Mathematical Model for Oil Recovery Prediction of Polymer Microsphere Conformance Control Based on the Stream Tube Method
Abstract
:1. Introduction
2. Theoretical Model Establishment
2.1. Stream Tube Model
2.2. Oil Displacement Efficiency
2.3. Areal Sweep Efficiency
2.4. Vertical Sweep Efficiency
3. Adapt Ability Analysis
3.1. Injection Period
3.2. Injection Rate
3.3. Injection Concentration
3.4. Polymer Microsphere Size
4. Comparison with Field Application
4.1. Reservoir Background
4.2. Field Application Scheme of Polymer Microsphere Flooding
4.3. Oil Recovery Comparison
5. Conclusions
- (1)
- The recovery factor calculation model can quickly and accurately evaluate the oil recovery performance of polymer microspheres’ conformance control. The equivalent mobility ratio was introduced to optimize the vertical sweep efficiency calculation method. A trapezoidal flow tube is proposed to characterize the streamline shape after PMs’ conformance control, and to calculate the areal sweep efficiency.
- (2)
- A series of adaptability analyses on the injection period, injection rate, injection concentration, and PMs’ size are conducted in order to reveal how these functional parameters affect results. The results indicate that long-term injection of small size and low concentration benefits higher oil recovery.
- (3)
- The theoretical oil recovery obtained from the proposed model is 1.37%, and the actual oil recovery of field application is 1.22%, with an error of 0.15%. The recovery factor calculated by the theoretical model agrees better with the field application. This model not only provides a faster and more accessible tool to predict and evaluate the production performance of the PMs’ flooding process, but also could be used to optimize the injection scheme of PMs’ conformance control.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Factors | Parameter Design Value | Default Value |
---|---|---|---|
1 | Injection period (d) | 50, 70, 90, 120, 150 | 90 |
2 | Injection rate (m3/d) | 25, 30, 35, 40, 45 | 40 |
3 | Injection concentration (ppm) | 2000, 3000, 4000, 5000, 6000 | 5000 |
4 | Polymer microsphere size (µm) | 0.1, 0.3, 0.8, 5, 10, 20 | 0.1 |
No. | Parameters Name | Default Value | No. | Parameter Name | Default Value |
---|---|---|---|---|---|
1 | Well spacing (m) | 300 | 12 | Expansion ratio | 5 |
2 | m | 1 | 13 | Irreducible water saturation (f) | 0.322 |
3 | C | 0.0864 | 14 | Split coefficient of injection volume (f) | 0.25 |
4 | Inner zone permeability (10−3 µm2) | 30 | 15 | Blocking rate (f) | 0.4 |
5 | Outer zone permeability (10−3 µm2) | 25 | 16 | Oil displacement efficiency (f) | 0.3 |
6 | Crude oil viscosity (MPa) | 1.80 | 17 | Vertical sweep efficiency (f) | 0.42 |
7 | Porosity (f) | 0.2 | 18 | Permeability variation coefficient (f) | 0.4 |
8 | Threshold pressure gradient (MPa/m) | 0.01 | 19 | Water viscosity (MPa) | 0.46 |
9 | Hole diameter (m) | 0.1 | 20 | Equivalent mobility ratio | 10 |
10 | Polymer microsphere density (g/cm3) | 1.2 | 21 | Recovery of polymer microsphere (f) | 0.85 |
11 | Water flooding recovery (f) | 0.4 | 22 | Production pressure differential (MPa) | 25 |
No. | Parameter Name | Default Value | No. | Parameter Name | Default Value |
---|---|---|---|---|---|
1 | Well spacing (m) | 360 | 12 | Expansion ratio | 2.6 |
2 | m | 1 | 13 | Irreducible water saturation (f) | 0.322 |
3 | C | 0.0864 | 14 | Split coefficient of injection volume (f) | 0.125 |
4 | Inner zone permeability (10−3 µm2) | 131 | 15 | Blocking rate (f) | 0.8 |
5 | Outer zone permeability (10−3 µm2) | 18.32 | 16 | Oil displacement efficiency (f) | 0.42 |
6 | Crude oil viscosity (MPa) | 1.95 | 17 | Vertical sweep efficiency (f) | 0.76 |
7 | Porosity (f) | 0.12 | 18 | Permeability variation coefficient (f) | 0.37 |
8 | Threshold pressure gradient (MPa/m) | 0.01 | 19 | Water viscosity (MPa) | 0.46 |
9 | Hole diameter (m) | 0.1 | 20 | Equivalent mobility ratio | 1.8 |
10 | Polymer microsphere density (g/cm3) | 1.1 | 21 | Recovery of polymer microsphere (f) | 0.86 |
11 | Water flooding recovery (f) | 0.4 | 22 | Production pressure differential (MPa) | 24 |
Parameter | Value |
---|---|
Size (nm) | 800 |
Concentration (ppm) | 5000 |
Rate (m3/d) | 42 |
Injection period (d) | 160 |
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Zhao, W.; Tang, H.; Lu, F.; Hu, S.; Liu, T.; Li, N.; Song, R. Mathematical Model for Oil Recovery Prediction of Polymer Microsphere Conformance Control Based on the Stream Tube Method. Materials 2023, 16, 1476. https://doi.org/10.3390/ma16041476
Zhao W, Tang H, Lu F, Hu S, Liu T, Li N, Song R. Mathematical Model for Oil Recovery Prediction of Polymer Microsphere Conformance Control Based on the Stream Tube Method. Materials. 2023; 16(4):1476. https://doi.org/10.3390/ma16041476
Chicago/Turabian StyleZhao, Wenyue, Huo Tang, Fan Lu, Shuai Hu, Tongjing Liu, Nannan Li, and Renzhi Song. 2023. "Mathematical Model for Oil Recovery Prediction of Polymer Microsphere Conformance Control Based on the Stream Tube Method" Materials 16, no. 4: 1476. https://doi.org/10.3390/ma16041476