Thermodynamics

Z-Factor (Gas Compressibility Factor)

The Z-factor quantifies deviation from ideal gas behavior. Accurate Z-factor determination is essential for gas density, pipeline hydraulics, compression calculations, and custody transfer metering throughout the midstream industry.

Launch Calculator Calculation Methods

Definition

Z = PV / nRT

Ratio of actual gas volume to volume predicted by ideal gas law at the same P and T.

Typical range

0.3 - 1.05

Pipeline gas: Z = 0.85-0.95. Near critical point Z can drop below 0.30.

Key standards

GPSA, AGA-8, SPE

Standing-Katz chart, DAK and HY correlations, AGA-8 DETAIL method for custody transfer.

Contents

Use this guide when you need to:

  • Understand the physical meaning of Z-factor.
  • Select the right Z-factor correlation for your application.
  • Apply sour gas corrections for H2S and CO2.
  • Determine when compositional methods (AGA-8) are required.

1. What is the Z-Factor?

The gas compressibility factor, universally denoted as Z, is a dimensionless correction factor that accounts for the deviation of real gas behavior from ideal gas predictions. It is defined as the ratio of the actual molar volume of a gas to the molar volume predicted by the ideal gas law at the same pressure and temperature.

Fundamental Definition

Compressibility Factor Definition: Z = PV / nRT = V_actual / V_ideal Where: Z = Compressibility factor (dimensionless) P = Absolute pressure (psia or kPa abs) V = Actual volume of gas (ft3 or m3) n = Number of moles (lbmol or kmol) R = Universal gas constant = 10.7316 psia-ft3/lbmol-degR (US customary) = 8.314 kJ/kmol-K (SI) T = Absolute temperature (degR or K) When Z = 1.0, the gas behaves ideally. When Z < 1.0, the gas is more compressible than ideal (attractive forces dominate). When Z > 1.0, the gas is less compressible than ideal (repulsive forces dominate).

Physical Interpretation

The Z-factor captures two competing molecular phenomena that the ideal gas law ignores:

Attractive forces

Z < 1.0

Intermolecular attraction pulls molecules closer together, making the gas occupy less volume than ideal. Dominates at moderate pressures (1 < P_r < 5) and temperatures near the critical point.

Repulsive forces

Z > 1.0

At very high pressures (P_r > 5-8), molecules are forced so close that repulsive forces dominate, making the gas occupy more volume than ideal. Common in high-pressure gas injection and deep well conditions.

The Real Gas Equation

Real Gas Law (Modified Ideal Gas): PV = ZnRT Rearranged for density: rho = (P x MW) / (Z x R x T) Or equivalently: rho_real = rho_ideal / Z Since Z < 1.0 for most pipeline conditions: rho_real > rho_ideal This means real gas is DENSER than ideal gas predicts.
Engineering significance: The Z-factor is not merely an academic correction. At typical transmission pipeline conditions (800-1200 psia), Z ranges from 0.82 to 0.92, meaning the actual gas volume is 8-18% less than ideal gas prediction. Ignoring Z at these conditions causes proportional errors in density, flow rate, and line pack calculations.

2. Why Z-Factor Matters

The Z-factor propagates through virtually every gas engineering calculation. An error in Z directly causes proportional errors in downstream results.

Gas density

Direct proportionality

rho = P x MW / (Z x R x T). A 5% error in Z produces a 5% error in calculated density, which propagates to mass flow, Reynolds number, and pressure drop.

Pipeline hydraulics

Line pack & capacity

Line pack (stored gas volume) is inversely proportional to Z. Accurate Z is essential for pipeline capacity planning, transient analysis, and nomination scheduling.

Compression

Power & temperature

Compressor power calculations use Z at suction and discharge conditions. Z_avg appears directly in horsepower equations. Discharge temperature depends on Z ratio across stages.

Flow metering

Custody transfer accuracy

Orifice meter equations (AGA-3) require Z for supercompressibility factor F_pv. A 0.5% Z error can translate to significant revenue loss in custody transfer applications.

Impact on Key Calculations

Calculation How Z Appears Impact of 5% Z Error
Gas density rho = P x MW / (ZRT) 5% density error
Standard volume Q_std = Q x (P/P_b) x (T_b/T) x (Z_b/Z) 5% flow rate error
Line pack LP = (V_pipe x P_avg) / (Z_avg x T_avg) 5% storage volume error
Compressor HP HP proportional to Z_avg x T_s 5% power sizing error
Orifice metering F_pv = sqrt(Z_b / Z_f) 2.5% flow measurement error
Relief valve sizing A_orifice proportional to sqrt(Z x T / MW) 2.5% orifice area error
Revenue impact: For a pipeline transporting 500 MMscfd of natural gas at $3/Mscf, a 1% error in Z-factor at flowing conditions translates to approximately $15,000 per day ($5.5 million/year) in measurement uncertainty. This is why custody transfer applications require AGA-8 accuracy of 0.1% or better.

