Procedures

Soave $\alpha$ function and it’s derivatives.

MathiasCopeman alpha function definition

$A^r$ models consistency tests.

Wrapper subroutine to the SRK/PR Residula Helmholtz function to use the general interface

Define beta limits to avoid overshooting when solving the Rachford-Rice equation.

Modify K-factor values to assure that $\beta$ lies between (0,1)

Calculate the LLV line from a converged critical end point (CEP).

Mixture repulsive parameter.

Quadratinc mixing rule for the repulsive parameter.

Quadratinc mixing rule for the repulsive parameter.

Quadratinc mixing rule for the repulsive parameter, using $b_{ij} = \frac{b_i + b_j}{2} (1 - l_{ij})$ as a combining rule.

Numerical continuation of a function.

Calculate residual heat capacity pressure constant given V and T.

Create a new generalized line. This function initializes a new instance of the GeneralizedLine type.

Critical point interpolation

Critical point interpolation

Calculates the critical line between two mixtures using the continuation method. The two mixtures compositions are restricted to the relation between them, by a parameter $\alpha$, which represents the molar fraction of the second fluid with respect to the whole mixture. Avoid compositions with negative values

Calculates a single critical point of a mixture using a Newton-Raphson method. It is possible to specify different variables to be fixed with the spec argument, the spec_CP variable helps when selecting the specified variable.

Calculate residual heat capacity volume constant given V and T.

RKPR $\delta_1$ parameter mixing rule.

Calculate the mole fraction second derivatives respect to mole numbers

Calculate the mole fraction first derivatives respect to mole numbers

Critical point detection

Critical point detection

Detect if the system is close to a critical point.

Calculates the Jacobian of the critical point function F_critical.

Calculates the Jacobian of the critical point function F_critical.

Attractive parameter mixing rule with quadratic mix.

Attractive parameter calculation for the Huron-Vidal mixing rule.

Mixing rule at infinite pressure as defined in the book of Michelsen and Møllerup.

Convert the mole fraction derivatives of a quantity (calculated so they do not sum to 1) to mole number derivatives (where the mole fractions do sum to one). Requires the derivatives and the mole fractions of the mixture. From https://chemicals.readthedocs.io/chemicals.utils.html?highlight=dxs_to_dns#chemicals.utils.dxs_to_dns

Calculate the eigenvalues and eigenvectors of a real symmetric matrix A using LAPACK’s dsyev. The eigenvectors are stored in the columns of eigenvectors. The eigenvalues are stored in eigenvalues.

Calculate residual enthalpy given volume and temperature.

Calculate residual entropy given volume and temperature.

Calculate Excess heat capacity.

Calculate Excess enthalpy and its derivatives.

Calculate Excess entropy and its derivatives.

Calculate Excess Gibbs and its derivatives.

Calculate Excess Gibbs and its derivatives.

Calculate the Gibbs excess energy of the UNIFAC model

Calculate the excess Gibbs free energy and its derivatives of the UNIQUAC model.

Excess Gibbs model generic interface

Function that should be equal to zero at a critical point is found. The second criticality condition is calculated as a numerical derivative with eps=1e-4.

Find a liquid-liquid phase boundary on the PT plane. At a specified pressure. The procedure consists in looking for the temperature at which the fugacity of a component in the mixture is higher than the fugacity of the same component in a pure phase. This is done for each component in the mixture. The component with the highest temperature is selected as it should be the first one appearing. If all components have a negative difference then the mixture is probably stable at all temperatures.

Find an initial guess for the critical L-L line of a binary mixture.

Flash algorithm using sucessive substitutions.

Flash algorithm using sucessive substitutions.

Subroutine to solve a point.

Calculate the UNIFAC combinatorial term of Gibbs excess energy

$G^E$ models consistency tests

Evaluate the UNIFAC residual term

Residual Helmholtz Energy for a generic Cubic Equation of State.

Residual Helmholtz Energy for a generic Cubic Equation of State.

Calculate the critical constants for each pure component.

Get index of the maingoup with id: maingoup_id

Get the interaction parameter $a_{ij}$

Get the interaction parameter $b_{ij}$

Get the interaction parameter $c_{ij}$

Get the saturation pressure for a given temperature.

Get index of the subgroup with id: subgroup_id

Get the subgroup’s maingroup

Get the subgroup’s $Q$ value

Get the subgroup’s $R$ value

Get the interaction parameter $a_{ij}$

Get the interaction parameter $b_{ij}$

Get the interaction parameter $c_{ij}$

Get the saturation temperature for a given pressure.

Extract the values of the variables from the vector X.

Extract the values of the variables from the vector X.

Extract the values of the variables from the vector X.

Calculate the fluid composition based on an amount of addition of second fluid.

Calculate Zc, OMa and OMb from the delta_1 parameter.

Calculate residual Gibbs energy given volume and temperature.

Calculate the reduced residual Helmholtz Energy and it’s derivatives with the RKPR EOS

This is the Huron-Vidal mixing rule that includes the NRTL model modified by Huron and Vidal.

Calculate residual internal energy given volume and temperature.

Linear interpolation.

Find the intersections of a single line with itself.

Calculate the intersection between two line segments.

