Gas Viscosity Formula — Lee-Gonzalez-Eakin Correlation

Gas viscosity is a required input for material balance, well-test interpretation, pipeline pressure drop, and reservoir simulation. The Lee, Gonzalez & Eakin (1966) correlation is the industry-standard semi-empirical method for natural gas. It requires gas density, which in turn requires Z-factor; in sour-gas systems the pseudocritical properties are first shifted by Wichert-Aziz before the Z-factor solve.

Overview

Natural gas viscosity at reservoir conditions ranges from 0.01 to 0.06 cp — one to two orders of magnitude lower than oil. Unlike liquids, gas viscosity rises with temperature at low pressure and shows complex P–T behavior at high pressure because density becomes the dominant control. The LGE correlation expresses gas viscosity as an exponential function of gas density, with coefficients that depend on molecular weight and temperature.

Sour-gas reservoirs (H₂S, CO₂, and N₂ content) require two corrections: (1) Wichert-Aziz adjusts the pseudocritical T and P to account for acid-gas effects on Z-factor, and (2) Carr-Kobayashi-Burrows applies an additive viscosity correction proportional to mole fraction of each impurity.

Theory

The full natural-gas viscosity workflow runs four steps: (1) Sutton or Standing correlations give pseudocritical T_pc and P_pc from gas gravity; (2) Wichert-Aziz applies the H₂S/CO₂ correction if sour; (3) a Z-factor solver (Hall-Yarborough or Dranchuk-Abou-Kassem) gives Z at reduced T_pr/P_pr; and (4) LGE computes viscosity from gas density (derived from Z) and molecular weight.

Formulas

Pseudocritical Properties (Sutton)

Tpc = 169.2 + 349.5*sg - 74.0*sg^2     (deg R)
Ppc = 756.8 - 131.0*sg - 3.6*sg^2      (psia)

sg = specific gravity (air = 1.0). Valid for sweet hydrocarbon gases with sg = 0.55–1.85.

Wichert-Aziz Sour-Gas Correction

A = yH2S + yCO2
B = yH2S
epsilon = 120*(A^0.9 - A^1.6) + 15*(B^0.5 - B^4)

Tpc_corrected = Tpc - epsilon
Ppc_corrected = Ppc * Tpc_corrected / (Tpc + B*(1-B)*epsilon)

y_H2S, y_CO2 = mole fractions of acid gases. Used in the GPSA Engineering Data Book and SPE textbooks.

Z-Factor (Hall-Yarborough)

t = 1 / Tpr

f(y) = -Ppr_term + (y + y^2 + y^3 - y^4)/(1-y)^3
       - (14.76*t - 9.76*t^2 + 4.58*t^3)*y^2
       + (90.7*t - 242.2*t^2 + 42.4*t^3)*y^(2.18 + 2.82*t)

Ppr_term = 0.06125 * Ppr * t * exp(-1.2*(1-t)^2)

Solve f(y) = 0 for y (Newton-Raphson)
Z = Ppr_term / y

Gas Density

rho_g = (P * M_w) / (Z * R * T)

M_w = 28.96 * sg    (molecular weight, lb/lbmol)
R = 10.732           (psia*ft^3 / lbmol / deg R)

P in psia, T in deg R, gives ρ_g in lb/ft³.

Lee-Gonzalez-Eakin (1966) Viscosity

K = (9.4 + 0.02*M) * T^1.5 / (209 + 19*M + T)
X = 3.5 + 986/T + 0.01*M
Y = 2.4 - 0.2*X

mu_g = 1e-4 * K * exp(X * rho_g^Y)

T in deg R, M = molecular weight in lb/lbmol, ρ_g in g/cc (or convert), gives μ_g in cp.

Carr-Kobayashi-Burrows Impurity Corrections

delta_mu_N2  = yN2  * (8.48e-3 * log10(sg) + 9.59e-3)
delta_mu_CO2 = yCO2 * (9.08e-3 * log10(sg) + 6.24e-3)
delta_mu_H2S = yH2S * (8.49e-3 * log10(sg) + 3.73e-3)

mu_g_total = mu_g + delta_mu_N2 + delta_mu_CO2 + delta_mu_H2S

Key Symbols

Symbol	Description	Units
mu_g	Gas viscosity	cp
rho_g	Gas density at P, T	g/cc
Z	Compressibility factor	dimensionless
Tpr, Ppr	Pseudoreduced T, P	dimensionless
M	Molecular weight	lb/lbmol
sg	Gas gravity (air = 1)	dimensionless

Worked Example

Given: Sweet gas, sg = 0.65, T = 250 °F (710 deg R), P = 4000 psia. No N₂, CO₂, or H₂S.