3. Real Gas vs Ideal Gas

The ideal gas law PV = nRT rests on two assumptions that become increasingly inaccurate at high pressures and low temperatures:

Ideal Gas Assumptions

  • Assumption 1 - No intermolecular forces: The ideal gas model assumes molecules do not attract or repel each other. In reality, van der Waals attractive forces become significant when molecules are close together (high pressure or low temperature).
  • Assumption 2 - Negligible molecular volume: The ideal model treats molecules as point masses occupying zero volume. At high pressures, the actual volume of molecules becomes a meaningful fraction of the container volume, reducing available free space.

When Does Ideal Gas Break Down?

The degree of non-ideal behavior depends on how close the gas conditions are to its critical point, expressed through reduced pressure (P_r = P/P_pc) and reduced temperature (T_r = T/T_pc):

Reduced Conditions Z-Factor Range Deviation from Ideal Typical Application
P_r < 0.1, any T_r 0.99 - 1.00 < 1% Low-pressure distribution, vent gas
P_r = 0.5, T_r > 1.5 0.93 - 0.97 3 - 7% Gathering systems, moderate pressure
P_r = 1.0 - 2.0, T_r = 1.1 - 1.3 0.70 - 0.85 15 - 30% Transmission pipelines, compressor discharge
P_r = 1.0, T_r = 1.05 0.25 - 0.35 65 - 75% Near critical point, retrograde condensation
P_r > 5.0, any T_r 1.0 - 2.0+ Variable High-pressure gas injection, deep wells

Behavior at Extreme Conditions

The Z-factor exhibits characteristic behavior across different pressure ranges:

  • Low pressure (P_r < 0.5): Z is close to 1.0 and decreases slightly with increasing pressure. Ideal gas law is adequate for most engineering purposes.
  • Moderate pressure (0.5 < P_r < 3): Z drops significantly below 1.0 as attractive forces dominate. The minimum Z occurs at P_r between 1 and 2, depending on T_r. This is the range where Z-factor corrections are most critical.
  • High pressure (P_r > 5): Z increases above 1.0 as repulsive forces and finite molecular volume effects dominate. The gas becomes harder to compress than ideal gas predicts.
  • Near critical point (T_r close to 1.0, P_r close to 1.0): Z shows extreme sensitivity to small changes in P and T. The minimum value of Z (around 0.27 for pure methane) occurs at the critical point itself.
Rule of thumb for natural gas: Use the ideal gas law only when operating pressure is below 100 psia. Between 100-500 psia, Z-factor correction improves accuracy by 2-7%. Above 500 psia, Z-factor correction is mandatory as errors from the ideal gas assumption exceed 5-15%.

4. Standing-Katz Chart

The Standing-Katz chart, published by Standing and Katz in 1942, remains the foundational graphical correlation for natural gas Z-factors. It plots Z as a function of pseudo-reduced pressure (P_pr) and pseudo-reduced temperature (T_pr).

How the Chart Works

Standing-Katz Chart Procedure: Step 1: Determine pseudo-critical properties P_pc = pseudo-critical pressure (psia) T_pc = pseudo-critical temperature (degR) Step 2: Calculate reduced properties P_pr = P / P_pc (pseudo-reduced pressure) T_pr = T / T_pc (pseudo-reduced temperature) Step 3: Read Z from chart Enter chart at P_pr on x-axis Follow curve for appropriate T_pr Read Z on y-axis Valid range: 0 < P_pr < 15 1.05 < T_pr < 3.0

Key Features of the Chart

  • Each curve represents a constant T_pr: Curves range from T_pr = 1.05 (near critical, showing deep dip in Z) to T_pr = 3.0 (far from critical, Z close to 1.0).
  • Minimum Z at each T_pr: The lowest Z values occur at P_pr between 1 and 3. For T_pr = 1.05, the minimum Z is approximately 0.27. For T_pr = 1.5, the minimum is around 0.65.
  • Convergence at low P_pr: All T_pr curves converge toward Z = 1.0 as P_pr approaches zero, confirming ideal gas behavior at low pressure.
  • Crossover at high P_pr: At very high reduced pressures (P_pr > 8-10), all curves show Z increasing above 1.0, reflecting the dominance of repulsive forces and molecular volume effects.

Principle of Corresponding States

The Standing-Katz chart relies on the principle of corresponding states: all gases at the same reduced pressure and reduced temperature have approximately the same Z-factor, regardless of their specific identity. This allows a single chart to represent methane, ethane, natural gas mixtures, and other hydrocarbon gases.

