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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Equation of State Pressure Formula

P=RTvmbavm2P = \frac{RT}{v_m-b} - \frac{a}{v_m^2}

Van der Waals Equation of State Pressure calculates pressure for pvt properties workflows in phase behavior and thermodynamics.

Calculate

How engineers use this formula

Use this formula when the listed inputs (R, T, v_m, a_vdw, b_vdw) are known and the assumptions behind the cited pvt properties relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, P equals 627.785263 psi.

Rpsi*ft^3/(lbmol*R)

10.7316

TR

600

v_mft^3/lbmol

10

a_vdwpsi*ft^6/lbmol^2

5000

b_vdwft^3/lbmol

0.5

Inputs

R

psi*ft^3/(lbmol*R)

Gas Constant

T

R

Absolute Temperature

v_m

ft^3/lbmol

Molar Volume

a_vdw

psi*ft^6/lbmol^2

van der Waals Attraction Parameter

b_vdw

ft^3/lbmol

van der Waals Covolume Parameter

Outputs

P

psi

Pressure

T

R

Absolute Temperature

a_vdw

psi*ft^6/lbmol^2

van der Waals Attraction Parameter

b_vdw

ft^3/lbmol

van der Waals Covolume Parameter

Source and review

reviewed

Engineering LibreTexts, Phase Relations in Reservoir Engineering, Section 7.04: The van der Waals Equation.

Source

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