Solution Gas-Oil Ratio (Rs) Correlations

Overview

The solution gas-oil ratio ($R_s$) is defined as the volume of gas dissolved in oil at reservoir conditions, expressed as standard cubic feet of gas per stock tank barrel of oil (scf/STB). It is one of the most important PVT properties for reservoir engineering calculations.

$$R_s = \frac{V_{gas}^{SC}}{V_{oil}^{SC}}$$

Where:

• $V_{gas}^{SC}$ = Volume of dissolved gas at standard conditions
• $V_{oil}^{SC}$ = Volume of oil at standard conditions

$R_s$ varies with pressure:

• Below bubble point ($P < P_b$): $R_s$ increases with increasing pressure as more gas dissolves
• At bubble point ($P = P_b$): $R_s$ reaches its maximum value ($R_{sb}$)
• Above bubble point ($P > P_b$): $R_s$ remains constant (all gas is dissolved)

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Theory

Physical Basis

Gas solubility in crude oil depends on:

1. Pressure: Higher pressure forces more gas into solution
2. Temperature: Higher temperature decreases gas solubility (opposite of water)
3. Gas composition: Lighter gases (methane) dissolve more readily
4. Oil composition: Lighter oils dissolve more gas

Correlation Approach

Since the 1940s, researchers have developed empirical correlations relating $R_s$ to readily available field data:

These correlations are region-specific, developed from PVT data collected in particular oil-producing areas. Selecting the appropriate correlation for your reservoir is critical for accuracy.

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Correlation Equations

Standing Correlation (1947/1981)

Developed from California crude oil data. One of the earliest and most widely used correlations.

$$R_s = \gamma_g \left[\left(\frac{P}{18.2} + 1.4\right) \cdot 10^{X}\right]^{1.2048}$$

Where:

$$X = 0.0125 \cdot \gamma_{API} - 0.00091 \cdot (T - 460)$$

Applicability Range:

Vasquez-Beggs Correlation (1980)

Developed from a worldwide database of over 6,000 data points. Uses corrected gas gravity for separator conditions.

For $\gamma_{API} \leq 30$:

$$R_s = C_1 \cdot \gamma_{gs} \cdot P^{C_2} \cdot \exp\left(\frac{C_3 \cdot \gamma_{API}}{T + 460}\right)$$

Where $C_1 = 0.0362$, $C_2 = 1.0937$, $C_3 = 25.724$

For $\gamma_{API} > 30$:

Where $C_1 = 0.0178$, $C_2 = 1.1870$, $C_3 = 23.931$

The corrected gas gravity accounts for separator conditions:

$$\gamma_{gs} = \gamma_g \left[1 + 5.912 \times 10^{-5} \cdot \gamma_{API} \cdot T_{sep} \cdot \log_{10}\left(\frac{P_{sep}}{114.7}\right)\right]$$

Applicability Range:

Glaso Correlation (1980)

Developed from North Sea crude oil samples. Particularly suitable for North Sea and similar light oils.

$$R_s = \gamma_g \left[\left(\frac{\gamma_{API}^{0.989}}{T^{0.172}}\right) \cdot 10^{F}\right]^{1.2255}$$

Where:

$$F = 2.8869 - \left[14.1811 - 3.3093 \cdot \log_{10}(P)\right]^{0.5}$$

Applicability Range:

Al-Marhoun Correlation (1988)

Developed specifically for Middle East crude oils (Saudi Arabia, UAE, Kuwait).

$$R_s = \left(185.843208 \cdot \gamma_g^{1.87784} \cdot \gamma_o^{-3.1437} \cdot T^{1.32657} \cdot P\right)^{1.3984}$$

Where $\gamma_o$ is oil specific gravity:

$$\gamma_o = \frac{141.5}{131.5 + \gamma_{API}}$$

Applicability Range:

Petrosky-Farshad Correlation (1993)

Developed for Gulf of Mexico crude oils. Particularly accurate for deepwater GOM reservoirs.

$$R_s = \left[\left(\frac{P}{112.727} + 12.340\right) \cdot \gamma_g^{0.8439} \cdot 10^{X}\right]^{1.73184}$$

