported and an EOS can be tuned to match its physical behavior. Fluid interactions can then be predicted, and a fluid model can be created.
Table 3 Compositional data for the Peng–Robinson EOS in the model oil.
Table 4 presents the Peng–Robinson EOS fluid description and binary interaction coefficients of the Bakken crude oil with different gases. Figure 6 represents the two-phase envelope for Bakken oil which was generated by WinProp-CMG.
Table 4 Binary interaction coefficients for Bakken oil.
Fig. 6 Two-phase envelope for Bakken oil which was generated by WinProp-CMG.
Results and discussion
Natural depletion for Bakken model
The reservoir model was initially run in natural depletion for 7300 days (20 years). The production well, which was hydraulically fractured, was subjected to the minimum bottom-hole pressure of 1500 psi. The simulated Bakken well performance in natural depletion is shown in Fig. 7. In the natural depletion scenario, it has been clear that the production well initially started with a high production rate. Then, it showed steep decline rate until it got leveled off at a low rate.
Fig. 7 Reservoir performance in natural depletion conditions.
This is the typical trend to what happens in the most, if not all, unconventional reservoirs of North America. If we investigate the pressure distribution in the reservoir model as shown in Fig. 5, it can be seen that the main reason to that fast reduction in production rate is the pressure depletion in the areas which are closed to the production well. However, the reservoir pressure is still high in the areas which are far away from the production well. This explains the poor feeding from neighboring areas in these types of reservoirs due to the tight formation matrix.
Flow-type determination in natural depletion stage and EOR stage
We calculated the Péclet number locally in each grid in both of natural depletion stage and EOR stage. In the formation matrix areas, the results indicated that Péclet number is way below 1 for both of gas phase and oil phase which means that the diffusion flow is the most dominant flow in formation matrix as shown in Fig. 8.
Fig. 8 Péclet number distribution: a long cross-section in the matrix model. a Gas phase. b Oil phase.
However, in the hydraulic fractures parts, the viscous flow is clearly dominated where Pe is way above 100. If we examine how Péclet number changes with time at 10 ft from the hydraulic fracture, we found that Pe number is not changing too much during natural depletion stage; however, it is changeable in EOR stage as shown in Fig. 9 (EOR stage started after 10 years of production life). Furthermore, we notice that there are two different behaviors for gas phase versus oil phase in EOR stage. Pe number is increasing with time for gas phase; however, Pe number is decreasing with time for oil phase as shown in Fig. 9.
Fig. 9 Péclet number change with time (At 10 ft from the hydraulic fracture). a Oil phase. b Gas phase.