Principle of Corresponding States: Z = f(P_r, T_r) for all gases This principle works well for: - Hydrocarbon gases (methane, ethane, propane, etc.) - Natural gas mixtures (sweet gas) This principle requires corrections for: - Gases with significant H2S or CO2 (sour gas) - Gases with high nitrogen content - Gases near critical conditions (within 5% of T_c)

Reading the Chart - Example

Example: Natural gas at 1000 psia, 100 degF, SG = 0.65 Step 1: Pseudo-critical properties (Sutton correlation) T_pc = 169.2 + 349.5(0.65) - 74.0(0.65)^2 = 365.4 degR P_pc = 756.8 - 131.0(0.65) - 3.6(0.65)^2 = 670.0 psia Step 2: Reduced properties T = 100 + 459.67 = 559.67 degR T_pr = 559.67 / 365.4 = 1.531 P_pr = 1000 / 670.0 = 1.493 Step 3: From Standing-Katz chart at P_pr = 1.49, T_pr = 1.53 Z = 0.855 (approximately) This means the gas occupies 85.5% of the volume predicted by the ideal gas law.
Limitations of the graphical method: The Standing-Katz chart has limited precision (reading accuracy of approximately 1-2%), cannot be automated for computer applications, and does not extend to sour gas without corrections. For these reasons, numerical correlations such as DAK and Hall-Yarborough were developed to reproduce the chart mathematically.

5. Pseudo-Critical Properties

Pseudo-critical properties are the effective critical pressure and critical temperature of a gas mixture. They are required to calculate reduced properties (P_pr and T_pr) for any Z-factor correlation. Two approaches exist depending on whether full gas composition is known.

Kay's Mixing Rule (Compositional Method)

When full mole-fraction composition is available, Kay's mixing rule calculates mixture pseudo-critical properties as molar averages:

Kay's Mixing Rule: P_pc = SUM(y_i x P_ci) for all components T_pc = SUM(y_i x T_ci) for all components Where: y_i = Mole fraction of component i P_ci = Critical pressure of component i (psia) T_ci = Critical temperature of component i (degR) Example: 90% methane, 5% ethane, 3% propane, 2% CO2 P_pc = 0.90(667.8) + 0.05(707.8) + 0.03(616.3) + 0.02(1070.9) P_pc = 601.0 + 35.4 + 18.5 + 21.4 = 676.3 psia T_pc = 0.90(343.3) + 0.05(549.8) + 0.03(665.7) + 0.02(547.6) T_pc = 309.0 + 27.5 + 20.0 + 11.0 = 367.4 degR

Component Critical Properties

Component Formula MW T_c (degR) P_c (psia)
Methane CH4 16.04 343.3 667.8
Ethane C2H6 30.07 549.8 707.8
Propane C3H8 44.10 665.7 616.3
n-Butane n-C4H10 58.12 765.3 550.7
i-Butane i-C4H10 58.12 734.7 529.1
n-Pentane n-C5H12 72.15 845.4 488.6
Nitrogen N2 28.01 227.3 493.0
Carbon Dioxide CO2 44.01 547.6 1070.9
Hydrogen Sulfide H2S 34.08 672.4 1306.0

Sutton Correlations (Specific Gravity Method)

When full composition is unavailable, Sutton (1985) correlations estimate pseudo-critical properties from gas specific gravity alone:

Sutton Correlation (1985): T_pc = 169.2 + 349.5 x SG - 74.0 x SG^2 (degR) P_pc = 756.8 - 131.0 x SG - 3.6 x SG^2 (psia) Valid for: SG = 0.57 to 1.68 (sweet gas only) Accuracy: +/- 1% for T_pc, +/- 2% for P_pc Piper-McCain-Corredor (2012): An improved correlation that accounts for non-hydrocarbon content: T_pc = 120.1 + 429.2 x SG_HC - 62.2 x SG_HC^2 P_pc = 671.1 - 14.0 x SG_HC - 34.3 x SG_HC^2 Where SG_HC is the hydrocarbon-only specific gravity. These provide better accuracy for gases with CO2 and N2.

Quick Reference: P_pc and T_pc vs SG

Gas SG Approx. MW T_pc (degR) P_pc (psia) Gas Type
0.57 16.5 349 681 Very lean (nearly pure methane)
0.60 17.4 356 677 Lean pipeline gas
0.65 18.8 365 670 Typical pipeline gas
0.70 20.3 374 662 Moderately rich gas
0.80 23.2 391 645 Rich gas (high C2+ content)
1.00 29.0 418 610 Very rich / condensate gas
When to use each method: Use Kay's mixing rule when a chromatographic gas analysis is available (preferred for sour gas, rich gas, or high-accuracy applications). Use Sutton correlations for quick estimates when only specific gravity is known and the gas is sweet (H2S + CO2 < 5 mol%).

6. Calculation Methods

Several numerical correlations have been developed to reproduce the Standing-Katz chart mathematically. The three most widely used methods in the midstream industry are described below.

6.1 Dranchuk-Abou-Kassem (DAK) Correlation

The DAK correlation (1975) fits the Standing-Katz chart with an 11-coefficient equation of state. It is the most widely used Z-factor correlation in pipeline simulation software and spreadsheet calculations.

