Formation Water PVT Properties

Overview

Formation water (brine) properties are essential for:

• Reservoir simulation — Aquifer influx, water coning
• Material balance — Water expansion drive calculations
• Production forecasting — Water breakthrough, water cut trends
• Well testing — Aquifer properties, permeability calculations
• Pressure-transient analysis — Total compressibility determination
• Production facility design — Separator sizing, water handling

Unlike oil and gas, formation water properties are primarily influenced by:

1. Temperature — Dominant effect on density and viscosity
2. Pressure — Affects compressibility and dissolved gas
3. Salinity — Total dissolved solids (TDS) concentration

The McCain (1991) correlations presented here provide comprehensive property predictions for formation water at reservoir conditions.

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Salinity and Units

Total Dissolved Solids (TDS)

Formation water contains dissolved salts (primarily NaCl, CaCl₂, MgCl₂). Salinity is expressed in multiple units:

In this document:

• S denotes weight % solids (0 to 30%)
• Pure water: S = 0%
• Typical seawater: S ≈ 3.5%
• Heavy brines: S = 20-30%

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Water Density (ρw)

Standard Conditions Density

Water density at standard conditions (14.7 psia, 60°F) is calculated from salinity:

$$\rho_w = 62.368 + 0.438603 S + 1.60074 \times 10^{-3} S^2$$

Where:

• $\rho_w$ = water density at standard conditions, lb/ft³
• $S$ = salinity, weight % (0 to 30%)

Accuracy: As accurate as laboratory measurement throughout full range of salinity.

Typical values:

• Pure water (S = 0%): ρw = 62.37 lb/ft³
• Seawater (S = 3.5%): ρw = 63.91 lb/ft³
• Heavy brine (S = 25%): ρw = 73.73 lb/ft³

Reservoir Conditions Density

Density at reservoir conditions is obtained from:

$$\rho_{w,res} = \frac{\rho_w}{B_w}$$

Where $B_w$ is the formation volume factor at reservoir pressure and temperature.

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Water Formation Volume Factor (Bw)

The water FVF relates reservoir volume to stock-tank volume:

$$B_w = \frac{V_R}{V_{ST}}$$

McCain provides correlations for pressure and temperature effects on water volume. The complete correlation accounts for:

1. Thermal expansion — Water expands with increasing temperature
2. Pressure compression — Water compresses with increasing pressure
3. Dissolved gas — Gas in solution increases volume

McCain Bw Correlation

The water FVF is correlated as:

$$B_w = (1 + \Delta V_{wT})(1 + \Delta V_{wp})$$

Where:

• $\Delta V_{wT}$ = volume change due to temperature (from 60°F to reservoir T)
• $\Delta V_{wp}$ = volume change due to pressure (from 14.7 psia to reservoir P)

Temperature effect:

Water expands with temperature. The McCain correlation provides accurate Bw over the range:

• Temperatures: to 260°F
• Pressures: to 5,000 psia
• Salinities: all concentrations

Accuracy: Within 2% of experimental data.

Physical trends:

• Bw increases with temperature (thermal expansion)
• Bw decreases with pressure (compressibility)
• Bw slightly affected by salinity (≈ 1% variation)
• Typical range: Bw = 1.00 to 1.06 bbl/STB

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Solution Gas-Water Ratio (Rsw)

Natural gas dissolves in water at reservoir conditions. The solution gas-water ratio is the volume of gas (at standard conditions) dissolved in one stock-tank barrel of water.

Pure Water Rsw

For pure water (S = 0%), McCain provides:

$$R_{swp} = A + B p + C p^2$$

Where:

$$A = 8.15839 - 6.12265 \times 10^{-2} T + 1.91663 \times 10^{-4} T^2 - 2.1654 \times 10^{-7} T^3$$$$B = 1.01021 \times 10^{-2} - 7.44241 \times 10^{-5} T + 3.05553 \times 10^{-7} T^2 - 2.94883 \times 10^{-10} T^3$$$$C = -10^{-7}(9.02505 - 0.130237 T + 8.53425 \times 10^{-4} T^2 - 2.34122 \times 10^{-6} T^3 + 2.37049 \times 10^{-9} T^4)$$

And:

• $R_{swp}$ = solution gas-water ratio for pure water, scf/STB
• $p$ = pressure, psia
• $T$ = temperature, °F

Applicability:

• Pressures: 1,000 to 10,000 psia
• Temperatures: 100 to 340°F
• Accuracy: Within 5% of original graphical correlation

Important: Do NOT use below 1,000 psia (correlation becomes inaccurate).

Formation Water Rsw (Brine)

Dissolved salts reduce gas solubility. The salinity correction factor is:

$$\log_{10}\left[\frac{R_{sw,brine}}{R_{sw,pure}}\right] = -0.0840655 S T - 0.285854$$

Therefore:

$$R_{sw} = R_{swp} \times 10^{(-0.0840655 S T - 0.285854)}$$

Where:

• $R_{sw}$ = solution gas-water ratio for brine, scf/STB
• $R_{swp}$ = Rsw for pure water (from previous correlation)
• $S$ = salinity, weight %
• $T$ = temperature, °F

Applicability:

• Salinities: to 30%
• Temperatures: 70 to 250°F
• Accuracy: Within 3% of graphical correlation

Physical trends:

• Rsw increases with pressure (more gas dissolves)
• Rsw increases with temperature (typically opposite to oil)
• Rsw decreases with salinity (salt-out effect)
• Typical values: 5 to 25 scf/STB at reservoir conditions

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Water Compressibility (Cw)

Water compressibility measures volume change with pressure:

$$C_w = -\frac{1}{V_w}\left(\frac{\partial V_w}{\partial p}\right)_T = -\frac{1}{B_w}\left(\frac{\partial B_w}{\partial p}\right)_T$$

