# Microscale Evaluation of Tight Oil Mobility: Insights from Pore Network Simulation

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## Abstract

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## 1. Introduction

## 2. Reconstruction of Pore Network Model

_{x}× N

_{y}× N

_{z}) is set before model generation. N

_{x}, N

_{y}, and N

_{z}are the number of nodes in the directions of x, y and z axes. The regular model is a kind of relatively idealized model, generated artificially. Although the number of nodes in the model is determined in the regular model, the size of the element representing the pore throat in the model can be generated according to the distribution of the pore-throat radius of the target core. Researchers can select appropriate pore-throat distribution schemes based on research purposes. Two commonly used pore-throat distribution schemes include the uniform pore-throat distribution scheme [31] and the truncated normal pore-throat distribution scheme [32]. The uniform pore throat distribution scheme can be used to analyze the influence of some factors on the hydrocarbon migration and accumulation process, under the condition of a uniform pore-throat distribution, in the model. Truncated normal pore-throat distribution schemes can be used to analyze the influence of some factors on the migration and accumulation process of hydrocarbon under different pore-throat distribution schemes. In both schemes, the distribution of pore-throat radii is mainly controlled by parameters such as the maximum pore-throat radius R

_{max}, the minimum pore-throat radius R

_{min}and the normalized parameter N. The mathematical description of these two methods can be given by the following equations.

## 3. Pore Network Model Simulation

_{c}= vμ/σ, where v is displacement velocity; μ is viscosity; and σ is the interfacial tension between the displacing and displaced phases [6]. In general, when the capillary number is high, the viscous force is dominant and the fluid flow velocity is fast. When the capillary force is low, the capillary pressure plays a dominant role and the fluid velocity is slow. Tight reservoirs have a large proportion of nanoscale pores, which are characterized by low porosity and low permeability. Therefore, many scholars [6,15,19] believe that the capillary force is more important than the viscous force in the process of oil migration and accumulation. This means that the migration and accumulation of shale oil is more inclined to the steady-state migration mode, dominated by capillary force.

^{−6}, the quasi-steady state model is sufficient to characterize multiphase flow in porous media. Obviously, the migration and accumulation process of shale oil satisfies this condition. Under the premise of accuracy and for convenience, we use the quasi-steady state pore network model to solve and analyze the migration and accumulation of shale oil. It should be noted that a flow mechanism in organic reservoirs is not involved in most existing pore network models. In order to accurately simulate the migration and accumulation process of shale oil, it is necessary to separate the flow laws in organic and inorganic pores.

#### 3.1. Water Phase Flow Characteristics

_{in}

_{-w}is water flow rate in inorganic pores, μ

_{w}is water viscosity, r = D/2 and D is pore diameter, dp is the pressure difference and dl is the length difference.

_{in}

_{-w}is the conductance of capillary water in inorganic pores.

_{in}

_{-f}is the flow rate of water film in inorganic pores, h

_{δ}is the thickness of the water film, μ

_{film}(h

_{δ}) is the viscosity of water film attached to solid wall and can be calculated by the method proposed by Wu [36].

_{in-f}is the conductance of water film attach to solid wall.

#### 3.2. Oil Phase Flow Characteristics

_{in-o}is the conductance of oil phase in inorganic pores, μ

_{o}is oil viscosity.

_{or-o}is the conductance of oil phase in organic pores.