Dranchuk-Abou-Kassem Correlation: Z = 1 + (A1 + A2/T_r + A3/T_r^3 + A4/T_r^4 + A5/T_r^5) x rho_r + (A6 + A7/T_r + A8/T_r^2) x rho_r^2 - A9 x (A7/T_r + A8/T_r^2) x rho_r^5 + A10 x (1 + A11 x rho_r^2) x (rho_r^2 / T_r^3) x exp(-A11 x rho_r^2) Where reduced density: rho_r = 0.27 x P_r / (Z x T_r) Eleven Coefficients: A1 = 0.3265 A7 = -0.7361 A2 = -1.0700 A8 = 0.1844 A3 = -0.5339 A9 = 0.1056 A4 = 0.01569 A10 = 0.6134 A5 = -0.05165 A11 = 0.7210 A6 = 0.5475 Solution Method: Iterative (Newton-Raphson) Initial guess: Z = 1.0 Convergence tolerance: 1E-8 typically Usually converges in 5-10 iterations Valid Range: 0.2 < P_pr < 30 1.0 < T_pr < 3.0 Accuracy: +/- 0.486% average vs Standing-Katz chart

6.2 Hall-Yarborough (HY) Correlation

The Hall-Yarborough method (1973) uses the Starling-Carnahan hard-sphere equation of state to represent Z. It generally has better convergence behavior than DAK near the critical point.

Hall-Yarborough Correlation: Z = (0.06125 x P_pr x t) / y x exp(-1.2 x (1 - t)^2) Where: t = 1 / T_pr (reciprocal reduced temperature) y = reduced density (solved iteratively) The reduced density y satisfies: F(y) = -A x P_pr + (y + y^2 + y^3 - y^4) / (1 - y)^3 - B x y^2 + C x y^D = 0 Where: A = 0.06125 x t x exp(-1.2 x (1 - t)^2) B = 14.76 x t - 9.76 x t^2 + 4.58 x t^3 C = 90.7 x t - 242.2 x t^2 + 42.4 x t^3 D = 2.18 + 2.82 x t Solution Method: Newton-Raphson on F(y) = 0 Initial guess: y = 0.0125 x P_pr x t x exp(-1.2 x (1 - t)^2) Converges reliably for T_pr > 1.0 Valid Range: 0 < P_pr < 25 (some sources say up to 30) 1.0 < T_pr < 3.0 (unreliable below T_pr = 1.05) Accuracy: +/- 0.3-0.5% vs Standing-Katz chart

6.3 AGA-8 DETAIL Method

AGA Report No. 8 (AGA-8) provides a high-accuracy equation of state specifically designed for natural gas custody transfer applications. Unlike DAK and HY, which use only specific gravity (via pseudo-critical properties), AGA-8 requires full gas composition.

AGA-8 Detail Characterization Method: Z = 1 + B_mix x rho_m - rho_m x SUM[C*_n x T^(-u_n)] x SUM[b_n x rho_m^(k_n)] x exp(-c_n x rho_m^(k_n)) Where: rho_m = Molar density (mol/L), solved iteratively B_mix = Second virial coefficient (from binary interaction parameters) C*_n, u_n, b_n, k_n, c_n = 58 terms from regression fit T = Temperature (K) Required Inputs: - Full gas composition (up to 21 components): Methane, Nitrogen, CO2, Ethane, Propane, n-Butane, i-Butane, n-Pentane, i-Pentane, n-Hexane, n-Heptane, n-Octane, n-Nonane, n-Decane, Hydrogen, Oxygen, CO, Water, H2S, Helium, Argon - Pressure (absolute) - Temperature (absolute) Accuracy: +/- 0.1% for pipeline-quality natural gas Valid: -200 to 400 degF, up to 40,000 psia When Required: - Custody transfer metering (contractual standard) - High-accuracy flow measurement - Revenue accounting - Calibration of other methods

Comparison of Methods

Feature DAK Hall-Yarborough AGA-8 DETAIL
Input required SG (or P_pc, T_pc) SG (or P_pc, T_pc) Full composition
Accuracy +/- 0.5% +/- 0.3-0.5% +/- 0.1%
Complexity Moderate (iterative) Moderate (iterative) High (58-term equation)
Sour gas Requires Wichert-Aziz Requires Wichert-Aziz Handles H2S/CO2 natively
Convergence Can struggle near T_pr = 1.0 More robust near critical Very robust
Best for Pipeline design, general engineering Process simulation, general engineering Custody transfer, metering
Spreadsheet friendly Yes Yes No (requires software)
Method selection guide: For pipeline design and process engineering where gas composition is unavailable or only specific gravity is known, use DAK or Hall-Yarborough with Sutton pseudo-criticals. For custody transfer, revenue metering, or any application where accuracy better than 0.5% is required, use AGA-8 DETAIL with full gas chromatography composition.

