Formation Water Properties Formula

Overview

Formation water in petroleum reservoirs is almost always a brine: a solution of NaCl and other salts in water. Salinity in producing reservoirs commonly ranges from 10,000 ppm in fresh-water aquifer systems to over 300,000 ppm in deep, mature basins. Salinity, temperature, and pressure each shift the brine's density, viscosity, compressibility, formation volume factor (Bw), and the amount of natural gas it can hold in solution.

The McCain (1990, 1991) correlations have been the workhorse for screening brine properties for three decades. The Spivey, McCain, and North (2004) correlations refine the density and compressibility predictions, particularly at high pressure and high salinity, and are now embedded in most commercial PVT and simulation packages. Both sets are based on regressions against laboratory data and require only T, P, and salinity (as TDS or NaCl equivalent) as inputs.

Theory

Brine density is dominated by salt concentration: every 10,000 ppm of NaCl adds roughly 0.0067 g/cc to the density of pure water at reservoir conditions. Bw is small (typically 1.00–1.05 rb/STB) because brines are nearly incompressible relative to oil. Solution gas in water is small but non-zero (0–20 scf/STB), and matters in deep, hot, low-salinity systems. Compressibility is a weak function of pressure and a strong function of salinity, and viscosity grows with salinity and falls with temperature.

Formulas

Water Formation Volume Factor (McCain)

Bw = (1 + dVwp)(1 + dVwT)

dVwT =  -1.0001e-2 + 1.33391e-4 * T + 5.50654e-7 * T^2
dVwp =  -1.95301e-9 * P*T - 1.72834e-13 * P^2 * T
        - 3.58922e-7 * P - 2.25341e-10 * P^2

where T is in °F, P in psia, and dVwT and dVwp are the thermal-expansion and pressure-compression corrections to pure-water FVF. Bw is then adjusted for salinity through the brine density.

Water Viscosity (McCain)

mu_w_1atm = A * T^B
A = 109.574 - 8.40564*S + 0.313314*S^2 + 8.72213e-3*S^3
B = -1.12166 + 2.63951e-2*S - 6.79461e-4*S^2 - 5.47119e-5*S^3 + 1.55586e-6*S^4

mu_w(P,T) = mu_w_1atm * (0.9994 + 4.0295e-5 * P + 3.1062e-9 * P^2)

where S is salinity in weight percent NaCl, T in °F, P in psia, and mu_w is in centipoise. Pressure correction is applied multiplicatively after the 1-atm value is computed.

Water Compressibility (Osif)

cw = 1 / (7.033*P + 541.5*S_ppm/10000 - 537*T + 403300)

cw in 1/psi, S in ppm of NaCl divided by 10,000 to convert to weight percent, T in °F, P in psia. Osif's expression is widely used as the screening compressibility correlation.

Gas Solubility in Water (McCain)

Rsw_pure = A + B*P + C*P^2

A =  8.15839 - 6.12265e-2 * T + 1.91663e-4 * T^2 - 2.1654e-7 * T^3
B =  1.01021e-2 - 7.44241e-5 * T + 3.05553e-7 * T^2 - 2.94883e-10 * T^3
C = -1.0e-7 * (9.02505 - 0.130237*T + 8.53425e-4*T^2 - 2.34122e-6*T^3 + 2.37049e-9*T^4)

log10(Rsw / Rsw_pure) = -0.0840655 * S * T^-0.285854

Rsw is gas-in-water solubility in scf/STB; the salinity correction reduces the pure-water solubility by an exponential function of weight-percent NaCl and temperature in °F.

Spivey-McCain-North Brine Density (2004)

rho_brine(T, P, m_NaCl) = rho_w(T, P) + delta_rho_NaCl(T, P, m_NaCl)

Spivey et al. (2004) extend McCain by computing pure-water density from a high-accuracy equation of state (IAPWS) and adding a NaCl-specific density increment derived from regression against laboratory data. Required when T > 250 °F or salinity > 250,000 ppm, where the original McCain regression starts to drift.

Brine Density in Field Units

rho_brine (lb/gal, ppg) = rho_brine (g/cc) * 8.345
rho_brine (lb/ft^3)     = rho_brine (g/cc) * 62.428

Worked Example

Given: T = 200 °F, P = 3000 psia, S = 100,000 ppm NaCl (10 wt%).

Step 1 — Bw via McCain:

dVwT = -1.0001e-2 + 1.33391e-4 * 200 + 5.50654e-7 * 200^2
     = -0.0100 + 0.0267 + 0.0220 = 0.0387

dVwp = -1.95301e-9 * 3000*200 - 1.72834e-13 * 3000^2 * 200
       - 3.58922e-7 * 3000 - 2.25341e-10 * 3000^2
     = -0.00117 - 0.000311 - 0.00108 - 0.00203 = -0.00459

Bw = (1 + -0.00459)(1 + 0.0387) = 0.9954 * 1.0387 = 1.0339 rb/STB

Step 2 — Viscosity at 1 atm:

A = 109.574 - 8.40564*10 + 0.313314*100 + 8.72213e-3*1000
  = 109.574 - 84.056 + 31.331 + 8.722 = 65.57

B = -1.12166 + 2.63951e-2*10 - 6.79461e-4*100 - 5.47119e-5*1000 + 1.55586e-6*10000
  = -1.1217 + 0.2640 - 0.0679 - 0.0547 + 0.0156 = -0.9647

mu_w_1atm = 65.57 * 200^(-0.9647) = 65.57 * 0.00600 = 0.394 cp

Step 3 — Compressibility (Osif):

cw = 1 / (7.033*3000 + 541.5*10 - 537*200 + 403300)
   = 1 / (21099 + 5415 - 107400 + 403300)
   = 1 / 322414 = 3.10e-6 /psi

Reading: A typical Texas Gulf Coast brine at 200 °F and 3000 psi with 10 wt% NaCl will show Bw ~ 1.03 rb/STB, viscosity ~ 0.4 cp, and compressibility ~ 3e-6 /psi.

Valid Ranges

When the correlations do not apply

• Brines dominated by CaCl₂, MgCl₂, or KCl rather than NaCl — use the ionic-composition-specific correlations from Numbere et al. or measured lab data.
• CO₂- or H₂S-rich systems (sour gas reservoirs, CCUS) — treat dissolved acid gas separately; gas solubility shifts dramatically.
• Geothermal or HPHT conditions above 530 °F or 30,000 psi — outside the regression envelope; use measured PVT.
• Drilling brines with engineered weighting agents (NaBr, ZnBr₂) — use vendor data sheets, not formation-water correlations.

References

1. McCain, W.D. Jr. (1990). The Properties of Petroleum Fluids, 2nd ed. PennWell. Chapter 12 (Water properties).
2. McCain, W.D. Jr. (1991). "Reservoir-Fluid Property Correlations — State of the Art." SPE Reservoir Engineering, 6(2), 266–272.
3. Spivey, J.P., McCain, W.D. Jr., & North, R. (2004). "Estimating Density, Formation Volume Factor, Compressibility, Methane Solubility, and Viscosity for Oilfield Brines at Temperatures from 0 to 275 °C, Pressures to 200 MPa, and Salinities to 5.7 mol/kg." J. Canadian Petroleum Technology, 43(7), 52–61.
4. Osif, T.L. (1988). "The Effects of Salt, Gas, Temperature, and Pressure on the Compressibility of Water." SPE Reservoir Engineering, 3(1), 175–181.
5. IAPWS (International Association for the Properties of Water and Steam). Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam.
6. PetroWiki — Water properties: https://petrowiki.spe.org/Water_properties