Thermodynamic phase equilibrium analysis based on a reduced composition domain
View Patent ↗A method of modeling phase characteristics of thermodynamic systems utilizing pseudo-properties strategy and a reduced number of variables is disclosed herein. The method describes a means of determining the probability of phase splitting of mixtures of materials at a given temperature, pressure, and composition by characterizing the functions that describe the system via pseudo-properties, and also by describing the system in n−1 or fewer variables, where n represents the number of components in the system of interest. In an embodiment, a multi-component system is characterized in one variable, thereby providing simplified thermodynamic models in a time-efficient manner. In addition, the information generated by this reduced-variable calculation can further be used as a starting point for calculations of equations of state.
1. A method, comprising:
a processor evaluating a tangent hyperplane distance function D (α) to Identify any points of intersection of a hyperplane tangent to a Gibbs energy function of a first material mature having a composition z comprised of n components having a mole fraction {z 1 , z 2 , . . . , z n } substantially in a first phase with a Gibbs energy function of a second material mixture, where D (α) is defined on a composition domain having k dimensions, where 1≦k<n, wherein the processor is in communication with a memory, the memory storing a thermodynamic modeling application, and wherein Identifying the any points of Intersection is based on the processor executing the thermodynamic modeling application;
the processor determining the probability of phase splitting of mixtures of materials at a given temperature, pressure, and composition by characterizing the functuons that describe the system via pseudo-properties; and
the processor evaluating a phase stability of the material mixture, where the material mixture is determined to be susceptible to a phase split when the hyperplane tangent to the Gibbs energy function of the first material mixture in the first phase intersects the Gibbs energy function of the second material mixture.
2. The method of claim 1 , further comprising the processor determining at least one of a single-stage flash condition and a distillation condition based on evaluating the phase stability of the material mixture.
3. The method of claim 1 , further comprising one of controlling a thermodynamic process, controlling a thermodynamic process control component, training an operator of the thermodynamic process, training an operator of the thermodynamic process control component, and predicting a failure time of the thermodynamic process control component, based on evaluating the phase stability of the material mixture.
4. The method of claim 1 , wherein the tangent hyperplane distance function D(α) is based, at least in part, on a Gibbs energy function of mixing using pseudo properties.
5. The method of claim 1 , further comprising determining an estimate of an equilibrium composition x comprised of n components having a mole fraction {x 1 , x 2 , . . . , x n } based on α.
6. The method of claim 5 , wherein x i ∝ ƒ i (α), where (α), is the value of (α) corresponding to the material composition z , where ƒ i (α z )=z i , is determined as a Taylor Series approximation of the form
∑
j
=
0
m
f
i
j
(
α
z
)
(
α
-
α
z
)
j
j
!
,
and where m is an integer.
7. The method of claim 6 , wherein m=1 and
x
i
=
z
i
+
(
α
-
α
z
)
1
ln
ϕ
i
z
,
where φ i z is the fugacity coefficient of the I-th mixture component at a specified temperature, at a specified pressure, In a specified phase and where
α
z
=
∑
i
=
1
n
z
i
ln
ϕ
i
z
.