7. Sour Gas Corrections

Natural gas containing hydrogen sulfide (H2S) and/or carbon dioxide (CO2) is classified as sour or acid gas. These non-hydrocarbon components have significantly different critical properties from hydrocarbons and cause the standard Z-factor correlations (which assume sweet gas) to produce errors of 5-15% or more. Correction methods adjust the pseudo-critical properties before entering the Z-factor correlation.

Wichert-Aziz Correction (1972)

The Wichert-Aziz method is the most widely used sour gas correction. It modifies pseudo-critical properties using a correction factor (epsilon) that depends on H2S and CO2 mole fractions.

Wichert-Aziz Correction: Step 1: Calculate correction factor epsilon A = y_CO2 + y_H2S (combined acid gas mole fraction) B = y_H2S (H2S mole fraction only) epsilon = 120 x (A^0.9 - A^1.6) + 15 x (B^0.5 - B^4.0) Where epsilon is in degrees Rankine (degR) Step 2: Adjust pseudo-critical temperature T_pc' = T_pc - epsilon Step 3: Adjust pseudo-critical pressure P_pc' = (P_pc x T_pc') / (T_pc + B x (1 - B) x epsilon) Step 4: Calculate adjusted reduced properties T_pr' = T / T_pc' P_pr' = P / P_pc' Step 5: Use T_pr' and P_pr' in Standing-Katz, DAK, or HY Valid Range: CO2: 0 to 54.4 mol% H2S: 0 to 73.8 mol% Combined (CO2 + H2S): up to 74 mol% Accuracy: +/- 0.5% for gases within valid range

Wichert-Aziz Example

Example: Gas with 10% CO2, 5% H2S, SG = 0.75 Given: y_CO2 = 0.10, y_H2S = 0.05 P = 1500 psia, T = 150 degF = 609.67 degR Step 1: Pseudo-critical properties (Sutton) T_pc = 169.2 + 349.5(0.75) - 74.0(0.75)^2 = 389.6 degR P_pc = 756.8 - 131.0(0.75) - 3.6(0.75)^2 = 656.5 psia Step 2: Wichert-Aziz correction A = 0.10 + 0.05 = 0.15 B = 0.05 epsilon = 120(0.15^0.9 - 0.15^1.6) + 15(0.05^0.5 - 0.05^4.0) epsilon = 120(0.1738 - 0.04067) + 15(0.2236 - 0.00000625) epsilon = 120(0.1331) + 15(0.2236) epsilon = 15.97 + 3.35 = 19.3 degR Step 3: Adjusted pseudo-criticals T_pc' = 389.6 - 19.3 = 370.3 degR P_pc' = (656.5 x 370.3) / (389.6 + 0.05(1-0.05)(19.3)) P_pc' = 243,102 / (389.6 + 0.917) = 622.6 psia Step 4: Adjusted reduced properties T_pr' = 609.67 / 370.3 = 1.647 P_pr' = 1500 / 622.6 = 2.409 Step 5: Enter DAK or HY with T_pr' and P_pr' Z = approximately 0.753

Piper-McCain-Corredor Method (2012)

The Piper-McCain-Corredor (PMC) correlation is a more recent approach that directly accounts for non-hydrocarbon components (H2S, CO2, N2) in the pseudo-critical property estimation, eliminating the need for a separate correction step.

Piper-McCain-Corredor Approach: This method uses a modified pseudo-critical calculation that directly incorporates the effects of H2S, CO2, and N2: J = a0 + a1(y_H2S) + a2(y_CO2) + a3(y_N2) + a4(SG_HC) K = b0 + b1(y_H2S) + b2(y_CO2) + b3(y_N2) + b4(SG_HC) Where SG_HC is the hydrocarbon portion specific gravity and J, K are Stewart-Burkhardt-Voo parameters. T_pc = K^2 / J P_pc = T_pc / J Advantages over Wichert-Aziz: - Single-step calculation (no separate correction) - Better accuracy for high CO2 content (> 20 mol%) - Handles N2 directly (Wichert-Aziz ignores N2) - Based on more modern regression data Use PMC when: - Gas has significant N2 content (> 5 mol%) - CO2 content exceeds 20 mol% - Higher accuracy is needed for sour/acid gas

When Sour Gas Corrections Are Needed

Acid Gas Content Z Error Without Correction Recommendation
CO2 + H2S < 2 mol% < 0.5% Correction optional; sweet gas methods adequate
CO2 + H2S = 2-5 mol% 0.5-2% Apply Wichert-Aziz for improved accuracy
CO2 + H2S = 5-15 mol% 2-8% Wichert-Aziz required; consider AGA-8
CO2 + H2S > 15 mol% > 8% Use AGA-8 or PMC; Wichert-Aziz at limit
CO2 > 50 mol% (acid gas injection) > 15% AGA-8 or specialized EOS required
Practical note: In the Permian Basin, many gas streams contain 2-15 mol% CO2 and 0.5-5 mol% H2S. Always apply Wichert-Aziz corrections for these gases. In acid gas injection applications (30-90 mol% H2S + CO2), specialized equations of state such as Peng-Robinson or CPA are preferred over Z-factor correlations.

