Real Gas Isothermal Compressibility Calculator
Enter absolute pressure in psia, dimensionless z and its isothermal pressure derivative in 1/psi. The result is gas compressibility in 1/psi, not z-factor.
Enter absolute pressure in psia, dimensionless z and its isothermal pressure derivative in 1/psi. The result is gas compressibility in 1/psi, not z-factor.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Calculate the real-gas isothermal compressibility coefficient from absolute pressure, z-factor and the pressure derivative of z at constant temperature. The output is an inverse-pressure coefficient in 1/psi, not the dimensionless compressibility factor z.
Use c_g = 1/P - (1/z)(dz/dP)_T when a compatible z value and local isothermal slope are available for the same gas. This page evaluates the supplied derivative; it does not calculate a z-factor curve from gas gravity or reservoir temperature.
Texas A&M reservoir-fluid appendix: gas compressibility, page A-19Solves for
c_g (1/psi)
Best next page
Formula, variables, and sourceCompressibility coefficient versus z-factor
The z-factor is dimensionless and describes departure from the ideal-gas volume relation. The coefficient c_g describes the fractional volume response to a pressure change at fixed temperature and has inverse-pressure units. Two gases or conditions with the same z can have different c_g when their local z-pressure slopes differ.
For an ideal gas, z = 1 and dz/dP = 0, so c_g = 1/P. A locally constant z also gives 1/P in this expression, even when z is not one. Neither check means that a general real-gas curve has zero slope throughout the pressure range.
Reproduce the derivative and sign check
At 3,000 psia, z = 0.85 and dz/dP = -0.00002 per psi, 1/P is 0.0003333333 per psi. Subtracting the negative derivative term gives c_g = 0.0003568627 per psi. Changing only the derivative to +0.00002 gives 0.0003098039 per psi; keeping the sign is essential.
A synthetic pair of points, z = 0.852 at 2,900 psia and z = 0.848 at 3,100 psia, gives (0.848 - 0.852)/(3,100 - 2,900) = -0.00002 per psi. This illustrates a local slope estimate, not measured PVT data or a recommended pressure interval. Use nearby, same-temperature, same-composition points and examine sensitivity to the interval.
| Synthetic pressure (psia) | z |
|---|---|
| 2,900 | 0.852 |
| 3,100 | 0.848 |
Match the derivative's pressure basis
If your source provides dz/dPr with Pr = P/Ppc, the derivative needed here is (dz/dPr)/Ppc on the same pressure basis. A derivative per bar must likewise be converted before combining it with 1/P when P is in psi.
Do not silently replace a suspicious result with an ideal-gas estimate. Review pressure datum, slope sign, units and phase behavior first; compare the underlying z data with an appropriate equation of state or laboratory model before using the coefficient in a reservoir calculation.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns c_g = 0.000357 1/psi. Defaults demonstrate the implementation; they are not recommended field values.
3000
0.85
-0.00002
Input definitions
P
psiaPressure
z
dimensionlessGas Compressibility Factor
dz_dP
1/psiIsothermal Derivative of Z Factor with Respect to Pressure
Output definitions
c_g
Real Gas Isothermal Compressibility
dz_dP
Isothermal Derivative of Z Factor with Respect to Pressure
Engineering use, assumptions, and limits
Use c_g = 1/P - (1/z)(dz/dP)_T when a compatible z value and local isothermal slope are available for the same gas. This page evaluates the supplied derivative; it does not calculate a z-factor curve from gas gravity or reservoir temperature.
Assumptions
- Pressure, z and the derivative refer to the same single-phase gas composition and temperature.
- The derivative is with respect to the pressure units entered, rather than reduced pressure or temperature.
Limitations
- A single z value is insufficient to determine its pressure derivative; the slope requires compatible PVT data or a model.
- This calculation does not resolve changing composition, temperature changes or phase transitions, and it does not validate the supplied z-factor model.
Common mistakes
- Entering gauge pressure for P, or treating dimensionless z as a compressibility coefficient.
- Entering dz/dPr directly where the formula requires dz/dP, without converting the pressure basis.
- Using the magnitude of a negative slope and losing its sign, or estimating a slope from points at different temperatures.
Frequently asked questions
What inputs does the Real Gas Isothermal Compressibility with Z-Factor Derivative calculator need?
The calculation uses Pressure (P), Gas Compressibility Factor (z), Isothermal Derivative of Z Factor with Respect to Pressure (dz_dP). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is real gas isothermal compressibility in 1/psi. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. A single z value is insufficient to determine its pressure derivative; the slope requires compatible PVT data or a model. Entering gauge pressure for P, or treating dimensionless z as a compressibility coefficient.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
Penn State PNG 520. Isothermal Compressibilities, real-gas compressibility, Equation 18.19.
Open source reference