Step 1 — Pseudocritical (Sutton):

Tpc = 169.2 + 349.5*0.65 - 74.0*0.65^2 = 169.2 + 227.2 - 31.3 = 365.1 deg R
Ppc = 756.8 - 131.0*0.65 - 3.6*0.65^2 = 756.8 - 85.2 - 1.5 = 670.1 psia

Step 2 — Reduced T, P:

Tpr = 710 / 365.1 = 1.94
Ppr = 4000 / 670.1 = 5.97

Step 3 — Z-factor (Hall-Yarborough):

Z ~ 0.876 (from iteration at Tpr = 1.94, Ppr = 5.97)

Step 4 — Gas density:

M = 28.96 * 0.65 = 18.82 lb/lbmol
rho_g = (4000 * 18.82) / (0.876 * 10.732 * 710)
      = 75280 / 6672
      = 11.28 lb/ft^3
      = 0.1807 g/cc

Step 5 — LGE viscosity:

K = (9.4 + 0.02*18.82) * 710^1.5 / (209 + 19*18.82 + 710)
  = (9.4 + 0.38) * 18914 / (209 + 357.6 + 710)
  = 9.78 * 18914 / 1276.6
  = 144.9

X = 3.5 + 986/710 + 0.01*18.82 = 3.5 + 1.389 + 0.188 = 5.08
Y = 2.4 - 0.2*5.08 = 1.38

mu_g = 1e-4 * 144.9 * exp(5.08 * 0.1807^1.38)
     = 0.01449 * exp(5.08 * 0.0930)
     = 0.01449 * exp(0.472)
     = 0.01449 * 1.604
     = 0.0232 cp

Valid Ranges

Parameter	Method	Valid Range
Viscosity	LGE 1966	P = 100–8000 psia, T = 100–340 °F, sg = 0.55–1.85
Pseudocritical	Sutton	sg = 0.55–1.85, hydrocarbon-dominated
Wichert-Aziz	sour gas	yCO2 ≤ 0.80, yH2S ≤ 0.74
Hall-Yarborough Z	Z-factor	Tpr > 1.0, Ppr = 0.1–15
CKB impurity	sour viscosity	yN2 ≤ 0.15, yCO2 ≤ 0.15, yH2S ≤ 0.15

When the correlations do not apply

Very rich gas condensates (sg > 1.85) — LGE drifts; use a tuned EOS PVT model.
Highly sour systems (yH2S > 0.30) — Wichert-Aziz envelope ends, use measured lab data or tuned EOS.
Near-critical or retrograde behavior — correlation outputs become unreliable; use a Peng-Robinson or SRK EOS.
CCUS injection streams (pure or near-pure CO₂) — use Fenghour-Wakeham CO₂ viscosity correlation, not LGE.

References

Lee, A.L., Gonzalez, M.H., & Eakin, B.E. (1966). "The Viscosity of Natural Gases." JPT, 18(8), 997–1000.
Carr, N.L., Kobayashi, R., & Burrows, D.B. (1954). "Viscosity of Hydrocarbon Gases Under Pressure." Trans. AIME, 201, 264–272.
Wichert, E. & Aziz, K. (1972). "Calculate Z's for Sour Gases." Hydrocarbon Processing, 51(5), 119–122.
Hall, K.R. & Yarborough, L. (1973). "A New Equation of State for Z-Factor Calculations." Oil and Gas Journal, June 18, 82–92.
Dranchuk, P.M. & Abou-Kassem, J.H. (1975). "Calculation of Z Factors for Natural Gases Using Equations of State." J. Canadian Petroleum Technology, 14(3), 34–36.
Sutton, R.P. (1985). "Compressibility Factors for High-Molecular-Weight Reservoir Gases." SPE 14265.
McCain, W.D. Jr. (1990). The Properties of Petroleum Fluids, 2nd ed. PennWell. Chapter 6.
GPSA Engineering Data Book, 13th ed., Section 23 (Physical Properties).