8. Typical Z-Factor Values

The following tables provide representative Z-factor values for common midstream operating conditions. These values are useful for quick estimation and reasonableness checks but should not replace rigorous calculations for final design or metering.

Z-Factor vs Pressure at Various Temperatures (SG = 0.65)

Pressure (psia) 60 degF 100 degF 150 degF 200 degF
14.73 (std) 0.998 0.999 0.999 1.000
100 0.975 0.981 0.987 0.991
250 0.935 0.948 0.962 0.972
500 0.870 0.895 0.921 0.940
750 0.823 0.855 0.888 0.913
1000 0.800 0.835 0.870 0.898
1200 0.800 0.832 0.865 0.893
1500 0.820 0.845 0.872 0.897
2000 0.875 0.888 0.905 0.920
3000 0.985 0.980 0.980 0.980

Z-Factor by Application

Application Typical P (psia) Typical T (degF) Gas SG Typical Z
Low-pressure distribution 30-60 40-100 0.60-0.65 0.99-1.00
Gathering system 200-600 60-120 0.65-0.80 0.88-0.96
Transmission pipeline 800-1200 50-90 0.58-0.65 0.82-0.90
Compressor suction 300-600 80-120 0.60-0.70 0.90-0.96
Compressor discharge 900-1500 150-250 0.60-0.70 0.84-0.92
Gas plant inlet 600-1000 80-120 0.70-0.85 0.80-0.90
Gas storage (depleted reservoir) 1500-3500 100-180 0.60-0.65 0.75-0.88
High-pressure gas injection 3000-10000 150-300 0.60-0.70 0.90-1.50

Effect of Gas Composition on Z-Factor

At 1000 psia and 100 degF, the Z-factor varies significantly with gas composition:

Gas Type SG Z at 1000 psia, 100 degF Notes
Pure methane 0.554 0.870 Lightest natural gas component
Lean pipeline gas 0.60 0.855 95%+ methane
Typical pipeline gas 0.65 0.835 90% methane, 5% C2+
Rich gas 0.75 0.795 10-15% C2+ content
Very rich gas 0.85 0.750 20%+ C2+, near retrograde
Sour gas (5% H2S, 10% CO2) 0.75 0.770 Requires Wichert-Aziz correction
Important: These tables are for reference and reasonableness checking only. Always perform rigorous Z-factor calculations using the appropriate correlation and pseudo-critical property method for final design, equipment sizing, and metering applications. The values shown assume sweet gas (no H2S or CO2) unless otherwise noted.

9. Practical Applications

The Z-factor appears in virtually every gas engineering calculation. This section demonstrates its role in the most common midstream applications.

Gas Density Calculation

Real Gas Density: rho = (P x MW) / (Z x R x T) Example: Calculate density of natural gas (SG = 0.65, MW = 18.83) at 1000 psia and 100 degF (Z = 0.835) T = 100 + 459.67 = 559.67 degR rho = (1000 x 18.83) / (0.835 x 10.7316 x 559.67) rho = 18,830 / 5,012.3 rho = 3.757 lb/ft3 Compare with ideal gas (Z = 1.0): rho_ideal = 18,830 / (1.0 x 10.7316 x 559.67) = 3.137 lb/ft3 Difference: 3.757 - 3.137 = 0.620 lb/ft3 (19.8% higher) Ignoring Z at this pressure would underestimate density by nearly 20%.

Line Pack Calculation

Line pack is the total mass of gas stored in a pipeline at any given time. It is essential for pipeline scheduling, transient analysis, and gas control operations.

Line Pack: Line Pack (scf) = (V_pipe x P_avg x T_b x Z_b) / (P_b x T_avg x Z_avg) Where: V_pipe = Pipeline internal volume (ft3) = pi/4 x D^2 x L P_avg = Average pipeline pressure (psia) T_avg = Average pipeline temperature (degR) Z_avg = Z-factor at P_avg, T_avg P_b = Base pressure (14.73 psia) T_b = Base temperature (519.67 degR = 60 degF) Z_b = Z at base conditions (approximately 1.0) Example: 24-inch pipeline, 100 miles, P_avg = 900 psia, T = 70 degF D_internal = 22.624 in = 1.8853 ft V_pipe = pi/4 x (1.8853)^2 x (100 x 5280) = 1,473,900 ft3 Z_avg = 0.855 (for SG = 0.65 at 900 psia, 70 degF) Line Pack = (1,473,900 x 900 x 519.67 x 1.0) / (14.73 x 529.67 x 0.855) Line Pack = 688,900,000,000 / 6,668 Line Pack = 103.3 MMscf If Z were incorrectly assumed = 1.0: Line Pack = 103.3 x 0.855 = 88.3 MMscf (underestimate by 14.5 MMscf)

