Tangent-Plane Algorithm for Multiphase Equilibrium Calculations

Computing & Wireless : Computing Methods

Available for licensing


  • Ryosuke Okuno, Ph.D. , Petroleum and Geosystems Engineering

Background/unmet need

Multiphase equilibrium calculations are required in many applications in chemical and petroleum engineering, such as numerical flow simulators and phase behavior simulators using an equation of state. Conventional algorithms require obtaining false solutions and correcting them until they converge to a solution. Even when a solution is obtained, they do not ensure that the solution corresponds to the true equilibrium state.

Invention Description

This invention is a design of algorithms for multiphase equilibrium calculations using a thermodynamic model. Minimization problems in thermodynamic equilibrium calculations are solved by searching for the tangent plane that defines the equilibrium phase properties in thermodynamic-variable space.


  • Robustness: This is the first algorithm that can solve multiphase isenthalpic flash for narrow-boiling fluids.
  • Efficiency: It requires many fewer iterations for multiphase equilibrium problems.
  • Flexibility: Good initial guesses are not required to solve for multiphase equilibrium properties.


  • The algorithm captures more information about thermodynamic stability during the iterative solution.
  • The algorithm is applicable for a variety of thermodynamic models and specifications.

Market potential/applications

Petroleum and chemical engineering

Development Stage

Beta product/commercial prototype