## 4. Results and Discussion

#### 4.1. Evaluation of Reservoir Flow Characteristics

^{−3}mD, and the porosity is 8%, which agrees with the previous experimental results of shale oil reservoir [37]. When simulating the migration process of shale oil in the target block, we set the upper limit of capillary pressure to 50 MPa to allow a full drainage process, and further simulated the oil–water two-phase permeability curve in the drainage process, as shown in Figure 4. It can be seen from the figure that the critical oil saturation was 0.163. That means when the oil phase saturation is higher than 0.163, the oil phase forms a continuous phase through the pore network and begins to flow. It should be noted that at the connate water saturation, the oil phase relative permeability is close to 0.9 (less than 1); that is because the connate water, including capillary water and film water, hinders the flow of the oil phase due to the reduction in flow space and the interaction between two phases. The relative permeability of oil phase increases slowly in the initial stage of the displacement process, which is mainly caused by the poor continuity of oil phase through the pore network. In the later stage, with the increase of oil phase continuity and its occupation of center space, the relative permeability of oil phase increases rapidly. At the same time, we can see that the shale oil reservoir is mainly composed of nanopores, and the connate water saturation is high, which reaches 0.3. However, the permeability of water phase is extremely low when water saturation is less than 0.4. The two-phase co-seepage area is only 0.457. Low co-seepage area means less recoverable oil from the reservoir.

#### 4.2. Effects of Organic Matter on Flow Characteristics

^{−3}mD to 3.79 × 10

^{−3}mD. The relationship between relative permeability and organic matter content during drainage process, in our case, is shown in Figure 6. The simulation results showed that, with the increase in organic matter content, the relative permeabilities of the water phase are identical at low water saturation, but gradually increase at high water saturation. This is because, at high water saturation, the continuity of the water phase is enhanced, and the enhanceming effect of organic matter on water phase seepage is more obvious. At the same time, it can be seen that with the increase of organic matter content, the isosmotic point of oil–water two-phase relative permeability shifts to the left, indicating that the wettability of the water phase gradually weakens, which is reasonable due to the increased proportion of organic matter.

## 5. Summary and Conclusions

- The shale oil reservoir is mainly nanopore, and the bound water saturation is high, reaching 0.3. However, the permeability of the water phase is extremely low when water saturation is less than 0.4. The two-phase co-seepage area is only 0.457. Low co-seepage area means less recoverable oil from the reservoir.
- With the increase in organic matter content, the relative permeabilities of water phase are identical at low water saturation, but gradually increase at high water saturation. This is because, at high water saturation, the continuity of the water phase is enhanced, and the promoting effect of organic matter on water phase seepage is more obvious.
- With the increase in organic matter content, the isosmotic point of oil–water phase permeability shifts to the left, indicating that the wettability of the water phase gradually weakens.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Segmentation of image. (

**a**) is the original image. (

**b**) shows the segmentation process, and the red dots represent the location of pores.

**Figure 2.**Segmentation of image. (

**a**) The original image; the grey represents the matrix of rock, and the red represents the pores. (

**b**) The segmentation process; the red dots represent the location of pores.

**Figure 3.**(

**a**) A pore network model of digital rock. The gray represents the throats, the thickness of the cylinder represents the size of the throat, the red represents pores, and the diameter of the spheres indicates the size of the pore. (

**b**) Pore and throat size distribution.

**Figure 6.**The relationship between relative permeability and organic matter content during migration process.

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**MDPI and ACS Style**

Wang, Y.; Xia, Y.; Feng, Z.; Shao, H.; Qiu, J.; Ma, S.; Zhang, J.; Jiang, H.; Li, J.; Gao, B.;
et al. Microscale Evaluation of Tight Oil Mobility: Insights from Pore Network Simulation. *Energies* **2021**, *14*, 4580.
https://doi.org/10.3390/en14154580

**AMA Style**

Wang Y, Xia Y, Feng Z, Shao H, Qiu J, Ma S, Zhang J, Jiang H, Li J, Gao B,
et al. Microscale Evaluation of Tight Oil Mobility: Insights from Pore Network Simulation. *Energies*. 2021; 14(15):4580.
https://doi.org/10.3390/en14154580

**Chicago/Turabian Style**

Wang, Yongchao, Yanqing Xia, Zihui Feng, Hongmei Shao, Junli Qiu, Suping Ma, Jiaqiang Zhang, Haoyuan Jiang, Jiyong Li, Bo Gao,
and et al. 2021. "Microscale Evaluation of Tight Oil Mobility: Insights from Pore Network Simulation" *Energies* 14, no. 15: 4580.
https://doi.org/10.3390/en14154580