Since a large amount of nanopores exist in tight oil reservoirs, fluid transport in nanopores is complex due to large capillary pressure. Recent studies only focus on the effect of nanopore confinement on single-well performance with simple planar fractures in tight oil reservoirs. Its impacts on multi-well performance with complex fracture geometries have not been reported. In this study, a numerical model was developed to investigate the effect of confined phase behavior on cumulative oil and gas production of four horizontal wells with different fracture geometries. Its pore sizes were divided into five regions based on nanopore size distribution. Then, fluid properties were evaluated under different levels of capillary pressure using Peng-Robinson equation of state. Afterwards, an efficient approach of Embedded Discrete Fracture Model (EDFM) was applied to explicitly model hydraulic and natural fractures in the reservoirs. Finally, three fracture geometries, i.e. non-planar hydraulic fractures, non-planar hydraulic fractures with one set natural fractures, and non-planar hydraulic fractures with two sets natural fractures, are evaluated. The multi-well performance with confined phase behavior is analyzed with permeabilities of 0.01 md and 0.1 md. This work improves the analysis of capillarity effect on multi-well performance with complex fracture geometries in tight oil reservoirs.

The pore sizes in tight reservoirs are nanopores, where the phase behavior deviates significantly from that of bulk fluids in conventional reservoirs. The phase behavior for fluids in tight reservoirs is essential for a better understanding of the mechanics of fluid flow. A novel methodology is proposed to investigate the phase behavior of carbon dioxide (CO₂)/hydrocarbons systems considering nanopore confinement. The phase equilibrium calculation is modified by coupling the Peng-Robinson equation of state (PR-EOS) with capillary pressure, fluid-wall interaction, and molecule adsorption. The proposed model has been validated with CMG-Winprop and experimental results with bulk and confined fluids. Subsequently, one case study for the Bakken tight oil reservoir was performed, and the results show that the reduction in the nanopore size causes noticeable difference in the phase envelope and the bubble point pressure is depressed due to nanopore confinement, which is conductive to enhance oil recovery with a higher possibility of achieving miscibility in miscible gas injection. As the pore size decreases, the interfacial tension (IFT) decreases whereas the capillary pressure increases obviously. Finally, the recovery mechanisms for CO₂ injection are investigated in terms of minimum miscibility pressure (MMP), solution gas-oil ratio, oil volume expansion, viscosity reduction, extraction of lighter hydrocarbons, and molecular diffusion. Results indicate that nanopore confinement effect contributes to decrease MMP, which suppresses to 650psi (65.9 smaller) as the pore size decreases to 2nm, resulting in the suppression of the resistance of fluid transport. With the nanopore confinement effect, the CO₂ solution gas-oil ratio and the oil formation volume factor of the oil increase with the decrease of pore size. In turn, the oil viscosity reduces as the pore size decreases. It indicates that considering the nanopore confinement effect, the amount of gas dissolved into crude oil increases, which will lead to the increase of the oil volume expansion and the decrease of the viscosity of crude oil. Besides, considering nanopore confinement effect seems to have a slightly reduced effect on extraction of lighter hydrocarbons. On the contrary, it causes an increase in the CO₂ diffusion coefficient for liquid phase. Generally, the nanopore confinement appears to have a positive effect on the recovery mechanisms for CO₂ injection in tight oil reservoirs. The developed novel model could provide a better understanding of confinement effect on the phase behavior of nanoscale porous media in tight reservoirs. The findings of this study can also help for better understanding of a flow mechanism of tight oil reservoirs especially in the case of CO₂ injection for enhancing oil recovery.