Compressor Design

Adiabatic Compressor Horsepower: HP = (3.027 x P_s x Q x T_s x Z_avg) / (E_a x (k-1)) x [(P_d/P_s)^((k-1)/k) - 1] Where: P_s = Suction pressure (psia) P_d = Discharge pressure (psia) Q = Flow rate (MMscfd) T_s = Suction temperature (degR) Z_avg = (Z_s + Z_d) / 2 k = Specific heat ratio (Cp/Cv) E_a = Adiabatic efficiency The Z_avg term accounts for real gas behavior: - Z_s = Z at suction conditions - Z_d = Z at discharge conditions Important: Z_s and Z_d can differ significantly. For example, compressing from 300 to 1000 psia at SG = 0.65: Z_s (300 psia, 80 degF) = 0.945 Z_d (1000 psia, 200 degF) = 0.898 Z_avg = 0.922 Using Z = 1.0 would underestimate HP by approximately 8%.

Orifice Metering (Supercompressibility Factor)

Supercompressibility Factor F_pv (AGA Report No. 3): F_pv = sqrt(Z_b / Z_f) Where: Z_b = Z-factor at base conditions (approximately 0.9993 for SG = 0.60) Z_f = Z-factor at flowing conditions The supercompressibility factor corrects the ideal gas assumption in orifice meter calculations. Example: Z_b = 0.999 Z_f = 0.880 (at 1000 psia, 80 degF) F_pv = sqrt(0.999 / 0.880) = sqrt(1.1352) = 1.0655 This means the actual flow is 6.55% higher than the ideal gas orifice equation predicts. Without F_pv correction, custody transfer measurements would be low by 6.55%.

Relief Valve Sizing

API 520 Gas Relief Valve Sizing: A = W x sqrt(T x Z) / (C x K x P_1 x K_b x sqrt(MW)) Where: A = Required orifice area (in2) W = Required relieving rate (lb/hr) T = Relieving temperature (degR) Z = Z-factor at relieving conditions C = Coefficient from k (specific heat ratio) K = Discharge coefficient P_1 = Upstream relieving pressure (psia) K_b = Back-pressure correction factor MW = Molecular weight Z appears under the square root: a 10% error in Z causes a 5% error in required relief valve area.
Common pitfall: When using Z-factor in calculations that reference both flowing and base (standard) conditions, remember that Z at base conditions (14.73 psia, 60 degF) is very close to 1.0 but NOT exactly 1.0. For custody transfer accuracy, use Z_b = 0.9993 to 0.9997 depending on gas composition, not Z_b = 1.0.

10. Limitations & Accuracy

All Z-factor methods have specific ranges of validity and known limitations. Understanding these boundaries is essential for selecting the right method and avoiding erroneous results.

Correlation Validity Ranges

Method P_pr Range T_pr Range Max H2S + CO2 Reported Accuracy
Standing-Katz (chart) 0 - 15 1.05 - 3.0 Sweet gas only 1-2% (reading accuracy)
DAK 0.2 - 30 1.0 - 3.0 Sweet gas only (use W-A) +/- 0.486%
Hall-Yarborough 0 - 25 1.0 - 3.0 Sweet gas only (use W-A) +/- 0.3-0.5%
Wichert-Aziz correction N/A N/A 74% (CO2 up to 54%) +/- 0.5% additional
AGA-8 DETAIL All (up to 40,000 psia) All (-200 to 400 degF) Handles natively +/- 0.1%

Known Limitations

  • Near-critical conditions (T_pr < 1.05): All correlations lose accuracy near the critical point where Z changes rapidly with small P/T changes. DAK may fail to converge. Hall-Yarborough performs somewhat better but still has increased uncertainty. Use equations of state (PR, SRK) or AGA-8 for near-critical work.
  • Very high pressures (P_pr > 15): The Standing-Katz chart was not measured at extreme pressures. DAK extrapolates reasonably to P_pr = 30, but accuracy degrades. For ultra-high pressure applications (gas injection at 5000-15000 psia), use AGA-8 or GERG-2008.
  • Retrograde condensate region: When gas conditions are between the cricondenbar and cricondentherm on the phase envelope, liquid dropout occurs and the single-phase Z-factor concept does not apply. Two-phase flash calculations with an equation of state are required.
  • Non-hydrocarbon gases: Pure CO2, pure N2, or mixtures with very high non-hydrocarbon content violate the principle of corresponding states assumption. Use component-specific equations or AGA-8.
  • Heavy hydrocarbon content: Gases with significant C7+ content (condensate gases) require special C7+ characterization. Lumping heavy ends incorrectly can introduce 2-5% Z-factor errors.