Where:

$$X = 7.916 \times 10^{-4} \cdot \gamma_{API}^{1.5410} - 4.561 \times 10^{-5} \cdot T^{1.3911}$$

Applicability Range:

Dindoruk-Christman Correlation (2001)

Developed for Gulf of Mexico crude oils with extended pressure range. Suitable for high-pressure reservoirs.

$$R_s = \left[a_1 \cdot \gamma_g^{a_2} \cdot \gamma_{API}^{a_3} \cdot T^{a_4} \cdot (P - 14.7)^{a_5}\right]^{a_6}$$

With coefficients:

• $a_1 = 0.0005121$
• $a_2 = 0.8403$
• $a_3 = 1.0891$
• $a_4 = 0.5187$
• $a_5 = 1.0000$
• $a_6 = 1.2321$

Applicability Range:

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Correlation Selection Guide

By Geographic Region

By Oil Type

By Pressure Range

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Applicability and Limitations

General Applicability

1. Valid only below or at bubble point: For $P \leq P_b$
2. Saturated oil condition: Gas is in solution with oil
3. Black oil assumption: No retrograde condensation

Limitations

1. Region-specific: Correlations developed for specific oil types may not transfer well to other regions.

2. Separator conditions: Vasquez-Beggs requires separator pressure and temperature for gas gravity correction. Other correlations assume standard separator conditions.

3. Extrapolation danger: Using correlations outside their development range can produce significant errors.

4. Volatile oils: Standard black oil correlations may underpredict $R_s$ for volatile oils with high GOR.

5. CO₂ content: High CO₂ content (common in some pre-salt fields) can significantly affect gas solubility. Most correlations do not account for this [2].

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Comparison with Laboratory Data

When laboratory PVT data is available, compare with correlations:

1. Calculate AARE (Average Absolute Relative Error):

$$AARE = \frac{100}{n} \sum_{i=1}^{n} \left|\frac{R_{s,calc} - R_{s,lab}}{R_{s,lab}}\right|$$

2. Acceptable error: AARE < 10-15% is generally acceptable for most engineering calculations

3. Bias check: Consistent over- or under-prediction suggests systematic error

Studies [2] have shown that for Brazilian pre-salt oils:

• Al-Shammasi (2001) showed best performance (AARE ~14%)
• Standing and Vasquez-Beggs also performed reasonably well

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Related Topics

• Oil Formation Volume Factor (Bo) - Related to Rs
• Bubble Point Pressure (Pb) - Determines Rs validity range
• Oil Viscosity - Affected by dissolved gas
• PVT Overview - Correlation selection guide

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References

1. Standing, M.B. (1947). "A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases." Drilling and Production Practice, API, 275-287.

2. Mangili, P.V. and Ahón, V.R.R. (2019). "Comparison of PVT Correlations for Predicting Crude Oil Properties: The Brazilian Campos Basin Case Study." Brazilian Journal of Petroleum and Gas, 13(3), 129-157.

3. Vasquez, M.E. and Beggs, H.D. (1980). "Correlations for Fluid Physical Property Prediction." Journal of Petroleum Technology, 32(6), 968-970. SPE-6719-PA.

4. Glaso, O. (1980). "Generalized Pressure-Volume-Temperature Correlations." Journal of Petroleum Technology, 32(5), 785-795. SPE-8016-PA.

5. Al-Marhoun, M.A. (1988). "PVT Correlations for Middle East Crude Oils." Journal of Petroleum Technology, 40(5), 650-666. SPE-13718-PA.

6. Petrosky, G.E. and Farshad, F.F. (1993). "Pressure-Volume-Temperature Correlations for Gulf of Mexico Crude Oils." SPE Reservoir Evaluation & Engineering, 1(5), 416-420. SPE-51395-PA.

7. Dindoruk, B. and Christman, P.G. (2004). "PVT Properties and Viscosity Correlations for Gulf of Mexico Oils." SPE Reservoir Evaluation & Engineering, 7(6), 427-437. SPE-89030-PA.