Gas injection is one of the most effective enhanced oil recovery methods for the unconventional reservoirs. Recently, CH₄ has been widely used; however, few studies exist to accurately evaluate the cyclic CH₄ injection considering molecular diffusion and nanopore effects. Additionally, the effects of operation parameters are still not systematically understood. Therefore, the objective of this work is to build an efficient numerical model to investigate the impacts of molecular diffusion, capillary pressure, and operation parameters. The confined phase behavior was incorporated in the model considering the critical property shifts and capillary pressure. Subsequently, we built a field-scale simulation model of the Eagle Ford shale reservoir. The fluid properties under different pore sizes were evaluated. Finally, a series of studies were conducted to examine the contributions of each key parameter on the well production. Results of sensitivity analysis indicate that the effect of confinement and molecular diffusion significantly influence CH₄ injection effectiveness, followed by matrix permeability, injection rate, injection time, and number of cycles. Primary depletion period and soaking time are less noticeable for the well performance in the selected case. Considering the effect of confinement and molecular diffusion leads to the increase in the well performance during the CH₄ injection process. This work, for the first time, evaluates the nanopore effects and molecular diffusion on the CH₄ injection. It provides an efficient numerical method to predict the well production in the EOR process. Additionally, it presents useful insights into the prediction of cyclic CH₄ injection effectiveness and helps operators to optimize the EOR process in the shale reservoirs.

The embedded discrete fracture model (EDFM) combines the advantages of previous numerical models for fractured reservoirs, achieving a good balance between calculation cost and simulation accuracy. In this work, an integrally embedded discrete fracture model (iEDFM) is introduced to further improve the simulation accuracy and expand the application of the model. The iEDFM has a new gridding method that can arbitrarily grid the fractures according to the requirements rather than finely subdividing fracture elements. Then, with a more precise pressure distribution assumption inside the matrix blocks, we are able to obtain a semi-analytic calculation method of matrix-fracture transmissibility applied to iEDFM. Several case studies were conducted to demonstrate the advantage of iEDFM and its applicability for intersecting and nonplanar fractured reservoirs, and a 3D case with a modified dataset from a reported seismic survey could be used to demonstrate the potential application of the iEDFM in real field studies.

Frequency reuse is a key concept for interference mitigation and thereby enhancing cell-edge performance in OFDMA networks. Two representative strategies are Fractional Frequency Reuse (FFR) and Soft Frequency Reuse (SFR). Both divide a cell into a center zone and an edge zone, and differentiate their levels of frequency reuse. Previous work on FFR and SFR has focused on networks of relatively small size with standard hexagon-shaped cells. And dividing the cell edge frequency band into three parts has been a common practice so far. However, for real-life networks, this is inadequate because of the irregular cell layout. We consider generalized FFR and SFR schemes, where the number of sub-bands is not restricted to three, and for SFR the power ratio is variable. To find optimal sub- band allocation for the generalized schemes, we present an approach based on large-scale optimization to deal with networks with irregular cell layout. The optimization process allows us to analyze the impact of the number of sub-bands and the SFR power ratio on cell-edge performance, and thereby compare the reuse schemes. We conduct experiments on large networks with realistic radio propagations and present a thorough numerical comparison.

The embedded discrete fracture model (EDFM), among different flow simulation models, achieves a good balance between efficiency and accuracy. In the EDFM, micro-scale fractures that cannot be characterized individually need to be homogenized into the matrix, which may bring anisotropy into the matrix. However, the simplified matrix–fracture fluid exchange assumption makes it difficult for EDFM to address the anisotropic flow. In this paper, an integrally embedded discrete fracture model (iEDFM) suitable for anisotropic formations is proposed. Structured mesh is employed for the anisotropic matrix, and the fracture element, which consists of a group of connected fractures, is integrally embedded in the matrix grid. An analytic pressure distribution is derived for the point source in anisotropic formation expressed by permeability tensor, and applied to the matrix–fracture transmissibility calculation. Two case studies were conducted and compared with the analytic solution or fine grid result to demonstrate the advantage and applicability of iEDFM to address anisotropic formation. In addition, a two-phase flow example with a reported dataset was studied to analyze the effect of the matrix anisotropy on the simulation result, which also showed the feasibility of iEDFM to address anisotropic formation with complex fracture networks.