K-factors regression done by Wilson, used for initialization.

Combining rule that uses constant $k_{ij}$ values.

Combining rule that uses temperature dependant $k_{ij}$ values. With the following expression: $$k_{ij}(T) = k_{ij}^0 + k_{ij}^\infty \exp\left(\frac{-T}{T^*}\right)$$

Calculation of the first restriction of a critical point.

Infinite pressure limit parameter $\Lambda$

Calculate natural logarithm of activity coefficients.

Calculate natural logarithm of fugacity given volume and temperature.

Calculate natural logarithm of fugacity given pressure and temperature.

Calculate natural logarithm of fugacity coefficent.

Function to create a MPEquilibriumState from the vector of variables X used in the multiphase generalized isopleths methods.

This subroutine calculates the excess Gibbs energy $G^E$ and its derivatives for a mixture using the NRTL model modified by Huron and Vidal. The NRTL model accounts for non-ideal interactions between components in a mixture. The expression for the excess Gibbs energy is:

Temperature dependent parameters for NRTL model

Temperature dependent parameters for NRTL model. The temperature dependence is linear:

Evaluate the Helmholtz derivatives with central finite difference.

Numeric $G^E$ model derivatives

Set a value to a default if it is not defined

Set a value to a default if it is not defined

Set a value to a default if it is not defined

Parameter table of the original GERG 2008 model

Calculate the pressure at a given T of a mixture using the Wilson equation.

PengRobinson76.

PengRobinson78.

PengRobinson 76 factory

PengRobinson 78 factory

Calculate pressure.

Solve pressure equality between two phases at a given temperature, total volume, vapor molar fractions and compositions.

Calculation of saturation pressure of a pure component using the secant method.

Calculation of a multiphase PT envelope.

PT two-phase envelope calculation procedure.

Function to solve at each point of a multi-phase envelope.

Function to solve at each point of a multi-phase envelope.

Function to solve at each point of a multi-phase envelope.

Function to solve at each point of a three phase envelope.

Perform a multiphase flash calculation at constant zPT.

Saturation pressures and temperatures for a pure component.

Fugacity of a pure component

Calculation of a multiphase Px envelope.

PX two-phase envelope calculation procedure.

System of equations to solve a multiphase-point at constant temperature.

Function to solve at each point of a three phase envelope.

Rachford-Rice equation for a two phase system. This equation is used to calculate the $\beta$ value that satisfies the mass balance between two phases.

Refit the $k$ parameter of the RKPR EoS to match the acentric factor

Residual Helmholtz model generic interface

RKPR Equation of State

RKPR $\delta_1$ parameter mixing rule.

Saturation pressure calculation function.

Saturation temperature calculation function.

Setup the basics variables that describe the model.

Instantiate a UNIFAC model

Instantiate a UNIQUAC model.

Get the size of the model.

SoaveRedlichKwong.

Function to solve the multiphase flash problem.

Function to solve the multiphase flash problem.

Solve the system of equations for a multiphase point.

Solve a saturation point for a pure component.

Solve a point in the multiphase envelope.

Solve the Rachford-Rice Equation using the Newton method.

Solve a linear sytem AX = b

Sort an array and return the indexes

…

SoaveRedlichKwong factory

Check the stability of a point in the critical line. The stability is determined by tpd analysis.

Calculate the temperature dependence term of the UNIQUAC model.

Calculate the area fraciton of each froup on each molecule.

Calculate the function vector and Jacobian for the three-phase line (LLV) of a binary mixture. Phases are defined as x, y and w. Which are two liquid phases and one vapor phase respectively.

Solve the system of equations defined in three_phase_line_F using a Newton-Raphson method. It will make a maximum of 50 iterations to converge. With a tolerance of 1e-9 in the maximum absolute value of the function vector or the step vector.

Michelsen’s modified $tpd$ function, $tm$.

Calculate the multiphase isobar of a mixture.

TX two-phase envelope calculation procedure.

Function to solve at each point of a multi-phase envelope.

Implementation of the $\psi(T)$ function of the UNIFAC model.

UNIFAC parameters

Change the specified variable for the next step.

Change the specified variable for the next step.

Change the specified variable for the next step.

Cubic EoS volume initializer. For a Cubic Equation of State, the covolume calculated with the mixing rule is a good estimate for the initial volume solver on the liquid region.

ROUTINE FOR CALCULATION OF VOLUME, GIVEN PRESSURE

Volume solver routine for the GERG2008.

Volume solver optimized for Cubic Equations of State.

Volume solver routine for residual Helmholtz models.

Volume solver at a given pressure.

Write the multiphase envelope to a file.

Calculation of lnphiP and derivatives rn mixture mole numbers (input) t temperature (k) (input) v volume (L) (input) p pressure (bar) (output) PHILOG vector of ln(phi(i)P) (output) 0 < INDIC < 5 DLPHIT t-derivative of ln(phi(i)) (const P, n) (output) 0 < INDIC = 2 or 4 DLPHIP P-derivative of ln(phi(i)) (const T, n) (output) 0 < INDIC < 5 FUGN comp-derivative of ln(phi(i)) (const t & P)(output) 2 < INDIC