Undersaturated Water Compressibility — Osif (1988)

For pressures above bubblepoint (no free gas):

$$C_w = \frac{1}{7.033 p + 0.5415 S - 537.0 T + 403,300}$$

Where:

• $C_w$ = water compressibility, psi⁻¹
• $p$ = pressure, psia
• $S$ = salinity, mg/L (note: different units!)
• $T$ = temperature, °F

Applicability:

• Temperatures: 200 to 270°F
• Pressures: 1,000 to 20,000 psia
• Salinities: to 200,000 mg/L

Physical trends:

• Cw decreases with pressure (harder to compress at high P)
• Cw decreases with temperature (more rigid structure at high T)
• Cw decreases with salinity (dissolved salts stiffen water)
• Typical values: (2 to 5) × 10⁻⁶ psi⁻¹

Saturated Water Compressibility — McCain (1991)

For pressures below bubblepoint (dissolved gas present):

$$C_w = -\frac{1}{B_w}\left(\frac{\partial B_w}{\partial p}\right)_T + \frac{B_g}{B_w}\left(\frac{\partial R_{sw}}{\partial p}\right)_T$$

The gas liberation term is:

$$\left(\frac{\partial R_{sw}}{\partial p}\right)_T = B + 2Cp$$

Using B and C from the Rsw correlation.

Note: McCain states this saturated Cw correlation has "unknown accuracy" and should be considered "order of magnitude" only.

Practical approach: For most reservoir engineering calculations, use Osif correlation (undersaturated). The gas liberation effect is small compared to oil systems.

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Water Viscosity (μw)

Viscosity at Atmospheric Pressure

Water viscosity at reservoir temperature and 1 atm pressure:

$$\mu_{w1} = A T^{-B}$$

Where:

$$A = 109.574 - 8.40564 S + 0.313314 S^2 + 8.72213 \times 10^{-3} S^3$$$$B = 1.12166 - 2.63951 \times 10^{-2} S + 6.79461 \times 10^{-4} S^2 + 5.47119 \times 10^{-5} S^3 - 1.55586 \times 10^{-6} S^4$$

And:

• $\mu_{w1}$ = water viscosity at 1 atm, cP
• $T$ = temperature, °F
• $S$ = salinity, weight %

Applicability:

• Temperatures: 100 to 400°F
• Salinities: to 26%
• Accuracy: Within 5% of graphical correlation

Pressure Correction

Water viscosity at reservoir pressure:

$$\frac{\mu_w}{\mu_{w1}} = 0.9994 + 4.0295 \times 10^{-5} p + 3.1062 \times 10^{-9} p^2$$

Where:

• $\mu_w$ = water viscosity at reservoir pressure, cP
• $\mu_{w1}$ = water viscosity at 1 atm (from previous correlation)
• $p$ = pressure, psia

Applicability:

• Pressures: to 10,000 psia (within 4%)
• Pressures: 10,000 to 15,000 psia (within 7%)

Physical trends:

• μw decreases with temperature (dominant effect, exponential)
• μw increases slightly with pressure (weak effect, quadratic)
• μw increases with salinity (dissolved salts increase viscosity)
• Typical values: 0.2 to 1.0 cP at reservoir conditions
• Pure water at 150°F: μw ≈ 0.35 cP
• Brine (S = 25%) at 150°F: μw ≈ 0.55 cP

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Comparison: Water vs. Oil Properties

Key differences:

• Water is nearly incompressible compared to oil
• Water viscosity is low and varies primarily with temperature
• Water holds very little dissolved gas (salting-out effect)
• Water FVF is close to 1.0 (small expansion)

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Practical Applications

Material Balance — Aquifer Influx

Water properties needed for Carter-Tracy aquifer model:

• Cw — Water compressibility for aquifer expansion
• μw — Water viscosity for aquifer mobility
• Bw — Water volume at reservoir conditions

Well Testing — Total Compressibility

Total compressibility in aquifer/water zone:

$$c_t = S_w c_w + S_o c_o + c_f$$

Where:

• $S_w$ = water saturation
• $c_w$ = water compressibility
• $c_f$ = formation (rock) compressibility

Production Forecasting — Water Cut

Water production rate:

$$q_w = q_t \times WC$$

Surface water rate from reservoir:

$$q_{w,surf} = \frac{q_{w,res}}{B_w}$$

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Related Documentation

• PVT Overview — Correlation selection guide
• Gas Properties — Natural gas PVT
• Oil Formation Volume Factor — Oil FVF correlations
• PTA Dimensionless Variables — Uses total compressibility

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References

1. McCain, W.D. Jr. (1991). "Reservoir-Fluid Property Correlations—State of the Art." SPE Reservoir Engineering, 6(2), pp. 266-272. SPE-18571-PA. Equations 52-65.

2. Osif, T.L. (1988). "The Effects of Salt, Gas, Temperature, and Pressure on the Compressibility of Water." SPE Reservoir Engineering, 3(1), pp. 175-181. SPE-13174-PA.

3. McCain, W.D. Jr. (1990). The Properties of Petroleum Fluids, 2nd Edition. Tulsa, OK: PennWell Books. Chapter 9: Properties of Produced Water.

4. Collins, A.G. (1975). Geochemistry of Oilfield Waters. Developments in Petroleum Science, Vol. 1. Amsterdam: Elsevier.

5. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Cambridge, MA: Gulf Professional Publishing. Chapter 7: Unconventional Gas Reservoirs.

6. Craft, B.C. and Hawkins, M.F. (1991). Applied Petroleum Reservoir Engineering, 2nd Edition. Englewood Cliffs, NJ: Prentice Hall. Chapter 2: Reservoir Fluids Properties.