When to Use Compositional Methods

The following situations require full compositional methods (AGA-8, Peng-Robinson, or GERG-2008) rather than specific-gravity-based correlations:

  • Custody transfer metering (contractual requirement for AGA-8)
  • Gas with more than 5 mol% CO2 or any H2S (unless Wichert-Aziz is applied)
  • Gas with more than 10 mol% nitrogen
  • Rich gas with more than 10 mol% C3+ (condensate gas)
  • Operating within 10% of the cricondenbar pressure
  • Cryogenic processing (below -100 degF)
  • LNG applications (GERG-2008 preferred)
  • Any application where Z-factor accuracy better than 0.5% is required

Convergence Issues

Troubleshooting Iterative Convergence: Both DAK and HY require iterative solution. Common issues: 1. No convergence: - Check that T_pr > 1.0 (correlation invalid for T_pr < 1.0) - Verify P_pr is within valid range - Try different initial guess (Z = 0.5 instead of Z = 1.0) 2. Multiple solutions: - Near critical point, the equation may have two valid roots - The physically meaningful root is typically the larger Z value - If Z < 0.15, re-check inputs (may indicate two-phase region) 3. Oscillating solution: - Reduce relaxation factor in Newton-Raphson - Use bisection method as fallback - Check for T_pr very close to 1.0 (increase to T_pr = 1.05 minimum) Recommended initial guesses: Z_initial = 1.0 for P_pr < 3 Z_initial = 0.5 for 3 < P_pr < 8 Z_initial = P_pr / (P_pr + 2) for P_pr > 8
Best practice: Always perform a reasonableness check on calculated Z-factor values. For typical natural gas (SG = 0.57-0.80), Z should be between 0.25 and 1.10 for any practical operating condition. Values outside this range almost certainly indicate an input error, convergence failure, or operation in the two-phase region. Cross-check critical calculations using two independent methods.

11. Industry Standards & References

Z-factor calculations in the midstream industry are governed by several key standards and reference documents. Understanding which standard applies to your application is essential for regulatory compliance and contractual accuracy.

Primary Standards

Standard Title Application
AGA Report No. 8 Compressibility Factors of Natural Gas and Other Related Hydrocarbon Gases Custody transfer metering, Z-factor for flow computers, supercompressibility
AGA Report No. 3 Orifice Metering of Natural Gas Orifice meter calculations including F_pv supercompressibility correction
GPSA Engineering Data Book Gas Processors Suppliers Association Comprehensive reference for Z-factor methods, pseudo-critical properties, and gas processing calculations
ISO 12213 Natural Gas - Calculation of Compression Factor International standard for Z-factor; references AGA-8 and SGERG-88 methods
API MPMS Ch. 14.2 Manual of Petroleum Measurement Standards Compressibility factor for hydrocarbon gases in measurement applications

Key Technical References

  • Standing & Katz (1942): "Density of Natural Gases" - Original graphical Z-factor chart, published in Transactions of AIME. Foundation for all subsequent correlations.
  • Hall & Yarborough (1973): "A New Equation of State for Z-Factor Calculations" - First widely-used numerical fit of Standing-Katz chart using Starling-Carnahan equation.
  • Dranchuk & Abou-Kassem (1975): "Calculation of Z Factors for Natural Gases Using Equations of State" - 11-coefficient correlation, most widely implemented in industry software.
  • Wichert & Aziz (1972): "Calculate Z's for Sour Gases" - Correction method for H2S and CO2, published in Hydrocarbon Processing.
  • Sutton (1985): "Compressibility Factors for High-Molecular-Weight Reservoir Gases" - Pseudo-critical property correlations from specific gravity, SPE paper 14265.
  • Piper, McCain & Corredor (2012): "Compressibility Factors for Naturally Occurring Petroleum Gases" - Updated pseudo-critical correlations with non-hydrocarbon handling, SPE paper 147669.

Standard Selection Guide

Custody transfer

AGA-8 Required

FERC-regulated pipelines and most gas purchase contracts require AGA Report No. 8 for Z-factor determination in flow measurement. Implemented in all modern flow computers and EFMs.

Pipeline design

DAK or HY Adequate

For pipeline hydraulics, sizing, and capacity studies, DAK or Hall-Yarborough correlations with Sutton pseudo-criticals provide sufficient accuracy (+/- 0.5%).

Process simulation

EOS Preferred

Commercial process simulators (HYSYS, ProMax, VMGSim) use Peng-Robinson or SRK equations of state, which internally calculate Z-factor as part of the full thermodynamic solution.

International trade

ISO 12213

International gas sales and LNG contracts typically reference ISO 12213, which allows AGA-8 DETAIL or SGERG-88 methods depending on available composition data.

Contractual implications: Gas measurement contracts typically specify which Z-factor method must be used. Using a different method can result in measurement disputes. Always verify the contractual requirements before selecting a Z-factor calculation method for custody transfer applications. For FERC-regulated interstate pipelines in the United States, AGA-8 is the de facto standard.

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